an electrician has a 16-foot spool of wire and he needs to cut an 11-foot, 4-inch piece from the spool to make a repair. how many inches of wire will he have left on the spool after he makes the repair

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.

The conclusion of the conditional statement is that; D) The angles are congruent.

Vertical angles are also called opposite angles and they are formed when two lines meet each other at a point.

Now, we are given the conditional statement "If two angles are vertical angles, then they are congruent."

Now, we can say that the conditional statement is always true according to the definition of vertical angles. Thus, we can say that the conclusion of the conditional is that The angles are congruent.

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The length of the loan in months is 151. 33 months

The formula for determining simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

Principal interest = $600

Simple interest = $681

Rate = 9%

Substitute the values into the formula

$681 = $600 × 9 × T/100

Multiply the numerators

$681 = 5400T/100

cross multiply

68100 = 5400T

Divide both sides by 5400

T = 68100/5400

T = 12. 61 years

Convert the years to months

T = 12.61(12)

T = 151. 33 months

Hence, the value is 151. 33 months

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Answer:

3/4 would represent the shaded in parts of the circle

Step-by-step explanation:

I cannot give you an accurate answer seeing as you did not give much detail

\(2+8p-3(12-5p)-(2-3p)(4)\\\\=2+8p-36+15p-8+12p\\\\=35p-42\)

Answer:

BD = 6

Step-by-step explanation:

Theorem:  The altitude to the hypotenuse of a right triangle is the mean proportional between the segments of the hypotenuse.

So, \(\frac{4}{BD} = \frac{BD}{9}\)

\(BD^{2} = 36\)

BD = 6

See how easy that is IF you know the theorem.

Answer:

A) \(430-45m = 310-25m\)

B) 6 months

Step-by-step explanation:

A) for Jonah, the equation would be \(430-45m\)

Because the money is being spent on the subs, you subtract that from his original savings.

The same thing is said for Rodrick, but his equation would be \(310-25m\)

to find out the number of months it will take for both gamers to have the

same amount of money left, you set their equations equal to each other:

\(430-45m = 310-25m\)

B) you solve for m.

\(430-45m = 310-25m\)

first by subtracting 310 on both sides to get:

\(430-310-45m=-25m\)

\(120-45m=-25m\)

then add 45m on both sides because we cant have negative months

\(120=-25m+45m\)

\(120=20m\)

divide by 20 on both sides to get the number of months

\(\frac{120}{20} =\frac{20m}{20}\)

\(m=6\)

1/8 -> 0.125

25% -> 0.25

0.02 -> 0.02

0.1 -> 0.10

least -> greatest

Haley, 0.02 -> Diego, 0.1 -> Rishi, 1/8 -> Monique, 25%

Arranging the persons from least to greatest

Haley < Diego < Rishi < Monique

A number expressed as a quotient, in which a numerator is divided by a denominator.

Given:

Rishi paints = 1/8 = 0.125

Monique paints = 0.250

Haley paints = 0.020

Diego paints = 0.100

Now, arranging the persons from least to greatest

Haley < Diego < Rishi < Monique

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The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer: if you are simplifying its 20x-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the given information, we can compute the table showing the summarized statistics of the two alloys A & B:

                                            Alloy A        Alloy B

Sample mean                    \(\bar {x} _A = 49.5\)      \(\bar {x} _B = 45.5\)

Equal standard deviation    \(\sigma_A = 5\)         \(\sigma_B= 5\)

Sample size                          \(n_A = 30\)        \(n_{B}= 30\)

Mean of the sampling distribution is :

\(\mu_{\bar{X_1}-\bar{X_2}}= 49.5-45.5 \\ \\ = 4.0\)

Standard deviation of sampling distribution:

\(\sigma_{\bar{x_1}-\bar{x_2} }= \sqrt{\sigma^2_{\bar{x_1}-\bar{x_2} }} \\ \\ = \sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma^2_2}{n_2} } \\ \\ =\sqrt{\dfrac{25}{30}+\dfrac{25}{30}} \\\\=\sqrt{1.667} \\ \\ =1.2909\)

Hypothesis testing.

Null hypothesis:  \(H_o: \mu_A -\mu_B = 0\)

Alternative hypothesis:  \(H_A:\mu_A -\mu_B > 4\)

The required probability is:

\(P(\overline X_A - \overline X_B>4|\mu_A - \mu_B) = P\Big (\dfrac{(\overline X_A - \overline X_B)-\mu_{X_A-X_B}}{\sigma_{\overline x_A -\overline x_B}} > \dfrac{4 - \mu_{X_A-\overline X_B}}{\sigma _{\overline x_A - \overline X_B}} \Big) \\ \\ = P \Big( z > \dfrac{4-0}{1.2909}\Big) \\ \\ = P(z \ge 3.10)\\ \\ = 1 - P(z < 3.10) \\ \\ \text{Using EXCEL Function:} \\ \\ = 1 - [NORMDIST(3.10)] \\ \\ = 1- 0.999032 \\ \\ 0.000968 \\ \\ \simeq 0.0010\)

This implies that a minimal chance of probability shows that the difference of 4 is not likely, provided that the two population means are the same.

b)

Since the P-value is very small which is lower than any level of significance.

Then, we reject \(H_o\) and conclude that there is enough evidence to fully support alloy A.

Answer:

513.45

Step-by-step explanation:

use intelligence

Answer:

3 : 10

Step-by-step explanation:

2 kg = 2000g

600g peanuts : 2000 cashew nuts

600 : 2000

divide both sides by a common divisor ( 200)

600/200 : 2000/200

3 : 10

Yes , it is true that two pairs of adjacent sides of a kite are equal .

A quadrilateral with two pairs of adjacent sides equal in length is called a kite. Kites also have one pair of opposite angle equal as shown in the figure below.

Hence , the given statement is true .

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Answer:

-1

Step-by-step explanation:

Note that by definition,

\(f(g(x))=x \implies f'(g(x)) g'(x) = 1 \implies g'(x)=\frac{1}{f'(g(x))}\)

Substituting x=1,

\(g'(1)=\frac{1}{f'(g(1))}\)

As g is the inverse of f,

\(f(-1)=1 \implies g(1)=-1 \\ \\ \implies g'(1)=\frac{1}{f'(-1)}\)

By the power rule, f'(x)=2x+1, so f'(-1)=-1.

\(\implies g'(1)=\frac{1}{-1}=-1\)

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Answer:

  y = √55

Step-by-step explanation:

All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:

  5/y = y/(5+6)

  y^2 = 55

  y = √55

_____

Comment on the geometry

There are three "geometric mean" relationships that apply to this geometry.

If you were aware of the last of these relationships, you could write down the answer without any "work."

  y = √(5(5 +6)) = √55

__

The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.

Answer:

\(m = 13 / -3 = -4.33333\)

Step-by-step explanation:

\(Equation: y = -4.33333x - 28.33333.\)

\(Y - intercept -28.333\\ \)\(Angle (θ) -77 deg \)

\(θ = arctan(-4.33333) = -7.70054 \)

\(Percentage grade-433.3% \)

\(Distance (d) 13.342 \)

\(Distance between x's (Δx) 3 \)

\(Distance between y's (Δy) 13 \)

\(d = √(Δy2 + Δx2) = √(132 + -32) = √178 = 13.34166\)

The measure of ∠QTS = 58°

Given; A triangle QPR

PQ = PR

this means that ∠ Q = ∠ R

and QR = QT this means ∠ R = ∠ T

And ST ║ QR

and QT is the transversal

From the above mentioned information we can conclude that

∠QTS = ∠TQR -------------- 1

Thus since ∠ Q = ∠ R  

by using angle sum property of triangle we can conclude that

∠ Q + ∠ R = 116  [ exterior angle sum property ]

2 ∠ Q = 116

∠ Q = 58°

this means ∠ TQR = 58°

And from 1 we know that this angle is equal to angle QTS

Thus ∠QTS = ∠TQR = 58°

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To find the distance between the seagull and the turtle, find the difference between their locations, taking the values below the sea as negative values:

They are 12 feet apart.

The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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The expression of the statement that is given above can be written as follows: 262144y³ + 27.

To determine how to express the given statement the following should be carried out.

When a number is said to be cubed, it means that the number should be times by itself three consecutive times.

That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,

= 64×64×64(y)³ + 3×3×3

= 262144y³ + 27.

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The total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.

We are given that:

Principal amount = P = $ 680

Time period = t = 3 years

Simple interest rate = r =  3.94 %

We know that, the formula for simple interest is given by:

SI = P × r × t

SI = 680 × 3.94 % × 3

SI = 80.376

Amount will become:

Amount = $ 680 + $ 80.376

Amount = $ 760.376

Therefore, we get that, the total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.

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Answer:

it's 10

Step-by-step explanation:

A ratio of 2:5 means it is probably counting by 5s. Since 5 X 5 equals 25, 2 X 5 equals 10. since ethe larger polygon is 25, this means the number can't be bigger than 25 so it is counting by fives.

Answer:

In mathematics, we call multiplying a number by itself “squaring” the number. We call the result of squaring a whole number a square or a perfect square. A perfect square is any number that can be written as a whole number raised to the power of 2. For example, 9 is a perfect square.

Step-by-step explanation:

Step-by-step explanation:

heres the formula A=12b(base)h(hight)

Answer:

Step-by-step explanation:

It has (1/2) included in the formula to find area