The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answer:c 20

Step-by-step explanation:

Answer:

x = - 4

Step-by-step explanation:

Since we are looking at a circle, we know that the sum of all arc angles should add up to 360°. This means that the following...

- 32x - 3 = 360 - 85 - 35 - 115

- 32x - 3 = 125

- 32x = 125 + 3

- 32x = 128

x = 128 / (-32)

x = - 4

Answer:

20x + 8

Step-by-step explanation:

5*4x + 5*5 -17

20x +25 -17

20x + 8

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Answer: Answer choice C: -1.3 and 1.3.

Step-by-step explanation:

We can start by using the formula for the distance, D, between the two trains as a function of time, T:

D = 55(T + 2.25) - 120T

Simplifying this equation, we get:

D = 55T + 123.75 - 120T

D = -65T + 123.75

To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:

40 = -65T + 123.75

-85 = -65T

T = 1.31

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.31) + 123.75

D = 40.0375

Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:

40 = -65T + 123.75

-83.75 = -65T

T = 1.29

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.29) + 123.75

D = 40.0375

Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.

Answer:

20 blue beads........20 black beads

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

x=-2

Step-by-step explanation:

subtract 8 from both sides you get -4x=-8

divide by -4

you get x=-2

Answer:

1 real solution, x=2

Step-by-step explanation:

Let's solve for x and see how many solutions exist.

To solve for x, we must get x isolated. To do this, perform the inverse operation to both sides of the equation.

8-4x=0

4x is being subtracted from 8. The inverse, or opposite, of subtraction is addition. Add 4x to both sides.

8-4x+4x=0+4x

8=0+4x

8=4x

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

8/4=4x/4

8/4=x

2=x

x is equal to 2, therefore there is 1 real solution.

Alice is a mathematics major and a computer science major can be classified as an invalid argument

An argument can be invalid even if the conclusion and the premises are all actually true

According to the statement that Alice is a mathematics major. Therefore, Alice is a mathematics major and a computer science major is an invalid argument since a course that can have a combination of math and computer science.

Hence Alice is a mathematics major. Therefore, Alice is a mathematics major and a computer science major can be classified as an invalid argument

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Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Answer:

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

both the numerator and denominator can be divided by 2

6/2=3

8/2=4

so 6/8 in lowest terms is 3/4

Answer:

124

Step-by-step explanation:

350 times 35.5% = 124.25 and obviously .25 of a person cant go to a movie so you round down to 124.

Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:

50 + 2.5r

Step-by-step explanation:

Answer:

A-  

✔ 50 + 2.5r

Step-by-step explanation:

EDG2021

The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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Answer:

2 years

Step-by-step explanation:

3% of $550 = 0.03 * $550 = $16.50

3% interest on $550 for 1 year is $16.50

$33/$16.50 = 2

Since 2 * $16.50 = $33, the loan was for 2 years.

Answer:

F

Step-by-step explanation:

Person's diastolic blood pressure at 6:00am is  94.5 mmHg.

Diastolic blood pressure is the lower number in a blood pressure reading. It indicates the pressure in the arteries when the heart muscle is resting between beats and refilling with blood. A normal diastolic blood pressure is between 80 and 90 mmHg (millimeters of mercury).

For example, if a person's blood pressure reading is 120/80 mmHg, the diastolic blood pressure is 80 mmHg. This means that the pressure in the arteries when the heart is at rest is 80 mmHg. High diastolic blood pressure (greater than 90 mmHg) is a risk factor for heart attack, stroke, and other cardiovascular problems.

The formula for diastolic blood pressure at time t is given by B(t) = 90 + 9 sin(t/12). To find the diastolic blood pressure at 6:00am, need to plug in t = 6 into the formula.

B(6) = 90 + 9 sin(6/12) = 90 + 9 sin(0.5) = 90 + 9(0.4794) = 94.5 mmHg.

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By solving a linear equation for the concentration we will see that the guy needs to use 18 ounces.

We know that the guy used 10 ounces of 6% solution with x ounces of a 12% solution to make a 8% solution, then we can write the concentration equation:

0.06*12 + 0.12*x = (12 + x)*0.08

So we just need to solve a linear equation for x.

0.06*12 + 0.12*x = (12 + x)*0.08

0.06*12 + 0.12*x = 12*0.08 + x*0.08

0.12*x - 0.08*x = 12*0.08 - 0.06*12

0.04*x = 0.06*12

x = 0.06*12/0.04 = 18

Which means that the guy needs to use 18 ounces of the 12% substance.

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The vertices of the feasible region is (4, 3)

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

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

4 x + 8 = negative 24 , 9 x + 18 = negative 24 are  equations have the same value of x .

What in mathematics is a linear equation?

A - 4 x + 8 = negative 24

E - 4 x = negative 32

ARE CORRECT ON EDGE.

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The complete question is-

Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.

4 x + 8 = negative 24

9 x + 18 = negative 24

4 x = negative 16

StartFraction 18 x + 36 over 2 EndFraction = negative 24

4 x = negative 32

The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.

A linear function containing one dependent and one independent variable.

It can be represented using the equation,

y = mx + c

where m is the slope

It is given in the question that,

Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.

After 4 seconds of driving, she was 70 meters away from the safe zone.

Let, D(t) be the distance to the safe zone (measured in meters) and t be the  time (measured in seconds)

After 4 seconds of driving, she was 70 meters away from the safe zone.

⇒ This means that at t = 4 seconds, D(4) = 70 meters

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative

⇒ m = - 24

y = mx + c

⇒ D(t) = (-24)t + c

Put t = 4,

D(4) = (-24)4 + c

70 = -96 + c ⇒ c = 166

⇒ D(t) = 166 - 24t

Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.

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If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~