A set of data items is normally distributed with a mean of 70 and a standard deviation of 8. Convert 70 to a z-score.

z70=
(Do not round until the final answer. Then round to the nearest hundredth as needed.)

The correlation coefficient for the data-set in this problem is given as follows:

r = 0.75.

To obtain the correlation coefficient of the data-set in this problem, we must insert the points of the data-set into a correlation coefficient calculator.

From the table, the points of the data-set are given as follows:

(0, 5.9), (0.8, 8.6), (1.3, 15.5), (1.6, 17.3), (13.3, 21.5).

Inserting these points into a calculator, the correlation coefficient is given as follows:

r = 0.75.

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The solution is,  the tangent of each angle that is not the right angle is:

angle tan A = 1.33

angle tan B = 0.75

Here, we have,

Given:

ABC is a right triangle.

angle ACB = 90

To find:

tan A

tan B

We know that tangent of an angle is given by the ratio

= opposite / adjacent

The opposite side and adjacent side is taken with respect to the angle for which the tangent is to be found.

tan A = BC/ AC

         = 8/6

         = 4/3

         = 1.33

and, tan B = AC/BC

                 = 6/8

                 =0.75

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The value of x in the rectangle is,

⇒ x = 6

We have to given that;

Corresponding angles are,

⇒ (8x + 19)° and (21x - 13)°

Hence, We can say that;

⇒ (8x + 19)° + (21x - 13)° = 180°

⇒ 29x + 6 = 180

⇒ 29x = 174

⇒ x = 174/29

⇒ x = 6

Thus, The value of x in the rectangle is,

⇒ x = 6

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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Answer:

2/3 or 67%

Step-by-step explanation:

To find the exact probability for you to reach into the orange balls you'll have to do a data table on which you'll include how many orange balls are by the total amount of balls that are within the urn.

For example:
The urn contains:

* 10 red balls
* 20 yellow balls
* 60 orange balls

Total amount of balls that you have on the urn is 90, you'll get this result by doing a simple addition of the table of content.

Afterwards, we have to find the probability, so you will have to take the amount of orange balls (which is 60) and divide it by 90 (Which is the total amount of balls you have on the urn).

60/90

A quick tip for you to do this on a simplified manner is by dividing the numerator and the denominator by their greatest common divisor (Which in this case is 30) (30x2 = 60) (30x3 = 90)

60/90 = (60 divided 30) / (90 divided 30) = 2/3

To resolve this problem, we get that the probability of selecting an orange ball is 2/3 or approximately 0.67 which we'll simplify to 67%

I hope this helped you

Answer:

Option A is the correct choice that shows a function.

Step-by-step explanation:

What is a function?

A function is when there are no repeating "x" values.

For example:

These set of points: {(1,1), (1,2), (1,3), (1,4)} does not  show a function because there is repeating "x" values.

Option A shows that the points {(4,5), (5,5), (6,1), (8,2) is a function because there is no repeating "x" values.

Answer: [tex]\frac{8}{15}[/tex]

Step-by-step explanation: In total, Patty placed 45 slips of paper in a bag(10+9+8+7+6+5). Out of those 45 slips of paper, only 24 had even numbers on them(10+8+6), resulting in the fraction [tex]\frac{24}{45}[/tex]. If you divide both 24 and 45 by 3, the fraction can be simplified to [tex]\frac{8}{15}[/tex].

A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.

The discount is the difference between the original price and the discounted price.

Discount = $200 - $94 = $106

To find the percentage discount, we need to calculate what percentage of the original price the discount represents:

Percentage discount = (Discount/Original price) x 100%

Percentage discount = ($106/$200) x 100%

Percentage discount = 53%

Therefore, the discount, as a percentage, is 53%.

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The balance on the loan at the end of month 4 is approximately $289,836.23.

We are given that;

Amount borrowed= $290,000

Time 25 years

Payment=  $1, 530.73

Now,

To calculate the balance on the loan at the end of month 4, we can use the following formula2:

Balance = (Loan amount - Debt payment) * (1 + Interest rate / 12) - Debt payment

Where:

Loan amount is the original amount borrowed ($290,000)

Debt payment is the amount of principal paid in each monthly payment ($564.06 for the first month and $565.94 for the second month)

Interest rate is the annual interest rate divided by 100 (0.04)

Plugging in the values, we get:

Balance = ($290,000 - $564.06) * (1 + 0.04 / 12) - $565.94 Balance = $289,435.94 * 1.003333 - $565.94 Balance = $290,402.17 - $565.94 Balance = $289,836.23

Therefore, by the interest the answer will be $289,836.23.

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The graph of the inequality y ≥ (x+2)^2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y is greater than or equal to (x+2)^2

Express the statement properly

So, we have

y ≥ (x+2)^2

The above expression is a an inequality of a quadratic function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the expression in a graphing tool and attach the display

See attachment for the graph

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Janeesa needs to drive about 6.9 mph faster than the speed limit to make it on time.

What is the  speed limit

To find out how fast Janeesa needs to drive to make it on time, one can use the formula:

distance = rate x time

In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:

rate = distance / time

Plugging in the values we know, we get:

rate = 247.5 / 4 = 61.875

To know how much faster Janeesa needs to drive, one has to subtract the speed limit from the required speed:

Speed Difference = Required Speed - Speed Limit

= 61.875 mph - 55 mph

 = 6.875 mph

Therefore, Janeesa needs to drive approximately 6.9 mph faster than the speed limit to make it on time.

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If both Tony and Marcus work on the job and the cost of labor is $48.00 per hour then labor estimate for the job is $576.00.

Marcus: 1 slab / 9 hours = 1/9 slab per hour

Tony: 1 slab / 3 hours = 1/3 slab per hour

The total amount of work they can do in one hour is the sum of their individual rates:

Marcus and Tony: 1/9 + 1/3 = 4/9 slab per hour

So together, Marcus and Tony can lay 4/9 of a slab per hour.

time = work / rate

time = 1 / (4/9) = 2.25 hours

total labor cost = hours worked x cost per hour

The total number of hours worked is the sum of the hours worked by Marcus and Tony:

total hours worked = 9 hours + 3 hours = 12 hours

The cost per hour is $48.00, so the labor estimate for the job is:

total labor cost = 12 hours x $48.00/hour

= $576.00

Therefore, the labor estimate for the job is $576.00.

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Check the picture below.

Answer:

Step-by-step explanation:

The equation given is:

120 + 1814x = 180 - 134x

We can simplify this equation by adding 134x to both sides:

120 + 1948x = 180

Next, we can subtract 120 from both sides:

1948x = 60

Finally, we can solve for x by dividing both sides by 1948:

x = 60/1948

Therefore, the solution is:

x = 0.0308 (rounded to four decimal places)

Answer:

To solve the equation, we need to first convert the mixed numbers to improper fractions:

120 + 18 1/4 x = 180 − 1 3/4 x

120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)

Multiplying both sides by 4 to eliminate the fractions, we get:

480 + 73x = 720 - 7x

Combining like terms, we get:

80x = 240

Dividing both sides by 80, we get:

x = 3

Therefore, the solution for x is 3.

"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".

A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.

The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.

In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.

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Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

The similarity statement is completed as below

Triangle MTA ~ triangle HTM ~ triangle HMA

A similarity statement is a statement in mathematics that expresses the affinity between two or more figures.

These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.

The similar triangles are

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The angle measures of w and x are given as follows:

In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.

The congruent side lengths are given as follows:

SR and RQ.

Hence the congruent angle measures are given as follows:

Hence angle w is given as follows:

w = 51º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:

x + 2 x 51 = 180

x = 180 - 102

x = 78º.

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Based on an equation, the minimum number of years it will take the population of North Dakota to equal the population of South Dakota given the current rates of growth is 15.3 years.

An equation describes the equality or equivalence of two or more mathematical expressions.

Equations use the equal symbol (=), while mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

The population of North Dakota in 2012 = 0.7 million

The yearly population growth rate = 0.028 million

The population of South Dakota in 2012 = 0.83 million

The annual population growth rate = 0.0195 million

Let the number of years for the populations to equal = x

0.7 + 0.028x = 0.83 + 0.0195x

0.0085x = 0.13

x = 15.3 years

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The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.

[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]

=1+4+25+16

=46

[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]

=1+1+1+100

=103

[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]

Therefore, [tex]A_2B_2=4738[/tex]

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

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An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 6)/(-6 - 0)

Slope (m) = 0/-6

Slope (m) = 0.

At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 0(x - 0)

y - 6 = 0

y = 6

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Answer:

180 square inches

5 x 6 = 32.5

32.5 x 4 = 130

5 x 5 = 25

25 x 2 = 50

130 + 50 = 180

Step-by-step explanation:

first find the area of all the sides (length times width)

width = 5

length = 6.5

5 x 6.5 = 32.5

32.5 is the area for one side. there are 4 others identical to it

32.5 (one side) x 4 (the amount of sides identical) = 130

then you need to find the area for the bottom/top side

5 = length

5= width

5(L) x 5(W) = 25

25 is the area for the bottom. the top is identical to it

25(bottom side) x 2 (the amount of sides identical)

now add all of the sides up

130 + 50 = 180

Only first figure of graph have an Euler circuit.

We have to given that;

There are 3 graphs are shown in figure.

Since, A graph has an Euler circuit if and only if the degree of every vertex is even.

Hence, In first graph,

Every vertex have even degree with 2 or 4.

Thus, It shows an Euler circuit.

In second graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

In third graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

Thus, Only first figure of graph have an Euler circuit.

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Answer:

Approximately 15.7 ft

Step-by-step explanation:

We want to find the circumference of the circle

C = pi * diameter

C = pi *5

C = 5pi ft or approximately 15.7 ft

Answer:

526.32

Step-by-step explanation:

Let's assume that the cost price of the bag is "C".

Selling Price = Cost Price - Loss

We get:

500 = C - 0.05C

500 = 0.95C

C = 500/0.95

C ≈ 526.32

Therefore, the cost price of the bag was approximately Rs 526.32.