A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.

Answer:

60%

Step-by-step explanation:

Percent means out of 100

Changing 3/5 to a denominator of 100

3/5*20/20

60/100

The percent is 60 %

Answer:

25

Step-by-step explanation:

use a Poisson process to model the arrival.

the mean rate of arrivals  is λ=4.5

The standard deviation is calculated as:

σ==√λ =2.1213

The z-value for a 98% CI is z=2.3262.

If the 98% CI has to be within a error of 0.5 then:

Ul-Ll=2z*σ/√n=2*0.5=1

√n=z*σ=2.3262*2.1213=4.9346

√n=4.9346  and n = 4.9346^2=24.35 rounded to 25

The sample size needed is n=25.

Answer:

76 cm

Step-by-step explanation:

To find the perimeter, add up all of the side lengths.

18 cm + 26 cm + 32 cm = 76 cm

I hope this helps :))

Answer: 95 degrees

Step-by-step explanation:

We can infer than angles 1, 4, 5, 8 are all equal and angles 2, 3, 6, 7 are also equal to eachother. These two sets of angles are supplementary(you’d get 180 by adding them)

So 3x+10=4x-15

if you rearrange you'll get

x=25

therefore angle 1 equals

3*25+10=85

angle 1 and 7 are supplementary

thus angle 7 equals

180-85=95

Answer:

A right triangle consists of two legs and a hypotenuse.

Step-by-step explanation:

The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Answer:

B. Average of the data set

Step-by-step explanation:

The mean is defined as the average of a data set and it's formula is

Mean = [tex]\frac{sum of observations}{number of observations}[/tex]

Answer:

The null and alternative hypothesis for this problem are:

[tex]H_0:\mu=380\\\\H_a: \mu>380[/tex]

Step-by-step explanation:

The alternative hypothesis shows the claim of the researchers. In this case, that the new type of fertilizer significantly increase the actual yield with the old fertilizer:

[tex]H_a: \mu>380[/tex]

The null hypothesis is the hypothesis to be nullified, so it states that the claim is not true and the yield is the same (or, at least, not significantly higher) as with the old fertilizer:

[tex]H_0: \mu=380[/tex]

Answer:

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Step-by-step explanation:

Two planes:

The first one's speed is x

The second is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x.

Two airplanes leave an airport at the same time, flying in the same direction

Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.

Means that after 1 hour, they will be x miles apart.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Hi

X-17 = -5

X = -5+17

X = 12

Answer:

Step-by-step explanation:

I'm pretty sure that you have to add 17 on both sides to keep the final number, not negative.  

So like:

x-17=-5

+17   +17

x-0=12            

and because 0 is nothing really, x=12

Answer:

Option c

Step-by-step explanation:

This is an experiment because the researcher wants to test efficiency of the magnetic bracelets in the elimination of motion sickness i.e. whether they experienced motion sickness even after wearing the magnetic bracelets.

Answer:

P(B) = 0.62

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B)

So, Putting the givens

0.89 = 0.48 + P(B) - 0.21

0.89 = 0.27 + P(B)

P(B) = 0.89 - 0.27

P(B) = 0.62

Answer:

x - 5 - (3/x+8)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

We need the function f(x) to be able to determine the required.

Suppose we were given a function

f(x) = y

f'(x) represents the first derivative of the function f(x) = y.

f'(1) represents the value of the first derivative of the function f(x) = y after replacing x by 1.

f'(5) represents the value of the first derivative of the function f(x) = y after replacing x by 5.

Example: Suppose f(x) = x² + 3x, find

f'(x), f'(1), and f'(5).

f'(x) = 2x + 3

f'(1) = 2(1) + 3 = 5

f'(5) = 2(5) + 3 = 13

Answer: About 6.2%

Step-by-step explanation:

He starts with 5500 and gains 893.75 in 2.5 years.

The equation is then 5500*(x)^2.5 = 5500+893.75, or

5500*x^2.5 = 6393.75.

x is about 1.0621, or about 6.2% because it's interest.

Hope that helped,

-sirswagger21

Answer: 137.5%

Step-by-step explanation

Answer: (-6, 0)

Step-by-step explanation:

X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".

In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":

y = (x + 6)(x - 3)

y = 0

(x + 6)(x - 3) = 0

With this equation, you can find which points lie on the x-axis.

