Reduce the fraction to lowest terms. Do not use spaces in your answer.

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:

4( x+6) (x-1)

Step-by-step explanation:

4x^2+20x-24

Factor out the greatest common factor

4(x^2 +5x-6)

What 2 numbers multiply to -6 and add to 5

6*-1 = -6

6+-1 = 5

4( x+6) (x-1)

Answer:

[tex]4(x-1)(x+6)[/tex]

Step-by-step explanation:

→Take out the GCF (Greatest Common Factor), which is 4:

[tex]4x^2+20x-24[/tex]

[tex]4(x^2+5x-6)[/tex]

→Split the middle term into two numbers that can be added to get 5 and multiplied to get 6:

[tex]4(x-1)(x+6)[/tex]

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).

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: 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:

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:

[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:

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

Then the mean would be:

[tex] \mu_{\bar X}= 2.02[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{3.00}{\sqrt{45}}= 0.447[/tex]

And the distribution would be given by:

[tex] \bar X \sim N(2.02, 0.447)[/tex]

Step-by-step explanation:

For this case we can define the variable of interest X as the amount of change in UF student's pockets and we know the following parameters:

[tex] \mu = 2.02, \sigma =3.00[/tex]

And we select a sample of n=45. Since this sample size is higher than 30 we can apply the central limit theorem and the distirbution for the sample size would be given by:

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

Then the mean would be:

[tex] \mu_{\bar X}= 2.02[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{3.00}{\sqrt{45}}= 0.447[/tex]

And the distribution would be given by:

[tex] \bar X \sim N(2.02, 0.447)[/tex]

Answer:

(7-2x)3 =9-10x

x= -3

Step-by-step explanation:

we let the number to be x.

twice a number=2x is decreased by 7 that is to say 7-2x, is multiplied by 3, we have (7-2x)3.

the result is 9 less than 10times the number which is =9-10x.

so bringing all these together we have;

(7-2x)3=9-10x.

what is the number?

solving, we have:

(7-2x)3=9-10x

21-6x=9-10x

21-9= -10x+6x

12= -4x

dividing both sides by -4 we have our number

x= -3.

for proof we can substitute x=-3 into the equation.

21-6(-3) =9-10(-3)

21+18=9+30

39=39

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 :

34.56

I hope it helps

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:

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:

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

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:

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

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:

44

Step-by-step explanation:

f(x) = 6x - 4

f(8) = 6(8) - 4

f(8) = 48 - 4

f(8)= 44

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:

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:

Step-by-step explanation:

A quadrilaterals are plane figures bounded by four sides. Examples are; square, rectangle, parallelogram, kite, trapezium etc.

Given: parallelogram WXYZ

           ZX ≅ WY

Prove: WXYZ is a rectangle

WZ ≅ XY (opposite sides property)

YZ ≅ WX (opposite sides property)

<WZY ≅ <ZWX ≅ <WXY ≅ <XYZ = [tex]90^{0}[/tex] (angle property of a rectangle)

<YZW ≅ <WXY (opposite angles are congruent)

ΔZYW ≅  ΔXTW (Side-Angle-Side property)

ZX ≅ WY

Therefore, the parallelogram is a rectangle.

Answer: This is the right answer

Step-by-step explanation:

Below

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: 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:

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:

Solution,

y-x+z

=6-4.6+0.59

=6+0.59-4.6

=6.59-4.6

=1.99

Hope this helps...

good luck on your assignment

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:

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:

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:

D

Step-by-step explanation:

because i took the test

Answer:

Option D: (9,3)

Step-by-step explanation: