construction worker cuts a pace of electrical wires that is 7/8 of an inch in the length heat and cuts and other piece that is 5/8 of an inch in length what is the combined length of the pieces of wire

Answer:

  A. If you moved the students from the top 25% in Class 1 into Class 2, the Class 2 median would increase.

Step-by-step explanation:

You want to know the effect of changing or combining class data, given the box plots show two classes with the same median.

We can consider the choices:

The medians of the two classes are the same. The maximum value of Class 1 is in the third quartile of Class 2, so the top 25% of Class 1 would be added to the data values currently in the 3rd quartile of Class 2.

In general, one might expect that adding data values above the median will raise the median. Whether this is actually true depends on the details of the distribution and the number of data points added.

It is probably true that the Class 2 median would increase.

The students who did no homework in Class 1 are the reason for the whisker extending to 0. Removing those from the data set will increase the minimum, likely increasing the value of Q1. This will cause the IQR to be reduced, not increased.

The range of the combined data sets will be the difference of the largest maximum (70) and the smallest minimum (0). The combined range will be 70, not 105.

Combining two data sets with the same median will result in a set of data with the same median. The median will not change, as half the combined data will be above it, and half the combined data will be below it.

Choice A is the only one that makes sense.

<95141404393>

The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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Answer:

  3) an = 8 +13(n -1); a20 = 255

  4) an = 6 -4(n -1); a20 = -70

Step-by-step explanation:

You want the rule and the 20th term for the arithmetic sequences ...

  3)  8, 21, 34, ...

  4)  6, 2, -2, ...

The n-th term of an arithmetic sequence is given in terms of the first term (a1) and the common difference (d) as ...

  an = a1 +d(n -1)

The first term is 8. The common difference is 21 -8 = 13. The rule is ...

  an = 8 +13(n -1)

The 20th term is ...

  a20 = 8 +13(20 -1) = 255

The first term is 6. The common difference is 2 -6 = -4. The rule is ...

  an = 6 -4(n -1)

The 20th term is ...

  a20 = 6 -4(20 -1) = -70

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Answer:

3. 255

4. -70

Step-by-step explanation:

3.

For the arithmetic sequence 8, 21, 34, 47, 60, ...

The common difference between consecutive terms is d =(21-8)= 13. Therefore, the nth term of the sequence can be expressed as:

[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]

where [tex]\bold{a_1}[/tex] is the first term of the sequence,

n is the term number, and d is the common difference.

Substituting [tex]a_1 = 8[/tex] and d = 13, we get:

[tex]a_n = 8 + (n - 1) * 13\\a_n = 13n - 5[/tex]

To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:

[tex]a_{20} = 13(20) - 5\\a_{20}= 255[/tex]

4.

For the arithmetic sequence 6, 2, -2, -6, -10, ...

The common difference between consecutive terms is d =(2-6)= -4. Therefore, the nth term of the sequence can be expressed as:

[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]

where [tex]a_1[/tex] is the first term of the sequence,

n is the term number, and

d is a common difference.

Substituting [tex]a_1[/tex]= 6 and d = -4, we get:

[tex]a_n = 6 + (n - 1) * (-4)\\a_n = 10 - 4n[/tex]

To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:

[tex]a_{20} = 10 - 4(20)\\a_{20}= -70[/tex]

The area of the triangle is 18.6 units²

Given data ,

Let the triangle be represented as ΔABC

Now , the sides of the triangle are

We can use the law of cosines to find the length of the third side of the triangle:

c² = a² + b² - 2ab cos(C)

c² = 5² + 8² - 2(5)(8)cos(79°)

c ≈ 9.05

Now, we can use Heron's formula to find the area of the triangle:

s = (5 + 8 + 9.05)/2 = 11.525

A = √(s(s-a)(s-b)(s-c))

A = √(11.525(11.525-5)(11.525-8)(11.525-9.05))

A ≈ 18.6

Hence , the area of the triangle is approximately 18.6 square units

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Answer: what subject, and i got you.

Step-by-step explanation:

When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.

How to know what is formed from a line intersecting a cone?

The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.

This means the intersecting line forms a right angle with the base of the right circular cone.

Therefore, from this interaction is a pair of intersecting lines.

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From the figure, the blanks are filed as follows

Common internal tangent: is matched to line HJ

point of tangency: is matched to G

Center: is matched to A

chord: is matched to line GK

secant: is matched to line CD

diameter: is matched to line EF

common external tangent = line KF

radius: is matched to line BF

semi-circle = arc EGF

Major arc: is matched to arc CDK

Minor arc: is matched to arc CK

In geometry the point of tangency is the point where a line or curve touches a circle or other curved shape at exactly one point without crossing over or intersecting it at another point.

At the point of tangency the tangent line is perpendicular to the radius of the circle that intersects it.

In the figure, the point of tangency is at F E G and K

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Answer: A ≈ 127.31 units²

Step-by-step explanation:

     We can use the given formula for the area of a regular hexagon, where a is equal to a given side (here, that is 7).

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]

     We will substitute known values and solve by computing and simplifying.

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} (7)^2[/tex]

        [tex]\displaystyle A=\frac{5.1961524}{2} 49[/tex]

        [tex]\displaystyle A=(2.59807621)(49)[/tex]

        [tex]\displaystyle A=127.3057[/tex]

        [tex]\displaystyle A\approx 127.31[/tex]

Answer:

Step-by-step explanation:

f(x) = [tex]\frac{3+x}{x-3}[/tex]

f(a+2) = [tex]\frac{3+a+2}{a+2-3}[/tex]

f(a+2) = [tex]\frac{5+a}{a-1}[/tex]

The surface area of the box which is a rectangular prism would be = 24 square inches. That is option D.

To calculate the area of the given box the formula that should be used is the formula of the area of a rectangular prism. That is;

Area of rectangular prism = length×width×height

Where:

length = 4 inches

width = 3 inches

height = 2 inches

Area = 4×3×2 = 24 square inches

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Answer: 0.68

Step-by-step explanation:

Answer: 98

Step-by-step explanation:

sailboats to dinghies = 5 : 7

if 5 is 70 then what is 7 to ?

well 70/5 is 14 so we had to multiply 5 by 14 to get 70.
That means we also have to multiply 7 by 14 to get 98

The capacity of the bottle is 16 ounces

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

A water bottle is 3/4 full.

When half of the water is drained, we have

Remainder = 1/2 * 3/4x

Evaluate

Remainder = 3/8x

Where x is the capacity of the bottle

We understand that 6 ounces of water remain in the bottle.

This means that

3/8x = 6

So, we have

x = 8 * 6/3

Evaluate

x = 16

Hence. the capacity of the bottle is 16 ounces

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The standard deviation of this sample of shopping time is equal to 50.

In order to calculate the standard deviation of this sample of shopping time, we would have to first determine the mean of the data set.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

For the total sum of data, we have:

F(x) = 42 + 27 + 22 + 37 + 32

F(x) = 132.1.

Mean = 160/5

Mean = 32

Now, we can calculate the standard deviation by using this formula:

Standard deviation, S = √(1/n × ∑(xi - u₁)²)

Standard deviation, S = √(1/5 × ∑(42 - 32)² + 1/5 × ∑(27 - 32)² + 1/6 × ∑(22 - 32)² + 1/5 × ∑(37 - 32)² + 1/5 × ∑(32 - 32)²

Standard deviation, S = 250/5

Standard deviation, S = 50.

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Answer:

Step-by-step explanation:

The 40 degree angle we are given is called an angle of depression. Because of geometry and the fact that the base of the triangle and this dotted line are parallel to one another, the base angle inside the triangle is also 40. These are called alternate interior angles. The x represents the hypotenuse of the triangle. We can use right triangle trig to find it. The side measuring 500 is OPPOSITE the reference angle of 40 and the missing side is the HYPOTENUSE, so the trig ratio we will use is sin which is, according to SohCahToa, opposite side over hypotenuse; namely:

[tex]sin40=\frac{500}{x}[/tex]

Algebraically, we will multiply both sides by x and then divide by sin40 to get:

[tex]x=\frac{500}{sin40}[/tex]

Make sure your calculator is in degree mode and not radian mode and enter the problem as you see it above to get that

x = 777.9m, choice A.

The required forms of the equation are;

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

Completing the square is a method used to rewrite a quadratic expression in standard form by adding and subtracting a constant to make it a perfect square trinomial. Completing the square is a useful method to solve quadratic equations and to rewrite quadratic expressions in standard form.

The standard form of a quadratic equation  is ax² + bx + c = 0

We have that;

x²-8x+5=0

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

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a. The z-score for a value of 25 is -0.57, to the nearest hundredth.

b. The percent of the data is greater than 34 is about 2%.

To find the z-score for a value of 25, we can use the following formula;

z = (x - μ) /σ

where;

z = (25 - 27) / 3.5

z = -0.57

Rounding to the nearest hundredth, we get the z-score of -0.57.

The z-score for x = 34 is calculated as follows;

z = (x - μ) / σ

z = (34 - 27) / 3.5

z = 2

Using a standard normal distribution table, we find that the percentage of data that is greater than 34 = 2.28%.

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Answer:

[tex]y = 1- |x + 1| [/tex]

Let's start by simplifying the left side of the inequality:

3(x+3) + 12 <= 3x + 28

3x + 9 + 12 <= 3x + 28

3x + 21 <= 3x + 28

Subtracting 3x from both sides, we get:

21 <= 28

This is a true statement, which means that the inequality is true for all values of x. In other words, there are infinitely many solutions.

To represent this graphically, we can draw a number line and shade in all values of x for which the inequality is true. Since it's true for all values of x, we shade in the entire number line:

<=======()------------------->

In this number line, the open circle () indicates that the inequality is not true for that particular value (in this case, there is no specific value for x that makes the inequality false). The arrow indicates that the inequality is true for all values of x to the left and right of the open circle.

In summary, the inequality 3(x+3)+12 <= 3x+28 is true for all values of x, and there are infinitely many solutions.

I'm 15 BTW

Answer:

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

Use the area formula:

We are given the circumference of the circle, which is C = 2πr.

So, we can set up an equation:

Now, we can plug this value of r into the area formula:

Therefore, the area of the circle is 42.25π or 132.73 square inches.

The mean score to the nearest whole number is equal to 5.0

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data based on the frequency, we have;

Total score, F(x) = 1(3) + 2(1) + 3(4) + 4(10) + 5(15) + 6(9) + 7(3) + 8(5)

Total score, F(x) = 3 + 2 + 12 + 40 + 75 + 54 + 21 + 40

Total score, F(x) = 247

Now, we can calculate the mean score as follows;

Mean = 247/50

Mean = 4.94 ≈ 5.0.

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The inverse of the function f(x) = 1/x is B. f⁻¹(x) = 1/x

The inverse of a function f(x) written as f⁻¹(x) is such that ff⁻¹(x) = f⁻¹f(x)

Given the function f(x) = 1/x,we desire to find its inverse. We proceed as follows.

Since f(x) = 1/x

Let f(x) = y

So,we have that

y = 1/x

Now, multiplying both sides by x,we have that

x × y = 1/x × x

xy = 1

Dividing though by y, we have that

xy/y = 1/y

x = 1/y

Now, relacing y with x and x with f⁻¹(x), the inverse of f(x), we have that

x = 1/y

x = 1

f⁻¹(x) = 1/x

So, the inverse is B. f⁻¹(x) = 1/x

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The value of permutation expression ₅₉P₂ is 3422.

A permutation is an arrangement of objects in a definite order.

To find the value of ₅₉P₂, we use the formula below

Formula:

Where:

Substitute these values into equation 1

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Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

As per the given situation, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are often represented using function notation.

To find k, we need to know the value of g(x) for a specific value of x. Let's say we want to find k when x = 3. Then:

g(3) = k · f(3)

g(3) = k · 2(3)

g(3) = k · 6

If we know the value of g(3), we can solve for k:

g(3) = 15

15 = k · 6

k = 15/6

k = 2.5

Therefore, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

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To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.

Cost of gear per person:

Shoes: $10

Helmet: $3

Gloves: $2.50

Harness: $5.00

Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50

Total cost of gear for 3 people: $20.50 x 3 = $61.50

Cost of trainer: $15.00

Total bill (including gear and trainer): $70.25

Remaining amount for zip lining:

=  $70.25 - $61.50 - $15.00

= $-6.25

Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.

However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.

Approximate number of hours:

Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours

Approximate amount each person paid:

Amount each person paid

= Total bill / 3

= $70.25 / 3

≈ $23.42

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Answer:

8 am

Step-by-step explanation:

First train has a 50 m/hr x 3 hr = 150 mile head start

Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance

 in 15 hours to catch the first train

2pm + 3 hours + 15 hours = 8 am

Answer: Congruent and Perpendicular

Step-by-step explanation:

If diagonals of a quadrilateral bisect each other then it is a rectangle and if they are perpendicular as well then it is a square.

9. The ball returns to 98.00% of its previous height after each bounce Option B

10. It will take 183 bounce until the ball bounces back to a height less than 3 inches.  Option B

To solve for k% of previous height after each bounce, we say

10×(k/100)⁵ = 9.04

k = [tex](9.04/10)^{1/5}[/tex]×100

k = 98.00

To find out how many bounces it takes for the ball to bounce back to a height less than 3 inches (or 0.25 feet), we use the inequality

10 × (0.961)ⁿ < 0.25

The logarithm of both sides gives

n × log(0.961) < log(0.025)

n > log(0.025) / log(0.961)

n > 182.593

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Answer:

Step-by-step explanation:

5(x - 3) ? x + 13

if x = 6

5(6 - 3) ? 6 + 13

15 ? 19

15 ≠ 19

Step-by-step explanation:

When substituting 6 for x, the equation becomes:

5(6 - 3) ?= 6 + 13

Now, we can solve both sides of the equation:

5(3) ?= 6 + 13

15 ?= 19

Since these are not equal, the equation is not true for x = 6.