We are working with exponential and logarithmic equations.
Your goal is to write an equation with exactly one real solution
and
Make it solvable with paper and pencil.
Be creative!

By answering the above question, we may state that As a result, the equation mass of all krill is about 11,485 times more than the mass of all blue whales.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

Given that there are several species with a wide range in population numbers, it is challenging to identify which animal is the least numerous. The vaquita porpoise, Javan rhinoceros, and Amur leopards are some of the rarest animals, albeit they all exist in the wild. The number of ants on Earth is believed to be 10 quadrillion, which is around 10,000,000,000,000,000 times greater than the population of any of the rarest species.

The estimated mass of all krill on Earth is around 379 million tonnes, whereas the estimated mass of all blue whales is approximately 33,000 tonnes. As a result, the mass of all krill is about 11,485 times more than the mass of all blue whales.

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The area of triangle PTSQ with sides ST=4, TQ=20, PQ=25, PS=13 is calculated to be 260 square units.

To find the area of triangle PTSQ, we can use the formula for the area of a triangle:

Area = (1/2) × base × height

First, we need to find the height of the triangle. We can do this by drawing an altitude from point T to side PS. Let the foot of the altitude be point R. Then, triangle TRS is similar to triangle TQP by the AA similarity criterion, since angle TRS = angle TQP (both are right angles), and angle STR = angle PTQ (both are vertical angles).

Therefore, we can set up the following proportion:

TR / TS = TQ / TP

TR / 13 = 20 / (25 - TP)

Cross-multiplying, we get:

25TR - 13TQ = 260

Substituting the given values, we get:

25TR - 13(20) = 260

25TR = 520

TR = 20.8

Now, we can use the formula for the area of triangle PTSQ:

Area = (1/2) × PQ × TR

Substituting the given values, we get:

Area = (1/2) * 25 * 20.8 = 260 square units

Therefore, the area of triangle PTSQ is 260² units.

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1. The x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept is -8.

3. g(x) has the greatest y-intercept.

1. The x-intercept of a function is found by setting f(x) = 0 and solving for x. So for f(x) = 2x²-8x+6, we have:

0 = 2x²-8x+6

0 = x²-4x+3

0 = (x-3)(x-1)

Therefore, the x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept of a function is found by setting x = 0 and evaluating f(x). So for f(x) = -x²-6x-8, we have:

f(0) = -(0)²-6(0)-8 = -8

Therefore, the y-intercept is -8.

For g(x), we have:

g(0) = 2(0)²+16(0)+31 = 31

Therefore, g(x) has the greatest y-intercept.

3. Similar to question 2, we find the y-intercept by setting x=0 and evaluating f(x):

f(0) = -(0)²-8(0)-12 = -12

Therefore, the y-intercept is -12.

4. To find the x-intercepts of f(x) = (x+8)²-4, we set f(x) = 0:

0 = (x+8)²-4

4 = (x+8)²

±2 = x+8

x = -8 ± 2

Therefore, the x-intercepts are x=-6 and x=-10. Since -6 is greater than -10, the greatest x-intercept is x=-6.

5. The axis of symmetry of a quadratic function in the form f(x) = ax²+bx+c is given by x = -b/(2a).

For f(x) = -2x²-12x-16, we have a = -2 and b = -12, so the axis of symmetry is x = -(-12)/(2*-2) = 3.

For g(x) = 2x²+16x+31, we have a = 2 and b = 16, so the axis of symmetry is x = -16/(2*2) = -4.

Therefore, f(x) has the greatest axis of symmetry.

6. To find the y-intercept, we set x=0 and evaluate the functions:

f(0) = 2(0-3)²+1 = 19

g(0) = 2(0+3)²+2 = 20

Therefore, g(x) has the greatest y-intercept.

7. To find the x-intercept, we set f(x) = 0:

0 = -(x+1)²+1

1 = (x+1)²

±1 = x+1

x = -1 ± 1

Therefore, the x-intercepts are x=-2 and x=0. Since -2 is greater than 0, g(x) has the greatest x-intercept.

8. Similar to question 6, we find the y-intercept by setting x=0 and evaluating the functions:

f(0) = -2(0+2)²+2 = -6

g(0) = 2(0+3)²-4 = 14

Therefore, g(x) has the greatest y-intercept.

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The value of hypotenuse for given right angles triangle is :

Part 1:  c = 1.5

Part 2: c = 3.5

Part 1:

a = 3, c = ?

using sin function.

sin 30 = 3/c

c = 3 * sin 30

c = 1.5

Part 2:

a = 7√3

cos 30 = 7√3 / c

c = cos 30 * 7√3

c = 7/2

c = 3.5

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The coordinates after the dilation with a scale factor of 1.5 are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The scale factor for this problem are given as follows:

k = 1.5.

Hence the coordinates of the image are obtained multiplying the coordinates of the original image by 1.5.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The margin of error with a 99% level of confidence for the population average speed is 3.2375. The correct answer is option c. 3.2375.

To find the margin of error with a 99% level of confidence for the population average speed, we need to use the formula for margin of error:

Margin of error = (z-score) * (standard deviation / √sample size)

The z-score for a 99% level of confidence is 2.576. The standard deviation is 20 km/h and the sample size is 64. Plugging these values into the formula, we get:

Margin of error = (2.576) * (20 / √64)

Margin of error = (2.576) * (20 / 8)

Margin of error = (2.576) * (2.5)

Margin of error = 6.44

The margin of error with a 99% level of confidence for the population average speed is 6.44 km/h. However, we need to divide this value by 2 to get the margin of error on either side of the mean:

Margin of error = 6.44 / 2

Margin of error = 3.22

Therefore, the margin of error with a 99% level of confidence for the population average speed is 3.22 km/h, which rounds to 3.2375 km/h. The correct answer is option c. 3.2375.

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The determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

The determinant of a 4x4 matrix can be calculated using the formula: \( \left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right| = a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right| - b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right| + c\left|\begin{array}{ccc}e & f & h \\ i & j & l \\ m & n & p\end{array}\right| - d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ m & n & o\end{array}\right|\)

Plugging in the values from the given matrix, we get: \(-3\left|\begin{array}{ccc}4 & 2 & 1 \\ 3 & -1 & -2 \\ -1 & 1 & 0\end{array}\right| - 0\left|\begin{array}{ccc}-1 & 2 & 1 \\ 0 & -1 & -2 \\ 5 & 1 & 0\end{array}\right| + 1\left|\begin{array}{ccc}-1 & 4 & 1 \\ 0 & 3 & -2 \\ 5 & -1 & 0\end{array}\right| - 2\left|\begin{array}{ccc}-1 & 4 & 2 \\ 0 & 3 & -1 \\ 5 & -1 & 1\end{array}\right|\)

Calculating the determinants of the 3x3 matrices, we get: \(-3(-4) - 0(0) + 1(-8) - 2(-4) = 12 - 8 + 8 = 12\)

Therefore, the determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

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The probability that no more than 32 patients out of 120 will have had side effects from the medicine is 0.8289.

The probability that a patient has side effects from the medicine is 23%, or 0.23. We can use the normal approximation to the binomial to find the probability that among 120 patients, no more than 32 will have had side effects.

First, we need to find the mean and standard deviation of the binomial distribution. The mean is np, where n is the number of trials (120 patients) and p is the probability of success (0.23). The mean is 120*0.23 = 27.6.

The standard deviation is sqrt(np(1-p)), or sqrt(120*0.23*(1-0.23)) = 4.65.

Now we can use the normal approximation to find the probability that no more than 32 patients will have had side effects. We need to find the z-score for 32, which is (32-27.6)/4.65 = 0.95. Using a z-table, we find that the probability of getting a z-score less than or equal to 0.95 is 0.8289.

Therefore, the probability that no more than 32 patients out of 120 will have had side effects from the medicine is 0.8289.

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In the word problem,  the 16 cups equals to a gallon.

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here A pint is equal to 2 cups (example: a large glass of milk!)

=>1 pint = 2 cups = 16 fluid ounces

When measuring many cups of liquid all put together we might want to use quarts.

A quart (qt) is the same thing as 4 cups or 2 pints.

=>1 quart = 2 pints = 4 cups = 32 fluid ounces

A gallon (gal) is the same as 16 cups or 8 pints or 4 quarts.  It is the largest liquid measurement.

Hence the 16 cups equals to a gallon.

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The average of the first ten terms of the series is 306.9. Alternative C. is correct.

The average of the first ten terms in a geometric series can be found by using the formula for the sum of a geometric series and then dividing by the number of terms. The formula for the sum of a geometric series is:

S = a(1 - rⁿ) / (1 - r)

Where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 3, r = 2, and n = 10. Plugging these values into the formula, we get:

S = 3(1 - 2¹⁰) / (1 - 2)
S = 3(-1023) / (-1)
S = 3069

Now, to find the average of the first ten terms, we simply divide the sum by the number of terms:

Average = S / n

Average = 3069 / 10

Average = 306.9

Therefore, the answer is (C) 306.9.

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The difference quotient for the function f(x) = 4x^2 + 1 is 8x

The difference quotient is a formula used to find the average rate of change of a function over an interval. It is represented by the formula: (f(x+h) - f(x))/h. In this case, we are asked to evaluate the difference quotient for the function f(x) = 4x^2 + 1.

Step 1: Substitute the function into the difference quotient formula:
(f(x+h) - f(x))/h = ((4(x+h)^2 + 1) - (4x^2 + 1))/h

Step 2: Simplify the expression:
= ((4x^2 + 8xh + 4h^2 + 1) - (4x^2 + 1))/h
= (8xh + 4h^2)/h

Step 3: Factor out h from the numerator:
= h(8x + 4h)/h

Step 4: Cancel out the h terms:
= 8x + 4h

Step 5: Substitute h = 0 to find the final answer:
= 8x + 4(0)
= 8x

Therefore, the difference quotient for the function f(x) = 4x^2 + 1 is 8x. This is the final answer for this Assignment. Remember to always show all work when evaluating the difference quotient.

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After solving the problem we found that Wags is approximately 15 years old and Scratch is approximately 5 years old today.

The solution uses algebraic equations and substitution to solve for the ages of Wags and Scratch, which is based on the concept of solving systems of linear equations.

Let's assume that Wag's age today is represented by W, and Scratch's age today is represented by S.

From the first piece of information, we can set up the following equation:

W - 1 = 3 + 3(S - 1)

Simplifying:

W - 1 = 3S - 6

W = 3S - 5

From the second piece of information, we can set up the following equation:

S + 2 = (1/4)(W + 2) + 2

Simplifying:

S + 2 = (1/4)W + 2.5

Substituting W = 3S - 5:

S + 2 = (1/4)(3S - 5) + 2.5

Solving for S:

S + 2 = (3/4)S - (5/4) + 2.5

S + 2 = (3/4)S + 3/4

1/4 S = 1 1/4

S = 5

Substituting S = 5 into W = 3S - 5:

W = 10 + 5

W = 15

Therefore, Wags is approximately 15 years old and Scratch is approximately 5 years old today.

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The x-coordinate of point P is approximately -5.33.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

To find the x-coordinate of point P, we can use the formula:

x-coordinate of P = (4x-coordinate of A + 2x-coordinate of B) / (4+2)

We are given the coordinates of points A and B:

A(-8, -9) and B(0, -2)

Using the formula, we can substitute the x- and y-coordinates of A and B into the formula and simplify:

x-coordinate of P = (4(-8) + 2(0)) / (4+2)

= (-32) / 6

= -5.33 (rounded to 2 decimal places)

Therefore, the x-coordinate of point P is approximately -5.33.

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Answer:

y=(x−3)2−1

Step-by-step explanation:

Since it only resolves one of the two inequalities, (1, -5) cannot be a solution to the given system of inequalities.

How are coordinates determined?

We must check that the point (1, -5) fulfils both inequalities in order to determine if it is a solution to the system of inequalities.

y > -6x - 11 is the first inequality. Inputting x = 1 and y = -5 results in:

[tex]-5 > -6(1) (1) - 11 \s-5 > -6 - 11 \s-5 > -17[/tex]

The first inequality is satisfied at the position (1, -5) since -5 is greater than -17.

y - x - 5 is the second inequality. Inputting x = 1 and y = -5 results in:

[tex]-5 ≥ -(1) (1) - 5 \s-5 ≥ -6[/tex]

The point (1, -5) does not satisfy the second inequality since -5 is not greater than -6.

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number 8 (i think) is d, 1 in 1,500, and number 9 is c, 1,513 cars :)

The best method to use to solve the system of equation will be Elimination method.

According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.

The two equations are:

3x+7y=-19

-3x+4y=12

From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.

Hence, the best method to use to solve the system of equation will be Elimination method.

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The t-statistic associated with this sample if information from the government reveals that the actual average salary is 2

The t-statistic can be calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / √(sample size))

In this case, the sample mean is $50,000, the population mean is $49,000, the sample standard deviation is $5,000, and the sample size is 100.

Plugging these values into the formula, we get:

t = ($50,000 - $49,000) / ($5,000 / √(100))

t = $1,000 / ($5,000 / 10)

t = $1,000 / $500

t = 2

Therefore, the t-statistic for this sample indicates that the actual average pay is $2, according to data from the government.

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Let's denote the distance from point A to the lighthouse as x and the distance from point B to the lighthouse as y. We can use the tangent function to set up the following equations:

tan(11) = 111/x

tan(21) = 111/y

We want to solve for the value of y-x. We can rearrange the two equations above to solve for x and y, respectively:

x = 111/tan(11)

y = 111/tan(21)

Now we can substitute these expressions into y-x to get:

y-x = 111/tan(21) - 111/tan(11)

Using a calculator, we can evaluate this expression to get:

y-x ≈ 381.3 feet

Therefore, the distance from point A to point B is approximately 381.3 feet.

Answer: I’m pretty sure it’s the first box, second box and third box

Step-by-step explanation:

-3C+50

(a) C+E and E+C = 2C (b) A+B = A+B (e) D-F = D-F (d) -3C+50 = -3C+50

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Mr Tan earns a total of $96.

Let the selling price of a cup of apple juice be x.

Then the selling price of a cup of lemon juice is 3/2 times x, which is (3/2)x.

Let the number of cups of lemon juice sold be L, and the number of cups of apple juice sold be A.

We know that for every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. So we can write:

A = (5/2)L

His earnings from apple juice minus his earnings from lemon juice is $12. So we can write:

Ax - L(3/2)x = $12

Simplifying this equation, we get:

(5/2)Lx - (3/2)Lx = $12

Lx = $24

Now we can use this information to find the values of L and A:

L = $24/x

A = (5/2)L = (5/2)($24/x) = $60/x

Finally, we can calculate Mr Tan's total earnings by adding his earnings from apple juice and lemon juice:

Total earnings = Ax + L(3/2)x

= $60 + (3/2)($24)

= $96

Therefore, Mr Tan earns a total of $96.

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The probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

The Bayes theorem's assumption that the prior probabilities are known with certainty is one of its limitations. These probabilities, however, could not be known or be impossible to predict precisely in many real-world settings. Moreover, Bayes' theorem makes the assumption that each occurrence is independent, which may not necessarily be true in real-world circumstances.

Given that,

P(D) = 0.001

P(D') = 1- 0.001 = 0.999

P(T|D) = 0.99 (the test is 99% effective in detecting the disease)

P(T'|D') = 0.995

The Baye's theorem is given as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Substituting the values:

P(T) = (0.99 * 0.001) + (0.005 * 0.999) = 0.00594

P(D|T) = (0.99 * 0.001) / 0.00594 ≈ 0.166

Hence, the probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

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The complete question is:

The coefficient is 3 and, in the situation, it represents the distance covered per unit

From the question, we have the following parameters that can be used in our computation:

M = 20 + 3d

Given an expression ax, where the variable is x

The coefficient in this variable is a

Using the above as a guide, we have the following:

The coefficient in M = 20 + 3d is 3

And it represents the slope of the relation

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Answer:

3/10

Step-by-step explanation:

0.3=30/100

30/100 simplyfied is 3/10

Therefore the answer is 3/10

hope this helped

\( \frac{-9 y-81}{y+9} \) simplifies to -9.

To simplify the given expression, \( \frac{-9 y-81}{y+9} \), we need to factor out the common factor of -9 from the numerator.

Factor out the common factor of -9 from the numerator.
\( \frac{-9(y+9)}{y+9} \)

Simplify the expression by canceling out the common factor of (y+9) from the numerator and denominator.
\( \frac{-9 \cancel{(y+9)}}{\cancel{y+9}} \)

The final simplified expression is -9.
\( -9 \)

\( \frac{-9 y-81}{y+9} \) simplifies to -9.

It is important to check for any restrictions on the variable y. In this case, y cannot be equal to -9, as it would make the denominator of the original expression equal to 0 and the expression would be undefined. Therefore, the simplified expression is valid for all values of y except -9.

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The solution to the system is (x, y, z) = (6, 0, -2).

To solve the system, we can use the elimination method. First, we will eliminate x from the second and third equations by adding the first equation to them:

{5y - 10z = 20
{-3y + 4z = -8

Next, we will eliminate y from the second and third equations by subtracting the second equation from the third equation:

{15y - 30z = 60
{15y + 20z = -40
{-10z = 20

Now we can solve for z:
z = -2

Next, we can substitute z back into the second equation to solve for y:

5y - 10(-2) = 20
2y + 20 = 20
2y = 0
y = 0

Finally, we can substitute z and y back into the first equation to solve for x:

2x + 3(0) - 4(-2) = 20
2x + 8 = 20
2x = 12
x = 6

So the solution to the system is (x, y, z) = (6, 0, -2).

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The total number of copies sold is 374,096, calculated using proportion and percentage based on the copies sold in the first month.

Let x be the total number of copies sold to date.

We know that the number of copies sold in the first month represents 8.3% of the total number of copies sold to date, so we can set up the following equation:

31,100 = 0.083x

Solving for x:

x = 31,100 / 0.083

x = 374,096.39

Rounding to the nearest whole number, we get:

x = 374,096

Therefore, approximately 374,096 copies have been sold to date.

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Answer:

720m

Step-by-step explanation:

60×4 = 240

240×3 = 720