Tell whether the ordered pair is a solution to the equation.


(1, 3); 4x – 3y = -5

Answer:

log4 (116)=−2

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (4)(4) of the right side (116)(116) equalsthe exponent (−2)(-2).

Answer:

a) $1250 b) $6250

Step-by-step explanation:

1. I = PRT

2. Sub in what you know into the equation.

I = $5000 x 0.025 x 10

3. Put this into a calculator and you get $1250. This is the simple interest earned.

4. For B, simply add $1250 to $5000 to get $6250. This is how much Jamals investment will be worth at the end of the term.

Answer:

$390

Step-by-step explanation:

The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour

40 hours would result in:

(40 hours)*($9.75/hour) = $390

Answer:

2x - 9y = 23

5x - 3y = -1

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

the number line is going up by 3's. It would start at -3 then 0 then 3 then 6 then 9 and so on. Hope this helps (:

A sample size of at least 1,521 Internet users would be necessary to estimate the proportion of interest (the proportion of Internet users who are willing to pay fees for website access) to within 2 percent in a 95 percent confidence interval.

To calculate the sample size required to estimate a proportion with a certain level of confidence and margin of error, we can use the following formula:

\(n = (Z^2 \times p \times (1 - p)) / E^2\)

where:

n is the required sample size

Z is the Z-score for the desired level of confidence (95% confidence corresponds to a Z-score of 1.96)

p is the estimated proportion of interest (the proportion of Internet users who are willing to pay fees for website access)

E is the desired margin of error (2% in this case, expressed as a decimal)

We are given that out of a sample of 13,000 Internet users surveyed in 1995, 2,938 were definitely not willing to pay fees for website access. This means that the proportion of interest (p) is:

p = (13,000 - 2,938) / 13,000 = 0.774

Now we can plug in the values and solve for n:

\(n = (1.96^2 \times 0.774 \times (1 - 0.774)) / 0.02^2\)

n ≈ 1,521

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Answer:

(5+3 = 8)

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio (5+3 = 8).

Answer:

Step-by-step explanation:

Since f(x) = k, is constant the value of k is same for any x.

From the given points we see:

It means k = 1 and the function is:

The value of f(0) = 1

Answer:

55

Step-by-step explanation:

40+y+30+y=180

40+2y+30=180

70+2y=180

2y=110

y=55

Checking: 55+40+(55+30) = 55+40+55+30 = 180

9514 1404 393

Answer:

  38 2/3 feet

Step-by-step explanation:

In shadow problems, the usual assumption is that object height and shadow length are proportional.

  height/length = b/16 = 5.8/2.4 . . . . . for building height b

  b = 16(5.8/2.4) = 38 2/3

The building is 38 2/3 feet tall.

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

$39

Step-by-step explanation:

The cups of shampoo concentrate that Devin needs to add to the water in order to make the shampoo solution is 8.

Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers together in order to determine the number of times one value is contained in another value.

The ratio of shampoo concentrate to water is 2 : 9

In order to determine the cups of shampoo concentrate to add, multiply the ratio of  shampoo concentrate by the cups of water used and divide by the ratio of water.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. The sign used to represent division is ÷.

Number of cups of shampoo concentrate needed = (2 x 36) / 9 = 8

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Answer:

y=250x+2750

Step-by-step explanation:

Answer:

  B.  61

Step-by-step explanation:

The sum of arcs around a circle is 360°. This means ...

  110° +128° +c° = 360°

  c° = 122° . . . . . . . . . . . . . subtract 238°

__

An inscribed angle in a circle has half the measure of the arc it subtends.

  a° = 1/2c° = 1/2(122°) = 61°

__

The other angles in the diagram are ...

  b° = 1/2(110°) = 55°

  d° = 1/2(128°) = 64°

Answer:

x - 3 > = 5

x > = 5 + 3

x > = 8

closed circle on 8...because of the equal sign.....shaded to the right...because of the > sign.

Step-by-step explanation:

The rectangular equation of the tangent line at θ = (3π/2) for the polar curve r = 5/(3 - cos(θ)) can be determined using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the tangent line, we need to differentiate the polar equation with respect to θ and evaluate it at θ = (3π/2). The slope (m) of the tangent line is given by dy/dx.

Let's calculate the slope (m):

r = 5/(3 - cos(θ))

Differentiating both sides with respect to θ:

dr/dθ = [d(5/(3 - cos(θ)))/dθ]

Using the quotient rule and chain rule, we can calculate dr/dθ as follows:

dr/dθ = [(-5sin(θ)(3 - cos(θ)) - 5*(sin(θ))*sin(θ)) / (3 - cos(θ))^2]

Substituting θ = (3π/2):

m = dy/dx = dr/dθ / (dθ/dx)

dθ/dx is the reciprocal of dx/dθ, which is 1/(dr/dθ) in this case.

Now we can find the slope (m) by substituting the values:

m = [-5sin(3π/2)(3 - cos(3π/2)) - 5*(sin(3π/2))*sin(3π/2)] / [(3 - cos(3π/2))^2]

Once you have the slope (m), you can substitute the point (3π/2, r) into the point-slope form of the equation to find the y-intercept (b) and write the equation of the tangent line.

To determine the rectangular equation of the tangent line at θ = (3π/2) for the given polar curve, you need to calculate the slope (m) using the derivatives and substitute the point into the point-slope form of the equation.

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Answer:

it would be 128 because 8 divded 2 is 4. 4 is the number of cereal boxes now multiply 4 x32 which would be 128

Answer:

1/7

Step-by-step explanation:

6 + 5 + 4 = 15

There are 15 marbles to start with.

p(event) = (number of desired outcomes)/(total number of outcomes)

First pick (there are 6 desired outcomes out of a total of 15 possible outcomes):

p(r) = 6/15

Now there are 5 red marbles left and a total of 14 marbles left.

Second pick (there are 5 desired outcomes out of a total of 14 possible outcomes):

p(r) = 5/14

These events are independent, so we multiply the two probabilities.

p(r, r) = 6/15 × 5/14

p(r, r) = 3/7 × 1/3

p(r, r) = 1/7

Answer:

157,9 pounds

Step-by-step explanation:

we know that he earn 12,50 per hour and that more  than 7 hour of work he earn x 1,4 than the normal.

1-  12,5 x 1,4= 17,5

2- 17,5 x 9 = 157,5

hope i helped u!!

Answer:

0.0651

Step-by-step explanation:

To find 21% of 0.31, we can use the following formula:

21% × 0.31

We can convert the percentage to a decimal by dividing by 100:

0.21 × 0.31

Multiplying these two numbers, we get:

0.0651

Therefore, 21% of 0.31 is 0.0651.

The true statement about exponential smoothing where w is the smoothing parameter is chosen as the value that minimizes a selected measure of forecast accuracy such as the mean squared error (option d).

Exponential smoothing is a forecasting method that assigns weights to past observations based on the value of the smoothing parameter. The smoothing parameter, denoted as w, determines the rate at which past observations contribute to the forecast. By adjusting the value of w, the forecaster can control the emphasis placed on recent observations versus older observations.

The choice of the smoothing parameter is important in determining the accuracy of the forecast. In practice, the value of the smoothing parameter is selected to minimize a chosen measure of forecast accuracy, such as the mean squared error (MSE). The aim is to find the value of w that yields the most accurate forecast by minimizing the difference between the forecasted values and the actual values of the time series.

Therefore, statement d is true regarding the selection of the smoothing parameter in exponential smoothing.

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Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opposite/ adjacent

tan x = 8/10

Take the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 (8/10)

x = tan ^-1 (8/10)

x =38.65980825

To the nearest tenth

x = 38.7

Answer:

38.7

Step-by-step explanation:

The value of n that makes a system of equations with a solution that has a y-value of 2 is n = 5

A system of equations is a pair of equation that contain two unknowns.

Given the system of equations

5x+6y= 32  (1)

2x + ny = 18  (2)

We desire the value of n where the value of y is 2

First, we make x subject of the formula from equation (1)

So, x = (32 - 6y)/5

Substituting x into equation (2), we have that

2x + ny = 18  (2)

2(32 - 6y)/5 + ny = 18  (2)

(64 - 12y)/5 + ny = 18

Multiplying through by 5, we have

64 - 12y + 5ny = 90

We now make n subject of the formula.

64 - 12y + 5ny = 90

- 12y + 5ny = 90 - 64

(- 12 + 5n)y = 26

-12 + 5n = 26/y

5n = 26/y + 12

n = 26/5y + 12/5

Since y = 2, substituting y into the equation, we have

n = 26/5(2) + 12/5

n = 26/10 + 12/5

n = (26 + 24)/10

n = 50/10

n = 5

So, the value of n = 5

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The amount of rain the city received in July is r = 2.5 inches

Given data ,

City received 3/4 inch of rain on July 31

Now , it represents 3/10 of the total amount of rain this to received in July

So , the equation is represented as A

Now , the value of A is

( 3/10 )r = 3/4

Multiply by 10 on both sides , we get

3r = 30/4

Divide by 3 on both sides , we get

r = 30/12

r = 2.5 inches

Hence , the city received 2.5 inches of rain

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To estimate y(1.4) using Euler's method with a step size of 0.1, we will iteratively calculate the values of y(x) at each step until we reach x = 1.4. The initial condition y(1) = 1 will be used to start the iteration.

Using Euler's method, we can approximate the solution of the initial-value problem y' = 3y + 2xy, y(1) = 1 by iteratively updating the values of y(x) at each step. We start with the initial condition y(1) = 1. The step size h is given as 0.1, so we will calculate y(x) at each point x = 1 + nh, where n represents the number of steps taken.

At each step, we use the equation:

y(x + h) ≈ y(x) + h * f(x, y),

where f(x, y) represents the derivative of y with respect to x, which is given as 3y + 2xy in this case.

Applying Euler's method, we have:

For the first step (n = 0):

x = 1, y = 1,

y(1 + 0.1) ≈ 1 + 0.1 * (3(1) + 2(1)(1)) = 1.3.

For the second step (n = 1):

x = 1.1, y = 1.3,

y(1.1 + 0.1) ≈ 1.3 + 0.1 * (3(1.3) + 2(1.1)(1.3)) = 1.679.

We continue this process, updating the value of y(x) at each step, until we reach x = 1.4. Finally, we find that y(1.4) ≈ 1.9195, rounded to four decimal places. This is our estimate of y(1.4) using Euler's method with a step size of 0.1.

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Answer:

400

Step-by-step explanation:

(4x10^6)/(1x10^4)

can be written as:

(4/1)*(10^6)/(10^4)

14(10^2) = 400