For the following exercises, use the fundamental identities to fully simplify the expression. 6. sin(x)cos (x)sec(x) 7. sin (-x)cos (-x)csc (-x)

A mean of a normal distribution's upper bound of a 95% confidence interval is 58.11.

For the given question,

The confidence bound's upper limit (UCB) is determined as follows:

UCB =  μ + z(α/2)×σ/√n

Now, α/2 = (1 - 0.95)/2

α/2 = 0.025

z(α/2) = 1.96  (obtain from t-distribution table for degree of freedom)

Put the values in the formula,

UCB =  μ + z(α/2)×σ/√n

UCB = 36.96 + 1.96×41.8/√15

UCB = 58.11

As a result, 58.11 is the upper bound of a 95% confidence interval for the mean of a normal distribution.

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Answer: The value of the marginal product of the ninth worker is $400

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The equation to illustrate the information that the number of tickets sold was 4 less than twice the cube of the participants is 2p³ - 4.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, for a fundraiser event, the number of tickets sold was 4 less than twice the cube of the participants.

Let the number of participants be p.

In this case, the tickets will be:

= 2(p³) - 4.

= 2p³ - 4

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Answer:

Yes, because there were 8 pieces to start with. Hernando ate 2, leaving six pieces to split equally between his other six friends.

Answer:

(A) yes,they are correct. Hernado divided 6 by 6

Step-by-step explanation:

\(\text {Hello! Let's solve this Equation!}\)

\(\text {Your First Step is to Simplify the Equation:}\)

\(\text {(2x+4x)+(8+3)}\)

\(\text {6x+11=3x-10}\)

\(\text {The Next Step is to Subtract 3x:}\)

\(\text {6x+11-3x=3x-10-3x}\\\text {3x+11=-10}\)

\(\text {Next Step is to Subtract 11:}\)

\(\text {Q: Why Subtract 11?}\)

\(\text {A: So they cancel out. We cross them out once we subtract.}\)

\(\text {3x+11-11=-10-11}\\\text {3x=-21}\)

\(\text {The Final Step is to Divide 3:}\)

\(\text {3x/3=-21/3}\)

\(\text {Your Answer will be}\)

\(\fbox {x=-7}\)

\(\text {Best of Luck!}\)

\(\text {-LimitedX}\)

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

Answer:

0-a/c-0 = -a/c

Step-by-step explanation:

Answer:

Slant height = 8 feet.

Step-by-step explanation:

If the perimeter of the square base = 12 then each side of the base = 12/4

= 3  feet and its area = 3*3 = 9 ft^2

The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.

So total surface area = 57 = 9 + 4 * 1.5h

9 + 6h = 57

6h = 48

h = 8 feet.

Answer:

x=1 is the correct answer

The probability that a white ball was transferred from bag b into bag a given that a black ball was drawn from bag a is approximately 0.5760.

Let us denote the events as follows,

A represents the ball drawn from bag a is black

B represents the ball transferred from bag b to bag a is white

Probability of event B given that event A has occurred is P(B|A).

Using Bayes' theorem ,

P(B|A) = P(A|B) × P(B) / P(A)  __(1)

P(A|B) = Probability of drawing a black ball from bag a given that a white ball was transferred from bag b to bag a.

P(A|B)

= (3/5)× (5/9) + (4/9)× (4/9)

= 43/81

P(B) = Probability of transferring a white ball from bag b to bag a

       = 5/9

P(A) = Probability of drawing a black ball from bag a.

Using the law of total probability,

P(A) = P(A|B) ×P(B) + P(A|B') × P(B')

Here, B' represents the event that a black ball was transferred from bag b to bag a.

P(B') = 4/9

P(A|B')

= (3/5) × (4/9) + (2/5) × (5/9)

= 22/45

Now,

P(A)

= (43/81) ×(5/9) + (22/45)× (4/9)

= 0.512

Substitute all the values into Bayes' theorem,

P(B|A)

= (43/81) ×  (5/9) / (0.512)

≈ 0.5760

Therefore, the required probability of transferring a ball from one bag to another is approximately 0.5760.

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The above question is incomplete, the complete question is:

Bag a contains 2 white and 3 black balls. Bag b contains 5 white and 4 black balls. One ball is drawn at random from bag b and is placed unseen in bag a. If the ball drawn from bag a is black, find the probability that a white ball was transferred from bag b into bag a?

Answer:

$ 3078.

Step-by-step explanation:

A square yard is 3 feet by 3 feet =  9 square feet

1800 sq ft / 9 sq ft/ sq yard =200 sq yrds

200 sq yds * $  15.39 / sq yd $ 3078.

Answer:

60 degrees

Step-by-step explanation:

I got the answer right

The width of a confidence interval will be option (A)  narrower for 99% confidence than 95% confidence.

A confidence interval is a range of values within which we believe a population parameter, such as the mean or proportion, is likely to fall. It is calculated based on a sample of data and a chosen level of confidence, typically expressed as a percentage.

The width of a confidence interval depends on three factors: the level of confidence, the sample size, and the standard deviation

The width of a confidence interval depends on the level of confidence, sample size, and standard deviation. A higher level of confidence results in a wider interval, while a larger sample size and a smaller standard deviation result in a narrower interval.

Therefore, A 99% confidence interval will be wider than a 95% confidence interval, as it needs to include a larger range of possible values to provide a higher level of confidence.

Therefore, the correct option is (A) narrower for 99% confidence than 95% confidence.

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The given question is incomplete, the complete question is:

The width of a confidence interval will be:

A. narrower for 99% confidence than 95% confidence.

B. narrower for a sample size of 100 than for a sample size of 50.

C. wider for 90% confidence than 95% confidence.

D. wider when the sample standard deviation (s) is small than when s is large

The solution for y in the expression is y = -53 and y = 63

From the question, the expression is given as

y = 5 ± 58

We start by expanding the expression

So, we have the following representation

y = 5 - 58 and y = 5 + 58

Evaluate the sum and the difference of the like terms in the above expression

So, we have the following representation

y = -53 and y = 63

Hence, the solution is

y = -53 and y = 63

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Answer:

\(\displaystyle 1-\dfrac{5}{4}x+\dfrac{5}{8}x^2-\dfrac{5}{32}x^3+\dfrac{5}{256}x^4-\dfrac{1}{1024}x^5\)

Step-by-step explanation:

A binomial expansion is the result of multiplying out the brackets of a polynomial with two terms.

Use the binomial formula to expand the given expression.

\(\displaystyle \left(1+ax\right)^n=1+\binom{n}{1}(ax)+\binom{n}{2}(ax)^2+\binom{n}{3}(ax)^3+...+(ax)^n\)

where:

\(\displaystyle \binom{n}{r}=\dfrac{n!}{r!(n-r)!}=\phantom{l}^nC_r\)

Given expression:

\(\left(1-\dfrac{1}{4}x\right)^5\)

Therefore:

Substitute a = -1/4 and n = 5 into the binomial formula:

\(\displaystyle =1+\binom{5}{1}\left(-\dfrac{1}{4}x\right)+\binom{5}{2}\left(-\dfrac{1}{4}x\right)^2+\binom{5}{3}\left(-\dfrac{1}{4}x\right)^3+\binom{5}{4}\left(-\dfrac{1}{4}x\right)^4+\left(-\dfrac{1}{4}x\right)^5\)

\(\displaystyle =1+5\left(-\dfrac{1}{4}x\right)+10\left(\dfrac{1}{16}x^2\right)+10\left(-\dfrac{1}{64}x^3\right)+5\left(\dfrac{1}{256}x^4\right)+\left(-\dfrac{1}{1024}x^5\right)\)

\(\displaystyle =1-\dfrac{5}{4}x+\dfrac{10}{16}x^2-\dfrac{10}{64}x^3+\dfrac{5}{256}x^4-\dfrac{1}{1024}x^5\)

\(\displaystyle =1-\dfrac{5}{4}x+\dfrac{5}{8}x^2-\dfrac{5}{32}x^3+\dfrac{5}{256}x^4-\dfrac{1}{1024}x^5\)

Therefore, the expansion of (1 - ¹/₄x)⁵ is:

\(\displaystyle \left(1-\dfrac{1}{4}x\right)^5=1-\dfrac{5}{4}x+\dfrac{5}{8}x^2-\dfrac{5}{32}x^3+\dfrac{5}{256}x^4-\dfrac{1}{1024}x^5\)

Please note there was note enough room to add the binomial coefficients calculations to the main calculation, so please find them below:

\(\displaystyle \binom{5}{1}=\dfrac{5!}{1!(5-1)!}=\dfrac{5\times \diagup\!\!\!\!4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}{1\times\diagup\!\!\!\!4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}=\dfrac{5}{1}=5\)

\(\displaystyle \binom{5}{2}=\dfrac{5!}{2!(5-2)!}=\dfrac{5\times 4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}{2 \times 1\times \diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}=\dfrac{20}{2}=10\)

\(\displaystyle \binom{5}{3}=\dfrac{5!}{3!(5-3)!}=\dfrac{5\times 4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}{\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1\times2 \times 1\times}=\dfrac{20}{2}=10\)

\(\displaystyle \binom{5}{4}=\dfrac{5!}{4!(5-4)!}=\dfrac{5\times \diagup\!\!\!\!4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1}{\diagup\!\!\!\!4\times\diagup\!\!\!\!3\times\diagup\!\!\!\!2\times\diagup\!\!\!\!1 \times 1}=\dfrac{5}{1}=5\)

Answer:

Therefore, the approximate monthly payment is $548.85

Step-by-step explanation:

The amount of student loans Erica currently has = $34,006.00

The duration over which Erica is to pay back the loan = 7 years

The annual interest rate for the loan = 9.1%

Therefore, we have the geometric sequence formula is given as follows;

\(A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ]\)

Where;

M = The monthly payment

P = The initial loan balance = $34,006.00

r = The annual interest rate = 9.1%

n = The number of monthly payment = 7 × 12 = 84

Aₙ = The amount remaining= 0 at the end of the given time for payment

Substituting the values into the above formula, , we get;

\(0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]\)

\(M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85\)

Therefore, the approximate monthly payment = $548.85

The equation will be changed into = f(x)= 32

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

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Answer:

The real numbers are divided into two large branches that are

Step-by-step explanation:

Sorry, but I don't understand the question. Maybe a translation would help?

Answer:

Se pueden dividir en números racionales e irracionales.

Step-by-step explanation:

They can be divided into rational and irrational numbers.

Answer:

(-3,2) is located in the solution region.

Step-by-step explanation:

Answer: 5

Step-by-step she has 5 yards of bow she needs one yard for one bow that means its 5

Answer:

25 (88-63=25)

Step-by-step explanation:

As I write this Reiner is standing at my side. He knows this is a love letter but he’s still sneaking glances. Honestly it’s no wonder the creep is still single.

That said, he did give me his word that he’d deliver this letter to you. He says he owes me for the time I doubled back to save him.

I’m sorry about that. I never would have imagined myself choosing those two over you.

I’m gonna die soon,

but I’ll die without regrets.

Or that’s what I’d like to say.

Truth is, I do have one.

It's that I never got to marry you...

With love, Ymir.

just subtract them

88 - 63 = 25

thus, the number would be 25

hope this helps :)

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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The equation is y = 20(1.40)^x

where x is the number of days and y is the future amount after x days go by

The 1.40 is from the fact that 1+r = 1+0.40 = 1.40, where r is the decimal form of 40%, so r = 0.40

-----------------------------

Plug in x = 7 to get

y = 20(1.40)^x

y = 20(1.40)^7

y = 210.827008

y = 211

We round to the nearest whole number since it doesn't make much sense to have a fractional portion of an algae. After 7 days, there are about 211 algae.

Answer:

x= -2

Step-by-step explanation:

2x + 6 + 10=12

2x + 16=12

2x=-4

x=-2

The probability of getting heads twice in a row at some point during three coin flips is 1/8.

Given info;

Assume that a fair coin has an equal chance of coming up heads or tails.

What is the likelihood that three coin flips will result in two consecutive heads at any point?

There is a three-coin flip. The potential results are;

(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)

1 is the number of successful results.

Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8

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Answer:

He bought 26.2 pounds.

Step-by-step explanation:

9.17/0.35 = 26.2

The quadratic equation of x2-6x+9=0 is C) (x-2)(x+3).

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

This equation is an example of a quadratic equation, which is an equation of the form ax2+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± √b2-4ac / 2a. Therefore, the solutions to this equation are x= -(-6) ± √(-6)2-4(1)(9) / 2(1), which simplifies to x=3 ± √3 /2, or x=3 ± √9 /2. This simplifies to x=3 ± √3, or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.

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Given the equation

Make x the subject and simplify

Hence, the value of x = -4/3 = -1 1/3