The product of two numbers was 9. If one number is three and three fourth, what was

the other number?

Answer:  k = -9

Step-by-step explanation:

kx² - 12x - 4 = 0

In order to have exactly one solution, it must be a perfect square.

Assume k is negative and factor out a negative 1.

-1(kx² + 12x + 4) = 0

[tex]\bigg(\sqrt{kx^2}+\sqrt4\bigg)^2=0\\\\[/tex]

The middle term = 12x [tex]= 2(\sqrt{kx^2})(\sqrt4)[/tex]

                               12x = 4x√k

                                3   = √k

                                9 = k

-1(9x² + 12x + 4) = 0

-9x² - 12x - 4 = 0

k=-9

Answer:

(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

  The given standard deviation = 3.4 minutes

The value of  n sample size = 45

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:y=3/2x-3

Step-by-step explanation: the slope of the graph is (y2-y1)/(x2-x1)

If we take points (0,-3) (2,0) the slope would be (0--3)/(2-0) = 3/2

And the y-intercept of the slope is -3

Answer:

19.2 feet square

Step-by-step explanation:

We khow that the area of an octagon is :

A= 1/2 * h * P where h is the apothem and p the perimeter

Answer: 20

Step-by-step explanation:

I guess that we want to distribute all the 7 candies between 4 kids

We have 3 options:

first 3, 2, 1 and 1. (the number of candies that each kid gets)

The possible permutations in this case:

if we leave the 3 fixed, the ones do are equal, so the permutations are only given by the change in the kid that gets 2 candies, we have 3 permutations for this.

And for the fixed 3, we have 4 possible places where we can fix it, so the total number of combinations is:

c = 3*4 = 12.

and the second option is (2, 2, 2, 1)

Here the only change is the kid that gets only one candy, we have 4 options in this case:

c = 4.

the third option is (4, 1, 1, 1)

Here the only change is the kid that gets 4 candies, and we have 4 options for this, so we have 4 combinations:

c = 4.

Then the total number of possible combinations is:

C = 12 + 4 + 4 = 20

Answer:

Experimental Study

Step-by-step explanation:

In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.

These studies are usually randomized ie subjects are group by chance.

As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.

Answer:

5n

Step-by-step explanation:

Think about it:

If Tommy has 4 friends (n = 4), then he will have to give 5 pencils to each person. The total number of pencils is 5 * n or 5 * 4 = 20.

Similarly, if Tommy has 0 friends (I can relate), then he will have to give 5 pencils to each of his imaginary friends. The total number of pencils he has to give out to his real friends is 5 * n or 5 * 0 = 0.

Hacen falta las expresiones para poder responder a tu pregunta, estuve investigando y adjuntaré una imagen que hace referencia a tus preguntas, espero no equivocarme.

Si este es el caso, son 9 expresiones y el nombre de cada propiedad es:

1. Inverso aditivo (Sumar un número por su opuesto el resultado es 0)

2. Ley conmutativa (El orden de los factores no altera el producto)

3. Ley asociativa (Agrupar los términos sin alterar el resultado)

4. Ley de la identidad, (Sumar un número con 0 se obtiene el mismo número)

5. Ley distributiva (La misma respuesta cuando multiplicas un conjunto de números por otro número que cuando se hace cada multiplicación por separado)

6. Ley distributiva

7. Ley distributiva

8. Ley asociativa

9. Ley conmutativa

Answer:

  6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

  x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

  h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

  V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

  dV/dx = 0 = 27 -(3/4)x²

  x² = (4/3)(27) = 36

  x = 6

  h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

Comment on maximum volume, minimum area

In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

we just have to use the Pythagoras theorem and then calculate the value of x and y.

Answer:C

Step-by-step explanation:

The vertical line test

Answer:

Option C

Step-by-step explanation:

The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.

It tests the claim that the row and column variables are independent of each other.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.

Answer:

  68

Step-by-step explanation:

The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.

  [tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]

The technician can test 68 chips in that time period.

Answer: 0.0023

Step-by-step explanation:

Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.

probability of success p = 32% = 0.32

Sample size : n= 10

Binomial probability function :

[tex]P(X=x)= \ ^nC_xp^x(1-p)^{n-x}[/tex]

Now, the probability that eight receipts will show that the above three food items were ordered :

[tex]P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023[/tex]

hence, the required probability = 0.0023

Answer:

3, 12

Step-by-step explanation:

Et x and y be the required integers.

Case 1: x = 5y - 3...(1)

Case 2: xy = 36

Hence, (5y - 3)*y = 36

[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]

Hence, the required integers are 3 and 12.

let

x  = one integer

y = another integer

x = 5y - 3

If the product of the two integers is 36, then find the integers.

x * y = 36

(5y - 3) * y = 36

5y² - 3y = 36

5y² - 3y - 36 = 0

Solve the quadratic equation using factorization method

That is, find two numbers whose product will give -180 and sum will give -3

Note: coefficient of y² multiplied by -36 = -180

5y² - 3y - 36 = 0

The numbers are -15 and +12

5y² - 15y + 12y - 36 = 0

5y(y - 3) + 12 (y - 3) = 0

(5y + 12) (y - 3) = 0

5y + 12 = 0      y - 3 = 0

5y = - 12           y = 3

y = -12/5

The value of y can not be negative

Therefore,

y = 3

Substitute y = 3 into x = 5y - 3

x = 5y - 3

x = 5(3) - 3

= 15 - 3

= 12

x = 12

Therefore,

(x, y) = (12, 3)

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Answer:

Betty should use T = 2.571 to construct the confidence interval

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571

Betty should use T = 2.571 to construct the confidence interval

Answer:

Use a graphing calc.

Step-by-step explanation:

Answer:

1/7 = 0.142857... repeating

Step-by-step explanation:

7^(-1) = 1/(7^1) =1/7 = 0.142857... repeating

Answer:

Solution,

[tex] {7}^{ - 1} \\ = \frac{1}{ {7}^{1} } \\ = \frac{1}{7} [/tex]

[tex] {x}^{0} = 1[/tex]

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] {( {x}^{m} )}^{n} = {x}^{m \times n} [/tex]

[tex] {x}^{ - m} = \frac{1}{ {x}^{m} } [/tex]

[tex] {x}^{ \frac{p}{q} } = \sqrt[q]{ {x}^{p} } [/tex]

Hope this helps ....

Good luck on your assignment...

Answer: CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F

Step-by-step explanation:

CITY C: Dew Point Temperature = 25°F, expected low Temperature = 20°F

CITY A: Dew Point Temperature = 65°F, expected low Temperature = 60°F

CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F

city B is going to have dew on their lawn in the morning as the dew point temperature is less than the lowest temperature.

When surface temperature drops, eventually reaching the dew point, atmospheric water vapor condenses to form small droplets on the surface. Thus dew will be formed as the conditions are suitable only for city B.

Answer:

C. -4/3

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

We know that line m is perpendicular to line l.

Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4.  Negate the fraction and find the reciprocal.

Negative: switch the sign

3/4 --> -3/4

Reciprocal: switch the numerator (top number) and denominator (bottom number)

-3/4 --> -4/3

Line m has a slope of -4/3 and C is correct.

Answer:

The right Riemann sum is 21.5.

The left Riemann sum is 29.5.

Step-by-step explanation:

The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:

[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].

To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].

Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]

Now, we just evaluate the function at the right endpoints:

[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]

Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]

The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:

[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].

To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].

Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]

Now, we just evaluate the function at the left endpoints:

[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]

Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:

[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]

Answer:

D. The graph of g(x) is shifted 2 units down

Step-by-step explanation:

Since we are modifying b in f(x) = mx + b, we are dealing with vertical movement up and down. Since it is -2, we are moving down 2.

Answer:

25%

Step-by-step explanation:

George is 33[tex]\frac{1}{3}[/tex]% ([tex]\frac{100}{3}[/tex]%) richer than Pete. Let Pete's percentage of wealth be 100%.

Thus George percentage of wealth = 100% + [tex]\frac{100}{3}[/tex]%

                                                           = [tex]\frac{400}{3}[/tex]%

                                                           = 133[tex]\frac{1}{3}[/tex]%

Pete's percent poorer than George can be determined by;

                                                           = [tex](\frac{100}{3})[/tex] ÷ [tex](\frac{400}{3} )[/tex] × 100

                                                           = [tex](\frac{100}{3})[/tex] × [tex]\frac{3}{400}[/tex] ×100

                                                           = 0.25 × 100

                                                           = 25%

Pete is 25% poorer than George.

Answer:

[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]

[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]\bar X= 7.72[/tex] represent the sample mean

[tex]s= 2.5[/tex] represent the sample deviation

[tex] n=20[/tex] represent the sample size

The confidence interval is given by:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:

[tex] df= n-1 = 20-1=19[/tex]

And the critical value would be:

[tex] t_{\alpha/2}= 2.539[/tex]

And replacing we got:

[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]

[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]

The 98% confidence interval is between 6.42 hamsters per liter to  9.02 hamsters per liter

Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98

α = 1 - C = 0.02

α/2 = 0.01

The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.

The margin of error E is:

[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]

The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)

Hence the 98% confidence interval is between 6.42 hamsters per liter to  9.02 hamsters per liter

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The area bounded by region between the curve [tex]y = x^2- 24[/tex]  and [tex]y = 1[/tex] is

[tex]0[/tex] square units.

To find the Area,

Integrate the difference between the two curves over the interval of intersection.

Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .

The point of Intersection is the common point between the two curve.

Value of [tex]x[/tex] and [tex]y[/tex] coordinate  will be equal for both curve at point of intersection

In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].

[tex]1 = x^2-24[/tex]

Rearrange, like and unlike terms:

[tex]25 = x^2[/tex]

[tex]x =[/tex]  ±5

The point of intersection for two curves are:

[tex]x = +5[/tex]  and  [tex]x = -5[/tex]

Integrate the difference between the two curve over the interval [-5,5] to calculate the area.

Area =   [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]

Simplify,

[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]

Integrate,

[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]

Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.

[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]

= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]

[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]

[tex]= 0[/tex]

The Area between the two curves is [tex]0[/tex] square  units.

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Answer:

X = 50

Step-by-step explanation:

(5x - 100) + (x - 20) = 180 (sum of angle on a straight line is = 180)

5x + x -100 -120 = 180

6x - 120 = 180

6x = 180 + 120

6x = 300

x = 300/6

x = 50

For y

3y + y + 140 = 180

4y = 180 -140

4y = 40

y = 40/4

y = 10

Answer:

Dy/Dx=1/√ (2x+3)

Yeah it's correct

Step-by-step explanation:

Applying differential by chain differentiation method.

The differential of y = √(2x+3) with respect to x

y = √(2x+3)

Let y = √u

Y = u^½

U = 2x +3

The formula for chain differentiation is

Dy/Dx = Dy/Du *Du/Dx

So

Dy/Dx = Dy/Du *Du/Dx

Dy/Du= 1/2u^-½

Du/Dx = 2

Dy/Dx =( 1/2u^-½)2

Dy/Dx= u^-½

Dy/Dx=1/√ u

But u = 2x+3

Dy/Dx=1/√ (2x+3)

Answer:

5/16

Step-by-step explanation:

Use the formula to find slope when 2 points are given.

m = rise/run

m = y2 - y1 / x2 - x1

m = 3 - 8 / -10 - 6

m = -5 / -16

m = 5/16

The slope of the line is 5/16.

Answer: m=5/16

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Answer:

a. Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. P(at least B) = 0.330

c. P(pass) = 0.855

Step-by-step explanation:

Professor Sanchez has been teaching Principles of Economics for over 25 years.

He uses the following scale for grading.

Grade     Numerical Score      Probability

A                       4                            0.090

B                       3                            0.240

C                       2                            0.360

D                       1                            0.165

F                       0                            0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

The cumulative probability distribution is given by

Grade = F

P(X ≤ x) = 0.145

Grade = D

P(X ≤ x) = 0.145 + 0.165 = 0.310

Grade = C

P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670

Grade = B

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910

Grade = A

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1

Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

At least B means equal to B or greater than B grade.

P(at least B) = P(B) + P(A)

P(at least B) = 0.240 + 0.090

P(at least B) = 0.330

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the course means getting a grade of A, B, C or D

P(pass) = P(A) + P(B) + P(C) + P(D)

P(pass) = 0.090 + 0.240 + 0.360 + 0.165

P(pass) = 0.855

Alternatively,

P(pass) = 1 - P(F)

P(pass) = 1 - 0.145

P(pass) = 0.855

Answer:

(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.

Step-by-step explanation:

You want to first add up everyone. So in total there are 18 people.

There is than a 38.8% chance that a independent will be picked first. 7/18.

But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.

There is now a 47% chance that a democrat will be picked next. 8/17.