The University of Central Florida’s cheerleading team has eighteen males and twenty-one females. If h represents the height of a team member, the inequality 260 ≤ 4h + 28 < 324, represents the range of heights of the cheerleaders, in inches. Select all possible heights for the University of Central Florida’s cheerleaders.
Group of answer choices

6 feet, 2 inches

5 feet, 11 inches

5 feet, 3 inches

4 feet, 9 inches

5 feet, 8 inches

5 feet, 4 inches

4 feet, 10 inches

If the expression is  10x2-18x-4.:

a. The greatest common factor of the expression 10x^2 - 18x - 4 is 2.

b. The expression 10x^2 - 18x - 4 can be factored completely as: 10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

C.  the factoring from Part B is correct.

Part A: To find the greatest common factor of the expression 10x^2 - 18x - 4, we need to find the largest factor that divides all three terms of the expression evenly. One way to do this is to factor out the greatest common factor using the distributive property.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Now, we need to factor the expression inside the parentheses further to see if we can find any additional common factors.

5x^2 - 9x - 2 can be factored using the quadratic formula, but it does not have any common factors other than 1.

Therefore, the greatest common factor of the expression 10x^2 - 18x - 4 is 2.

Part B: To factor the expression completely, we can start by using the greatest common factor of 2.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Next, we need to factor the expression 5x^2 - 9x - 2 further. We can use the factoring method of product and sum:

The product of 5 and -2 is -10, and the sum of the factors that multiply to -10 and add to -9 is -10 and 1.

So, we can write 5x^2 - 9x - 2 as:

5x^2 - 10x + x - 2

= 5x(x - 2) + 1(x - 2)

= (5x + 1)(x - 2)

Therefore, the expression 10x^2 - 18x - 4 can be factored completely as:

10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

Part C: To check our factoring from Part B, we can multiply the factors using the distributive property and simplify:

2(5x + 1)(x - 2) = 2(5x)(x) + 2(5x)(-2) + 2(1)(x) + 2(1)(-2)

= 10x^2 - 20x + 2x - 4

= 10x^2 - 18x - 4

Therefore, the factoring from Part B is correct.

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Answer:

1. m ∠ 1 = 86°

  m ∠ 2 = 4°

- Problem in the picture

2. m ∠ 1 = 6°

   m ∠ 2 = 84°

Step-by-step explanation:

I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)

1.

m Z1 = (x+84)° and m2 = 2xº.

m ∠ 1 = (x + 84)°

m ∠ 2 = 2x°

Complementary angles are equal to 90°

(x + 84) + 2x = 90

x + 84 + 2x = 90

3x + 84 = 90

      -84    -84

----------------------

3x = 6

÷3  ÷3

-----------

x = 2°

m ∠ 1 = (x + 84)°

m ∠ 1 = (2 + 84)°

m ∠ 1 = 86°

m ∠ 2 = 2x°

m ∠ 2 = 2(2)°

m ∠ 2 = 4°

2. (Problem in the picture)

m ∠ 1 = (x - 6)°

m ∠ 2 = 7x°

Complementary angles are equal to 90°

(x - 6) + 7x = 90

x - 6 + 7x = 90

8x - 6 = 90

     +6    +6

---------------------

8x = 96

÷8    ÷8

----------------

x = 12

m ∠ 1 = (x - 6)°

m ∠ 1 = (12 - 6)°

m ∠ 1 = 6°

m ∠ 2 = 7x°

m ∠ 2 = 7(12)°

m ∠ 2 = 84°

I hope this helps!

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array.  In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.

given

Eigen values ( λ )

| A - λI | = 0

=  ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0

= λ = 7 , 11 , 11

eigen vector for λ = 7

( A - IB ) X = 0

= Let y = 1 , n1 = ( -1  1  0 )

eigen vector for λ = 11

( A - λI ) X = 0

n2 = ( 0 1 0 ) let n3= ( -2 0 1 )

D = ( 7 0 0 ,  0 11 0 , 0 0 11 )

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

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For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

Both equations in a system of linear equations have y-intercepts at (0,2) but it is not possible for this system to have only one solution because it depends on another point as well. Option C

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given :Both equations in a system of linear equations have y-intercepts at (0,2).

The following steps can be used in order to determine the system have only one solution or not:

According to the given data, both equations in a system of linear equations have y-intercepts at (0,2).

The equation of a line is given by: \(\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} - y_{1} }{x_{2} -x_{1} }\)

From the above steps, it can be concluded that it does not say that the system to have only one solution because it depends on another point as well.

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From linear equations solution, janeen will need to work total 22.699 hours per week for make equal the amount that shari makes in a week.

We two persons named janeen and shari.

number of hours worked by janeen in a week = 20 hours

Amount of money janeen earned after working 20 hours in a week = $24.92

Number of hours worked by shari in a week = 12 hours

Let Janeen make amount in dollars = $x per hour

Shari make amount in dollars= $y per hour.

According to seniror, 12y - 20x = $24.92 --(1)

Shari makes one dollar less than twice the amount that Janeen makes per hour

=> y = 2x - 1 ---- (2)

Now, we have to linear equations and we have to solve these for determining the values of x and y. So, substitute value of y from equation (2) in (1)

=> 12 (2x -1) - 20x = 24.92

=> 24x - 12 - 20x = 24.92

=> 4x = 24.92 + 12

=> 4x = 36.92

=> x = 9.23

Therefore, Janeen earns $9.23 per hour.

Then, y = 2x-1

=> y = 2× 9.23 -1

=> y= $17.46

Now, shari makes in a week = $17.46 × 12

=$209.52

Janeen makes in a week = 20× $9.23

= $184.6

Janeen need to work to equal the amount that shari makes in a week = \(\frac{209.52}{9.23}\)

= 22.699

Hence, required value is 22.699 hours.

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The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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9514 1404 393

Answer:

  see below

Step-by-step explanation:

We have elected to use a table, so that the rows and columns have labels that identify the table content. A matrix can be made from the data in the table.

Answer:

The sum of 25 and 16 is 41.

Step-by-step explanation:

The sum of two numbers, 25 and 16, you can break apart the addends and add them separately to simplify the process. Here's how you can do it:

Break apart the numbers into their place values: For 25, you have 20 and 5, and for 16, you have 10 and 6. This step helps you work with the place values individually.

Add the tens place: In this case, you have 20 (from 25) and 10 (from 16). Adding them gives you 30.

Add the ones place: Now you add the ones place, which is 5 (from 25) and 6 (from 16). Adding them gives you 11.

Combine the sum of the tens place and the sum of the ones place: Take the sum of 30 (from step 2) and 11 (from step 3). Adding them together gives you 41.

So, the sun is 41.

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Fisher's Exact Test is used when there are two independent samples of categorical data, and it is a valuable tool for analyzing small sample sizes where other tests may not be appropriate.

Fisher's Exact Test is used when there are two independent samples of categorical data. This test is specifically designed to determine if there is a significant association between two categorical variables in a 2x2 contingency table.

It is commonly used when the sample size is small, which can cause issues with other statistical tests such as the chi-square test.

The two independent samples refer to two different groups or populations that are being compared. For example, we might be interested in comparing the success rates of a new drug treatment versus a placebo in a clinical trial, where success and failure are the two categories being considered.

Fisher's Exact Test calculates the probability of observing the data given the null hypothesis of no association between the variables. It does this by considering all possible arrangements of the data that have the same marginal totals. If the calculated probability is very small (typically less than 0.05), we reject the null hypothesis and conclude that there is a significant association between the variables.

In summary, Fisher's Exact Test is used when there are two independent samples of categorical data, and it is a valuable tool for analyzing small sample sizes where other tests may not be appropriate.

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Rafe and Ashley used approximately 5353.2 square inches of canvas to make the lamp.

Let's call the length of the base rectangle "L" and the width "W." From the picture, we can see that the base rectangle measures 18 inches by 18 inches. Therefore, the area of one base rectangle is given by:

Area of a rectangle = Length × Width

Area of one base rectangle = L × W = 18 in × 18 in = 324 square inches

Since there are two identical base rectangles, the combined area of both rectangles is:

Total area of base rectangles = 2 × Area of one base rectangle = 2 × 324 square inches = 648 square inches

Let's calculate the perimeter of the base rectangle first:

Perimeter of a rectangle = 2 × (Length + Width)

Perimeter of the base rectangle = 2 × (18 in + 18 in) = 2 × 36 in = 72 inches

Now, the height of the triangular prism is given as 20.1 inches. Therefore, the area of each lateral face rectangle is given by:

Area of a rectangle = Length × Width

Area of one lateral face rectangle = Perimeter of base rectangle × Height = 72 in × 20.1 in = 1447.2 square inches

Since there are three identical lateral face rectangles, the combined area of all three rectangles is:

Total area of lateral face rectangles = 3 × Area of one lateral face rectangle = 3 × 1447.2 square inches = 4341.6 square inches

The height of the triangular face is the same as the height of the prism, given as 20.1 inches. Therefore, the area of each triangular face is given by:

Area of a triangle = (Base × Height) / 2

Area of one triangular face = (18 in × 20.1 in) / 2 = 181.8 square inches

Since there are two identical triangular faces, the combined area of both triangles is:

Total area of triangular faces = 2 × Area of one triangular face = 2 × 181.8 square inches = 363.6 square inches

Now, to find the total surface area of the lamp, we sum up the areas of all the faces:

Total surface area = Total area of base rectangles + Total area of lateral face rectangles + Total area of triangular faces

Total surface area = 648 square inches + 4341.6 square inches + 363.6 square inches

Total surface area = 5353.2 square inches

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Complete Question:

Marius and his dad build a lamp in the shape of a triangular prism, open on the top and bottom. How many square inches of canvas did Marius and his dad use to make the lamp?

Answer:

y=-2x-6

Step-by-step explanation:

Slope intercept form of a line: y=mx+b (m is the slope and b is the y-intercept)

Convert our given line 6x+3y=4 into slope-intercept form to find the slope

Subtract 6x on both sides

3y=-6x+4

Divide 3 on both sides

y=-2x+4/3

The slope of the given line is the coefficient of x, -2

Parallel lines have the same slope, so the equation we're solving for also has a slope of -2

We also know that the y-intercept is -6, so we now have all the info we need to make the equation:

y=-2x-6

Answer:

Step-by-step explanation:

Step one:

we are told that the expression for profit is

\(p = 1.25n - 475\)-----------------1

the above equation represents the situation

given

profit is  $950

Required

n=number of bars

950=1.25n-475

collect like terms

950-475=1.25n

475=1.25n

divide both sides by 1.25

n=475/1.25

n= 380candy bars

Answer:

(0, 13)

Step-by-step explanation:

The midpoint is halfway between the line segment. First find the distance from the starting point to the midpoint.

2-1 = 1. So Since the midpoint is behind the start point, we are going backwards (moving to the left on the x axis).

So 1 space left from the midpoint is 1-1=0.

For y, the distance between the start and mid is 6 - -1 = 6+1 = 7 spaces. Then add 7 spaces to the midpoint value of 6, so 7+6 = 13. We moved upwards on the y axis.

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Answer:

Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Answer:

\(x < 1\)

For any number to be less than the given number in an inequality, the number on the right side has to match up with the word problem given. The problem says the number was less than 8, and to get anything less than 8, you must multiply any number below 1 by that number.

According to the question we have  the correct answer is option 2, with a volume of 1664 cubic units.

The volume of the solid lying under the circular paraboloid z = x^2 + y^2 and above the rectangle R = (-4, 4] x [-6, 6] can be found using a double integral. First, set up the integral with respect to x and y over the given rectangular region:

Volume = ∬(x^2 + y^2) dA

To evaluate this integral, we will use the limits of integration for x from -4 to 4, and for y from -6 to 6:

Volume = ∫(from -4 to 4) ∫(from -6 to 6) (x^2 + y^2) dy dx

Now, integrate with respect to y:

Volume = ∫(from -4 to 4) [(y^3)/3 + y*(x^2)](from -6 to 6) dx

Evaluate the integral at the limits of integration for y:

Volume = ∫(from -4 to 4) [72 + 12x^2] dx

Next, integrate with respect to x:

Volume = [(4x^3)/3 + 4x*(72)](from -4 to 4)

Evaluate the integral at the limits of integration for x:

Volume = 1664

Therefore, the correct answer is option 2, with a volume of 1664 cubic units.

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Answer:

circumference of circle=2πr

hope it helps.

Answer:

1.4 cubic meters

Step-by-step explanation:

Answer:

69

Step-by-step explanation

you eat a subway sandwhich than poop it all out, and then you search up the answer and is 69!!!!! WOW!!!

The answer is: x-component of vector = 5.0 cm/s, y-component of vector = 0 cm/s.

The given vector v has an x-component of 5.0 cm/s and a y-component in the negative x-direction. Since the y-component is in the negative x-direction, it means the y-component is negative and has the same magnitude as the x-component.

Given vector v = (5.0 cm/s, −x-direction).

The vector is having magnitude 5.0 cm/s along the negative x-direction.

x-component of vector = 5.0 cm/s (magnitude of vector)v and y-component of vector is 0 since there is no component of v along y-axis.

Therefore, the x- and y-components of the vector v are 5.0 cm/s and 0 cm/s respectively.

Hence, the answer is: x-component of vector = 5.0 cm/s, y-component of vector = 0 cm/s.

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The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

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The square root of the quantity x plus 7 end quantity minus 1 equals x=2.

To find the square root:

Check for extraneous solutions:

Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.

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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x

Respuesta:

$ 52.5

Explicación paso a paso:

Dado

Costo de la chaqueta = $ 75

Mark off = 30%

Descuento = 30% de $ 75

Precio de descuento = 0,3 * 75

Precio de descuento = $ 22.5

Costo después de la venta = $ 75 - $ 22.5

Costo después de la venta = $ 52.5

Por lo tanto, el costo después de la venta es de $ 52.5

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

Given that,

Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.

Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.

(1) 3. 5 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

\(\frac{1}{2}\) hour = 1800 seconds

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

So,

We can write,

Distance = speed * time

3.5 * 1800 = 6300 meters    (Equation-1)

(2) 1. 6 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

\(\frac{1}{2}\) hour = 1800 seconds

So,

We can write,

Distance = speed * time

1.6 * 1800 = 2880 meters       (Equation-2)

Then,

We can add the equation - 1 and 2,

= 6300 meters + 2880 meters  

= 9180 meters

Therefore,

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

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Hi :)

15x^12/18x^2

Factor 3 out of 15 and 18

3(5x^12)/3(6x^2)

Divide

5x^10/6

Answer:

\( \frac{15 {x}^{12} }{18 {x}^{2} } \\ \frac{15}{18} \times \frac{ {x}^{12} }{ {x}^{2} } \\ \frac{5}{6} \times {x}^{12- 2} \\ \frac{5}{6} \times {x}^{10} \\ \frac{5 {x}^{10} }{6} \)

The approximate solution to the equation ex = x² - 1 is x ≈ 2.54, rounded to two decimal places. The correct option is (2.54).

To solve the equation `ex = x² - 1` using a graphing calculator, follow these steps:

1. Enter the equation into the calculator: `y1 = ex - x^2 + 1`.

2. Graph the equation to visualize its behavior.

3. Look for the points where the graph of the equation intersects the x-axis, which correspond to the solutions of the equation.

Using a graphing calculator or software, we can plot the equation `y = ex - x² + 1` and find its x-intercepts. The x-values of the intercepts are the solutions to the equation.

After performing the calculations, the approximate solutions to the equation are x ≈ 2.54, x ≈ -1.15, and x ≈ -0.71.

Therefore, the correct answer is (2.54).

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Answer:  resultant

Step-by-step explanation:

The total surface area of the triangular prism is 680 cm².

To find the total surface area of the triangular prism with dimensions 30

cm, 18 cm, 7 cm, and 24 cm, follow these steps:

Identify the dimensions: The base of the triangular prism is a triangle with

sides 30 cm, 18 cm, and 24 cm. The height of the prism is 7 cm.

Calculate the area of the triangular base: Use Heron's formula to find the

area of the triangle. First, find the semi-perimeter (s) of the triangle:

s = (30 + 18 + 24) / 2 = 72 / 2 = 36 cm.

Apply Heron's formula: Area = √(s(s - a)(s - b)(s - c)), where a, b, and c are

the side lengths of the triangle.

Area = √(36(36 - 30)(36 - 18)(36 - 24)) = √(36 × 6 × 18 × 12) = √31104 = 176 cm².

Calculate the area of the three rectangular faces: The three rectangular

faces have dimensions 30 cm x 7 cm, 18 cm x 7 cm, and 24 cm x 7 cm.

Find their areas by multiplying the dimensions:

30 × 7 = 210 cm², 18 × 7 = 126 cm², and 24 × 7 = 168 cm².

Add the areas of all the faces together: Add the triangular base area and

the areas of the three rectangular faces to find the total surface area:

176 cm² (base) + 210 cm² + 126 cm² + 168 cm² = 680 cm².

The total surface area of the triangular prism is 680 cm².

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By dοing the mental math, the summatiοn is 300.

Use mental math: If the numbers are small, yοu can add them up in yοur head.

Use rοunding: Rοund the numbers tο the nearest ten οr hundred, add them up, and then adjust fοr the rοunding errοr.

We can grοup the numbers in pairs with οne easy-tο-add number and οne slightly harder-tο-add number: (39+61) + (87+13) + 62 + 38

We can simplify this further: 100 + 100 + 62 + 38

Nοw we can add the remaining numbers easily: 200 + 100

Sο the final οrder in which we cοuld mοst easily add the numbers is: (39+61) + (87+13) + 62 + 38 = 200 + 100 = 300

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