Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r. Then write a sentence to explain your answer.

Answer:

V≈5.58ft³     d=2.2 ft

Step-by-step explanation:

V=4  3πr3

d=2r

Solving for V

V=1  6π d3 =1  6·π·2.23≈5.57528ft³

Hope this helps! :D

Answer:

5.6 ft  

Step-by-step explanation:

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=  

3

4

​  

πr  

3

\text{radius} = \frac{\text{diameter}}{2} = \frac{2.2}{2}=1.1

radius=  

2

diameter

​  

=  

2

2.2

​  

=1.1

feet

\text{Plug in:}

Plug in:

\frac{4}{3}\pi (1.1)^3

3

4

​  

π(1.1)  

3

5.57527976257

The average waiting time in minutes is approximately 0.317 minutes.

To determine the average waiting time in minutes, we can use the queuing theory formula for average waiting time in an\($\mathrm{M} / \mathrm{M} / \mathrm{c}$\) queue:

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}$$\)

Where:

\($W_q$\) is the average waiting time in the queue.

\($\rho$\) is the traffic intensity, given by $\frac{\lambda}{c \cdot \mu}$.

\($c$\) is the number of service channels (cashiers).

\($\mu$\) is the service rate (customers per hour).

\($\lambda$\)  is the arrival rate (customers per hour).

Given:

\($\lambda=85.5$\)customers per hour.

\($\mu=19$\) customers per hour.

\($c=5$\) cashiers.

First, let's calculate $\rho$ :

\($$\rho=\frac{\lambda}{c \mu}=\frac{85.5}{5 \cdot 19} \approx 0.9011$$\)

Now, let's calculate \($W_q$\) :

\($$W_q=\frac{\rho^{c+1}}{c ! \cdot(1-\rho)} \cdot \frac{1}{\mu-\lambda}\\=\frac{0.9011^{5+1}}{5 ! \cdot(1-0.9011)} \cdot \frac{1}{19-85.5} \\\approx 0.317 \text { (rounded to two decimal places) }$$\)

Therefore,the average waiting time in minutes is approximately 0.317 minutes.

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Nia needs 165.4cm trim.

What is a rectangle measure?

It has a tight, flat form. There are 4 corners, 4 angles, and 4 sides. It has length and width as its 2 dimensions. A rectangle has 90° angles on each side. The opposing sides are parallel and equal. A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel. There are many rectangular objects around us.

Here, we have

Given: Nia is fixing a rectangular sign. She plans to place metal trim around the sign edges. The rectangle measures 64.5 cm x 18.2 cm.

P = 2*L + 2*W

L = 64.5 cm

W = 18.2 cm

P = 2*(64.5) + 2*(18.2)

P = 129+36.4

P = 165.4cm

Hence, Nia needs 165.4cm trim.

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The area of the regular octagon inscribed in a circle with a radius of 16 feet can be found using the formula A = (2 + 2sqrt(2))r^2, where r is the radius of the circle. Plugging in the value for r, we get:

A = (2 + 2sqrt(2))(16)^2

A = (2 + 2sqrt(2))(256)

A = 660.254 ft^2

Therefore, the area of the regular octagon is approximately 660.254 square feet.

To derive the formula for the area of a regular octagon inscribed in a circle, we can divide the octagon into eight congruent isosceles triangles, each with a base of length r and two congruent angles of 22.5 degrees. The height of each triangle can be found using the sine function, which gives us h = r * sin(22.5). Since there are eight of these triangles, the area of the octagon can be found by multiplying the area of one of the triangles by 8, which gives us:

A = 8 * (1/2)bh

A = 8 * (1/2)(r)(r*sin(22.5))

A = 4r^2sin(22.5)

We can simplify this expression using the double angle formula for sine, which gives us:

A = 4r^2sin(45)/2

A = (2 + 2sqrt(2))r^2

Therefore, the formula for the area of a regular octagon inscribed in a circle is A = (2 + 2sqrt(2))r^2.

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Answer:

3 1/2

Step-by-step explanation:

|3 1/2|

= | 7/2|

= 7/2

= 3 1/2

The quadratic function answer for 2(x^2-3x+6) is 4x^2 - 6x + 12.

I believe that is correct

Answer:

14 gallons

Step-by-step explanation:

Answer:

14 gallons

Step-by-step explanation:

The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.

To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:

A = P * \(e^{(rt)\),

where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:

0 = 6600 * \(e^{(0.10 * 5)\)- k * 5,

Simplifying the equation, we have:

\(e^{(0.5)\) = k / 6600.

Now, we can solve for k by multiplying both sides of the equation by 6600:

k = 6600 * \(e^{(0.5)\),

Using a calculator or software, we find that k is approximately $943.57 per year.

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Answer:

32.92

Step-by-step explanation:

well you just do base times height

the height is 3.5

the area of the base is 3 * pi which is 9.42 if you round pi to 3.14

so 3.5*9.42= 32.92

Answer:

slope is 25 because the equation is y=25x+50

Step-by-step explanation:

heres the official answer

Answer:

number is 3

Step-by-step explanation:

let n be the number , then 3 more than the number is n + 3 and six less than 4 times the number is 4n - 6 , so

4n - 6 = n + 3 ( subtract n from both sides )

3n - 6 = 3 ( add 6 to both sides )

3n = 9 ( divide both sides by 3 )

n = 3

the number is 3

The zero of polynomials is -2. The polynomials is p(y) = \(3y^{3} - 16 y - 8\).

According to the question,

The polynomials is p(y) = \(3y^{3} - 16 y - 8\). In order to find the zero of polynomials only if we substitute the value and polynomials become zero.

p(-2) = \(3(-2)^{3} - 16 (-2) - 8\)

= 3(8) + 32 -8

= 0

Hence, the zero of polynomials is -2. The polynomials is p(y) = \(3y^{3} - 16 y - 8\).

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Answer:

16

Step-by-step explanation:

9-9:9 +9 - 9 :9 =

9 - 1 +9 - 1 =

8 +9 - 1 =

17 - 1 =

16

Answer:

2 cups

Step-by-step explanation:

to make one cup of orange

1/3 (multiply by 3) = 1 cup

then also multiply 2/3 by 3 =2

so you need 2 cups of pineapple

Answer:

y = 3x + 3

Step-by-step explanation:

As x increases, y increases by 3. Therefore, the slope of the function is 3.

Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).

Overall, the function rule for the given data set is y = 3x + 3.

The line integral ∫C -2dy + 1dx is equal to 0 for C1 and -4 for C2.

To compute the line integral ∫C -2dy + 1dx, we need to parameterize the curve C and then evaluate the integral along that parameterization.

The curve C consists of two line segments. Let's denote the first line segment as C1 and the second line segment as C2.

C1 goes from (0, 0) to (-2, -1), and C2 goes from (-2, -1) to (-4, 0).

Let's parameterize C1 using t ranging from 0 to 1:

x(t) = (1 - t) * 0 + t * (-2) = -2t

y(t) = (1 - t) * 0 + t * (-1) = -t

Now, let's parameterize C2 using s ranging from 0 to 1:

x(s) = -2 + s * (-4 - (-2)) = -2 - 2s

y(s) = -1 + s * (0 - (-1)) = -1 + s

We can now compute the line integral ∫C -2dy + 1dx by splitting it into two integrals corresponding to C1 and C2:

∫C -2dy + 1dx = ∫C1 -2dy + 1dx + ∫C2 -2dy + 1dx

For C1, we have:

∫C1 -2dy + 1dx = ∫[0,1] -2(-dt) + 1(-2dt) = ∫[0,1] 2dt - 2dt = ∫[0,1] (2 - 2) dt = 0

For C2, we have:

∫C2 -2dy + 1dx = ∫[0,1] -2(ds) + 1(-2ds) = ∫[0,1] (-2 - 2ds) = ∫[0,1] (-2 - 4s)ds = -2s - 2s^2 evaluated from s = 0 to s = 1 = -2 - 2 = -4.

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The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).

To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).

For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.

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Answer:

x=-3

Step-by-step explanation:

-4(-2x+5)-5x+5=-24

8x-20-5x+5=-24

3x-15=-24

3x=-9

x=-3

I hope that this helped you!

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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Answer:

−2(−9x+5)−4x=2(x−5)−4

Step 1: Simplify both sides of the equation.

−2(−9x+5)−4x=2(x−5)−4

(−2)(−9x)+(−2)(5)+−4x=(2)(x)+(2)(−5)+−4(Distribute)

18x+−10+−4x=2x+−10+−4

(18x+−4x)+(−10)=(2x)+(−10+−4)(Combine Like Terms)

14x+−10=2x+−14

14x−10=2x−14

Step 2: Subtract 2x from both sides.

14x−10−2x=2x−14−2x

12x−10=−14

Step 3: Add 10 to both sides.

12x−10+10=−14+10

12x=−4

Step 4: Divide both sides by 12.

12x

12

=

−4

12

x= -1/3

Step-by-step explanation:

Good luck! Hope this helps! <3

Answer :

\(x = - \frac{1}{3} \)

or you can just write x = -0.3

hope this helps!

let's first off, convert the mixed fractions to improper fractions.

\(\stackrel{mixed}{8\frac{2}{5}}\implies \cfrac{8\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{42}{5}}~\hfill \stackrel{mixed}{6\frac{7}{10}} \implies \cfrac{6\cdot 10+7}{10} \implies \stackrel{improper}{\cfrac{67}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{42}{5}-\cfrac{67}{10}\implies \cfrac{(2)42~~ - ~~(1)67}{\underset{\textit{using this LCD}}{10}}\implies \cfrac{84-67}{10}\implies \cfrac{17}{10}\implies 1\frac{7}{10}\)

Answer:

y=1.25x + 17

Coordinate, (-8,7) ==> (x,y)

Slope is 5/4 ==> 1.25

y=mx + b (m is slope)

Plug in coordinate and slope to find b

7 = 1.25(-8) + b

Multiply

7 = -10 + b

Add -10 to isolate b

17 = b

Answer:

Coordinate, (-8,7) ==> (x,y)

Slope is 5/4 ==> 1.25

y=mx + b (m is slope)

Step-by-step explanation:

After constructing a circle, the next step in constructing an inscribed hexagon by hand is to draw two diameters of the circle that are perpendicular to each other.

Drawing two diameters of the circle that are perpendicular to each other is the next step in constructing an inscribed hexagon because it helps to determine the positions of the vertices of the hexagon. The diameters divide the circle into four equal quadrants, with the center of the circle as the point of intersection. By connecting the points where the diameters intersect the circle, we can identify the six vertices of the hexagon. These vertices will lie on the circumference of the circle and will form the six sides of the inscribed hexagon.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

180

Step-by-step explanation:

Volume = base * height(depth)

V=1.2*1.35=1.62 m³

1 m³=1000 liter

1.62*1000=1620 liter

1620/9=180 ( 9 liter bucket)

a) the function y=x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, (x > 0).

b) The value of c for which the solution satisfies the initial condition y(8) = 6 is c = -3712.

a) To verify that the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, we first need to find the derivative y' using algebra:
y = x^2 + c/x^2
y' = 2x - 2c/x^3

Now, plugging y and y' into the given differential equation:

x(2x - 2c/x^3) + 2(x^2 + c/x^2) = 4x^2

Next, simplify the equation:
2x^2 - 2cx^(-2) + 2x^2 + 2c/x^2 = 4x^2

Combine the like terms:
4x^2 = 4x^2

The equation holds true, so the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2.

b) To find the value of c for which the solution satisfies the initial condition y(8) = 6, plug in x = 8 and y = 6 into the function y = x^2 + c/x^2:

6 = (8^2) + c/(8^2)

Solve for c:
6 - 64 = c/64
-58 = c/64
c = -58 * 64
So, the value of c is -3712.

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The given quadratic equation gives the parameters of the shape of the

graph of the equation.

Reasons:

The given function is n(t) = -2.82·t² + 25.74·t + 60.87

by analyzing the above function, we have;

At t = 0

n(0) = -2.82 × 0² + 25.74 × 0 + 60.87 = 60.87

Which gives;

\(\displaystyle t = -\frac{25.74}{2 \times (-2.82)} \approx 4.564\)

The maximum value of the function is therefore;

n(4.564) = -2.82 × 4.564² + 25.74 × 4.564 + 60.87 ≈ 119.61

The characteristics of the equation are;

Initial value of equation = 60.87

t-coordinate of the maximum point, t ≈ 4.564

Maximum value of the of the function = 119.61

By comparing with the given graphs, we have;

Therefore, the graph that will most likely be associated with the model is; graph B.

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Answer:

The correct answer is graph B.

Step-by-step explanation:

I got it right on the Edmentum test.

Answer:

Step-by-step explanation: