A trapezoid is shown. The lengths of the bases are 4 and 8. The height of the altitude is 4. What is the area of the trapezoid?

Answer:

10.03% probability of getting a cup weighing more than 8.64oz

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 8, \sigma = 0.5[/tex]

What is the probability of getting a cup weighing more than 8.64oz

This is the 1 subtracted by the pvalue of Z when X = 8.64. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.64 - 8}{0.5}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a pvalue of 0.8997

1 - 0.8997 = 0.1003

10.03% probability of getting a cup weighing more than 8.64oz

Answer:

6

Step-by-step explanation:

Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.

x = 8 *3/4 = 6

Answer:

D

Step-by-step explanation:

It's a football ....=> So ... A sphere !!

Step-by-step explanation:

work is shown and pictured

Answer:

27 stuffed bears

Step-by-step explanation:

Erin: 55   Su: 15

Erin: 55-7=48 ( 7 will be kept for herself)

Erin and her sisters: 48/4= 12

Each sister besides Erin and Su have 12

Su: 15+12=27

Thus, Su will have 27 stuffed bears

Answer:

31 Stuffed Bears

Step-by-step explanation:

55 - 7 = 48

48 / 3 = 16

16 + 15 = 31

Sue has 31 stuffed bears

Answer:

Step-by-step explanation:

[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]

Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.

Problem solved

Answer:

Thus; the slope is positive

Step-by-step explanation:

Given that :

the sample size = 20

for the slope; the degree of freedom df = n - 2

= 20 -2

= 18

Using ∝ = 0.05

From t -table , one tailed, at df =18)

[tex]t_{\alpha , df}}= t_{0.05, df = 18} = 1.734[/tex]

Thus the t- critical for the right tailed test is 1.734. This simply refers to the fact that the critical region is test statistics.

Incorporating the Excel Formula [ T.INV (1 - 0.05).18) = 1.734063607

≅ 1.734

the correct answer is 59.

Answer:

59

Step-by-step explanation:

Answer:

4z + 2 - 5/2z

Step-by-step explanation:

8z^2 + 4z -5

divided by 2z

8z^2 /2z = 4z

4z/2z =2

5/2z = 5/2z

Putting them back together

4z + 2 - 5/2z

Answer:

A   4z + 2 - 5/2z

Step-by-step explanation:

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]

Compute the probability that on a randomly selected day she will have five messages as follows:

[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]

               [tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Answer:

(x+4)^2+(y+6)^2 = 25

Step-by-step explanation:

The radius squared is equal to the distance between the center and the point

3^2 + 4^2 = 25

We can shift the center like this

(x+4)^2+(y+6)^2 = 25

I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.

Answer:

[tex]g^{-1}(x)=\frac{x-1}{6}[/tex]

Answer:

Step-by-step explanation:

Hello!

I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values

When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.

In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.

The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.

Watching the example, the median is 33

I hope this helps!

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

for |2x+5|=

[tex]\left \{ {{2x+5}~~~~if~~~~2x+5 > 0 ~~or ~~~~x>\frac{-5}{2}~~(case 1) \\ \atop {-2x-5}} ~~~~~if~~~2x+5 <0 ~~~~or~~~x<\frac{-5}{2}~~(case 2)[/tex]

for |x-1| = [tex]\left \{ {{x-1 } ~~~~if~~~x-1>0 ~~~or~~~x>1 ~~(case 3)\atop {1-x}} ~~~~if ~~~~x-1<0 ~~~~or~~~x<1 \right. (case 4)[/tex]

Answer:

C.

Step-by-step explanation:

Measure of arcURN = 270°

In radians:

270° = 270π/180

270° = 3π/2

Now

Area of sector = 1/2r²∅

= 1/2(10)²(3π/2)

= 50(3π/2)

= 75π

Answer:

The volume of the crystal is [tex]V=125 \:cm^3[/tex].

Step-by-step explanation:

The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.

To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula

                                                         [tex]V=s^3[/tex]

where:

s is the length of any edge of the cube.

From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is

[tex]V=5^3=125 \:cm^3[/tex].

In the given point(-4,b) -4 is the x value.

Locate -4 on the graph and find the y value where the line is located. The y value would be b.

B = 1

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

Answer:

33084

Step-by-step explanation:

22056 divided by 2 =11028

altogether (on sunday and monday) the total amount would be..

22056+11028=33084

Answer:

33084

Step-by-step explanation:

If 22056 people came to the game on Sunday and Half as many people came on Monday, you do

22056 divided by 2. this is how many people cam on monday

Add this answer to 22056 and this is how many people came on both days.

Answer:

False

Step-by-step explanation:

The greatest sum of two consecutive even integers would be 200 + 198, or 398

Answer:

its true

Step-by-step explanation:

Answer:

e. the gender of the students in a class

Step-by-step explanation:

Quantitative data is measured is numbers. For example 1, 2, 3.5,...

Qualitative data are labels, that is, tall, short, male, female, Brazilian, Colombian,...

In this question:

The only data that is not measured in numbers is the gender of the studens in class, which can be male or female, they do not assume any numeric value. So the answer is e.

The quantitive data example does not include option e. the gender of the students in a class.

learn more about the data here: https://brainly.com/question/20296761

Answer:

Step-by-step explanation:

Answer:

height = 5

Step-by-step explanation:

The volume of a prism is V = l*w*h

You are not given any information about the exact values of l and w.

You do know however that L and w when multiplied together = 20, so you can put that in for l*w. Then the formula becomes

V = 20*h

You are told that the volume is 100. Now the problem is simplified. You get

100 = 20 * h               Divide both sides by 20

100/20 = 20*h/20     Combine like terms.

5 = h

Answer:

n2-6n-16

Step-by-step explanation:

n(n+2)-8(n+2)

n2+2n-8n-16=

n2-6n-16

Answer: n 2 + 6n - 16

Step-by-step explanation:

Answer:

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Step-by-step explanation:

(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=

–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Answer:

h ≈ 77 cm

Step-by-step explanation:

Let us convert the liters to cm³.

Smaller barrel

0.001 litres = 1 cm³

100 litres = 100000  cm³

Larger barrel

0.001 litres = 1 cm³

160 litres = 160000  cm³

For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.

This means

h³/90³ = 100000/160000

cube root both sides

h/90 =  ∛100000 / ∛160000

h/90 = 46.4158883/54.2883523

cross multiply

54.2883523h = 46.4158883 × 90

54.2883523h = 4177.429947

divide both side by  54.2883523

h = 4177.429947/54.2883523

h = 76.9489175858

h ≈ 77 cm

Answer: 0.149

Step-by-step explanation:

As Scientists wondered how the snails could travel such long distances. A recent study provides the answer. Biologist Shinichiro Wada fed 174 live snails to birds and found that 26 of the snails were excreted live out the other end.

The best estimate for the proportion of all snails of this type to live after being eaten by a bird can be achieved by calculating the ratio of survival/number of eaten snails

Where the number of eaten snails = 174

The number of survivors = 26

Estimated proportion = 26/174 = 0.1494

Therefore, the best estimate for the proportion of all snails of this type to live after being eaten by a bird will be 0.149 approximately.

Answer:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Step-by-step explanation:

For this case we can use the following function to model the population of protzoa:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Answer:

360 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes