What is the correct reason for 2?

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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Answer:

Its A- 25 coin tosses

Step-by-step explanation:

I took the test

Answer:

30%

Step-by-step explanation:

Answer:

65-50=15/50 x 100= 30%

Step-by-step explanation:

Based on the information, statement (A) False is correct.

The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.

It should be noted that since the proportion of females who work part-time only in the summer (84%) is greater than the overall proportion of students who work part-time only in the summer (80%), we can conclude that gender and working part-time only in the summer are dependent. This means that knowing someone's gender gives us information about the likelihood that they work part-time only in the summer.

Therefore, statement (A) False is correct.

The probability will be:

0.80 x 0.50 x 0.84 = 0.336

The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.

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The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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Answer:

An equivalant faction would be 10/12

Step-by-step explanation:

Answer:

10/12

Step-by-step explanation:

12/6 = 2

5/6 * 2/2 = 10/12

Answer: 10/12

A.01 level of significance instead of a .05 level of significance, a researcher is more likely to make a Type II error. This means that they are more likely to fail to reject a false null hypothesis, which could result in inaccurate conclusions being drawn from the research.

The setting a more stringent level of significance, the researcher is requiring stronger evidence in order to reject the null hypothesis. This means that they are less likely to find statistically significant results, even if they are present in the data. This can lead to a higher likelihood of accepting a false null hypothesis, which is a Type II error.

while using a .01 level of significance may help to reduce the risk of Type I errors (rejecting a true null hypothesis), it also increases the risk of Type II errors (failing to reject a false null hypothesis). Researchers must carefully consider their level of significance and balance the risks of these two types of errors in order to draw accurate conclusions from their research.

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Rounding to the nearest tenth, the area of the triangular windowpane is approximately 8.2 square feet.

To find the area of a triangular windowpane, we need to use the formula for the area of a triangle, which is:

Area = (1/2) x Base x Height

In this case, the base is 4 feet 8 inches and the height is 3 feet 6 inches. However, we need to convert these measurements to the same units before we can calculate the area. Since there are 12 inches in 1 foot, we can convert the measurements as follows:

Base = 4 feet + 8 inches/12 = 4.67 feet

Height = 3 feet + 6 inches/12 = 3.5 feet

Now we can plug in these values into the formula and calculate the area:

Area = (1/2) x 4.67 feet x 3.5 feet

Area = 8.1675 square feet

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Answer:

Option B

Step-by-step explanation:

\(a^{m} + a^{n} = a^{m+n}\) ( by using laws of exponents )

Therefore option B is correct

Hope this helps

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Answer:

The sum of the length of the two legs is equal to the length of the hypotenuse.

The factors of the quadratic expression x² + 3x - 4 are (x + 4) and (x - 1).

To find the factors of the quadratic expression x² + 3x - 4, we need to factorize it.

Let's consider each option and determine if it is a valid factorization:

Option 1: (x + 4) and (x - 4)

If we multiply (x + 4)(x - 4), we get x² - 16, which is not equal to the original expression x² + 3x - 4.

Therefore, this option is incorrect.

Option 2: (x + 3) and (x - 4)

If we multiply (x + 3)(x - 4), we get x² - x - 12, which is not equal to the original expression x² + 3x - 4.

Therefore, this option is also incorrect.

Option 3: (x + 4) and (x - 1)

If we multiply (x + 4)(x - 1), we get x² + 3x - 4, which is exactly equal to the original expression.

Therefore, this option is the correct factorization of x² + 3x - 4.

Option 4: (x + 3) and (x - 1)

If we multiply (x + 3)(x - 1), we get x² + 2x - 3, which is not equal to the original expression x² + 3x - 4.

Therefore, this option is also incorrect.

In conclusion, the factors of the quadratic expression x² + 3x - 4 are (x + 4) and (x - 1).

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Complete question =

What are the factors of x² + 3x - 4?

(x + 4) and (x – 4)

(x + 3) and (x – 4)

(x + 4) and (x – 1)

(x + 3) and (x – 1)

The probability that the mean weight of the sample babies would be less than 4068 grams is 0.8666.

We have mean weight as 4022grams,and standard deviation as 266 grams.

We need to check mean weight of the sample will be less than 4068 grams.

It means that on left side mean range is=4022-4068=-46,and

right side mean range =4022+4068=8090

So, we need to find the probability if mean range varies in between from -46 to 8090.

So, we use z-score table to find the z-score for -46 and 8090,we get

We use Z-formula which is given by

Z = (X-μ)/SE

where X is the standard mean.

Using the Z-score table, we get

Z = 0.16917 and -0.161917

Using z-score table, we get that P(0.16917)=0.4333.

Since, both of the probability occupies same space area, due to that total probability =0.4333×2=0.8666

Hence, the probability will be 0.8666.

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Step-by-step explanation:

a) y=x;y=kx

36=3k

divide both sides by 3

k=12

b) z=1/x;z=K/x

2=k/4

k=2×4;K=8

c) z=cy^n

let c=1,y=2,n=3

z=1×2³

Z=2³

Z=8

where C,Y,N are Real number

y = 4*x^2 represents the direct proportion relationship between y and x. The inverse proportion of z and x can be expressed as z = 8/x, equivalent to z = c y^n with c=8 and n=-1.

Since y is directly proportional to x^2, we can express y as y = k*x^2, where k is the constant of proportionality. Given that when x = 3, y = 36, we can replace the x and y values to find k. Hence, 36 = k * 3^2, leading to k = 4.

Therefore, the equation y in terms of x is y = 4*x^2.

z is inversely proportional to x, which means z = c/x, where c is a constant. With x = 4, and z = 2, replace the x and z values to find c. Hence, 2 = c/4, resulting in c = 8. Thus, the equation is z = 8/x. Comparing this with z = c y^n, we see that c = 8 and n = -1 (because y is x in this case and it's in the denominator hence the negative exponent).

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Answer:

Correct Answer is A

Step-by-step explanation:

5×14 = 70

using the addition law of indices

(x¹. x⁷) ( y⁰. y⁵)

Add the powers

Therefore: x^(1+7) = x⁸

y^(0+5) = y⁵

Answer: 70x⁸y⁵

(27d^(2))/(8c^(2)) contains the C term with the same exponent and the d term with a different exponent as compared to the given expression.  The correct is option (C).

The given expression is ((3C^(4)d^(4))/(2d^(9)))^(3).

We need to find the expression that is equivalent to the given expression. Here, we will use the properties of exponents to simplify the given expression, and then we will compare it with the expressions .

Let us simplify the given expression.

((3C^(4)d^(4))/(2d^(9)))^(3) = (3C^(4)d^(4)/2d^(9))^(3) = (3/2)(C^(4)d^(4-9))^(3) = (3/2)(C^(4)d^(-5))^(3) = (3/2)C^(4*3)d^(-5*3) = (3/2)C^(12)/d^(15)

Now, we need to compare this expression with the expressions given in the answer choices.

Option (A) (3d^(4))/(2c^(2)) cannot be the equivalent expression because it does not contain C and d terms with the same exponents.

Option (B) (81d^(6))/(8C^(6)) cannot be the equivalent expression because it contains the C term with a different exponent as compared to the given expression.

Option (C) (27d^(2))/(8c^(2)) contains the C term with the same exponent and the d term with a different exponent as compared to the given expression. Hence, this expression is equivalent to the given expression.

Hence, this expression is equivalent to the given expression .Therefore, the correct is option (C) (27d^(2))/(8c^(2)).

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The price elasticity of demand (PED) for the logo T-shirts is 1.67, indicating that the demand for T-shirts is elastic. Lowering the price from $15 to $10 increased the total revenue, suggesting that the T-shirt made a good decision in lowering the price. This is because the price change led to a significant increase in quantity demanded and overall revenue.

To calculate the price elasticity of demand (PED), we can use the following formula:

PED = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

Given that Q1 = 25, Q2 = 50, P1 = $15, and P2 = $10, we can substitute these values into the formula:

PED = ((50 - 25) / ((50 + 25) / 2)) / (($10 - $15) / (($10 + $15) / 2))

Simplifying this expression:

PED = (25 / 37.5) / (-5 / 12.5)

PED = (-2/3) * (-2.5) = 1.67

The price elasticity of demand (PED) for the logo T-shirts is 1.67.

Since PED is greater than 1, it indicates that the demand for T-shirts is elastic. This means that a decrease in price by 1% will result in a greater than 1% increase in quantity demanded. To determine if lowering the price was a good decision, we can analyze the effect on total revenue. The price-total revenue test states that:

If PED is elastic (greater than 1), a decrease in price will lead to an increase in total revenue.

If PED is inelastic (less than 1), a decrease in price will lead to a decrease in total revenue.

If PED is unit elastic (equal to 1), a change in price will have no effect on total revenue.

Let's calculate the total revenue at both prices:

Total Revenue at $15 = $15 * 25 = $375

Total Revenue at $10 = $10 * 50 = $500

Comparing the total revenue at each price, we can see that lowering the price from $15 to $10 increased the total revenue from $375 to $500. Therefore, the T-shirt made a good decision in lowering the price because it led to an increase in total revenue.

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Answer:

9(2x + 1) < 9x - 18

9(2x + 1) < 9(x - 2)

2x + 1 < x - 2

x < -3

So -4 is in the solution set.

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

The total number of non-fictional biography books in the library will be equal to 1/5.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Let the total number of books is x.

3/5 of total books are non-fiction, then,

3/5 × x = 3/5x

1/3x of them are biographies.

Then, the number of non-fictional biographies are,

3/5 × 1/3

=1/5

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Answer:false

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because for A, the question is "How many weeks until the bank is full?" which is looking for X. That part is checked off. It says 100x+50=710. 710 is the total in A too so that is checked off. In the equation, the piggy bank starts with 50 coins so that is checked off. Everything is in order so A is the answer. WEAR A  MASK AND STAY SAFE DURING THIS HARD TIME! ;)

Answer:

The answer is D

Step-by-step explanation:

The original equation ..

100x +50 = 710

100x=710-50

100x=660

Divide on both sides

X =6.6

When you solve equation D in the same way, the same result will appear

The probability of rolling a sum of 8 when rolling two dice is 5/36. Explanation: There are 36 possible outcomes when rolling two dice, as each die has 6 possible outcomes. Out of these 36 outcomes, there are 5 ways to obtain a sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). Therefore, the probability is 5/36.

To find the probability of obtaining a sum of 8 when rolling two dice, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

The total number of possible outcomes can be calculated by multiplying the number of outcomes on each die. Since each die has 6 possible outcomes (numbers 1 through 6), the total number of possible outcomes is 6 x 6 = 36.

Next, we need to determine the number of favorable outcomes, i.e., the number of ways we can obtain a sum of 8. We can list all the possible combinations that result in a sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). There are five such combinations.

Finally, we divide the number of favorable outcomes by the total number of possible outcomes to obtain the probability. In this case, 5 favorable outcomes divided by 36 possible outcomes gives us 5/36.

Therefore, the probability of rolling a sum of 8 when rolling two dice is 5/36.

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The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:

C

Step-by-step explanation:

Answer:

3,675 people

Step-by-step explanation:

First row, a = 20

Common difference, d = 5

number of terms, n = 35

Sn = n/2 {2a + (n - 1)d}

= 35/2 {2*20 + (35 - 1)5}

= 35/2 {40 + ( 34)5}

= 17.5(40 + 170)

= 17.5(210)

= 3,675 people

The answer is actually 3675.

My reasoning: Plug it in and you shall see!

Answer:

(D)5

Step-by-step explanation:

Given a line: \(y=\dfrac{3}{4}x+3\)

Comparing with the slope-intercept form y=mx+c

Slope, m \(=\dfrac{3}{4}\)

Definition: Two lines are perpendicular if the product of their slopes equals -1.

Therefore, the slope of a line perpendicular to the given line

\(m=-\dfrac{4}{3}\)

Therefore, a line that is perpendicular and passes through the point (3,1) is:

\(y-y_1=m(x-x_1)\\y-1=-\dfrac{4}{3}(x-3)\\y-1=-\dfrac{4}{3}x+4\\y=-\dfrac{4}{3}x+4+1\\y=-\dfrac{4}{3}x+5\)

Comparing with the slope-intercept from: y=mx+c

The y-intercept of the perpendicular line is therefore 5.

The correct option is D.

Answer:

D

Step-by-step explanation:

Took the test!