According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.

The number of units that must be sold for the company to earn a profit of $50,000 is 30,000 units.

To determine the number of units that must be sold for the company to earn a profit of $50,000, we need to use the following formula:

Profit = Total Revenue - Total Cost

Where Total Revenue = Selling Price × Number of Units Sold

And Total Cost = Fixed Cost + (Variable Cost × Number of Units Sold)

Plugging in the given values into the formula, we get:

$50,000 = ($12 × Number of Units Sold) - ($70,000 + ($8 × Number of Units Sold))

Simplifying the equation, we get:

$50,000 = $12 × Number of Units Sold - $70,000 - $8 × Number of Units Sold

$50,000 = $4 × Number of Units Sold - $70,000

$120,000 = $4 × Number of Units Sold

Number of Units Sold = $120,000 / $4

Number of Units Sold = 30,000

Therefore, the company must sell 30,000 units to earn a profit of $50,000.

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The product between f(x) and g(x) is equal to -6x² + 37x - 35.

The product of two functions, (fg)(x), is defined as f(x)*g(x). Therefore, to find the product of the given functions, we simply need to multiply them together:

(fg)(x) = (6x -7)(5 - x)

Using the distributive property, we can simplify this expression:

(fg)(x) = (6x)(5) - (6x)(x) - (7)(5) + 7(x)

(fg)(x) = 30x - 6x² - 35 + 7x

Combining like terms, we get:

(fg)(x) = -6x² + (30x + 7x) - 35

(fg)(x) = -6x² + 37x - 35

So the product of the two functions is (fg)(x) = -6x² + 37x - 35.

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The total decline in employment over the 5-year period is 384 employees.

In 2000, a business had 4000 employees. Each year for the next 5 years, the number of employees decreased by 2%. To find the number of employees at the end of the 5-year period, we can use the formula:

Number of employees = Initial number of employees * (1 - percentage decrease) ^ number of years

= 4000 * (1 - 0.02) ^ 5

= 4000 * 0.98 ^ 5

= 4000 * 0.9039

= 3615.6

Therefore, the number of employees at the end of the 5-year period is approximately 3616.

To find the total decline in employment over the 5-year period, we can subtract the final number of employees from the initial number of employees:

Total decline in employment = Initial number of employees - Final number of employees

= 4000 - 3616

= 384

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The final answer of values of m and n that make the system of linear equations have infinite number of solutions are m = 11/10 and n = 11/5.

To determine the values of m and n so that the following system of linear equations have infinite number of solutions, we need to make the coefficients of both equations proportional.

This means that the ratio of the coefficients of x, y, and the constant term should be the same for both equations.

Let's start by finding the ratio of the coefficients of x and y for the first equation:

(2m-1)/3 = 3/(n-1)

Cross-multiplying gives us:

3(2m-1) = 3(n-1)

Simplifying:

6m-3 = 3n-3

6m = 3n

Dividing both sides by 3:

2m = n

Now, let's find the ratio of the coefficients of x and the constant term for the first equation:

(2m-1)/(-5) = 3/(-2)

Cross-multiplying gives us:

-10m + 5 = -6

Simplifying:

-10m = -11

Dividing both sides by -10:

m = 11/10

Substituting this value of m back into the equation 2m = n, we get:

2(11/10) = n

n = 22/10

n = 11/5

Therefore, the values of m and n that make the system of linear equations have infinite number of solutions are m = 11/10 and n = 11/5.

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Answer:

sorry I don't know the answer :(

Step-by-step explanation:

Make sure all words are spelled correctly.

Try different keywords.

Try more general keywords.

Try fewer keywords.

Answer:

6.72^2

Step-by-step explanation:

6.72^2 is an expression correctly written in scientific notation

1. Find the domain of the equation
(a) √(x + 2) - √2 = 2x
The domain of this equation is all real numbers greater than or equal to -2. This is because the expression inside the square root must be greater than or equal to zero in order for the equation to be defined. Therefore, x + 2 ≥ 0, which simplifies to x ≥ -2.

(b) sin^3 x = sin x + 1
The domain of this equation is all real numbers. This is because the sine function is defined for all real numbers.

(c) tan x + cot x = sin x
The domain of this equation is all real numbers except for values of x that make the denominator of the tangent or cotangent function equal to zero. These values are x = nπ, where n is any integer. Therefore, the domain is all real numbers except for multiples of π.

(d) (x+1) / (x^2 -1) + cos x = csc x
The domain of this equation is all real numbers except for values of x that make the denominator of the first term equal to zero. These values are x = 1 and x = -1. Therefore, the domain is all real numbers except for 1 and -1.

2. Simplify each expression using the fundamental identities
(a) (sin^2 θ) / (sec^2 θ -1)
Using the fundamental identity sec^2 θ = 1 + tan^2 θ, we can simplify the denominator to get:
(sin^2 θ) / (tan^2 θ)
Using the fundamental identity tan^2 θ = (sin^2 θ) / (cos^2 θ), we can simplify the expression further to get:
(cos^2 θ)

(b) (1 / (1 + tan^2 x) + (1 / (1 + cot^2 x)
Using the fundamental identities tan^2 x = (sin^2 x) / (cos^2 x) and cot^2 x = (cos^2 x) / (sin^2 x), we can simplify the expression to get:
(cos^2 x) + (sin^2 x)
Using the fundamental identity cos^2 x + sin^2 x = 1, we can simplify the expression further to get:
1

(c) 1 – (cos^2 x / 1 + sin x)
Using the fundamental identity cos^2 x = 1 - sin^2 x, we can simplify the expression to get:
1 - ((1 - sin^2 x) / (1 + sin x))
Distributing the negative sign and combining like terms gives us:
(sin^2 x) / (1 + sin x)

(d) sin θ / cos θ tan θ
Using the fundamental identity tan θ = (sin θ) / (cos θ), we can simplify the expression to get:
(sin θ) / ((cos θ) * ((sin θ) / (cos θ)))
Simplifying the denominator gives us:
(cos^2 θ) / (sin θ)
Using the fundamental identity cos^2 θ = 1 - sin^2 θ, we can simplify the expression further to get:
(1 - sin^2 θ) / (sin θ)

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By Pythagorean theorem, the length of line segment x is approximately equal to 2.609 feet.

In this problem we find a geometric system where line segment x is perpendicular to the hypotenuse of a right triangle. This system can be represented well by Pythagorean theorem:

4.6² = (5.8 - y)² + x²

3.5² = x² + y²

First, eliminate variable x and solve for y:

4.6² = (5.8 - y)² + (3.5² - y²)

4.6² = 5.8² - 10.6 · y + y² + 3.5² - y²

4.6² = 5.8² - 10.6 · y + 3.5²

10.6 · y = 5.8² + 3.5² - 4.6²

y = 2.333

Second, determine variable x:

x = √(3.5² - 2.333²)

x = 2.609

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The area of a triangle with sides \( a=10 \) and \( b=15 \) and included angle 70 degrees is 70.47675 square units.

To find the area of a triangle with sides a and b and included angle C, we can use the formula:

\[Area = \frac{1}{2}ab\sin{C}\]

In this case, we have a = 10, b = 15, and C = 70 degrees. Plugging these values into the formula, we get:

\[Area = \frac{1}{2}(10)(15)\sin{70}\]

\[Area = 75\sin{70}\]

Using a calculator, we find that sin(70) = 0.93969. So:

\[Area = 75(0.93969)\]

\[Area = 70.47675\]

Therefore, the area of the triangle is approximately 70.47675 square units.

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The range of scores that lies within two standard deviations from the mean is (43.68, 56.32), the lowest score which lies two standard deviations above the mean is 56.32, and the highest score which lies three standard deviations below the mean is 40.52.

The random variable X has a normal distribution with mean 50 and variance of 10. The standard deviation of X is the square root of the variance, which is √10 ≈ 3.16.

a. The range of scores that lies within two standard deviations from the mean is (50 - 2*3.16, 50 + 2*3.16) = (43.68, 56.32).

b. The lowest score which lies two standard deviations above the mean is 50 + 2*3.16 = 56.32.

c. The highest score which lies three standard deviations below the mean is 50 - 3*3.16 = 40.52.

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The maximum possible number of solutions for the given equation (3x⁵ - bx² + cx + d = ax⁴ + 7) is 5.

Go through the entire list of numbers and compare each value to discover the largest value (the maximum) among them. The largest value discovered after comparing all values is the maximum in the list.

This is because the highest degree in the equation is 5, which is the power of x in the term (3x⁵). The highest degree of a polynomial equation determines the maximum number of solutions the equation can have.

Therefore, the maximum possible number of solutions for this equation is 5.

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The mean of the list  is 7

The standard deviation of the list is 4/69

The linear regression equation is y = 227.5 + 0.65*x
The percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

2a) The mean of the list can be computed by adding all of the numbers in the list together and dividing by the number of items in the list.

Mean = (9+2+5+4+12+10)/6 = 42/6 = 7

2b) The standard deviation of the list can be computed by finding the difference between each number in the list and the mean, squaring these differences, finding the average of these squared differences, and then taking the square root of this average.

Standard deviation = sqrt(((9-7)^2 + (2-7)^2 + (5-7)^2 + (4-7)^2 + (12-7)^2 + (10-7)^2)/6) = sqrt(22) = 4.69

3a) The linear regression equation can be found using the formula:

y = b0 + b1*x

Where b0 is the y-intercept and b1 is the slope. The slope can be found using the formula:

b1 = r*(SDy/SDx)

Plugging in the given values:

b1 = 0.80*(85/105) = 0.65

The y-intercept can be found using the formula:

b0 = meany - b1*meanx

Plugging in the given values:

b0 = 570 - 0.65*525 = 227.5

So the linear regression equation is:

y = 227.5 + 0.65*x

To predict the Math score of a student who receives a 720 on the Verbal portion of the test, plug in x = 720 into the equation:

y = 227.5 + 0.65*720 = 693

So the predicted Math score is 693.

3b) To find the percentile rank on the Math portion for a student with a Verbal percentile rank of 80%, use the formula:

z = (x-mean)/SD

Where z is the z-score, x is the score, mean is the mean of the scores, and SD is the standard deviation of the scores.

Plugging in the given values for the Verbal scores:

z = (x-525)/105

Solving for x:

x = 105*z + 525

Since the Verbal percentile rank is 80%, the z-score is 0.84 (from a z-table). Plugging this into the equation:

x = 105*0.84 + 525 = 613.2

So the Verbal score corresponding to the 80th percentile is 613.2.

To find the Math score corresponding to this Verbal score, plug in x = 613.2 into the linear regression equation:

y = 227.5 + 0.65*613.2 = 623.6

So the Math score corresponding to the 80th percentile on the Verbal portion is 623.6.

To find the percentile rank on the Math portion for this score, use the formula:

z = (x-mean)/SD

Plugging in the given values for the Math scores:

z = (623.6-570)/85 = 0.63

Using a z-table, the corresponding percentile rank is approximately 73.5%.

So the percentile rank on the Math portion for a student with a Verbal percentile rank of 80% is approximately 73.5%.

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a. The probability that a randomly sampled individual has two copies of the C allele is 0.0169.
b. The probability that a randomly sampled individuTherefore, the answers are:
al is a homozygote is 0.7074.
c. The probability that a randomly sampled individual is AS is 0.0332.
d. The probability that a randomly sampled individual is AS or AC is 0.1411.

The probability of an individual having two copies of the C allele can be calculated using the formula for the probability of independent events: P(CC) = P(C) x P(C) = 0.13 x 0.13 = 0.0169.

The probability of an individual being a homozygote can be calculated by adding the probabilities of having two copies of each allele: P(AA) + P(SS) + P(CC) = (0.83 x 0.83) + (0.04 x 0.04) + (0.13 x 0.13) = 0.6889 + 0.0016 + 0.0169 = 0.7074.

The probability of an individual being AS can be calculated using the formula for the probability of independent events: P(AS) = P(A) x P(S) = 0.83 x 0.04 = 0.0332.

The probability of an individual being AS or AC can be calculated by adding the probabilities of each event: P(AS) + P(AC) = 0.0332 + (0.83 x 0.13) = 0.0332 + 0.1079 = 0.1411.

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$a = -8$ and $b = \frac{-520}{49}$

The matrix equation you provided is:

$$\left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]=\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]$$

We can solve for the missing values by using the matrix equation $A \cdot B = C$. In this case, we have $A \cdot B = C$, where $A$ is the matrix on the left, $B$ is the matrix on the right, and $C$ is the matrix on the far right.

We can solve for $a$ and $b$ by using the inverse of $A$. To calculate the inverse of $A$, we use the formula: $$A^{-1} = \frac{1}{\det(A)}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$

The determinant of $A$ is $5 \cdot -5 - 4 \cdot a = -25 - 4a$, so $$A^{-1} = \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]$$

We can then calculate $b$ by multiplying the inverse of $A$ by the matrix $C$. $$\begin{align*}
A^{-1} \cdot C &= \frac{1}{-25 - 4a}\left[\begin{array}{cc} -5 & a \\ 4 & 5 \end{array}\right]\left[\begin{array}{rr} 6 \\ -7 \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -5\cdot 6 + a\cdot (-7) \\ 4 \cdot 6 + 5 \cdot (-7) \end{array}\right]\\
&= \frac{1}{-25 - 4a}\left[\begin{array}{rr} -30 - 7a \\ 24 - 35 \end{array}\right]
\end{align*}$$

Solving for $b$, we have $$\begin{align*}
b &= \frac{-30 - 7a}{-25 - 4a}\\
&= \frac{-30 - 7a}{-25 - 4a}\cdot \frac{25 + 4a}{25 + 4a}\\
&= \frac{25\cdot(-30 - 7a) + 4a\cdot(-25 - 4a)}{25^2 + 4a^2}\\
&= \frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}
\end{align*}$$

Now, we can solve for $a$ by substituting $b$ into the equation $A \cdot B = C$. $$\begin{align*}
A\cdot B &= \left[\begin{array}{rr} 5 & a \\ 4 & -5 \end{array}\right]\left[\begin{array}{rr} b & -4 \\ -1 & 5 \end{array}\right]\\
&= \left[\begin{array}{rr} 5b + a(-4) & 5(-4) + a(5) \\ 4b - 5(-1) & -5(-1) - 5(5) \end{array}\right]\\
&= \left[\begin{array}{rr} -20 - 4a & 25 + 5a \\ 4b - 5 & 25 - 25 \end{array}\right]
\end{align*}$$

Comparing this to the equation $A\cdot B = C$, we can solve for $a$: $$\begin{align*}
6 &= -20 - 4a\\
-7 &= 4b - 5\\
&= 4\left(\frac{-750 - 175a - 100a - 16a^2}{625 + 16a^2}\right) - 5\\
&= \frac{-3000 - 700a - 400a - 64a^2}{625 + 16a^2} - 5\\
&= \frac{-3500 - 700a - 400a - 64a^2}{625 + 16a^2}\\
\end{align*}$$

By comparing this to the equation $6 = -20 - 4a$, we can solve for $a$: $$\begin{align*}
-3500 - 700a - 400a - 64a^2 &= -20 - 4a\\
64a^2 + 400a + 700a + 3520 &= 0\\
a^2 + 5a + 56 &= 0\\
(a + 8)(a + 7) &= 0\\
a &= -8 \;\text{or}\; -7
\end{align*}$$

Thus, the missing values are $a = -8$ and $b = \frac{-520}{49}$.

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The solution to the equation (5.825)^(x-3)=120 is x ≈ 4.76.

To solve the equation (5.825)^(x-3)=120 using inverse operations and algebraic methods, we need to use the following steps:

Step 1: Take the natural logarithm of both sides of the equation to isolate the exponent. This gives us:

ln(5.825)^(x-3) = ln(120)

Step 2: Use the property of logarithms that allows us to move the exponent to the front of the logarithm:

(x-3) ln(5.825) = ln(120)

Step 3: Divide both sides of the equation by ln(5.825) to isolate the variable:

x-3 = ln(120)/ln(5.825)

Step 4: Add 3 to both sides of the equation to solve for x:

x = ln(120)/ln(5.825) + 3

Step 5: Use a calculator to find the value of the natural logarithms and simplify:

x ≈ 4.76

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The probability of spinning an even number is 39/10

The missing barchart is added as an attachment

The bar chart (see attachment) represents the graph that would be used to calculate the required probability

On the bar chart, we have the sample size of the even number

Even number = 18 + 21

Even number = 39

So, we have

P(Even) = Even/Total

By substitution. we have

P(Even) = 39/100

Hence, the probability is 39/100

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Answer:$880

Step-by-step explanation:

1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3
4    8   12  16  20 24 28 32 36 40 44 48 52 56 60 64

55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55
so to explain 1 cheese pizza to 3 pepperonis(1/3) that is 4 pizzas together, and we do that until 64. If pepperoni pizza is 15 each, we time that by 3 which is 45, plus the 10 for cheese pizza which makes it 55. we do 55 dollars until we equal the 64 pizzas, which is 16 together. so 55 x 16=880 dollars selling pizza

Therefore, the cost of eggs in the given years are as follows:

2015: $1.87

2016: $1.94

2017: $2.01

2018: $2.09

2019: $2.16

2020: $2.24

2021: $2.31

2022: $2.39

The cost of eggs is increasing in a linear fashion, meaning that it is increasing at a constant rate. To find the cost of eggs in a specific year, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line. The slope is the change in y divided by the change in x. In this case, y is the cost of eggs and x is the year.

Slope = (y2 - y1)/(x2 - x1) = ($2.52 - $1.66)/(2022 - 2010) = $0.86/12 = $0.0717

Next, we need to find the y-intercept. We can use one of the points and the slope to solve for b in the equation y = mx + b.

$1.66 = ($0.0717)(2010) + b

b = $1.66 - ($0.0717)(2010) = -$141.44

Now we have the equation for the cost of eggs in a given year:

y = $0.0717x - $141.44

To find the cost of eggs in a specific year, we can plug in the value of x and solve for y.

For example, to find the cost of eggs in 2015:

y = ($0.0717)(2015) - $141.44 = $1.87

Therefore, the cost of eggs in 2015 was $1.87.

Similarly, we can find the cost of eggs in other years:

In 2016: y = ($0.0717)(2016) - $141.44 = $1.94

In 2017: y = ($0.0717)(2017) - $141.44 = $2.01

In 2018: y = ($0.0717)(2018) - $141.44 = $2.09

In 2019: y = ($0.0717)(2019) - $141.44 = $2.16

In 2020: y = ($0.0717)(2020) - $141.44 = $2.24

In 2021: y = ($0.0717)(2021) - $141.44 = $2.31

In 2022: y = ($0.0717)(2022) - $141.44 = $2.39

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The value of A⁻¹ is given by the following matrix:

[[1/5, -2/15, 1/10],
[-1/5, 3/15, -1/10],
[4/5, -4/15, 1/10]]

This can be calculated by solving the equation A x A⁻¹ = I, where I is the identity matrix. In this equation, we can solve for A⁻¹ by multiplying both sides of the equation by the inverse of A, which can be found by solving the system of equations A x X = I.

After solving this system of equations, the inverse of A is the matrix X. The value of A⁻¹ is then found by substituting the values of X into the matrix A⁻¹.

To find the inverse of A, first find the determinant of A, which can be calculated using the formula |A| = (-3)(3)(-1) + (-2)(1)(4) + (2)(4)(1) = -20. Since the determinant is not 0, A is invertible and the inverse can be found.

To solve for A⁻¹, first calculate the cofactor matrix C for A by taking the transpose of the matrix of minors for A, which can be found by calculating the determinants of each submatrix of A.

Then, take the determinant of A and divide each element in C by it, giving the matrix C⁻¹. Finally, multiply A and C⁻¹ to get the inverse of A, which is the matrix A⁻¹.

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Consider the matrix A given by

A = [[-3,-2,2],[1,3,1],[4,4,-1]]

Find the value of A⁻¹.

The equation of the line in point-slope form is y - (-6) = (-1/4)(x - 8), and the equation of the line in slope-intercept form is y = (-1/4)x - 4.

First, we need to find the slope of the line that is perpendicular to the given line. The slope of the given line is 4, so the slope of the perpendicular line will be the negative reciprocal of 4, which is -1/4.

Next, we can use the point-slope form of an equation to write the equation of the line. The point-slope form of an equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope and the given point, we get:

y - (-6) = (-1/4)(x - 8)

Simplifying, we get:

y + 6 = (-1/4)x + 2

Finally, we can rearrange the equation to get it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Subtracting 6 from both sides of the equation gives us:

y = (-1/4)x - 4

So the equation of the line in slope-intercept form is y = (-1/4)x - 4.

In summary, the equation of the line in point-slope form is y - (-6) = (-1/4)(x - 8), and the equation of the line in slope-intercept form is y = (-1/4)x - 4.

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Sure, here are the answers to Exercises 4.4 1 for Propositions 1.5 through 1.8:

Proposition 1.5: If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angles but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angles can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.6: If two triangles have two angles and a side of one equal to two angles and a side of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same angle measures and side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same angle measures and side lengths can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the angle measures and side lengths of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.7: If two triangles have two sides and an angle of one equal to two sides and an angle of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths and angle measures but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere since the side lengths and angles are not independent. Two triangles with the same side lengths and angle measures can have different shapes on a sphere.

If it does hold, does Euclid's proof work? If it does not, briefly explain what goes wrong.

Euclid's proof assumes that the side lengths and angles of the triangles are independent, which is not the case on a sphere. Therefore, his proof does not work for triangles on a sphere.

Proposition 1.8: If two triangles have three sides of one equal to three sides of the other, then the triangles are congruent.

Does the proposition hold on a sphere?

No, the proposition does not hold on a sphere. A counterexample is two triangles on a sphere with the same side lengths but with different shapes.

If it does not, give a counterexample and briefly explain what goes wrong.

The problem is that the definition of congruence for plane triangles does not apply to triangles on a sphere

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Answer:

"t3"   was replaced by   "t^3".  

1 more similar replacement(s).Step by step solution :

STEP 1:Equation at the end of step 1 (((9 • (t6)) - (2•7t3)) + 4t) - 1 = 0

STEP 2 :Equation at the end of step 2: ((32t6 - (2•7t3)) + 4t) - 1 = 0

STEP 3:Checking for a perfect cube  3.1    9t6-14t3+4t-1  is not a perfect cube 

Trying to factor by pulling out : 3.2      Factoring:  9t6-14t3+4t-1 

Thoughtfully split the expression at hand into groups, each group having two terms:

Group 1:  4t-1 

Group 2:  -14t3+9t6 

Pull out from each group separately:

Group 1:   (4t-1)

(1)Group 2:   (9t3-14) • (t3)

Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Polynomial Roots Calculator : 3.3  

  Find roots (zeroes) of :  F(t) = 9t6-14t3+4t-1

Polynomial Roots Calculator is a set of methods aimed at finding values of  t  for which   F(t)=0  Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  t  which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading CoefficientIn this case, the Leading Coefficient is  9  and the Trailing Constant is  -1.  The factor(s) are: of the Leading Coefficient :  1,3 ,9  of the Trailing Constant :  1  Let us test ....  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      18.00        -1     3      -0.33      -1.80        -1     9      -0.11      -1.43        1     1      1.00      -2.00        1     3      0.33      -0.17        1     9      0.11      -0.57   Polynomial Roots Calculator found no rational roots Equation at the end of step 3: 9t6 - 14t3 + 4t - 1 = 0

STEP 4:Equations of order 5 or higher: 4.1     Solve   9t6-14t3+4t-1 = 0In search of an interavl at which the above polynomial changes sign, from negative to positive or the other wayaround.Method of search: Calculate polynomial values for all integer points between t=-20 and t=+20 Found change of sign between t= -1.00 and t= 0.00 Approximating a root using the Bisection Method :We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).The function is   F(t) = 9t6 - 14t3 + 4t - 1At   t=   0.00   F(t)  is equal to  -1.00 At   t=   -1.00   F(t)  is equal to  18.00 Intuitively we feel, and justly so, that since  F(t) is negative on one side of the interval, andpositive on the other side then, somewhere inside this interval,  F(t)  is zero Procedure :(1) Find a point "Left" where F(Left) < 0(2) Find a point 'Right' where F(Right) > 0(3) Compute 'Middle' the middle point of the interval [Left,Right](4) Calculate Value = F(Middle)(5) If Value is close enough to zero goto Step (7)Else : If Value < 0 then : Left <- MiddleIf Value > 0 then : Right <- Middle(6) Loop back to Step (3)(7) Done!! The approximation found is MiddleFollow Middle movements to understand how it works :  Left Value(Left) Right Value(Right)

0.000000000 -1.000000000 -1.000000000 18.000000000

0.000000000 -1.000000000 -1.000000000 18.000000000

-0.500000000 -1.109375000 -1.000000000 18.000000000

-0.500000000 -1.109375000 -0.750000000 3.508056641

-0.500000000 -1.109375000 -0.625000000 0.454410553

-0.562500000 -0.473213613 -0.625000000 0.454410553

-0.593750000 -0.050185024 -0.625000000 0.454410553

-0.593750000 -0.050185024 -0.609375000 0.191316528

-0.593750000 -0.050185024 -0.601562500 0.067944440

-0.593750000 -0.050185024 -0.597656250 0.008233857

-0.595703125 -0.021135877 -0.597656250 0.008233857

-0.596679688 -0.006491229 -0.597656250 0.008233857

-0.596679688 -0.006491229 -0.597167969 0.000861241

-0.596923828 -0.002817510 -0.597167969 0.000861241

-0.597045898 -0.000978764 -0.597167969 0.000861241

-0.597106934 -0.000058919 -0.597167969 0.000861241

-0.597106934 -0.000058919 -0.597137451 0.000401122

-0.597106934 -0.000058919 -0.597122192 0.000171092

-0.597106934 -0.000058919 -0.597114563 0.000056084

-0.597110748 -0.000001418 -0.597114563 0.000056084

-0.597110748 -0.000001418 -0.597112656 0.000027333

-0.597110748 -0.000001418 -0.597111702 0.000012957

-0.597110748 -0.000001418 -0.597111225 0.000005770     Next Middle will get us close enough to zero:      F( -0.597110868 ) is   0.000000379       The desired approximation of the solution is:        t ≓ -0.597110868      
Note, ≓ is the approximation symbol One solution was found :       t ≓ -0.597110868              
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There is 1 solution to this equation.

An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equals sign (=), and expresses a relationship between the two expressions. Equations can be used to represent a variety of problems and can help solve real-world problems. For example, an equation can be used to calculate the amount of money someone will have after a certain period of time, or to calculate the distance between two points.

In order to answer this question, we must first solve the equation. 9t6-14+³ +4+- 1 = 0 can be written as 9t6 - 11 + 4 - 1 = 0. After simplifying, this equation becomes 9t6 - 7 = 0, which can be further simplified to t6 = 7. Taking the sixth root of both sides, we can determine that t = √7. Therefore, there is 1 solution to this equation.

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The graph of g(x) is a parabola that opens up, goes through (0, 1), has a vertex at (2, -3), and goes through (4, 1).

What is parabola ?

A parabola is a U-shaped curve that is formed by graphing a quadratic function. In other words, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

The graph of g(x) can be obtained by translating the graph of f(x) = x^2 to the left by 2 units and down by 3 units.

The vertex of g(x) is obtained by subtracting 2 from the x-coordinate and subtracting 3 from the y-coordinate of the vertex of f(x). Thus, the vertex of g(x) is (2, -3).

The point (-2, 4) on f(x) is translated left by 2 units to (−4, 4) on g(x) and then down by 3 units to (−4, 1). The point (2, 4) on f(x) is translated left by 2 units to (0, 4) on g(x) and then down by 3 units to (0, 1).

Therefore, the graph of g(x) is a parabola that opens up, goes through (0, 1), has a vertex at (2, -3), and goes through (4, 1).

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Answer:

A

Step-by-step explanation:

Answer:

[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]

Both products finish at the same time, which is D) 42 hours later.

The factory produces Product A every 6 hours and Product B every 21 hours.

If they started at the same time, they will finish at the same time after the lowest common multiple of the two intervals, which is 42 hours.

Therefore, the answer is D. 42 hours.

LCM is the short form for “Least Common Multiple.” The least common multiple is defined as the smallest multiple that two or more numbers have in common.

For example: Take two integers, 2 and 3.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ….

6, 12, and 18 are common multiples of 2 and 3. The number 6 is the smallest. Therefore, 6 is the least common multiple of 2 and 3.

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Answer:

[tex]x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}[/tex]

Step-by-step explanation:

The dividend is the polynomial which has to be divided.

The divisor is the expression by which the dividend is divided.

Given:

Following the steps of long division, divide the given dividend by the divisor:

[tex]\large \begin{array}{r}x^2+5x+4\phantom{)}\\x^2+5x-4{\overline{\smash{\big)}\,x^4+10x^3+25x^2+3x-24\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+\phantom{(}5x^3-\phantom{(}4x^2)\phantom{-b)))))))))}}\\5x^3+29x^2+3x-24\phantom{)}\\-~\phantom{()}\underline{(5x^3+25x^2-20x)\phantom{)))..}}\\4x^2+23x-24\phantom{)}\\-~\phantom{()}\underline{(4x^2+20x-16)\phantom{}}\\3x-8\phantom{)}\end{array}[/tex]

The quotient q(x) is the result of the division.

The remainder r(x) is the part left over:

The solution is the quotient plus the remainder divided by the divisor:

[tex]\implies q(x)+\dfrac{r(x)}{b(x)}=\boxed{x^2+5x+4+\dfrac{3x-8}{x^2+5x-4}}[/tex]

14 : 25 best represents the number of unshaded squares to total squares. The solution has been obtained by using arithmetic operations.

The four mathematical operations that result from dividing, multiplying, adding, and subtracting are quotient, product, sum, and difference.

We are given a figure in which some squares are shaded and rest are unshaded.

Number of total squares = 10 × 10 = 100

Number of shaded squares = 44

So, Number of unshaded squares = 100 - 44 = 56

Ratio of unshaded squares to total squares is as follows

56 : 100

Reducing to the lowest, we get

14 : 25

Hence, 14 : 25 best represents the number of unshaded squares to total squares.

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It will take 62 minutes for the printer to print 93 cards.

We are given the equation p=1.5m, where p represents the number of cards printed and m represents the time in minutes. We can use this equation to find out how many minutes it will take to print 93 cards.

First, we can substitute p=93 into the equation:

93 = 1.5m

Next, we can solve for m by dividing both sides of the equation by 1.5:

m = 93 / 1.5

m = 62

We can verify this answer by plugging in m = 62 into the original equation and checking that we get p = 93:

p = 1.5m

p = 1.5(62)

p = 93

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The complete question is:

The equation p = 1.5m represents the rate at which the printer prints cards where p represents the number of cards and m represents minutes. How many minutes will it take the printers to print 93 cards?

(5z+2)/(z) is the possible rational expression.

To subtract the two rational expressions, we can combine the numerators and keep the common denominator. The subtraction of the two rational expressions is shown below:

(19z+6)/(3z) - (4z)/(3z) = (19z+6-4z)/(3z)

Simplifying the numerator gives:

(15z+6)/(3z)

We can further simplify the expression by factoring out a common factor of 3 from the numerator:

3(5z+2)/(3z)

The 3 in the numerator and denominator cancel out, leaving us with the final simplified expression:

(5z+2)/(z)

Therefore, the answer is (5z+2)/(z).

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a) The confidence interval of a 95% confidence interval for the proportion of returns at the store in Maniou province is exactly between 0.3718 and 0.4282

b) Do not reject the null hypothesis. The correct answer is option C.

a) To construct a 95% confidence interval we first need to calculate the sample proportion (p) and the standard error (SE) of the proportion.

p = 12/80 = 0.15
SE = sqrt[(p*(1-p))/n] = sqrt[(0.15*0.85)/80] = 0.0347

Using the Z-score for a 95% confidence interval (1.96), we can calculate the lower and upper bounds of the interval:

Lower bound = p - 1.96*SE = 0.15 - 1.96*0.0347 = 0.083
Upper bound = p + 1.96*SE = 0.15 + 1.96*0.0347 = 0.217

Therefore, the 95% confidence interval for the proportion of returns at the store in Maniou province is between 0.083 and 0.217.

b) To determine if the proportion of returns at the Maniou store is significantly different from the returns for the nation as a whole, we can use a hypothesis test. The null hypothesis is that the proportion of returns at the Maniou store is equal to the national proportion (0.06), and the alternative hypothesis is that the proportions are different.

Using the sample proportion (p) and standard error (SE) calculated above, we can calculate the Z-score:

Z = (p - 0.06)/SE = (0.15 - 0.06)/0.0347 = 2.59

Using a Z-table, we can find the p-value for this Z-score. The p-value is 0.0096, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that the proportion of returns at the Maniou store is significantly different from the returns for the nation as a whole.

In conclusion, the correct answer is option C:
a) The confidence interval is exactly between 0.083 and 0.217
b) Reject the null hypothesis

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The function with the largest rate of change is function a.

The rate of change defines how fast the function grows.

So, the most "vertical" or the one that grows the fastest is the function with the largest rate of change.

By looking at the graph, we can see that the fastest growing (the steepest) one is function a, so that is the correct option.

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