Solve the linear equation x + 4 + 3x = 72. State the property that justifies your first step and why you chose it

Please Help!!!!!!!!!

The periodic interest rate is 16% when Elise took a loan of $500 for 2 weeks.

What is periodic interest?

Typically, a daily periodic interest rate is multiplied by the balance owed at the end of each day to calculate interest. The amount of interest is compounded daily since it is added to the balance from the previous day.

Given that, Elise took a loan of amount $500.

The interest that he paid after 2 week is $80.

The interest rate is (interest amount/principal) × 100

Here interest is $80.

Principal is $500.

The interest rate is  (80/500) × 100%

= 16%

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Answer:

the rivers in the area resulted in fish becoming a main food source

Step-by-step explanation:

i took the k12 test

How were the Catawba people affected by the environment of the region that they settled in?A.They built their homes high up in trees above the marshlands.B.They built shelters from clay bricks using the soil found in the area.C.They built their villages near rivers of the region and relied on fish as a food source.D.They built villages in the mountainous areas to avoid flooding rivers.

Answer:

\(344 {cm}^{2} \)

Step-by-step explanation:

\(area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ \)

\(area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ \)

\(area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ \)

Answer:

7X^2

.

.

.

is the correct answer

Answer:

d=7.211103

Step-by-step explanation:

A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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Answer:

6 ways

Step-by-step explanation:

1 way for true or false and 5 ways for multiple choice questions

The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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Answer:

£210

Step-by-step explanation:

1/4 of 600= 150

2/5 of 600= 240

240 + 150= 390

600 - 390 = 210

She has £210 left

All the three collinear points on line l are,

⇒ points A, F, and G

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

To find All the three collinear points on line l.

Hence, By figure;

All the three collinear points on line l are,

⇒ points A, F, and G

Thus, All the three collinear points on line l are,

⇒ points A, F, and G

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Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

The correct answer is A). One must assume that the samples were random or otherwise independent of each other.

It must also be assumed that the distributions are roughly normal, so it would be a good idea to check a histogram to make sure there is no strong skewness or outliers.

In order to perform inference on these two samples, it is important that they are random or independent samples. This ensures that the samples are representative of the population and that the results can be generalized.

Additionally, assuming that the distributions are roughly normal is important for conducting statistical tests and making accurate inferences. Checking a histogram helps to assess the shape of the distributions and identify any potential skewness or outliers that may affect the validity of the analysis. So, the correct answer is A).

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--The given question is incomplete, the complete question is given below " do consumers spend more on a trip to store a or store b? suppose researchers interested in this question collected a systematic sample for 83 store a customers and 82 store b customers by asking customers for their purchase amount as they left the store. the data collected are summarized in the given table. to perform inference on these two samples, what conditions must be met? are they? explain.

Choose the correct answer below.

A One must assume the that samples were random or otherwise independent of each other. It must also be assumed that the distributions are roughly normal so it would be a good idea to check a histogram to make sure there is not strong skewness or outliers.

B. One must assume that the samples represent more than 50% of the total population. It must also be assumed that these distributions are reasonably symmetric, so it would be a good idea to check a histogram to make sure this condition is met.

C. One must assume that that the sample sizes are sufficiently large enough to make the inferences on these two samples.

D. One must assume that the samples are independent of each other and that the individual purchases are dependent upon each other with each sample."--

Let pieces be x

ATQ

\(\\ \sf\longmapsto 2:4=3:x\)

\(\\ \sf\longmapsto \dfrac{2}{4}=\dfrac{3}{x}\)

\(\\ \sf\longmapsto \dfrac{1}{2}=\dfrac{3}{x}\)

\(\\ \sf\longmapsto x=6\)

\(\displaystyle \rm 2w-4 \ piecec \\ . \ \ \ \Big \slash \!\!\!\!\! \Big\backslash\\3w-x \ piecec \\\\\\ 2x=4\cdot 3 \\\\ \boxed{\rm x=6 \ piecec}\)

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

XY = 12

Step-by-step explanation:

The midsegment XY is half the length of the base CE , that is

XY = \(\frac{1}{2}\) × 24 = 12

Answer:

3 rational numbers between -5 and -6 include -5.6, -5.7, and -5.1.

Step-by-step explanation:

Answer:

-5.2, -5.6, and  -5.8.

Step-by-step explanation:

3 rational numbers between -5 and -6.

-5 > x > -6

Where x is a rational number, that can be expressed in p/q form.

The numbers can be -5.2, -5.6, and -5.8.

-5.2 = -26/5

-5.6 = -28/5

-5.8 = -29/5

The numbers can be expressed in p/q form, so they are rational.

This model must be completed to represent 377 ÷ 12 as follows;

      30     1___

12 | 360  | 17 | 5.

In order to divide the given numbers by using the box method, we would write an expression to represent the number of times in which the number (377) can be divided by the number (12), while including the remainder (17) as follows;

377 ÷ 12 = (360 + 17) ÷ 12

377 ÷ 12 = (360 ÷ 12) + (17 ÷ 12)

377 ÷ 12 = 30 + (17 ÷ 12)

Note: 12 would divide 17 to give an output of one (1) remainder five (5).

In this context, the above mathematical expression would be re-written as follows;

377 ÷ 12 = 30 + 1 R 5.

Where:

The variable R represents remainder.

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If an AP has first term 7 and common difference 4. If the sum of all it's terms is 900, then there are 3 terms.

Let's use the formula for the sum of an arithmetic progression to solve this problem:

S = n/2[2a + (n-1)d]

where S is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

We know that a = 7 and d = 4, and we're given that S = 900. Substituting these values into the formula, we get:

900 = n/2[2(7) + (n-1)(4)]

Simplifying the expression inside the brackets:

900 = n/2[14 + 4n - 4]

900 = n/2[10 + 4n]

Multiplying both sides by 2 to eliminate the fraction:

1800 = n[10 + 4n]

Simplifying the right-hand side:

1800 = 4n^2 + 10n

Rearranging to get a quadratic equation in standard form:

4n^2 + 10n - 1800 = 0

We can solve for n using the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 4, b = 10, and c = -1800, so:

n = (-10 ± √(10^2 - 4(4)(-1800))) / 2(4)

n = (-10 ± √(100 + 28800)) / 8

n = (-10 ± √(28900)) / 8

n = (-10 ± 170) / 8

n = 20/8 or n = -180/8

n = 2.5 or n = -22.5

Since the number of terms must be a positive integer, we can discard the negative solution and conclude that there are 2.5 terms. However, this doesn't make sense because the number of terms in an arithmetic progression must be a whole number. Therefore, we need to round up to the nearest whole number, which gives us:

n = 3

Therefore, there are 3 terms in the arithmetic progression with first term 7 and common difference 4, and the sum of these terms is 900.

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The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Answer:

186

Step-by-step explanation:

10×9+32×3

90+96

=186

HOPE THIS HELP YOU

Answer: Hi!

First we will substitute the variables and then solve the equation.

The equation will look like this after we substitute:

10(9) + 32(3)

We will multiply:

(90) + (96)

We will add:

186

This equation is equal to 186.

Hope this helps!

The original cost of the car was $12,935.74 (rounded to the nearest $100).

(a) To find the depreciation rate for a car that originally cost $20,000 and is worth $12,000 after 4 years, we can use the formula:

\(C = (1 - r)^n * C_0\)

where C is the value of the car after n years, C_0 is the original cost of the car, and r is the yearly depreciation rate.

Plugging in the values given, we get:

\(12,000 = (1 - r)^4 * 20,000\)

Solving for r, we get:

\(1 - r = (12,000/20,000)^(1/4) = 0.8185\)

r = 1 - 0.8185 = 0.1815

The depreciation rate for the car is 18.2% (rounded to the nearest tenth of a percent).

(b) To find the original cost of a car that has a yearly depreciation rate of 11% and is worth $10,000 after 2 years, we can use the same formula:

\(C = (1 - r)^n * C_0\)

Plugging in the values given, we get:

\(10,000 = (1 - 0.11)^2 * C_0\)

Solving for C_0, we get:

\(C_0 = 10,000 / (0.89)^2 = $12,935.74\)

The original cost of the car was $12,935.74 (rounded to the nearest $100).

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To find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and x=3y^2 about x=-4, we can use the method of cylindrical shells.

First, we need to sketch the region to visualize it. The two curves intersect at (0,0) and (4/27,2/3). The region we want to rotate is bounded by the x-axis and the two curves.

Next, we need to find the height of the cylinder at any given x-value. This can be done by subtracting the two functions:

h(x) = x^2 - 3y^2

Since we are rotating about the line x=-4, we need to shift our x-values by 4 units to the right:

h(x+4) = (x+4)^2 - 3y^2

Now we can set up the integral to find the volume:

V = ∫(from 0 to 4/27) 2πrh(x+4) dx

where r is the distance from x=-4 to the curve, which is simply x+4.

V = ∫(from 0 to 4/27) 2π(x+4)[x^2 - 3(1/3)(x^2)] dx

V = ∫(from 0 to 4/27) 2π(x+4)(2/3)x^2 dx

V = 2π ∫(from 0 to 4/27) (2/3)x^3 + (8/3)x^2 dx

V = 2π [(1/2)(2/3)(4/27)^4 + (1/3)(8/3)(4/27)^3]

V = (32π/729) units^3

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and x=3y^2 about x=-4 is (32π/729) cubic units.

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The price of gasoline increased by approximately 5.71% over the course of one week, rising from $3.50 to $3.71.

To calculate the percentage increase in the price of gasoline, we can use the formula: Percentage increase = ((New price - Old price) / Old price) * 100. Applying this formula to the given scenario, we have ((3.71 - 3.50) / 3.50) * 100 = 0.21 / 3.50 * 100 ≈ 0.06 * 100 ≈ 5.71%. Therefore, the price of gasoline rose by approximately 5.71%.

This percentage increase indicates the relative change in price from the initial value. In this case, the gasoline price increased by 5.71%, meaning that it rose by about 5.71% compared to its original value. This increase could be influenced by various factors such as changes in crude oil prices, supply and demand dynamics, geopolitical events, and taxes. It is essential to monitor such fluctuations as they affect consumers, businesses, and the overall economy.

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Answer:

y=salary=32.000

x=years

salary after 15 years       y+1800x  

32000+1800(15)

32000+27000=59000

Step-by-step explanation:

The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

Answer:

Volume of rectangular prism = 1200 cubic inches

Step-by-step explanation:

Given that:

Length of rectangular prism = 10 inches

Width of rectangular prism = 8 inches

Height of rectangular prism = 15 inches

Volume of rectangular prism = Length * Width * Height

Volume = 10 * 8 * 15

Volume = 1200 cubic inches

Hence,

Volume of rectangular prism = 1200 cubic inches

Answer:60°

Step-by-step explanation: First, think about the rule of the degrees for all triangles. Angles must equal 180°.

Second, because all angles must equal 180°, see that the triangle given has equal sides (assuming this, because no other measurements are given).

Equilateral triangles have equal angles, meaning 60° for each angle.

Answer:426.6

Step-by-step explanation:

.138 x =.088(x - 69.7) + .394(69.7)

.138 x -  .088x = 69.7(.394 - .088)

.05x = 21.3282

/

x = 426.564

This rounds to x = 426.6

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

Linear Function:

y = mx + b

When X = 2, Y should equal 3

(2, 3)

When X = 4, Y should also equal 3

(4, 3)

Another way to ask this question if you are curious:

"Write a linear equation that passes through the points (2, 3) and (4 , 3)

Using the points though, we can use the slope formula equation to get the slope:

y2 - y2

----------

x2 - x1

-plug in the numbers from the points-

3 - 3

------

4 - 2

=

0 / 2

So the slope is going to be 0.

y = 0x + 3

y = 3