Multiply and write in standard form.
(3x − 2)(5x2 – 3x + 4)​

Answer:

Step-by-step explanation:

Use the given functions to set up and simplify

C.A⋅16−ounce=16A−ounce200mil.ligrams=−200m2l2grasC=−200m2l2grams

250%=2.5C=2.5100%=1C=1

Answer:

80 milligrams

Step-by-step explanation:

The volume of bottle is 16-ounce, and the amount of vitamin C in the bottle is 200 mg.

Since the 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. Then for 100% of the daily alowence, we need to multiply 200/250 by 10. We get 80. The picture shows a dubble number line for paper homework. Good luck!

Answer:

1 is neither prime nor a composite number because it only has 1 divisor, 1 and 1, and it doesn't have more than 2 integral divisors, like stated, it only has 1. So it falls in neither category.

Answer:

because

Step-by-step explanation:

A prime number has exactly two integral divisors: 1 and itself. Because it contains only one divisor, the number 1 is not a prime. A whole number with more than two integral divisors is called a composite number. So, with the exception of 0 and 1, all whole integers are either prime or composite.

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

The single fraction is 7x/20

A fraction can be defined as the part of a whole variable, number or element.

The different types of fractions are;

Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.

They are made of operations such as multiplication, addition, subtraction, division, etc

Given the expression;

3/4x - 2/5x

Find the LCM

15x - 8x/20

7x/20

Thus, the value is 7x/20

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Decentralization is a management approach that involves the delegation and assignment of decision-making rights from top levels of management to lower levels of management. Option A

It is an effective way to empower employees and to improve decision-making processes within an organization. The benefits of decentralization include the following:

It empowers more employees at lower levels of management: Decentralization allows employees to take ownership of their work, to be more accountable, and to make decisions that are in the best interest of the organization. This, in turn, leads to improved job satisfaction, employee engagement, and better overall performance.

It allows for better and more timely decision-making: Decentralization ensures that decisions are made closer to where the work is being done. This leads to faster decision-making, improved responsiveness to changes in the market, and better coordination between different departments and teams.

It trains future managers: Decentralization provides employees with the opportunity to gain valuable management experience, which can help prepare them for future leadership roles within the organization.

However, one benefit of decentralization that is not accurate is that it forces top levels of management to focus on individual units. In fact, decentralization can free up top management to focus on the big picture and long-term strategy, rather than getting bogged down in day-to-day operations.

In conclusion, decentralization is a useful management approach that can help organizations improve decision-making, empower employees, and train future managers.

By delegating decision-making rights to lower levels of management, organizations can improve overall performance and become more adaptable to changes in the market.

So Option A is correct.

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complete question:

The benefits of decentralization i.e. delegation and assignment of decision rights include all of the following except:

a it forces top levels of management to focus on individual units

b it empowers more employees at lower levels of management

c it allows for better and more timely decision making

d it trains future managers

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer: D

Step-by-step explanation:

We have the two points (2,2) and (2,-2) which have a repeated x coordinate. This is not allowed if we wanted a function. A function must have any x input lead to exactly one and only one output (assuming the input is in the domain).

y=5

x=30

Explanation: since all 3 angles of triangles are marked equal we can see that it is equilateral which means 8y=40 so y=5. Then we can find that the other triangle is an 120 30 30 triangle thus x is 30. You can also do this if you can see straight away that the big triangle is a 30-60-90 triangle and just use 90-60.

The equation to solve is

Let us solve the equation for "x". THe steps are shown below:

For x = 3, the equation is 0 = 0.

At this point, no matter what value you put into "x", this equation holds true.

Thus, there are infinite solutions to the equation.

On comparing the given expressions we get-

\(9^{-2} < (\frac{1}{9}) ^{-1}\)

\((\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}\)

\(9^{-1} > 9^{-2}\)

Here, we are given 3 pairs of expression. Let us evaluate them one by one.

\(9^{-2}\) _ \((\frac{1}{9}) ^{-1}\)

The negative exponent means that the base is the reciprocal raised to a positive power. Thus, \(9^{-2}\) can be written as- \((\frac{1}{9}) ^{2}\) = 1/81

similarly, \((\frac{1}{9}) ^{-1}\) can be written as- \((9}) ^{1}\) = 9

Thus, the expression becomes-

1/81 _ 9

clearly we can see that 1/81 < 9

Now, we have \((\frac{1}{9}) ^{-1}\) _ \((\frac{1}{9}) ^{-2}\)

As shown above, the expression can be simplified as-

\((9) ^{1}\) _ \((9) ^{2}\)

9 _ 81

clearly we can see that 9 < 81

Next, we have- \(9^{-1}\) _ \(9^{-2}\)

we can write this as-

1/9 _ 1/81

Clearly, 1/9 > 1/81

Hence, we have solved the given inequalities.

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x < 100

So, x = 0,1,2...99

but x cannot be equal to 100

So, the number line will be:

Answer : B)

The total amount that he will owe after the loan period of 25 weeks is; $806.25

The formula to calculate simple interest is;

I = PRT/100

Where;

P is principal

R is rate

T is time

We are given;

P = $780

R = 7%

T = 25 weeks = 25/52 years

Thus;

I = (780 * 7 * 25/52)/100

I = $26.25

Total payoff = $780 + $26.25

= $806.25

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Answer:

x=64

Step-by-step explanation:

I solved the equation for you

Your welcome and i hope it helps! :)

Answer:

here you go

Step-by-step explanation:

9514 1404 393

Answer:

  1. a = 4, b = 2√2

Step-by-step explanation:

The right triangle is isosceles, so b is the same length as the marked side:

  b = 2√2

The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

  a = (√2)(2√2) = 2·2 = 4

The missing sides are ...

  a = 4, b = 2√2

Answer:

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

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation of the line going through (-6, 0) and (0, -3) is:

y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))

y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is:

y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)

y = 2x + 3

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Answer:

2

-1/2

Step-by-step explanation:

2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

Answer:

the number of vegetables did farmer bring to the market is 1764 vegetables

Step-by-step explanation:

The calculation of the number of vegetables did farmer bring to the market is given below:

= 18 bags × 42 kgs + 28 bags × 36 kgs  

= 756 + 1008

= 1764 vegetables

Thus, the number of vegetables did farmer bring to the market is 1764 vegetables

Answer:

x=−3

Step-by-step explanation:

A bond purchased at a premium, it will have a yield to maturity and current yield that is lower than its coupon rate.

This is usually above its face value which may be as a result of the interest rate being higher than the current market interest rates.

When a bond is traded at a premium, the yield to maturity and current yield will be lower than its coupon rate.

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Answer:

en cuanto la suma de respuesta

Step-by-step explanation:

Que vez de gallinas de =650

Answer : 23.77

Pythagoras theorem states that in any right angled triangle , the sum of squares of base and perpendicular is equal to the square of hypotenuse .

\(\sf\longrightarrow (base)^2+(perpendicular)^2=hypotenuse^2\\\)

\(\sf\longrightarrow x^2 +(19.1)^2 = (30.5)^2 \\\)

\(\sf\longrightarrow x^2 + 364.81 = 930.25 \\\)

\(\sf\longrightarrow x^2 = 930.25 -364.81\\\)

\(\sf\longrightarrow x^2 = 565.44\\\)

\(\sf\longrightarrow x=\sqrt{565.44} \\\)

\(\sf\longrightarrow \underline{\boxed{\bf base (x) = 23.77 }} \\\)

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Recall that:

Therefore:

Simplifying the above result we get:

Answer: 0.016.

When a whole number greater than 1 has a negative integer exponent, the value of the expression is greater than zero but less than one.

The standard format of an exponential expression is given as follows:

\(a^b\)

In which:

When we have a negative exponent, the equivalent expression with a positive exponent is obtained inverting the base.

If we have a positive base greater than one to a negative exponent, we invert the base, meaning that it is less than one with a positive exponent, hence the value of the expression is greater than zero but less than one.

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Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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The probability of both people being Democrats is 0.243, and the probability of one person being a Republican and one person being a Democrat is 0.486.

To find the probability of each of the following, we can use the formula for the probability of selecting a group of items from a larger group with replacement:

P(A and B) = P(A) * P(B)

Where P(A) is the probability of selecting the first item, and P(B) is the probability of selecting the second item.

Both people are Democrats:

There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting two Democrats is (16/31) * (16/31) = 0.243.

One person is a Republican and one person is a Democrat:

There are 15 Republicans and 31 total people, so the probability of selecting a Republican is 15/31. There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting one Republican and one Democrat is (15/31) * (16/31) = 0.486.

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The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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