What are the zeros of the function below? Check all that apply.
(x - 1)(x + 1)
----------------
6(x-4)(x+7)
A. 7
B. 1
C. -1
D. 4
E. 6
F. -7​

The area, in square units, bounded by f(x)=-3x⁸ and g(x)=-4x⁵ over the interval [12,21] is approximately 4746616.5.

To explain, we can use the definite integral formula for finding the area between two curves:
∫[a,b] (f(x) - g(x)) dx
In this case, a=12, b=21, f(x)=-3x⁸ and g(x)=-4x⁵. So, we have:
∫[12,21] (-3x⁸ - (-4x⁵)) dx
= ∫[12,21] (-3x⁸ + 4x⁵) dx
= [-3/9x⁹ + 4/6x⁶] from 12 to 21
= (-3/9(21)⁹ + 4/6(21)⁶) - (-3/9(12)⁹ + 4/6(12)⁶)
= approximately 4746616.5

In summary, the area bounded by the two curves over the given interval is approximately 4746616.5 square units.

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Answer:

97 1/3 or 97.3333

Step-by-step explanation:

multiply 2 2/3 by 36 1/2

:)

The required decrease in dollars was $1222 and the amount of money in Bob's account at the end of last year was $3978.

To find the decrease in dollars and the amount of money in Bob's account at the end of last year, we can use the following steps:

Calculate the amount of the decrease. We can do this by multiplying the original amount by the percentage decrease as a decimal:

Decrease = 0.235 x $5200 = $1222

So, the decrease in dollars is $1222.

Calculate the amount of money in Bob's account at the end of last year. We can do this by subtracting the decrease from the original amount:

Amount at end of last year = $5200 - $1222 = $3978

So, the amount of money in Bob's account at the end of last year was $3978.

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The proportion of cranberries required for the muffins is 4 pounds x 16 ounces/pound = 64 ounces of cranberries. Therefore, to make the muffins for the party, you will need 64 ounces of cranberries.

To calculate the amount of cranberries needed for the muffins at a party of 12 people, making 11/2-ounce muffins and assuming each person will have three muffins, we need to convert the measurements and quantities.

Given that each muffin weighs 11/2 ounces, and each person will have three muffins, we can calculate the total weight of muffins needed. 11/2 ounces is equivalent to 1.5 ounces, so each person will consume 1.5 ounces x 3 muffins = 4.5 ounces of muffins.

For a party of 12 people, the total amount of muffins required is 4.5 ounces/person x 12 people = 54 ounces of muffins.

Now, to determine the amount of cranberries needed for the muffins, we need to consider the recipe's proportion. The recipe makes 15 pounds of dough and calls for 4 pounds of cranberries. To convert pounds to ounces, we know that 1 pound is equal to 16 ounces.

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Answer:

80$ for 4 / 16$

Step-by-step explanation:

If you see the price on one note book and its 20$, and you want 4 note book you have to mutiply the price by 4 and you'll get 80$!  

Hope this helped

Happy Halloween!

Answer:

x = -17

Step-by-step explanation:

7(2x + 3) = 12x - 13

Distribute

7*2x +7*3 = 12x-13

14x +21 = 12x-13

Subtract 12x from each side

14x-12x+21 = 12x-12x-13

2x+21 = -13

Subtract 21 from each side

2x+21-21 = -13-21

2x = -34

Divide by 2

2x/2 = -34/2

x = -17

Answer:

2√3/3

Step-by-step explanation:

Sec(330°)

=1/cos(330°)

=1/√3/2 (since Cos (330°)=√3/2

=1×2/√3

=2/√3×√3/√3

=2√3/3

Answer:

\(\implies \sec 330^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}\)

Step-by-step explanation:

Given :-

And we need to find out its value . Firstly we know that 330° lies in 4th quadrant . And In fourth quadrant , cosine and secant are positive . Therefore , the result will be positive. Now we know that ,

\(\implies \sec (360^o-\theta)= \sec\theta \)

Using this ,

\(\implies \sec (330^o) \\\\\rm\implies sec(360^o-30^o) \\\\\rm\implies \sec 30^o \)

And the value of sec 30° is ,

\(\implies \sec 30^o = \dfrac{2}{\sqrt3}\)

And by question we need to write it with a rational denominator .So on rationalising the denominator , we have ,

\(\implies \sec 30^o = \dfrac{2}{\sqrt3}=\boxed{\red{\dfrac{2\sqrt3}{3}}}\)

Hence the required answer is 2√3/3.

The length of BC in this problem is given as follows:

BC = 3.6.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADE.

Hence the proportional relationship for the side lengths is given as follows:

3/5 = BC/6.

Applying cross multiplication, the length BC is given as follows:

BC = 6 x 3/5

BC = 3.6.

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The high R-squared value indicates that time is a strong predictor of the number of married people in the United States, it is important to consider the limitations of the equation and the uncertainty in the prediction.

First, let's talk about the R-squared value of your trendline equation.

Now, let's talk about your belief that there will never be a time when we have zero married people. This belief is not accounted for in your trendline equation, as it is purely based on your personal belief rather than any data or statistical analysis.

When it comes to confidence level, we need to consider the uncertainty in the prediction. Since we know that there will likely always be some people who want to get married, we can say with a high level of confidence that the number of married people will never actually reach zero.

In mathematical terms, we can use the equation for the confidence interval to determine the range of values within which we can be confident the true value will fall.

This equation takes into account the standard error of the estimate (the degree of variability in the data) and the desired level of confidence (typically 95% or 99%). However, since we know that the true value will never be zero, this equation is not particularly useful in this case.

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The length of Jimmy's string is 17.75 inches and the length of Sam's string is 30.67 inches. To find out how much longer Sam's string is than Jimmy's string, we subtract the length of Jimmy's string from the length of Sam's string.

Jimmy's string is (71)/(4) inches long, which can be converted into a decimal form by dividing 71 by 4. This gives us a length of 17.75 inches. Sam's string is (92)/(3) inches long, which can be converted into a decimal form by dividing 92 by 3. This gives us a length of 30.67 inches.

To find out how much longer Sam's string is than Jimmy's string, we subtract the length of Jimmy's string from the length of Sam's string:
30.67 - 17.75 = 12.92

Therefore, Sam's string is 12.92 inches longer than Jimmy's string. To express this answer as a fraction, we can convert the decimal into a fraction:
12.92 = 1292/100

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4:
1292/100 = (323/25)/(4/4) = 323/25

Therefore, the answer is 323/25 inches.

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The fire is 39.2 miles from tower A. This is calculated using the law of sines, which states that the ratio of the sine of an angle to the length of the opposite side is equal for all sides of a triangle. In this case, the angle is 40 degrees, the opposite side is 28 miles, and the unknown side is the distance from tower A to the fire. Solving for the unknown side, we get 39.2 miles.

The law of sines is a trigonometric equation that can be used to solve for the sides of a triangle when two angles and one side are known. In this case, we know two angles and one side (the angle opposite the unknown side is 40 degrees, the angle opposite the 28-mile side is 116 degrees, and the 28-mile side is known). Solving for the unknown side, we get 39.2 miles.

Tower height:

The tower is 312 ft tall. This is calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the height of the tower, and the other two sides are the 648-ft guy wire and the 295-ft distance from the tower to the point where the wire is attached to the ground. Solving for the height of the tower, we get 312 ft.

The Pythagorean theorem is a mathematical equation that can be used to solve for the length of the hypotenuse of a right triangle when the lengths of the other two sides are known. In this case, we know the lengths of the other two sides (the guy wire is 648 ft and the distance from the tower to the point where the wire is attached to the ground is 295 ft). Solving for the height of the tower, we get 312 ft.

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Answer:

\(7^-^1\)

Step-by-step explanation:

So, when multiplying numbers with exponents that have the same base, all you have to do is combine the exponents.

Arranging the expressions in increasing value of their solutions is;

10.1x - 1.6x + 44 = -7  <  7.9x + x + 4 = -1.1x - 16  <  3.2x + 5.7 = -2.5x  <  ¹/₄x + ⁵/₂x - 2 = 4 - ¹/₄x

A) ¹/₄x + ⁵/₂x - 2 = 4 - ¹/₄x

Multiply through by 4 to get;

x + 10x - 8 = 16 - x

x + 10x + x = 16 + 8

12x = 24

Divide both sides by 12 to get;

x = 24/12

x = 2

B) 7.9x + x + 4 = -1.1x - 16

7.9x + x + 1.1x = -16 - 4

10x = -20

Divide both sides by 10 to get;

x = -2

C) 3.2x + 5.7 = -2.5x

3.2x + 2.5x = 5.7

5.7x = 5.7

divide both sides by 5.7 to get;

x = 1

D) 10.1x - 1.6x + 44 = -7

8.5x = -7 - 44

x = -51/8.5

x = -6

Arranging the expressions in increasing value of their solutions is;

10.1x - 1.6x + 44 = -7 < 7.9x + x + 4 = -1.1x - 16 < 3.2x + 5.7 = -2.5x < ¹/₄x + ⁵/₂x - 2 = 4 - ¹/₄x

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Answer:

B. The total amount of tweets...

E. NCAA basketball tournament

F. Butterfly population doubles each month

An exponential function is a function that grows exponentially.

Exponential functions have a multiplicative rate of change. This means each term can be multiplied by a specific number to get to the next.

Example of an exponential function:

1, 2, 4, 8, 16, 32, 64, 128, 256...

Knowing this, let's look at each example.

A.

The rocket grows at a rate of 45 m/s, but then goes back down. This is not an exponential function. This is most likely a quadratic function.

B.

Each term is being multiplied by 4. This is correct.

C.

This is too vague. We cannot determine what this is.

D.

This is a linear function. It has an additive rate of change; not a multiplicative one. This is wrong.

E.

Each term is 50% of the previous one. This is correct.

F.

The population is multiplied by 2 each month. This is correct.

Answer:

2, 5, 6

(tweets, basketball, butterfly)

Step-by-step explanation:

Rocket:  Quadratic function

Tweets: Exponential function  (quadruples each time)

Water Park:  Quadratic function (or absolute function)

Savings: Linear function (if simple interest)

**compound interest is exponential, but as it stops earning interest after the first year, it is not continually exponential**

Basketball:  Exponential function  (halves each round)

Butterfly:  Exponential function  (doubles each month)

Answer:

the ansewr is b

Step-by-step explanation:

Answer:

-8<y≤-7

.Step-by-step explanation:

7.99, -7.567854, -7.1, -7, but it COULD NOT be -8.

The level of significance is 0.05, indicating that  are using a 5% significance level to make decisions in the chi-square test of independence.

The level of significance, often denoted by α (alpha), is the probability threshold used to determine whether to reject or fail to reject the null hypothesis in a statistical test the level of significance is given as 0.05, which corresponds to a 5% significance level.

When conducting a chi-square test of independence, the significance level is used to determine the critical value or the p-value to make a decision about the null hypothesis. If the p-value is less than the significance level, typically 0.05, the null hypothesis and conclude that there is evidence of a significant relationship between the variables. If the p-value is greater than the significance level,  fail to reject the null hypothesis and conclude that there is not enough evidence to establish a significant relationship.

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

By using graph of a function, the graph of the equation y + 6 = x + 4 has been shown below

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

here, we have,

At first, it is important to know about function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of points of the form (x, f(x))

The equation is y + 6 = x + 4

y = x + 4 - 6

y = x - 2

The graph has been shown below

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\(2.5x = 15\)

\(x = \frac{15}{2.5} = 6\)

Answer:

or Also

\( \frac{5}{2} x = 15 \\ 5x = 15 \times 2 \\ 5x = 30 \\ 5x \div 5 = 30 \div 5 \\ x = 6\)

This is an inverse proportion question, which means that as the number of men decreases, the time taken to build the bridge will increase, and vice versa. We can use the formula:

Men x Days = Constant

To solve this problem, we need to first find the constant. We know that eight men can build the bridge in 12 days, so:

8 x 12 = 96

Therefore, the constant is 96. Now we can use this to find the time taken for 6 men to build the same bridge:

6 x Days = 96

Days = 16

Therefore, 6 men can build the same bridge in 16 days. It's important to note that this assumes that the amount of work required to build the bridge is the same regardless of the number of men working on it. In reality, this may not be the case, and other factors such as efficiency and productivity may come into play.

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

The null and alternative hypotheses for the given scenario are:

H0: σ = 14.7

Ha: σ < 14.7

The given scenario involves testing a claim made by the principal of a middle school that the test scores of seventh-graders in her school vary less than the test scores of seventh-graders in neighboring schools, which have a variation of σ = 14.7. The null hypothesis (H0) in this case is that the standard deviation of test scores in the principal's school is equal to the standard deviation of test scores in neighboring schools, which is 14.7. The alternative hypothesis (Ha) is that the standard deviation of test scores in the principal's school is less than 14.7.

To test these hypotheses, one could conduct a one-tailed z-test for the population standard deviation. The test statistic would be calculated as:

z = (s - σ) / (σ / √(n))

Where s is the sample standard deviation, σ is the hypothesized population standard deviation, and n is the sample size. The p-value for this test would be calculated based on the z-score and the directionality of the alternative hypothesis. If the p-value is less than the significance level (α), the null hypothesis would be rejected in favor of the alternative hypothesis.

Therefore, in conclusion, the correct answer is option A, and the null and alternative hypotheses for this scenario are H0: σ = 14.7 and Ha: σ < 14.7.

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Answer:

9/10 1/2 1/8 0.25 0.6

Step-by-step explanation:

Answer:

he played 141 games in 2020 and he would play 133.95 in 2021

In the given scenario, the average current produced within the loop is approximately 2.13 A.

We can begin by computing the change in magnetic flux across the loop as it expands to determine the average current generated within the loop.

The following equation provides the magnetic flux across a loop:

Φ = B * A * cos(θ)

ΔΦ = B * ΔA

ΔA = A₂ - A₁ = π * (1.00 m)² - π * (0.40 m)² = π * (1.00² - 0.40²) = π * (1.00 + 0.40)(1.00 - 0.40) = π * (1.40)(0.60) = 0.84π m²

So,

ΔΦ = B * ΔA = (24 mT) * (0.84π m²) = 20.25π m²·T

emf = ΔΦ / Δt = (20.25π m²·T) / (1.0 s) = 20.25π V

As:

emf = I * R

So, again

I = emf / R = (20.25π V) / (30 Ω) ≈ 2.13 A

Thus, the average current produced within the loop is approximately 2.13 A.

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To write the form of the partial fraction decomposition of the given rational expressions, we need to express them as a sum of simpler fractions. The general form of a partial fraction decomposition is:

f(x) = A/(x-a) + B/(x-b) + C/(x-c) + ...

where A, B, C, etc., are constants and a, b, c, etc., are distinct linear factors in the denominator.

For the rational expression x^2 - 7x:

The denominator has two distinct linear factors: x and (x - 7). Therefore, the partial fraction decomposition form is:

(x^2 - 7x)/(x(x - 7)) = A/x + B/(x - 7)

For the rational expression 6x + 5 / (x + 8):

The denominator has one linear factor: (x + 8). Therefore, the partial fraction decomposition form is:

(6x + 5)/(x + 8) = A/(x + 8)

For the rational expression 20 - 3 / (4x + 3):

The denominator has one linear factor: (4x + 3). Therefore, the partial fraction decomposition form is:

(20 - 3)/(4x + 3) = A/(4x + 3)

In each case, we write the partial fraction decomposition form by expressing the given rational expression as a sum of fractions with simpler denominators. Note that we have not solved for the constants A, B, C, etc., as requested.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

Step-by-step explanation:

First of all you need to use BIDMAS/BODMAS whatever you call it. You can clearly see that division comes before addition so you need to do:

Answer:

True the absolute value is how many digits away the number is from zero.

Step-by-step explanation: