For Q1-Q4 use mathematical induction to prove the statements are correct for ne Z+(set of positive integers). 3) Prove that for integers n > 0 3 n + 5n is divisible by 6.

Answer:

$2

Step-by-step explanation:

$10+$10=$20

$20-$18= $2

Answer:

10

Step-by-step explanation:

given :

length WX ≅ (congruent means equal) length XY

therefore ,  WX = 3

WZ = WX + XZ

WZ = 3 + 7

WX = 10

Answer: r = (V/(2π))¹/³ and h = V/(πr²)

To find the dimensions that will use the least material for a right circular cylinder with a given volume, follow these steps:

1. Recall the formula for the volume of a right circular cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height.

2. We want to minimize the surface area (material used) for a given volume. The surface area of a cylinder is given by the formula: A = 2πr² + 2πrh.

3. To minimize the surface area, we'll use calculus. Differentiate the surface area formula with respect to r, and set the resulting equation to zero. To eliminate h from the equation, substitute the volume formula: h = V/(πr²).

4. Differentiate the surface area formula: dA/dr = 4πr - 2V/r².

5. Set dA/dr = 0 and solve for r: 4πr - 2V/r² = 0.

6. Rearrange the equation: r³ = V/(2π).

7. Solve for r: r = (V/(2π))¹/³.

8. Now, find the height h by substituting the r value into the volume formula: h = V/(πr²).

9. Calculate the dimensions using the given volume with the found r and h values.

In summary, the dimensions of the right circular cylinder with the least material for a given volume can be found by solving for r and h using the formulas r = (V/(2π))¹/³ and h = V/(πr²).

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Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation: your answer is b - 7/9

Answer: Slope = 8.000/2.000 = 4.000

x-intercept = 14/-4 = 7/-2 = -3.50000

y-intercept = 14/1 = 14.00000

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(4*x+14)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-4x-14 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-4x-14 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 14/1 so this line "cuts" the y axis at y=14.00000

y-intercept = 14/1 = 14.00000

Calculate the X-Intercept :

When y = 0 the value of x is 7/-2 Our line therefore "cuts" the x axis at x=-3.50000

x-intercept = 14/-4 = 7/-2 = -3.50000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 14.000 and for x=2.000, the value of y is 22.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 22.000 - 14.000 = 8.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 8.000/2.000 = 4.000

Geometric figure: Straight Line

Slope = 8.000/2.000 = 4.000

x-intercept = 14/-4 = 7/-2 = -3.50000

y-intercept = 14/1 = 14.00000

Answer:

12.73%

Step-by-step explanation:

24 + 32 = 56(veggie sandwich)

112 + 150 = 262

262 + 64 = 326

326 + 58 = 384

384 + 56(veg sand) = 440

440 = total number of students

Divide 100 by 440 and you get 0.23

Multiply that by 56 and you get 12.73%

:)

Answer:

Step-by-step explanation:

B

Answer:

The length of each side of the triangular collage:

a = smallest side = 3 feet

b = other side(second side) = 5 feet

c = Longest side = 6 feet

Step-by-step explanation:

She has 14 feet of edging to go around the collage.

14 feet = Perimeter of the triangle

The Perimeter of a Triangle = a + b + c where

a = smallest side

b = other side(second side)

c = Longest side

From the question, we are told that:

If the longest side is twice the smallest

c = 2a

The other side is four less than three times the smallest,

The other side = b

b = 3 × a - 4

b = 3a - 4

Hence,

P = a + b + c

14 = a + 3a - 4 + 2a

14 = a + 3a + 2a -4

14 = 6a - 4

Collect like terms

14 + 4 = 6a

18 = 6a

a = 18/6

a = 3ft

Therefore the smallest side = 3

The Longest side(c) = 2a

c = 2 × 3

c = 6ft

The other side(b) = 3a - 4

= 3(3) - 4

= 9 - 4

= 5 feet.

Therefore, the length of each side of the triangular collage:

a = smallest side = 3 feet

b = other side(second side) = 5 feet

c = Longest side = 6 feet

On a surface analysis chart, the solid lines that depict sea level pressure patterns are called isobars.

Isobars are lines connecting points of equal atmospheric pressure at sea level. They provide a visual representation of pressure variations across a geographical area.

Isobars are typically displayed on weather maps to illustrate high and low pressure systems, as well as the strength and location of pressure gradients. High-pressure systems are indicated by circular isobars, while low-pressure systems are depicted by oval or elongated isobars.

By examining the spacing and configuration of isobars, meteorologists can interpret weather patterns and make predictions.

Areas with tightly packed isobars indicate strong pressure gradients, which signify strong winds and potentially severe weather conditions. On the other hand, widely spaced isobars suggest weaker pressure gradients and calmer weather.

Overall, isobars on a surface analysis chart are crucial in understanding and analyzing atmospheric pressure patterns and their implications on weather conditions.

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,

Answer:

y = (1+cos x)/sin x

Step-by-step explanation:

Tìm tập xác định của các hàm số

The equation of a line that passes through points (0, 2) and (-2,0) is y=1x+2

Answer:

3

Step-by-step explanation:

i believe this should be the answer, simply because 15÷5 is 3. if you were to find x, you would multiply the scale factor value by the first triangle

Looking at the plot we could roughly draw a line between the points.

This would would have a positive slope. so the association would be linear and positive.

Here are the amounts of weight change (in pounds) for the 12 women:

-1, -3, -8, 7.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The list represents the amount of weight change (in pounds) for 12 women during their first year of work after graduating from college. The values in the list can be positive or negative. A positive value indicates that a woman gained weight during the year, while a negative value indicates that she lost weight.

Looking at the list, we can see that the first three women lost weight, with weight changes of -1, -3, and -8 pounds respectively. The fourth woman gained weight, with a weight change of 7 pounds, and the fifth woman gained even more weight, with a weight change of 15 pounds.

The sixth woman also gained weight, but only by 3 pounds. The next woman on the list lost weight, with a weight change of -11 pounds, and the following woman lost weight as well, with a weight change of -6 pounds.

The last four women on the list all gained weight. The eighth woman gained 12 pounds, the ninth woman did not experience any weight change, the tenth woman lost 4 pounds, and the final woman on the list lost 11 pounds.

Therefore, Here are the amounts of weight change (in pounds) for the 12 women:-1, -3, -8, 7.

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Correct question is " Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight, and negative values correspond to women who lost weight -1 -3 -8 7 15 3 -11 -6 12 0 -4 -11

Find the amounts of weight change (in pounds) for the 12 women?"

Answer: A

Step-by-step explanation:

She found the ratio of the circumference to the sector. not the ratio of the sector to the circumference.

The potential difference between the two plates is approximately 970 volts.

The potential difference between the two plates can be calculated using the formula:

V = Q / C

where V is the potential difference, Q is the charge on the plates, and C is the capacitance of the system.

Assuming the two plates form a parallel plate capacitor with a separation distance d and a plate area A, the capacitance can be calculated as:

C = ε0 × A / d

where ε0 is the permittivity of free space.

Substituting the given values, we get:

C = ε0 × A / d = 8.85 × 10^-12 F/m × A / 1 × 10^-3 m = 8.85 × 10^-9 F

Q = 8.6 × 10^-6 C (given)

Therefore, the potential difference between the two plates is:

V = Q / C = (8.6 × 10^-6 C) / (8.85 × 10^-9 F) = 970.06 volts

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Left-handedness is more common than usual among mathematicians and more common than usual among artists option (d) more; more is correct.

An equation set and a set of variables that define connections between the variables make up a mathematical model, which often explains a system.

As we know,

Mathematicians are more likely than average to be left-handed, while artists are more likely than average to be left-handed.

Thus, Left-handedness is more common than usual among mathematicians and more common than usual among artists option (d) more; more is correct.

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45 OR 46

It depends on which month and day she is born on in 1975.

If you want it from todays current date, she would be 46.

If her birthday is the 11 / 04 / 1975 (eleventh of April) -  31 / 12 / 1975 (thirty-first of December) then she is 45 years old. If her birthday has already passed in 2021 she is 46.

Answer:

12

Step-by-step explanation:

We just need to divide the number of laps to the number of swimmers to find the unit rate.

240 / 20 = 12

216 / 18 = 12

168 / 14 = 12

108 / 9 = 12

Best of Luck!

Answer: 12

Step-by-step explanation:

Sorry I don't like to show my work.

Answer:

3360 minutes

Step-by-step explanation:

4 weeks is 28 days

2 hours is 120 minutes

So you would multiply 120*28 to get 3360 minutes

I hope this helps!

Step-by-step explanation:

sin^-1√-3/2=300°

cos300°=0.5

Answer:

x = -7, 7

Step-by-step explanation:

Step 1: Write out equation

-2x² - 9 = -107

Step 2: Add 9 on both sides

-2x² = -98

Step 3: Divide both sides by -2

x² = 49

Step 4: Square root both sides

x = ±7

Step 5: Arrange

-7 < 7

So x = -7, 7

On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.

Explanation:

When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur

For example:

if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:

P(2) = P(1, 1) = (1/6)² = 1/36

P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1

2) = P(6, 6) = (1/6)² = 1/36

So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.

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Answer:

I think the answer is B because i counted all the beads the students had picked out and then put it as the denominato,r and then put the red colored beads as the numerator.

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

8x + 7

Step-by-step explanation:

To evaluate f(2x + 3) , substitute x = 2x + 3 into f(x) , that is

f(2x + 3) = 4(2x + 3) - 5 = 8x + 12 - 5 = 8x + 7

Answer:

8x+9

Step-by-step explanation:

f(x)=4x-5

f(2x+3)=4(2x+3)-5

=8x+12-5

=8x+9

this is your answer.I hope this will help you

if it crosses the y-axis as -12, that means that's its y-intercept, and we know its slope.

\(\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~~ \implies ~~y=\stackrel{\stackrel{m}{\downarrow }}{5}x\underset{\underset{b}{\uparrow }}{-12}\)

18/35 fraction of students are girls who brought their lunch today.

A fraction is a mathematical concept that denotes a component of a whole or, more generally, any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.

Let's say,

Total number of students over school = x

Number of girls = (6/7)x

Number of girls who brought their lunch = 3/5 of (6/7)x

⇒ 3/5(6/7)x

⇒ (18/35)x

Hence "18/35 fraction of students are girls who brought their lunch today".

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