If the first 4 terms of an infinite geometric sequence are 150, 120, 96, and 76.8, then the sum of all the terms in the sequence is ______.

Answer: 8 years ago

Step-by-step explanation:

w = woman's age

d = daughter's age

Hypothetically, find the woman's age eighteen years ago when the daughter is 1 year old.

(18 years ago):

w = 20 + 3d

w = 20 +3(1)

w = 23

The woman is 23 years old.

Now, find the age of the daughter 18 years ago when the woman is three times her age:

w + x = 3(d + x)

**x is the number of years that pass, so it needs to be added to the raw age of the woman and her daughter. That's why it's inside the parenthesis.**

w + x (- x) = 3d + 3x (- x)

w = 3d + 2x

(23) = 3(1) + 2x

**Now, we plug in the initial raw ages to find the number of years that have passed.**

20 = 2x

x = 10

18 - (10) = 8 years ago

Since our math took place 18 years ago, we fast-forward 10 years, making the woman 3 times older than her daughter 8 years ago.

Answer:

x = 80

Step-by-step explanation:

using the rules of logarithms

log x - log y = log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

log5x - log4 = 2

log ([tex]\frac{5x}{4}[/tex] ) = 2

note that log is actually [tex]log_{10}[/tex]

then

[tex]log_{10}[/tex] ( [tex]\frac{5x}{4}[/tex] ) = 2

[tex]\frac{5x}{4}[/tex] = 10² = 100 ( multiply both sides by 4 to clear the fraction )

5x = 400 ( divide both sides by 5 )

x = 80

An equation that expresses the total cost in terms of the number of hours required to complete the job is [tex]C = 32h + 31.50[/tex]

We will use "h" to represent the number of hours required to complete the job.

As cost per hour is K32, so, if it takes "h" hours to complete the job, then the cost will b:

=  K32 *  h.

We have one-time charge of K31.50, which is added to the total cost. So, the equation that expresses the total cost "C" in terms of the number of hours required to complete the job "h" is C = 32h + 31.50

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The equations when solved would have the solutions of:

To solve the equation tan(x - π/2) = -1 on the interval (-∞, ∞), we can start by finding the general solution for x:

x - π/2 = -π/4 + kπ, where k is an integer.

Now, we can solve for x:

x = π/2 - π/4 + kπ

x = π/4 + kπ

To solve the equation 2cos(x/3) + 1 = 0 on the interval [0, 2π), we can follow these steps:

2cos(x/3) + 1 = 0

cos(x/3) = -1/2

x/3 = 2π/3, 4π/3

x = 2π, 4π

However, since the interval is closed on the lower bound and open on the upper bound, we should only include x = 2π as our solution.

To solve the equation 2cos²(x) - 3cos(x) + 1 = 0 on the interval [0, 2π), we can factor the quadratic equation:

(2cos(x) - 1)(cos(x) - 1) = 0

Now, we have two cases to consider:

Case 1: 2cos(x) - 1 = 0

cos(x) = 1/2

x = π/3, 5π/3

Case 2: cos(x) - 1 = 0

cos(x) = 1

x = 0

So, the solutions on the interval [0, 2π) are x = 0, π/3, and 5π/3.

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We can see here that the probability that a randomly selected customer did not purchase a Toes Knows shoe or is not displeased is: 0.939

Mathematics' study of random events and their likelihood of happening is known as probability.

We can calculate the probability thus:

We will use: P(not Toes Knows or not displeased) = 1 - P(Toes Knows and displeased)

Calculating P(Toes Knows and displeased), we have:

P(Toes Knows and displeased) = P(Toes Knows) × P(displeased | Toes Knows).

We can find  P(Toes Knows)  which will give us:

P(Toes Knows) =  (8+3)/(12+13+10+3+8+3) = 11/49

P(displeased | Toes Knows) = 3/11

Thus, P(Toes Knows and displeased) = (11/49) × (3/11) = 3/49

So, we can now find  the probability that a randomly selected customer did not purchase a Toes Knows shoe or is not displeased which is:

P(not Toes Knows or not displeased) =

1 - P(Toes Knows and displeased) =

1 - 3/49 = 46/49 ≈ 0.939

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the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

To divide 300 million by 9.2 quintillion, you can use the following calculation:

[tex]300[/tex] million ÷  [tex]9.2[/tex] quintillion

First, let's convert 300 million to scientific notation:

[tex]300 million = 300,000,000 = 3 \times 10^8[/tex]

Next, let's convert 9.2 quintillion to scientific notation:

[tex]9.2 quintillion = 9.2 \times 10^18[/tex]

Now, we can perform the division:

[tex](3 x 10^8) ÷ (9.2 x 10^18)[/tex]

When dividing numbers in scientific notation, we subtract the exponents:

[tex]3 ÷ 9.2 = 0.32608695652173913[/tex]

And we subtract the exponent of 10:

[tex]10^(8-18) = 10^(-10)[/tex]

Therefore, Putting it all together, the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

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The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3).

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

To find the coordinates of polygon A'B'C'D' after a 180° rotation, we need to reflect each vertex across the x-axis and then the y-axis.

To reflect a point across the x-axis, we change the sign of the y-coordinate.

To reflect a point across the y-axis, we change the sign of the x-coordinate.

Using this method, we can find the coordinates of A'B'C'D':

A(0, 0) reflects to A'(0, 0) (no change)

B(5, 2) reflects to B'(-5, 2) (reflect across y-axis)

C(5, -5) reflects to C'(-5, -5) (reflect across y-axis)

D(0, -3) reflects to D'(0, 3) (reflect across x-axis)

Therefore, the coordinates of polygon A'B'C'D' are:

A'(0, 0), B'(-5, 2), C'(-5, -5), D'(0, 3)

Hence,  the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180° are A′(0, 0), B′(−5, 2), C′(−5, −5), D′(0, 3) and the graph is attached is in the attached image.

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The linear regression equation for the given data set is: y = -2.33x + 86.36 and The correlation coefficient is r = -0.75.

What is linear regression ?

To find the linear regression equation for this data set, we need to use the formula:

y = a + bx

where y is the dependent variable (final exam score), x is the independent variable (number of classes missed), b is the slope of the regression line, and a is the y-intercept.

First, we need to calculate the means of x and y:

mean(x) = (2+10+3+22+15+2+20+18+9)/9 = 10.11

mean(y) = (99+72+90+35+60+80+40+43+75)/9 = 67.22

Next, we need to calculate the values of b and a:

b = Σ[(xi - mean(x))(yi - mean(y))] / Σ(xi - mean(x))^2

a = mean(y) - b * mean(x)

Using these formulas, we get:

b = (-31.44) / 496.78 = -0.0633

a = 67.22 - (-0.0633) * 10.11 = 67.85

Therefore, the linear regression equation is:

y = -0.0633x + 67.85

To round to the nearest hundredth, we get:

y = -0.06x + 67.85

However, this is not the final answer as we need to round the values of the slope and intercept to two decimal places. To do so, we need to use the actual values of b and a before rounding to substitute into the equation:

y = -0.0633x + 67.85

y = -0.06x + 86.36 (rounded to the nearest hundredth)

Therefore, the linear regression equation for the given data set is:

y = -2.33x + 86.36

What is correlation coefficient:

Finally, we need to calculate the correlation coefficient (r) to determine the strength and direction of the linear relationship between x and y. We can use the formula:

r = Σ[(xi - mean(x))(yi - mean(y))] / √[Σ(xi - mean(x))² * Σ(yi - mean(y))²]

Using this formula, we get:

r = (-31.44) / √[496.78 * 3121.60] = -0.75

Therefore, the correlation coefficient for the linear regression is r = -0.75, indicating a strong negative linear relationship between the number of classes missed and final exam score.

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The equations which represents circles that have a diameter of 12 units and a center that lies on the y-axis are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

Recall, the equation of a circle takes the form;

(x - h)² + (y – k)² = r² where r = radius = diameter/2 and (h, k) is the center.

Therefore, if diameter is; 12, the radius of the circle is; 6 so that; r² = 36 and if the center lies on the y-axis, the value of h must be 0.

Ultimately, the equations that satisfy the given conditions are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

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The total number of possible outcomes is n = 16

Given data ,

Let the total number of digits be represented as A

Now , the value of A = { 8 , 4 , 3 , 2 }

So , the total number of possible two digits numbers are

n = 2⁴

n = 16 outcomes

Let the outcomes be represented as B

B = { 82 , 83 , 84 , 88 , 42 , 43 , 44 , 48 , 22 , 23 , 24 , 28 , 32 , 33 , 34 , 38 }

Hence , the number of outcomes is n = 16

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Answer:

12 × 4 × 18 = 864

( Use the volume formal L × W × H to help in all volume equations )

Answer:

9/7, 6/5

Step-by-step explanation:

An improper fraction is a fraction whose numerator is greater than the denominator.

Answer: 9/7, 6/5

The measurement of KL is given as follows:

KL = 5.86.

Similar triangles are triangles that share these two features listed as follows:

Considering the similar triangles in this problem, the proportional relationship for the side lengths is given as follows:

8.7/KL = 7.8/LJ = 12.18/8.2

Hence the length KL is obtained as follows:

8.7/KL = 12.18/8.2

12.18KL = 8.2 x 8.7

KL = 8.2 x 8.7/12.18

KL = 5.86.

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Answer:

Step-by-step explanation:

since there is one square and 4 circles, the answer is 1/4

The rate of change of the quantity is 90%.

What is the rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.  The pace at which one quantity changes in relation to another quantity is known as the rate of change function.

Here, we have

Given: The function f(t) = [tex]300(1.9)^{t}[/tex] represents the change in a quantity over t months.

Since the base of the exponent 1.9 is greater than 1.

The nature of f(t) is increasing.

Now,

f(t+1) = [tex]300(1.9)^{t+1}[/tex]

f(t+1)/f(t) =  [tex]((1.9)^{t+1})/((1.9)^{t}[/tex] = 1.9

Hence, an increase in f(t)

(f(t+1) -f(t))/f(t) = f(t+1)/f(t) - 1

= 1.9 - 1

= 0.9

% increase = 0.9 × 100 = 90%

Hence, the rate of change in the quantity is 90%.

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4. The Federal Reserve System does d. all of these central bank functions.

5. The portion of its revenue that the United States spends on defense is a) about 10 percent.

The federal reserve is a federal government agency charged with the responsibility of managing the government's monetary policies, including playing the role of the banker's bank.

In other countries, the federal reserve is described as the central bank.

Defense spending refers to the amount of money spent by a government to provide its military with weapons, equipment, and soldiers.

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Answer:

To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.

Setting x^2 - 10x + 31 equal to x + 1:

x^2 - 10x + 31 = x + 1

Rearranging the equation to standard quadratic form:

x^2 - 10x + 30 = 0

Now, we can factorize the quadratic expression:

(x - 5)(x - 6) = 0

Setting each factor equal to zero and solving for x:

x - 5 = 0 or x - 6 = 0

x = 5 or x = 6

So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.

Answer:

To find the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other, we can set them equal to each other and solve for x.

Setting x^2 - 10x + 31 equal to x + 1:

x^2 - 10x + 31 = x + 1

Rearranging the equation to standard quadratic form:

x^2 - 10x + 30 = 0

Now, we can factorize the quadratic expression:

(x - 5)(x - 6) = 0

Setting each factor equal to zero and solving for x:

x - 5 = 0 or x - 6 = 0

x = 5 or x = 6

So, the values of x for which the expressions x^2 - 10x + 31 and x + 1 are equal to each other are x = 5 and x = 6.

Answer:

x = 5 or x = 6

Step-by-step explanation:

Given expressions:

[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]

To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:

[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]

Using the zero-product property, set each factor equal to zero and solve for x:

[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]

Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.

Answer:

x = 5 or x = 6

Step-by-step explanation:

Given expressions:

[tex]\begin{cases}x^2-10x+31\\x+1\end{cases}[/tex]

To find the values of x for which the given expressions are equal to each other, first set the expressions equal to each other and rearrange so that we have a quadratic equal to zero:

[tex]\begin{aligned}x^2-10x+31&=x+1\\x^2-10x+31-x&=x+1-x\\x^2-11x+31&=1\\x^2-11x+31-1&=1-1\\x^2-11x+30&=0\end{aligned}[/tex]

Factor the quadratic:

[tex]\begin{aligned}x^2-11x+30&=0\\x^2-6x-5x+30&=0\\x(x-6)-5(x-6)&=0\\(x-5)(x-6)&=0\end{aligned}[/tex]

Using the zero-product property, set each factor equal to zero and solve for x:

[tex]\begin{aligned}x-5=0 \implies x&=5\\x-6=0 \implies x&=6\\\end{aligned}[/tex]

Therefore, the values of x that make the given expressions equal to each other are x = 5 or x = 6.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:  the volume of the box is 31.25 cubic feet.

Step-by-step explanation: The volume of the box can be found by multiplying the area of the square base by its height:

Volume = Base Area x Height

Since the base of the box is a square with 2.5 feet wide on a side, its area can be calculated as:

Base Area = Side Length x Side Length = 2.5 ft x 2.5 ft = 6.25 sq. ft

And since the height of the box is 5 feet, the volume can be calculated as:

Volume = Base Area x Height = 6.25 sq. ft x 5 ft = 31.25 cubic feet

Therefore, the volume of the box is 31.25 cubic feet.

A) cos 35⁰ = y/5

=> y = cos 35⁰ × 5 ≈ 0.82 × 5 ≈ 4,1

B) cos 45⁰ = y/6

=> y = cos 45⁰ × 6 = (√2)/2 × 6 = 3√2

Answer: a) 4,1 b) 3√2

Ok done. Thank to me >:333

Answer:

20 days

Step-by-step explanation:

We can model this situation using the linear equation, whose general form is

f(x) = mx + b, where m is the slope and b is the y-intercept

f(x) = -5/8x + 25/2, where f(x) is the amount remaining in the vitamin bottle and x is the number of days

Explaining the formula:

We essentially want to find the x value that will make f(x) = 0 since that is when the bottle will be empty:

0 = -5/8x + 25/2

-25/2 = -5/8x

20 = x

We can check by plugging in 20 for x and see whether we get 0:

0 = -5/8(20) + 25/2

0 = -25/2 + 25/2

0 = 0

1) A and D are linear equations while B and C are non linear

2) The rule of the equation is given by option C

3) The solution is option C

4) The area is option B

5) The standard form expressions are shown by option C

We know that;

y = x + 3

-2x + y = 1

Then

x - y = -3 ---- (1)

-2x + y = 1 ---- (2)

x = -3 + y --- (3)

Substitute (3) into (2)

-2(-3 + y) + y = 1

6 - 2y + y = 1

6 -y = 1

-y = 1 -6

y = 5

Substitute y = 5 into (1)

x - 5 = -3

x = -3 + 5

x = 2

Thus the solution is (2, 5)

a^2 = 10^2 - 8^2

a = √100 - 64

a = 6

A = 1/2bh

A = 0.5 * 8 * 6

A = 24cm^2

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Answer: 6.02

Step-by-step explanation:

use SOH CAH TOA, or in this case SOH

the Sine equals Opposite over Hypotenuse, which in this case is sin37=x/10.

Plug into a calculator and you get 6.02 after rounding.

Hope this helps :)

(and thanks for answering one of my questions)

The value of x is 6.01815 cm.

Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.

We have,

Angle = 37

Hypotenuse = 10 cm

Using Trigonometry

sin 37 = P/ H

0.601815 = x/ 10

x= 6.01815 cm

Thus, the value of x is 6.01815 cm.

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Applying the tangent ratio, the value of x, to the nearest degree is determined as: 41.8 degree.

The formula we would use to find the value of x is the tangent ratio, which is expressed as:

tan ∅ = length of opposite side / length of adjacent side.

reference angle (∅) = x

Length of opposite side = 17

Length of adjacent side = 19

Plug in the values:

tan x = 17/19

x = tan^(-1)(17/19)

x ≈ 41.8 degree (to nearest tenth of a degree)

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The square inches of pizza each boy eats to the nearest whole square inch is 67 square inches.

The correct answer choice is option D.

A pizza has the shape of a circle

Area of a circle = πr²

Radius, r = diameter / 2

= 16/2

= 8 inches

Area of a circle = πr²

= 3.14 × 8²

= 3.14 × 64

= 200.96 square inches

The pizza was cut into 12 equal slices

Area of each slice = 200.96 square inches / 12

= 16.75 square inches

Area of pizza each boy eats = 16.75 square inches × 4

= 66.99 square inches

Ultimately, the square inches of pizza each boy eats is approximately, 67 square inches.

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Answer:

To find the probability of the next drink being an espresso, we need to know the total number of drinks sold.

In this case, the total number of drinks sold is:

3 cappuccinos + 7 espresso drinks = 10 drinks

The probability of the next drink being an espresso can be calculated by dividing the number of espresso drinks sold by the total number of drinks sold:

Probability of next drink being an espresso = Number of espresso drinks sold / Total number of drinks sold

Probability of next drink being an espresso = 7/10

Probability of next drink being an espresso = 0.7 or 70%

Therefore, the probability of the next drink being an espresso is 0.7 or 70%.

1. Find the radius. The pizza has a diameter of 16, which means it has a radius of 8.
2. Put (8) into the area of a circle formula. A = πR2 or A = π(8)2
3. Find area. 201.06 square inches.
4. Divide by 12. 201.06 ÷ 12 = 16.755.
5. Multiply by 4 (since they each ate 4 slices). 16.755 × 4 = 67.020

Therefore, each boy ate 67 square inches of pizza.