Steven has a rope that is 6ft long. He cuts it into 9 pieces. How many are in each piece

The probability that the sample's mean length is greater than 6.3 inches is0.8446.

Here, we have,

Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event.

It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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Answer:

Lance would need 3.125 gallons of water.

Step-by-step explanation:

Divide the value by 16

After converting the volume into gallons, Lance needs 3.125 gallons of water for the runners in a race.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Lance needs 50 cups of water for the runners in a race.

We know that;

⇒ 1 gallons = 16 cups

⇒ 1 cups = 1/16 gallons

Here, Lance needs 50 cups of water for the runners in a race.

Hence, We get;

⇒ 50 cups = 50 × 1/16 gallons

                 = 3.125 gallons

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It is add five two both sides.

Answer:

See below for answers and explanations (along with a graph for reference)

Step-by-step explanation:

A is true because the end behavior shows that as x gets larger, y also gets larger

B isn't true because that is an incorrect interpretation of the end behavior while the statement itself is true.

Any real value of x can be defined on the graph with an output, therefore C is also correct.

D is not true because that would contradict option C which we said was right since the domain and range are both all real numbers.

E is true because the y-intercept of the graph is (0,20) which is positive (marked in purple)

Answer:

B. As x approaches negative infinity, y approaches negative infinity.

C. The domain of the function is all real numbers.

E. The graph has a positive y-intercept.

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!!

Answer:

plz explain simplier

Step-by-step explanation:

Answer:

Set A has a college student population with the sum closest to 78,000.

Step-by-step explanation:

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

First, we need to determine the sums of college student populations.

Set 1: 18,432 + 32, 761 + 27, 390 = 78, 583

Set 2: 15, 791 + 47, 318 + 27, 522 = 90, 631

Set 3: 22, 109 + 38, 569 + 32, 780 = 93, 458

Set 4: 27, 420 + 47, 338 + 22, 183 = 96, 941

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

Now we determine the difference in populations between the given sets and 78,000...

Step 1: 78, 583 - 78, 000 = 583

Step 2: 90, 631 - 78, 00 = 12, 631

Step 3: 93, 458 - 78, 000 = 16, 458

Step 4: 96, 941 - 78, 000 = 18, 941

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Thus, the answer to your problem is, Set A.

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Hence, in answering the stated questiοn, we may say that As a result, we  equatiοn must add (2x - 1)2 + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.

A algebraic equatiοn is a strategy fοr linking twο prοpοsitiοns and expressing equivalence using the equals symbοl (=). A mathematical sentence that shοws the equivalency οf twο fοrmulas is knοwn as an equatiοn in algebra. In the calculatiοn 3x + 5 = 14, fοr example, the equal sign puts a space between the values 3x + 5 and 14. Tο describe the relatiοnship between the twο sentences printed alοng either side οf a letter, a mathematical fοrmula can be utilised. Usually, the insignia and the prοgramme are the same. 2x - 4 = 2, fοr example.

Tο identify what shοuld be added tο 6x² + 9x - 8 tο create 4x² - 8x + 6, we need tο undertake a methοd called "cοmpleting the square".

We can cοnclude frοm cοmparing the twο fοrmulas that a = 4, b = -8, and c = 6.

Sο we must "finish the square" by adding and remοving a term equal tο (b/2a)2. In this instance, we have:

(b/2a)² = (-8/2(4))

a² = 1

4x² - 8x + 6 + 1 - 1

(4x² - 8x + 1) + (6 - 1) (6 - 1)

(4x² - 8x + 1) is a perfect square trinοmial, which may be factοred as (2x - 1)².

As a result, the ultimate sοlutiοn is:

6x² + 9x - 8 + 1 - 1 + (2x - 1) (2x - 1)

a² + 5

As a result, we must add (2x - 1)² + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.

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Answer:

-3(3y-1)

Step-by-step explanation:

−9y−3

Factor out 3.

3(−3y−1)

Rearrange Terms.

-3(3y-1)

Answer:

26018.979

yea...

Answer:

63

Step-by-step explanation:

given the sight of the angle it should be 63, correct me if I'm wrong.

The estimated raw material Inventory balance at the end of July is $27,750.

The estimated raw material inventory balance at the end of July, we need to follow the given information and calculations:

a. Each unit of finished goods requires 5 pounds of raw materials. Therefore, the total raw materials needed for production in August can be calculated as follows:

23,000 units (budgeted unit sales for September) × 5 pounds/unit = 115,000 pounds

b. The ending raw materials inventory equals 10% of the following month's raw materials production. Based on the information provided, the estimated raw materials needed to meet production in August is 111,000 pounds.

111,000 pounds × 0.10 (10%) = 11,100 pounds

This means that the ending raw materials inventory for July should be 11,100 pounds.

c. The cost of raw materials is $2.50 per pound. To find the value of the raw material inventory at the end of July, we multiply the pounds by the cost per pound:

11,100 pounds × $2.50/pound = $27,750

Therefore, the estimated raw material inventory balance at the end of July is $27,750.

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Answer:

The option u chose is the correct one

Answer:

Step-by-step explanation:

(0,0)

i hope this helps

Answer:

  D.  13

Step-by-step explanation:

The first step in evaluating a piecewise function at a particular point is to find the piece that includes the point.

For x = 0, the relevant domain specification is x ≤ 0, the one applicable to the third piece. That piece of the function definition tells you ...

  f(0) = 13

Answer:

Following are the solution to this question:

Step-by-step explanation:

C'(t) was its time, in years, or t shift of cash per unit. That C'(1980) meaning, therefore, becomes the change of cashier's population to t = 1980.  

They could either use t = 1970 or t = 1990 to approximate the C'(1980) price. When using t = 1970:

\(C'(1980) = \frac{[C(1980) - C(1970)]}{[1980 - 1970]}\\\\\)

              \(= \frac{(571 - 265)}{10}\\\\ = \$ \ 30.6 \\\)

t = 1990:

\(C'(1980) = \frac{[C(1980) - C(1990)]}{[1980 - 1990]}\)

              \(= \frac{(571 - 1063)}{ -10} \\\\= \$ \ 49.2\)

Answer:

90

Step-by-step explanation:

We can translate this into the following equation:

x - 0.4x = 54

Simplifying the left side of the equation, we get:

0.6x = 54

Dividing both sides by 0.6, we get the following:

x = 90

Therefore, 90 is the number decreased by 40% leaving 54.

Answer:

LJ and GE

Step-by-step explanation:

Answer:

Angles IJG and KJL are vertical angles

Step-by-step explanation:

Vertical angles are formed when two lines intersect.  It's a terrible name for them, because the name has nothing to do with the common word "vertica" (up-and-down).

The attached image shows an example of a pair of vertical angles.  Another pair is angles AED and CEB.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

Norma performed best on the aptitude test and should be offered the job.

Step-by-step explanation:

We are given that three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Tobias got a score of 74.7; this version has a mean of 61.7 and a standard deviation of 13. Norma got a score of 351; this version has a mean of 291 and a standard deviation of 25. Vincent got a score of 7.38; this version has a mean of 6.9 and a standard deviation of 0.4.

Now, to find which of the applicants should be offered the job, we have to find the z-score of each of the applicants, and the one who gets the highest z-score will get the job.

The z-score probability distribution for the normal distribution is given by;

                            Z = \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean and \(\sigma\) = standard deviation

Firstly, we will find the z-score for Tobias;

The z-score of 74.7 = \(\frac{X-\mu}{\sigma}\)

                                 = \(\frac{74.7-61.7}{13}\) = 1

Now, we will find the z-score for Norma;

The z-score of 351 = \(\frac{X-\mu}{\sigma}\)

                               = \(\frac{351-291}{25}\) = 2.4

Now, we will find the z-score for Vincent;

The z-score of 7.38 = \(\frac{X-\mu}{\sigma}\)

                                 = \(\frac{7.38-6.9}{0.4}\) = 1.2      

As we can clearly see that the z-score is highest for Norma which means that Norma performed best on the aptitude test and should be offered the job.

Answer:

$283. 81

Step-by-step explanation:

Start with P = 200.00 dollars.

If the interest is compounded continuously, then after t = 7 years the at the rate r = 5% = .05, the total amount of money in the account will be A.

\(A= P e^{r*t}\)

\(A = 200*e^{.05*7}\)

A = 283.8135097

A ≈ $283. 81

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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The reconciliation for Bane can be summarized as,

Adjusted bank balance = $1380.

A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.

Given that,

Beginning checkbook balance is $1400.

Service charge = $20

Adjusted balance = $1400 - $20 = $1380

Also, given that,

Ending balance on the statement = $1480

Deposit in transit = $200

Checks outstanding = $300

Adjusted balance = $1480 + 200 - 300

                              = $1380

Hence the adjusted balance is $1380.

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Answer:

x = -4

Step-by-step explanation:

3x=-12

Using the division property of equality, we can divide both sides by 3 to isolate x...

x=-12/3

x = -4

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Answer:

\(\huge\boxed{\sf n = 5}\)

Step-by-step explanation:

\(\sf \frac{4}{n} = \frac{4}{5} \\\\Cross \ Multiplying \\\\n * 4 = 4*5\\\\Divide \ both \ sides \ by \ 4 \\\\\frac{n*4}{4} = \frac{4*5}{4} \\\\n = 5 \\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

n = 5

Step-by-step explanation:

\( \frac{4}{n} = \frac{4}{5} \)

Dividing 4 on both the sides gives ,

\( = > \frac{4}{n} \div 4 = \frac{4}{5} \div 4\)

\( = > \frac{4}{n} \times \frac{1}{4} = \frac{4}{5} \times \frac{1}{4} \)

Cancelling 4 from numerator and denominator from both the sides ,

\( = > \frac{1}{n} = \frac{1}{5} \)

Cross-multiplying the denominators of both sides,

\( = > n = 5\)