Diego wants to survey a sample of students at his school to learn about the percentage of students who are satisfied with the food in the cafeteria. He decides to go to the cafeteria on a Monday and ask the first 25 students who purchase a lunch at the cafeteria if they are satisfied with the food. Do you think this is a good way for Diego to select his sample? Explain your reasoning.

Answer:

2(x−2)(x+3)

Step-by-step explanation:

2x^2+2x−12

=2(x−2)(x+3)

2(x-2)(x+3) is your answer :)

Solve the equation by replacing x with -7 and then -1.

Then subtract the two to find the difference and divide that by the difference between -7 and -1.

f(-7) = -7^2 + 2(-7) -8 = 49 -14 -8 = 27

f(-1) = -1^2 + 2(-1) -8 = 1 -2 - 8 = -9

Difference between 27 and -9 = -36

Difference between -1 and -7 = -6

Rate of change = -36 /-6 = 6

Answer:

[tex]\$11.13[/tex]

Step-by-step explanation:

step 1

Find the surface area of the cylinder

The surface area of the cylinder is equal to

[tex]SA=\pi r^{2} +2\pi rh[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=5\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]SA=(3.14)(1.5)^{2} +2(3.14)(1.5)(5)=54.165\ in^{2}[/tex]

Find the cost

[tex]54.165*(0.75)=\$40.62[/tex]

step 2

Find the surface area of the square prism

The surface area of the prism is equal to

[tex]SA=b^{2} +4bh[/tex]

we have

[tex]b=3\ in\\ h=5\ in[/tex]

substitute

[tex]SA=(3)^{2} +4(3)(5)=69\ in^{2}[/tex]

Find the cost

[tex]69*(0.75)=\$51.75[/tex]

step 3

Find the difference of costs

[tex]\$51.75-\$40.62=\$11.13[/tex]

Answer:

1510 vehicles

Step-by-step explanation:

First you need to determine how many feet cars and trucks occupy.

In 5 miles:

Cars fill up 80%     = 0.80 x 5 miles = 4 miles

Trucks fill up 20%  = 0.20 x 5 miles = 1 mile

Because we know the lengths and distances of the cars and trucks in feet, let's convert the miles they cover into feet.

Cars = 4 miles x 5280 ft/mile = 21,120 ft

Trucks = 1 mile x 5280 ft/mile =  5280 ft

So how many cars would there be if they covered at least 21,120 ft?

Considering that there is 3 ft between each car and a car has a length of 13.5 ft, a single car will cover 16.5 ft.

To see how many cars then fit in 21,120 ft, just divide it by the distance one car covers.

[tex]\dfrac{21,120ft}{16.5 ft/car} = 1,280 cars[/tex]

So how many trucks would there be if they covered at least 5,280 ft?

A truck is 20 ft long and again there is a space of 3 ft in between. So we add that up to see how many feet a single truck needs.

20 ft + 3 ft = 23 ft

We then take that total and divide the feet covered by trucks.

[tex]\dfrac{5,280ft}{23ft/truck}= 229.57 trucks[/tex]

Since we cannot have half a truck, we round that off to the nearest whole number which will be 230 trucks.

So we add the number of trucks and cars to get the number of vehicles in total:

1280 + 230 = 1,510 vehicles

Answer:

Skewed to the right

Step-by-step explanation:

As we can see in the table, the first three intervals have smaller frequency and last 4 intervals have higher frequency values. When the class intervals and frequency will be plotted on graph while taking class intervals on x-axis and frequency at y-axis, the graph will be skewed to the right because of the larger frequency values in the last intervals..

Answer: The line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Step-by-step explanation:

By definition, a line intersects the y-axis when the value of "x" is zero ([tex]x=0[/tex]), then if the y-intercept  is 1, then the point where the line intersects the y-axis is:

(0,1)

By definition, a line intersects the x-axis when the value of "y" is zero ([tex]y=0[/tex]), then if the x-intercept  is -7, then the point where the line intersects the x-axis is:

(-7,0)

Therefore, now you know this, you can graph a line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Answer:

Check the attached graph

Step-by-step explanation:

Given that y-intercept is 1.

That means graph passes through the point (0,1).

Given that x-intercept is -7.

That means graph passes through the point (-7,0).

Now we need to graph the line using above information. So begin by graphing both points .

Now draw a line joining both points to get the final graph.

Answer:

7.5 ab and cd

4 bd and ac

Step-by-step explanation:

Answer:

i believe the answer is 7.5 ab and cd, 4 bd and ac

Answer:

A. 2x^5y^8 and 12xy^7

Step-by-step explanation:

The question is on laws of indices

when we have x^a × x^b = x^(a+b)

Given in the question 24x^6y^15

24 could be 2×12............for the length and width

Then x^6 = x^1 × x^5 = x^(1+5) = x^6

And  y^15 = y^8 ×y^7 = y^(8+7) = y^(15)

Answer:

The correct answer is :[tex]l=2x^5y^8,w = 12xy^7[/tex]

Step-by-step explanation:

Let the dimension of the rectangle be l and w.

A = [tex]24x^6y^{15}[/tex]

[tex]24x^6y^{15}=l\times w[/tex]

A) If the dimension are :

[tex]l=2x^5y^8,w = 12xy^7[/tex]

Area of the rectangle

[tex]= 2x^5y^8\times 12xy^7=24x^6y^{15}=A[/tex]

B) If the dimension are :

[tex]l=6x^2y^3,w = 4x^3y^5[/tex]

Area of the rectangle

[tex]= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A[/tex]

C) If the dimension are :

[tex]l=10x^6y^{15},w = 14x^6y^{15}[/tex]

Area of the rectangle

[tex]= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A[/tex]

D) If the dimension are :

[tex]l=9x^4y^{11},w = 12x^2y^4[/tex]

Area of the rectangle

[tex]= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A[/tex]

If you divide any number by 1, the answer is itself. The answer is 7 and 1/2.

Hope this helps!

Answer:

7 1/2

Step-by-step explanation:

Take it like the following scenario.

There are 7 1/2 M&M's left in a bag.

Neither of your friends want any so you get to have all of them.

So, the 7 1/2 M&M's divided by one person is 7 12 since all of the M&M's go to you.

[Rememember that any number you divide by 1, the answer is itself

Ex: 4 divided by 1 = 4]

I hope this helps!

The paddle wheel takes approximately 967 seconds to complete 100 full revolutions.

To calculate the time it takes for the paddle wheel to complete 100 full revolutions, we need to determine the distance traveled by the fins and divide it by their speed. The diameter of the paddle wheel is given as 4 feet, so the radius is half the diameter, or 2 feet. The distance traveled by one fin along the outer edge is equal to the circumference of a circle, which is 2π times the radius. In this case, the distance is 2π * 2 feet, or approximately 12.57 feet.

Since we want to find the time it takes for 100 full revolutions, we need to multiply the distance traveled by one fin by 100. So the total distance is 12.57 feet * 100, which equals 1257 feet.

Now we can divide the total distance by the speed of the fins to find the time it takes. The speed is given as 1.3 feet per second, so the time is 1257 feet divided by 1.3 feet per second, which is approximately 967 seconds. Rounding to the nearest second, it takes the paddle wheel approximately 967 seconds to complete 100 full revolutions.

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The paddle wheel takes approximately 392 seconds to complete 100 full revolutions.

To find the time it takes for the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the wheel and divide it by the speed at the outer edge.

The circumference of the wheel is the diameter (4 feet) times π. So, the circumference is 4π feet.

Dividing the circumference by the speed of the fins (1.3 feet per second) gives us the time it takes for one revolution. To find the time for 100 revolutions, we multiply this time by 100 and round to the nearest second.

Therefore, the paddle wheel takes approximately 392 seconds to complete 100 full revolutions.

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Answer:

Leah has 48 marbles.

Step-by-step explanation:

Represent the number of marbles that each person has by L and D.

Leah has 28 more marbles than Dan:  L = D + 28.

Then (1/3)L = (4/5)D.  Here the LCD is 15, and so multiplying this equation by 15 will remove the fractions:  15(1/3)L = 15(4/5)D.  

Therefore, 5L = 12D, and D = 5L/12.

Then, since L = D + 28,        L = (5/12)L + 28, or

12L = 5L + 336, or

7L = 336, or

L = 336/7 = 48.

Leah has 48 marbles.  That means that Dan has 20 marbles.

The number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

Let x be the number of marbles Leah has.

Let y be the number of marbles Dan has.

Leah has 28 more marbles than Dan:  

x = y + 28

(1/3)x = (4/5)y

Solving above two linear equation, we get:

5x = 12y

5(y + 28) = 12y

5y + 140 = 12y

12y - 5y = 140

7y = 140

y = 140/7 = 20

x = 20 + 28 = 48

Thus, the number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

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Like $45.95 I think I’m sorry if you get it. Wrong

The question is based on exponential growth, the worker will be earning an hourly wage of $10.00 after approximately 5.9 years of receiving a 4% annual raise.

The subject of this problem is exponential growth, which is based on the formula y = a(1 + r)^t, where a is the initial amount, r is the rate of growth (expressed as a decimal), and t is the time period. In this case, your initial wage (a) is $7.95 per hour and the rate of growth (r) is 4% or 0.04. The future wage (y) is $10.00 per hour. So, the equation becomes:
10 = 7.95 * (1.04 ^t).
To solve for 't', you first divide both sides by 7.95 to isolate (1.04 ^t) on one side, resulting in 1.26 = (1.04 ^t).
You then take the natural logarithm (log base e, also represented as 'ln') of both sides of the equation to eliminate the exponential, resulting in ln(1.26) = t * ln(1.04).
Finally, you divide both sides by ln(1.04) to solve for 't', resulting in an approximate value of 't' as 5.9 years.
Therefore, the worker will be earning $10.00 per hour approximately after 5.9 years.

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Employers frequently offer full-time employees benefits such as health insurance, retirement plans like 401(k)s, life insurance, paid vacation, and tuition reimbursement, in addition to legally required contributions to Social Security and unemployment insurance.

Employers often provide a range of benefits to their full-time employees beyond the usual salary. Common benefits include:

Health insurance, which helps cover medical expenses that are not covered by public health care plans.

Retirement plans, such as a 401(k) plan where employees can have a portion of their salary deducted and invested for retirement, often with some form of employer match.

Life insurance, offering financial security to an employee's beneficiaries in the event of their passing.

Paid vacation, allowing employees to have paid time off from work.

Tuition reimbursement programs, where employers provide financial support to employees who pursue further education.

These benefits are crucial as they provide a sense of security and support employees’ work-life balance, health and welfare, and professional development.

In addition to these, employers are required by law to make contributions towards legally required benefits such as Social Security, unemployment, and worker's compensation insurance. Some employers may offer additional perks like telecommuting options or employee assistance programs. However, benefits like free gasoline, rent, or sabbaticals are less common and tend to be specific to certain companies or industries.

Answer: Sample B: A random sample of 100 customers leaving a store

Step-by-step explanation: In mathematics and especially when gathering data, you will gather the most accurate results with a larger portion. The larger portion will ensure a more accurate reading.

[tex] \frac{8}{t} + 5 = t - \frac{3}{t} + 5 + \frac{1}{3} \\ \\ 1. \: \frac{8}{t} = - \frac{3}{t} + \frac{1}{3} \\ \\ 2. \: 24 = 3t^{2} - 9 + t \\ \\ 3. \: 24 - 3t^{2} + 9 - t = 0 \\ \\ 4. \: 33 - 3t ^{2}- t = 0 \\ \\ 5. \: t = \frac{1 + \sqrt{397} }{ - 6} \: \frac{1 - \sqrt{397} }{ - 6} \\ \\ 6. \: t = - \frac{1 + \sqrt{397} }{6} \: - \frac{1 - \sqrt{397} }{6} [/tex]

Answer:

Final answer is t=7.

Step-by-step explanation:

[tex]\frac{8}{t+5}=\frac{t-3}{t+5}+\frac{1}{3}[/tex]

[tex]=\frac{8}{t+5}\cdot3\left(t+5\right)=\frac{t-3}{t+5}\cdot3\left(t+5\right)+\frac{1}{3}\cdot3\left(t+5\right)[/tex]

[tex]8\cdot3=3\left(t-3\right)+\left(t+5\right)[/tex]

[tex]24=3t-9+t+5[/tex]

[tex]24=4t-9+5[/tex]

[tex]24=4t-4[/tex]

[tex]24+4=4t[/tex]

[tex]28=4t[/tex]

[tex]\frac{28}{4}=t[/tex]

[tex]7=t[/tex]

[tex]t=7[/tex]

Hence final answer is t=7.

Answer:

Can I see the options because the way the test worded this question is a bit confusing

Step-by-step explanation:

R; all quadratic functions are going to have *ALL REAL NUMBERS*.

Altitude is how high or low you are in relation to sea level, while temperature is how hot or cold it is. Altitude often effects the temperature. As high altitude places are usually get cold.

Hope this helps!

Answer:

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Step-by-step explanation:

we know that

The equation of the given parabola is

[tex](y-k)=a(x-h)^{2}[/tex]

we have

the vertex is the point (5,-4)

substitute

[tex](y+4)=a(x-5)^{2}[/tex]

The y-intercept is the point (0,96)

substitute and solve for a

[tex](96+4)=a(0-5)^{2}[/tex]

[tex]100=a(25)[/tex]

[tex]a=100/25=4[/tex]

The equation of the vertical parabola is equal to

[tex](y+4)=4(x-5)^{2}[/tex]

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

[tex]4=4(x-5)^{2}[/tex]

Simplify

[tex]1=(x-5)^{2}[/tex]

Rewrite

[tex](x-5)^{2}=1[/tex]

square root both sides

[tex](x-5)=(+/-)1[/tex]

[tex]x=(+/-)1+5[/tex]

[tex]x=(+)1+5=6[/tex]

[tex]x=(-)1+5=4[/tex]

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Answer:

$16,384

Step-by-step explanation:

The amount of money Nadir saves increases exponentially by a factor of 2. If you keep multiplying each previous number by 2 until you get to the 15th number, (2*2, 4*2, 8*2, 16*2), you will get 16,384.

Answer:

$16,384

Step-by-step explanation:

Let's find the general equation for his savings:

The first day he saves $1 = [tex]2^{0}[/tex]

The second day, $2 = 1*2 = [tex]2^{1}[/tex]

The third day, $4 = 1*2*2 = [tex]2^{2}[/tex]

The fourth day, $8 = 1*2*2*2 = [tex]2^{3}[/tex]

In general, in the n-th day, he saves [tex]2^{n-1}[/tex]

With this, we can calculate the amount that he will save on the fifteenth day:

[tex]2^{15-1} = 2^{14} = \$16,384[/tex]  

Answer:

1.8, -2.8

Step-by-step explanation:

1.8, -2.8 in decimal form rounded to the nearest tenth.

In quadratic form its originally [tex]x=\frac{-1+\sqrt{21} }{2} ,\frac{-1-\sqrt{21} }{2}[/tex]

Hope this helps

Answer:

13. B) You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.

14. A) 1/2.

How this helps you! (:

-Hamilton1757

Answer:

13. Option 1

14. Option 2 : 1/4

Step-by-step explanation:

13. First option is correct.

If two marbles are drawn from a bag without replacement then the second event will depend upon the first event i.e. the occurrence of first event will affect the occurrence of second event.

14. If two coins are tossed, the outcomes are

S = {HH, HT, TH, TT}

There is only one outcome that favors the given scenario i.e. first coin showing heads and second showing tails.

So, probability of showing heads first and then second showing tails = 1/4

So second option is correct..

Answer:

$106,147

Step-by-step explanation:

The price of the house is $160,000. The value of the house is going down by 5% each year, and we need to find the price of the value after 8 years.

Year 0:

$160,000

Year 1:

$160,000×0.95 = $152,000

Year 2:

$152,000×0.95 = $144,400

Year 3:

$144,400×0.95 = $137,180

Year 4:

$137,180×0.95 = $130,321

Year 5:

$130,321×0.95 = $123,804.95

Year 6:

$123,804.95×0.95 = $117,614.7025

Year 7:

$117,614.7025×0.95 = $111,733.967375

Year 8:

$111,733.967375×0.95 = $106,147.26900625  ≈  $106,147

Therefore, the correct answer is the second ONE. ✔️✔️

Answer:

x ≈ 9.2

Step-by-step explanation:

When 2 chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

5x = 9 × 5.1 = 45.9 ( divide both sides by 5 )

x ≈ 9.2

A. Traffic on the side with the broken yellow line. The dashes signify the “openness” of the ability that the drivers on that side have to pass.

Answer:

A). Traffic on the side with broken yellow line

Step-by-step explanation:

A solid yellow line used in two lane roadways where passing or crossing is strictly prohibited. It is dangerous and may lead to serious accidents while violating this.

                             On the other hand, broken yellow line on the roadways indicates that vehicles moving can pass or cross the road when only it is safe to cross the lane.

Therefore, when the center line is one solid yellow line and one broken yellow line, then the vehicles on the side of the broken lines may cross the line to pass only when it is safe to cross.

Answer:

The best possible answer is A

Step-by-step explanation:

Answer:

Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Step-by-step explanation:

Given:

Radius of the Cylinder , r = 11 in.

Height of the Cylinder , h = 13 in.

We have to find the Surface Area of Cylinder to the nearest Whole number.

We know that,

Surface Area of the Cylinder = 2πr(r+h)

                                                 = 2 × 22/7 × 11 ( 11 + 13 )

                                                 = 2 × 22/7 × 11 × 24

                                                 = 1659.42 in.²

                                                 = 1659 in.²  (nearest whole number)

Therefore, Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Answer:

The equation of the hyperbola is x²/16 - y²/9 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

- The length of the transverse axis is 2a

- The coordinates of the vertices are (±a , 0)

- The length of the conjugate axis is 2b

- The coordinates of the co-vertices are (0 , ±b)

- The coordinates of the foci are (± c , 0),  

- The distance between the foci is 2c where c² = a² + b²

- The distance between the vertex and the focus in-front of it is c - a

* Now lets solve the problem

- The distance from a vertex to the center of the mirror

∵ The vertex of the mirror is (a , 0)

∵ The distance between a vertex and the center of the mirror

  is 4 inches

∴ a = 4

∵ The distance between the vertex and a focus in front of  the surface

  of the mirror is 1

∵ The distance between the vertex and the focus in-front of it is c - a

∴ c - a = 1

∴ c - 4 = 1 ⇒ add 4 to the both sides

∴ c = 5

- The mirror has a horizontal transverse axis and the hyperbola is

 centered at (0, 0)

∴ The equation of the hyperbola is x²/a² - y²/b² = 1

- Lets find b from a and c

∵ c² = a² + b²

∵ c = 5 and a = 4

∴ (5)² = (4)² + b²

∴ 25 = 16 + b² ⇒ subtract 16 from both sides

∴ 9 = b² ⇒ take √ for both sides

∴ b = ±3

- Lets write the equation

∴ x²/(4)² - y²/(3)² = 1

∴ x²/16 - y²/9 = 1

* The equation of the hyperbola is x²/16 - y²/9 = 1

The distance of the focus from the center is the sum of the distance from

the focus to the surface and the vertex distance.

Correct response:

Given:

Distance of the vertex from the center = 4 inches

Distance of the focus from the mirror surface = 1 inches

Coordinates of the center of the mirror = (0, 0)

Required:

To write the equation of the hyperbola that can be used to model the mirror

Solution:

The equation of an hyperbola having an horizontal transverse axis is presented as follows;

Where;

(h, k) = The coordinate of the center

a = Center to vertex distance

b² = c² - a²

Where;

c = The from the center to the vertex

Therefore;

a = 4

(h, k) = (0. 0)

c = 4 + 1 = 5

b² = 5² - 4² = 9

b = √9 = 3

The equation of the hyperbola is therefore;

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Answer:

Second option: [tex]x + x + 18[/tex]

Step-by-step explanation:

You know that "x" represents the Avery's weigth (in pounds).

Let be "y" the weight of Jada in pounds.

Since Jada weighs 18 pounds more than Avery, you can write this expression:

[tex]y=x+18[/tex]

The weight of them together is:

[tex]weight\ together=x+y[/tex]

Substituting, you get:

[tex]weight\ together=x+x+18[/tex]

Therefore, the expression that tells how much the two of them weigh together is the one provided in the second option:

[tex]x + x + 18[/tex]

Answer:

$2000

Step-by-step explanation:

the profit would be determined by how many computers are involved, so that would vary

Answer:

2000

Step-by-step explanation: