find the product (x+3y^2) (3x-3y^2)

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²

b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:

Left side: 1³ = 1

Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

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a) The equation is not true for n = 1, so P(1) is false.

b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1

a) To find P(1), we substitute n = 1 into the equation given:

13 = (1(1 + 1) / 2)²

13 = (1 / 2)²

13 = 1/4

The equation is not true for n = 1, so P(1) is false.

b) To complete the basic step of the proof, we need to show that P(1) is true.

However, we have just shown that P(1) is false.

This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.

Therefore, the proof cannot proceed and is incomplete.

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Answer: 2*(n-7) , (Twice the difference of a #' and 7') .

Answer:

y = 2x - 10

Step-by-step explanation:

\(y=mx+b\)

\(y=2x+b\)

\(-2=2(4)+b\)

\(-2=8+b\)

\(b=-2-8\)

\(b=10\)

\(y=2x-10\)

Equation:

\(\sf{y = 2x - 10}\)

Explanation:

First, I will write the equation in point slope:

\(\sf{y-y_1=m(x-x_1)}\)

Where:

Plug in the data:

\(\sf{y-(-2)=2(x-4)}\)

\(\sf{y+2=2(x-4)}\\\sf{y+2=2x-8}\\\sf{y=2x-8-2}\\\sf{y=2x-10}\)

Hence, the answer is y = 2x - 10.

Step-by-step explanation:

for triangle HLM

180-2x

180-(3x+6)

H

2x=3x-10

x=10°

180-36=144°

36-20=16°

H=2x

H= 180-144-16= 20°

The midpoint of a class is indeed calculated by adding the lower and upper limits of the class and then dividing the sum by two. The statement is true.

This concept is commonly used in statistics and data analysis.

In statistical data, classes are often created to group data points within a range. Each class has a lower limit and an upper limit, defining the range of values it encompasses. The midpoint is a representative value within the class that provides a measure of its central tendency.

To calculate the midpoint, the lower and upper limits of the class are added together, resulting in the total range of the class. Dividing this sum by two gives the midpoint. It is important to note that the midpoint is not necessarily an actual data point; rather, it is a statistical measure used to represent the central value within a class.

For example, suppose we have a class with a lower limit of 10 and an upper limit of 20. Adding these values gives us 30, and dividing by two yields a midpoint of 15. This means that, for the purposes of analysis, we can consider the midpoint of the class as 15.

By calculating midpoints for each class in a data set, statisticians can summarize and analyze data in a more manageable and meaningful way. Midpoints help provide a sense of the central tendencies and distributions within the data, facilitating further statistical analysis and interpretation.

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Answer:

x = 31

Step-by-step explanation:

Given that the triangles are congruent, then corresponding angles are congruent, then

∠ D = ∠ A

The sum of the 3 angles in a triangle = 180° , thus

∠ A = 180° - (61 + 57)° = 180° - 118° = 62°

Thus

2x = 62 ( divide both sides by 2 )

x = 31

The number of tosses in the second case (64 tosses) is four times greater than the number of tosses in the first case (16 tosses).

We have two cases: the first case with 16 tosses and the second case with 64 tosses.

To determine how many times the second case is greater than the first case, we divide the number of tosses in the second case (64) by the number of tosses in the first case (16).

Performing the division, 64 divided by 16 equals 4.

The result of 4 indicates that the number of tosses in the second case is four times greater than the number of tosses in the first case.

When we say "four times greater," it means that the second case has four times the number of tosses compared to the first case.

In other words, if we compare the quantity of tosses, the second case has four times as many tosses as the first case.

To determine how many times 64 is greater than 16, we can divide 64 by 16. The result is 4, indicating that 64 is four times greater than 16. This means that the number of tosses in the second case (64 tosses) is four times more than the number of tosses in the first case (16 tosses).

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The measure of arc ECF in Circle G is 98°.Therefore, the correct option is 98°.Option A is incorrect. Option B is correct. Option C is incorrect. Option D is incorrect.

Given that Circle G is inscribed with triangle EFD, Point C is on the circle between points E and F, angle E is 79 degrees, and the measure of arc ED is 104 degrees.

We need to find the measure of arc ECF in Circle G.

From the given information, we can say that angle ECF is an inscribed angle in the circle.

So, the measure of the angle ECF is half the measure of the arc EDF.

That is:

∠ECF = 1/2(arc EDF)

         = 1/2(104)

         = 52

Thus, the measure of arc ECF in Circle G is 98°.

Therefore, the correct option is 98°.Option A is incorrect. Option B is correct. Option C is incorrect. Option D is incorrect.

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Answer:

y=25

Step-by-step explanation:

y=4+4x+x^2

x=3

y=4+4(3)+(3)^2

y=4+12+(3)^2

y=4+12+(3x3)

y=4+12+(9)

y=16+9

y=25

If this helps please mark as brainliest

Answer:

x = −2 or x = 10

Step-by-step explanation:

for the explanation see the image

A coach may use 240 different player combinations on the rink.

What are some permutation and combination examples?

The arrangement of people, numerals, numbers, alphabets, letters, and colors are a few examples of permutations.

Combinations include picking the meal, the cuisine, the attire, the subjects, and the team, for instance.

Forward 6C3 = 20

Defence 4C2 = 6

Golie 2C1 = 2

No. of possible Combination = 20 * 6 * 2 = 240

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1. The cost per square inch of the apple pie is $0.32.

2. 3 of the 8 equal pieces is 231 square feet.

3. The area of a circle with a diameter of 16 meters is 64π square meters.

4. After one of the members of the family ate one eighth of the pizza, 395.64 square inches of pizza remained.

5. The area of the circle with a segment drawn from one point on the circle to another point on the circle through the center of the circle labeled 10 feet is 78.5 ft².

Question 1: To find the cost per square inch of the apple pie, we first need to find the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Since the diameter of the pie is 6 inches, the radius is 3 inches. So the area of the pie is A = π(3)² = 9π square inches. Now we can find the cost per square inch by dividing the cost of the pie by the area: $9.15 / 9π ≈ $0.32.

Question 2: To find the area of 3 of the 8 equal pieces of the circle, we first need to find the area of the whole circle using the formula A = πr².

The radius of the circle is 14 feet, and π is 22/7, so the area of the whole circle is A = (22/7)(14)² = 616 square feet.

Now we can find the area of one of the 8 equal pieces by dividing the area of the whole circle by 8: 616 / 8 = 77 square feet.

Finally, we can find the area of 3 of the pieces by multiplying the area of one piece by 3: 77 x 3 = 231 square feet.

Question 3: To find the area of the circle, we can use the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is 16 meters, the radius is 8 meters. So the area of the circle is A = π(8)² = 64π square meters.

Question 4: To find the area of the whole pizza, we can use the formula A = πr², where r is the radius of the circle.

Since the diameter of the pizza is 24 inches, the radius is 12 inches. So the area of the whole pizza is A = π(12)² = 144π square inches.

Now we can find the area of one eighth of the pizza by dividing the area of the whole pizza by 8: 144π / 8 = 18π square inches.

Finally, we can find the area of the remaining pizza by subtracting the area of one eighth of the pizza from the area of the whole pizza: 144π - 18π = 126π ≈ 395.64 square inches.

Question 5: To find the area of the circle, we can use the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is 10 feet, the radius is 5 feet. So the area of the circle is A = π(5)² = 25π ≈ 78.5 ft².

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Due to proportionality, y has a value of 13 when x = 1.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.

Given that If y varies directly with x and y = 39 when x = 3

Since x is directly proportional to the x

thus,

y ∝ x

we can write it in a ratio form

y₂ / y₁ = x₂ / x₁ (asked value of y at x = 1)

y₂ / 39 = 1/ 3

y₂ = 13

Therefore, the Value of y at x = 1 is 13 due to proportionality.

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Answer:

the answer is t=47°

Step-by-step explanation:

72°-25°=47°

Answer:

t = 47°

Step-by-step explanation:

72° appears to be equal to t + 25°

Therefore, you subtract 25° from 72° to get 47°

Answer:

C

Step-by-step explanation:

Standard form is [ ax² + bx + c ]

The exponents and variables determine what comes first.  In [ 11x³ - 6x² + 5x ], we can see that the exponents are going from greatest to least and the last number doesn't have an exponent so it goes last. Essentially we can think of this as sorting each part from greatest to least using exponents -> variables -> number to determine that.

Best of Luck!

Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

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Answer:

48

Step-by-step explanation:

72 ÷ 3 = 24

so you know that the men is 24 × 2 = 48

48:72 = 2:3

i looked it up and it says x=4 and theres 12 men but i dont think that helps im so sorry i couldnt find anything:(

Answer:

A

Step-by-step explanation:

Because it would be how many adults times 36. And how many ever children times 15. And that total would be equal to $234

Answer:

-3.5

Step-by-step explanation:

You can do this without a calculator.

Since √16 = 4 and √25 = 5, you can be sure that √20 will be between 4 and 5. So your answer will be between -8+4 and -8+5.

This is between -4 and -3, and there is only one answer listed, answer C.

BTW, the unrounded answer is: -3.527864045000420607181652662537447529118763280776948551458205509...

-8+√20=-3.5

We need to find value of -8+√20 and we have to round it to nearest tenth

What is a surd?

An expression with square root , cube root or other root symbol

-8+√20=-8+√(4*5)

=-8+2√5

=-8+2(2.23606)

=-8+4.47212

=-3.527

Therefore the answer is -3.5

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Answer:Me!" (stylized in all caps) is a song recorded by American singer-songwriter Taylor Swift featuring American singer Brendon Urie of Panic! at the Disco. It was released on April 26, 2019, through Republic Records, as Swift's first single after signing with the label. The song was revealed and released at the end of a thirteen-day countdown, as the lead single from her seventh studio album, Lover (2019). It was written by Swift, Joel Little and Urie, and produced by Swift and Little. The song was recorded at Electric Lady Studios, New York City and Golden Age West in Auckland, New Zealand in 2018. "Me!" is a cheery, campy bubblegum pop and synth-pop duet, driven by a marching band drumline. It is about embracing one's individuality, with lyrics on self-affirmation and self-love.

"Me!" debuted at number 100 on the US Billboard Hot 100, before surging up to number two the next week, breaking the record for the biggest single-week jump in the chart's history. The song reached the top five in several other countries. It broke several Amazon Music records, including the most first-day streams, most first-week streams and most on-demand voice requests with Alexa of a single debut on the platform. Upon release, the song received mixed reviews from music critics, who were favorable towards the bubbly production and the duo's vocal chemistry, but divided over the lyrics—some complimented the tongue-in-cheek songwriting, while others called it weak. "Me!" has since been certified double-platinum by Recording Industry As

Step-by-step explanation:

Answer:

D. Group A, because four children in the group have the least forearm length of 10 inches.

Step-by-step explanation:

It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A.

So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.

In order to verify the claim let us find the mean

Mean of Group A

Mean of Group B

So, group A has shorter average forearm length.

Answer:

0 or nothing

Step-by-step explanation:

the two ts cross out so its 0t=1

Answer:

so in order to solve this you have to first distribute: 1-2t=2-2t

then you subtract the one from both sides of the equation: -2t+1(-1)=-2t+2(-1)

simplify: -2t=-2t+1

then add 2t to both sides of the equation: -2t(+2t)=-2t+1(+2t)

simplify again: 0=1

technically this means that there is no real solution although, depending on what grade you are in the teacher could expect you to know the imaginary function

Step-by-step explanation:

Based on the given information , the appropriate hypothesis test for this scenario would be an independent samples t-test.

The independent samples t-test is used to compare the means of two independent groups.

To determine if there is a significant difference between them.

In this case, the two groups are women who smoked during pregnancy and women who did not smoke during pregnancy.

The variable of interest is the bone mineral content of healthy newborns.

The null hypothesis (H₀) would state that ,

There is no significant difference in the mean bone mineral content between,

newborns of women who smoked during pregnancy and newborns of women who did not smoke during pregnancy.

The alternative hypothesis (Hₐ) would state that there is a significant difference in the mean bone mineral content between the two groups.

To conduct the independent samples t-test,

We would calculate the t-statistic using the sample means, sample sizes, and standard deviations of the two groups.

The t-statistic is then compared to a critical value from the t-distribution with appropriate degrees of freedom.

To determine if the difference in means is statistically significant.

Assumption of normality and equal variances between the groups, should be checked before conducting the t-test.

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The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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Answer:

C. 12:15 or 12/15

Step-by-step explanation:

There are 12 boys in the class and 15 girls.

The question asks for boys to girls.

12 boys: 15 girls is the same as saying 12:15, 12/15, or 12 boys to 15 girls in Tina's class.

You have to pay attention to the order in which the question asks for because 15:12 is NOT the same thing as 12:15. (15:12 ≠ 12:15)

Answer:

B

Step-by-step explanation:

\(\sqrt{x}\) + 6 = x ( subtract 6 from both sides )

\(\sqrt{x}\) = x - 6 ( square both sides )

x = (x - 6)² ← expand using FOIL

x = x² - 12x + 36 ( subtract x from both sides )

0 = x² - 13x + 36 , that is

x² - 13x + 36 = 0 ← in standard form

(x - 4)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 9 = 0 ⇒ x = 9

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 4

left side = \(\sqrt{4}\) + 6 = 2 + 6 = 8

right side = x = 4

Since 8 ≠ 4 then x = 4 is an extraneous solution

x = 9

left side = \(\sqrt{9}\) + 6 = 3 + 6 = 9

right side = x = 9

Thus the solution is x = 9 → B

The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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This information could provide insights into the impact of mental health on individuals' perceptions of their overall health.

In statistics, a frequency table is a table that shows how often each value or range of values of a variable occurs in a dataset. In this case, the variable of interest is "perception of general health," and there are five possible responses: excellent, very good, good, fair, and poor.

The table of frequencies you mentioned would show the number of individuals in each group who responded with each of the five possible responses. For example, the table might show that out of the 200 individuals with a depressive disorder, 10 responded with "excellent," 50 responded with "very good," 60 responded with "good," 30 responded with "fair," and 50 responded with "poor." The table would also show the corresponding frequencies for the 200 individuals without a mental health diagnosis.

A frequency table can be used to calculate various statistics, such as the mode (the most common response), the median (the middle response), and the mean (the average response). Additionally, frequency tables can be used to create charts and graphs that visually display the distribution of responses.

In this particular study, the researcher is interested in whether there are differences in the perception of general health between individuals with a depressive disorder and those without a mental health diagnosis. The frequencies for each group could be compared to see if there are any notable differences in the distribution of responses. This information could provide insights into the impact of mental health on individuals' perceptions of their overall health.

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