Which integer in the set has the smallest value (7, -7, -2, 2)?
A. -7
B. -2
C. 2
D. 7

Answer:

300

Step-by-step explanation:

Let x be the number of people in the survey

81/x = 27%

81/x = 0.27

x = 81/0.27

x = 300

Using  the Law of Syllogism the new conditional statement that follows from the pair of true statements  is: B. If she passes her final class, then she will graduate college.

Law of Syllogism  can be defined as a type of reasoning in which an inference can only be true if the premises is true.

If she passes her final class, then she will graduate college is a new conditional statement which implies that the premises is If she passes her final class  and the conclusion is then she will graduate college.

Therefore the correct option is B.

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Answer:

1. The fraction converts into a repeating decimal.

Step-by-step explanation:

1/3=0.33333333333

Given that the volume of a rectangular prism is 240 cubic inches. We need to find the value of x.Let the length of the rectangular prism be l, the width of the rectangular prism be w and the height of the rectangular prism be x.

Therefore, Volume of rectangular prism = Length × Width × HeightV = l × w × xVolume of the rectangular prism is given as 240 cubic inches.240 = l × w × xThis is the required equation that will help us to determine the value of x in terms of l and w.

Now we can rearrange the equation to get the value of x in terms of l and w as:240 / lw = xThus, the value of x = 240 / lw Hence, the value of x is 240/lw.

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The graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points.

The answer is (C) Three.To determine the number of points where the graph of the equation y = x(x² - 2)(x² + x + 1) intersects the x-axis, we need to find the x-values that make the equation equal to zero.

Setting y = 0, we have:

0 = x(x² - 2)(x² + x + 1)

Since the product of three factors is zero, at least one of the factors must be zero.

1. Setting x = 0:

0 = 0(x² - 2)(x² + x + 1)

This gives us one solution: x = 0.

2. Setting x² - 2 = 0:

x² = 2

Taking the square root of both sides:

x = ±√2

This gives us two additional solutions: x = √2 and x = -√2.

3. Setting x² + x + 1 = 0:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, there are no real solutions for this quadratic equation.

In summary, we have found three different x-values where the equation intersects the x-axis: x = 0, x = √2, and x = -√2.

Therefore, the graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points. The answer is (C) Three.

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The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Answer:

x=15

Step-by-step explanation:

4x+2x=90 degrees

6x=90

x=15

The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).

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The value of both numbers in fractions will be 207/2 and 207/2.

Given that:

Equation: x + y = 207

The two numbers' product is:

P = xy

P = x(207 - x)

P = 207x - x²

Differentiating P with regard to x. Then we have

dP/dx = 0

207 - 2x = 0

x = 207/2

Then the other number is calculated as,

x + y = 207

207/2 + y = 207

y = 207/2

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Answer:

1/24

Step-by-step explanation:

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 11 by 8, and get 88.Then we multiply 7 by 12, and get 84.

Next we give both terms new denominators -- 12 × 8 = 96.

So now our fractions look like this:

88 /96 -84 /96

Step 2

Since our denominators match, we can subtract the numerators.

88 − 84 = 4

So the answer is:

4 /96

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:            

4 /96 ÷ 2 =2 /48

Let's try dividing by 2 again...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

2 /48 ÷ 2 =1 /24

Let's try dividing by 2 again...

No good. 2 is larger than 1. So we're done reducing.                                    There you have it! The final answer is:

11 /12 -7 /8=1 /24

Answer:

1/24

Step-by-step explanation:

Given function:

Simplifly the denominator:

Subtract the fraction term:

Simplifly the fraction term:

Therefore, 11/12-7/8=1/24.

Answer:

16. -16+7=-9

17. -11+1=-10

18. 12+13=25

19. -4+(-8)=-12

Answer:

15

Step-by-step explanation:

Change x to the declared value: \(5|6-9|\)

Subtract: \(5|6-9| = 5|-3|\)

NOTE: remember that little minus big = negative of big minus little.

i.e.: 6-9 = -(9-6) = -(3) = -3

Evaluate the Absolute Value: \(5|-3| = 5(3)\)

NOTE: remember that the absolute value of a number = the number's distance from 0 (always a positive number).

i.e.: |-2| = 2; |5| = 5

Multiply: \(5(3) = 15\)

Answer:

9 feet

Step-by-step explanation:

3X3=9 feet therefore 3 yards is equal to 9 feet

Answer:

I believe it would be $31.39

Step-by-step explanation:

Original Price - $45

Price With Sale And Tax $31.39

Hope that helps!

Answer:

Simplify  

.

First, multiply both the numerator and denominator by

✔ 7 – i

.

The product in the numerator is

⇒ -20 +

⇒ 10i.

The product in the denominator is

⇒ 50.

The quotient of 5i and 2 − i is

⇒ -1 +

⇒ 2i..

Step-by-step explanation:

Answer:

the last option on edge

Step-by-step explanation:

7 - i

Answer:

The Communitive Property of Addition

Step-by-step explanation:

The properties are

Communitive: You can switch the order and still get the same answer

Assosiative: You can switch what numbers are in the parentheses and still get the same answer (if you're only adding) a+(b+c)=c+(a+b)

Distributive: (a*b)+(a*c)=a*(b+c)

Identity: You can add a number with 0 and get the same number you started with

y+x=x+y is the communitive property because, no matter which order the numbers are, you get the same answer

Answer:

73.6%

Explanation: 38 is the old value and 66 is the new value. In this case we have a positive change of 73.68... percent because the new value is greater than the old value.

a larger sample size will yield a smaller margin of error. Therefore, the best option among the given choices is D. 32.

To estimate the mean with 99% confidence and find the smallest margin of error, you should consider the sample size. The options provided are:

A. 9
B. 13
C. 28
D. 32

In general, a larger sample size will yield a smaller margin of error. Therefore, the best option among the given choices is D. 32. With a sample size of 32, the researcher will have a smaller margin of error for the mean estimation with 99% confidence.

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Answer:

4760

Step-by-step explanation:

Simple interest= principal× time ×rate/100

=3500×4×9/100

= 1260

Amount that will be in the bank after 4years= 3500+1260

=4760

Answer:

1/36

Step-by-step explanation:

6^-1 is the same as 1/6,

1/6^2 is 1/36

Answer:

1/36

Step-by-step explanation:

have a good semester

The expressions that equal 36 is:

E) 53 − (2. 5 × 30) − 20

Evaluated the mathematical expressions in each response to see if they equal 36.

A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.

B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.

C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.

D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.

Thus, only the expressions listed in my previous answer equal 36.

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(17.) The factored form of the expression m²n + 7m²n²-3mn is mn(m + 7mn - 3). The correct answer is option A.  

(18.) The factored form of the expression 6y² - 5y - 25 is (3y - 5)(2y - 5). The correct answer is option B.

(19.) By completing the square, we get x = 12, x = 4. The correct answer is option B.

(20.) By using the quadratic formula, we get x = -5, x = -10. The correct answer is option B.

(17.) To factor the expression m²n + 7m²n² - 3mn, let's find the greatest common factor (GCF) of the terms.

The terms in the expression are m²n, 7m²n², and -3mn. Let's analyze the variables m and n in each term and find the highest power that appears in all of them.

The highest power of m that appears in all terms is m².

The highest power of n that appears in all terms is n.

Therefore, the GCF of the terms is m²n.

Now, we can factor out the GCF from each term:

m²n + 7m²n² - 3mn

= mn(m + 7mn - 3)

Therefore, the factored form is mn(m + 7mn - 3). The option A is correct answer

(18.) To factor the expression 6y² - 5y - 25, we need to find the greatest common factor (GCF) of the terms.

The terms in the expression are 6y², -5y, and -25. Let's analyze the coefficient and the variable y in each term and find the GCF.

The coefficient GCF of 6, -5, and -25 is 1.

The variable GCF of y² and y is y.

Therefore, the GCF of the terms is y.

Now, we can factor out the GCF from each term:

6y² - 5y - 25

= y(6y²/y - 5y/y - 25/y)

= y(6y - 5 - 25/y)

= (3y - 5)(2y - 5).

So, the correct option is (B) (3y - 5)(2y - 5).

(19) To solve the quadratic equation x² + 8x = 48 by completing the square, we can follow these steps:

Move the constant term (48) to the right side of the equation:

x² + 8x - 48 = 0

Divide the coefficient of x by 2, square the result, and add it to both sides of the equation to complete the square:

x² + 8x + (8/2)² = 48 + (8/2)²

x² + 8x + 16 = 48 + 16

x² + 8x + 16 = 64

Factor the perfect square trinomial on the left side:

(x + 4)² = 64

Take the square root of both sides, considering both the positive and negative square root:

√((x + 4)²) = ±√64

x + 4 = ±8

Solve for x by isolating it on one side of the equation:

x = -4 ± 8

Simplifying the expression, we have two possible solutions:

x₁ = -4 + 8 = 4

x₂ = -4 - 8 = -12

Therefore, the correct option is (B) x = 12, x = 4.

(20) To solve the quadratic equation x² - 5x = 50 using the quadratic formula, we can follow these steps:

Identify the coefficients of the quadratic equation:

a = 1 (coefficient of x²)

b = -5 (coefficient of x)

c = -50 (constant term)

Substitute the values of a, b, and c into the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case:

x = (-(-5) ± √((-5)² - 4(1)(-50))) / (2(1))

x = (5 ± √(25 + 200)) / 2

x = (5 ± √225) / 2

x = (5 ± 15) / 2

Simplify the expression:

x₁ = (5 + 15) / 2 = 20 / 2 = 10

x₂ = (5 - 15) / 2 = -10 / 2 = -5

Therefore, the correct option is (B) x = -5, x = -10.

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Complete Question:

(17) Factor m²n + 7m²n²-3mn.

Hint: Find the GCF first

Options:

(A) mn(m + 7mn - 3)

(B) mn(m-7mn - 3)

(18) Factor 6y² - 5y - 25.

Hint: Find the GCF first

Options:

(A) (3y + 5)(2x - 5)

(B) (3y - 5)(2y - 5)

(19) Solve for "X" by completing the square.

x²  - 8x = 48

Options:

(A) x = 12, x = -4

(B) x = 12, x = 4  

(20) Solve for "X" by using the quadratic formula.

x²-5x = 50

Options:

(A) x = −5, x = 10

(B) x = -5, x = -10

Answer:

2.9 per second

Step-by-step explanation:

Answer:

The information on the graph shows a positive nonlinear correlation and the weight of the dinosaur tends to increase according to its length.

A discrete graph is also known as a scatter plot that shows the discontinuous and the nonlinear data point on the graph.

From the graph, we can see the increasing weight of the Dinosaur size vertical y-axis and the increasing length of the feet on the horizontal x-axis.

Therefore, we can conclude that the data points show an increasing nonlinear weight on the graph as the length increases.

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Answer:

8+6= 14

Step-by-step explanation:

I think but I'm not sure

Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

\(v^2=v_0^2+2a\)Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

\(v^2=(7.5)^2+2(-9.8)(-34)\)

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

\(v^2=56+670\) and

\(v=\sqrt{56+670}\)

That leaves us with

v = 26.94438j

But don't forget we round that to the tens place which comes out in the end, finally, to

v = 30 m/s

Answer:

19%

Step-by-step explanation:

We need to find what percent is $17.32 of $92.00.

To find what percent a part is of the whole, divide the part by the whole and multiply by 100%.

percent = part/whole × 100%

percent = 17.32/92 × 100%

percent = 18.826...%

Answer: 19%

The p-value for testing the claim that the proportion of homeowners owning lawn mowers in Charlotte is higher than 65% is 0.005 (rounded to three decimal places)

We can perform a hypothesis test to determine if the proportion of homeowners owning lawn mowers in Charlotte is significantly higher than 65%.

Null hypothesis: p <= 0.65

Alternative hypothesis: p > 0.65 (claim of the manufacturer)

We can use the sample proportion and the population proportion to compute the test statistic and p-value.

Sample proportion: P = 340/497 = 0.683

Population proportion: p = 0.65

Sample size: n = 497

The test statistic is calculated as:

z = (P - p) / sqrt(p*(1-p)/n)

z = (0.683 - 0.65) / sqrt(0.65*0.35/497)

z = 2.57

Using a standard normal distribution table or calculator, we find that the area to the right of z = 2.57 is 0.0051. Since this is a one-tailed test (alternative hypothesis is p > 0.65), the p-value is 0.0051.

Therefore, the p-value for testing the claim that the proportion of homeowners owning lawn mowers in Charlotte is higher than 65% is 0.005 (rounded to three decimal places). Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the proportion of homeowners owning lawn mowers in Charlotte is higher than 65%.

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Answer:

18321.77m^3

Step-by-step explanation:

V=πr2h=π·182·18≈18321.76836m³

Answer:

18,329.14 (2 DP)

Using 22/7 for pi

V = πr²h = π × 18² × 18 ≈ 18,329.14

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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