how is 27.25 divided by 5 = 5.05. Doesn't it equal 5.45

z =  -2.114, test statistic used to test the claim that fewer than 90% of the company employees opted to work from home at least one day a week at the 5% significance level.

A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.

The p value of your findings, which aids in determining whether to accept or reject your null hypothesis, is calculated using the test statistic.

P = [tex]\frac{x}{n}[/tex]

= [tex]\frac{36}{41}[/tex]

1 - P₀ = 1 - 0.95 = 0.05

Test statistic= z

=P - P₀ / {√P₀ * (1 - P₀)/ n}

=0.8780 - 0.95 /√(0.95 * 0.05) / 41

z = -2.114

Test statistic used to claim that is, z = -2.114 .

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The Expected value for 4 tickets = $ 7.6

Given - A lottery offers one $900 prize, one $600 Prize, three $400 prizes, and four $100 prizes. One thousand tickets are sold at $5 each.

To find - Find the expectation if a person buys four tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

Proof -

Given that,

A lottery offers

one $ 900 prize

one $ 600 prize

three $ 400 prizes

Four $ 100 prizes

And

One thousand tickets are sold at $ 5 each

Now,

If the person bought 1000 tickets then the prize he gets is

= 900 + 600 + 3×400 + 4×100

= 900 + 600 + 1200 + 400

= $3100

And

The cost of 1000 tickets = 5×1000 = $ 5000

Now,

Price 1 ticket =   $ 3.1

⇒Expectation of 1 ticket = 5 - $ 3.1  = $ 1.9      (Here $5 is price of 1 ticket)

⇒Expected value for 4 tickets = $ 4× -1.9 = $ 7.6

⇒Expected value for 4 tickets = $ 7.6

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Answer:

8.4-16.2n²

Step-by-step explanation:

2.4-5.4n3n+6

= 2.4-16.2n²+6

= 8.4-16.2n²

The real life example of cartesian coordinate system, is given below.

What is cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

The real life use of cartesian coordinate system is,

In real life, there are many straightforward situations where the Cartesian coordinate plane of x and y works well.

For instance, you can create a two-dimensional grid representing the room and use the appropriate unit of measurement to plan where to place various pieces of furniture in the room.

Define a location as your starting point and choose one direction to be x and the other (perpendicular) direction to be y. (i.e., the zero coordinate on both axes).

For example, (3, 5) would be 3 meters in the x-direction and 5 meters in the y-direction from your selected (0, 0) point. You can specify any position in the room with two numbers in the format (x, y).

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The measure of the angle L in the parallelogram LMNO with the given conditions is equal to 40°.

As given in the question,

In the parallelogram LMNO,

Measure of angle L = (2x)°

Measure of angle O = (4x +60)°

In parallelogram LMNO,

LM is parallel to NO

And LO is the transversal

∠MLO and ∠NOL forms the interior angles

Interiors angles formed by two parallel lines are always supplementary.

m∠L + m∠O = 180°

⇒ (2x)° + (4x + 60)° = 180°

⇒ 6x° = 180° - 60°

⇒ x° = 120°/6

⇒ x° = 20°

Here, m∠L = 2x°

                  = 2(20°)

                  =40°

Therefore, the measure of angle L in the parallelogram is equal to 40°.

The complete question is :

What is the measure of angle L in parallelogram LMNO such that measure of angle L is (2x)° and measure of angle O is (4x + 60)° ?

a. 20°               b. 30°                c.  40°                   d. 50°

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Answer:

c

Step-by-step explanation:

source: trust me bro

Answer:

x = 51

y = -82

(51, -82)

Step-by-step explanation:

Look at the attachment

A fence surrounding the field that is 200 feet long and 100 feet wide will cost $2400 to construct.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

Area of rectangle=20,000 square feet

Cost of building fence for north and south=$3 per feet

Cost of building fence for east and west=$6 per feet

Let the sides be x and y,

area=x*y

20000=xy

y=20000/x

Perimeter=2l+2b

=2(x+y)

Total cost will be,

=3*2x+6*2y

=6x+12y

C=6x+12*20000/x

C=6x+240000/x

dC/dx=6-240000/x²

dC/dx=0

6=240000/x²

6x²=240000

x²=40000

x=200 feet

y=100 feet

C=6*200+12*100

C=$2400

The cost of building a fence around the field of length 200 feet and width 100 feet is $2400.

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The true mean number of pushups that can be performed, as determined by the t-distribution, is within a 95% confidence interval of (9, 21).

Since we know the sample standard deviation for this issue, the t-distribution is applied.

Given,

The sample mean, x = 15 .

The sample standard deviation, s = 9 .

The sample size, n = 10 .

As a result, df = 9. Next, we determine the number of degrees of freedom, which is one less than the sample size.

The crucial value for a 95% confidence interval is then determined by looking at the t-table or using a calculator, yielding t = 2.2622.

The margin of error;

M = t × s/n

Then,

M = 2.2622 × 9/√10 = 6

The confidence interval is:

x ± M

Then

x - M = 15 - 6 = 9

x + M = 15 + 6 = 21

Therefore,

The confidence interval is (9, 21).

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The required dimensions of the package for maximum volume are radius = 14, height = 44 inches.

A cylinder is round and has a top and base looking like a circle. The top and base are level and consistently a similar size. I figure the most effective way to portray the state of a chamber is to consider a container of soup

We have,

combined length and girth is 132 inches.

So, Girth = 2πr

If length of cylinder is h,

2πr + h = 132

h = 132- 2πr

the dimensions at which the max volume can be sent

Volume of cylinder; V = πr²h

put 132 - 2πr for h to get

V = πr²(132 - 2πr)

V =132πr² - 2π²r³

Differentiating with respect to r ,

dV/dr = 264πr - 6π²r²

For max volume will be when dV/dr = 0

Then,

264πr - 6π²r² = 0

adding 6π²r² to both sides

264πr = 6π²r²

264/6 = (π²r²)/πr

44 = πr

r =44/π = 14 inches

Radius =  14 inches

Put 44/π for r in h = 132 - 2πr to get;

h = 132 - 2π(44/π)

h = 132 -88

h = 44 inches

Thus, required height is  44 inches.

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The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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The 96th term of the given arithmetic sequence is -220

From the question, we are to determine the 96th term of the given arithmetic sequence.

The given arithmetic sequence is

-30, -32, -34

The nth term of an arithmetic sequence is given by

aₙ = a + (n - 1)d

Where a is the first term

and d is the common difference

From the sequence,

a = -30

d = a₂ - a₁ = -32 - (-30)

d = -32 + 30

d = -2

Thus,

The 96th term is

a₉₆ = -30 + (96 -1)-2

a₉₆ = -30 + (95)-2

a₉₆ = -30 + (-190)

a₉₆ = -30 - 190

a₉₆ = -220

Hence, the 96th term is -220

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Answer: Could be 7.

Step-by-step explanation:

The required 90% confidence interval for population mean age is (22.35,23.45)

Given,

Sample size, n = 20

Sample mean, μ = 22.9 years

Standard deviation, σ = 1.5 years

Significance level, α = 0.05

We have to find the 90% confidence interval;

Here,

x ± z(critical) σ/√n

Substituting the values;

z(critical) at  α₀.₀₅ = ±1.64

22.9 ± 1.64 (1.5/√20)

= 22.9 ± 0.55

= (22.35, 23.45)

That is,

(22.35,23.45) is the required 90% confidence interval for population mean age.

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Answer:

B. 48

Step-by-step explanation:

plug in the value of h into the expression and simplify from there

Answer:

dS > dC + 4 LY

Yes, The relation represent a function.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The points are,

{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) } ​

Now,

Since, The points are,

{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) } ​

Clearly, All inputs having exactly one output.

Thus, The relation represent a function.

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Kevin should decrease his prices toward the end of the season to avoid having unsold produce.

What is price?

The price of a product is the amount that customers are willing to spend. While also taking into account supply costs, seasonal discounts, competitor prices, and retail markup, marketers must connect the price to the product's actual and perceived value.

Consider the following,

Price per Pound (dollars)       Quantity Sold (pounds)

            1.00                       ⇔                       5,700

            2.00                      ⇔                       4,100

            3.00                      ⇔                       2,300

Kevin has seen that demand increases when prices decrease.

Hence, Kevin should decrease his prices toward the end of the season to avoid having unsold produce.

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Complete question:

Kevin owns a fruit stand alongside a busy road. For several years, he has kept track of the number of apples that people purchase at different prices. He decides to graph the number of apples sold and the various prices at which he sold them. The graph shows his record of the number of apples sold at different prices.

Fill in the table with the number of apples Kevin sold at each price. Use the graph to estimate approximate quantities of apples.

What is the relationship between the price of apples and the demand for apples among Kevin’s customers?

Based on your answer to part B, should Kevin increase or decrease his prices toward the end of the season to avoid having unsold produce?

Answer: Kevin has seen that demand increases when prices decrease, so he should decrease his prices toward the end of the season to avoid having unsold produce.

Step-by-step explanation: PLATO answer :)

The confidence interval for the given data be,

(144.83 , 155.17).

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17).

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The total area will be;

⇒ 7.514 × 10⁷ km²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The area of the Okhotsk Sea is 1.583 × 10⁶ km².

And, The area of the Indian Ocean is 7.3556 × 10⁷ km².

Now,

Since, The area of the Okhotsk Sea is 1.583 × 10⁶ km².

And, The area of the Indian Ocean is 7.3556 × 10⁷ km².

Hence, The total area = 1.583 × 10⁶ + 7.3556 × 10⁷

                                  = 1.583 × 10⁶ + 73.556 × 10⁶

                                  = 75.14 × 10⁶

                                  = 7.514 × 10⁷ km²

Thus, The total area will be;

⇒ 7.514 × 10⁷ km²

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a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.

b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table shows the number of times that each value, or values in each range, appears in the data-set.

11 weights are between 20 and 30, hence:

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As x and f(x) vary directly when x = 11 , f(x) = 110/3.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and f(x) varies directly, let f(x) be y.

∴ y = kx.

150 = 45k.

k = 150/45.

k = 30/9.

K = 10/3.

Now, when x = 11.

y = (10/3)×11.

y = 110/3.

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the scores on a standardized test have an average of 1200 with a standard deviation of 60 and 99.7% of the students scored between (44.67 , 56.33) i.e.

between 44 and 56.

On Subtracting 1 from your sample size, we get

100 – 1 = 99.

On Subtracting confidence level from 1, and then divide by two.

(1 – .997) / 2 = 0.0015

Now, df = 99 and α = 0.0015

from the table at df = 99 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(100) = 2.8

Now, 2.262 × 2.8 = 6.33

So, the confidence interval be,

(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)

Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.

between 44 and 56.

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Even when water is supercooled to 86 degrees Fahrenheit below its normal freezing point (32 degrees Fahrenheit), it will not freeze. Therefore, x-32≥-86

The process of lowering a liquid or gas's temperature below its melting point without causing it to solidify is known as supercooling, sometimes known as undercooling. It accomplishes this in the absence of a seed crystal or nucleus around which a crystal structure can form.

Let temperature be x

The temperature at which water turns into a liquid or a gas is represented by inequality is x-32≥-86

The reason is that as water will not freeze even when supercooled to 86°F below its typical freezing point (32°F).

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Answer:

m<D = 108

Step-by-step explanation:

m<ACD = 28 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent.

m<CAD = 44 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent. (Same reasoning.)

Now, since the sum of all angles in a triangle is 180 degrees, we can use the two angles that we know as well as angle D to add up to 180 and figure out how much D is. (All of the angles in triangle ADC)

<CAD + <ACD + <D = 180

Substitute the values in.

44 + 28 + <D = 180

72 + <D = 180

Subtract on both sides

<D = 108

The measure of angle D is 108 degrees.

Answer:

equilateral triangle

Step-by-step explanation:

all of the sides to a equilateral triangle equal to 60 degrees.

The two found rational expressions with the difference that completes the equation is  (x + 2)/(x² - 36) and 1/(x² + 6x).

Consider the two rational expressions.

(x + 2)/(x² - 36)    ...eq 1

and 1/(x² + 6x)   ....eq 2

Subtract the second from the first.

=  [(x + 2)/(x² - 36)] - [1/(x² + 6)]

Factorise the denominator of the first equation-

= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]

Taking the LCM

= [x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]

Further simplifying,

= [x² + x + 6]/[x(x-6)(x + 6)]

Thus, the two found rational expressions with the difference that completes the equation is  (x + 2)/(x² - 36) and 1/(x² + 6x).

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The complete question is-

Drag each expression to the correct location in the equation. Not all expressions will be used.

Determine the two rational expressions whose difference completes this equation.

x² + x + 6

x(x-6)(x + 6)

The percentage of French-speaking Canadians went down between 2006 and 2011.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In 2006, in Canada, 7.4 million out of 31.4 million of canadians said they spoke french. The percentage will be:

= 7.4/31.4 × 100

= 23.6%

Since Canada's population went up 6%, the bee population will be:

= 31.4 million × (6% × 31.4 million)

= 33,284,000

The number of Canadians speaking french went up 300 000.

The percentage will be:

= 7,700,000/33,284,000 × 100

= 23%

Therefore, the percentage reduced.

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The t-score should be used to find the 80% confidence interval for the population mean is $1.304

the interval of confidence:  This indicates the degree of confidence and ambiguity in a sampling process. It provides us with a range of outcomes, indicating that we would be reasonably certain that our genuine value or variable falls inside the range.

The sample size was 40 pharmacies (n=40). To calculate the degrees of freedom, use the formula: df=n-1=40-1=39.

The scenario specifies an 80% confidence level. So,α=1−CL=1−0.8=0.2 However, we wish to utilize the value for 2, which would be 0.22=0.1. We ought to locate the row for 39 freedom degrees and the column for t0.1 using the table. So the t-score for determining the 80% confidence interval is 1.304. We may alternatively use a calculator and enter 1-α2=0.9 as well as the degrees of freedom into invT, and then enter invT. (0.9,39).

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The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given phrase,

f(x) = 1/(x-2)

g(x) = (x + 2)²

f(g(x)) = 1/((x + 2)² - 2)

The above function will be defines except (x + 2)² - 2 = 0

(x + 2)² = 2

x + 2 = ±√2

x = √2 - 2 and x = -√2 - 2

Thus, the domain will be  (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).

Hence "The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞)".

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