2.4.16
Let:
U= {a,b,c,d,e,f,g,h}
A = {b,d,e}
B = {a,d,e}
C={a,c,f,g,h}
Find the set (AnB) U (Anc).
Select the correct choice below and if necessary fi

Here the l'Hospital's Rule is appropriate, as the limit is in the form [tex]\infty / \infty[/tex]. Take a look at the procedure below -

[tex]\lim_{x \to \infty} x^4e^{-x^3} = \lim_{x \to \infty} \frac{x^4}{e^{x^3}}[/tex],

At this point, one can conclude that the solution should " boil down " to the expression [tex]4 / \infty[/tex], and thus the solution is 0.

Hope that helps!

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]

This probability is not equal or less than 0.05, so it is not significant at 0.055.

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

yes, because they intercept the same arc

Step-by-step explanation:

Answer:

d = 3 in

Step-by-step explanation:

Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.

Answer:

4.167(10²)

Step-by-step explanation:

Step 1: Put number into proper decimal form

416.7 = 4.167

Step 2: Figure out exponent

Since we are moving the decimal places 2 places to the right, our exponent is 2

Answer:

4.167 × 10^2

Step-by-step explanation:

= 4.167 × 10^2

(scientific notation)

= 4.167e2

(scientific e notation)

= 416.7 × 10^0

(engineering notation)

(one)

= 416.7

(real number)

Answer:

Option (4)

Step-by-step explanation:

From the graph attached,

A dotted line passes through two points (3, 1) and (-3, -3)

Let the equation of the given line is,

y = mx + b

where 'm' = slope of the line

b = y-intercept

Slope of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

For the given points,

m = [tex]\frac{1+3}{3+3}[/tex]

m = [tex]\frac{2}{3}[/tex]

y-intercept 'b' = -1

Therefore, equation of the given line will be,

[tex]y=\frac{2}{3}x-1[/tex]

Since graphed line is a dotted line so it's representing an inequality(having < or > sign)

And the shaded part is below the dotted line,

Inequality will be,

y < [tex]\frac{2}{3}x-1[/tex]

Therefore, Option (4) will be the answer.

Answer:

D

Step-by-step explanation:

Correct:)

The correct answer is $216

Explanation:

The chart shows the price users need to pay for visiting the museum or riding on the train. This includes a difference in price between adults and students. However, as the club includes only students (27 students) the price that should be considered are $3 for visiting the museum and $5 for the train ride. Additionally, you can know the total the student spend if you multiply the prices by the total number of students.

27 (number of students) x $3 (price for visiting the museum) =  $81 (total for visiting the museum)

27 (number of students) x $5 (price for the train ride) =  $135 (total for the train ride)

Additionally, you will need to add both results to know the total: $81 + $135 = $216

You can also get the same result if you consider each student will spend $8 (price for visiting the museum and for the train ride) and then multiply this by the number of students ($8 x 27 = $216)

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

Answer:

13

Step-by-step explanation:

We can find the missing side length by using the pythagorean theorem

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

So, 13 is the missing side length.

Answer:

A. 7√3 in

Step-by-step explanation:

We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:

tan60° = x/7

x = 7tan60°

x = 7√3

Answer:

It's A

Step-by-step explanation:

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

━━━━━━━☆☆━━━━━━━

▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

-17x + y = 128

Step-by-step explanation:

First, find the slope.

[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{9-(-8) }{-7-(-8)}\\m=\frac{9+8 }{-7+8}\\m=\frac{17}{1} \\m=17[/tex]

Now, use point-slope form to find the equation.

y - y = m(x - x)

y - 9 = 17(x - (-7))

y - 9 = 17(x + 7)

y - 9 = 17x + 119

y = 17x + 128

Since your equation needs to be in Ax + By = C form, rearrange the equation so that the x and y values are on the left side of the equation.

y = 17x + 128

-17x + y = 128

Answer:

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean is significantly less than 5.4.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]

The significance level is 0.05.

The sample has a size n=44.

The sample mean is M=5.31.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=44-1=43[/tex]

This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]

As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population mean is significantly less than 5.4.

This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.

If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.

Answer:

x = -3/2

Step-by-step explanation:

0 = 4x² + 12x + 9

4x² + 12x + 9 = 0

(2x + 3)² = 0

2x + 3 = 0

2x = -3

x = -3/2

Hope this helps! :)

Answer:

57

Step-by-step explanation:

The range of a data set is

Largest data value - Smallest data value

62 - 5

= 57

The range of the data set is 57 pounds.

Answer:

[tex]\boxed{\red{57}}[/tex]

Step-by-step explanation:

[tex]\blue {range \: \: of \: \: a \: \: data \: \: set \: \: means}[/tex]

you have to subtract the smallest value from the largest value in the data set.

[tex]\boxed{\green{largest \: \: value - smallest \: \: value}} \\ \boxed{\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 62 - 5}} \\ \: \: \: \: \: \: \: \: \boxed{\pink{ =57}}[/tex]

Question:

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

30

∑  (−3i+5)

i=1

Answer:

The first three terms are : 2, -1 and -4

The last term is: -85

The sum of the sequence is: -1245

Step-by-step explanation:

Given;

==================================

30

∑  (−3i+5)                    -------------------(i)

i=1

==================================

Where the ith term aₙ is given by;

[tex]a_{i}[/tex] = [tex]-3i + 5[/tex]         -------------------(ii)

(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;

[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2

[tex]a_2 = -3(2) + 5 = -1[/tex]

[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]

Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;

[tex]a_{30} = -3(30) + 5 = -85[/tex]

(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;

[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex]   -----------------(iii)

Where;

n = number of terms in the sequence = 30

[tex]a_1[/tex] = first term = 2

[tex]a_n[/tex] = last term = -85

Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;

[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]

[tex]s_n[/tex] = 15[-83]

[tex]s_n[/tex] = -1245

Answer:

Hey there!

The product of these two fractions would equal 15.

Hope this helps :)

Answer:

Hi! The answer to your question is 7 11/14 or rounded will be 15

Step-by-step explanation:

So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.

Now we do LCD (least common denominator)

4/14+7/14=11/14

So the answer is 7 11/14 or 15

(In mixed number the answer is 7 11/14 and in whole the answer is 15)

Hope this helps! :)

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Answer:

Probability of answering 5out of 10 correctly= 0.246

Step-by-step explanation:

Total question answered= 2

Question answered correctly= 1

Probability of answered correctly= 1/2

Probability of answered correctly= 0.5

Probability of answered incorrectly = 0.5

Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5

Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)

Probability of answering 5out of 10 correctly= 0.246

Answer:

(n- 2/3)²

Step-by-step explanation:

We have:

It can be put as:

Here we consider n = a and -2/3 = b, then

Now we add 4/9 to a given binomial to make it perfect square:

So, added 4/9 and got a perfect square (n- 2/3)²

Answer:

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

Step-by-step explanation:

Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.

If total cost = C(x, y)

Average cost = C(x, y) ÷ (x+y)

For this question, total cost function is

C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾

The average cost is simply this total cost function divided by the total number of units produced.

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.

Hope this Helps!!!

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

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

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

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

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

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

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

See more about statistics at brainly.com/question/2289255

Answer:

angle of bc= 180-168= 12°

length of bc= 12/360 × π × diameter

= 12/360 × 22/7 × 21

= 12/360 × 66

= 2,20 cm (b)

Answer:

more info is needed

Step-by-step explanation:

Answer:  243/5 = 48.6

Step-by-step explanation:

  a₁,  375,  a₃,   a₄,  81 , a₆

First, let's find the ratio (r). There are three multiple from 375 to 81.

[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]

Next, let's find a₆ which is one multiple from 81.

[tex]a_6=81\bigg(\dfrac{3}{5}\bigg)^1\\\\\\.\quad =\large\boxed{\dfrac{243}{5}}[/tex]

Answer:

Step-by-step explanation:

H0: mu is equal to $108.50

Ha: mu is not equal to $108.50

This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.

z = x-u / sd/√n

Where x is $112, u is $108.50 sd is $16 and n is 64

z = 112-108.50 / 16/√64

z = 3.5/(16/8)

z = 3.5/2

z = 1.75

To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50

Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation: