Here is a number machine.
input
x 4
a) Work out the output when the input is 6
b) Work out the input when the output is 31
- 5
output

An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = -5/7(x - (-35))

y - 10 = -5/7(x + 35)

y - 10 = -5x/7 - 25

y = -5x/7 - 15

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The area of the composite figure is 41 ft square.

The figure is a composite figure. A composite figure is a figure that has two or more shapes.

Therefore, the area of the composite figure is the sum of the individual area of the shapes.

Therefore,

area of the figure = area of rectangle 1 + area of rectangle 2

area of rectangle 1 = lw

where

Therefore,

area of rectangle 1 = 2 × 4 = 8 ft²

area of rectangle 2 = 11 × 3 = 33 ft²

Hence,

area of the figure =  = 8 + 33

area of the figure = 41 ft²

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Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

What is continuously compounded interest?

Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.

The formula for continuous compounding is given by:

[tex]A = Pe^{rt}[/tex]

where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.

We want to find P when A = $15,000, r = 0.04, and t = 5 years.

Substituting these values into the formula, we get:

[tex]15000 =Pe^{0.04*5}[/tex]

Simplifying the right-hand side, we get:

[tex]15000 =Pe^{0.2}[/tex]

Dividing both sides by e^(0.2), we get:

[tex]P= \frac{15000}{e^{0.2}}[/tex]

Using a calculator, we get:

P ≈ $10,994

Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

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Answer: A tangent to the x-axis means that the y-coordinate of the point of tangency is 0. So, we can find the possible values of d by setting y = 0 and solving for x:

0 = x^3/3 + 7x^2/2 + 10x + d

This is a cubic equation, so it can be solved using various methods such as factoring, completing the square, or using a numerical method such as the Newton-Raphson method. If the equation can be factored or the method used is numerical, there might be multiple possible values of d. If the method used is completing the square, there would be only one possible value of d.

However, without a specific method, it's not possible to find the exact value(s) of d. The possible values of d will depend on the specific solution method used to solve the equation.

Step-by-step explanation:

Answer:

a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.

b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weights:

Weight Lower Bound = Mean + (z-score * Standard Deviation)

Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g

Weight Upper Bound = Mean + (z-score * Standard Deviation)

Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.

c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.

d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (-0.9332 * 20) = 346.64 g

So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.

Step-by-step explanation:

Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet

The surface area of cylinder is given by the formula =2πrh+2πr²

The radius is Diameter/2

2.6/2=1.3

The radius is 1.3

Surface area =2π(1.3)(4.4)+2π(1.3)²

So =2.6π(4.4)+2π(1.3)²

Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

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Answer:

Step-by-step explanation:

Weighed averages show that the student has a grade point average of 2.33.

The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.

A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.

B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.

C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.

D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.

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STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is  1,000,016.

To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.

0 hours:

Population = 10^6 + (10^4)0 -(10^3)0^2

Population = 10^6 - 10^3

Population = 10^3 or 1,000

4 hours:

Population = 10^6 + (10^4)4 -(10^3)4^2

Population= 10^6 + 40,000 - 16,000

Population= 1,000,024

8 hours:

Population = 10^6 + (10^4)8 -(10^3)8^2

Population= 10^6 + 80,000 - 64,000

Population= 1,000,016

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a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

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7/8 of sixteen times a half of 30 is 210.

What is a PEMDAS rule?

PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Start with the expression inside the parentheses: half of 30 is 15.

Multiply 16 by 15: 16 times 15 is 240.

Find 7/8 of 240:

7/8 of 240 = (7/8) x 240

                  = 210

Hence, 7/8 of sixteen times a half of 30 is 210.

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The IQR is the best measure of variability, and it equals 45.

Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.

The range is the best measure of variability for the data shown, and its value is 45.

The range is defined as the difference between the largest and smallest values in a set of data.

In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.

The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.

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Answer:

Step-by-step explanation:

Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".

Now we can set up the equation for the problem:

4 * (x + (x + 2) + (x + 4)) = 240 + 6x

Expanding the parentheses on the left side:

4 * (3x + 6) = 240 + 6x

Simplifying the left side:

12x + 24 = 240 + 6x

Subtracting 6x from both sides:

6x + 24 = 240

Subtracting 24 from both sides:

6x = 216

Dividing both sides by 6:

x = 36

So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.

Answer:

x = 9.75

Step-by-step explanation:

1 / 4 * ( 8x + 2) = 20

( 8x + 2) = 20 / (1/4)

8x + 2 = 20 * 4

8x + 2 = 80

8x = 78

x = 9.75

Answer:

x=39/4  (39 over 4 as a fraction)

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;

[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]

[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7

[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE

A piecewise function is a function that has rules or definition based on the interval of reference of the function.

The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;

The points on the line of the graph are;

(1, 1), and (3, 3)

The slope of the graph as x tends to 2⁺ is therefore;

Slope = (3 - 1)/(3 - 1) = 1

The equation of the line is therefore;

y - 1 = x - 1

y = f(x) =  x

Therefore;

f(x) - 4 = x - 4

f(x + 3) = x + 3

[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]

The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;

f(f(x) + 4) = f(x + 4) = x + 4

[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;

[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;

The equation of the function at x = 2 is; y = f(x) = x

f(2 + h) = 2 + h

f(2) = 2

Therefore;

[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h

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The equation of the line which is parallel to the line x = -4 will be x = -3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is x = -4. The y-intercept is zero for the line.

The equation of the line parallel to the equation will be,

x = -3

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Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.

A. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:

TC = wL + rK,

where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.

To calculate the short-run average cost curve, we need to divide the total cost by the level of output:

SAC = TC / Q

Where Q is the level of output.

B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:

SMC = dTC / dQ

At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:

TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150

So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 12.5)))

At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:

TC = 4 * 100 + 1 * 100 = 400

So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 100)))

SMC = 4.01

C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.

D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.

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The domain of the function for this situation is given as follows:

B. All whole numbers greater than or equal to 0 and less than or equal to 7.

The domain of a function is the set that contains all the values assumed by the input of the function.

Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.

The values that compose the domain of the graph are given as follows:

0, 1, 2, 3, 4, 5, 6 and 7.

Which is best described by option B.

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PLEASE GIVE BRAINLIEST
thank you and have a good day :)

Answer:

You figure out the slope

Step-by-step explanation:

Rise/Run is a formula that calculates the slope.  This determines the direction of the line and how steep it is.

Answer:

its a math term yw my boy

Step-by-step explanation:

The numbers on a number line is

    |-------|-------|-------|-------|

    0      1       2       3       4

                  *       *

               1 1/2   2 2/5

From the question, we have the following parameters that can be used in our computation:

Plot 1 1/2 and 2 2/5

To plot 1 1/2 and 2 2/5 on a number line, we can follow these steps:

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The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.

The new coordinates of B will be:

x-coordinate: 4 x (-2) = -8

y-coordinate: 4 x (-1) = -4

So the new vertex B' is (-8, -4).

The new coordinates of C will be:

x-coordinate: 4 x (2) = 8

y-coordinate: 4 x (-2) = -8

So the new vertex C' is (8, -8).

The new coordinates of D will be:

x-coordinate: 4(1) = 4

y-coordinate: 4(2) = 8

So the new vertex D' is (4, 8).

Therefore, the image of the resultant figure is given in the image below.

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Answer:

285.76 kilograms       1.1 cubic yard

Step-by-step explanation:

Answer:

1.11121 cubic yards.

Step-by-step explanation:

First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:

1 lb = 0.45359237 kg

42 lbs = 42 * 0.45359237 kg = 19.05 kg

So, the weight of 1 bag of garden soil is 19.05 kilograms.

Next, let's find the weight of 15 bags of garden soil:

15 bags * 19.05 kg/bag = 285.75 kg

So, 15 bags of garden soil weigh 285.75 kilograms.

Next, let's find the volume of 15 bags of garden soil in cubic yards:

1 cubic foot = 0.037037 cubic yards

2 cubic feet * 15 bags = 30 cubic feet

30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards

So, 15 bags of garden soil have a volume of 1.11121 cubic yards.

Answer:

EF, GH

Step-by-step explanation:

both go on forever from one point

Answer:

A and B

Step-by-step explanation:

Because they go infinitly in one direction and end in another.

The probability that at least 1 of the 4 cards drawn is a face card is 0.6.

A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.

Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.

A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:

P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).

The likelihood that none of the four draws will produce a face card is:

P(no face cards are present) = (10/13)4 = 0.432

As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:

P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568

The chance, rounded to one decimal place, is roughly 0.6.

Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.

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The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.

It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?

On this note, since the graph of the equation is such that g

it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.

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