A straight line ax+by=16.it passes through a(2,5) and b(3,7).find values of a and b​

The volume of the solid will be 32/7 √3.

Since base of a solid whose cross-sections is perpendicular to the w-axis are equilateral triangles

Now base of triangle. is f(x) = x³ and the Area of Equilateral Triangle is ✓3/4 base²

The volume of the solid will be:

= ✓3/4 (x^7/7)²

= ✓3/4 (128/7)

= 32/7 √3

Therefore, the volume of the solid will be 32/7 √3.

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The capacity of one glass is 36/37 liters.

Let's begin by representing the capacity of one jug as "J" and the capacity of one glass as "G". From the first piece of information, we know that:

J = 6G

This means that the capacity of one jug is equal to 6 times the capacity of one glass.

Next, we are given that 36 liters of water is needed to fill 3 jugs and 19 glasses. We can use this information to form an equation in terms of J and G.

The total capacity of 3 jugs is 3J and the total capacity of 19 glasses is 19G. Therefore, we can say:

3J + 19G = 36

Now we can substitute J with 6G (from the first equation) and simplify:

3(6G) + 19G = 36

18G + 19G = 36

37G = 36

G = 36/37

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The Houston Marathon is one of the largest marathon events of the time in Texas. If 1 afar is roughly 1. 61 kilometers, 42.182 kilometers are in 26. 2 long hauls.

The marathon is a long- distance bottom event with a distance of42.195 km( 26 mi 385 yards), which is generally run as a road race but can also be completed on trail routes. Running or a run/ walk strategy can be used to negotiate the marathon.

There are wheelchair divisions as well. Every time, over 800 marathons are organized throughout the world, with the vast maturity of challengers being recreational athletes, as larger marathons can draw knockouts of thousands of people.

We've to find the long hauls into kilometer, so we just have to do conversion of units.

1 mile = 1.61 km

26.2 miles = 1.61 ×26.2 km

= 42.182 km

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The five rational numbers between  -1/5 and 1/5 are:-1/6, -1/10, 0, 1/10 and 1/6

2) The five rational numbers between 1/10 and 3/10 are:  1/10, 3/30, 5/30, 7/30, and 9/30

3) the five rational numbers between 2/7 and 3/5 are 1/5, 12/35, 13/35, 2/5, and 3/7.

To find the five rational numbers between -1/5 and 1/5, we need to see the common difference between these numbers.

The difference between the two fractions is 1/5 - (-1/5)

                                                                             = 2/5.

To find the common difference between the five fractions, we divide 2/5 by 6 so it will be

2/5 ÷ 6

= 1/15

So we need to begin with -1/5 and add 1/15 repeatedly to get the five fractions:

-1/5 + 1/15 = -1/6

-1/6 + 1/15 = -1/10

-1/10 + 1/15 = 0

0 + 1/15 = 1/10

1/10 + 1/15 = 1/6

2. To find the five rational numbers between 1/10 and 3/10, the difference between the two fractions is"

3/10 - 1/10 = 2/10 = 1/5.

So we divide 1/5 by 4

1/5 ÷ 4 = 1/20

Hence:

1/10 + 1/20 = 1/10

1/10 + 2/20 = 3/30

1/10 + 3/20 = 5/30

1/10 + 4/20 = 7/30

1/10 + 5/20 = 9/30 = 3/10

3. One need to find a common denominator for 2/7 and 3/5, which is 35.

Convert both fractions to have a denominator of 35:

2/7 = 10/35

3/5 = 21/35

So to get the rational number, it will be:

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The percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3 %

the percent change in carbon dioxide According to a WMO report in 2019 greenhouse gas concentrations, it was discovered that carbon dioxide growth rates were nearly 20% higher than the previous five years and that the percentage increase from 2015 and 2019 was approximately 2.88%. which is approximately 3 %.

carbon dioxide in the atmosphere in 2015 = 399 parts per million

carbon dioxide in the atmosphere in 2019 = 410.5 parts per million

Percentage change can be calculate by using

% change = [tex]\frac{Final - initial }{initial}[/tex] × 100

% change = [tex]\frac{410.5 - 399}{399} \[/tex] × 100

% change = 2.88 %

Hence, the percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3%

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The correct answer is b. 3%.

To answer this question, we need to compare the concentration of carbon dioxide in the atmosphere between 2015 and 2019. The concentration of carbon dioxide is measured in parts per million (ppm). In 2015, the concentration of carbon dioxide in the atmosphere was around 400 ppm, while in 2019, it was around 414 ppm.

To calculate the percent change between these two years,

Percent Change = [(New Value - Old Value) / Old Value] x 100%

Percent Change = [(414 - 400) / 400] x 100%

Percent Change = 3.5%

Therefore, the correct answer is b. 3%.

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Answer:

After selling 98 cups, she made $98

Step-by-step explanation:

If she sold 98 cups, and each one went for $1, then you can set up an equation:

98(1)=98

Answer:

Ashley made $98.

Step-by-step explanation:

If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.

The probability that at least one of the six patients has an injection site reaction is 0.536or 53.6%.

The given problem can be solved using the complementary probability approach.

According to the question:

The probability that patient experience an injection-site reaction is = 0.12

Hence the probability that a patient does not have an injection-site reaction is = 1-0.12 =0.88

Number of persons who received injections with this type of needle =6

Assuming that the reactions are independent, the probability that none of the six patients has an injection site reaction is:=[tex](0.88)^{6}[/tex]= 0.464

Hence the probability that at least one of the six patients has an injection-site reaction is:

1-0.464 =0.536

Therefore, the probability that at least one of the six patients has an injection site reaction is 0.536 or 53.6%.

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Answer:

18x^5 - 7x^2y - 2xy^2 + 17y^4

Step-by-step explanation:

Standard form means that the variables are in alphabetical order, and the degree of the variable closer to the start of the alphabet decreases while the degree of the variable closer to the end of the alphabet increases.

No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.

The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.

However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.

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The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12

To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.

The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.

Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes

Sum of 11: (5, 6), (6, 5) = 2 outcomes

Sum of 12: (6, 6) = 1 outcome

Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.

Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.

To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:

Sum of 2: (1, 1) = 1 outcome

Sum of 3: (1, 2), (2, 1) = 2 outcomes

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

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A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.

To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of  the sample mean, sample standard deviation, as well as sample size.

The null hypothesis =  750 grams,

The  alternative hypothesis=  less than 750 grams.

so we need to calculate the test as:

t = (746 - 750) / (8 / √(20)) = -2.236

Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so  n-1 =19)

When you a t-distribution table, the critical t-value to be -1.734.

Therefore, know that -2.236 < (less than) -1.734,  so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.

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Answer:

Step-by-step explanation:

Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:

Ending balance = Beginning balance * (1 + r)

where r is the annual interest rate as a decimal.

The scale factor of Winston's drawing of the elementary school is 0.008. The scale factor represents the relationship between the measurements on the drawing and the corresponding actual measurements.

To find the scale factor of Winston's drawing that has a scale of 8 centimeters = 10 meters,

So, the scale factor of Winston's drawing of the elementary school is 0.008.

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The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.

When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:

1.9891 x 10^30

To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.

Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.

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The probability is less than 0.489 is approximately 0.8980 or 89.80%  that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489

First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:

Mean = p = 0.48

Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071

Next, we need to standardize the sample proportion using the formula:

z = (sample proportion - population proportion) / standard deviation

z = (0.489 - 0.48) / 0.071 = 1.27

Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.

Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.

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Ali's Gulf club account will have a future value of BD 101.93 at the end of the term on October 7. The calculation was done using the formula for future value of an annuity with monthly payments, interest rate of 8% per year, and a term of 2.9 months.

We can first calculate the number of months from July 11 to October 7: 2 months and 27 days (or approximately 2.9 months).

Then, we can use the formula for future value of a present sum with simple interest

FV = P(1 + rt)

where FV is the future value, P is the present sum (in this case, BD 100), r is the annual interest rate (8% = 0.08), and t is the time in years (2.9/12 = 0.2417 years).

Substituting the values, we get

FV = 100(1 + 0.08*0.2417)

= 100(1.01934)

= BD 101.93

Therefore, the future value of Ali's golf club account is BD 101.93.

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847 cubic feet of cement will be needed for the job.

To find the amount of cement needed for the cistern, we need to calculate the difference in volume between the outer and inner cylinders.

First, let's find the volume of the outer cylinder:
Outer radius (R) = (Inner diameter + 2 * Wall thickness) / 2 = (10 + 2 * 1) / 2 = 6 feet
Outer height (H) = 20 feet
Outer cylinder volume (V1) = π * R^2 * H = 3.14 * 6^2 * 20 = 3.14 * 36 * 20 ≈ 2260.96 cubic feet

Next, let's find the volume of the inner cylinder:
Inner radius (r) = Inner diameter / 2 = 10 / 2 = 5 feet
Inner height (h) = Outer height - 2 * Wall thickness = 20 - 2 * 1 = 18 feet
Inner cylinder volume (V2) = π * r^2 * h = 3.14 * 5^2 * 18 = 3.14 * 25 * 18 ≈ 1413.72 cubic feet

Finally, subtract the inner cylinder volume from the outer cylinder volume to find the amount of cement needed:
Cement volume = V1 - V2 ≈ 2260.96 - 1413.72 ≈ 847.24 cubic feet

To the nearest cubic foot, approximately 847 cubic feet of cement will be needed for the job.

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Therefore, the volume of the cone is approximately 800π cubic centimeters, or approximately 2512.44 cubic centimeters when rounded to two decimal places.

Volume is a measure of the amount of space occupied by a three-dimensional object or a substance. The volume of a solid object can be determined by measuring its dimensions, such as its length, width, and height, and applying an appropriate mathematical formula depending on its shape.

Here,

The volume of a cone can be calculated using the formula:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is a constant equal to approximately 3.14. In this case, we are given the radius of the cone as 10 cm and the slant height as 26 cm. We can use the Pythagorean theorem to find the height of the cone:

h² = (slant height)² - (radius)²

h² = 26² - 10²

h² = 576

h = √576

h = 24

Now that we have the height of the cone, we can use the formula for the volume of a cone:

V = (1/3)πr²h

V = (1/3)π(10²)(24)

V = (1/3)π(100)(24)

V = (1/3)(2400π)

V = 800π

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Answer:

Volumeof a cone=2,723.8095238095

Step-by-step explanation:

Slant height = 26cm

radius = 10cm

volume of a cone = ‽

The volume of cone =

[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]

[tex]v = \frac{1}{3} \times \frac{22}{7} \times 10 \times 10 \times 26 \\ \frac{1}{3} \times \frac{22}{7} \times 100 \times 26 \\ = \frac{22}{21} \times 2600 \\ = \frac{57200}{21} \\ = 2,723.8095238095cm[/tex]

Answer:

Step-by-step explanation:

To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.

Vertical asymptote:

The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.

x^2 - 20 = 0

x^2 = 20

x = ±√20

The vertical asymptotes are x = √20 and x = -√20.

Horizontal asymptote:

To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is

y = 0.

X-intercepts and y-intercept:

To find the x-intercepts, we need to set the numerator equal to zero.

5x + 20 = 0

x = -4

Therefore, the x-intercept is (-4,0).

To find the y-intercept, we need to set x equal to zero.

f(0) = (5(0) + 20) / (0^2 - 20)

f(0) = -1

Therefore, the y-intercept is (0,-1).

Hole:

We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.

To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:

Vertical asymptotes at x = √20 and x = -√20

Horizontal asymptote at y = 0

X-intercept at (-4,0)

Y-intercept at (0,-1)

Hole at x = -4

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The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.

Let's denote the length of the bookmark as L and the width as W.

The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.

From the given information, we have two equations:

Equation 1: A = 150 square centimeters

Equation 2: P = 62 centimeters

Substituting the formulas for area and perimeter, we get:

Equation 1: L * W = 150

Equation 2: 2L + 2W = 62

To solve these equations, we can use substitution or elimination. Let's solve by substitution:

From Equation 1, we can express one variable in terms of the other:

L = 150 / W

Substituting this into Equation 2:

2(150 / W) + 2W = 62

300 / W + 2W = 62

300 + 2W^2 = 62W

2W^2 - 62W + 300 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

[tex]2W^2 - 62W + 300 = 0[/tex]

(W - 10)(2W - 30) = 0

This gives us two possible solutions:

W - 10 = 0 -> W = 10

2W - 30 = 0 -> W = 15

Since the width cannot be longer than the length, we discard the solution W = 15.

So, the width of the bookmark is W = 10 centimeters.

Now, we can substitute this value into Equation 1 to find the length:

L * 10 = 150

L = 150 / 10

L = 15

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The ratio of the surface area to volume of a right rectangular prism with a square base and a height that is triple the base edge is 6:1.

Let x be the length of one side of the square base of the prism. Then the height of the prism is 3x. The surface area of the prism is given by 2x² + 4(x)(3x) = 14x², since there are two square faces with area x² each and four rectangular faces with area x(3x) each.

The volume of the prism is x²(3x) = 3x³. Therefore, the ratio of surface area to volume is (14x²)/(3x³) = 14/3x = 4.67/x. Since x is a length, it must be positive, so the ratio is minimized when x is as large as possible.

Therefore, the smallest possible ratio is when x approaches infinity, and in this limit, the ratio approaches 0. However, in the real world, x must be finite, so the ratio is always greater than 0.

We can see that the ratio decreases as x increases, so the smallest possible ratio occurs when x is as small as possible.

The smallest possible positive value of x is 0.000000...01, which is very close to 0 but not equal to 0. Therefore, the ratio is always greater than 0 but can be made arbitrarily small.

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The standard deviation of the sample mean differences is; 0.6898

From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45

From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60

Formula for standard deviation of the sample mean differences is;

σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]

Thus;

σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]

σm₁ - σm₂ = 0.6898

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Answer: 2.704 2.74 4.2 4.27 4.72

Step-by-step explanation:

Answer:

A = 4(16) + (1/2)π(8^2) = 64 + 32π cm^2

= 164.5 cm^2

To estimate I = S." (+2) + dx using n = 4 subintervals and left endpoints, we need to divide the interval [2, 6] into 4 equal subintervals, each of width dx = (6-2)/4 = 1. Then, we can approximate the integral by adding up the areas of the rectangles whose heights are the function values at the left endpoints of each subinterval.

(a) Using left endpoints, the approximation of the integral is:

I ≈ sum from i=0 to 3 of f(2+i*dx)*dx
 = f(2)*dx + f(3)*dx + f(4)*dx + f(5)*dx
 = f(2)*1 + f(3)*1 + f(4)*1 + f(5)*1

(b) Using right endpoints, the approximation of the integral is:

I ≈ sum from i=1 to 4 of f(2+i*dx)*dx
 = f(3)*dx + f(4)*dx + f(5)*dx + f(6)*dx
 = f(3)*1 + f(4)*1 + f(5)*1 + f(6)*1

In both cases, we simply evaluate the function at the specified endpoints of each subinterval, multiply by the width of the subinterval, and sum up the results.

Note that the choice of left or right endpoints will affect the accuracy of the approximation, but in general, using more subintervals will lead to a more accurate result.
(a) Left Endpoints:

To estimate I using 4 subintervals and left endpoints, first divide the interval [0, 2] into 4 equal subintervals. Each subinterval has width Δx = (2 - 0) / 4 = 0.5. The left endpoints of these subintervals are x = 0, 0.5, 1, and 1.5. The integral estimate is:

I ≈ Δx[f(0) + f(0.5) + f(1) + f(1.5)]

Evaluate the function at these points, and then multiply the sum by Δx.

(b) Right Endpoints:

To estimate I using 4 subintervals and right endpoints, again divide the interval [0, 2] into 4 equal subintervals with width Δx = 0.5. The right endpoints of these subintervals are x = 0.5, 1, 1.5, and 2. The integral estimate is:

I ≈ Δx[f(0.5) + f(1) + f(1.5) + f(2)]

Evaluate the function at these points, and then multiply the sum by Δx.

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Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.

Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.

The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.

Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.

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The missing value in the frequency table from the electronics manufacturers would be 150.

The class interval of the battery life is in fives which means that between 25 and 30, the shaded region on the histogram would represent 28 ≤ x < 30.

Looking at the y axis, we can tell that the class interval is 50 thanks to the 120 achieved by 15 ≤ x < 20. This then means that as 28 ≤ x < 30 is sitting on the third y interval, we know that it has a value of 150.

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Answer:

76

Step-by-step explanation:

If the mean of 28 numbers is 18 then the sum of those numbers=28×18=504

if one number is added then 29×20=580

the new number therefore=580-504=76

Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.

The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:

2/3 = 8/12

1/4 = 3/12

Now we can add these two fractions:

8/12 + 3/12 = 11/12

So the total amount of sugar required to make the banana pudding is 11/12 of a cup.

The mean score of all the students together is 83.1 (rounded to one decimal place).

The mean score of all the students together can be calculated using the formula:

(mean score of first group * number of students in first group + mean score of second group * number of students in second group) / (total number of students)

Substituting the values, we get:

(86.9 * 37 + 74.4 * 22) / (37 + 22)

= (3215.3 + 1636.8) / 59

= 4852.1 / 59

= 82.3

Therefore, the mean score of all the students together is 82.3, rounded to one decimal place.

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