The length of a rectangle is five less than its width. The area of the rectangle is 84 square feet. Write a quadratic equation in standard form, ax^2+bx+c=0

Answer:

6x(x+3)(x-2)=6x^3+6x^2-36x

3(x-2)(x +9)=3x^2+21x-54

Step-by-step explanation:

Answer:

6x(x+3)(x-2)=6x^3+6x^2-36x

3(x-2)(x +9)=3x^2+21x-54

Step-by-step explanation:

Answer:

The volume of this prism is 64 mililmeters cubed.

Step-by-step explanation:

What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters?

The volume of this prism can be calculated as:

[tex]V=l\cdot w \cdot h\\\\V=2\cdot 4\cdot 8=64[/tex]

The volume of this prism is 64 mililmeters cubed.

Answer:

D

Step-by-step explanation:

Sorry if it's wrong.

Answer:

[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]

Step-by-step explanation:

The second derivative is found by integrating it:

[tex]f''(t) = \frac{1}{2}\cdot t^{2} -5\cdot \sin t + C[/tex]

The first derivative is:

[tex]f' (t) = \frac{1}{6}\cdot t^{3}+5\cdot \cos t + C\cdot t + D[/tex]

Lastly, the function is:

[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]

Given that,

f'''(t) = t — 5cos(t)

We want to find f(t) so we need to integrate this function three times to get f(t)

First anti derivative

∫ f'''(t) dt = ∫ (t —5cos(t)) dt

Note, the integral of cos(t) is sin(t), and the integral of sin(t) is —Cos(t)

Integrating third derivatives decreases it to second derivatives i.e. f'''(t) to f''(t)

f''(t) = t²/2 — 5sin(t) + C

Where C is the first anti derivative constant

Second anti derivative

f''(t) = t²/2 — 5sin(t) + C

∫ f''(t) = ∫ (t²/2 — 5sin(t) + C) dt

f'(t) = t³/6 + 5Cos(t) + Ct + D

Where D is the second anti derivative constant

Third anti derivative

f'(t) = t³/6 + 5Cos(t) + Ct + D

∫ f'(t) = ∫ t³/6 + 5Cos(t) + Ct + D) dt

f(t) = t⁴/24 + 5Sin(t) + Ct²/2 + Dt + E

Where E is the third anti derivative constant.

So the required f(t) function is

f(t) = t⁴/24 + 5Sin(t) + ½Ct² + Dt + E

Answer:

incorrect because the square area would be 440

Step-by-step explanation:

Answer:

He is incorrect. The path will have an area of (4) (40) = 160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.

Step-by-step explanation:

Answer:

Yes. They are Right Triangles

Step-by-step explanation:

To determine if the triangles are right triangles, all you need to do is verify whether or not the dimensions satisfy the Pythagoras Theorem.

Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

Note that in a right triangle, the longest side is always the hypotenuse.

Given the length of the sides 1.5 feet, 2.0 feet, 2.5 feet

[tex]2.5^2=1.5^2+2.0^2\\6.25=2.25+4\\6.25=6.25[/tex]

Since the Pythagoras theorem holds, the triangles are in fact right triangles.

Answer:

90

Step-by-step explanation:

Answer:

It would be 4 hours and 22 minutes because from 1 to 5 would be 4 hours and then 22 because of the 44 so ur answer would be 4 hours and 22 minutes.

Step-by-step explanation:

Answer:

262 minutes

Step-by-step explanation:

4 hours and 22 minutes difference in time

4x60=240

240+22=262 minutes

Answer:

93.5 inches

Step-by-step explanation:

Length times width

Answer:

a = 27400 ( borrow)

b = -21600  ( do not borrow)

c = -84600  ( do not borrow)

Step-by-step explanation:

a) Success probability = 88%

Expected payout = 88($430,000) +  0.12(-$270000) = $34600

Cost of borrowing = $270000(1+ 0.18) = 318600

EXPECTED PROFIT = 27400 you can borrow.

b) Probability of success  is 81%

Expected payout  = 0.18($430000) + 0.19(-$270000)  

= $297,000

Cost of borrowing  = $270000 (1+0.18) = 318600

Expected loss = -21600 do not borrow

c) Probability of of success = 72%

Expected payout = 0.72($430000) + 0.28(-$270000) = $234000

Cost of borrowing = $270000(1+ 0.18) = 318600

Expected loss = -84600 do not borrow

Answer:

(a)  Wilson Motors should borrow the money.

(b)  Wilson Motors should not borrow the money.

(c) Wilson Motors should not borrow the money.

Step-by-step explanation:

(a) If the probability of success is 91​%?

Expected return = 0.91*$430,000 + 0.09*(-$290,000)

                                = 391,000 - 26,100

                                = $364,900

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $364,900 - $324,800

                         = $40,100

Since it results in profit, Wilson Motors should borrow the money.

(b) If the probability of success is 85​%?

Expected return = 0.85*$430,000 + 0.15*(-$290,000)

                                = 365500 - 43,500

                                = $322,000

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $322,000 - $324,800

                         = -$2800

Since it results in loss, Wilson Motors should not borrow the money.

 c) If the probability of success is 75​%?      

Expected return = 0.75*$430,000 + 0.25*(-$290,000)

                                = 322500 - 72,500

                                = $250,000

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $250,000 - $324,800

                         = -$74800

Since it results in loss, Wilson Motors should not borrow the money.

After rotating the point A(-5, 1) counterclockwise by 90 degrees, its new coordinates become (-1, -5).

When a point or shape is rotated counterclockwise by 90 degrees about the origin, its coordinates are transformed using the following rule:

For a point (x, y), the new coordinates after a 90-degree counterclockwise rotation are (-y, x).

Let's apply this rule to the point A(-5, 1):

Original coordinates of A: (x, y) = (-5, 1)

New coordinates after rotation: (-y, x) = (-(1), -5) = (-1, -5)

So, after rotating the point A(-5, 1) counterclockwise by 90 degrees, its new coordinates become (-1, -5).

This rotation swaps the x and y coordinates while changing the sign of the new x-coordinate. This transformation corresponds to a 90-degree counterclockwise rotation around the origin.

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The new coordinate of A (-5, 1) after rotation will be (1, 5).

When a point is rotated 90 degrees counterclockwise around the origin in the coordinate plane, the rule for the transformation is (x, y) → (-y, x). This means that each point (x, y) will move to the position (-y, x).

Given the point A at coordinates (-5, 1), applying the rotation rule:

The new coordinate of A (-5, 1) after rotation will be (1, 5).

Answer:

Step-by-step explanation:

a) Your question supplies the formula for N(t):

  N(t) = N0·e^(kt)

__

b) Given the initial population and doubling time (in months), the population function can also be written as ...

  N(t) = 10,000·2^(t/14) . . . . . t in months

Then in 4 years the population will be ...

  N(48) = 10,000·2^(48/14) ≈ 107,672.02

The population 4 years from now will be approximately 107,672 people.

_____

Comment on the formula for N(t)

In order to use the formula of the first part in answering the second part, we need to find the value of k. It will be an irrational number. In order to obtain accurate results in the second part, k would need to be good to at least 6 significant digits. Its value, for t in months, is ...

  k = ln(2)/14 ≈ 0.0495105

For t in years, it is 12 times this value, or ...

  k ≈ 0.594126

The advice not to do any rounding (even for the value of k) is appropriate.

__

As we can see from the above, it is not necessary to determine k in order to answer the question in part b.

The population of a city with exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex]. The growth factor k is found to be approximately 0.592. Using this, the population 4 years later is found to be approximately 43609.

The population of a city showing exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex] where N(t) is the population at time t, N0 is the initial population, e is the natural logarithmic base (approx. 2.71828), and k is the growth rate.

