In how many different ways can we distribute 5 different books among 10 children if any child can get any number of books?

Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.

Answer:

5.66

Step-by-step explanation:

→ State Pythagoras' theorem

a² + b² = c²

→ Substitute in the values

4² + 4² = c²

→ Simplify

32 = c²

→ Square root both sides

√32 = c

Answer:

Step-by-step explanation:

4^2 + 4^2 = c^2

16 + 16 = c^2

32 = c^2

c= √32

c= 5.66

Answer:

Gina reads 30 pages per day.

Step-by-step explanation:

120 / 4 = 30

I hate to ask, but please give me Brainliest. I need it to level up <3.

Answer:

Gina reads 30 pages per day.

Step-by-step explanation:

Answer:

74.3

Step-by-step explanation:

we can use the tangent ratio to solve for X

first, set up the equation

tan(22 deg)= 30/x

next, solve for x

multiply both sides by x

(x)(tan(22 deg))=30

then, divide both sides by tan (22 deg)

x=30/tan (22 deg)

plug this into a calculator

this gives us approximately 74.25

The true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

The expression is given as:

\(x^{2} -7x + 6\)

Expand;

\(x^{2} -6x - x +6\)

Factorize;

x(x-1) - 6 (x- 1)

Factor out x - 6

(x - 6) (x- 1)

This means that the factors of \(x^{2} -7x + 6\) are x - 1 and x - 6

Hence, the true statement is (c) that He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x^2, –x, –6x, and 6.

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Answer: Answer is C

Step-by-step explanation:

Answer:

x=0.5

Step-by-step explanation:

Simplifying

4x + -3(2x + -1) + -4x = 0

Reorder the terms:

4x + -3(-1 + 2x) + -4x = 0

4x + (-1 * -3 + 2x * -3) + -4x = 0

4x + (3 + -6x) + -4x = 0

Reorder the terms:

3 + 4x + -6x + -4x = 0

Combine like terms: 4x + -6x = -2x

3 + -2x + -4x = 0

Combine like terms: -2x + -4x = -6x

3 + -6x = 0

Solving

3 + -6x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + -6x = 0 + -3

Combine like terms: 3 + -3 = 0

0 + -6x = 0 + -3

-6x = 0 + -3

Combine like terms: 0 + -3 = -3

-6x = -3

Divide each side by '-6'.

x = 0.5

Simplifying

x = 0.5

Answer:

-29

Step-by-step explanation:

1+3-1-32

4-1-32

3-32

-29

anything raised to the power of 0 is on

please mark brainiest thank you

The formula

x + y = 32

Find our X value

y + 14 = x

Sub for x

(y + 14) + y = 32

Remove Parathesis

y + 14 + y = 32

Add

2y + 14 = 32

Subtract

2y = 18

Divide

y = 9

Sub for y

x + 9 = 32

Subtract

x = 23

Double Check:

9 + 14 = 23

23 + 9 = 32

I hope this helps! :)

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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we calculated confidence interval = 0.48±0.16

confidence interval represents the accuracy of a particular estimation.

proportion of population is the ratio of random sample to the total available sample.

Given, size of samples that means number of total iPhones, n = 25

size of random samples that means iPhone with 85 downloaded apps, p= 12,

critical value for 90% confidence interval z* = 1.65

proportion of samples, p^ = p/n = 12/25 =0.48

finally, confidence interval = p^±z*[√{p^(1-P^)/n}]

                                               0.48±1.65[√{0.48(1-0.48)/25}]

                       hence, the confidence interval = 0.48±0.16

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Answer:

2 2/9

Step-by-step explanation:

6 1/3 - 4 1/9

1/3: 1x3 3x3= 3/9

1/9: 1x1 9x1= 1/9

3/9 - 1/9 = 2/9

6-4=2

Answer: 2 2/9

Answer:

$173.59

Step-by-step explanation:

54.11+51.96+67.52=173.59

Answer:

$170!

Step-by-step explanation:

Add: $54.11 + 51.96= 106.07

Then: 106.07 +  67.52 = $173

Round it!= 173 rounded to the nearest tenth!

Answer: $170

Hope this helps!! -3-ll

Answer:

The solutions for the equations are x = 0.1644 and x = -12.1644

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(x^{2} + 12x - 2 = 0\)

So

\(a = 1, b = 12, c = -2\)

\(\bigtriangleup = 12^{2} - 4*1*(-2) = 152\)

\(x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644\)

\(x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644\)

The solutions for the equations are x = 0.1644 and x = -12.1644

Answer:

59,582π/375 (approximately 499.153) square centimeters

Step-by-step explanation:

Volume:

\( \frac{1}{3} \pi {(6.2)}^{2} (12.4)\)

\( \frac{1}{3} {( \frac{31}{5}) }^{2} ( \frac{62}{5} )\pi\)

\( \frac{59582\pi}{375} \)

using quotient formula

The total work done on the gas during the entire process is -3nRT ln(3). And the net energy transfer can be sorted in three stages, which can be summarized below:

Stage 1: Net energy transfer to the environment (work done by gas, no heat transfer)

Stage 2: Net energy transfer to the gas (work done on gas, no heat transfer)

Stage 3: Net energy transfer to the environment (heat removed from gas, no work transfer)

The entire process can be classified into three stages,

Isothermal expansion: The gas expands isothermally from volume V to 3V and pressure p to 3p. Since the pressure is directly proportional to the volume, the process can be described by the equation PV = constant. Thus, the final pressure and volume can be related to the initial pressure and volume as follows:

P(3V) = 3pV = 3PV = 3nRT (where n is the number of moles of gas and R is the gas constant)

Therefore, the work done during this stage can be calculated using the formula:

W = - ∫PdV = - ∫(nRT/V)dV = - nRT ln(3)

The net energy transfer in this stage is to the environment, as the gas is doing work on the piston, but there is no heat transfer since the process is isothermal.

Isobaric compression: The gas is compressed isobarically from volume 3V to V. Since the pressure is constant, the work done during this stage can be calculated as:

W = -PΔV = -2nRT ln(3)

The net energy transfer in this stage is to the gas, as work is done on the gas, but there is no heat transfer since the process is isobaric.

Isochoric cooling: The gas is cooled isochorically from volume V to its initial volume V and pressure p. Since the volume is constant, the work done during this stage is zero. The change in internal energy can be calculated using the equation:

ΔU = Q = -nCvΔT

Here, Cv is the molar specific heat at constant volume. Since the process is isochoric, Cv can be considered constant. The temperature change can be calculated using the ideal gas law:

P1V1/T1 = P2V2/T2

Therefore calculating T2 = T1(P2V2)/(P1V1) = 3T1

Thus, the change in internal energy can be calculated as:

ΔU = -nCvΔT = -nCv(2T1)

The net energy transfer in this stage is to the environment, as heat is removed from the gas to cool it down, but there is no work transfer since the process is isochoric.

Therefore, the total work done on the gas during the entire process is:

W_total = W1 + W2 + W3 = -nRT ln(3) - 2nRT ln(3) + 0 = -3nRT ln(3)

And the net energy transfer in each stage can be summarized as:

Stage 1: Net energy transfer to the environment (work done by gas, no heat transfer)

Stage 2: Net energy transfer to the gas (work done on gas, no heat transfer)

Stage 3: Net energy transfer to the environment (heat removed from gas, no work transfer)

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Answer:

x=−83

    25

Step-by-step explanation:

Let's solve your equation step-by-step.

−25(x+3)=8

Step 1: Simplify both sides of the equation.

−25(x+3)=8

(−25)(x)+(−25)(3)=8(Distribute)

−25x+−75=8

−25x−75=8

Step 2: Add 75 to both sides.

−25x−75+75=8+75

−25x=83

Step 3: Divide both sides by -25.

−25x

−25

=

83

−25

x=

−83

25

Answer:

x=

−83

25

Answer:

or it can be 3.32 if you need to put it in decimal form

Answer:

Here,

-18.3=b+ -8.3

-18.3+8.3=b

-10=b

the value of b is -10.

Answer:

g(x) = 3x - 14 → A

Step-by-step explanation:    

y - 3x = - 14  

y = 3x - 14 so,  y = g(x)  

Answer:

Apply the 15% discount first, and the final purchase price is $332.50.

Step-by-step explanation:

The 15% discount of the two coupons should be applied first so that the final price is cheaper.

The final purchase price at the department store is $332.5.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Cost = $450

Two coupons.

Offer = 15% discount

off = $50

Now,

15% discount first and then $50 off.

(450 - 15/100 x 450) - 50

= (450 - 67.5) - 50

= $332.5

Now,

$50 off first and then the 15% discount.

(450 - 50) = 400

400 - 15/100 x 400

= 400 - 60

= $340

We see that,

When the 15% discount is applied first the final price is cheaper.

Thus,

15% discount should be applied first.

The final purchase price is $332.5.

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Answer:

Question (a)

Midpoint of a line segment:

\(M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Given:

\(\implies \textsf{midpoint of }JL=\left(\dfrac{-2+4}{2},\dfrac{2+0}{2}\right)=(1,1)\)

Given:

\(\implies \textsf{midpoint of }MK=\left(\dfrac{3-1}{2},\dfrac{7-5}{2}\right)=(1, 1)\)

Question (b)

Find slopes (gradients) of JL and MK then compare.  If the product of the slopes of JL and MK equal -1, then JL and MK are perpendicular.

\(\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}\)

Given:

\(\implies \textsf{slope of }JL=\dfrac{0-2}{4+2}=-\dfrac13\)

Given:

\(\implies \textsf{slope of }MK=\dfrac{-5-7}{-1-3}=3\)

\(\textsf{slope of }JL \times \textsf{slope of }MK=-\dfrac13 \times3=-1\)

Hence segments JL and MK are perpendicular

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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Step-by-step explanation:

10. not a function (repeating x values)

11 Function

12 not a function (repeating x values)

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

A graph of the cube root function g(x) = 1/2x³ is shown in the image below.

In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.

When the parent cube root function f(x) = x³ is vertically shrunk by a scale factor of 1/2, the transformed function g(x) is given by;

g(x) = kf(x)

g(x) = 1/2f(x)

g(x) = 1/2x³.

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Answer:

B, C, D

I Just Did It On Khan Academy

Step-by-step explanation:

Answer:

density: 0.25 g/cm³

Explanation:

density = mass/volume

Here given:

· mass: 16 grams

· volume: side³ = 4³ = 64 cm³

Find density:

· mass/volume

· 16/64

· 0.25 g/cm³

Answer:

The correct answer will be 18

Step-by-step explanation:

First mutiply your object of the question which is 9 times 16 then make sure you have the right answer then divide it by 8 and 144 the answer you got, and you get 18