How do I find the area?

The amount loaned at 5% interest is $7,500. Let's say the bank loaned out x dollars. The amount loaned at 5% interest is 0.05x dollars, and the amount loaned at 10% interest is 0.10x dollars.

We know that the total interest received in one year was y dollars. We can set up the following equation to represent this information:

0.05x + 0.10(x - 0.05x) = y

Simplifying the right side of this equation, we get:

0.05x + 0.10x - 0.05x = y

0.05x = y

Dividing both sides of this equation by 0.05, we get:

x = y / 0.05

x = 20y

We are given that the total interest received was $y = $1,500. Plugging this value into the equation, we get:

x = 20(1,500)

x = $30,000

Therefore, the amount loaned at 5% interest is $30,000 / 2 = $15,000. However, we are asked for the amount loaned at 5% interest, not 10% interest. So, we need to divide this amount by 2:

$15,000 / 2 = $7,500

Therefore, the amount loaned at 5% interest is $7,500.

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QUESTION:

A bank loaned out $18,000, part of it at the rate of 8% per year and the rest at 16% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?

Given : 2.31/0.790 =?, (2.08 x 10³) x (3.11 x 10²) = 10⁵We know that division is the arithmetic operation used to separate the objects into equal groups. Also, the division is the inverse operation of multiplication.

Therefore,To solve the problem 2.31/0.790 = Step 1: First, write the given values. Step 2: Divide 2.31/0.790=2.924050633 Step 3: Finally, the value of the given problem is 2.924050633. Hence 2.31/0.790=2.924050633To solve the problem (2.08 x 10³) x (3.11 x 10²) = 10⁵Step 1: First, write the given values.

Step 2: Multiply 2.08 x 10³ and 3.11 x 10²=6.4608 x 10⁵Step 3: Finally, the value of the given problem is\(6.4608 x 10⁵. Hence (2.08 x 10³) x (3.11 x 10²) = 6.4608 x 10⁵Therefore, 2.31/0.790 = 2.924050633, (2.08 x 10³) x (3.11 x 10²) = 6.4608 x 10⁵.

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Answer:

x=75

Step-by-step explanation:

Sum of the interior angles of a trapezoid = 360°

That being said we can calculate the measure of the missing angle (x) by subtracting the given angles (131, 107 and 47) from 360

so x = 360 - 131 - 107 - 47

360 - 131 = 229

229 - 107 = 122

122 - 47 = 75

so x = 75

Step-by-step explanation:

For ratio questions, add up the both ratio to know the exact ratio, similar to percentage question.

5:8 total ratio is 13

Save ratio : 5/13

Spend ratio : 8/13

Saved money : 5/13 x 910 = 350

Spent money : 8/13 x 910 = 560

To double check answer, you can try add up the saved and spend money. If it gets to initial money 910, then its correct. Have fun learning ^-^

Answer:

He's 24

Step-by-step explanation:

x+28=2x+4

x=28-4

x=24

Answer:

Now, he is 24.

Step-by-step explanation:

Now, the man is x years old.

In 28 years, he'll be x + 28.

In 2 years, he'll be x + 2.

x + 28 = 2(x + 2)

x + 28 = 2x + 4

-x = -24

x = 24

Answer: Now, he is 24.

Answer:

\( - 2x - h\)

Step-by-step explanation:

We are given a function \(g(x)=2-x^2\). We want to find \((g(x+h)-g(x))/h\) To do so, first we need to work out the numerator

\(g(x+h)=2-(x+h)^2\). Therefore

\(g(x+h)-g(x)\implies 2-x^2-2xh-h^2-2x-x^2\)

like terms cancel out leaving us with

So,

\( \displaystyle\frac{g(x + h) + g(x)}{h} = \frac{ h( - 2x - h )}{h} = \boxed{ - 2x - h}\)

SOLUTION

solve for x



-5/3n = -3​

cross - multiply we have:

-5 = 3 n X 3

-5 = 9n

Divide both sides by 9, we have;

n = -5 / 9

Answer: 90 miles in 180 minutes

Step-by-step explanation: Since 90 minutes is two times 45, there would be 2 miles in one minute. Then, you multiply 2 times 45 so therefore you get 90 miles in 180 minutes.

Answer:

Step-by-step explanation:

Equation of circle:

Substitute the values of h, k, r to get:

The line is:

Substitute y into equation of circle and solve for positive x, since we are interested in the intersection in the first quadrant:

Find corresponding value of y:

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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In a speculation test, a blunder happens when we dismiss invalid speculation that's really genuine, whereas a Sort II mistake happens when we fall flat to dismiss a null theory that's really wrong.

Since a Sort I error is more genuine in this situation, we need to play down the likelihood of making such a mistake. This implies we ought to select a lower level of noteworthiness, which decreases the likelihood of dismissing genuine invalid speculation.

In rundown, the leading choice of level of noteworthiness for this double-blind therapeutic test would be a lower level, such as 0.01 or 0.001, to minimize the likelihood of making a Sort I mistake, which is more genuine in this situation.

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Answer: 31 7/8

Step-by-step explanation:

Firstly, we add the whole part which is 31 into the fraction making it an improper fraction. Then solve the problem by making a common denominator of 3/4  from the whole fraction into 6/8 and adding it to the previous fraction, then subtracting the spilled amount. To make the improper fraction a whole fraction/normal, just divide by the denominator. That's all!

31 x 8 = 248

248 + 6 = 254

254 - 7 = 247

247 ÷ 8 = 31 + \(\frac{7}{8}\)

OR 31 \(\frac{7}{8}\)

Answer:

B

Step-by-step explanation:

The power set of set a, denoted as P(a), contains all possible subsets of set a. The elements of P(a) are:

P(a) = {∅, {c}, {d}, {e}, {c, d}, {c, e}, {d, e}, {c, d, e}} , The power set of set a, P(a), contains 8 elements, and the power set of P(a), P(P(a)), contains 255 elements.

The power set of a set A, denoted as P(A), is the set of all possible subsets of A, including the empty set and A itself. To construct P(A), we consider all the possible combinations of elements in A. In this case, set a = {c, d, e}, so P(a) includes subsets with 0, 1, 2, and 3 elements.

To calculate P(a), we list all the subsets: ∅ (empty set), {c}, {d}, {e}, {c, d}, {c, e}, {d, e}, and {c, d, e}. These subsets represent all the possible combinations of elements from set a.

To find P(P(a)), we need to consider the power set of P(a). Each subset in P(a) can be either included or excluded in P(P(a)). Since P(a) has 8 elements, we have 2⁸ = 256 possible subsets. However, one of these subsets is the empty set (∅), so we subtract 1 to get 255 elements in P(P(a)).

The number of elements in P(a) = 2 power (number of elements in a) = 2³ = 8.

The number of elements in P(P(a)) = 2 power(number of elements in P(a)) = 2⁸ = 256.

However, since P(a) includes the empty set (∅), we subtract 1 from the total number of subsets in P(P(a)).

Therefore, the final number of elements in P(P(a)) is 256 - 1 = 255.

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Answer: They are equal, but if you are buying something else with it,, say a case, the website

Step-by-step explanation:

Website:

1/4 +1/4 = 1/2

Store:

1/2

Answer:

the 50% off is the better deal

Step-by-step explanation:

200 x .50= 100 so on the first phone you save $100

the website you get 25% off so .25 x 200=50 so 200 - 50 =150 then you get another 25% off .25 x 150 =37.50 so 150 - 37.50 = 112.50.

Answer:

Step-by-step explanation:

The length of the original car is approximately 12 feet. Given that the similarity ratio of the replica car is 2:45, and the length of the replica car is 6.4 inches, we can set up a proportion to find the length of the original car in feet.

Let x be the length of the original car in feet.

Using the proportion:

(2/45) = (6.4/x)

Cross-multiplying, we get:

2x = 45 * 6.4

2x = 288

x = 288/2

x = 144 inches

To convert the length from inches to feet, we divide by 12 since there are 12 inches in a foot:

144 inches / 12 = 12 feet

Therefore, the length of the original car is approximately 12 feet.

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To develop a multiple linear regression model for estimating the market value as a function of both the age and size of the house, we need to use the provided data. Let's denote the market value as Y, age as X1, and size as X2.

The model can be stated as follows:

MarketValue = β0 + β1 * Age + β2 * Size

Now, we need to estimate the values of the coefficients β0, β1, and β2 using regression analysis. The estimated model would be:

MarketValue = 59274.161 + (-588.462) * Age + 39.156 * Size

The R2 value, which measures the proportion of the variation in the dependent variable (MarketValue) explained by the independent variables (Age and Size), is 0.741. This means that approximately 74.1% of the variation in the market value can be explained by the age and size of the house.

The significance F value is 17.823. This value tests the overall significance of the regression model. With an alpha of 0.05, we compare the F value to the critical F-value to determine if the model is statistically significant or not.

To obtain the p-values for individual variables, we can perform hypothesis tests. The p-value for Age is 0.000, which is less than the significance level of 0.05. This indicates that the age variable is statistically significant in explaining the market value. Similarly, the p-value for Size is 0.001, also indicating its statistical significance.

In summary:

MarketValue = 59274.161 - 588.462 * Age + 39.156 * Size

R2 = 0.741, indicating that approximately 74.1% of the variation in the market value is explained by the age and size of the house.

Significance F = 17.823, suggesting that the regression model is statistically significant as a whole.

Age p-value = 0.000, indicating that the age variable is statistically significant in explaining the market value.

Size p-value = 0.001, indicating that the size variable is statistically significant in explaining the market value.

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Answer: no 3 is grade then -6 as 3 is positive number and 6 is negative number so positive is greater then negative number.

Step-by-step explanation:

In order to indicate if a number is greater than or less than another, we use the symbols > and <. For example, 10 is greater than 3, so we write it 10 > 3.

Answer:10

Step-by-step explanation:

2+3+2+3

is

10

In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.

In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.

a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".

A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.

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The speed of light is 3.0 ×108m/s.

We have ask about the theory of Albert Einstein,

According to einstein, nothing in the universe can move faster than light

Albert Einstein said that nothing travels faster than the speed of light, and the speed of light is

\(3.0\times108 m/s\)

So that the nothing can travels faster than the speed of light.

light travels with very high speed.

Therefore we get the correct option is 3.

That is the speed of light is 3.0 ×108m/s.

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Answer:

8 cm and 10 cm

Step-by-step explanation:

Hello, I can help you with this.

Step 1

According to the question there are two rectangles A and B,

Rectangle A is a scale drawing of Rectangle B and has 25% of its area

in other words

\(Area_{A}=0.25*Area_{B} (Equation\ 1)\\\)

Step 2

Let

Rectangle A

length (1)= 4 cm

length (2)= 5 cm

\(Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}\)

put this value into equation 1

\(Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}\)

Now, we know the area of rectangle B, to know its length we need to formule other equation

Step 3

\(Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\)

the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then

\(\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)\)

Step three

using Eq 1 and Eq 2 find the lengths

put the value of length(1B) into equation (2)

\(length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm\)

Now, put the value of length(2B) into equation 3 to know length (1B)

\(length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm\)

I really hope this helps you, have a great day.

Answer:

m = undef

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{-1-(-5)}{-3-(-3)}\)

\(m=\frac{-1+5}{-3+3}\)

\(m=\frac{4}{0}\)

m = undef

The values of each number using power 10 is shown below.

1. 79 x 10

= 790

2. 15 x 100

= 1500

3. 22 x 1,000

= 22,000

4. 15 x 1000

= 15,000

5. 83 x 102

= 8,466

6. 23 x 10²

= 2300

7. 72 x 10²

= 7200

8. 4 x 10²

= 400

9. 75 x 10²

= 7500

10. 55 x 10²

= 5500

11. 81 x 10³

= 81,000

12. 3 x 10³

= 3000

13. 85 x 10³

= 85, 000

14. 98 x \(10^{-1\)

= 9.8

15. 86 x \(10^{-3\)

= 0.086

16. 65 x \(10^{-2\)

= 0.65

17. 19 x 10³

= 19,000

18. 3.49 x \(10^{9\)

= 349,000,000,000

19. 2.79 x \(10^{8\)

= 27,900,000,000

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Answer:

82 is your answer

Step-by-step explanation:

3x6 = 18

8x8=64

18+64=82

Answer:

82 m²

Step-by-step explanation:

The blue figure is composed of a square ( on the right ) and a rectangle on the upper left )

Area of blue figure is the sum of the 2 areas , that is

Area = (8 × 8) + (6 × 3) = 64 + 18 = 82 m²