-7x + 4y = 24
4x - 4y = 0
solve by substitution - please add explanation and work

The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.

In order to find the cube root of unity let us say,

x³ = 1

Solving further,

x³-1 = 0

Now,

(x-1)(x²+x+1)=0

For, x-1=0

x = 1.

And,

For, (x²+x+1)

Solving by using quadratic formula,

x = -1±√(-3)/2.

x = -1±i√3/2

x = -1+i√3/2 and,

x = -1-i√3/2

also, x = 1.

So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.

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We reject the null hypothesis and come to the conclusion that their argument is adequately supported.

Given that,

z = 2.14 and p value = 0.0162

a) Hypotheses are

H₀ : p≤  0.40

H₀ : p > 0.40  (claim)

This is right tailed test.

b) p value = 0.0162

c) Test statistic Z =2.14

P(Z>2.14) = 1 - P(Z≤2.14)

               = 1 - 0.98382

               = 0.01618

P value ≈  0.01618

d) P value is less than α = 5% = 0.05

So, we reject the null hypothesis and conclude that they have enough evidence in support of their claim

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(1 – 3cosx – 4cos^2x) / sin^2x = 

(1+cos x)(1-4cos x) /(1-cos^2 x) =

 (1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] = 

(1-4cos x) /(1-cos x)
Factor:

1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =

RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED

A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes. So the correct option is D.

In the given question we have to find what type of variable is required to construct a confidence interval for a population proportion.

As we know that;

Population proportion is the percentage of the entire population that possesses the given quality (which is qualitative in nature). The confidence interval for the population proportion must thus be constructed using a qualitative variable with two possible outcomes.

So, the correct option is identified from nature of different type of the variables. A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes.

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The right question is:

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

Answer: 10 months

Step-by-step explanation:

432 + 40x >505 + 32x

40x >32x + 73

8x > 73

8x/8 > 73/8

x > 73/8 = 9.125

Round 9.125 to 10

The number of months that will take Lola to have more trading cards is obtained as 8.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The number of cards with Lola and Joel are 432 and 505 respectively.

Suppose the number of required month be x.

Then, the inequality expression can be written for the given case as,

432 + 40x > 505 + 32x

⇒ 40x - 32x > 505 - 432

⇒ 8x > 63

⇒ x > 63/8

The number of months should be an integer value.

And, the nearest integer value of the greater than 63/8 is 8.

Hence, the number of months required for the given case is 8.

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The length of OM is 20 if MN=20 and N0=14

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

To find the length of OM

Given,

MN=20

ON=14

∠O≅∠N

Since, ∠O≅∠N

ΔMNO is isosceles triangle with

OM=MN=20

Hence, the length of OM is 20.

Therefore, The length of OM is 20 if MN=20 and N0=14

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The distance between the rock and the surface is 827.20 cm.

Given data,

There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.

How far is the rock from the camera?

From the given data,

tan c = AB/BC

tan 13.33° = 196/BC

BC = 196/tan 13.33°

BC = 827.20 cm

Hence, the distance between the rock and the surface is 827.20 cm.

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The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

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The complete question is:

A kindergarten teacher has five books to distribute to 20 children in her class.

(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?

(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.

(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?

By evaluating the piecewise function we will see that the difference is:

f(1) - f(-7) = 3

Here we have a piecewise function defined on the image, and we want to find the difference:

f(1) - f(-7).

First, let's find these values.

f(1) means that we need to evaluate the function in x = 1.

Notice that the second piece can be used on the domain 4 < x ≤ 1, so we need to use that part.

f(1) = -(1)^2 - 3*1

f(1) =-1 - 3 = -4

To evaluate in x = -7 we need to use the first piece of the function:

f(-7) = |-7 + 5| - 9

f(-7) = |-2| - 9 = -7

Then the difference is:

f(1) - f(-7) = -4 - (-7) = -4 + 7 = 3

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Answer: 6.25%

Step-by-step explanation:

To find what percent 61 is of 976, we divide 61/976. This comes out to be 0.0625. Multiply by 100 to get your percentage, and it's 6.25%.

here you are the answer.

Answer:

=

Step-by-step explanation:

As described in probability Null hypothesis is 0.64

what is probability?

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.

Solution:

Null hypothesis H0 : p =  0.64

Alternate hypothesis Ha : p ≠ 0.64

therefore  Null hypothesis is 0.64

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$600 is the original price of the article if the  price of an article is 20% and new price is $150

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The increase in price of an article is 20%

The new price is $150

We need to find the original price of the article.

Let 20% of x=150

20/100x=150

0.2x=150

Divide both side by 0.2

x=750

Now subtract 750 and 150 we get original price

750-150

600

Hence, $600 is the original price of the article if the  price of an article is 20% and new price is $150

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Answer:

When you combine like terms, you look for the same variable or look for constants. In this case, the same variable if 'k'. Now you add the coefficients 7 and 3, which is 10. So the expression simplifies to 10k + 11.

Hope this helps!

Answer:

10k + 11

Step-by-step explanation:

Like terms are terms that have the same amount of the same variables.

In this case, note that two of the terms have the variable "k" attached:

7k & 3k, respectively.

In this case, the question asks you to combine like terms, or to simplify the given expression:

7k + 3k + 11

(7k + 3k) + 11

10k + 11

10k + 11 is your answer.

~

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The probability that the sample mean will be between 1195 and 1205 is 0.445

What is a probability distribution?

In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.

Given, mean = [tex]\mu[/tex] = 1200

standard deviation = [tex]\sigma[/tex] = 60

n = 50

[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]

[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]

= P(-0.59 < Z <0.59 )

= P(Z <0.59 ) - P(Z <-0.59 )  

Using the z table, we get

=0.7224-0.2776

=0.4448 = 0.445 ( rounded to 3 decimal places)

Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445

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The age of the fossil is 24, 312 years assuming an exponential decay model.

Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:

P = 100 e^(-kt)

Where P is the remaining quantity, k is the constant of decay, and t is time.

As the half life of the carbon 14 is 5700, when 50% of the substance remains,

50 = 100 e^(-5700k)

1/2 = e^(-5700k)

In(1/2) = In(e^(-5700k))

- In (2) = -5700k

k = In(2)/5700 = 0.0001216

Since, 5.2% carbon-14 remains,

5.2 = 100 e^(-0.0001216t)

0.052 = e^(-0.0001216t)

In(0.0052) = - 0.0001216

t = In(0.052) * - 0.0001216

t ≈ 24, 312 years.

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The probability of getting 5 black chips and 6 white chips is [tex]\frac{7}{22}[/tex].

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to data in the given question,

We have the given information:

Total number of different colored chips = 35

Number of black chips = 20

Number of white chips = 15

And you draw 11 chips at random.

Now, we will calculate the probability of getting 5 black chips and 6 white chips,

[tex]P(B) = \frac{5}{20} =\frac{1}{4} \\P(W) = \frac{6}{15} =\frac{2}{5} \\P( black and white ) = \frac{\frac{1}{4}*\frac{2}{5}}{\frac{11}{35} } \\=\frac{\frac{1}{2}*\frac{1}{5}}{\frac{11}{35} }\\=\frac{1}{10}*\frac{35}{11}=\frac{7}{22}[/tex]

Therefore, the probability of getting 5 black chips and 6 white chips is 7/22.

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If the top slips down the wall at a rate of 2 ft/s, then 3.476 ft/s fast the foot will be moving away from the wall when the top is 10 feet above the ground.

In the given question, a 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s.

We have to find how fast will the foot be moving away from the wall when the top is 10 feet above the ground.

As given, 15ft ladder dy/dt= -2y=13ft

Let the length be x and height be y

So from the Pythagorean theorem

x^2+y^2=h^2

Now apply the above formula to get the value

x^2+y^2=15^2

Take the derivative with respect to time

2x * dx/dt+2y*dy/dt=0

dx/dt= -y/x *dy/dt

When y = 13

then x^2+13^2=15^2

x = 7.48

dx/dt= -13/748 * (- 2)

dx/dt= 3.476 ft/s

Hence, if the top slips down the wall at a rate of 2 ft/s, 3.476 ft/s fast will the foot be moving away from the wall when the top is 10 feet above the ground.

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Answer:

Step-by-step explanation:

a^2 +b^2 =c^2

8^2 +14^2=y^2

64+196 =y^2

260=y^2

(260)^1/2 =y

Simplified: 4^1/2  * 65^1/2= 2(65^1/2)

The null hypothesis is

H₀:The defendant is innocent

The alternative hypothesis or research hypothesis is

H₁ : The defendant is guilty

Which of the two hypotheses is correct is unknown to the jury.

Given that,

Think about a case where a jury must choose between the hypotheses that the defendant is guilty and the defendant is innocent.

We have to find which of the hypotheses ought to be the null hypothesis in the context of hypothesis testing and the American legal system.

We know that,

A jury in a trial must choose between two hypotheses. The null hypothesis is

H₀:The defendant is innocent

The alternative hypothesis or research hypothesis is

H₁ : The defendant is guilty

Which of the two hypotheses is correct is unknown to the jury. They must decide based on the information provided.

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Answer:

ITS B

Step-by-step explanation:

Step-by-step explanation:

v=1/3πr²h

98=1/3×22/7×(5.13)²×h

98=1/3×22/7×(27.2403)×h

98=28.537×h

h=28.537/98

h=0.291m

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Answer:

Answer to your question is in the attachment

The sum of DE+FG+HI=90 if DE, FG, HI are all parallel to BC and BC=60.

Quadrilaterals with at least one set of parallel sides are referred to as "trapezoid" quadrilaterals. In British and other dialects of English, the word "trapezium" is used.

Euclidean geometry dictates that a trapezoid must be a convex quadrilateral. The base of the trapezoid is referred to by its parallel sides. If the other two sides are parallel, the trapezoid is a parallelogram, and there are two pairs of bases. If not, the other two sides are known as the legs (or lateral sides). Unlike the specific situations below, a scalene trapezoid is a trapezoid where none of the sides have equal lengths.

Given,

ΔABC is a scalene triangle.

And BC=60

DE, FG, HI are all parallel to BC.

From the midpoint-theorem,

DE||BC then,

DE=(1/2)BC

FG||BC

FG=(1/2)BC

HI ||BC

HI=(1/2)BC

DE+FG+HI=(1/2BC+1/2BC+1/2BC)

=(1/2(3BC))

1/2(3(60))

=90

Therefore,

The sum of DE+FG+HI=90

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Answer:

The answer is    x=2

Step-by-step explanation:

1. Rearrange terms-

29x + 3 (  5 - 35x) = - 119 - 9x

29x + 3 ( - 35x + 5) = - 119 - 9x

2. Distribute-

29x + 3 ( - 35x + 5) = - 119 - 9x

29x - 105x + 15 = - 119 - 9x

3. Combine like terms-

29x - 105x + 15 = - 119 - 9x

- 76x + 15 = -119 -9x

4. Rearrange terms-

- 76x + 15 = - 119 - 9x

- 76x + 15 = - 9x - 119

5. Subtract 15 from both sides-

- 76x + 15 = - 9x - 119

- 76x +15 -15 = -9x - 119 - 15

6. Simplify-

- 76x = - 9x - 134

7. Add 9x to both sides-

- 76x + 9x = - 9x - 134 + 9x

8. simplify-

- 67x = - 134

9. Divide both sides by the same factor-

[tex]\frac{-67x}{-67} = \frac{-134}{-67}[/tex]

10. Simplify-

x = 2

Answer: 5.072

Step-by-step explanation: -0.8-2.14=-6.2

                                                     +2.14 |  +2.14

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

                                                              -4.06/-0.8=5.072

Answer:

D. (-3, 4)

Step-by-step explanation:

Hope it helps!

Answer:

Step-by-step explanation:

What are you supposed to do

The formula for the area of a circle is pi times the radius squared (A = π r²)

A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre." The line of reflection symmetry is formed by every line that passes through the circle. It also has rotational symmetry around the center for all angles.

It is a curved portion of its circumference. A semicircle is an arc that connects the endpoints of the diameter and has a measure of 180°. The circle is divided into two parts by an arc. The minor arc is the smaller part, and the major arc is the larger part.

To find the area goes thus;

Identify the radius of a circle.

Square the radius.

Multiply by pi. Pi.

In conclusion, the formula is πr².

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Complete question

what is the formula for the area of a circle?