The parabola (showed in the picture) opens?

Answer:

The pattern is you are subtracting by 8. The subsequent three terms are 51, 43, and 35.

Step-by-step explanation:

First, you can subtract the first value from the second to find the common difference. Then you continue on this pattern. Simple!

The rate of change of the revenue function R(x) is given by its derivative R'(x) = 190 - 0.8x. To find where the rate of change is equal to 0, we set R'(x) = 0 and solve for x:

190 - 0.8x = 0
0.8x = 190
x = 237.5

Therefore, the revenue function is constant when x = 237.5.
To find the value of x where revenue is constant, we need to find the point where the rate of change of the revenue function R(x) is equal to 0. This can be achieved by finding the derivative of R(x) with respect to x, and then setting it equal to 0.

R(x) = 190x - 0.4x^2

The derivative of R(x) with respect to x is:

R'(x) = dR(x)/dx = 190 - 0.8x

Now, set R'(x) equal to 0 and solve for x:

0 = 190 - 0.8x

0.8x = 190

x = 190 / 0.8

x = 237.5

The revenue function is constant when x = 237.5.

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The algebraic expressions representing the books Jan and Jackie have left are J - 4 and J - 2 - 4, respectively, where J is the initial number of books checked out by both.

Let's use "J" to represent the number of books Jan and Jackie checked out from the library. After 3 weeks, Jan turned in 4 books, so she has J - 4 books left.

Jackie returned 2 books after the first week, so she has J - 2 books left. When she returned 4 more books later, she had J - 2 - 4 = J - 6 books left. Therefore, the algebraic expressions for the number of books Jan and Jackie have left are

Jan: J - 4

Jackie: J - 6

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In statistical analysis, the mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the data set. For Doctor A's data set on corrective lenses, the MAD is calculated as 0.42, while for Doctor B's data set, it is calculated as 0.38.

This shows that Doctor B's data set has a slightly smaller variation compared to Doctor A's data set.

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(a) The three different trigonometric ratios that could have been used to find the distance x between Emma and the base of the tree are sin(60°) = 43.3/50, cos(60°) = x / 50, and tan(60°) = 43.3 / x. The distance is 25 ft.

(b) Using the Pythagorean theorem, the distance x between Emma and the base of the tree is 25 ft.

(a) We can use sine, cosine, and tangent trigonometric ratios to find the distance x between Emma and the base of the tree.

1. Sine:
sin(60°) = opposite/hypotenuse = (tree height) / 50
tree height = 50 * sin(60°) = 43.3 ft (since it's given that the tree is 43.3 ft tall)

2. Cosine:
cos(60°) = adjacent/hypotenuse = x / 50
x = 50 * cos(60°) = 25 ft

3. Tangent:
tan(60°) = opposite/adjacent = (tree height) / x
x = (tree height) / tan(60°) = 43.3 / tan(60°) ≈ 25 ft

(b) To find the distance x between Emma and the base of the tree using the Pythagorean theorem, we can consider the triangle formed by Emma, the base of the tree, and the top of the tree.

Let's call the distance from the base of the tree to the top of the tree (tree height) y.

Emma's distance to the cat (50 ft) is the hypotenuse, the distance x is one leg, and the tree height y (43.3 ft) is the other leg of the right triangle.

Using the Pythagorean theorem: x² + y² = hypotenuse²
x² + 43.3² = 50²
x² + 1874.89 = 2500
x² = 625.11
x ≈ 25 ft

So, the distance between Emma and the base of the tree is approximately 25 ft.

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Step-by-step explanation:

area= base*height (8+10)*16=288

perimeter=2L+2B

to find L we will use Pythagorean theorem(check attachment for the solving to find L)

L=17.8

perimeter= 2(17.8)+2(18)

=71.77

=71.8

The function given is y = 18000(0.76)^t, where y represents the value of the car and t represents the time in years.

This is an exponential decay function, meaning that the value of the car decreases over time. To determine if the value of the function will ever be 0, we would need to find if there exists a time t when y = 0. Let's analyze the function:

0 = 18000(0.76)^t

In an exponential decay function, the base (0.76 in this case) is between 0 and 1, so as time (t) increases, (0.76)^t will approach 0, but it will never actually reach 0. Thus, the value of the car will keep decreasing over time but will never be exactly 0.

In summary, the value of the function, which represents the car's value, will never be 0, but it will get infinitely close to 0 as time progresses. This is a characteristic of exponential decay functions, where the value never reaches 0 but approaches it as time goes on.

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Answer:

568.2 in

Step-by-step explanation:

To find this we first have to divide 1894/10 then we get 189.4 which we multiply by 3 to find how much more sand we need.

The expected cost of Bob's lunch is $8.75.

To find the expected cost of Bob's lunch, we need to determine the probability that Bob and Anna will meet at Sally's Restaurant at the same time.

There are 4 possible times for Bob and Anna to choose from: 1 PM, 2 PM, 3 PM, and 4 PM. Since they are choosing randomly, the probability of them both choosing the same time is 1/4 (one out of four choices).

Now we can calculate the expected cost of Bob's lunch. If they meet successfully, Bob's lunch will cost $5. If they do not meet, Bob's lunch will cost $10. We can find the expected cost by multiplying the probability of each outcome by its corresponding cost, and then adding these products together.

Expected cost = (Probability of meeting) * (Cost if they meet) + (Probability of not meeting) * (Cost if they don't meet)

Expected cost = (1/4) * $5 + (3/4) * $10

Expected cost = $1.25 + $7.50

Expected cost = $8.75

The expected cost of Bob's lunch is $8.75.

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To find the volume of a cone, we use the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.

In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.

First, we need to find the slant height of the cone. We can use the Pythagorean theorem:

[tex]l = \sqrt{(r^2 + h^2)[/tex]

[tex]l = \sqrt{(6^2 + 10^2)[/tex]

[tex]l = \sqrt{\\(36 + 100)[/tex]

[tex]l = \sqrt{136[/tex]

[tex]l = 11.66 ft[/tex]

Now we can substitute the values into the formula for the volume:

[tex]V = (1/3)\pi r^2h[/tex]

[tex]V = (1/3)\pi (6^2)(10)[/tex]

[tex]V = 120\pi /3[/tex]

[tex]V = 40\pi[/tex]

[tex]V= 125.6 cubic feet[/tex]

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The phrases that imply correlation without causation are:

These correlations do not imply a causal relationship, meaning that an increase or decrease in one variable does not directly cause a corresponding change in the other variable.

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The cost of a bag of chips is $0.75 and the cost of a cheeseburger is $3.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

let the cost of a cheesburger be x.

let the cost of a bag of chips be y

therefore, it is given that x + y = 3.75                ...........(i)

it is also given that 2x + 3y = 8.25                     ............(ii)

multiplying the equation in( i) by 2 we get 2x + 2y = 7.50     ......(iii)

subtracting the equation in iii) from the equation in ii) we get y = $0.75

Therefore ,the cost of a bag of chips is $0.75

Substituting the value of y found in (ii) we get x = 3.

therefore ,the cost of a cheeseburger is $3.

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The complete question is ,

Nathan ordered 1 cheeseburger and 1 bag of chips for 3. 75 jack ordered 2 cheeseburgers and 3 bags of chips for 8. 25.find the value of one cheeseburger and one bag?

The derivative of f(x) is -3/4.

To find the derivative, use the definition of a derivative:

f'(x) = lim h→0 [f(x + h) - f(x)] / h

Substitute f(x) = √(4x + 3) into this definition:

f'(x) = lim h→0 [√(4(x + h) + 3) - √(4x + 3)] / h

Multiplying by the conjugate of the numerator:

f'(x) = lim h→0 [(√(4(x + h) + 3) - √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3))] / [h * (√(4(x + h) + 3) + √(4x + 3))]

Expanding the numerator, we get:

f'(x) = lim h→0 [(4(x + h) + 3) - (4x + 3)] / [h * (√(4(x + h) + 3) + √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3)))]

f'(x) = lim h→0 [4h] / [h * (√(4(x + h) + 3) + √(4x + 3)))]

Canceling out the h terms, we get:

f'(x) = lim h→0 4 / (√(4(x + h) + 3) + √(4x + 3)))

Now, we can evaluate the limit as h approaches 0:

f'(x) = 4 / (√(4x + 3) + √(4x + 3))

f'(x) = 4 / (2√(4x + 3))

f'(x) = 2 / √(4x + 3)

Therefore, the derivative of f(x) is -3/4.

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Answer:

Step-by-step explanation:

Car are the preferred transportation for 168 residents.Together, Walk and Streetcar are the preferred transportation for 55 residents.Bus is the preferred transportation for 45 residents.Bicycle is the preferred transportation for 50 residents.Question 2(Multiple Choice Worth 2 points)(Appropriate Measures MC)The box plot represents the number of tickets sold for a school dance.A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the numb

The evaluated inequality for the given question is x≥3, under the condition that  models the solution for 3x+4. 5≤5(x-2).

Then the given model for the solution for 3x+4. 5≤5(x-2), so we have to apply the principles of solving inequality

5 ≤ 5(x - 2)

5 ≤ 5x - 10

15 ≤ 5x

3 ≤ x

Then, the inequality that represents the given model is  x≥3.

Inequality refers to a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used to compare the size or order of two values on the number line. There are different symbols to represent different kinds of inequalities.

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If total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

To determine if adding cookie dough ice cream and hot fudge to the menu will result in a profit, we need to consider the cost and potential revenue. If the cost of adding these items is $42, we need to calculate how many orders of cookie dough ice cream with hot fudge we need to sell to cover that cost and make a profit.

Assuming the profit margin on each order of cookie dough ice cream with hot fudge is $5 (for example), we would need to sell at least 9 orders (rounding up from 8.4) to cover the $42 cost and break even. If we sell more than 9 orders, we would make a profit.

Assuming we sell 20 orders of cookie dough ice cream with hot fudge, the total revenue generated would be $100 ($5 profit per order x 20 orders). Subtracting the $42 cost of adding these items, the net profit would be $58.

Therefore, if total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

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The p-value for this hypothesis test is approximately 0.1317.

To calculate the p-value for the hypothesis test, we need to perform a one-sample proportion test using the sample data provided.

Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of Marriott customers carrying two Wi-Fi devices is equal to or less than 0.60.

Alternative hypothesis (H₁): The proportion of Marriott customers carrying two Wi-Fi devices exceeds 0.60.

Sample size (n) = 120

Number of customers with two Wi-Fi devices (x) = 78

To test the hypothesis, we can use the normal approximation to the binomial distribution since the sample size is reasonably large.

First, calculate the sample proportion:

[tex]\hat{p}[/tex] = x / n = 78 / 120 = 0.65

Next, calculate the test statistic (z-score):

z = [tex]\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]

= (0.65 - 0.60) / √((0.60 * (1 - 0.60)) / 120)

= 0.05 / √(0.24 / 120)

= 1.1180

Now, we can find the p-value corresponding to the calculated test statistic using a standard normal distribution table or a statistical calculator.

In this case, the p-value for a one-sided test (since we are testing if the proportion exceeds 0.60) is approximately 0.1317.

Therefore, the p-value for this hypothesis test is approximately 0.1317.

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Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.

Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.

For T1:

The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).

For T2:

The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).

Now, resolving the forces in the vertical direction, we have:

T1cos(40°) + T2cos(30°) - mg = 0

where m is the mass of the star and g is the acceleration due to gravity.

Substituting the values:

T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0

T1cos(40°) + T2cos(30°) = 392.4 N

Next, resolving the forces in the horizontal direction, we have:

T1sin(40°) = T2sin(30°)

Now we have two equations with two unknowns:

T1cos(40°) + T2cos(30°) = 392.4 N

T1sin(40°) = T2sin(30°)

Solving these equations simultaneously, we get:

T1 = 266.4 N

T2 = 205.1 N

Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.

Step-by-step explanation:

To administer a daily dose of 375 mg of naproxen using 250 mg scored tablets, the patient would need to take 1.5 tablets, rounded up to 2 tablets of 250 mg each.

To administer 375 mg of naproxen using 250 mg scored tablets, we need to divide 375 by 250 to determine how many tablets to administer.

375 mg / 250 mg per tablet = 1.5 tablets

Therefore, the dosage of 375 mg of naproxen would require 1.5 tablets.

Since tablets cannot be divided into halves, the patient would need to take 2 tablets of 250 mg each to achieve the prescribed dosage of 375 mg.

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The area of the semi-circular window in Sandra's dining room by rounding to nearest tenth is approximately 100.5 square inches.

To find the area of a semi-circle, we need to first calculate the area of a full circle and then divide it by 2. The formula for the area of a circle is

A = π * r²,  where A is the area and r is the radius.

Rounding to the nearest tenth, the area of the window in the shape of semi-circle in Sandra's dining room is approximately 100.5 square inches.

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The equation is Gross Income = Taxes Owed / 0.09.

To solve for the gross income for each family based on their taxes owed and the fact that this represents 9% of each family's gross income, follow these steps:

1. Write the equation: Taxes Owed = 0.09 * Gross Income
2. Rearrange the equation to solve for Gross Income: Gross Income = Taxes Owed / 0.09
3. Substitute the Taxes Owed value for each family into the equation and calculate their Gross Income.

For each family, input their taxes owed into the equation and you will find their gross income. Remember, the equation is Gross Income = Taxes Owed / 0.09.

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The indicated coefficients are:

[tex]c_2 = -(-2) = 2[/tex]

[tex]c_4 = 5/2[/tex]

[tex]c_5 = -22[/tex]

To find the power series solution of the differential equation about x = 0, we assume that the solution has the form:

y(x) = ∑(n=0 to infinity) [tex]c_n x^n[/tex]

where [tex]c_n[/tex] are the coefficients of the power series.

Differentiating y(x), we get:

y'(x) = ∑(n=1 to infinity) [tex]n c_n x^{(n-1)}[/tex]

Next, we substitute y(x) and y'(x) into the differential equation:

([tex]x^2[/tex] - x + 1)y' - y + 8y = 0

([tex]x^2[/tex] - x + 1) ∑(n=1 to infinity)[tex]n c_n x^{(n-1)}[/tex] - ∑(n=0 to infinity)[tex]c_n x^n[/tex] + 8∑(n=0 to infinity)[tex]c_n x^n[/tex] = 0

Simplifying this expression and grouping the terms with the same power of x, we get:

∑(n=1 to infinity) [tex]n c_n x^n (x^2 - x + 1)[/tex]+ ∑(n=0 to infinity) [tex](8c_n - c_{(n+1)}) x^n[/tex] = 0

Since this equation holds for all values of x, we must have:

[tex]n c_n (n+1) - (n+2) c_(n+2) + 8c_n - c_(n+1) = 0[/tex]

for all n ≥ 0, where we have set [tex]c_{(-1){ = 0[/tex]and [tex]c_{(-2)}[/tex]= 0.

Using the initial conditions y(0) = 0 and y'(0) = 4, we have:

[tex]c_0 = 0[/tex]

[tex]c_1 = y'(0) = 4[/tex]

Substituting these values into the recurrence relation, we can recursively find the coefficients of the power series solution:

[tex]n = 0: 0 c_0 - 2 c_2 + 8 c_0 - c_1 = 0 = > c_2 = (4-8c_0+c_1)/(-2) = -2[/tex]

[tex]n = 1: 1 c_1 - 3 c_3 + 8 c_1 - c_2 = 0 = > c_3 = (9c_1-c_2)/3 = 6[/tex]

[tex]n = 2: 2 c_2 - 4 c_4 + 8 c_2 - c_3 = 0 = > c_4 = (10c_2-c_3)/(-4) = 5/2[/tex]

[tex]n = 3: 3 c_3 - 5 c_5 + 8 c_3 - c_4 = 0 = > c_5 = (11c_3-c_4)/5 = -22/15[/tex]

[tex]n = 4: 4 c_4 - 6 c_6 + 8 c_4 - c_5 = 0 = > c_6 = (9c_4-c_5)/(-6) = -64/45[/tex]

Hence, the power series solution of the differential equation about x=0 is:

[tex]y(x) = 4x + 2x^2 - 4x^3 + 23x^4 - 44/9 x^5 + 24/5 x^6 - 326/315 x^7 + ...[/tex]

Therefore, the indicated coefficients are:

[tex]c_2 = -(-2) = 2[/tex]

[tex]c_4 = 5/2[/tex]

[tex]c_5 = -22[/tex]

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It will take 15 months for the number of basic subscriptions to match the number of deluxe subscriptions.

Let's denote the number of months passed by "m".

In m months, the number of basic subscriptions will be 288 - 5m (since 5 basic subscriptions are decreasing each month), and the number of deluxe subscriptions will be 93 + 8m (since 8 deluxe subscriptions are increasing each month).

We want to find out when the number of basic subscriptions will match the number of deluxe subscriptions, so we can set the two expressions equal to each other:

288 - 5m = 93 + 8m

We can then solve for m:

288 - 93 = 8m + 5m

195 = 13m

m = 15

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Answer:

28 degrees and 62 degrees

Step-by-step explanation:

Set up your equation like this:

x+(x-34)=90

2x-34=90

2x=56

x=28

28+34=62

So the smaller angle is 28 degrees and the larger angle is 62 degrees.

Hope this helps!! :D

To solve this integral, we'll use a trigonometric substitution. Let x = (1/6)tan(θ), which implies dx = (1/6)sec^2(θ)dθ.

Now, we can rewrite the integral as:

∫√(1 + 36(1/6tan(θ))^2) (1/6)sec^2(θ)dθ

Simplify the expression inside the square root:

∫√(1 + 6^2tan^2(θ)) (1/6)sec^2(θ)dθ

Now, recall the trigonometric identity: 1 + tan^2(θ) = sec^2(θ). Using this identity, we have:

∫√(sec^2(θ)) (1/6)sec^2(θ)dθ

Simplify and integrate:

(1/6)∫sec^3(θ)dθ

Unfortunately, the integral of sec^3(θ) is non-elementary, so we cannot find a closed-form expression for it. However, you can look up the techniques used to evaluate this integral, such as integration by parts or reduction formulas, if you need a more detailed solution.

Remember to convert the result back to the original variable x using the substitution x = (1/6)tan(θ), and don't forget to add the constant of integration, C, at the end.

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The expression that is equivalent to 3v+2v is:

D. v+v+v+v+v

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

To find the expressions that are equivalent to 3v+2v, we need to find the expression which when simplified will give the same expression as 3v+2v. That is: 3v + 2v = 5v

v*5 = 5v

v+5 = v + 5

v+5v = 6v

v+v+v+v+v = 5v

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Answer: x = -1, y = 6

Step-by-step explanation:

lets substitute the value of y from the first equation into the y in the second equation.

-2x + 4 = -3x + 3

4 - 3 = -3x + 2x

1 = -1x

x = -1

we know from before that y = -2x + 4

so y = -2(-1) + 4

y = 6

The measures of the angles JIK and JIL are 67 degrees and 157 degrees

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

The inscribed angle opposite to the same arc is half of the external angle

Using the above as a guide, we have the following:

JIK = 90 - 46/2

JIK = 67 degrees

Also, we have

JIL = 90 + JIK

So, we have

JIL = 90 + 67

JIL = 157 degrees

Hence, the measure of the angle JIL is 157 degrees

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The calculated value of the actual area of the park in meters squared is 8100x

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

A scale drawing of a rectangular park had a scale of 1 cm = 90 m.

This means that

Scale factor = 90/1

Evaluate

Scale factor = 90

The actual area of the park in meters squared is calculated as

Area = Area of scale * Scale factor^2

Substitute the known values in the above equation, so, we have the following representation

Area = Area of scale * 90^2

Evaluate

Area = Area of scale * 8100

Let Area of scale = x

So, we have

Area = 8100x

Hence, the actual area of the park in meters squared is 8100x

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The equation that could be used to calculate the average speed of each vehicle is C. 140x = 95x + 40, where x represents the average speed of the helicopter in miles per hour and 140x represents the distance traveled by the small private airplane.

The equation that can be used to calculate the average speed of each vehicle is:

C. 140x = 95x + 40

Let's break it down:

Since the time taken by both vehicles is the same, the distances covered by each vehicle can be equated, giving us the equation 140x = 95x + 40.

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