10)
Solve the triangle. Round decimal answers to the
nearest tenth.

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

  no. 2/3 is not a natural number

Step-by-step explanation:

If the dividend is not a multiple of the divisor, the result of the division will not be a natural number. 2/3, for example, is not a natural number.

Answer:

\(0.64 \pm 1.645\sqrt{\frac{0.64*0.36}{50}}\), option D

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

From a random sample of 50 students, she found that 32 students read at least 1 book last month.

This means that \(n = 50, \pi = \frac{32}{50} = 0.64\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

Confidence interval:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.64 \pm 1.645\sqrt{\frac{0.64*0.36}{50}}\)

So the correct answer is given by option D.

Answer:

Horizontal shift to the RIGHT of one unit

Step-by-step explanation:

When looking at a square root equation, the transformation form is:

\(f(x) = a\sqrt{b(x-h)} +k\)

'h' represents a horizontal shift of the graph. Therefore, in this instance:

\(f(x) = \sqrt{x-1}\)

This means that there is a horizontal shift to the RIGHT of one unit.

Answer:

12

Step-by-step explanation:

You do 6+6, or 2+2+2+2+2+2=12

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

66640 divided by 31 is approximately equal to 2149.68.

Division is a basic arithmetic operation that is used to split a quantity into equal parts or to find out how many times one quantity is contained within another quantity.

When 66640 is divided by 31, the result is:

66640 ÷ 31 =2149.68 (rounded to two decimal places)

Therefore, 66640 divided by 31 is approximately equal to 2149.68.

In general, when we perform division, we are asking the question "how many times does the divisor fit into the dividend?" The dividend is the number being divided, the divisor is the number we are dividing by, and the result is the quotient.,

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1) probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

What is Probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

1) Probability of answering 6 questions correctly:

Since there are 4 choices for each question, the probability of guessing the correct answer for a single question is 1/4.

P(6 correct) = \((1/4)^{6}\) = 0.00024414 ≈ 0.00024

So the probability that Ed will answer all 6 questions correctly is approximately 0.00024.

2) Probability of answering exactly 2 questions correctly:

The probability of guessing exactly 2 questions correctly can be calculated using the binomial probability formula:

P(exactly 2 correct) = (6 choose 2) * (1/4)² * \((3/4)^{4}\)

P(exactly 2 correct) ≈ 0.29663

So the probability that Ed will answer exactly 2 questions correctly is approximately 0.29663.

3) Probability of answering at least 2 questions correctly:

P(at least 2 correct) = P(2 correct) + P(3 correct) + P(4 correct) + P(5 correct) + P(6 correct)

P(k correct) = (6 choose k) * \((1/4)^{k}\) * \((3/4)^{(6-k)}\)

where k can be 3, 4, or 5.

P(at least 2 correct) ≈ 0.46606

So the probability that Ed will answer at least 2 questions correctly is approximately 0.46606.

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Answer:

x = 12

Step-by-step explanation:

the other explanation might be confusing so here is the answer again to sum it up

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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Answer:

\(37 \frac{7}{12}\) inches.

Step-by-step explanation:

Let's start by converting all of these mixed numbers to improper fractions to handle them a little better.

56 × 4 = 224 ⇒ 224 + 1 = \(\frac{225}{4}\)

18 × 3 = 54 ⇒ 54 + 2 = \(\frac{56}{3}\)

So, we have our improper fractions. Now, we need to convert each to twelfths so we can subtract.

225 × 3 = 675

56 × 4 = 224

\(\frac{675}{12} - \frac{224}{12}\) = \(\frac{451}{12}\)

\(\frac{451}{12} = 37 \frac{7}{12}\)

So, the answer is \(37 \frac{7}{12}\) inches.

The number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.

An average refers to a central value obtained after adding together several amounts and then dividing this total by the number of variables added.

An average is a central value in a dataset.

Average sales per month = 80 units

Number of months involved = 5 months

Total for five months based on the average = 400 units

Total units sold in four months = 328 (95 + 47 + 114 + 72)

Sales units required to meet the average target = 72 (400 - 328)

Thus, the number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.

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Answer:

57.23

Step-by-step explanation:

Multiplied it out, and two negatives make a positive, so boom you get the answer :)

Answer:

57.23

Step-by-step explanation:

AWW, that's easy. -5.9 x -9.7 or 5.9 x 9.7, same result. All u have to do is know how to multiply. I cannot really tell you step by step conveniently...

Answer:

x^5+4x^4+9x is what I would simplify it to.

To save for Malcom's education, his parents put $1,200 into a savings account when

Malcom was born in 2006. Every birthday, Malcolm's parents deposit 10% more than the

previous year.

Part A

In this problem we have an exponential function of the form

y=a(1+r)^x

where

a is the initial deposit

r is the rate of change

x is the number of years

y is the amount deposited in the saving account

so

we have

a=$1,200

r=10%=0.10

substitute

y=1,200(1+0.10)^x

y=1,200(1.10)^x --------> explicit formula

Part B

2006 -----> For x=0 -------> y=$1,200

2010 -----> For x=4 -----> y=$1,756.92

2014 ----> For x=8 -----> y=$2,572.31

2018 ----> For x=12 ----> y=$3,766.11

2022 ----> For x=16 ----> y=$5,513.97

Part C

we have an geometric sequence

To find out the sum

we use the formula

where

a is the first term

n is the number of terms

r is the common ratio

In this problem

a=$1,200

r=1.1

n=18

substitute

The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

Answer:

80%/100%×$24

Step-by-step explanation:

I don't see any options here so let's work it out.

If all prices are reduced by 20%,it implies that 80% of the original value is charged to the buyer as sales price.

Since original value of the pants is $24-100%

then sales value(80%)=(80%/100%×$24)

Answer:

$30

Step-by-step explanation:

I took the test on k12 and got it correct.

Answer:

The answer is C

Step-by-step explanation:

Just took the test

The measure of angle B is given as follows:

m < B = 49.2º.

Two angles are said to be complementary angles when the sum of their measures is of 90º.

The measures are given as follows:

As the angles are complementary, the value of x is obtained as follows:

x + 21 + 4x - 30 = 90

5x - 9 = 90

5x = 99

x = 19.8.

Hence the measure of angle B is obtained as follows:

m < B = 4 x 19.8 - 30

m < B = 49.2º.

The measures are given as follows:

The angles are complementary, and it asks for the measure of angle B.

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Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.

Given the data in the question;

To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.

Sine of angle n = Opposite of angle n / Hypotenuse

sin(n) = Opposite / Hypotenuse

Plug in the given values and simplify

sin(n) = Opposite / Hypotenuse

sin (n) = 2 / 2√5

Next, rationalize the denominator.

Cancel out the common factor 2.

sin (n) = 2 / 2√5

sin (n) = 1 /√5

Multiply both the numerator and the denominator by √5.

sin (n)  = (1×√5) / (√5 × √5)

sin (n)  = √5/5

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

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Answer:

CD = 27

Step-by-step explanation:

Given the triangles are similar then the ratios of corresponding sided are equal, that is

\(\frac{CD}{KD}\) = \(\frac{CB}{KL}\) , substitute values

\(\frac{CD}{9}\) = \(\frac{30}{10}\) = 3 ( multiply both sides by 9 )

CD = 27

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that, a certain truck traveled 7,605 miles in 15 days.

The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,

Suppose the average number of miles traveled per day is x,

x=76015 / 15

x=507 miles per day.

Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.

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So the equation in the form y=kx is: y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equal sign, with the expression to the left of the equal sign indicating the left-hand side of the equation, and the expression to the right of the equal sign indicating the right-hand side of the equation. Equations can be used to describe relationships between variables, to solve problems, and to model real-world phenomena.

Here,

a. Yes, the cost of the commercials is proportional to the length of time the commercial aired.

b. To find the cost of a commercial in dollars per second, we need to divide the cost by the length of the commercial in seconds. Using the given values, we get:

For a 15-second commercial: $2,700,000 ÷ 15 = $180,000 per second

For a 60-second commercial: $10,800,000 ÷ 60 = $180,000 per second

For a 90-second commercial: $16,200,000 ÷ 90 = $180,000 per second

For a 120-second commercial: $21,600,000 ÷ 120 = $180,000 per second

We can see that the cost per second is constant at $180,000. So the equation in the form y=kx is:

y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

y = \(\frac{-21}{2}x+5\)

Step-by-step explanation:

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.

To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.

Let's assume that the full tank of petrol has a capacity of 1 unit.

Othniel used 2/5 of the full tank of petrol to travel to Kumasi.

The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.

Othniel used 2/6 of the full tank of petrol to travel to Accra.

To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.

Converting the fraction 2/5 to have a denominator of 30:

(2/5) * (6/6) = 12/30

Converting the fraction 2/6 to have a denominator of 30:

(2/6) * (5/5) = 10/30.

Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.

Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.

Simplifying the fractions, we have:

Journey to Kumasi: 12/30 = 2/5.

Journey to Accra: 10/30 = 1/3.

Therefore, the journey to Kumasi required more petrol than the journey to Accra.

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