Factor 4x^2+20x-24 into bionomials

Answer:

x = 0.4

Step-by-step explanation:

Let me rewrite it so it looks better:

[tex]\frac{3}{4} x=\frac{3}{10}[/tex]

The first way is to cross multiply.

30x = 12

x=0.4

The other way is to see that the two numerators are the same except for the x on the left side.

You can see the the denominators are 4 and 10.

You can create a proportion of 4 : 10 and apply it to the fractions.

You get that you have to multiply the left side by 0.4, so x = 0.4

Answer:

0.4

Step-by-step explanation:

Answer:

3.17% probability of selecting first a green apple and then a nectarine.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

P(a green apple then a nectarine)

This is the probability of selecting first a green apple and then a nectarine.

Initially, there are 8+11+5+12 = 36 fruits, of which 8 are green apples. So 8/36 probability of choosing a green apple.

Now, there are 35 fruits, of which five are nectarines. So 5/35 probability of choosing a nectarine.

Then

[tex]p = \frac{8}{36}\times\frac{5}{35} = 0.0317[/tex]

3.17% probability of selecting first a green apple and then a nectarine.

Answer:

Step-by-step explanation:

Answer:

The carts velocity= 2m/s

Step-by-step explanation:

It took Manuel 87 seconds to push a shopping cart directly to his car.

One third of 87 = 87/3 = 29

In 29 seconds the carts moved 58 meter's.

The carts velocity = distance/time

The carts velocity = 58/29

The carts velocity= 2m/s

Answer:

3/2

Step-by-step explanation:

(3/4) / (1/2) is equivalent to (3/4)*(2/1), or 6/4, or 3/2.

To divide by a fraction, invert the fraction and multiply instead.

Answer:

the answer is 1 and 1/2

Answer:

1443.3 in³ or 0.835 ft³

Step-by-step explanation:

Let's begin by listing out the given variables:

length (l) = 100 ft = 1200 in, nominal size = 4 in

From the copper tube of industry standard guide of the design and the installation of piping system, the dimension and physical characteristics of type M copper tubing of nominal size 4 inch is given as

Outer diameter (Do) = 4.125 in ⇒ ro = Do ÷ 2 = 2.0625 in, Inner diameter (Di) = 3.935 in ⇒ ri = Di ÷ 2 = 1.9675 in

calculate the volume of the pipe, we use the formula

V = π(ro² - ri²) * l

V = π(2.0625² - 1.9675²) * 1200

V = 1443.3 in³ or 0.835 ft³

Answer:

a=0.000000002

b=0.95762

c=$2800

Step-by-step explanation:

Kindly check attached picture for other calculation and the Poisson Probability Distribution for the problem.

Answer:

a) s = (4-t)/(t^2+4)^2,   a(t) = (2t^3-24t)/(t^2+4)^3

b) s = 0.2ft, v = 0.12 ft/s,  a = -0.176 ft/s^2

c) t = 2s

d) slowing down for t < 2, speeding up for t > 2

e) 0.327 ft

Step-by-step explanation:

The position function of a particle is given by:

[tex]s(t)=\frac{t}{t^2+4},\ \ \ t\geq 0[/tex]   (1)

a) The velocity function is the derivative, in time, of the position function:

[tex]v(t)=\frac{ds}{dt}=\frac{(1)(t^2+4)-t(2t)}{(t^2+4)^2}=\frac{4-t^2}{(t^2+4)^2}[/tex]   (2)

The acceleration is the derivative of the velocity:

[tex]a(t)=\frac{dv}{dt}=\frac{(-2t)(t^2+4t)^2-(4-t^2)2(t^2+4)(2t)}{(t^2+4)^4}\\\\a(t)=\frac{(-2t)(t^2+4)-4t(4-t^2)}{(t^2+4)^3}=\frac{2t^3-24t}{(t^2+4)^3}[/tex] (3)

b) For t = 1 you have:

[tex]s(1)=\frac{1}{1+4}=0.2\ ft\\\\v(1)=\frac{4-1}{(1+4)^2}=0.12\frac{ft}{s}\\\\a(1)=\frac{2-24}{(1+4)^3}=-0.176\frac{ft}{s^2}[/tex]

c) The particle stops for v(t)=0. Then you equal equation (2) to zero ans solve the equation for t:

[tex]v(t)=\frac{4-t^2}{(t^2+4)^2}=0\\\\4-t^2=0\\\\t=2[/tex]

For t = 2s the particle stops.

d) The second derivative evaluated in t=2 give us the concavity of the position function.

[tex]\frac{d^2s}{dt^2}=a(2)=\frac{2(2)^3-24(2)}{(2^2+4)^3}=-0.062<0[/tex]

Then, the concavity of the position function is negative. For t=2 there is a maximum. Before t=2 the particle is slowing down and after t=2 the particle is speeding up.

e) Due to particle goes and come back. You first calculate s for t=2, then calculate for t=5.

[tex]s(2)=\frac{2}{2^2+4}=0.25\ ft[/tex]

[tex]s(5)=\frac{5}{5^2+4}=0.172\ ft[/tex]

The particle travels 0.25 in the first 2 seconds. In the following three second the particle comes back to the 0.172\ ft. Then, in the second trajectory the particle travels:

0.25 - 0.127 = 0.077 ft

The total distance is the sum of the distance of the two trajectories:

s_total = 0.25 ft + 0.077 ft = 0.327 ft

Answer:

8/3 km

Step-by-step explanation:

we can represent the given information on a table:

Kilometers        time (hours)

      2/5           ⇔         1 1/2

and since we want to know how many kilometers (x) will be paved on 10 hours:

Kilometers        time (hours)

      2/5           ⇔         1 1/2

        x             ⇔         10

The relationship these 3 numbers have can be described by using the rule of three, which is to multiply the cross quantities on the table (2/5 by 10) and then divide by the remaining amount (1 1/2):

x = [tex]\frac{2}{5}*10[/tex] ÷ [tex]1\frac{1}{2}[/tex]

x = [tex]\frac{20}{5}[/tex] ÷ [tex]1\frac{1}{2}[/tex]

we use [tex]1\frac{1}{2}=\frac{3}{2}[/tex]

x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex]

and we make the division:

x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{20*2}{5*3}=\frac{40}{15}[/tex]

we simplify the fraction by dividing the numerator and denominator both by 5, and we get the result:

x = [tex]\frac{8}{3}[/tex]

thus, in 10 hours the crew will pave 8/3 km. Which is about 2.66 km.

Answer: there is a relationship between study hours and test score. as the hours of studying increase, the test scores increase.

Answer:

C) There is a relationship between study hours and test score. As the hours of studying increase, the test scores increase.

Step-by-step explanation:

In the scatter plot, I can see that when the hours increase, so does the test scores. Thus, the answer is C

Answer:

[tex]X \sim N(200000,100000)[/tex]  

Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

[tex] Number = 1216*0.16 = 194.56[/tex]

And the answer woud be between 194 and 195 houses

Step-by-step explanation:

Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200000,100000)[/tex]  

Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

[tex] Number = 1216*0.16 = 194.56[/tex]

And the answer woud be between 194 and 195 houses

Answer:

B because when you compare y= mx+ c where M is the slope or gradient

Answer:

Step-by-step explanation:

For brand A,

Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44

standard deviation, s1 = √(summation(x - mean)²/n

Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338

Standard deviation = √(49.6338/9

s1 = 2.35

For brand B,

Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89

Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024

Standard deviation = √(124.5024/13

s2 = 3.09

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.

Degree of freedom =

(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20

z = 2.528

x1 - x2 = 33.44 - 36.89 = - 3.45

Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935

The 98% confidence interval is

- 3.45 ± 2.935

Answer:

[tex]\sigma = 5.5[/tex]

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:

[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]

And the standard error would be:

[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]

And replacing we got:

[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]

Step-by-step explanation:

For this case we know the population deviation given by:

[tex]\sigma = 5.5[/tex]

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:

[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]

And the standard error would be:

[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]

And replacing we got:

[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]

Answer:

20.7 miles

Step-by-step explanation:

[tex]2(5.4)+2t=52.2 \\\\10.8+2t=52.2 \\\\2t=41.4 \\\\t=20.7[/tex]

Hope this helps!

Given:

To find out:

Find the value of t ?

Formula used:

Perimeter = 2 ( length + Breadth )

Solution:

We know that,

Perimeter = 2 ( length + Breadth )

☆ Substituting the values in the above formula,we get

=> 52.2 = 2 ( 5.4 + t )

=> 52.2 = 10.8 + 2t

=> 2t = 52.2 - 10.8

=> 2t = 41.4

=> t = 41.4/2

=> t = 20.7

Answer:

0.927

Step-by-step explanation:

Hope this helps.

Answer:

I think it would just be 0.927

Step-by-step explanation:

with 0.9267, 6 is in the thousandth spot. 2 is in the hundredth spot, and 9 is in the tenth spot. Since the number behind 6 is larger than five, you'd round your number 6 in the thousandth spot to a 7. Therefore, you should have 0.927.

Answer:

40

Step-by-step explanation:

let the numbers be a+b+c+d.

the average of 4 numbers is 38

; (a+b+c+d)/4 = 38

(a+b+c+d) = 152 ......equ1

the average of the first two numbers is 42

; (a+b)/2 = 42

(a+b) = 84 ...... equ2

the average of the last three numbers is 36

; (b+c+d)/3 = 36

(b+c+d) = 108 .....equ3

substitute equ3 into equ1

a + 108 = 152

a= 152 - 108

a = 44

input the value of a into equ2

44 + b = 84

b = 40

the second number is 40.

I hope this helps.

Answer:

C/B

Step-by-step explanation:

Ax + By = C

Subtract Ax from each side

Ax -Ax+ By =-Ax+ C

By = -Ax +C

Divide each side by B

By/B = -A/Bx +C/B

y = -A/Bx +C/B

The y intercept is C/B

Answer:

$0.95 per song.

Step-by-step explanation:

If it is $6.65 for 7 songs, divide that cost by the number of songs and you get the unit rate. Hope this helps!

Answer:

Interquartile range IQR = 5.5

Step-by-step explanation:

Interquartile range IQR = third quartile Q3 - first quartile Q1

IQR = Q3 - Q1 ........1

arranging the data in ascending order;

1,3,5,6,6,7,8,11,12

The median of the data is the 5th number which is 6

Separating the data into two halves;

(1,3,5,6,),6,(7,8,11,12)

The first quartile Q1 is; (the median of the first half)

Q1 = (3+5)/2 = 4

The third quartile Q3 is; (the median of the second half)

Q3 = (8+11)/2 = 9.5

The interquartile range IQR can be derived using equation 1;

IQR = Q3 - Q1 = 9.5 - 4

IQR = 5.5

Answer:

44

Step-by-step explanation:

f(x) = 6x - 4

f(8) = 6(8) - 4

f(8) = 48 - 4

f(8)= 44

Answer: A. 85ᴼC

Step-by-step explanation:

0 degrees Celsius is at 32 degrees Fahrenheit.

100 degrees Celsius is at 212 degrees Fahrenheit.

212 - 32 = 180

180 / 100 = 1.8

So, every degree Celsius is 1.8 degrees Fahrenheit, starting at 32 of course.

1.8 * 85 = 153

153 + 32 = 185

Answer:

The correct answer is 85°C.

Step-by-step explanation:

I use the equation 9C = 5F - 160 to solve for temperatures.

Therefore, we just insert values for each variable except for the one that we want to solve for. In this case, we are doing Fahrenheit → Celsius, so we are solving for the unknown variable of C. We are given a value for F, 185°.

Therefore, just insert these into the equation and solve for C.

[tex]9C = 5(185)-160[/tex]

[tex]9C = 925 - 160[/tex]

[tex]9C = 765[/tex]

[tex]\frac{765}{9} = 85[/tex]

C = 85°C

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]

This is a left tailed test.

Step-by-step explanation:

A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has decreased from the 2001 mean of ​$47.79.

Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.

The null hypothesis will state that the monthly bill does not differ significantly from $47.79.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]

As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.

Answer:

ten-thousandths place

Step-by-step explanation:

You start by going to the right side of the decimal. The order is tenths, hundredths, thousandths, ten-thousandths.

Answer: 21 is the least common denominator

Step-by-step explanation:

The least common denominator of 7 and 6 is 42, but will be simplified.

The fractions would turn into 30/42 and 28/42.

Now simplify.

15/21 and 14/21

This cannot be simplified any further without losing the common denominator

Answer:

The least common denominator is 21.

Step-by-step explanation:

Put the fractions out of a denominator of 42

5/7 = 30/42          4/6 = 28/42

Divide both fractions by 2

35/42 = 15/21       4/6 = 14/21

Answer: The answer is given below

Step-by-step explanation:

In statistics, a stratified sampling is a method of sampling that is gotten from a population that can be divided into subpopulations.

Based on th information provided in n the question, the 6 most populous counties and their populations are provided below

Mecklenburg County, North Carolina 969,031

Wake County, North Carolina 952,151

Guilford County, North Carolina 500,879

Forsyth County, North Carolina 358,137

Cumberland County, North Carolina 324,049

Durham County, North Carolina 279,64

Answer:

I think it's just E.

Step-by-step explanation:

When you name triangles, you would often put a Δ and then the letters of the 3 angles. The only answer that fits that criteria is E.

The valid name for the given triangle is ΔΧΜΑ.

A triangle is a 3-sided polygon that consists of three edges and 3 vertices. The most vital asset of a triangle is that the sum of the inner angles of a triangle is identical to a hundred and eighty tiers. This belonging is called the attitude sum property of the triangle.

Learn more about triangle here https://brainly.com/question/2938476

#SPJ2

Answer:

80 shipments will be 80 * 431 = 34,480 coats.

Answer:

(A)C,D,A,B

Step-by-step explanation:

[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]

a)

[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]

b)

[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]

c)

[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]

d) f(5) : g(2)

[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]

9514 1404 393

Answer:

  |m-2.5| ≤ 0.08

  2.42 ≤ m ≤ 2.58

Step-by-step explanation:

The equation of interest is the one that says the positive difference from the ideal mass is at most 0.08 ounces:

  |m -2.5| ≤ 0.08 . . . an absolute value inequality

The solution is found by solving the equivalent compound inequality:

  -0.08 ≤ m -2.5 ≤ 0.08

  2.42 ≤ m ≤ 2.58 . . . . the range of masses

Answer:

[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]

[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]

And the 95% confidence interval would be given (0.107;0.227).

Step-by-step explanation:

Information given

[tex]X= 25[/tex] number of trees with signs of disease

[tex] n= 150[/tex] the sample selected

[tex]\hat p=\frac{25}{150}= 0.167[/tex] the proportion of trees with signs of disease

The confidence interval for the true proportion would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 95% confidence interval the significance is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], and the critical value would be

[tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]

[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]

And the 95% confidence interval would be given (0.107;0.227).