the hypotenuse of a right triangle is 3 times as long as its shorter leg. the longer leg is 12 centimeters long. to the nearest tenth of a centimeter, what is the length of the triangle's shorter leg?

Answer: This is a quadratic function in standard form:

f(x) = x^2 - 10x + 9

The vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

To rewrite the given function in vertex form, we need to complete the square:

f(x) = x^2 - 10x + 9

= (x - 5)^2 - 16

Now we can see that the vertex is at (5, -16) and the axis of symmetry is x = 5.

To find the x-intercepts, we set y = 0:

0 = (x - 5)^2 - 16

16 = (x - 5)^2

±4 = x - 5

x = 1 or x = 9

Therefore, the x-intercepts are (1, 0) and (9, 0).

To find the y-intercept, we set x = 0:

f(0) = 9

Therefore, the y-intercept is (0, 9).

The graph of the function is a parabola that opens upward with vertex at (5, -16), x-intercepts at (1, 0) and (9, 0), and y-intercept at (0, 9).

Step-by-step explanation:  

the vertex is at (5, -16)

y-intercept is (0, 9).

the x-intercepts are (1, 0) and (9, 0).

axis of symmetry is x = 5

the range of the function is all real numbers greater than or equal to -16. In interval notation, we can write this as [-16, ∞).

the domain of the given function f(x) = x^2 - 10x + 9 is all real numbers.

Step-by-step explanation:

35/7   is an IMPROPER FRACTION ....  it REDUCES to an INTEGER = 5

The fraction 35/7 equals to 5, which is an integer because it is a whole number without a fractional or decimal component.

The fraction 35/7 equals to 5. The number 5 is a whole number that can be written without a fractional or decimal component, hence it is classified as an integer.

In general, an integer includes all whole numbers and their negative counterpart excluding fractions or decimals. Examples of integers are ...-3, -2, -1, 0, 1, 2, 3... and so on.

So the answer to your question is, 35/7 is an integer.

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The values of the sides PQ and QR are 2 and 2√3 respectively using the trigonometric ratio of cosine and sine 60° for the right triangle PQR.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

recall that cos 60° = 1/3 and sin 60° = √3/2

cos 60° = PQ/4 {adjacent/hypotenuse}

1/2 = PQ/4

PQ = 4 × 1/2 {cross multiplication}

PQ = 2.

sin 60° = QP/4 {opposite/hypotenuse}

√3/2 = QP/4

QP = 4 × √3/2

QP = 2√3

Therefore, the values of the sides PQ and QR are 2 and 2√3 respectively using the trigonometric ratio of cosine and sine 60° for the right triangle PQR.

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a) A function f is a rule that assigns to each element x in a set A exactly one element called f(x) in a set B.

b) Both tables define y as a function of x, but they have different domains and ranges

Both tables represent functions because they assign each value of x in the domain to a unique value of y in the range.

First table

f(1) = 5

f(2) = 7

f(3) = 6

f(4) = 8

Second table

f(1) = 5

f(2) = 1

f(3) = 7

f(4) = 6

f(5) = 8

So both tables define y as a function of x, but they have different domains and ranges. The first table has a domain of {1, 2, 3, 4} and a range of {5, 6, 7, 8}, while the second table has a domain of {1, 2, 3, 4, 5} and a range of {1, 5, 6, 7, 8}.

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The percentage by which the price of chicken parmesan will increase is 153.76%.

Food cost is defined as the cost of ingredients and raw materials that are required to make a dish. Food cost is also known as menu cost or recipe cost.

Menu pricing strategy determines the selling price of a dish or menu item. To price the menu, the food cost is usually divided by the desired percentage of profit. Let's solve the problem using the following formula:

Menu Price = (Food Cost ÷ Desired Percentage Markup) + Food Cost

Given, Price for chicken parmesan = $11.99

Food cost for this item = $4.31

New menu price will be 30% of the food cost.

Menu Price = (30% × 4.31) + 4.31= 1.293 + 4.31= 5.6033 ≈ $5.60

The percentage increase in the price of chicken parmesan is given by the following formula:

Percentage increase = (New Price - Old Price) / Old Price × 100%

Percentage increase = (5.60 - 11.99) / 11.99 × 100%

Percentage increase ≈ -53.76%

This is a negative value which implies that the price is decreased instead of increasing. So we have to add the absolute value of the percentage increase to 100% to get the actual percentage increase.

Percentage increase = 53.76% + 100%

Percentage increase = 153.76%

So, the percentage by which the price of chicken parmesan will increase is 153.76% rounded to two decimal places .

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The product of 32 and 0.9 is 28.8.

The product of a set of numbers is the result of multiplying all the numbers together. For example, the product of 2, 3, and 4 is:

2 x 3 x 4 = 24

In general, if we have n numbers, the product is:

a1 x a2 x a3 x ... x an

where a1, a2, a3, ..., an are the individual numbers.

The product of two negative numbers is positive, while the product of a negative and a positive number is negative. The product of any number and 0 is always 0.

To find the product of 32 and 0.9, you can multiply these two numbers together:

32 x 0.9 = 28.8

Therefore, the product of 32 and 0.9 is 28.8.

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Answer:

To find the equation of the linear function, we need to find the slope and y-intercept of the line passing through the given points. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

slope = (y2 - y1)/(x2 - x1)

Using the given points (0,12) and (1,3), we can calculate the slope as:

slope = (3 - 12)/(1 - 0) = -9

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points. Using the point (0,12), we get:

y - 12 = -9(x - 0)

Simplifying, we get:

y = -9x + 12

Therefore, the equation of the linear function that passes through the points (0,12) and (1,3) is:

y = -9x + 12

Exponential function:

To find the equation of the exponential function, we can use the general form of an exponential function:

y = a*b^x

where a and b are constants. We can use the given points to form a system of equations to solve for a and b.

Using the point (0,12), we get:

12 = ab^0

12 = a1

a = 12

Using the point (1,3), we get:

3 = 12b^1

3 = 12b

b = 1/4

Therefore, the equation of the exponential function that passes through the points (0,12) and (1,3) is:

y = 12*(1/4)^x

Therefore, the population mean, u, is the mean of 340 runners' times, regardless of the sample size. The correct answer is (B) 340.

In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data, which represents the average value of the data. It is commonly known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of values.

Here,

The population mean, u, is the mean of the times for all 340 runners in the population. If a sample of 226 runners is taken from the population, then the mean of the sample will be an estimate of the population mean. However, the population mean itself is not affected by the size of the sample.

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The number of total kids at Lincoln's school, considering the proportions, is given as follows:

775 kids.

The total number of kids at the Lincoln school is obtained applying the proportions in the context of the problem.

40% of all the Lincoln students participated in the St. Baldrick's event, and this percentage is equivalent to a total of 310 kids.

Hence the number of total kids at Lincoln's school is obtained applying the proportion as follows:

0.4n = 310

n = 310/0.4

n = 775 kids.

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Option D will result in an image that is rotated 180 degrees equation counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.

Counterclockwise, also known as anticlockwise, is a direction of rotation that is opposite to the direction in which the hands of a clock move. It is the direction that is typically associated with the rotation of objects in the Northern Hemisphere.

counterclockwise rotation is the positive direction of rotation in a coordinate system, where the x-axis increases to the right and the y-axis increases upwards.

Option B, "Reflect over the y-axis, and then reflect again over the y-axis," will result in an image that maps onto itself.

When you reflect an image over the y-axis, the left and right sides of the image switch places. If you then reflect the already reflected image over the y-axis again, the left and right sides switch places once more, effectively returning the image to its original orientation.

Option A will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the x-axis, which will not map the image onto itself.

Option C will result in an image that is reflected over the y-axis and then reflected over the x-axis, which will produce an image that is flipped both horizontally and vertically and therefore not map the image onto itself.

Option D will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.

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Answer:

Option B i think

Step-by-step explanation:

hope this helps

If A (3, 5), B (-2, 6), and C (0, 16) are the vertices of a triangle, then the slope of the segment AC is -11/3

To find the slope of segment AC, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates of the two endpoints A and C.

The change in the y-coordinates between A and C is

yC - yA = 16 - 5 = 11

The change in the x-coordinates between A and C is

xC - xA = 0 - 3 = -3

Therefore, the slope of segment AC (mAC) is

mAC = (yC - yA) / (xC - xA) = 11 / (-3) = -11/3

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 700[1+(0.04)(2)] \implies A=700(1.08)\implies A = 756[/tex]

• Domain: All real numbers

• Range: (-∞, ∞)

• To find the local minimum/maximum and intervals of increase/decrease, we need to take the first and second derivatives of the function:

First derivative: -4x^3 + 6x + 2

Setting this equal to zero and solving for x, we get critical points at x ≈ -1.23, x ≈ 0.65, and x ≈ 1.23.

Second derivative: -12x^2 + 6

• At x ≈ -1.23, the second derivative is negative, so we have a local maximum.

• At x ≈ 0.65, the second derivative is positive, so we have a local minimum.

• At x ≈ 1.23, the second derivative is negative, so we have a local maximum.

• As x —> -∞, the function approaches ∞.

• As x —> ∞, the function approaches ∞.

• To find the x-intercepts, we set the function equal to zero and solve for x:

-x^4+3x^2+2x+2 = 0

This is a quartic equation that can be solved using various methods, such as factoring or using the quadratic formula. One solution is x ≈ -1.38. The other three solutions are complex numbers.

• To find the y-intercept, we set x = 0:

-y^4 + 2 = 0

Solving for y, we get y ≈ ±1.19. So the y-intercepts are (0, 1.19) and (0, -1.19).

Answer:

Domain- (−∞,∞),{x|x∈R}

Range-  (−∞,17+6√3(over)4], {y∣y≤17+6√3(over)4}

Local Minimum/Maximum- (−1,2) is a local maxima

(1+√3(over)2 ,17+6√3(over)4) is a local maxima

(1−√3(over)2 ,17−6√3(over)4)is a local minima

Intervals of Increase/Decrease- Increasing on: (−∞,−1)(1−√3(over)2,1+√3(over)2)

Decreasing on: (−1,1−√3(over)2),(1+√3(over)2,∞)

Step-by-step explanation:

i hope this helps !

Answer:

1,460

Step-by-step explanation:

Answer:

if i answered it would be 0

Step-by-step explanation:

If the difference between the number of dots in each term is 8, it means that the number of dots in each successive term is increasing by 8.

If you have a sequence or pattern in which the difference between the number of dots in each term is 8, it means that the number of dots in each successive term is increasing by 8.

For example, if the first term has 5 dots, the second term would have 5 + 8 = 13 dots, the third term would have 13 + 8 = 21 dots, and so on. The difference between the number of dots in each term is always 8 because the pattern or sequence is increasing by 8 dots each time.

It is important to note that this is just one example of a pattern in which the difference between the number of dots in each term is 8. There can be many different patterns or sequences that exhibit this property, and the specific details will depend on the problem or context.

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28.26 inches of wax is needed to make a candle.

What is the volume of a cylinder?

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr2h where r is the radius of the circular base and h is the height of the cylinder determines the volume of a cylinder.

Here, we have

Given: Sean uses a candle mold to make candles that are perfect cones. the diameter of the cone is 6 inches with a height that is half as long as the diameter.

The volume of cylinder =  π · r² · h

r = 3 inches

h = 3 inches

= π  (3)² · 3

= 27π

Volume of sphere = 4/3πr³

= 4/3π(3)³

= 36π

Total volume = 36π - 27π

= 9π  = 9×3.14 = 28.26

Hence, 28.26 inches of wax is needed to make a candle.

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The best way to ensure that conclusions can be generalized to the whole is random sampling; population in survey research. The correct answer is c. Random sampling; population

Random sampling means that a representative sample of the population is chosen and the results of the study can be applied to the population as a whole.
Random sampling is a sampling technique that is used to create a sample from a larger population. Each member of the population has an equal chance of being selected in random sampling.

Survey research is a quantitative research technique that collects information from a representative sample of a population. This research technique can be used to collect data from respondents by asking questions on a pre-determined topic or topics.

In survey research, random sampling is one of the best ways to ensure that conclusions can be generalized to the whole population. In this process, each member of the population is given an equal opportunity to be included in the sample. This approach lowers the possibility of sampling error and ensures that the results are more accurate and reliable.

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Answer:

the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Step-by-step explanation:

Given that a fair die is rolled. We know there are six numbers in a fair die.On rolling a die, the Sample space of the given event E = {1, 2, 3, 4, 5, 6}Sample space of numbers less than 5 = {1, 2, 3, 4}Clearly we can see that the number of favorable outcomes = 4Hence, P(values less than 5) = 4/6 = 2/3.To find the complement of rolling a number less than 5, we use the formula P' = 1 - P, where P' is the complement of P.So, let P' be the complement probability of getting numbers less than 5Now, P'(numbers less than 5) = 1 - P(numbers less than 5)= 1 - 2/3= 1/3.Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Answer:

1/3

Step-by-step explanation:

This means that, the dice can be rolled at value from 1-4 and there are 6 numbers so it would be 4/6 simplified 2/3. Now subtract that value from 1 and you get 1/3

Answer:

according to my equation it is 61.6

Step-by-step explanation:

The equation of the transformed function, after being compressed horizontally by a factor of 3 and translated up 2 units, is g(x) = sqrt(x/3) + 2.

If f(x) is a function, and we want to compress it horizontally by a factor of 3 and translate it up 2 units, we can apply the following transformations:

Horizontal compression by a factor of 3 means that we need to replace x with x/3 in the function.

Translation up 2 units means that we need to add 2 to the function.

The equation of the transformed function is g(x) = sqrt(x/3) + 2, which represents a function that has been compressed horizontally by a factor of 3 and translated up 2 units from the original function f(x) = sqrt(x).

Therefore, the equation of the transformed function is:

g(x) = sqrt(x/3) + 2

Note that g(x) represents the transformed function, and we have used the square root symbol to indicate that the function is the square root of x/3.

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Check the picture below.

[tex]\cfrac{\sin(15^o)}{9}=\cfrac{\sin(B)}{12}\implies \cfrac{12\sin(15^o)}{9}=\sin(B)\implies \sin^{-1}\left( \cfrac{12\sin(15^o)}{9} \right)=B \\\\\\ 20.19^o\approx B\hspace{12em}\stackrel{180-20.19-15}{C\approx 144.81^o} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(15^o)}{9}=\cfrac{\sin(144.81^o)}{c}\implies c=\cfrac{9\sin(144.81^o)}{\sin(15^o)}\implies \boxed{c\approx 20.0}[/tex]

We need 3 liters of water to fill the cylinder up to 2/3 of its capacity.

The formula for the volume of a cylinder is V=π r2 h, where V is the volume, π is pi, r is the radius and h is the height. The radius of the cylinder is half of the diameter, so the radius of this cylinder is 6 cm, and the height is 25 cm. Applying the formula, the volume of the cylinder is V=π[tex]*6^2*25[/tex]

=4500π cm3.

To fill it up to 2/3 of its capacity, we need 3000π cm3 of water. To convert this to liters, we need to divide by 1000, so the answer is 3000π/1000=3 liters of water.

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Each term in the second sequence is one-third of the corresponding term in the first sequence and is the statement that correctly describes the relationship between these two sequences: 18, 21, 24, 27, 30 and 6, 7, 8, 9, 10.

Each term in the second series is one-third of the equivalent term in the first sequence, which is the right way to characterize the relationship between the two sequences.

This means that for each term in the second sequence (6, 7, 8, 9, 10), the corresponding term in the first sequence (18, 21, 24, 27, 30) is three times larger. For example, the first term in the second sequence (6) is one-third of the first term in the first sequence (18), and the second term in the second sequence (7) is one-third of the second term in the first sequence (21), and so on.

It is important to note that the statement "Each term in the first sequence is double the corresponding term in the second sequence" is not correct, as this relationship does not exist between the two sequences.

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(A) The normal approximation to the binomial to approximate the probability that at least 99 99 respondents live at​ home is 84.21%

(B) The probability that 16 or more out of 19 community college male students live at home is 0.0037.

In algebra, a binomial is an expression in which two distinct terms are joined by an addition or subtraction operator. For example, 2xy + 7y is a binomial because there are two terms. Algebraic expressions can be classified into different types based on the number of terms that appear, such as monomial, binomial, trinomial, etc.

(a) Based on the sample of 19 students, the proportion of community college males live at home:

p = 16/19= 0.8421 or 84.21%.

(b) the probability that 16 or more out of 19 community college male

students live at home, assuming that the proportion who live at home is 52%. Using binomial distribution with parameters

n = 19, p = 0.52, q = 1-p = 0.48,

The probability that 16 or more out of 19 community college male students live at home is

P (16 or more) = P19 (16)+ P19 (17)+ P19 (18)+ P19 (16)=

= C₁₉ ¹⁶P Q³ + C₁₉ ¹⁷P Q² + C₁₉ ¹⁸P Q¹ + C₁₉ ¹⁸P Q⁰= 0.0037.

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Let's start by setting up an equation to represent the problem.

Let's say Jake started with x amount of money.

After giving 1/3 to his wife, he has 2/3 left: (2/3)x

After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600

We can solve for x by isolating it:

(1/4)(2/3)x = $600

Multiplying both sides by 12/2 gives:

(2/3)x = $3600

Dividing both sides by 2/3 gives:

x = $5400

So Jake started with $5400.

To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:

(1/4)(2/3)($5400) = $900

So he gave his mother $900.

Step-by-step explanation:

x = original amount of money

the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.

x - (1/3)x - (1/4)x = 600

so let's bring every fractional term to .../12.

12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600

12x/12 - 4x/12 - 3x/12 = 600

5x/12 = 600

5x = 600×12

x = 600×12/5 = 120×12 = $1440

he gave to his mother

(1/4) × 1440 = $360

Pls Add A Picture : Will Update.

When a figure is rotated counterclockwise about the origin, its original coordinates of point P [tex](x,y)[/tex] will now be positioned as P' [tex](-y,x)[/tex].

[tex]\text{X} \ (1,-1) \longrightarrow \text{X'} \ (1,1)[/tex]

[tex]\text{Y} \ (3,4) \longrightarrow \text{Y'} \ (-4,3)[/tex]

[tex]\text{Z} \ (5,-1) \longrightarrow \text{Z'} \ (1,5)[/tex]

The correct set of image points for triangle [tex]\text{X'Y'Z'}[/tex] is [tex]\text{X'}(1,1)[/tex], [tex]\text{Y'}(-4,3)[/tex], and [tex]\text{Z'(1,5)}[/tex].

The equation can be rewritten using the same base as: 3⁻³ =  3⁻⁴ˣ⁺⁶.

The solution for x is: x = 9/4

An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=).

1) To rewrite an equation using the same base, we need to apply the following property of exponents:

(1/27)ˣ = 3⁻⁴ˣ⁺⁶

(1/3³) =  3⁻⁴ˣ⁺⁶

3⁻³ =  3⁻⁴ˣ⁺⁶

2) We can equate the exponents and then solve for x. That is:

3⁻³ =  3⁻⁴ˣ⁺⁶

-3 = -4x + 6

4x = 6 + 3

4x = 9

x = 9/4

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