t (minutes) = 0, 4, 7, 9.
r(t) (gallon per minutes) = 9, 6, 4, 3.
Water is flowing into a tank at the rate r(t), where r(t) is measured in gallons per minute and t is measured in minutes. The tank contains 15 gallons of water at time t = 0. Values of r(t) for selected values of t are given in the table above. Using a trapezoidal sum with the three intervals indicated by the table, what is the approximation of the number of gallons of water in the tank at time t = 9? (A) 52
(B) 57 (C) 67 (D) 77 (E) 79

The inequality that represents the number of animals at the shelter for expenses to be at least $1170 a week is x ≥ 70.

To solve this problem, we need to start by setting up an equation that represents the total weekly expenses of the animal shelter. Let's call the number of animals in the shelter "x".

The fixed expenses are $750, and each animal costs an additional $6 per week, so the total weekly expenses can be represented by the equation:

Total Weekly Expenses = $750 + $6x

We also know that during the summer months, the total weekly expenses are at least $1170. So, we can set up an inequality to represent this:

$750 + $6x ≥ $1170

To solve for x, we can start by subtracting $750 from both sides of the inequality:

$6x ≥ $420

Then, we can divide both sides by $6 to isolate x:

x ≥ 70

This means that there must be at least 70 animals in the shelter for the total weekly expenses to be at least $1170.

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The mean absolute deviation of the given data set, 94, 86, 95, 99, 88, 90, is 4

The values differ from the mean by an average of 4.

From the question, we are to calculate the mean absolute deviation of the given data

The given data

94, 86, 95, 99, 88, 90

To calculate the mean absolute deviation of the given data,

First, we will calculate the mean

Mean = (94 + 86 + 95 + 99 + 88 + 90) / 6

Mean = 552 / 6

Mean = 92

Now,

We will determine the absolute value of the difference between each data and the mean

|94 - 92| = 2

|86 - 92| = 6

|95 - 92| = 3

|99 - 92| = 7

|88 - 92| = 4

|90 - 92| = 2

Now,

We will determine the mean of these absolute differences

Mean absolute deviation = (2 + 6 + 3 + 7 + 4 + 2) / 6

Mean absolute deviation = 4

Hence,

The mean absolute deviation is 4

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Answer:

R59.96

Step-by-step explanation:

250 x 4 = 1000

14.99 x 4 = 59.96

Answer:

  q = 2

Step-by-step explanation:

You want to find q such that the difference between the two roots of 3x²-5x+q is 1/3.

In quadratic ax²+bx+c, the sum of the roots is (-b/a). For roots p and s, this tells us ...

  p + s = -(-5)/3 = 5/3

The problem statement tells us the difference is ...

  p - s = 1/3

Adding these two equations gives ...

  2p = (5+1)/3 = 2

  p = 1 . . . . . . . . . . . . . divide by 2

  s = p -1/3 = 2/3 . . . . find the smaller root

The product of the two roots is (c/a) = (q/3):

  ps = (1)(2/3) = q/3

  q = 2 . . . . . multiply by 3

The value of q is 2.

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There are no points where the graph of f(x) = x² intersects the line y = x - 2, and the equation has no real solutions.

To solve x² - 2 = 2x using the graph of the function f(x) = x² we can start by rewriting the equation as x^2 - 2x - 2 = 0.

Then, we can graph the function f(x) = x² and find the points where the graph intersects the line y = x - 2.

These points correspond to the solutions of the equation x² - 2x - 2 = 0.

We can then use the quadratic formula to solve for x:

x = (-(-1) ± √((-1)² - 4(1)(2))) / (2(1))

x = (1 ± √(-7)) / 2

Since the discriminant is negative, there are no real solutions to the equation x² - 2 = 2x.

Therefore, there are no points where the graph of f(x) = x² intersects the line y = x - 2, and the equation has no real solutions.

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The total recruiting expense is  $91,200 which includes Recruitment Cost, Interview Costs, Job Posting fee, Family travel cost and more

The total recruiting expense would be:

Recruitment Costs: $43,600

Interview Costs: $2,000 x 3

= $6,000

Job Posting fee: $1,000

1st year fee: 10% x $130,000

= $13,000

Real Estate Fee: 6% x $360,000

= $21,600

Shipping fee: $4,000

Family travel cost: $400 x 5

= $2,000

Total = $43,600 + $6,000 + $1,000 + $13,000 + $21,600 + $4,000 + $2,000

= $91,200

Hence, the total recruiting expense is  $91,200

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The proportion that could be used to find the width of Grace's model car is 1/2 = Model width / 12 inches.

To find the width of Grace's model car, a proportion can be set up using the lengths of the actual car and the desired model:

Proportion: Actual width / Actual length = Model width / Model length

Given values:

Actual length = 8 feet

Actual width = 4 feet

Model length = 12 inches

Converting the units:

12 inches = 1 foot (since 1 foot = 12 inches)

Substituting the values into the proportion:

4 feet / 8 feet = Model width / 12 inches

Simplifying the proportion:

1/2 = Model width / 12 inches

To find the model width, cross-multiply and solve for the unknown:

Model width = (1/2) * 12 inches = 6 inches

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1. We can use the expression in option D

2. ║YC║ IS 3

3. ║BX║is 1.2

Similar triangles have several important properties. One of the key properties is that their corresponding angles are congruent, which means they have the same measures.

When triangles are similar, their corresponding sides are proportional. This means that if you take the ratio of the lengths of any two corresponding sides.

We know that;

║BC║ / ║YC║ = ║AB║ /  ║AX║

15/  ║YC║ = 10/2

║YC║ = 15 * 2/10

= 3

Also;

║BC║ /  ║YC║ =  ║AB║ /  ║BX║

10/2 = 6 / ║BX║

║BX║ = 2 * 6/10

= 1.2

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We need to use some basic algebraic equations. Let's assume that the initial payment made by Frankie was x, and the total amount he has to pay for the computer is y. Also, let's assume that Frankie will make n monthly payments.

Now, we know that Frankie has already paid x, and he has to pay y-x more. Since he will pay this amount in n monthly installments, we can represent the monthly installment as (y-x)/n.

So, the equation that represents the relationship between n and y can be written as:

y = x + n*(y-x)/n

Simplifying this equation, we get:

y = x + y-x

y = y

This means that the equation is true for any value of n and y, as long as x is a valid initial payment amount. Therefore, the equation that represents the relationship between n and y is:

y = x + n*(y-x)/n

The equation we derived above is a simple but important concept in mathematics and finance. It shows us that we can calculate the total amount we need to pay for something by multiplying the monthly installment by the number of payments and adding the initial payment to it. This concept is used in many financial transactions, such as car loans, mortgages, and credit card payments.

Moreover, this equation also helps us to plan our finances and manage our budget effectively. We can use it to calculate how much we need to save every month to reach our financial goals, or to compare different payment options and choose the one that suits us best.

In conclusion, the equation that represents the relationship between the number of monthly payments and the total amount paid is an essential tool for anyone who wants to make wise financial decisions. By understanding this equation, we can save money, avoid debt, and achieve our financial goals more easily.

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c) the volume of the solid is 243/28 cubic units.

a. To find the area of R, we need to determine the points of intersection of the graphs y = sqrt(x) and y = x/3 in the first quadrant.

Setting sqrt(x) = x/3, we get x = 9/4. So, the region R is bounded by x = 0, x = 9/4, y = sqrt(x), and y = x/3.

Thus, the area of R is given by the integral:

∫[0,9/4] [sqrt(x) - x/3] dx

= [2/3 x^(3/2) - 1/6 x^2] evaluated from 0 to 9/4

= (2/3)(9/2)^(3/2) - (1/6)(9/4)

= 3√2 - 3/8

Therefore, the area of R is 3√2 - 3/8 square units.

b. To find the volume of the solid generated when R is rotated about the vertical line x = -1, we use the disk method. Each disk has a radius equal to the distance from x = -1 to the curve, and a thickness of dx.

The distance from x = -1 to y = sqrt(x) is 1 + sqrt(x), and the distance from x = -1 to y = x/3 is 1 + 3y. So, the volume of the solid is given by the integral:

∫[0,9/4] π[(1 + sqrt(x))^2 - (1 + 3x)^2] dx

= π ∫[0,9/4] (2sqrt(x) - 8x - 8sqrt(x)x) dx

= π [(4/3)x^(3/2) - 4x^2 - 4/3 x^(5/2)] evaluated from 0 to 9/4

= (16/3)π - (81/2)π/5 + (64/15)π

= (152π/15) - (81π/10)

= 19π/30

Therefore, the volume of the solid generated when R is rotated about the vertical line x = -1 is 19π/30 cubic units.

c. Since the cross sections perpendicular to the y-axis are squares, the area of each cross section is equal to the square of the corresponding value of y. So, the volume of the solid can be found by integrating the area of each cross section with respect to y.

The height of each cross section is given by the difference between the y-coordinates of the curves y = sqrt(x) and y = x/3 at a given value of y.

Thus, the volume of the solid is given by the integral:

∫[0,3] y^2 [sqrt(y) - y/3]^2 dy

= ∫[0,3] y^(5/2) - 2y^(7/2)/3 + y^3/9 dy

= [2/7 y^(7/2) - 4/27 y^(9/2) + 1/12 y^4] evaluated from 0 to 3

= (54/7) - (324/27) + (81/4)

= 54/7 - 36/1 + 81/4

= 243/28

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The possible value of positive constant b for an absolute maximum value of function g(x), [tex]g(x) = xe^{-x} + be^{-x} [/tex] at x = [tex] \frac{2}{3} [/tex] is equals to the [tex] \frac{1}{3} [/tex].

An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, [tex]g(x) = xe^{-x} + be^{-x} [/tex], where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.

Differentiating the function g(x) with respect to x

=> [tex]g'(x) = - x e^{-x} + e^{-x} - be^{-x} [/tex]

[tex]= (1 - x - b )e^{-x}[/tex]

[tex]= \frac{1 - x - b }{e^{x}}[/tex]

For obtaining absolute maximum value put, g'(x) = 0

=> [tex]\frac{1 - x - b }{e^{x}} = 0[/tex]

Substitute x = 2/3, in above expression,

[tex] \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0[/tex]

=> [tex]1 - \frac{2}{3} - b = 0[/tex]

=> [tex] b = \frac{1}{3}[/tex]

Hence, the required value of b is [tex] \frac{1}{3} [/tex].

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Complete question:

Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.

The percentage decrease in flight time between Air New Zealand's first flight from Auckland to Sydney, which took nine hours, and the current flight time of about three hours can be calculated. The percentage decrease represents the reduction in flight time as a proportion of the original flight time.

   To calculate the percentage decrease, we first need to find the difference in flight time between the first flight and the current flight. The difference is obtained by subtracting the current flight time from the original flight time: 9 hours - 3 hours = 6 hours.

Next, we calculate the percentage decrease by dividing the difference in flight time by the original flight time and multiplying by 100:

Percentage decrease = (6 hours / 9 hours) * 100 = 66.67%

Therefore, there has been a 66.67% decrease in flight time between Air New Zealand's first flight from Auckland to Sydney and the current flight time. This represents a significant reduction in the time it takes to complete the journey.

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Answer:

12 hours

Step-by-step explanation:

1 3/4=1.75

21÷1.75=12

The steps to graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7) are given below.

To graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7), we need to apply the following steps:

Plot the original figure on a coordinate plane.

Draw a point at the center of dilation (2, −7).

Draw lines connecting the vertices of the original figure to the center of dilation.

Extend each line from the center of dilation by a factor of 3.

Plot the new vertices where the extended lines intersect.

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An ounce of the chemical cost in 2018 is $98.54.

Given:

The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.

Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

x represents the number of years since 2010.

An ounce of the chemical cost in 2018 is,

= 72 × (1.04)⁸

= $98.54

Therefore, the cost is $98.54.

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The research method that involves collecting data repeatedly on the same person as he or she ages is longitudinal.

Longitudinal research involves studying the same group of individuals over an extended period of time, typically years or even decades. This type of research allows researchers to collect data on changes in behavior, attitudes, or health outcomes over time, and can provide valuable information on the effects of age, development, or life events on these outcomes. Longitudinal research can be especially useful in studying developmental processes, as it allows researchers to track changes in individuals as they grow and develop.

However, longitudinal studies can also be expensive and time-consuming, as researchers must track and collect data from the same group of individuals over many years, and there is a risk of attrition or drop-out over time.

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Hello !

Minimum = 6 (the smallest value)

First quartile = 8 (25% of 7 = 1,75    => 2nd value)

Median = 15 (the value in the middle)

Third quartil = 23 (75% of 7 = 5,25    => 6th value)

Maximum = 31 (the greatest value)

It's C

Answer:

C. The 3.rd Answer :)

The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

Solution:

When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, y reflection )'s across the x-axis is (x, -y).

the point (x , y)→ (x , -y).

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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complete question:

Find the coordinates of the vertices of each figure after the given transformation

3) reflection across the x-axis

Enter Question Text

A U'(1,3),V'(4,3), W'(5,4),T'(1,4)

B U'(3,1),V'(3,4,), W'(4,5),T'(4,1)

D U'(-1,3),V'(-4,3), W'(-5,4),T'(-1,4)

(3)(4-3);W(Sp-4)T(4)

U

T

X

Answer:

what is 478/6 +7*25+78+123-568

Step-by-step explanation:

To find f(x + h), we substitute x + h for x in the function f(x):

f(x + h) = (x + h)^2 + 2(x + h) + 1

Now we simplify by expanding the square:

f(x + h) = x^2 + 2hx + h^2 + 2x + 2h + 1

We can combine like terms to simplify this expression:

f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1)

Therefore, f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1).

Answer:

[tex]f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1[/tex]

Step-by-step explanation:

In this question, we have to plug (x + h) into the given function and simplify.

[tex]f(x) = x^2 + 2x + 1[/tex]

↓ replacing all instances of x with (x + h)

[tex]f(x+h) = (x+h)^2 + 2(x+h) + 1[/tex]

↓ expanding the quadratic term (x + h)²

[tex]f(x+h) = (x^2 + 2xh + h^2) + 2(x+h) + 1[/tex]

↓ applying the distributive property ... [tex]2(x+h) = 2x + 2h[/tex]

[tex]\boxed{f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1}[/tex]

No further simplification can be done.

Answer:

Down below

Step-by-step explanation:

2)(-6,3)

where h=-6&k=3

(x-h)²+(y-k)²=R²

(x-(-3)²+(y-6)²=11²

(x+3)²+(y²-6²)=11²

3)(x-3)²+(y+4)²=25

(x-h)²+(y-k)²=R²

h=3

k=-4

(

C(3,-4)

4)(x+1)²+(y-6)²=361

(x-h)²+(y-k)²=R²

R²=361

√R²=√361

R=19

Answer:

4/3

Step-by-step explanation:

Tan(x)=Opposite/adjacent

We need to find the opposite side.

We can use the Pythagorean theorem to help us:

5^2=3^2+x^2

25=9+x^2

16=x^2

x=4

4 is the measure of the opposite side

The adjacent side has measure of 3

Tan(theta)= 4/3

*theta is the weird 0 with a bar thingy at the angle, its some letter in the greek alphabet that denotes an unknown angle in geometry

Answer:

48m^2 + 56m

Step-by-step explanation:

-8m(-6m - 7)

Use the distributive property. (-8m*-6m & -8m*-7)

-8m*-6m = 48m^2

-8m*-7 = 56m

48m^2 + 56m

The area of the banner is 24 square feet.

We have,

Since the spirit spanner is in the form of a triangle.

We can use the area of a triangle to calculate the area of the banner.

The area of a triangle is given by the formula:

Area = (1/2) x base x height

Substituting the given values.

Area = (1/2) x 8 feet x 6 feet

Area = 24 square feet

Therefore,

The area of the banner is 24 square feet.

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The mean of the data set is 33.7.

The median is 34.5

The mode is 34

The range is 33

Suppose the value 26 is added:

The mean decreases by 0.7

The median decreases by 0.5

The mode is 34

The range is 33

The data set is as follows:

{34, 35, 42, 18, 20, 51, 19, 47, 37, 34}

Let's arrange it in ascending order.

{18, 19, 20, 34, 34, 35, 37, 42, 47, 51 }

The mean, or arithmetic mean, is the average value of a set of numbers. Therefore, let's find the mean.

mean = 18 + 19 + 20 + 34 + 34 + 35 + 37 + 42 + 47 + 51 / 10

mean = 337 / 10

mean = 33.7

The median is the middle number. Therefore,

median = 34 + 35 / 2

median = 34.5

Let's find the mode. The mode is the number that appears most.

mode = 34

The range is the difference between the highest number and the smallest number.

range = 51 - 18 = 33

Suppose the value 26 is added to the data set.

mean when 26 is added = 337 + 26 / 11 = 33

The mean decreases by 0.7

The median decreases by 0.5

The mode is 34

The range is 33

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an equation to represent the relation is,

⇒ y = 10/x

We know that,

Proportion is extensively explained. Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion states that two ratios are equal. In this case, a and b can be any two integers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.

Since, The relation represents an inverse variation because as the values of x is increasing the values of y is decreasing.

Hence, We can formulate;

y = k/x

Plug y = 5, x = 2;

5 = k/2

Solve for k;

k = 5 x 2

k = 10

Thus, The required equation is y = 10/x

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The complete question is :

does the relation in the table represent direct variation, inverse variation, or neither? if it is direct or inverse variation, write an equation to represent the situation. Explain your answer

x 5, 10, 15, 20

Y 2, 1, 2/3, 1/2

Answer:

The Correct answer is C

communicative property