John didnt have money for a game system, so he bought it with his credit card. he paid for it monthly over the course of a year. The $350.00 game system ended up costing $429, What percentage of the game system price did he pay in interest?

Answer:

C

Step-by-step explanation:

(3,15) and (4,12)

Answer:

C or (3, 15) and (4, 12)

Step-by-step explanation:

I just took the test on Edge 2020

Answer:

The sample size required is, n = 502.

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}[/tex]

The margin of error is:

[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]

Assume that 50% of the people would support this political candidate.

The margin of error is, MOE = 0.05.

The critical value of z for 97.5% confidence level is:

z = 2.24

Compute the sample size as follows:

[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]

       [tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]

           [tex]=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502[/tex]

Thus, the sample size required is, n = 502.

Answer:

1/5k-2/3j and -2/3j+1/5k

Step-by-step explanation:

This is because the sign of both of the terms stay the same and the fractions and variables stay the same for each term as well.

Answer:

  4 blue fish for every 5 orange fish

Step-by-step explanation:

(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation

(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction

(orange fish)/(blue fish) = 5/4  . . . . .  divide by "blue fish"

There are 4 blue fish for every 5 orange fish.

Answer:

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Step-by-step explanation:

The general form of a regression equation is:

[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]

Here,

α = y-intercept

βi = regression coefficients, (i = 1, 2, ..., n)

A regression analysis is performed to determine whether the predictor variables are statistically significant or not.

The output of the regression analysis consists of two tables.

One is the regression output and the other is the ANOVA table.

The regression output table is used to display which predictor variables are statistically significant and which are not.

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

And the ANOVA table displays overall regression analysis.

The F-test statistic is used to for the overall regression analysis.

Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Answer:

200√3

Step-by-step explanation:

The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.

Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.

Answer:

Step-by-step explanation:

This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.

nCr = n!/(n-r)r!

According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.

12C10 = 12!/(12-10)!10!

= 12!/2!10!

= 12*11*10!/2*10!

= 12*11/2

= 6*11

= 66 different ways

Answer:

C. (2, -3)

Step-by-step explanation:

Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.

Answer:

Solve for y in the first equation.

Step-by-step explanation:

Given

3x+y=9

15x-3y = 1

Required

Determine the first step to avoid fractions

From the list of given options, the option that best answered the question is to Solve for y in the first equation.

Solving for y will let you substitute the expression for y in the second equation

Going by that:- Solve for y in the first equation.

[tex]3x + y = 9[/tex]

Subtract 3x from both sides

[tex]3x - 3x + y = 9 - 3x[/tex]

[tex]y = 9 - 3x[/tex]

Substitute 9 - 3x for y in the second equation

[tex]15x - 3y = 1[/tex] becomes

[tex]15x - 3(9 - 3x) = 1[/tex]

[tex]15x - 27 + 9x = 1[/tex]

Collect like terms

[tex]15x + 9x = 1 + 27[/tex]

[tex]24x = 28[/tex]

Divide both sides by 24

[tex]\frac{24x}{24} = \frac{28}{24}[/tex]

[tex]x = \frac{28}{24}[/tex]

Divide numerator and denominator by 4

[tex]x = \frac{7}{6}[/tex]

Substitute 7/6 for x in the [tex]y = 9 - 3x[/tex]

[tex]y = 9 - 3 * \frac{7}{6}[/tex]

[tex]y = 9 - \frac{7}{2}[/tex]

Solve fraction

[tex]y = \frac{18-7}{2}[/tex]

[tex]y = \frac{11}{2}[/tex]

Answer:

It's B (the one above is right)

Step-by-step explanation:

Answer:

  3 square units

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  A = 12(1/2)² = 12(1/4) = 3 . . . square units

__

Comment on the working

It might be helpful to you to see how this works when the units of the number are attached to the number.

  A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²

I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.

Hey there! :)

Answer:

[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]

Step-by-step explanation:

In rectangular coordinates, the form is:

(r·cosθ, r·sinθ)

In this instance:

Polar coordinates: (9, 150°). Use the coordinates above to solve for the rectangular coordinates.

(r · cos 150°, r· sin 150°)

(9 · cos 150°, 9· sin 150°)

cos 150° = -√3/2

sin 150° = 1/2

Plug these values into the equation:

(9 · (-√3/2), 9 · 1/2)

Multiply and simplify:

(-9√3/2, 9/2)

Therefore, the coordinates in rectangular form are:

[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]

Answer:

45°

Step-by-step explanation:

The diagram for this question has been attached to this response. Please check.

The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.

From the diagram;

θ is the angle of elevation

x = height of the tree

y = length of the shadow of the tree = x

Therefore,

tanθ = [tex]\frac{x}{y}[/tex]           [Remember that y = x? Then substitute into the equation]

tanθ = [tex]\frac{x}{x}[/tex]

tanθ = 1

θ = tan⁻¹(1)

θ = 45°

Therefore, the angle of elevation is 45°

Answer:

Slope: 1

y-intercept: 8

Step-by-step explanation:

x, y

-8,0

0,8

Answer:

[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3[tex]x^{7}[/tex] + 2x³ + x , then

[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]

    = - 21[tex]x^{6}[/tex] + 6x² + 1

The solution to given system of linear equations is (7, 3)

A linear equation is defined as an equation in which the highest power of the variable is always one.

Given,

x-3y = -2

x+3y =16

Adding the both equations,

2x=14

So, x=7

Substitute the value of x=7 in equation x+3y =16

7+3y =16

3y =16-7

y=3

Thus, the solution to given system of linear equations is (7, 3)

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Answer: A. (7,3)

Step-by-step explanation: I just did the quiz and got 100%, hope this helps!

Answer:

  D.  65°

Step-by-step explanation:

The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:

  m∠XYZ = (1/2)(arc XZ +arc WV)

  m∠XYZ = (1/2)(86° +44°) = 130°/2

  m∠XYZ = 65°

Answer:

10.3

Step-by-step explanation:

Answer:10.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

For a geometric sequence

U(n) = ar^n - 1

Where

n is the number of terms

r is the common ratio

a is the first term

From the sequence

a = 2

r = - 6 /2 = -3

U(n) = 2(-3) ^ n - 1

For the 7th term

U(7) = 2(-3) ^ 7 - 1

= 2(-3)^6

The final answer is

= 1458

Hope this helps you

Answer:

x =23/11, y =4/11

Step-by-step explanation:

subtract equation 1 from equation 2

2x-x + 5y-(-3) =6-1

x + 8y = 5

make x the subject of formula

x = 5-8y(equation#)

substitute x = 5-8y in equation 1

5-8y-3y = 1

5-11y = 1

collect like terms

5-1 = 11y

4= 11y

divide both sides by 11

4/11 = 11y/11

y = 4/11

put y = 4/11 in equation #

x = 5-8(4/11)

x = 5-32/11

LCM= 11

x = 55-32/11

x = 23/11

so, x =23/11, y = 4/11

Answer:

AB = 8.39 inches

AC = 13.1 inches

(corrected to 3 significant figures.)

Step-by-step explanation:

In a right triangle, AB is the opposite side; BC is the adjacent side, and AC is the hypotenuse side.

since tanθ = opposite / adjacent,

we can use this to find side AB.

tan40° = AB / 10

AB = 8.39 in. (corrected to 3 significant figures.)

since cosθ = adjacent / hypotenuse

we can use this to find AC.

cos40° = 10 / AC

AC = 13.1 in. (corrected to 3 significant figures.)

Answer:

AB= 8.4

AC= 13.1

Step-by-step explanation:

Answer:

0.0885 = 8.85% probability that the sample mean will exceed 2,500.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]\mu = 2400, \sigma = 210, n = 8, s = \frac{210}{\sqrt{8}} = 74.25[/tex]

Calculate the probability that the sample mean will exceed 2,500.

This is 1 subtracted by the pvalue of Z when X = 2500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2500 - 2400}{74.25}[/tex]

[tex]Z = 1.35[/tex]

[tex]Z = 1.35[/tex] has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the sample mean will exceed 2,500.

Answer:

20

Step-by-step explanation:

1/2(a+b)=180

1/2(6+12)=18

1/2(18)=180

9/9=180/9

=20

Answer:

C

Step-by-step explanation:

The equation must be equal to c since that is the total cost.

c = 1.18v

Plug in 98 for v to find the answer.

c = 1.18(98)

c = $115.64

Answer:

$36

Step-by-step explanation:

30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.

If we add another sixth, we get 36, which will be the total cost of the game.

Answer:

20 Lizard lollies.

Step-by-step explanation:

There are 10 lizard lollis.  This is out of 10+4+6 = 20 total treats.  This makes the probability of drawing a lizard lollis 10/20 = 1/2.

This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.

Answer:

15 8 ounce containers and 52 6 ounce containers

Step-by-step explanation:

First figure out how much soup must be in the 50 small containers

50 * 6 = 300

Subtract that from the total amount of soup

432 - 300 = 132

We have to put 132 ounces of soup into 6 ounce and 8 ounce containers

Let x be the number of 6 ounce and y be the number of 8 ounce containers

6x+8y = 132

x+y = minimum

We want to use as many 8 ounce containers as possible

132/8 = 16.5

16*8 = 128 r4  we cannot use 16 because we do not have a 4ounce container

15*8 = 120  r12  12/6 =2  we can do this because we can use 2 6 ounce containers

We need 15 8 ounce containers and 2 6 ounce for the 132 ounces left

We have 50 for the 300 ounces

For a total of

15 8 ounce containers and 52 6 ounce containers

Answer:

20

Step-by-step explanation:

224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20

If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.

Hence:

4 [2 (3x - 12) -40] = 224

4 [6x - 24 - 40] = 224

Collect like term

24x - 256= 224

24x/24 = 480/24

Divide both side by 24

x=480/24

x=$20

Therefore How much did he start with the first week is $20.

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Answer: B. f is always negative on the interval

========================================================

Explanation:

-1/5 = -0.2

Pick any number for x that will make the interval -0.2 < x < 2 to be true. I find x = 0 to be easiest.

Plug it into f(x)

f(x) = (5x+1)(4x-8)(x+6)

f(0) = (5(0)+1)(4(0)-8)(0+6)

f(0) = (1)(-8)(6)

f(0) = -48

We get a negative result.

So we can rule out choice A which says that f is always positive. Either f is always negative on this interval, or it's a mix of being positive and negative.

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

Note that the roots of f(x) are -1/5, 2 and -6. This is from solving f(x) = 0

Use the zero product property to solve (5x+1)(4x-8)(x+6) to find the three roots mentioned.

The roots of -1/5 and 2 form the boundary of the interval mentioned at the top of the problem. There are no roots in between -1/5 and 2, so this means that f(x) stays entirely negative on this interval. There is no way f(x) becomes positive on this interval because it would have to cross over the x axis, thus forming another root. But again there are no roots between -1/5 and 2.

A graph confirms we have the correct answer. Check out the image attached below. Note the portion from x = -0.2 to x = 2 is entirely below the x axis.

Answer:

first term = -2

fourth term = -16

eighth term = -256

Step-by-step explanation:

Given;

A sequence with function;

A(n) = -2x2^(n-1)

The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;

First term A(1); n = 1

A(1) = -2x2^(1-1) = -2×1 = -2

Fourth term A(4); n = 4

A(4) = -2x2^(4-1) = -2×8 = -16

Eighth term A(8); n = 8

A(8) = -2x2^(8-1) = -2×128 = -256

Therefore,

first term = -2

fourth term = -16

eighth term = -256