Write the equation of an exponential function that passes through the points
(1,12) and (3,108)

It should be noted that to determine the amplitude of a sinusoidal function from a graph:

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical distance between the peak and the midline of the graph (the line halfway between the highest and lowest points).

The amplitude of the sinusoidal function is half of this vertical distance.

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical coordinate of the midline of the graph (the line halfway between the highest and lowest points).

Write the equation of the midline as y = the vertical coordinate of the midline.

To determine the maximum value of a sinusoidal function from a graph:

Identify the highest point (peak) of the graph of the sinusoidal function.

The maximum value of the sinusoidal function is the vertical coordinate of this peak.

To determine the minimum value of a sinusoidal function from a graph:

Identify the lowest point (valley) of the graph of the sinusoidal function.

The minimum value of the sinusoidal function is the vertical coordinate of this valley.

To determine the period of a sinusoidal function from a graph:

Identify two consecutive peaks or valleys of the graph of the sinusoidal function.

Find the horizontal distance between these two points.

The period of the sinusoidal function is twice this horizontal distance.

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The arc length generated by a radius r is S = 11πr

The formula for arc length is given by:

S = θr

where θ is the central angle in radians and r is the radius of the circle.

For a full revolution, a radius r revolves around the center of the circle at an angle of 2 radians. Therefore, the central angle for 5 1/2 revolutions would be:

θ = (5 1/2) * 2π radians

θ = 11π radians

So, the arc length generated by a radius r rotating 5 1/2 revolutions is:

S = θr

S = 11πr

Note that if the radius is not given, then the arc length cannot be determined.

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Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]

The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.

The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.

To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:

12x²9x = 3x(4x)3(3x) = 3x(4x3)

So the GCF of 12x²9x is 3x.

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Answer:

630

Step-by-step explanation:

v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help

Answer:

Step-by-step explanation:

b

Answer:

47 + 9f [tex]\leq[/tex] 120

Step-by-step explanation:

B is the correct answer.

1.The measure of the central angle is 90°.

2.Equation of x=12.

3.The measure of the angle that bisects the minor arc is 45°.

4.The measure of the major arc is 270°.

The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.

The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.

Radians to degrees conversion

5π * (180/π) = 90° degrees

Therefore, the measure of the central angle AOB is 90° degrees.

To find  Equation of x,

8x=96°

x=96°/8

x=12

Hence, Equation of x will be 12.

The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:

(1/2) * 90° = 45°

The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:

2πr - 5π = 15π

for major arc,

We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:

15π * (180/π) = 270°

Therefore, the measure of the major arc ACB is 270°.

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Answer:

A. 60 miles

Step-by-step explanation:

2 in. = 15mi or like 2in+2in+2in+2in = 8in

15mi+15mi+15mi+15mi = 60mi

2×4 =8

/

/

v

4 × 15mi = 60mi

The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

[tex]\text{A} = \pi \text{r}^2[/tex]

The circumference of a circle is expressed mathematically as;

[tex]\text{C} = 2\pi \text{r}[/tex]

Given that the area of the circle is 20π cm², we determine the radius of the circle.

[tex]\text{A} = \pi \text{r}^2[/tex]

[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]

[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]

[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]

[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]

[tex]\text{r} = 4.47 \ \text{cm}[/tex]

Now, we determine the circumference of the circle.

[tex]\text{C} = 2\pi \text{r}[/tex]

[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]

[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]

[tex]\text{C} = 8.94\pi[/tex]

Therefore, the circumference of the circle is 8.94π centimeters.

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Answer:

2/15 litre

Step-by-step explanation:

There is 1 litre in total. Max used 1/5 litre.

1 - 1/5 = 4/5 litre

Then he used 5/6 of the remaining 4/5 litre. He would have 1/6 of 4/5 litre left.

1/6 * 4/5 = 2/15 litre

or

You could do 5/6 * 4/5 to find out how much syrup he used on Sunday and then subtract that from 4/5 litre. It will give you the same answer

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

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Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.

The percentage of the people that preferred cooking who where surveyed would be = 87.2%

The total number of people surveyed = 8

The total number of people that preferred cooking = 7

The percentage of people that preferred cooking;

= 7/8×100/1

= 700/8

= 87.2%

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Answer:

Therefore, the original price of the dish was $12.61.

Step-by-step explanation:

Let the original price of the dish be "x".

After raising the price by 15%, the new price becomes:

x + 0.15x = 1.15x

We know that the new price is $14.50, so we can set up the equation:

1.15x = 14.5

To solve for x, we can divide both sides by 1.15:

x = 14.5 / 1.15

x = 12.61 (rounded to two decimal places)

Answer:

30508

Step-by-step explanation:

5800(1+0.052)^5

The solutions the inequalities -2(c-4) ≤-4 and d-6>-4 have in common are values greater than 2

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

-2(c-4) ≤-4 and d-6>-4

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

-2(c - 4) ≤ -4

Divide by -2

c - 4 ≥ 4

So, we have

c ≥ 0

Next, we have

d - 6 > -4

Add 6 to both sides

So, we have

d > 2

This means that the solutions are c ≥ 0 and d > 2

So, the solutions the inequalities have in common are values greater than 2

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The features of function g if g(x) = -f(x)-1 include the following:

B. domain of (0, ∞).

C. vertical asymptote of x = 0.

D. x-intercept at (1/2, 0).

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:

Domain = (0, ∞)

Range = (-∞, ∞).

vertical asymptote, x = 0.

x-intercept = (1/2, 0).

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Answer:

  (I₁, I₂) = (1, 1)

Step-by-step explanation:

You want the matrix version of the given circuit equations, and the solution by matrix methods and by Cramer's rule.

The coefficients of the variables fill matrix A; the constants fill matrix (column vector) B:

  AI = B

  [tex]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}20\\30\end{array}\right][/tex]

The solution to this matrix equation can be found by left-multiplying both sides by the inverse of matrix A. The inverse of a 2×2 matrix is the transpose of the cofactor matrix, divided by its determinant. It can be written down, as the form is simple: diagonal elements are swapped; off-diagonal elements are negated.

  [tex]A^{-1}=\dfrac{1}{15(5)-25(5)}\left[\begin{array}{cc}5&-5\\-25&15\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\\\\\textsf{Multiplying by $A^{-1}$, we have ...}\\\\\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{c}20\\30\end{array}\right][/tex]

  [tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}(-0.1)(20+(0.1)(30)\\(0.5)(20)+(-0.3)(30)\end{array}\right]\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

Cramer's rule requires we find three determinants. We already found the determinant of the coefficient matrix, above. It is D = -50. The other two are ...

  [tex]D_1=\left|\begin{array}{cc}20&5\\30&5\end{array}\right|=(20)(5)-(30)(5)=-50\\\\\\D_2=\left|\begin{array}{cc}15&20\\25&30\end{array}\right|=(15)(30)-(25)(20)=-50\\\\\\I_1=\dfrac{D_1}{D}=\dfrac{-50}{-50}=1\qquad I_2=\dfrac{D_2}{D}=\dfrac{-50}{-50}=1\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.

The standard error of the mean (SE) can be calculated as:

SE = σ / √(n)

where σ is the standard deviation of the population, n is the sample size.

Substituting the given values, we get:

SE = 1150 / √(600)

≈ 47.03

The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:

z = (x - μ) / SE

z = ($90) / 47.03

≈ 1.915

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.

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✓ - True If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.

       ➜ This is true. The clerk is currently going at 6 transactions per 1/3 hours. 6 * 3 = 18, and 18 > 16.

✗ - False At his current rate, the clerk will complete 12 transactions in 1 hour.

       ➜  This is false. As stated above, he will complete 18.

✓ - True At his current rate, the clerk will complete 9 transactions every half hour.

       ➜ Let us set up a proportion to check. Then we will cross-multiply and solve.

[tex]\frac{20\;min}{6} =\frac{30\;min}{x}[/tex]

180 = 20x

x = 9

       ➜ Yes, he will complete 9 every half hour.

✗ - False If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.

       ➜  We can utilize a proportion again. 6 hours is equal to 360 minutes. Then, we will cross-multiply and solve.

[tex]\frac{20\;min}{6} =\frac{360\;min}{x}[/tex]

20x = 2,120

x = 106

       ➜ He will complete 106 transactions, not 96. It depends on if they're asking for exactly 96 or at least 96.

Answer:

D. 263 degrees

Step-by-step explanation:

We know that central angles are congruent to the arcs they encompass or intercept. So, if the minor arc is 97 degrees, and the total measure of a circle's arcs are 360 degrees, then the major arc is 263 degrees.

Therefore, the answer is D.

The length of AB can be found to be 9. 85 units .

To find the length of AB, we can use the distance formula which is:

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

The vertices for AB are:

A - ( 1, 7 )

B - ( 10, 3 )

When the values are plugged into the formula, we get :

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

d = √ ( ( 10 - 1 )^ 2 + ( 3  - 7) ^2 )

d = √ ( 81 + 16 )

d = √ 97

d = 9. 85 units

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The least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

Given that, a restaurant owner will use the data below to place new orders for plates and spoons. Packages of nine plates and twelve spoons are available for purchase. Equal quantities of plates and spoons are ordered by the restaurant owner.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

If the plates are sold in packages of 9 and there are 12 packages the number of plates will be 108.

If the plates are sold in packages of 12 and there are 9 packages the number of plates will be 108.

Thus, the least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.

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The break-even point for the division is as follows:

The break-even point is the unit or dollar value where the total revenue equals the total costs.

The total costs consist of the fixed and variable costs.

Selling price per unit of the income tax app = $8

The variable cost per unit = $3

Contribution margin per unit = $5 ($8 - $3)

Contribution margin ratio = 62.5% ($5 ÷ $8 x 100)

Fixed cost per month = $20,000

Break-even point in units = Fixed Costs/Contribution margin per unit

= 4,000 units ($20,000 ÷ $5)

Break-even point in dollars = Fixed Costs/Contribution margin ratio

= $32,000 ($20,000 ÷ 62.5%)

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Find the break-even point for the division.

The restrictions on the polynomial expression [tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex] are at x = -5, -2, 1 and 6

From the question, we have

[tex]\frac{27x^2y^3}{45x^4}[/tex]

Divide the variables

So, we have

[tex]\frac{27y^3}{45x^2}[/tex]

Divide 27 and 45 by 9

So, we have

[tex]\frac{3y^3}{5x^2}[/tex]

Hence, the solution is [tex]\frac{3y^3}{5x^2}[/tex], x ≠ 0

Given that

[tex]\frac{x + 2}{x^2 - 5x - 14}[/tex]

Factorize the numerator

So, we have

[tex]\frac{x + 2}{(x + 2)(x - 7)}[/tex]

Divide

[tex]\frac{1}{x - 7}[/tex]

So, the solution is [tex]\frac{1}{x - 7}[/tex] , where x ≠ 7

The hole is given as (2, 1/3)

This means that the graph is undefined at (2, 1/3)

One possible equation from the list of options is

[tex]f\left(x\right)\:=\:\frac{x\:-\:2}{x^2\:-\:x\:-\:2}[/tex]

The expression is given as

[tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex]

The restrictions on the polynomial is the domain

When solved graphically, we have the restrictions to be at x = -5, -2, 1 and 6

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The angle AOB is approximately 98 degrees.

The measure of the angle AOB of the sector can be found as follows:

AOB is the central angle.

Therefore,

length of an arc = ∅ / 360 × 2πr

where

Therefore,

12 = ∅ / 360 × 2 × 3.14 × 7

12 = 43.96∅ / 360

cross multiply

360 × 12 =  43.96∅

4320 = 43.96∅

divide both sides by 43.96

∅ = 4320 / 43.96

∅ = 98.271155596

Therefore,

∅ = 98 degrees

AOB = 98 degrees

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By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

[tex]A = P(1 + r/n)^{(nt)[/tex]

[tex]22,099.87 = P(1 + 0.022/2)^{(2*13)[/tex]

[tex]22,099.87 = P(1.011)^{26[/tex]

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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The range of the function is all real numbers.

In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We know,

The x-values (Input values) on the graph define the domain of the function.

and, The y-values (output values) on the graph determine the range of a function.

From the graph attached,

Here the x value start from +1 to ∞.

Thus, the range of the function is all real numbers.

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Answer: 11 Cookies

Step-by-step explanation:

let C be cookies

17($3.25) + 1.60C = $72.85

$55.25 + 1.60C = $72.85

1.60C = $17.60

C=11

She sells 11 cookies

Answer:

11

Step-by-step explanation:

To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.

I AM SO SORRY IF THIS DIDN'T MAKE SENSE!