Ifx-10 is a factor of x2 - 8x - 20, what is the other
factor?
x +

Answer:

The solution to [tex]3x\:-\:1\ge 12[/tex] is [tex]x\ge \frac{13}{3}[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following symbols: inequalities involving "<", "≠" or ">" are referred to as "strict inequalities", while inequalities involving "≤" or "≥" are not.

Solving an inequality means finding all of its solutions. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.

To find the solution to [tex]3x\:-\:1\ge 12[/tex]

[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\\\3x-1+1\ge \:12+1\\\\\mathrm{Simplify}\\\\3x\ge \:13\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}\ge \frac{13}{3}\\\\\mathrm{Simplify}\\\\x\ge \frac{13}{3}[/tex]

The right answer is 9 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment:)

Answer:

48.30

Step-by-step explanation:

First determine the tip

42 *15%

42 *.15 =6.30

Add this to the amount of the tip

42 + 6.30 =48.30

The total amount is 48.30

Answer:

Step-by-step explanation:

$48.30

Answer:

0.6

Step-by-step explanation:

4/7 can be considered a suspended division problem.  To find the answer, 4 must be divided by 7.  This yields the result 0.57142, which can be rounded to 0.6.

Step-by-step explanation:

[tex]sin(1 \div 4a + 20) = \sqrt{3} \div 2 \\ sin(1 \div 4a + 20) =sin 60[/tex]

1÷4a+20=60

1÷4a=4

a=1/160

Answer:

40+5x=y

60+3x=y

Step-by-step explanation:

The first park is 40+5x

The second park is 60+3x

Now set them both equal to y

Answer:

T15 = 31

Step-by-step explanation:

Its in the picture

I hope it helps :)

Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

[tex]X \sim N (\mu = 75 , \sigma^2 = 75)[/tex]

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

[tex]= 6*10^{-4}[/tex]

= 0.0006 to four decimal places

Answer:

what is this it is not understand able

Answer:

11

Step-by-step explanation:

<TKF = 90° ( BECAUSE OF THE BISECTOR)

BUT

<TKF = 5(x+7)

So

5(x+7) = 90

5x+35 = 90

5x = 90-35

5x = 55

Dividing by 5(both sides)

x = 11

Answer:

44.70 USD

Step-by-step explanation:

250÷1.3687

=182.655074158

182.655074158-150

=32.655074158

32.655074158×1.3687

=44.6950000001

The 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip.

After returning to the United States he converts his money back to US dollars. H

Let x be the total original 250 US dollars Phelan now have:

The value of x can be found as follows:

x = (250/1.3687 - 150)x1.3687

After simplification:

x = 44.69 ≈ 44.70 US dollars

Thus, the 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.

Learn more about the unit conversion here:

https://brainly.com/question/11543684

#SPJ2

Answer:

fifth angle = 102°

Step-by-step explanation:

A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles .And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will  be 180 × 3 = 540°. The sum of interior angles of a pentagon = 540°.

The general rule for calculating sum of the interior angles of a polygon is

sum of interior angle = (n−2) × 180°

where

n = number of sides

n = 5 since we are dealing with a  pentagon.

sum of interior  angle of a pentagon = 540°

The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.

fifth angle = 540 - (88 + 118 + 132 + 100)

fifth angle = 540 - 438

fifth angle = 102°

Answer:

its C on edg

Step-by-step explanation:

Answer:

P=48 millimeters

Step-by-step explanation:

p=4l

p=4 x 12

p=48 mm

Answer:

$ 44

Step-by-step explanation:

If we analyze the statement well, we can observe something very crucial to solve it, the jumbo biscuits require 2 oz of flour and give a profit of $ 0.08, the Regular one that only requires 1 oz of flour leaves a profit of $ 0.11, which means that requiring a smaller quantity of flour leaves a greater profit, so in terms of profit it is not profitable to make Jumbo, only Regular.

Therefore, since you can make 400 biscuits, they would all be regular since there are 600 oz of flour available, it is enough to make 400, therefore the maximum profit would be:

$ 0.11 * 400 = 44

The maximum possible profit is $ 44

Answer:

B:

Step-by-step explanation:

IN THE ATTACHED FILE

Steps:

Shape: Cube

Solved for side length of the cube

Volume: 343 cubic feet

Formula: a=V⅓

Description:

Using the formula for the volume of the cube a=V⅓. We are going to calculate the side length of the cube. Your answer will be 7 feet. Meaning the correct answer for this question is C.

Answer: a≈7ft

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Answer:

f(x) = 15

Step-by-step explanation:

"If f(x)= 5x + 40, what is f(x) when x = -5?"

Substitute x for -5:

f(x) = 5x + 40

f(x) = 5(-5) + 40

f(x) = -25 + 40

f(x) = 15

Answer:

displacement x = - 0.046sin4t +0.006cos4t

Step-by-step explanation:

The model of the equation of motion is a forced motion equation and to determine the displacement of the weight as a function of time; we have:

the weight balances of the  elastic force in the spring  to be expressed by the relation:

mg = kx

where;

x=4 in (i.e  1/3 ft )

mass m = 6lb

let make k the subject; then:

k = mg/x = 6×32/(1/3) = 576

assuming  x to be the displacement form equilibrium;

Then;

[tex]F = 27sin 4t-3cos4t +k(x+1/3) - mg -3v[/tex]

(since F(t)=27sin 4t-3cos4t somehow faces downwards, mg=downwards and k(x+1/3)= upwards and medium resistance 3v =  upwards)

SO;

[tex]d2x/dt2 = 27sin 4t-3cos4t +kx - 3dx/dt[/tex]

[tex]d2x/dt2 +3dx/dt - 576x = 27sin 4t-3cos4t[/tex]

Assuming : [tex]x = asin4t + bcos4t[/tex]

[tex]dx/dt = 4acos4t - 4bsin4t[/tex]

[tex]d2x/dt2 = -16asin4t - 14bcos4t[/tex]

replacing  these values in the above equation

[tex]= -16asin4t - 14bcos4t + 12acos4t - 12bsin4t -576asin4t-576bcos4t = 27sin 4t-3cos4t[/tex]

[tex]= sin4t (-592a-12b) + cos4t(12a -590b) = 27sin 4t-3cos4t[/tex]

equating sin and cos terms

a = - 0.046 ;  b = 0.006

displacement x = - 0.046sin4t +0.006cos4t

36 - k = 4 + k

36 - 4 = k + k

32 = 2k

32/2 = k

16 = k

Steps:

Step 1: Simplify both sides of the equation

36−k=4+k

36+−k=4+k

−k+36=k+4

Step 2: Subtract k from both sides

−k+36−k=k+4−k

−2k+36=4

Step 3: Subtract 36 from both sides

−2k+36−36=4−36

−2k=−32

Step 4: Divide both sides by -2

−2k/−2 = −32/−2

Description:

Since we are trying to find the value of K, we need to simplify both sides of the equation. After that your answer will come as −k+36=k+4.  Now the second step is to  subtract k from both sides, your equation will come as −2k+36=4.  Thirdly we need to subtract 36 from both sides, your equation will come as −2k=−32.  Now you need to divide both sides by -2. After you do that, you will get your answer which is k=16.

Answer: k=16

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Hope this helps.

Answer:

1/5x = h(x)

Step-by-step explanation:

6x+y = 4x+ 11y

Subtract y from each side

6x+y -y = 4x+ 11y-y

6x = 4x+10y

Subtract 4x from each side

6x-4x = 4x+10y-4x

2x = 10y

Divide each side by 10

2x/10 = 10y/10

1/5x = y

1/5x = h(x)

Answer:

Yes! Extrapolation is fine. Don't worry about it.

Step-by-step explanation:

Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.

Step-by-step explanation:

The way i like to remember it is that the exponent inside of the radical will be the numerator of the fraction and the index of the radical will be the denominator so the answer is 2^(-5/3).

Answer:

A

Step-by-step explanation:

2/3x=1-5

2/3x=-4

x=-4/2/3

x=-6

Answer:

a. It is not likely that a winning ticket will be selected

b. The probability of winning enough to pay for the ticket expressed as a simplified fraction is 13/71

Step-by-step explanation:

To answer this question, there are some important notes to know.

1. The selection is only once

2. To win, you have to select a note which has a greater value than $8

Now, the total number of notes that we have = 38 + 20 + 7 + 5 + 1 = 71

The number of bills present that are greater than $8 are; 7 $10 bills , 5 $20 bills and 1 $100 bill

This makes a total of 7 + 5 + 1 = 13

Thus, the probability of selecting a bill which would pay for the charges is 13/71

Now, the probability of not selecting is 1- probability of selecting = 1-13/71 = 58/71

Since the probability of not selecting is greater than the probability of selecting, it means that it is not likely that a winning ticket will be selected

Answer:

a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Step-by-step explanation:

For this case our random variable of interest for the weights is bell shaped and we know the following parameters.

[tex]\mu = 55, \sigma =6[/tex]

We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.

Part a

For this case and using the empirical rule we can find the limits in order to have 9% of the values:

[tex] \mu -2\sigma = 55 -2*6 =43[/tex]

[tex] \mu +2\sigma = 55 +2*6 =67[/tex]

95% of the widget weights lie between 43 and 67

Part b

For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

[tex] 100 -0.15-2.5 = 97.85[/tex]

Part c

We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Answer: 26

Step-by-step explanation:

32-6 = 26

Answer:

14.25°

Step-by-step explanation:

distance from middle of the net = 8 m

width of the net = 2 m

this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.

We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.

We use the trigonometric function;   tan∅ = opp/adj

opp is the side facing the angle = 1 m

adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)

adj = 8 m

tan∅ = [tex]\frac{1}{8}[/tex] = 0.125

∅ = [tex]tan^{-1}[/tex] 0.125 = 7.125°

Angle within which Lars must fire his shot = 2 x ∅

= 2 x 7.125° = 14.25°

Answer: 573.75 meters^3

Step-by-step explanation:

Volume = Length x width x height

Volume = 17 x 13.5 x 2.5

Answer:

30

Step-by-step explanation:

You can have any number on the first die, and any number besides the first one on the second. 6*5=30