Find the exact value of the expression. Do not use a calculator.
sin 79°-cos 11°

I got 0. I'm not sure if that's right.

Answer:

x=54.5

Step-by-step explanation:

x+62+x+9=180

2x+71=180

2x+71-71=180-71(subtract 71 from both sides)

2x=109

2x/2=109/2(divide both sides by 2)

x=54.5

Answer:

x=54.5

Step-by-step explanation:

1. Combine like terms

x+62+x+9=180

2x+71=180

You can only combine the x and 62 and 9 in this equation.

2. Subtraction property of equality

2x+71=180

    -71 = -71

2x=109

Subtract 71 from both sides to isolate the variable, x.

3. Division property of equality

2x=109

/2     /2

x=54.5

Hope this helps!

The smallest factor (other than 1) of 111 would be 15.

Option (A) is correct.

What is the smallest factor of a number other than 1?

A number can have a maximum of one factor, and only one has that many factors. Every other number has more than one factor.

Prime numbers have two factors, for example, 2,3,5,7,11...,2729...,2927, 9999959999, and so on. Prime numbers have only one factor the number itself.

The factors of 111 are 1, 3, 37, and 111.

for option (A), the factors of 15 are 1, 3, 5, and 15.

for option (B), the factors of 22 are 1, 2, 11, and 22.

for option (C), the factors of 28 are 1, 2, 4, 7, 14, and 28.

for option (D), the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

So if you observe all the options, the smallest factor (other than 1) of 111 would be 15.

Hence, the smallest factor (other than 1) of 111 would be 15.

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The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Two congruent figures.

Each figure's total sum of the angles must be 360.

The figures are congruent so the corresponding angles must be equal.

From the first figure we get,

∠A = 133 ( Corresponding angles )

∠A + ∠B + ∠C + ∠D = 360

133 + ∠B + 41 + 86 = 360

∠B = 360 - 260

∠B = 100

Now,

∠k = ∠B = 100

∠L = ∠C = 41

∠M = ∠D = 86

Thus,

The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

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Answer:

…………………………………………/,,/,,..,,.,…….

Step-by-step explanation:

Answer:.

Step-by-step explanation: .

The Actual Unemployment rate is 7%.

Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.

Cyclical Unemployment Rate = 1%

Natural Unemployment Rate = 6%

The Actual Unemployment rate will be:

= Cyclical Unemployment Rate + Natural Unemployment Rate

= 1% + 6%

= 7%

The unemployment is 7%.

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Answer: The answer to this question would either be 8 or it would be 7.

Answer: It does not appear to show a function because the numbers are not multiples of each other

Step-by-step explanation: Hope this helps :-)

Answer:

1. 3  donuts

2.$76.90

Step-by-step explanation:

Answer: 0.865 to (1dp)

Step-by-step explanation:

when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.

What is External validity?

The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.

An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.

Question

When you are interrogating the external validity of a sample, which is the most important question to ask?

a. how many people are in the sample?

b. how was the sample collected?

c. how were the participants measured?

d. how many people are in the population?

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Answer:

17

Step by step explanation

15-6=21

38-21=17

The coordinates to the intercepts of the functions are given as follows:

c - i) Point P: P(-4,0).

c - ii) Point Q: Q(0,2).

d - i) Point P: P(-3,0).

d - ii) Point Q: Q(0,9).

The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.

For item c, the function is:

2y = x + 4.

Hence the x-intercept is obtained as follows:

x + 4 = 0

x = -4.

Then the coordinates of point P are:

P(-4,0).

For item d, the function is:

y = 3x + 9

Hence the x-intercept is obtained as follows:

3x + 9 = 0

3x = -9

x = -3.

Then the coordinates of point P are:

P(-3,0).

The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.

For item c, the function is:

2y = x + 4.

Hence the y-intercept is:

2y = 4

y = 2.

The coordinates of Q are:

Q(0,2).

For item d, the function is:

y = 3x + 9.

Hence the y-intercept is:

y = 3(0) + 9 = 9.

The coordinates of Q are:

Q(0,9).

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The probability of a type I error is 0.022.

Given,

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

That is,

The probability of a type I error is 0.022.

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The probability of getting heads twice in a row at some point during three coin flips is 1/8.

Given info;

Assume that a fair coin has an equal chance of coming up heads or tails.

What is the likelihood that three coin flips will result in two consecutive heads at any point?

There is a three-coin flip. The potential results are;

(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)

1 is the number of successful results.

Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8

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The common factor for the rational expression presented in this problem is given as follows:

A. (x²-1).

The rational expression in this problem is given as follows:

4/(x - 1) - 1/(x² - 1) = 6/(x - 1).

It is called a rational expression as it has the variable x in the denominator.

The common factor, which is the expression that multiplies each term, is obtained considering all the terms that are present in the denominators.

The denominators to each term of the expression are listed as follows:

Hence the two terms present in the denominators of the expression are:

(x - 1)(x + 1) = x² - 1 -> subtraction of perfect squares.

Hence option A gives the correct term.

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Answer:

3rd choice

No, it is NOT a linear function because the variable x is in the denominator. x will be multiplied by y.

The speed of the output shaft is 182 rpm.

Given:

Gear index i = 0.33

Input speed = 60 rpm.

Let output shaft speed is x.

we know that:

gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]

i = 60/x

0.33 = 60/x

x = 60/0.33

= 60/033/100

= 60*100/33

= 6000/33

= 181.818 ≈ 182 rpm.

Therefore The speed of the output shaft is 182 rpm.

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Answer:

B 1/4

Step-by-step explanation:

f(x) = y = x⁴ + 5

the inverse function is

y - 5 = x⁴

x = 4th root(y - 5)

now we rename y and x to make it a regular function definition :

g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)

because g(6) = 1 (positive), we have

g(x) = (x - 5)^(1/4)

and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.

g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)

because (x - 5)' = 1

g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =

= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4

please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.

Answer:

G. 12

Step-by-step explanation:

Step 1: Use PEMDAS to start solving

Step 2: Solve the problem

Answer:

Answer:The total change in the number of bushels she has for sale after 5 days is 83.125 bushelsStep-by-step explanation:The given parameters are;The initial number pf bushels the farmer has = 120 bushelsThe amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625 The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushelsThe total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 daysThe total change in the number of bushels she has for sale after 5 days = 83.125 bushels.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(i)

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

(k + x)² = m² + (k - x)² ← expand factors on both sides using FOIL

k² + 2kx + x² = m² + k² - 2kx + x² ( add 2kx to both sides )

k² + 4kx + x² = m² + k² + x² ( subtract k² + x² from both sides )

4kx = m² ( divide both sides by 4k )

x = [tex]\frac{m^2}{4k}[/tex]

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

(ii)

the area A of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = m and h = k - x

A = [tex]\frac{1}{2}[/tex] m (k - x) ← substitute x = [tex]\frac{m^2}{4k}[/tex]

  = [tex]\frac{1}{2}[/tex] m ( k - [tex]\frac{m^2}{4k}[/tex] ) ← distribute parenthesis

  = [tex]\frac{mk}{2}[/tex] - [tex]\frac{m^3}{8k}[/tex]  ← express as a single fraction

  =  [tex]\frac{4mk^2-m^3}{8k}[/tex] ← factor out m from each term in the numerator

  = [tex]\frac{m(4k^2-m^2)}{8k}[/tex] ← factor (4k² - m² ) as a difference of squares

  = [tex]\frac{m(2k+m)(2k-m)}{8k}[/tex]

Answer:

u = 2

Step 1: Simplify both sides of the equation.

−7u −u +2u +11u = 10

−7u +−u +2u +11u = 10

(−7u +−u +2u +11u) = 10 (Combine Like Terms)

5u = 10

Step 2: Divide both sides by 5.

5u/5 = 10/5

Hope this helped!

The logarithm of 5.238 with solution is  0.71916549409.

= log(5.238)

= log(5238/1000)

= log(5238) - log(1000)

= 3.71916549409 - log([tex]10^{3}[/tex])

= 3.71916549409 - 3log10

= 3.71916549409 - 3

=  0.71916549409.

Therefore the logarithm of 5.238 with solution is 0.71916549409.

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To determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

Rate of Change:

A rate of change describes how an output quantity changes relative to the change in the input quantity. The units on a rate of change are “output units per input units.”

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

[tex]\frac{\triangle y}{\triangle x} = \frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1}}[/tex]

How to determine:

Given the value of a function at different points, calculate the average rate of change of a function for the interval between two values [tex]x_{1}[/tex] and [tex]x_{2}[/tex].

Hence the answer is to determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

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Answer:

(g.f)(-2) = -44

Step-by-step explanation:

Given:

f(x) = 3x² - 3x - 7

g(x) = -3x - 10

[tex] \rm \implies(g.f)( - 2) = [3 {( - 2)}^{2} - 3( - 2) - 7][ - 3( - 2) - 10] \\ \\ \rm \implies(g.f)( - 2) = [3 (4) + 6 - 7][ 6 - 10] \\ \\ \rm \implies(g.f)( - 2) =(12 - 1)( - 4) \\ \\ \rm \implies(g.f)( - 2) =11 \times ( - 4) \\ \\ \rm \implies(g.f)( - 2) = - 44[/tex]

To see the attachment of graph of linear inequality.

Given,

In the question:

The linear inequality is given as:

y ≤ x -5

To graph the above inequality.

Now, According to the question:

What is linear inequality?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Math. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Math are polynomial inequality, rational inequality, absolute value inequality.

Hence, To see the attachment of graph of linear inequality.

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