Write an equation for the function f (x) that has roots of 3, -4, and -1 and a leading coefficient of 2.

Answer:

75/7

Step-by-step explanation:

5/7 x 15

5/7 x 15/1

5 x 15 / 7 * 1

75/7

Hopefully this helps!

Brainliest please?

The simplified form of the expression is 75/7.

A fraction describes a part of a whole.

Given an expression 15x5/7

Solving the expression we get,

15x5/7

= 75/7

Hence, the expression 15x5/7 = 75/7

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Answer:

3.6

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

see attached image

Answer:

Not solutions.

Step-by-step explanation:

-5x+6y=-5

6y=-5+5x

6y=5x-5

y=5/6x-5/6

-5/6 is about -0.833

And the slope is 5/6.

So for every x there is 5/6y.

This means (1, 4) won't work cause it's too low.

Also 5/6*6=5. this is too low too.

So they aren't solutions.

Answer:

5 times the quantity x plus 6

5x + 6

32 divided by the quantity y + 12

\(\frac{32}{y+12}\)

Step-by-step explanation:

Pls do mark me brainliest:)

The average number of gallons of fruit juice consumed per person in the country in​ 2006 is 7.8 gallons.

Given:

Total consumption of fruit juice in a particular country in 2006 was about 1.56 billion gallons.

The population of that country in 2006 was 200 million.

Average number of gallons = Total consumption of fruit juice in 2006 / Population in 2006.

= 1.56 billion gallons / 200 million

= 7.8 gallons.

Therefore The average number of gallons of fruit juice consumed per person in the country in​ 2006 is 7.8 gallons.

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The function that models the cone's height as a function of its volume is; h = 3V/28²π.

Since Volume, V is given by the formula;

To determine a function that models the cone's height as a function of its volume; we must evaluate as follows;

As such, when the volume of the cone is 5488π cm3;

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The coordinates of the midpoint M of the segment FG is (-2,2).

This question is incomplete, the complete question is;

What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point F (-7, 12)

Point G (3,-8)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )

M = ( ( -4 )/2, ( 12 - 8 )/2 )

M = ( ( -4 )/2, ( 4 )/2 )

M = ( -2, 2 )

Therefore, the  midpoint M of the segment is (-2,2)

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Answer:

10,101

Step-by-step explanation:

Percent (%) means 'out of one hundred'

29.5%= 29.5/100 'out of one hundred'

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

How to increase the number 7,800

by 29.5% of it's value?

1.) Calculate the new value of the number increased by the percentage of it's initial value

The new value=

7,800+ The value of the percentage increase=

7,800 + (29.5% x 7,800) =

7,800 + 29.5% x 7,800=

(1 + 29.5%) x 7,800=

(100% + 29.5%) x 7,800=

129.5% x 7,800

129.5 ÷ 100 x 7,800=

129.5 x 7,800 ÷ 100=

1,010,100 ÷ 100=

10,101

-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-

I hope this was helpful!

If the summation of residual equals zero for the simple linear model, then it does not imply the summation of random errors and the expectation of the summation of random errors in the model equal to zero. Because both are independent factors.

The information is about linear regression. The summation of residual equals zero in case of the simple linear model. The sum of all the residuals is the multiplcation of expected value tothe total no of data points. Subsequently the expectation of residuals is 0, the sum of all the residual terms is zero. The summation of residuals equals zero for the simple linear model. This however doesn't mean that the random error summations are zero. The summation of residuals goes to zero only because of the equivalence of negative and positive residuals, i.e., the values have residues on both negative and positive sides equally. The summation of random errors cannot be zero as the errors are present in the system and are independent, unlike the residuals. Thus, the expectation of the summation of random errors can be zero or non-zero as they are independent factors and are unknown to the observer.

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

a. Probability of a standard normal variable being between 0 and 0.60 is 0.2257.

b. Probability of a standard normal variable being between -1.65 and 0 is 0.4505.

c. Probability of a standard normal variable being greater than 0.30 is 0.3821.

d. Probability of a standard normal variable being greater than or equal to -0.35 is 0.6368.

e. Probability of a standard normal variable being less than 2.03 is 0.9798.

f. Probability of a standard normal variable being less than or equal to -0.80 is 0.2119.

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

a. P(0 ≤ z ≤ 0.60) = 0.2257

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being between 0 and 0.60 is 0.2257.

b. P(-1.65 ≤ z ≤ 0) = 0.4505

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being between -1.65 and 0 is 0.4505.

c. P(z > 0.30) = 0.3821

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being greater than 0.30 is 0.3821.

d. P(z ≥ -0.35) = 0.6368

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being greater than or equal to -0.35 is 0.6368.

e. P(z < 2.03) = 0.9798

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being less than 2.03 is 0.9798.

f. P(z ≤ -0.80) = 0.2119

Using a standard normal table or calculator, we can find that the probability of a standard normal variable being less than or equal to -0.80 is 0.2119.

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The growth factor in the function is 5.

An exponential function with the form A(t) = \(C a^t\), where a > 0

When t = 0, the function's initial value is represented by the number C, and the growth (or decay) factor is represented by the number a.

If a > 1, the function represents growth; If 0 < a < 1, the function represents decay.

Given:

y = 4 x \(5^7\\\)

we know the general form of Exponential function

g(x) = \(ab^x\)

where a is the initial amount

b is the growth or decay factor

and, x is the time

Now, comparing to the given function

Initial amount= 4

Growth factor = 5

time = 7

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well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

Density = mass / volume

We are given the mass of the liquid, which is 53.64 grams. We also know that the volume of the liquid is 18.0 milliliters.

However, we need to take into account the temperature of the liquid to determine its density at 15°C. The density of liquids typically changes with temperature.

Assuming that we know the density of the liquid at some other temperature, we can use the following formula to adjust the density to 15°C:

Adjusted Density = Measured Density / [1 - (T2 - T1) * Coefficient]

where:

Measured Density is the density of the liquid at some known temperature

T1 is the known temperature in Celsius

T2 is the desired temperature in Celsius (in this case, 15°C)

Coefficient is the coefficient of thermal expansion for the liquid

The coefficient of thermal expansion varies depending on the specific liquid. For water, which has a coefficient of thermal expansion of 0.00021 per degree Celsius, the adjusted density formula becomes:

Adjusted Density = Measured Density / [1 - (T2 - T1) * 0.00021]

Assuming that the liquid in question has a coefficient of thermal expansion similar to that of water, we can use this formula to adjust the density to 15°C.

Density = mass / volume = 53.64 g / 18.0 mL = 2.98 g/mL

Using the adjusted density formula:

Adjusted Density = 2.98 / [1 - (15 - 20) * 0.00021] = 2.98 / [1 - (-0.00105)] = 2.982 g/mL

Therefore, the density of the liquid at 15°C is approximately 2.982 g/mL.

Answer:

height = 8/3

Step-by-step explanation

I'm assuming that this is a question to a triangle. So since an area of a triangle is 12 you solve by the formula 1/2(base)(height). You would solve for height so your equation would look smth like this: 12 = 1/2(base)(height). So you would end up with 24/8 which would simplify to 8/3.

Answer:

about $2.31 per pound

Step-by-step explanation:

35.99/15.6 = 2.30705128205

2.31

Have a good day! :)

Answer:

Solutions given:

Velocity ratio V.R =5

effort =500N

efficiency =80%

magnitude of load=?

mechanical advantage [M.A ]

we have

efficiency =M.A/V.R*100%

80=M.A./5*100

80/100*5=M.A

M.A.=4

again

we have

M.A =load/effort

4=load/500

load=500*4

load=2000N

Answer:

x = 17

Step-by-step explanation:

(5x-23) + (7x-1) = 180

12x - 24 = 180

12x = 204

x = 17

Answer:

x = 17

Step-by-step explanation:

The 2 given angles are same- side interior angles and sum to 180° , then

7x - 1 + 5x - 23 = 180

12x - 24 = 180 ( add 24 to both sides )

12x = 204 ( divide both sides by 12 )

x = 17

Answer:

x= -3

y= -4

Step-by-step explanation:

If 11/17 and x goes together then this is what I got.  Oh plug them in in case its wrong.  Good Luck

Answer:

450

Step-by-step explanation:

Answer:

If referring to surface area, it would be equal to 114 ft²

Step-by-step explanation:

Area = BH or LW

Multiply the two dimensions given

12 * 9.5 = 114

114 square feet

The given limit is lim x→-∞ (7/x - x/6). To evaluate this limit, we can simplify the expression by finding a common denominator.

Taking a common denominator of 6x, we get (42 - x^2) / (6x).

As x approaches negative infinity, both the numerator and denominator of the expression tend to infinity. However, the denominator grows faster than the numerator because of the x^2 term. This means that the fraction approaches zero as x approaches negative infinity.

Therefore, the limit lim x→-∞ (7/x - x/6) is equal to 0.

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To find the limit as x approaches negative infinity of the expression (7/x - x/6), we can simplify the expression and evaluate the limit. The result of the limit is negative infinity.

As x approaches negative infinity, both terms in the expression (7/x and x/6) tend to zero. The first term, 7/x, approaches zero because the denominator x becomes very large in magnitude as x goes to negative infinity. The second term, x/6, also approaches zero because the numerator x becomes very large in magnitude.

Therefore, the expression (7/x - x/6) simplifies to (0 - 0) = 0.

Hence, the limit as x approaches negative infinity of (7/x - x/6) is 0.

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Answer:

Dimensions of rug:

Length = 28 ft

Width =  27 ft

Step-by-step explanation:

The given dimensions of the room is:

Length = 30 ft

Width = 29 ft

Area of carpeting = 756 sq ft

Kindly refer to the attached image.

Let the uniform strip around floor is of length = \(x\) ft

This \(x\) feet will be 2 times along the length and

2 times along the width of room.

So, length of rug = 30 -2 \(\times\) \(x\) and

Width of rug = 29 -2 \(\times\) \(x\)

It will be rectangular in shape.

Area of a rectangle is given as:

\(A = Length\times Width\)

\(756 = (30-2x) (29-2x)\\\Rightarrow 756 = 870 - 118x+4x^2\\\Rightarrow 4x^2-118x+114=0\\\Rightarrow 2x^2-59x+57=0\\\Rightarrow 2x^2-57x-2x+57=0\\\Rightarrow x =1, -\dfrac{57}{2}\)

Negative length not possible.

So,Length of strip,  \(x = 1\ ft\)

Dimensions of rug:

Length = 30 -2 = 28 ft

Width = 29 -2 = 27 ft

The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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Rοunding up tο the nearest whοle cupcake, yοu shοuld buy 8 cupcakes tο ensure that yοur rοbοt has enοugh cupcakes tο last fοr the next 14 days.

An equatiοn is a mathematical statement that indicates that twο expressiοns are equal. It cοntains an equals sign (=) between twο expressiοns, with οne expressiοn οn each side οf the equals sign. Equatiοns can cοntain variables, cοnstants, cοefficients, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Here,

If yοur rοbοt eats 4 cupcakes every 7 days, it means it eats 4/7 = 0.57 cupcakes per day (rοunded tο twο decimal places).

Tο buy enοugh cupcakes fοr the last 14 days, yοu need tο multiply the number οf days by the daily cοnsumptiοn rate:

0.57 cupcakes per day x 14 days = 7.98 cupcakes

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Complete question:

If your robot eats 4 cupcakes every 7 days. So to buy enough cupcakes for the last 14 days, how much cupcake is consumed daily?

Answer:

x=13

Step-by-step explanation:

26.= 6000ft.

1.convert the yards to feet 100 yards= 300 ft

2. to find the area multiply the 20 ft by 300 ft

3. answer is 6000 ft

4 . if the answer needs to be in yards use a converter to convert the feet to yards

The percentages paid are given as follows:

a) 14.29%.

b) 2.5%.

The percentages are obtained applying the proportions in the context of the problem.

A proportion is applying because the percentage is calculated dividing the $5 fee by the total fee of the transaction, and then multiplying by 100%.

Hence, for item a, the percentage is given as follows:

5/35 x 100% = 14.29%.

For item b, the percentage is given as follows:

5/200 x 100% = 2.5%.

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