Evaluate the expression for j = -9 and k = -1.
jk - 4 =

Answer:

<1 and <2

Step-by-step explanation:

Complementary angles are two angles which their measure add up to 90 degrees.

There are only one angle pair that meet this requirement:

angle 2 and angle 1

To estimate the number of times the earth will rotate on its axis during a human's lifetime, we first need to determine the average length of a human's lifetime.

According to the World Health Organization, the global average life expectancy at birth in 2020 was approximately 72 years. Next, we need to calculate the number of days in 72 years. 72 years x 365 days/year = 26,280 days.

Since the earth rotates once every 24 hours, we can calculate the number of rotations by dividing the number of days by 24. 26,280 days ÷ 24 hours/day = 1,095 rotations. Therefore, we can estimate that the earth will rotate on its axis approximately 1,095 times during a human's lifetime.

I decided on using the average human's lifetime based on data from the World Health Organization to provide a general estimate. However, it's important to note that life expectancy can vary greatly depending on factors such as geography, lifestyle, and genetics.

we can use this formula: Number of rotations = Average lifespan (in years) x Rotations per year
Number of rotations = 72 years x 365 rotations/year
Number of rotations ≈ 26,280 rotations, So, we can estimate that the Earth will rotate on its axis about 26,280 times during an average human's lifetime.

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Answer:

x=-10

Step-by-step explanation:

Answer:

x=-10,y=-20

this is a required answer.

Answer:

b= -9

Step-by-step explanation:

Plug in -9 for b.

3= -9+12

Solve.

3=3

Since both sides are equal, the answer is -9

I hope this helped you ;)

The recursive definition for a set of positive integers that are not divisible by 3 can be defined using two components: a base case and a recursive step.

The base case specifies the starting point, while the recursive step defines the pattern of the sequence.

Base case: The first positive integer not divisible by 3 is 1.

Therefore, the base case is S(1) = 1.

Recursive step:

To generate subsequent integers in the sequence, we can use a rule that adds a fixed constant to the previous integer, provided the result is not divisible by 3. One way to achieve this is by adding 2.

Hence, the recursive step is defined as S(n) = S(n-1) + 2 if (S(n-1) + 2) % 3 ≠ 0, where n > 1 and "%" denotes the modulo operator.

This definition ensures that the sequence consists of positive integers that are not divisible by 3, starting with the base case and following the recursive step.

For example, the first few terms of the sequence would be 1, 4, 5, 7, 10, 11, 13, and so on.

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The value of c 0.097 can satisfy the probability condition p(z ≤ c) = 0.52.

We need to find a value of c such that the probability of a standard normal random variable, Z, being less than or equal to c is 0.52, i.e., P(Z ≤ c) = 0.52.

We can use a standard normal table or a calculator to find the value of c that corresponds to a probability of 0.52. For example, using a calculator or a table, we can find that the 0.52 percentile of the standard normal distribution is approximately 0.097.

Therefore, we have:

P(Z ≤ c) = 0.52

c = 0.097 (from the standard normal table or calculator)

So, the value of c that satisfies the given probability condition is approximately 0.097.

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Answer:

1000

Step-by-step explanation:

2x²(x - 5) ÷ 10x

x = 10

2(10)²(10 - 5) ÷ 10(10)

20²(5) ÷ 100

100² ÷ 100

100000 ÷ 100

1000

Answer:

50

Step-by-step explanation:

5x-6=64

x=14

64-14=50

Answer:

\( { \tt{ {r}^{2} + 2 {r}^{3} = {r}^{2} (1 + 2r) }}\)

Answer:

We can't add these two terms since they're not like terms

Step-by-step explanation:

We cannot add variables if they have different exponents

It will take Joe 738.3 seconds (12.3 minutes) to climb from street level to the roof of the sears tower.

To find how long will it take joe to climb from street level to the roof of the sears tower:

Therefore, it will take Joe 738.3 seconds (12.3 minutes) to climb from street level to the roof of the sears tower.

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer: 17%

Step-by-step explanation:

1. First divide the percentages by 100 to turn the percentages into a decimal (28/100) x (63/100) = 0.1764

2. Then turn that decimal into a percentage again.

0.1764 x 100 = 17.64 but if you’re rounding to the nearest tenth without any decimals it’ll just be 17%

a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer:

9(2x-1)

Step-by-step explanation:

common factor of both 9 and 18 is 9

thus, you can take a 9 out

9(2x-1)

(to check if it is correct, you can expand it, and if it is the same as original then it is correct )

Answer:

9 (2x-1)

Step-by-step explanation:

Grouping

1. Common factor:

18x-9

Solution:

9 (2x-1)

Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2  such that f'(c) = 0.

Given:

Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.

f(x)=x^2−4x+8, [0,4]

when, x = 0

f(x) = x^2 -4x +8

f(0) = y = 0 - 0 + 8 = 8

when, x=4

f(5) = y = 16 - 16+8 =

thus, we have 2 points (0, 8) ; (4, 8)

slope,m = {8-(8)} / {4-0} = 0

hence, we have to calculate all the points,x where 0<x<8 and slope=0

f '(x) = 2x - 4 = 0

or, f '(c) = 2c - 4 = 0

c = 4/2 =2 ( 0<x<4)

hence, the there is only one solution c=2 which satisfies Rolle's theorem.

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Answer:

Choice A: \(2x^4+12x^3+26x^2+8x+12\)

Step-by-step explanation:

This can be done without computing the entire product and difference with a little bit of thought. If you look at the answer choices they have different values for the coefficient of \(x^4\) Choices B and C do not even have a term for \(x^4\)

So if we focus on only the part of the multiplication which will produce an \(x^4\) term we can find the right choice

The area of Shape A is (3x² + 2)(7x² + 4x + 8)

One of the terms arises from 3x² x 7x² = \(21x^4\)

The area of Shape B = (3x²+2)(3x^2+2)

So the

Look at the answer choices.
The first component has x term \(x^4\) which is obtained by multiplying

(3x²)(3x²) = \(9x^4\)

If we subtract the area of Shape B from Shape A , we get the \(x^4\) term as
\(21x^4 - 9x^4 = 12x^4\)

The only choice which has \(12x^4\) as a term is the first one, Choice A

So answer is Choice A: \(2x^4+12x^3+26x^2+8x+12\)

Answer:

12x^(4)+12x^(3)+26x^(2)+8x+12

Step-by-step explanation:

Plato/Edmentum

Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

The number of coins that are mistakes in 20 days are 12000000

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

Mistake on 3% of the coins

Rate = 20000000 coins a day,

This means that

Mistakes = 3% * 20000000 * days

For the coins that are mistakes in 20 days, we have

Mistakes = 3% * 20000000 * 20

Evaluate

Mistakes = 12000000

Hence, the coins are mistakes in 20 days are 12000000

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Answer:

c

Step-by-step explanation:

trust it is

Answer:

D. (Y+w)(z+x)

Solution for all options

A= yx-yz-wx-wz

B= xz-xy-wz-wy

C= xz+xw+yz+yw

D= yx+yz+xw+zw

Answer:

119,940 books are not about math.

What I did:

60x2000=120,000

120,000-60=119,940

Answer:

119940

Step-by-step explanation:

.05 % are about math

b= books

b * .05% = 60

Change to decimal form

b * .0005 = 60

Divide each side by .0005

b = 60/.0005

b =120000 books in the store

we want the ones not about math

120000-60

119940

Answer:

C

Step-by-step explanation:

Answer:

m∠ 1 = 165°

m∠ 2 = 15°

Step-by-step explanation:

We Know

∠1 + ∠2 = 180°

Let's solve

5x + (x - 18) = 180

5 + x - 18 = 180

6x - 18 = 180

6x = 198

x = 33

Now we put 33 in for x and solve for ∠1 and ∠2 !

m∠ 1 = 5x°

m∠ 1 = 5(33)

m∠ 1 = 165°

m∠ 2 = (x - 18)

m∠ 2 = 33 - 18

m∠ 2 = 15°

Answer:

m∠1 = 165°

m∠2 = 15°

Step-by-step explanation:

Note that, when the angle measurements are combined, the total measurement is 180°, based on the definition of a straight line.

It is given that m∠1 = 5x°, and m∠2 = (x - 18)°. Set the two angle measurements equal to the total measurement:

\(5x + (x - 18) = 180\)

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

\((5x + x) - 18 = 180\\(6x) - 18 = 180\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents

Multiplications

Divisions

Additions

Subtractions

~

First, add 18 to both sides of the equation:

\(6x - 18 = 180\\6x - 18 (+18) = 180 (+18)\\6x = 180 + 18\\6x = 198\\\)

Next, divide 6 from both sides of the equation:

\(6x = 198\\\frac{6x}{6} = \frac{198}{6}\\ x = \frac{198}{6} = 33\)

x = 33. Next, plug in 33 for x for both measurements:

\(m\angle1 = 5x\\m\angle1 = 5 * (33)\\m\angle1 = 165\\\\m\angle2 = x - 18\\m\angle2 = (33) - 18\\m\angle2 = 15\)

Check. Both, when combined, should make 180°

165 + 15 = 180

180 = 180 (True)

~

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The remaining sides and angles in ΔDEF are:

Side DF ≈ 15.6,,Angle D≈ 34.2°, Angle E≈ 55.8°,

Side DF: To find the length of side DF, we can use the Pythagorean theorem. Since ∠F is a right angle, DF is the hypotenuse of the right triangle. Using the given values, we have:

DF² = DE² + EF²

DF² = (10)² + (12)²

DF² = 100 + 144

DF² = 244

DF ≈ 15.6

Angle D: To find angle D, we can use the inverse tangent function (arctan) since we know the lengths of the opposite and adjacent sides. Using the given values, we have:

tan(D) = DE / DF

tan(D) = 10 / 15.6

D ≈ arctan(10 / 15.6)

D ≈ 34.2°

Angle E: Angle E can be found using the fact that the sum of angles in a triangle is 180°. Since we know ∠F is a right angle (90°) and ∠D is approximately 34.2°, we can calculate ∠E as:

E = 180° - F - D

E ≈ 180° - 90° - 34.2°

E ≈ 55.8°

In a right triangle, the Pythagorean theorem allows us to relate the lengths of the sides. By substituting the known values of d=10 and e=12 into the theorem, we can find the length of the remaining side DF. The angles can be calculated using trigonometric functions. Angle D can be found using the tangent function, as it relates the lengths of the opposite and adjacent sides. Angle E can be calculated by subtracting the known angles F and D from the sum of the angles in a triangle, which is 180 degrees.

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Answer:

$145.50

Step-by-step explanation:

C = 45.50 + 2n

45.50 + 2X 100 = $145.50

The probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is denoted as P(S|C'). Here's the explanation for each option:

P(S∣C): This denotes the probability of receiving an A in Statistics given that the student received a B or better grade in Calculus I. However, this is not the probability asked in the question.

P(S'∣C'): This denotes the probability of not receiving an A in Statistics given that the student did not receive a B or better grade in Calculus I. Again, this is not the probability asked in the question.

P(C∣S): This denotes the probability of receiving a B or better grade in Calculus I given that the student received an A in Statistics. This is also not the probability asked in the question.

Therefore, the correct notation for the probability that a student received an A in Statistics given that the student received less than a B grade in Calculus I is P(S|C').

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Answer:

The value of the number is either 1 or -10/3

Step-by-step explanation:

If the same number is added to triple the square of a number seven times, the result is 10. What is that number?

Let the number = x

Therefore, we have;

3·x² + 7·x = 10

Therefore, we have;

3·x² + 7·x - 10 = 0

Dividing by 3 gives;

x² + 7/3·x - 10/3 = 0

Factorizing gives;

(x - 1)·(x + 10/3) = 0

x = 1 or -10/3

The number is either 1 or -10/3.

Answer:

he faked too much

Step-by-step explanation: