adding unlike denominator mixed fraction ​

Answer:

He will need to pitch 79

Step-by-step explanation:

90 + 85 +  92 + 95 + 82 + 92 + 89 + 79 = 704

704/8 =79

To expand its manufacturing capacity with a $20 million investment in new machinery while maintaining its current capital structure and dividend policy, Gardial GreenLights must seek external equity of $8 million.

The capital structure of Gardial GreenLights is characterized by a 50% debt-to-total-assets ratio. Since the company plans to maintain this ratio, the remaining 50% of the assets must be financed through equity. The investment in new machinery is $20 million, which represents 50% of the total assets needed for expansion. Therefore, the total assets required for expansion would be $40 million (20 million divided by 0.5). To determine the amount of external equity needed, we subtract the company's existing equity from the total assets required. Given that the company's dividend policy entails distributing 25% of the year's net income, we can calculate the retained earnings. This year's net income was $8 million, and 25% of that ($2 million) would be distributed as dividends. Therefore, the retained earnings amount to $6 million ($8 million - $2 million). Since external equity is the difference between the total assets required and retained earnings, Gardial GreenLights must seek external equity of $34 million ($40 million - $6 million) to finance its expansion plans.

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Answer: 42

Step-by-step explanation:

7 * 90/15 = 42

Answer:

the nth term of a sequence is usually denoted by the symbole an . a1 =2 the second term is a2=6 and so....

A term is multiplied by 3 to get the next term . if you know the formula for the nth term of a sequence of n , then you can find any term .

formula : an =a1 + ( n - 1 ) d

hope its helpful . Good luck ;)

Answer:

To find the real and complex roots of the function f(x) = x^4 + 74x^2 - 567, we can use the quadratic formula to solve for x^2 and then find the square roots of the solutions.

Let's first set y = x^2, then we can rewrite the function as:

f(y) = y^2 + 74y - 567

Using the quadratic formula, we can find the roots of this quadratic equation as:

y = (-74 ± sqrt(74^2 + 4*567))/2y = (-74 ± sqrt(5929))/2y = (-74 ± 77)/2

So, we have two solutions for y:

y1 = -75.5

y2 = 1.5

Now, we can find the square roots of these solutions to get the values of x:

x1 = ±sqrt(-75.5) = ±8.68i

x2 = ±sqrt(1.5) = ±1.22

Therefore, the complex roots of the function are x1 = 8.68i and x2 = -8.68i, and the real roots are x3 = 1.22 and x4 = -1.22

To determine whether the normal quantile plot depicts sample data from a population with a normal distribution, you should visually inspect the plot. If the data points fall approximately along a straight line without any noticeable curvature.

To examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution, we need to understand the characteristics of a normal quantile plot and interpret its visual patterns.

A normal quantile plot, also known as a Q-Q plot (quantile-quantile plot), is a graphical tool used to assess the normality of a dataset. It compares the quantiles of the observed data against the quantiles of a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data is normally distributed. On the other hand, deviations from a straight line indicate departures from normality.

Here's how you can interpret a normal quantile plot:

1. Straight Line: If the plotted points form a straight line, it indicates that the data closely follows a normal distribution. The more closely the points align with the line, the stronger the evidence for normality.

2. Curvature: If the plotted points exhibit curvature, such as bending or bowing away from a straight line, it suggests departures from normality. Curvature may indicate skewness or heavy-tailedness in the data.

3. Outliers: Points that deviate significantly from the expected line can indicate outliers. Outliers might suggest the presence of extreme values or errors in the data.

4. S-shaped or Concave Shape: If the plotted points form an S-shaped curve or concave shape, it suggests a distribution that is not normal. This shape may indicate bimodal or multimodal distributions.

Therefore, to determine whether the normal quantile plot depicts sample data from a population with a normal distribution, you should visually inspect the plot. If the data points fall approximately along a straight line without any noticeable curvature, it suggests that the sample data follows a normal distribution. However, if there is significant curvature, the presence of outliers, or an S-shaped or concave shape, it suggests deviations from normality.

It's important to note that visual inspection alone may not provide a definitive conclusion. Statistical tests, such as the Shapiro-Wilk test or the Anderson-Darling test, can provide quantitative measures of normality. These tests evaluate the null hypothesis that the data comes from a normally distributed population.