Given that the population doubled in 14 months, which is about 1.17 years, we have: 2*N0 = N0 * [tex]e^(^1^.^1^7^k^)[/tex]. Solving this equation for k, we get k = ln(2)/1.17. Hence, the growth rate (k) is approximately 0.592.

To find the population 4 years from now, we substitute t=4 and k=0.592 into the equation. So, N(4) = 10000 * [tex]e^(^4^*^0^.^5^9^2^)[/tex]. After calculating, we get a population of approximately 43609.

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Answer:

The bridge's height above the water is 130 feets.

Step-by-step explanation:

A rock is thrown upward from a bridge into a river below :

[tex]h(t)=-16t^2+41t+130[/tex]

Here t is time in seconds

It is required to find the bridge's height above the water. When it reaches the height of the rock above the surface of the water, then :

h(t) = 0

[tex]f(0)=-16t^2+41t+130\\\\f(0)=-16(0)^2+41(0))+130\\\\f(0)=130\ ft[/tex]

So, the bridge's height above the water is 130 feets.

Answer:

Probability that the sample proportion will be greater than 0.5 is 0.8133.

Step-by-step explanation:

We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.

Suppose that the polling organization takes a simple random sample of 500 voters.

Let [tex]\hat p[/tex] = sample proportion

The z-score probability distribution for sample proportion is given by;

               Z = [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion

           p = population proportion = 48%

           n = sample of voters = 500

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be greater than 0.5 is given by = P( [tex]\hat p[/tex] > 0.50)

  P( [tex]\hat p[/tex] > 0.50) = P( [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }[/tex] ) = P(Z < 0.89) = 0.8133

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.

Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.

Answer:

a. Dependent variable - fatalities

   Independent variable - age of the driver

b.  Dependent variable - grocery bills

   Independent variable - number of family members

c.  Dependent variable - insurance

   Independent variable - age of applicant

d.  Dependent variable - utility bill

   Independent variable - power consumption

e.  Dependent variable - crime rate

   Independent variable - higher education

Step-by-step explanation:

The independent variable is the variable that is used to predict the other variable, while the dependent variable is the variable that is been predicted.

The simple regression model comprises of one dependent variable (y)(y) and one independent variable (x)(x). It is used to predict the value of a dependent variable based on one independent variable.

Therefore,

a. The dependent variable is fatality and the independent variable is the age of the driver.

b. The dependent variable is grocery bills and the independent variable is the number of family members.

c. The dependent variable is insurance premium and the independent variable is the age of the applicant.

d. The dependent variable is the utility bill and the independent variable is power consumption.

e. The dependent variable is the crime rate and the independent variable is higher education.

Final answer:

a. Independent variable: age; Dependent variable: fatalities per 100,000 drivers.

b. Independent variable: number of family members; Dependent variable: weekly grocery bill.

c. Independent variable: age of applicant; Dependent variable: insurance premium.

d. Independent variable: power consumption; Dependent variable: utility bills.

e. Independent variable: higher education (years); Dependent variable: crime rates.

Explanation:

In the field of research, particularly in scientific and sociological studies, it's crucial to distinguish the independent variable (IV) from the dependent variable (DV). The independent variable is the condition that is manipulated or selected by the researcher to determine its effect on the dependent variable, which is the outcome that is measured. Here's the delineation between the IV and DV in given scenarios:

Each of these examples illustrates the relationship principle where the dependent variable changes in response to the independent variable, providing insight into the cause-effect dynamics at play.

The length of the curve defined by the parametric equations x = 1 + 9t^2 and y = 2 + 6t^3 for t ranging from 0 to 2 can be found using the formula for the length of a curve defined by parametric equations. First, compute the derivatives of x and y with respect to t and then integrate the square root of the sum of their squares from t = 0 to t = 2.

Given the parametric equations x = 1 + 9t2 and y = 2 + 6t3, with t ranging from 0 to 2, we can find the length of the curve using the formula for the length of a curve defined by parametric equations.

The formula is: Length = ∫ab sqrt[(dx/dt)2 + (dy/dt)2] dt where dx/dt and dy/dt are the derivatives of x and y with respect to t.

We first find the derivatives dx/dt = 18t and dy/dt = 18t2. Then, we square these, add them together and take the square root to get √[324t2 + 324t4].

Finally, we integrate this from t = 0 to t = 2 to find the length of the curve. As a hint for the integration part, you can use the formula for the integral of tn, which is (tn+1)/(n+1).

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Answer:

I did the question and the answer is b and e

Step-by-step explanation:

Or 4 in and 12 cubic yards

Final answer:

The algebraic equation representing "The number of medals won by the United States is 26 more than three times the number of medals won by Italy" is U = 3I + 26, where U is the number of medals won by the United States, and I is the number of medals won by Italy.

Explanation:

The question requires us to write an algebraic equation based on the statement: "The number of medals won by the United States is 26 more than three times the number of medals won by Italy." Let's use U to represent the number of medals won by the United States and I for the number of medals won by Italy. Following the given statement, we can write the equation as:

U = 3I + 26

This equation signifies that to find the number of medals won by the United States, we need to multiply the number of medals won by Italy (I) by 3 and then add 26 to this total.

Answer:

The number = 5

Step-by-step explanation:

Let the number be x

[tex]\frac{2+x}{3-2x}=-1\\\\2+x=-1*(3-2x)\\\\2+x=(-1)*3-(-1)*2x\\\\2+x=-3+2x\\\\x=-3+2x-2\\\\x-2x=-5\\\\-x=-5\\\\x=5[/tex]

Answer:

B) median < mean

Step-by-step explanation:

To find the median, take away one of the frequencies until you have only one left. The median is 6.

To find the mean add up all of the numbers and divide by how many numbers are used. 3 + 4(3) + 6(8) + 8(3) + 10(2) + 11 = 118/17 = 6.94

This means that the mean is greater than the median.

If this answer is correct, please make me Brainliest!

Answer:

B) median < mean

To find the median, take away one of the frequencies until you have only one left. The median is 6.

Step-by-step explanation:

The corresponding 'x' value is an estimation of the median. If we divide a cumulative frequency curve into quarters, the value at the lower quarter is referred to as the lower quartile, the value at the middle gives the median and the value at the upper quarter is the upper quartile.

Answer:

sam stop ;)

Step-by-step explanation:

jk i do this to!

The decimal which is equal to [tex]\frac{4}{3}[/tex] is; Choice D: 1.333 option D is correct.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the extension of the numeral system to non-integer numbers. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities. For instance, there is one complete pizza and a half of another pizza in the photograph.

[tex]\frac{4}{3} =1.333[/tex]

Therefore, option D is correct.

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Answer:

-7 degrees Celsius

Step-by-step explanation:

You subtract 25 by 32 and get -7 degrees.

Answer:

-7 degrees celcius

Step-by-step explanation:

To do this we just need to subtract 32 from 25, indicated by "dropped."

25-32=-7

Answer:

The salmon size is less than equal to 10.28 inches represent bottom 25% of all salmon.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12.5 inches

Standard Deviation, σ = 3.3

We are given that the distribution of salmon size is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.25

[tex]P( X < x) = P( z < \displaystyle\frac{x - 12.5}{3.3})=0.25[/tex]  

Calculation the value from standard normal z table, we have,  

[tex]\displaystyle\frac{x - 12.5}{3.3} = -0.674\\\\x = 10.2758\approx 10.28[/tex]  

Thus, the salmon size is equal to or less than 10.28 inches, they are considered small and young and represent bottom 25% of all salmon.

Answer:

The answer is (2u-1)(5u+1)=0

Step-by-step explanation:

Answer:

(2u-1)(5u+1)=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here, 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.

Therefore:

2.1 40 72 130

The sample sizes are:

721 69 722 349 2

Two proportions and their difference are:

400.580 0.580 p = =_= 69 130 1300.372 D =-= n2 349 p1-P2 = 0.580-0.372 = 0.208

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c) For 95% confidence level, critical value of z is 1.96.

The large-sample 95% confidence interval for the difference in proportions is:

n1 7l n2 0.580(1 - 0.580) 0.372(1- 0.372) 0.208 ± 1.96 0.208 t 0.127 or (0.081,0.335)

We are 95% confident that the difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt lies between 0.081 and 0.335. Since 0 does not lie in the confidence interval, we can conclude that higher proportion of male customers left a tip who were served by a server wearing a red shirt than those who were served by a server wearing a different colored shirt.

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

d) The hypotheses are:

\\H_0:p_1=p_2 \\H_a:p_1\ne p_2

The pooled proportion is:

1240 +130 +n2 69+34 0.4067

The test statistic is:

pi-2 0.580 0.372 V mi-P)(4+4) ν/0 4067(1-04067) (かー = 3.20 ) 0.4067(1-0.4067) (69 т 349

The p-value is:

p-value = P(z <-3.20) + P(z > 3.20) = 0.0007 0.0007 = 0.00 1 4

Since p-value is less than 0.05, reject the null hypothesis. We can conclude that there is significant difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt.

Please see attachment for better indentation and formula input in the solution.

The 95% confidence interval provides a range where the true difference in tipping behavior may lie, while a large-sample significance test assesses if the difference is statistically significant.

For part a, the objective is to establish a 95% confidence interval for the difference in proportions. The proportion of individuals who tip when served by a server wearing a red shirt (p1) is 40/69, and the proportion of individuals who tip when served by a server wearing a different colored shirt (p2) is 130/349. The difference in proportions (p1 - p2) will give us the estimated difference. The standard error can then be calculated. Z is typically 1.96 for a 95% confidence interval.

For part b, a large-sample significance test is performed to test the null hypothesis that the two proportions are the same against the alternative hypothesis that the two proportions are not the same. Z score is calculated using the difference in proportions and standard error. P-value can then be derived from the z-score. The p-value will indicate whether the difference is statistically significant or not.

The confidence interval gives us the range of values within which the actual difference in proportions might fall 95% of the time, whereas the significance test helps determine if there is a substantial difference in the tipping habits depending on the color of the shirt worn by the server.

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The surface area of the given pyramid is [tex]2124112 m^{2}[/tex].

"The surface area of a pyramid is a measure of the total area that is occupied by all its faces."

The base of the square pyramid is 230 meters by 230 meters.

Therefore, the base area of the pyramid is

[tex]= (230)^{2} m^{2} \\= 52900 m^{2}[/tex]

The perimeter of the base

[tex]= 4(230) m\\=920 m[/tex]

Therefore, the lateral surface area of the pyramid

[tex]= \frac{1}{2}[/tex] × perimeter × slant height

[tex]= \frac{1}{2}(920)(187) m^{2} \\= 2071212 m^{2}[/tex]

Therefore, the surface area of the pyramid is

= Base area + lateral surface area

[tex]= (52900 + 2071212)m^{2} \\= 2124112 m^{2}[/tex]

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Answer:

y=-6

Step-by-step explanation:

Divide -11 by 66 to isolate y to get 6

Answer:

the answer is y=-6

Step-by-step explanation:

you are welcome

Answer:

555

Step-by-step explanation:

Answer:

the edges only would be 16 pieces.

Step-by-step explanation:

Think of it as a square. The top row is 5 pieces, bottom row is 5 pieces.

The left vertical side is 3 and the right vertical side is 3. Because the corner pieces are already there, you don't count them twice.

Answer:

128

Step-by-step explanation:

2x2x2x2x2x2x2 is 128

Answer:

B

Step-by-step explanation: