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Andru [333]
3 years ago
7

9) Janelle has $20 and is saving $6 per week. April has $150 and is spending $4 per week. When will

Mathematics
1 answer:
Lynna [10]3 years ago
7 0

Answer:

13 weeks; 98 dollars.

Step-by-step explanation:

Let's say x represents the number of weeks, and y the number of dollars. For Janelle, an equation to find out how much money she has is y = 20 + 6x. For April, the equation is y = 150 - 4x. Now we need to find how long it will take them to have the same amount of money, and how much that is. A new equation to figure that out is 150 - 4x = 20 + 6x. To solve, make it so the variable is only one side. Add 4x to both sides. You now get 150 = 20 + 10x. Then we continue solving. Subtract 20 from both sides to get 130 = 10x. Then divide both sides by 10 to get 13 = x. This means in thirteen weeks, they will have the same amount of money. To find out how much money they have, choose one (or both to be sure) of the equations and solve for y. For example, Janelle's equation is y = 20 + 6x. Fill in 13 for x to get y = 20 + 6(13). y = 20 + 78. y = 98. This means in 13 weeks, Janelle will have 98 dollars. To be sure, also check with April's equation. y = 150 - 4x. y = 150 - 4(13). y = 150 - 52. y = 98. Therefore, in 13 weeks, both people will have 98 dollars.

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3 years ago
Solve for X if possible:<br> 5x -4y = 24<br><br> x =
Llana [10]

Answer:

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2 years ago
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Math SAT: Suppose the national mean SAT score in mathematics was 510. In a random sample of 50 graduates from Stevens High, the
sukhopar [10]

Answer:

Mean SAT score for Stevens High graduates are not the same as the national average.    

Step-by-step explanation:

We are given the following information in question:

Population mean, μ = 510

Sample mean, \bar{x} = 501

Sample size, n = 50

Alpha, α = 0.10

Sample standard deviation, s = 30

First, we design the null and the alternate hypothesis

H_{0}: \mu = 510\\H_A: \mu \neq 510

We use Two-tailed t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} } Putting all the values, we have,

t_{stat} = \displaystyle\frac{501 - 510}{\frac{30}{\sqrt{49}} } = -2.1 Now,

t_{critical} \text{ at 0.10 level of significance, 49 degree of freedom } = \pm 1.6765 Since,              

t_{stat} < t_{critical}

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis and mean SAT score for Stevens High graduates are not the same as the national average.

3 0
3 years ago
Give 1 pair of Vertical and 1 pair of Supplementary angles
mojhsa [17]

Solution:

Vertical angles are a pair of opposite angles formed by intersecting lines. re vertical angles. Vertical angles are always congruent.

These two angles (140° and 40°) are Supplementary Angles because they add up to 180°:

Notice that together they make a straight angle.

Hence,

From the image

The following pairs form vertical angles

\begin{gathered} \angle1=\angle3(vertical\text{ angles)} \\ \angle2=\angle4(vertical\text{ angles)} \\ \angle5=\angle7(vertical\text{ angles)} \\ \angle6=\angle6(vertical\text{ angles)} \end{gathered}

Hence,

One pair of the vertical angles is ∠1 and ∠3

Part B:

Two angles are said to be supplementary when they ad together to give 180°

Hence,

From the image,

The following pairs are supplementary angles

\begin{gathered} \angle5+\angle6=180^0(supplementary\text{ angles)} \\ \angle5+\angle8=180^0(supplementary\text{ angles)} \\ \angle7+\angle8=180^0(supplementary\text{ angles)} \\ \angle6+\angle7=180^0(supplementary\text{ angles)} \\ \angle1+\angle2=180^0(supplementary\text{ angles)} \\ \angle1+\angle4=180^0(supplementary\text{ angles)} \\ \angle2+\angle3=180^0(supplementary\text{ angles)} \\ \angle3+\angle4=180^0(supplementary\text{ angles)} \end{gathered}

Hence,

One pair of supplementary angles is ∠5 and ∠6

8 0
1 year ago
-9+{-7-[-(4+1)+(5-9)}-3
maks197457 [2]
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