Scott and Nikki each have a full 1.5-gallon container of liquid laundry detergent. The lid on Scott’s container can hold 3 fluid ounces of detergent, while the lid on Nikki’s container can hold 4 fluid ounces of detergent. How many more lids full of detergent does Scott have than Nikki?

Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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Answer:

8 nickels and 18 dimes

Step-by-step explanation:

Make a system of equations:

n + d = 26

5n +10d = 220

Solve by elimination by multiplying the top equation by -5. This gives you:

-5n -5d = -130

5n +10d = 220

Then solve to get 5d= 90, then d= 18.

Then plug 18 for d in the equation n + d= 26, so n + 18= 26

n= 8

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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The values given: P(A2|E) = 0.50 * 0.8 / (0.36 * 0.2 + 0.50 * 0.8) = 0.4566 (rounded to four decimal places)

Events A1 and A2 are mutually exclusive and form a complete partition of the sample space S, which means that one of the events must happen and they cannot happen simultaneously.

P(A1) = 0.2 and P(A2) = 0.8, which means that the probability of event A1 happening is 0.2 and the probability of event A2 happening is 0.8.

P(E|A1) = 0.36 and P(E|A2) = 0.50, which means that the probability of event E happening given that event A1 happened is 0.36 and the probability of event E happening given that event A2 happened is 0.50.

We want to find P(A2|E), which is the probability of event A2 happening given that event E happened.

We can use Bayes' theorem to find this probability:

P(A2|E) = P(E|A2) * P(A2) / (P(E|A1) * P(A1) + P(E|A2) * P(A2))

Substituting the values given:

P(A2|E) = 0.50 * 0.8 / (0.36 * 0.2 + 0.50 * 0.8) = 0.4566 (rounded to four decimal places)

Therefore, the answer is (a) 0.4566.    

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Answer:

10.8 or 5 4/5

Step-by-step explanation:

Im guess its right answer

Answer: D. (-4, 4)

Step-by-step explanation:

just the x, y

Answer:The answer is A (4, 4)

Step-by-step explanation: When reflected across the y-axis, the y coordinates stay the same, but the x coordinated change signs. In this case, the original x coordinate was -4. But after flipped across the y axis, the -4 changes to a positive 4, since it is in quadrant 1.

For Gail to receive a b in the course, her final exam score range must be between x = 79 and x = 84.

There would be a total of 10 examinations, including the ones listed, if the final exam was worth six test scores. The sum must be 800 in order to divide it by 10 to obtain the lowest average of 80, and it must be 830 in order to obtain the maximum average of 83. The following two equations are necessary in order to obtain the final exam scores that determine these averages:

84 + 76 + 83 + 83 + 6x = 800

and

84 + 76 + 83 + 83 + 6x = 830

So, in each equation, we can add like terms and get

326 + 6x = 800

and

326 + 6x = 830

6x = 474 and 6x = 504

x = 79 and x = 84.

The complete question is:

Gail needs to earn a b in her algebra class. Her current test scores are 84, 76, 83, and 83. Her final exam is worth 6 test scores . In order to get a b Gail average must lie between 80 and 83 inclusive. What range of scores can Gail receive on the final exam to earn a b in the course.

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The value of tan(t−π) is 4/9.

According to the statement

we have given that  tan(t)=4/9 and we have to find the value of tan(t−π).

So,

tan(t−π)  -(1)

take negative sign common from equation (1) it then

tan(t−π) = -tan(-t+π)

and we know that the according to the mathematics formula it become

tan(-t+π) is -tan t

then

tan(t−π) = -(-tan t)

it becomes

tan(t−π) = tan t

then its value becomes

tan(t−π) = tan(t)=4/9.

because we have given that the value of tan t is tan(t)=4/9.

So, The value of tan(t−π) is 4/9.

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Answer:

  x = -8 and x = 2

Step-by-step explanation:

The given equation resolves into two:

The solution to the first can be found by subtracting 3:

  x = 2

The solution to the second can be found by multiplying by -1, then subtracting 3.

  x +3 = -5

  x = -8

The solution set is {-8, 2}.

Answer:

b)

x= 5

Step-by-step explanation:

4x = 20

:4

x=5

To find the divisor (div) and the remainder (mod):

a) To find div and mod, we use the formula: a = m x div + mod.
For a=228 and m=119:
- div = floor(a/m) = floor(1.9244) = 1
- mod = a - m x div = 228 - 119 x 1 = 109
Therefore, div = 1 and mod = 109.

b) For a=9009 and m=223:
- div = floor(a/m) = floor(40.4469) = 40
- mod = a - m x div = 9009 - 223 x 40 = 49
Therefore, div = 40 and mod = 49.

c) For a=-10101 and m=333:
- div = floor(a/m) = floor(-30.3903) = -31
- mod = a - m x div = -10101 - 333 x (-31) = -18
Therefore, div = -31 and mod = -18.

d) For a=-765432 and m=38271:
- div = floor(a/m) = floor(-19.9885) = -20
- mod = a - m x div = -765432 - 38271 x (-20) = -2932
Therefore, div = -20 and mod = -2932.

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The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Answer:

8y(7x^3-4x+2)

Step-by-step explanation:

Group and factor out the greastest common factor then combine

Answer:

this is my alt here ya go champ

Step-by-step explanation:

Answer:

linear function I think...

Answer:

Step-by-step explanation:

Answer:

The cost of one bag of windflower bulbs is $5 each

The cost of one package of crocus bulbs is $10 each

Step-by-step explanation:

4 bags of windflower bulbs would be $20

4 x 5=20

7 packages of crocus bulbs would be $70

7 x 10=70

so for the total it would be $90

4 bags of windflower bulbs would be $20

4 x 5=20

1 package of crocus bulbs would be $10

so for the total it would be 30$

Answer:

it's 1

Step-by-step explanation:

take any two points;

I've taken (0, -3) and (2, -2)

find the slope= -2-(-3)/2

=1/2

as other option doesn't have the slope 1/2 you so it must be option A

Answer:

$86.36

Step-by-step explanation:

Tax: 7%, or 0.07

Tip: 20%, or 0.2

Substitute the values:

Tip: 68 * 0.07 = 4.76

Tip: 68 * 0.2 = 13.6

Just the meal cost: 1 * 68 = 68

Add these all together

4.76 + 13.6 + 68 = 86.36

Thus, the total cost of the meal would be $86.36

They support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. the correct answer is (d) 0.40.

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data

set.  The mean, median and mode are the three commonly used measures of central tendency.

To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of

values.

The mean, μ, of the sampling distribution of p can be found using the formula

μ = p,

where p is the proportion of adults in the entire population who support the increase.

In this case, 40% of all adults in Ohio support the increase, so p = 0.40.

Therefore, the mean of the sampling distribution of p is:

μ = 0.40

So the correct answer is (d) 0.40.

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Answer:

in the last one 3+4+4×15=67

in the first if we see there are three shapes if we divide 45/3 so the value of each shape is 15

in the second there are two bananas and one shape as we know the value of shape so 23-15=8 as there are two bananas so the value of each banana is 4

in the third there are two clocks and one banana as we know the value of banana so 10-4=6 as there are two clocks so the value of each clock is 3

from above

shape=15 banana=4 and clock =3 pitting in the equation gives us the value of 67

Step-by-step explanation:

i hope this will help you :)

The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Answer:

\(H_{o}\): Larger proportion of news media = democrats

Ha : Large proportion of news media \(\neq\) democrats  

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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Answer:

\(\frac{6}{7}\)

Step-by-step explanation:

Given a number n then the multiplicative inverse is \(\frac{1}{n}\)

Thus

the multiplicative inverse of \(\frac{7}{6}\) is \(\frac{1}{\frac{7}{6} }\) = \(\frac{6}{7}\)

Formula: y=mx+b

Plug in your numbers. Y=1/4x-5

1/4 is the slope so it takes the place of m, and our y-intercept is -5 so it replaces b.

I can't put a graph on here, but go on desmos.com and put the equation in and it graphs it for you ;)

Answer:

6

Step-by-step explanation:

9. P(exactly one defective)= 0.384

10. P(at most one defective) = 0.512 + 0.384 = 0.896

To solve these probability problems, we can use the binomial probability formula. Let's tackle each question separately:

The probability that exactly one item will be defective in a sample of three items can be calculated as follows:

P(exactly one defective) = C(3, 1) × (0.2)¹ × (0.8)²

Here, C(3, 1) represents the number of ways to choose 1 item out of 3, which is equal to 3.

P(exactly one defective) = 3× (0.2)¹ ×(0.8)²

= 3× 0.2× 0.64

= 0.384

Therefore, the answer is B. 0.3840.

The probability that at most one item will be defective in a sample of three items can be calculated by summing the probabilities of having exactly zero and exactly one defective item:

P(at most one defective) = P(zero defective) + P(exactly one defective)

P(zero defective) = C(3, 0)× (0.2)⁰× (0.8)³

= 1 × 1 × 0.512

= 0.512

P(exactly one defective) = C(3, 1)×(0.2)¹ × (0.8)²

= 3×0.2×0.64

= 0.384

P(at most one defective) = 0.512 + 0.384

= 0.896

Therefore, the answer is D. 0.8960.

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