When x = -6, the equation is: 0 * -9 = 0, which is correct.

When x = 3, the equation is 9 * 0 = 0, which is correct.

Make sure you're picking the correct coordinate out of the answer choices.

The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.

The correct answer is (-6, 0).

(3, 0) is also correct, but the question does not require it.

Answer:

D

Step-by-step explanation:

Answer:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]

So the answer for this case would be n=369 rounded up to the nearest integer

Step-by-step explanation:

We know the following info given:

[tex] \sigma = 1.8[/tex] represent the standard deviation

[tex]\mu = 5.8[/tex] the true mean that she believes

[tex] ME = 0.12[/tex] represent the margin of error

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]

So the answer for this case would be n=369 rounded up to the nearest integer

Answer:

D: <K = 35°

Step-by-step explanation:

<E = 55

<L = 90°

Now

<LKE = 180-90-55

<K = 35°

Answer:

[tex]\fbox{\begin{minipage}{8.8em}Option D is correct\end{minipage}}[/tex]

Explanation:

Here, we state again the definition of inscribed angle in circle:

(1) An inscribed angle has the vertex on the circle and the sides are chords.

=> In the picture shown, angle ELK is inscribed angle with vertex L and LE and LK are chords.

(2)An inscribed angle also creates an intercepted arc whose endpoints are on the angle.

=> Inscribed angle ELK creates intercepted arc EK.

(3) According to the Inscribed Angle Theorem, the measure of intercepted arc is twice as the measure of its inscribed angle.

=> Angle ELK = (1/2) arc EK

Arc EK, whose EK is diameter, is equal to measure of half of circle, or 180 degree, in other words.

=> Angle ELK = (1/2) x 180 = 90 deg

(4) As the property of sum of 3 angles inside a triangle, this sum is equal to 180 degree.

=> Considering triangle ELK:

ELK + LEK + LKE = 180 deg

or

90 + 55 + LKE = 180 deg

or

LKE = 180 - 90 - 55 = 35 deg

Hope this helps!

:)

Answer19/40=x/3.6

By cross multiplication

19*3.6=40*x

68.4 =40x

x=68.4/40

x=1.71

x=

Answer: C

Step-by-step explanation:

[tex]\frac{19}{40} = \frac{x}{3.6}[/tex]     solve by cross product

40x = 68.4   Divide both sides by 40

x =  1.71

Answer:

C.

Step-by-step explanation:

According to theorem, "the measure of central angle of minor Arc of a circle is doubleto that of the angle subtended by the corresponding major Arc."

So

m<AOB = 2(m<AZB)

m<AZB = M<AOB / 2

m<AZB = 68/2

m<AZB = 34°

Answer:

34° is right answer

Step-by-step explanation:

correct answer is 34

We have a right triangle and we're given the leg lengths.  

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

tan X = YZ / XZ = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

Answer:

A. 1/2

Step-by-step explanation:

In this uniform distribution (from 6 to 12 pounds), the probability of any given range (from 'a' to 'b' pounds) is determined by:

[tex]P = \frac{b-a}{12 - 6}[/tex]

For a = 8 pounds and b = 11 pounds, the probability is:

[tex]P=\frac{11-8}{12-6}\\P=\frac{3}{6}=\frac{1}{2}[/tex]

The probability of the range of pounds lost being between 8 pounds and 11 pounds is 1/2.

Answer:

Option (2). x = 20°

Step-by-step explanation:

In the figure attached,

ΔABC is an equilateral triangle.

By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.

By this property,

m∠B = 60°

and y = 46 - 16 = 30

By applying Sine rule in ΔBCD,

[tex]\frac{\text{sin}60}{BD}=\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{DC}[/tex]

[tex]\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{y}[/tex]

sin(∠CBD) = [tex]\frac{30\times \text{sin}80}{46}[/tex]

                 = 0.6423

m∠CBD = 39.96

              ≈ 40°

m∠ABD = 60° - 40°

             = 20°

Therefore, Option (2). 20° will be the answer.

Answer:

Step-by-step explanation:

) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left?

Skewed to the left.

Symmetric

Skewed to the right.

(b) Two measures of center for this distribution are 1 friend and 5.3 friends. Which is most likely to be the mean and which is most likely to be the median?

Mean=

Median=

a)

as proportion of people with 0 friends is 43% whcih is on left side and maximum ; and % decrease with increasing number of friends

skewed to the right

b)

as it is skewed to the right ; therefore mean is greater than median

mean=5.3

median=1

[since for skwewed to the right distribution :mean is always greater than median, therefore higher value should be mean which is 5.3 and lower value is median which is 1]

Part(a): Skewed to the right

Part(b) The required values are,

mean=5.3

median=1

a)

As a proportion of people with 0 friends are 43% which is on the left side and maximum; and % decrease with an increasing number of friends

skewed to the right

b)

As it is skewed to the right; therefore mean is greater than the median

mean=5.3

median=1

Learn More:https://brainly.com/question/11729451

Answer:

4 pizza's

Step-by-step explanation:

hope this helps :)

Answer:

First we need to calculate 1 part.

Calculate big part first

13*15 = 195

7*12 = 84

195+84=279

279

279 is answer

Answer: 279 yd^2

Step-by-step explanation:

Separate this into two separate rectangles: the larger top rectangle (13 yd x 15 yd) and the smaller bottom rectangle (12 yd x 7 yd).

area of rectangle 1 + area of rectangle 2 = total area of figure

b1(h1) + b2(h2) = total area

13(15) + 7(12) = total area

195 + 84 = total area

279 yd^2 = total area

Answer:

a) at 5 minutes: 162 gal/min

b) at 10 minutes:  144 gal/min

c) at 20 minutes:  108 gal/min

d) at 50 minutes: 0 gal/min

Step-by-step explanation:

Considering the formula given by the volume of water remaining in the tank:

we can find the rate of water draining from the tank, (that is change in volume divided elapsed time) with the derivative of the function at the different times. Notice that this function has a decaying curvature (see attached image) of volume as a function of time, and the idea is therefore to find the slope of the tangent line at the different requested times.

So we first calculate the derivative of this function at any time 't":

[tex]V(t)=4500\,(1-\frac{1}{50} \,t)^2\\V'(t)=9000\,(1-\frac{1}{50} \,t)\,(-\frac{1}{50})\\V'(t)=-180(1-\frac{1}{50} \,t)\\V'(t)=-180+3.6\,t[/tex]

And now we estimate this derivative at the different requested points for time values:

a) at 5 minutes:  [tex]V'(5)=-180+3.6\,(5) = -162\,\,gal/min[/tex]

b) at 10 minutes:   [tex]V'(10)=-180+3.6\,(10) = -144\,\,gal/min[/tex]

c) at 20 minutes:   [tex]V'(20)=-180+3.6\,(20) = -108\,\,gal/min[/tex]

d) at 50 minutes:  [tex]V'(50)=-180+3.6\,(50) = 0\,\,gal/min[/tex]

All the negative signs preceding indicate that the remaining volume in the tank is reducing as time goes by, so the volume at which the water is draining is actually the absolute value of those numbers.

Answer:

432

Step-by-step explanation:

l x w

4x3

4x19

8x24

8x19

432

Answer:

A.

Step-by-step explanation:

Since they are similar, hence taking proportionality,

CA/CB = d1/d2

Cross Multiplying

We get

CA × d2 = CB × d1

OR

d1×CB = d2 × CA

answer is g(x)=|x+2|-1

[tex]answer \\ g(x) = - |x + 2| - 1\\ as \: we \: can \: see \: from \: the \: given \: graph \\ above \: that \: the \: graph \: of \: absolute \\ function \: has \: been \: reflected \: over \: the \\ x \: axis \: \: shifted \: 2 \: units \: left \: and \: 1 \: \\ units \: down. \\ due \: to \: reflection \: there \: is \: a \: negative \\ sign \: shift \: of \: 2 \: units \: left \: is \: given \\ by \: x + 2 \: and \: 1 \: units \: down \: is \: given \\ by \: - 1 \\ hope \: it \: helps[/tex]

Answer:

a) H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

b) [tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

c) [tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Step-by-step explanation:

Information provided

n = 10 sample size

s= 1.186 the sample deviation

[tex]\sigma_o =1.34[/tex] the value that we want to test

[tex]p_v [/tex] represent the p value for the test

t represent the statistic  (chi square test)

[tex]\alpha=0.01[/tex] significance level

Part a

On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:

H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

The statistic is given by:

[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]

Part b

The degrees of freedom are given by:

[tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

Part c

Replacing the info we got:

[tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

Part d

For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34