The base (b) of the triangle is units. The height (h) of the triangle is units. The area of the triangle is square units.

Answer:

3.00

Step-by-step explanation:

3.14 is rounded to 3.00

Answer:

141.3 m²

Step-by-step explanation:

V= πr²h

V=3.14*(6/2)²*5= 141.3 m²

Answer:

Step-by-step explanation:

Hello!

Hypotheses:

H₀: μ₁ = μ₂

H₁: μ₁ < μ₂  

α: 0.05

Using the following sample information:

Sample 1

n₁= 15

X[bar]₁= 10

S₁= 4

Sample 2

n₂= 27

X[bar]₂= 8

S₂= 7

This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:

[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*16+26*49}{15+27-2} }= \sqrt{\frac{1498}{40} } = 6.119= 6.12[/tex]

[tex]t= \frac{(10-8)-0}{6.12*\sqrt{\frac{1}{15} +\frac{1}{27} } }= 1.01[/tex]

The p-value of this test is 0.1593

To decide using the p-value approach you have to use the following rule:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.

I hope this helps!

Answer:

Height h = 5 cm

Step-by-step explanation:

Given;

Volume of box V = 180 cm^3

Base area of box A = 36 cm^2

Height = h

Volume = base area × height

height = volume/base area

h = V/A

Substituting the values;

h = (180cm^3)/(36cm^2)

Height h = 5 cm

Answer:

Yo

Step-by-step explanation:

Answer:

Step-by-step explanation:

The null hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is less than or equal to the national average: u ≤ 150

The alternative hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average: u > 150

Since the p-value of 0.0099 was gotten which is less than the significance level of 0.05, we reject the null hypothesis and conclude that actually there is a statistically significant evidence to prove that the mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average

Answer: P = 0.28

Step-by-step explanation:

If we pick it at random, the probability of selecting each tile must be equal. this means that the probability of picking a tile of a giving color is equal to the number of the tiles of that color divided the total number of tiles.

We have 14 beige tiles and 20 + 14 + 16 = 50 tiles in total.

Then the probability of piking a beige tile is:

P = 14/50 = 0.28

Answer:

2x^2 -3x -8

Step-by-step explanation:

f(x) = 2x^2 - 5

g(x) = 3x + 3,

(f - g)(x)=  2x^2 - 5 -(3x + 3)

Distribute the minus sign

(f - g)(x)=  2x^2 - 5 -3x - 3

Combine like terms

            = 2x^2 -3x -8

Answer:

The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).

Step-by-step explanation:

The question is incomplete:

"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."

We start by calculating the mean of the sample:

[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is know and is σ=24.

The sample mean is M=146.

The sample size is N=9.

As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]

The 95% confidence interval for the population mean is (130.32, 161.68).

Answer:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]

Step-by-step explanation:

Total Number of People on Campus =1000

Let the number of people who have contracted the flu =x(t)

Therefore, the number of people who have not contracted the flu =1000-x(t)

Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.

[tex]\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)][/tex]

Introducing the proportional constant k, we obtain:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)][/tex]

At t=0, there was no infected on the campus, therefore the initial condition is given:

[tex]x(0)=0[/tex]

Therefore, a differential equation for the number of people x(t) who have contracted the flu is:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]

Answer:

Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.

Step-by-step explanation:

We are given that a recent study reported that 73% of Americans could only converse in one language.

A random sample of 130 Americans was randomly selected.

Let [tex]\hat p[/tex] = sample proportion of Americans who could only converse in one language.

The z score probability distribution for sample proportion is given by;

                                 Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion of Americans who could only converse in one language = 73%

           [tex]\hat p[/tex] = sample proportion = [tex]\frac{100}{130}[/tex] = 0.77

           n = sample of Americans = 130

Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77)

      P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.77-0.73}{\sqrt{\frac{0.77(1-0.77)}{130} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.08) = 0.8599                    

The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.

Answer:

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Step-by-step explanation:

[tex]5y^3/5y^-2[/tex]

as 5 is both in numerator and denominator it will get cancelled so we have now expression

[tex]y^3/y^-2[/tex]

we will use  law of indices wherein if there is

[tex]a^x/a^y = a^(x-y)[/tex]

which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept

here power in numerator is 3 and power in denominator  is -2

hence we will be subtracting -2 from 3

[tex]y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5[/tex]

Thus,

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Length and width of rectangle is 86 unit and 15 unit

Given that;

Perimeter of a rectangle = 202

Length of rectangle = 26 + 4[Width]

Find:

Dimensions of rectangle

Computation:

Assume;

Width of rectangle = a

So,

Length of rectangle = 4a + 26

Perimeter of a rectangle = 2[l + b]

202 = 2[(4a + 26) + a]

101 = 4a + 26 + a

5a + 26 = 101

5a = 75

a = 15

Width of rectangle = 15 unit

Length of rectangle = 4a + 26

Length of rectangle = 4(15) + 26

Length of rectangle = 60 + 26

Length of rectangle = 86 unit

Learn more:

https://brainly.com/question/16669749?referrer=searchResults

Answer:

Ashley’s backpack is the better buy.

Step-by-step explanation:

You have to calculate the price that was paid for each backpack after the discount was applied.

Ashley’s backpack: $65*0.25= $16.25

Final price= $65-$16.25= $48.75

Robbin's backpack: $75*0.3= $22.5

Final price= $75-$22.5= $52.5

According to this, the backpack that is the better buy is the one that Ashley bought because after the discounts were applied it cost $48.75 and Robbin's backpack cost $52.2 which means that Ashley's backpack was cheaper.

Answer:

  y = 0; z = -5

Step-by-step explanation:

Excluded values are ones that make the fraction "undefined." That will be the case when the denominator is zero.

When y = 0, the denominator is zero.

When z = -5, the denominator is zero.

Excluded values are y = 0; z = -5.

Answer:

-5

Step-by-step explanation:

Answer: 16.1 ounces per minute

Step-by-step explanation:

in 7 days, he painted by 4 hours each day, so we have a total of 28 hours.

In a hour we have 60 minutes, so we have a total of:

28*60 = 1680 minutes.

He used 211 gallons, and knowing that 1 gallon is 128 ounces, then 211 gallons is:

211*128 ounces = 27,008 ounces.

Then the ounces dispensed each minute are:

R = 27,008/1680 ounces per minute = 16.1 ounces per minute

Answer:

Step-by-step explanation:

The arrow with two tips is translated as "if and only if". The symbols [tex]\land, \lor[/tex] and read as "and" and "or"respectively.

If we have the following p: it is hot today. q: it is sunny r: it is raining

Then

i. q ↔ p : It is sunny if and only if it is hot today.

ii. p ↔ ( q ˄ r ) : it is hot today if and only if it is sunny and it is raining

iii. p ↔ ( q ˅ r) : it is hot today if and only if it is sunny or it is raining

iv. r ↔ ( p ˅ q) : it is raining if and only if it is hot today or it is sunny

Answer:

He needs four packs.

Step-by-step explanation:

6*4=24 there is 23 so he will need 4 packs in total.

Answer:

4 packs

Step-by-step explanation:

3 packs only gives him 18 and he needs atleast 23. The closest number that meets 23 is 24. It takes 4 packs of 6 to get 24.

Answer:

yes this right, it depends on what one tho

Step-by-step explanation:

Answer:

Null hypothesis H0: p = 0.01

Alternative hypothesis Ha: p < 0.01

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.

H0: p = 0.01

The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.

Ha: p < 0.01

Answer:

135°, 63°, 63°, 99°

Step-by-step explanation:

Find attached the diagram used in solving the question.

We would use formula for sum of interior angles to get each exterior angle.

From the diagram, we added additional variables to be able to solve for sum of interior angles.

Sum of angle on a straight line = 180°

a° +15z° = 180°

b° +7z° = 180°

c° +7z° = 180°

d° +11z° = 180°

Where a,b,c and d are interior angles

Sum of interior angles = 180(n-2)

n = number of sides

For quadrilateral, n= 4

a°+b°+c°+d° = 180(n-2)

180-15z +180-7z+180-7z+180-11z = 180(4-2)

720-40z = 180(2)

720 - 360 = 40z

z = 360/40

z = 9

Each exterior angle:

15z = 15×9 = 135°

7z = 7×9 = 63°

7z = 7×9 = 63°

11z = 11×9 = 99°

Answer:

5

To find the first term

T(1)=(1×2)+3

=2+3

=5

Answer:

a) 10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.

b) 90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.

Step-by-step explanation:

Meaning of a percentile:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

(a) The 10th percentile of the weight of males 36 months of age in a certain city is 11.0 kg.

10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.

(b) The 90th percentile of the length of newborn females in a certain city is 53.3 cm.

90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.

Answer:

Y=2x-9

Step-by-step explanation:

Answer:

37.27% probability that he or she will have a heart attack.

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Periodontal disease

Event B: Heart attack

Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums.

This means that [tex]P(A|B) = 0.82[/tex]

Only 33% of healthy people have this disease.

This means that [tex]P(A) = 0.33[/tex]

Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.

This means that [tex]P(B) = 0.15[/tex]

If someone has periodontal disease, what is the probability that he or she will have a heart attack

[tex]P(B|A) = \frac{0.15*0.82}{0.33} = 0.3727[/tex]

37.27% probability that he or she will have a heart attack.

Answer:

1st one, I think so. I'm pretty positive

Answer:

Step-by-step explanation:

So, in this image, there are 6 blocks in total!

The little guy standing in front would only be able to see the bottom two cubes, along with the top two, making 4 blocks in total! :3

#SpreadTheLove <3

Answer:

No porque si sumas los dos el resultado es más de 90 grados.

Step-by-step explanation:

Answer:

a) Surviving the year: $ -161. Not surviving: 99,839.

b) 0.9986 * -161 + (1-0.9986) * 100000 = -20.7746

c) As the expected value is negative from the male's perspective, it is positive from the insurance company's perspective. So as the number of people purchasing this insurance becomes large, the company's profit will converge to an average value of 20.7746 per male. So the company is indeed profitting.

Answer:

Length = 2.823 in (to 3 decimal places)  

Step-by-step explanation:

assuming that the box is a cubic box:

volume of box = [tex]22\frac{1}{2}[/tex] in³ = 22.5 in³

volume = Length × Length × Length = (Length)³

∴ (Length)³ = 22.5

∴ Length = ∛(22.5)

using the calculator punch ∛(22.5), and the answer is:

∴ Length = 2.823 in (to 3 decimal places)

Answer:

[tex]sin\;60 =\frac{\sqrt{3} }{2}[/tex]

Answer:

Step-by-step explanation:

Adding the numbers because that is the only step.  Making it the last operation.