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Answer:

\( \frac{67}{100} \)

Answer:

67/100

Step-by-step explanation:

6/99 = 0.6666......

67/100 = 0.67     This is the answer

67/99 = 0.676767676.....    

7/100 = 0.07

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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Answer:

Rs 750

Step-by-step explanation:

Given, No. of kurtas: 18, Each with CP = Rs 1000.

So, SP of 18 kurtas: 18*1000 = Rs. 18000

Also, 3 sets of kurtas were damaged.

Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.

SP of 15 kurtas: 15*1250 = Rs. 18750

So, Clearly SP>CP, Profit.

We know Profit= SP-CP

= 18750-18000 = Rs 750

The missing information for q2 is the mean squares for treatment, which can be calculated by dividing the sum of squares for treatment. The missing information for q3 is the sum of squares for error.The missing information for q4 is the mean squares for error, which can be calculated by dividing the sum of squares for error.To find the p-value for the above ANOVA table, we need to use the F-distribution with degrees of freedom for treatment  and degrees of freedom for error.

Using the given mean squares for treatment (25.25) and mean squares for error (2.95), we can calculate the F-statistic as follows:

F = mean squares for treatment / mean squares for error
F = 25.25 / 2.95
F = 8.5593

The p-value can then be calculated using a one-tailed F-test with alpha level of 0.05:

p-value = pf(F, degrees of freedom for treatment, degrees of freedom for error)
p-value = pf(8.5593, 3, 16)
p-value = 0.0006

Therefore, the answer is A.
Q2: Mean squares (treatment) = Sum of squares (treatment) / Degree of freedom (treatment)
Mean squares (treatment) = 75.75 / 3
Mean squares (treatment) = 25.25
So, the answer for q2 is: a. 25.25

Q3: Mean squares (error) = Sum of squares (error) / Degree of freedom (error)
Mean squares (error) = 47.2 / 16
Mean squares (error) = 2.95
So, the answer for q3 is: b. 2.95

Q4: F-value = Mean squares (treatment) / Mean squares (error)
F-value = 25.25 / 2.95
F-value ≈ 8.5593
So, the answer for q4 is: c. 8.5593

Q5:P-value = 1 - pf(F-value, Degree of freedom (treatment), Degree of freedom (error))
P-value = 1 - pf(8.5593, 3, 16)

So, the answer for question 5 is: c. 1- pf(8.5593, 3, 16)

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Horatio devotes 30 hours to the harder book and 10 hours to the easier one.

Calculations

Let X be the hours spent reading the more difficult book

Let Y be the hours spent reading the less difficult book

Total hours spent = X + Y = 40

Number of pages of difficult book in X hours at 12 pages per hour = 12X

Number of pages of easier book in Y hours at 25 pages per hour = 25Y

Total pages read = 12X + 25Y

So we have two equations in X and Y and we can solve them simultaneously. Equations are:

X + Y = 40                    (1)

12X + 25Y = 610             (2)

We can eliminate one of the variable terms by making the coefficients of the other term equal and then subtracting

Multiply (1) by 12 to make X terms equal

12(X + Y) = 12 x 40

12X + 12Y = 480                (3)

Subtract (3) from (2)

(2) - (3)

==> 12X + 25Y - (12X + 12Y) = 610 - 480

==> 12X + 25Y - 12X - 12Y = 130

==> 25Y - 12Y = 130                           (12X terms cancel)

==> 13Y = 130

==> Y = 130/13                                     (divide both sides by 13)

==> Y = 10

Using (1)

X + Y = 40

==> X + 10 = 40

==> X + 10 - 10 = 40 - 10

==> X = 30

So answer:

Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book

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The identity csc^2 x * (1 - cos^2 x) = 1 using basic trigonometric identities and algebraic manipulation. This identity is useful in solving trigonometric equations and simplifying expressions involving cosecants and cosines.

To prove the identity csc^2 x * (1 - cos^2 x) = 1, we will use trigonometric identities and algebraic manipulation.

Starting with the left-hand side of the identity, we have:

csc^2 x * (1 - cos^2 x)

Using the identity 1 - cos^2 x = sin^2 x, we can simplify this expression as:

csc^2 x * sin^2 x

Using the identity csc^2 x = 1/sin^2 x, we can simplify further as:

1/sin^2 x * sin^2 x

This expression simplifies to:

1

Therefore, we have shown that the left-hand side of the identity is equal to 1. Thus, the identity is true.

To understand why this identity is true, it is helpful to know some basic trigonometric identities. The cosecant of an angle is defined as the reciprocal of the sine of that angle, or csc x = 1/sin x. The sine and cosine of an angle are related by the identity sin^2 x + cos^2 x = 1. Using this identity, we can derive the identity 1 - cos^2 x = sin^2 x, which we used above.

Substituting this identity into the original expression and simplifying, we were able to show that the left-hand side of the identity is equal to 1. This means that the identity is true for all values of x, except where sin x = 0 (i.e., x = nπ, where n is an integer). In these cases, the left-hand side is undefined, but the right-hand side is still equal to 1.

In conclusion, we have proven the identity csc^2 x * (1 - cos^2 x) = 1 using basic trigonometric identities and algebraic manipulation. This identity is useful in solving trigonometric equations and simplifying expressions involving cosecants and cosines.

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Answer:

Hello! :) have a good day!

(10x+6)4 = 40x +24

Answer: C. $5166,667

Step-by-step explanation:

AI-generated answer

Let's begin with calculating the total amount saved over 15 years. The savings decrease by 3% every year from $25,000 in year 1. To calculate this, we can use the geometric series formula:

S = a(1 - r^n) / (1 - r)

Where S is the sum of the geometric series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 25000, r = 0.97 (since the savings decrease by 3% every year), and n = 15.

S = 25000(1 - 0.97^15) / (1 - 0.97)

S = $267,929.90

Next, we need to calculate the total amount at the end of year 15 with a 120% interest rate per year. We can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where A is the total amount, P is the principal (in this case, $267,929.90), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year (in this case, 1 since it's compounded annually), and t is the number of years (in this case, 15).

r = 120% = 1.2

A = 267929.90(1 + 1.2/1)^(1*15)

A = $5,166,667.00

Therefore, the closest option is C. $5,166,667.

The probability that they are the 4 oldest people in the group = 4/9

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

the group of people = 9

you randomly select 4 of them

the probability that they are the 4 oldest people in the group?

According to the formula :

Probability = expected number of outcome/Total number of outcome

If there are group of 9 people, then the total outcome of events will be 9.

If we are to select 4 oldest people from the group, then the expected outcome is 4.

So,

The probability that they are the 4 oldest people in the group = 4/9

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We can say that a and b are identical in absolute value if a and b are nonzero integers such that a divides b (a | b) and b divides a (b | a). That is to say, a =± b.

The transitive property of divisibility serves as evidence for this. We know that there are numbers k and l such that b = ak and a = bl exist if a | b and b | a. We obtain a = alk by substituting the expression for b into the second equation. We can divide both sides by a to get l = 1/k because an is not zero. Given that k and l are both integers, they must both either be 1 or -1. B Equals ak if k = 1, else then b = ak = a(1) = a, and if k = -1, then b = ak = a(-1) = -a. In either case, we have shown that a = ±b.

So if a and b are nonzero integers such that a divides b and b divides a, then we can conclude that a and b have the same absolute value, but possibly opposite signs.

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The given statement "Using p-value rule for a population proportion or mean, if the level of significance is less than p-value, null hypothesis is rejected." is True because the hypothesis is rejected in this case.

In hypothesis testing, the p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, assuming that the null hypothesis is true. The level of significance, denoted by alpha, is the maximum probability of rejecting the null hypothesis when it is actually true.

If the p-value is less than the level of significance, it means that the observed test statistic is unlikely to have occurred by chance alone, assuming the null hypothesis is true. Therefore, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

For example, suppose we are testing the hypothesis that the population mean is equal to a certain value. If the p-value is 0.02 and the level of significance is 0.05, we would reject the null hypothesis because the p-value is less than the level of significance.

This means that there is strong evidence against the null hypothesis and we can conclude that the population mean is likely different from the hypothesized value.

In summary, if the level of significance is less than the p-value, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

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Answer:

1

Step-by-step explanation:

To find the average rate of change, you have to use this formula:

\(ROC=\frac{f(b)-f(a)}{b-a}\), when a and b are the x and y coordinates of the problem.

To find f(b) and f(a), you have to insert -2 and 1 for f(x) because a = -2 and b=1. (So you would do f(1)=1 and f(-2)=-2). Doing this will give you 1 and -2 when f(b) is 1 and f(a) is -2.

So because we have the f(b) and f(a), we can insert this in the formula.

\(ROC=\frac{f(b)-f(a)}{b-a}\\\\ROC= \frac{1--2}{1--2}\\\\ROC= \frac{1+2}{1+2}\\\\ROC= \frac{3}{3}\\\\ROC= 1\)

So that is how the original problem's answer is 1.

I hope this helped!

(Also I would LOVE to get brainilest, I'm trying to get to the expert status)

Answer:

h

Step-by-step explanation

12 inches in 1 foot.

2.54 cm in 1 inch.

5x 12=60 inches

60 +4=64inches.

64 x 2.54=162.56 cm

Answer:

H. 162.56 cm

Step-by-step explanation:

12 inches in 1 foot.

2.54 cm in 1 inch.

5x 12=60 inches

60 +4=64inches.

64 x 2.54=162.56 cm

Answer:

Edith will get £49

Zayn will get £36.75

Step-by-step explanation:

Here, given the ratio above, we want to share the amount of money between these two

We start by adding the ratio together

The total we have is 3 + 4 = 7

The amount of money that Zayn will get will be;

3/7 * 85.75 = 36.75

The amount of money Edith will get will be

4/7 * 85.75 = 49

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer:

There u go.

Step-by-step explanation:

Answer:

x=2y+2

Step-by-step explanation:

ur welcome

Answer:

y = 1/2x - 1

Step-by-step explanation:

This formula is currently written in point-slope form (y+ + y1 = m (x + x1). To graph it easier, the first thing you would do is make it slope-intercept form (y=mx + b).

First, distribute the 1/2 into the parenthesis.

1/2(x+2)

1/2x + 1

Then, the equation should look like this: y+2 = 1/2x + 1

The next step is to subtract the 2 from both sides.

It should look like this:

y = 1/2x -1

Graph it by first plotting the y-intercept, -1, on the y-axis, and counting up 1 space and to the right 2 spaces, then drawing a line. I hope this helped!  

Answer:

false

Step-by-step explanation:

To solve this problem, you can use the fact that the sum of the digits of a number is equal to the remainder when that number is divided by 9. This is because the digits of a number represent multiples of powers of 10, and the sum of these multiples will be equal to the remainder when the number is divided by 9.

For example, consider the number 12345. The sum of the digits is 1 + 2 + 3 + 4 + 5 = 15. Dividing 12345 by 9 gives a remainder of 6, which is the same as the sum of the digits.

Using this fact, you can convert the problem of finding the number of positive integers less than 1,000,000 with a sum of digits equal to 19 into a problem of finding the number of positive integers less than 1,000,000 with a remainder of 19 when divided by 9.

To do this, you can start by finding the remainder when 1,000,000 is divided by 9. Since 1,000,000 is divisible by 9, the remainder will be 0. Therefore, the remainder of any positive integer less than 1,000,000 when divided by 9 will be an integer between 0 and 8.

Since 19 is not between 0 and 8, there are no positive integers less than 1,000,000 with a remainder of 19 when divided by 9. Therefore, there are no positive integers less than 1,000,000 with a sum of digits equal to 19.

Answer:

Step-by-step explanation:

I would say you can distribute the money by saving $25 dollars for your medium and log term and $50 for your short term. Because you will eventually raise enough from your paycheck to get your laptop. Then, once you get your laptop you put more money to your other terms.

Answer: To determine whether the condition of equal standard deviations is met in this case, we can perform a quick check by comparing the sample standard deviations of each group. If the sample standard deviations are roughly equal, then we can assume that the condition of equal standard deviations is met.

Alternatively, we can use Levene's test for equality of variances, which tests the null hypothesis that the population variances are equal across all groups. If the p-value of the test is greater than the significance level (usually 0.05), then we can assume that the condition of equal standard deviations is met.

Without the data or the sample standard deviations, it is not possible to determine whether the condition of equal standard deviations is met in this case.

Step-by-step explanation: