Drew’s goal was to earn $150 during a four-week period in the summer.

A. The first week, Drew earned a 50% of his goal amount. What was the total amount of money Drew earned the first week? Show or explain your answer.

B. The second week, Drew earned 50% of the part of his goal amount that he had left to earn after the first week. What was the total amount of money that Drew earned the second week?

C. The third week, Drew earned 50% of the part of his goal amount that he had left to earn after the second week. What was the total amount of money that Drew earned the third week?

D. The fourth week, Drew earned exactly enough money to reach his goal amount. What percent of Drew’s original goal amount did he earn in the fourth week?

The linear demand equation: x = m(p) + b, where x is the number of occupied units, p is the monthly rent, and m and b are constants and the linear demand equation in this case is:

x = -1.04p + 44.16

To find the linear equation, we need to determine the slope (m) and the y-intercept (b). Using the two points provided, we can write a system of equations:

When p = $780, x = 40 units

40 = m($780) + b

When p = $852, x = 36 units

36 = m($852) + b

Solving for m and b, we get:

m = -1.04 and b = 44.16

So, the linear demand equation is:

x = -1.04p + 44.16

This equation represents the inverse relationship between the monthly rent and the demand, where a higher rent results in a lower demand and vice versa.

For more questions like  Linear demand equation click the link below:

https://brainly.com/question/2829481

#SPJ4

The standard form from (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is B) 9[tex]x^{2}[/tex] - 15x - 12.

This is a quadratic equation. To simplify the equation, we need to arrange the equation to be standard form or quadratic equation which is

a[tex]x^{2}[/tex] + bx + c

(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7

Group of a[tex]x^{2}[/tex] --> It will be 9[tex]x^{2}[/tex]

Group of bx ---> It will be -7x-8x = -15x

Group of c ---> It will be -5-7 = -12

We just combine the group into standard equation

(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7

                                      = 9[tex]x^{2}[/tex] -15x - 12

So the simplification of equation (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is 9[tex]x^{2}[/tex] - 15x - 12, or from the answer, it's B)

Learn more about quadratic equation here

https://brainly.com/question/17177510

#SPJ4

The circumference of the circle with the diagram of 2.25 cm is 14.13 cm.

The circumference, also known as the length of a circle, is its circumference. By using the radius or diameter, we can calculate the circumference of a circle.

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed centre. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "small ring," is the source of the English word "circle."

Given that the diameter of the circle is 4.50 cm. The circumference of the circle is calculated as:-

C = 2πr

C = 2 x π x 2.25

C = 14.13 cm

Therefore, the circumference of the circle with the diagram of 2.25 cm is 14.13 cm.

To know more about circumference follow

https://brainly.com/question/20489969

#SPJ1

Mateo will be able to choose a gym membership plan that best meets his needs and budget.

To help Mateo decide on the best gym membership plan, the following information would be important:

By considering these factors, Mateo will be able to choose a gym membership plan that best meets his needs and budget.

Learn more about Mateo gym membership visit the link :

https://brainly.com/question/28848020

#SPJ4

It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

Now, According to the question:

"Information available from the question"

A physicist measures the remaining radioactivity in a sample.

She finds that it reduces by 18% each year.

If there was 1.52 g of radioactive material left after 4 years.

In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

The final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g × [tex](1-0.18)^4[/tex]

Initial Quantity = 1.52 g × 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

Learn more about Radioactive at:

https://brainly.com/question/14415679

#SPJ4

Answer:

1    - 1/3     1/9

Step-by-step explanation:

Common ratio is

 81 * r = - 27

       r= - 1/3

-3 * - 1/3  = 1

1 x - 1/3    = -1/3

-1/3  * - 1/3  = 1/9

The composite function which expresses the given correspondence correctly is f of g of x

Composite functions are when the output of one function is used as the input of another. If we have a function f and another function g, the function f g ( x ) fg(x) fg(x), said as “ f of g of x”, or “ f g fg fg of x”, is the composition of the two functions.

The composite function rule shows us a quicker way. If f(x) = h(g(x)) then f (x) = h (g(x)) × g (x). In words: differentiate the 'outside' function, and then multiply by the derivative of the 'inside' function.

Learn more about the composite functions here :

https://brainly.com/question/5614233

#SPJ4

A triangular land has area 336 q meter, perimeter 84 meter and length of an edge 26 meter. The lenght of the remaining two sides are both 29 meters long.

Let's call the length of the remaining two sides x.

Since the perimeter of the triangle is 84, then the sum of all three sides is 84, so:

x + x + 26 = 84

Therefore, the sum of the remaining two sides is:

2x = 84 - 26 = 58

And the length of each remaining side is:

x = 58 / 2 = 29 meters required lenght of the remaining two sides.

You can learn more about lenght of the sides of triangle at

https://brainly.com/question/24597672

#SPJ4

The figure below is made of 222 rectangular prisms.

Completed question :

Part D

Wendell plans to paint the doghouse after it’s built. He wants to know what the surface area of the outside of the doghouse will be. To find the surface area, first break up any composite shapes into rectangles and triangles. Which shape is considered a composite shape? When the shape is decomposed, what are the dimensions of the resulting shapes necessary for finding surface area?

Given data :

The volume of a rectangular prism is given as follows.

Volume of a rectangular prism = length x breadth x height

Therefore, the volume of 222 rectangular

prism

= 2 x 2 x 2

= 8 cubic units

Volume of 222 rectangular prisms = 222

×Volume of a rectangular prism

=222× 8

= 1776 cubic units

Learn more about Rectangular prism refer to :

https://brainly.com/question/24284033

#SPJ4

Answer:

The surface area is 5,052 inches

The value that makes the pair of ratios equivalent is x = 7.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

The given pair of ratios is:

12:42 = 2:x

12 /42 = 2/ x

Using cross multiplication we have:

12x = 2(42)

x = 7

Hence the value that makes the pair of ratios equivalent is x = 7.

Learn more about cross multiplication here:

https://brainly.com/question/15209325

#SPJ1

Lukes's age is 47

Gibson's age is 26

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Lukes's age = x

Gibson's age = y

Now,

x + y = 73 ______(1)

x = 2y - 5

Substituting in (1)

2y - 5 + y = 73

3y = 78

y = 26

Now,

x = 2 x 26 - 5

x = 52 - 5

x = 47

Thus,

Lukes's age = 47

Gibson's age = 26

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The car travel before stopping is 400 meters

The car's initial speed was 80 m/s.

Acceleration/Deferral = 8 m/s2.

The following is the equation of motion for time t and distance s:

v = u + at

s = ut + 1/2 * a * t ^2

v = final velocity = 0 where

Thus, s = 80 * 10 - 1/2 * 8 * 10 *10

= 800 - 400

= 400 meters were covered before stopping, giving us 0 = 80 - 8 * t t

= 80/8

= 10 seconds.

Know more about Acceleration

https://brainly.com/question/460763

#SPJ4

The full question:

A car moving a straight highway with a speed of 80 m/s is forced to slow down at a rate of 8 m/s^2. How far does a car travel before stopping?

x=6 m<ABD=20 *I think*

Step-by-step explanation:

Find x

plug in your answer

The formula is also used to ensure that the patient is not overdosed or underdosed ,24.1 kg of body weight, 723 mg of cephalexin should be administered per day.

The conversion from 24.1 kg of body weight to milligrams (mg) of cephalexin administered per day can be calculated using the following formula:

Dose (mg) = Desired dose (mg/kg) x Body Weight (kg).

In this case, the Desired dose is 30 mg/kg. So, to calculate the total dose of cephalexin per day:

Dose (mg) = 30 mg/kg x 24.1 kg

Dose (mg) = 723 mg/day

Thus, for 24.1 kg of body weight, 723 mg of cephalexin should be administered per day.

The formula used in this calculation is a standard formula used to calculate the dose of medication to be administered to a patient based on their body weight. The formula is used to ensure that the patient receives the appropriate dosage of medication and that the medication is safe and effective. The formula is also used to ensure that the patient is not overdosed or underdosed, which can cause side effects or other medical problems.

Learn more about standard formula here:

https://brainly.com/question/12391516

#SPJ4

Answer: A) 16.425 in^2.

Step-by-step explanation: The figure is broken down, so let's find the area of the rectangle first. We are given 4 in and 2.3 in, which can be multiplied to get 9.2 in. Now, we need to find the area of the two triangles, but let's start with the one to the left. The area of a triangle is b x h x 1/2. 2.3 in x 2.5 in is 5.75 in, but we need to multiply that by 1/2 which is 2.875 in. Finally, we can find the area of the bottom triangle by using the same formula. 3 in x 2.9 in is 8.7 in, but we need to multiply it by 1/2, which is 4.35 in. Now, all we need to do is add all the areas we found together to get the total area of the figure. 9.2 in + 2.875 in + 4.35 in is 16.425 in^2, which means that option A is your answer.

Let me know if this is right! :)

Answer:

16.425 in²

Step-by-step explanation:

total area of the figure= area of (left triangle+ rectangle+ down triangle)

=1/2*base*height+length*breath+ 1/2*base*height

=1/2*2.5*2.3+4*2.3+1/2*3*(5.2-2.3)

=16.425 in²

The coordinates of point T' is (2, -2)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.

So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)

So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

y = -4 + 1.4

Step-by-step explanation:

y+3/5 = -4(x-1/2)

y + 3/5 = -4x + 2

y + 0.6 = -4x + 2

y = -4 + 1.4

the helix r(t) = cos(πt/2), sin (πt/2),t) intersects the sphere x^2 + y^2 + z^2 = 2 in two points.

the angle of intersection at each point: θ = cos⁻¹ (√2/√π²+4)

the angle of intersection at each point: α = cos⁻¹(-√2 /(√π² +4))

Scientists in the fields of physics, engineering, and biology all do research on helices, which are a significant topic in the theory of curves in differential geometry. Helix (or generic helix) is defined as tangent vector field in 3-dimensional Euclidean space establishing a fixed angle with the curve's direction. A curve for which the tangent forms a constant angle with a fixed line is referred to as a helix or coil.

helix: r(t) = < cos(πt/2), sin(πt/2), t >    sphere: x² + y² + z² = 2

put it in the sphere's equation we get:

next, {cos(πt/2)}² + {sin(πt/2)}² + t² = 2

or, 1 + t² = 2

or, t² = 1

or, t = ± 1

thus, points of intersection r(1) = < cos(π/2), sin(π/2), 1 > = < 0, 1, 1 >

r(-1) = < cos(-π/2), sin(-π/2), -1 > = < 0, -1, -1 >

angle intersection is angle between their tangent:

helix:

r(t) = < -π/2 sin(πt/2), π/2 cos(πt/2), 1 >

r'(1) = < -π/2, 0, 1 > .........(i)

r'(-1) = < π/2, 0, 1 > ......... (ii)

sphere:

f = (x² + y² + z² - 2) = 0

Δf = <2x, 2y, 2z>

Δf (0,1,1) = <0,2,2> ................ (iii)

Δf (0,-1,-1) = <0,-2,-2> .............(iv)

angle between (i) and (iii) (at, t = 1)

cosθ = {r'(1) Δf (0,1,1)} / {|r'(1)| |Δf (0,1,1)|]

θ = cos⁻¹ (√2/√π²+4)

angle between (ii) and (iv) (at, t = 1)

cosα = r'(-1)Δf (0,-1,-1) / ||r'(-1)|| ||Δf (0,-1,-1) ||

cos α = -√2 /(√π² +4)

α = cos⁻¹(-√2 /(√π² +4))

To know more about sphere refer to:

https://brainly.com/question/10171109

#SPJ4

Work Shown:

x = initial cost before any discounts

x-100 = cost after taking off $100

0.7(x-100) = cost after taking 30% off from the previous value

Therefore, we end up with h(x) = 0.7(x-100)

Optionally you could distribute to get h(x) = 0.7x-70, but I think the first version of this is a bit more descriptive.

The logarithm and exponential functions are inverse of each other. The exponential function raises a number to a power and the logarithm gives the power that the number has to be raised to in order to equal a given value. In other words, the exponential function expresses exponential growth, while the logarithm expresses exponential decay.

For example, if y = 2^x, then x = log2(y). This logarithmic relationship is useful in solving exponential problems and understanding exponential dynamics.

In exponential dynamics, logarithms are used to study and model changes that occur at exponential rates, such as population growth or decay, interest rate calculations, and many other real-world applications. The logarithmic relationship helps to simplify the exponential equations and make them easier to work with.

In summary, the logarithm and exponential functions are important in understanding exponential dynamics because the logarithmic relationship helps to simplify exponential problems and make them easier to solve.

To know more about exponential functions  click on the link below:

https://brainly.com/question/11154952#

#SPJ11

Answer:

False - The standard deviation is always positive.

Answer:

0.2643

Step-by-step explanation:

Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives Summary: When a fair die is tossed 200 times, the probability of obtaining at most 30 fives is 0.2643.

The probability of selecting a yellow and then a yellow without replacement is 3/10.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 1

Number of green marbles = 1

Number of yellow marbles = 3

Total number of marbles = 5

The probability of selecting a yellow and then a yellow without replacement.

= 3/5 x 2/4

= 6/20

= 3/10

We are using 2/4 since yellow marbles become 2 and the total marbles become 4 when the condition of without replacement is given.

Thus,

The required probability is 3/10.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

A linear function would better approximate the data.

A linear function would better approximate the data described. This is because a linear function has a constant rate of change, while an exponential function has a changing rate of change. For example, if we take the data from 10 K to 15 K, we can calculate the rate of change for each 1 K increase in temperature. The rate of change of volume for a 1 K increase in temperature is calculated by taking the difference between the volumes at the two temperatures and dividing by the difference in the temperatures. With the given data, this would yield a rate of change of 0.7 cm3/K, 0.38 cm3/K, 0.92 cm3/K, 1.4 cm3/K, and 1.6 cm3/K. As we can see, the rate of change does not remain constant, but increases over the temperature range, indicating a nonlinear relationship. Therefore, a linear function would better approximate the data.

Learn more about linear function here:

https://brainly.com/question/29205018

#SPJ4

The statement "The results of the experiment do not agree with the theory, there's something wrong with the experiment" is wrong as it does not indulge any other reasons for the results of the experiment not agreeing with the theory.

This statement assumes that the experiment is always at fault and neglects the possibility that the theory may be incorrect or incomplete.

The outcome of an experiment can be influenced by various factors, such as measurement errors, incorrect experimental design, or limitations of the equipment used.

Thus, it is always important to consider multiple explanations before concluding that there is a problem with the experiment.

To know more on statement

https://brainly.com/question/30257297

#SPJ4

Answer:

9c

Step-by-step explanation:

16+25=41

50-41=9

fnfnx

The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

The Maclaurin series for arctan(x) is an alternating series, meaning that the signs of the terms alternate between positive and negative. The terms of the series also get smaller in magnitude as n increases, so the series converges rapidly for small values of x.

The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

This Maclaurin series representation of arctan(x8) is useful for approximating the value of the function for small values of x. To obtain more accurate results for larger values of x, one can use more terms from the series or use other numerical methods to calculate arctan(x8).

Therefore, The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

To learn more about the Maclaurin series,

Visit; brainly.com/question/24188694

#SPJ4

Answer: In statistics, the term linear model is used in different ways according to the context.

Step-by-step explanation: The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning.

Answer: $2171.79

Step-by-step explanation: