a right conical tank with the point oriented down, a height of 14 feet, and a radius of 6 feet has sprung a leak. how fast does the depth of water change when the water is 2 feet high if the cone leaks water at a rate of 13 cubic feet per minute?

The measures of the angles are m∠1 = 74° and m∠2 = 74°.

Given,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

We need to find the measure of these angles.

The straight line angle is 180 degrees.

If the angle is split the sum must be equal to 180 degrees.

We have,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

The figure is at a straight-line angle.

So we have,

[tex]m\angle1 + m\angle2 = 180^\circ[/tex]

[tex]2x^\circ + (x + 69)^\circ = 180[/tex]

[tex]2x + x + 69 = 180[/tex]

[tex]3x + 69 = 180[/tex]

[tex]3x = 180 - 69[/tex]

[tex]3x = 111[/tex]

[tex]x = 111\div3[/tex]

[tex]x = 37[/tex]

Now,

[tex]- m\angle1[/tex]

[tex]= 2x[/tex]

[tex]=2 \times 37[/tex]

[tex]= 74[/tex]

[tex]- m\angle2[/tex]

[tex]= x + 37[/tex]

[tex]= 37 + 37[/tex]

[tex]= 74[/tex]

Thus the measures of the angles are m∠1 = 74° and m∠2 = 74°.

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The probability that 4 women have a mean weight below 108 lb is approximately 0.008.

The probability that 58 women have a mean weight below 108 lb is zero.

The probability is determined using the central limit theorem.

(b) If 4 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(4)

standard deviation = 14.5 lb.

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 14.5

z = -2.41

Using a standard normal distribution table or calculator, the probability of z being less than -2.41 is approximately 0.008.

(c) If 58 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(58)

standard deviation = 3.81 lb

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 3.81 ≈ -9.21

Using a standard normal distribution table or calculator, the probability of z being less than -9.21 is extremely small, practically zero.

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The car that cost $[tex]$35750[/tex] in [tex]2014[/tex] will be valued $[tex]14,919.48[/tex] in [tex]2022[/tex] if the annual depreciation rate is [tex]10.5%[/tex]%

The depreciation rate is the percentage at which an object depreciates over its anticipated useful life.

It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expenditure over the course of the asset's useful life.

Given.

Value for the [tex]1[/tex]st Year ([tex]2014-2015[/tex]) is $ [tex]$35,750[/tex] -$([tex]350,750*10.5[/tex]%) =

$[tex]31,981.25[/tex]

Value for [tex]2 years[/tex] [tex](2015-2016)[/tex] =$[tex]31,981.25-([/tex]$[tex]31,981.25*10.5[/tex]%) =

$[tex]28,604.41[/tex]

Value for [tex]8 years[/tex] ($[tex]16550.09[/tex] -$[tex]16550.09*10.5[/tex]%) = $[tex]14919.48[/tex]

Therefore the car that cost $[tex]$35750[/tex] in [tex]2014[/tex] will be valued $[tex]14,919.48[/tex] in [tex]2022[/tex] if the annual depreciation rate is [tex]10.5%[/tex]%

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Answer:

1/10

Step-by-step explanation:

Just 6 and 16, so there are 2/20 numbers simplified is 1/10.

:)

Therefore , the solution of the given problem of angles comes out to be lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4.

Both the largest and the tiniest walls of a skew are determined by an intersection of the lines that connect that make up its ends. A junction could possibly bring two routes together. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

The abbreviated formula for f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x) is as follows:

f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x)

f(x) = [(4x³ - 12x) + (9x² - 3)] / (x(x² - x - 6))

f(x) = [4x(x² - 3) + 3(3x² - 1)] / [x(x - 3)(x + 2)]

f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]

Consequently, the abbreviated form is:

f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]

Direct substitution can be used to find the limit of the equation g(x) = (x2 - 4)/(x - 2) as x approaches 2, which results in the undetermined form 0/0. In order to take the derivative of the numerator and denominator with regard to x, we can apply L'Hopital's rule as follows:

g(x) = (x² - 4)/(x - 2)

g'(x) = [(2x) * (x - 2) - (x² - 4) * 1] / (x - 2)²

g'(2) = 4

As x gets closer to 2, the maximum of g(x) is as follows:

lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4

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Answer:

Step-by-step explanation:

a. -3 < x <= 4

x = -2, -1, 0, 1, 2, 3, 4.

b. -3 < x < 4

x = -2, -1, 0, 1, 2, 3.

Answer: By using the slope

Step-by-step explanation:

Brianliest pls:)

Leslie's dad is 38.5 kg heavier than the combined weight of Leslie and her brother.

To solve the problem, we first need to find the total weight of the two children together, and then subtract that from the weight of Leslie's dad:

Total weight of the two children = Leslie's weight + her brother's weight

Total weight of the two children = 12.4 kg + 16.7 kg

Total weight of the two children = 29.1 kg

Weight difference between Leslie's dad and the two children = Leslie's dad's weight - Total weight of the two children

Weight difference between Leslie's dad and the two children = 67.6 kg - 29.1 kg

Weight difference between Leslie's dad and the two children = 38.5 kg

Therefore, Leslie's dad is 38.5 kg heavier than the two children combined.

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Answer:

Step-by-step explanation:

the sum of the internal angles in any triangle is 180°, we have a 60° angle and a right angle (90°). We remove the known angles (90° and 60°) from 180° and we have 30° which is the value of the unknown angle (L).

Angle L = 180 - 90 - 60 =

30°

To find the measure of angle QZX, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle ZWQ:

Angle WZQ + Angle WZX = 180 degrees

92 degrees + 63 degrees = 155 degrees

Therefore, angle ZWQ has a measure of 155 degrees.

Now, we can find the measure of angle QZX:

Angle ZWQ + Angle QZX = 180 degrees

155 degrees + Angle QZX = 180 degrees

Subtracting 155 from both sides, we get:

Angle QZX = 25 degrees

Therefore, the measure of angle QZX is 25 degrees.

The data distribution is skewed to the right. This is because the bars are clustered towards the left side of the histogram and taper off towards the right side.

The histogram of distances students live from school provided in the question shows that the majority of students in Tuan's homeroom live within a short distance of the school, with only a few students living farther away. The distribution is skewed to the right because the bars are clustered towards the left side of the histogram and taper off towards the right side. This indicates that there are fewer students who live farther away from school. A skewed distribution means that the data is not evenly distributed and tends to cluster towards one end. In this case, the distribution is skewed to the right because there are fewer students living farther away from school.

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Complete question is in the image attached below

Answer:

B. skewed.

Step-by-step explanation:

and then the next part is

1

hope this helps :)

Answer:

SOHCAHTOA

Step-by-step explanation:

Sine=Opposite/hypotenuse

Cosine= Adjacent/hypotenuse

Tangent: Opposite/adjacent

You can use SOHCAHTOA to memorize all the basic functions.

SOH for sine

CAH for cosine

TOA for tangent    

Answer:

Sin= opp/hyp

Cos=adj/hyp

Tan=opp/adj

The area of this triangle was 18 square units.

Let's use the given information to set up some equations. We are told that the sum of the lengths of the three sides of the triangle is 18. Let's call the lengths of the two shorter sides a and b, and the length of the hypotenuse c. Then, we have a + b + c = 18.

We are also told that the sum of the squares of the lengths of the three sides is 128. Using the Pythagorean theorem, we know that a² + b² = c². So, we can rewrite this equation as a² + b² + c² = 128.

Now we have two equations with three variables. We need to find a way to eliminate one of the variables. We can do this by using the first equation to solve for one of the variables in terms of the other two. Let's solve for c:

c = 18 - a - b

Now we can substitute this expression for c into the second equation:

a² + b² + (18 - a - b)² = 128

Expanding and simplifying, we get:

2a² + 2b² - 36a - 36b + 144 = 0

Dividing by 2, we get:

a² + b² - 18a - 18b + 72 = 0

We can rewrite this equation as:

(a² - 18a + 81) + (b² - 18b + 81) = 38

Completing the square, we get:

(a - 9)² + (b - 9)² = 5

So we have:

(a - 9)² = 1

(b - 9)² = 1

This gives us four possible solutions:

a = 8, b = 10, c = 18 - a - b = 0 (not possible)

a = 10, b = 8, c = 18 - a - b = 0 (not possible)

a = 9, b = 9, c = 0 (not possible)

a = b = c = 6√2

The only valid solution is the last one, where all three sides have the same length of 6√2. To find the area of the triangle, we can use the formula:

Area = (base x height)/2

Since this is a right triangle, one of the sides is the base and the other is the height. So we can choose any two sides to use as the base and height. Let's choose a and b:

Area = (a x b)/2

Substituting the values a = 6√2 and b = 6√2, we get:

Area = (6√2 x 6√2)/2

Area = 36/2

Area = 18

Therefore, the area of the right triangle with sides of length 6√2 is 18 square units.

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Step-by-step explanation:

L X W X D = volume = 25 X 10 X 8 = 2000 cm^3

Answer:

2,000 cubic units are the volume of the fish tank

Step-by-step explanation:

The formula of volume is length x width x height

So to find the volume just multiply 25 x 10 x 8

To get the volume of the fish tank which is 2,000 cubic units

Answer:

BC ≈ 17.8 cm

Step-by-step explanation:

Answer:yes

Step-by-step explanation: i took the test

The points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

The coordinate plane is a two-dimensional space formed by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin. Each point in the plane is identified by a pair of numbers called its coordinates, where the first number represents its position along the x-axis and the second number represents its position along the y-axis. Coordinates are typically written as (x, y), with the x-coordinate listed first and the y-coordinate listed second. The coordinate plane is commonly used in mathematics to graph and analyze equations, functions, and geometric shapes.

Let x be the number of bags of popcorn and y be the number of bags of cotton candy. Then the cost constraint is:

3x + 7y ≤ 56

We also have the constraint that Chris needs at least 7 bags of popcorn:

x ≥ 7

To graph these constraints, we can rewrite them in slope-intercept form:

y ≤ (-3/7)x + 8

x ≥ 7

The first inequality has a slope of -3/7 and a y-intercept of 8, and the second inequality is a vertical line at x = 7.

To plot the points that are part of the solution set, we can simply plug them into the two inequalities and see if they are true. The points that satisfy both inequalities are part of the solution set.

(3, 7) satisfies both inequalities:

7 ≤ (-3/7)(3) + 8

3 ≥ 7

(2, 2) does not satisfy the first inequality:

2(7) > 3(2) + 7

(8, 1) satisfies both inequalities:

1 ≤ (-3/7)(8) + 8

8 ≥ 7

(10, 2) satisfies both inequalities:

2 ≤ (-3/7)(10) + 8

10 ≥ 7

(5, 5) does not satisfy the first inequality:

5(7) > 3(5) + 7

Therefore, the points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

To graph these on the coordinate plane, we can plot the vertical line x=7 and the line y= (-3/7)x + 8, and then shade in the feasible region below the line and to the right of the vertical line.

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Yes, the variable is statistically significant if the t-statistic is 2.54.

Follow these steps:

1. Identify the degrees of freedom (df) for your sample. The df is typically calculated as the sample size minus 1 (n-1).

2. Choose a significance level (α), commonly used values are 0.05 or 0.01.

3. Consult a t-distribution table using the chosen α and degrees of freedom to find the critical t-value.

4. Compare the t-statistic (2.54) to the critical t-value.

If the t-statistic (2.54) is greater than the critical t-value, the variable is statistically significant at the chosen significance level.

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Answer: 0.5 miles

Step-by-step explanation:

= 2 miles/4

= 0.5 miles

The newer energy star washing machines uses less water compare to older models is equals to 25%.

Newer Energy Star washing machines use approximately 25% less water than older models.

Energy Star-certified washing machines are designed to use less water.

And energy while still providing the same or better washing performance compared to traditional models.

According to Energy Star, certified models use about 25% less energy and 33% less water than non-certified models.

Therefore, the percent of less water used by newer energy star washing machine than older modals is equals to 25%.

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a) Sienna's page is now [tex]\frac{1}{3}[/tex] full after giving [tex]\frac{1}{3}[/tex] of her cards to Daniel.

b) Daniel can fit all the cards on one page in his binder since his binder page can hold up to 30 cards and he has a total of 70 cards after receiving [tex]\frac{1}{3}[/tex] of Sienna's cards.

a) Sienna's page was [tex]\frac{6}{9}[/tex] full, which can be simplified to [tex]\frac{2}{3}[/tex]. We know that she gave [tex]\frac{1}{3}[/tex] of her cards to Daniel, so the fraction of cards she has left is:

[tex]\frac{2}{3} - \frac{1}{3} =\frac{1}{3}[/tex]

Therefore, Sienna's last page is now [tex]\frac{1}{3}[/tex] full.

b) To determine whether Daniel can fit all the cards on one page in his binder, we need to know how many cards he has and how many cards his binder pages can hold.

Let's assume that Daniel's binder page can hold 30 cards, and he has 2 full pages plus the [tex]\frac{1}{3}[/tex] of Sienna's cards that she gave him, which is approximately 10 cards.

Therefore, he has a total of 2 x 30 + 10 = 70 cards.

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The complete question is:

Sienna also collects baseball cards in a binder just like Daniel's. Her page was 6/9 full, but she gave ⅓ of those cards to Daniel.

a What fraction of Sienna's last page is full now? Use numbers, labeled sket or words to model and solve the problem.

b Can Daniel fit the cards from his first page, his second page, and the cards Sienna gave him all on one page in his binder? Use labeled sketches, numbers or words to show your thinking.

Answer:

domain (-4,8,9,1)

range. (4,-1,-9,2,8)

Step-by-step explanation:

the percent increase from running 19 miles in the first week to 25 miles in the second week is 31.58%. This means that Mackenzie increased her mileage by 31.58% from the first week to the second week.

To calculate the percent increase from running 19 miles in the first week to 25 miles in the second week, we first need to find the difference between the two numbers.

The difference is calculated as follows:

25 - 19 = 6

So, the difference between the two weeks is 6 miles.

To find the percent increase, we need to divide the difference by the original value and then multiply by 100.

The formula for percent increase is:

(percent increase) = [(new value - old value) / old value] x 100%

Using this formula, we can find the percent increase in Mackenzie's training as follows:

(percent increase) = [(25 - 19) / 19] x 100%

(percent increase) = (6 / 19) x 100%

(percent increase) = 0.3158 x 100%

(percent increase) = 31.58%

So, the percent increase from running 19 miles in the first week to 25 miles in the second week is 31.58%. This means that Mackenzie increased her mileage by 31.58% from the first week to the second week.

It's important to note that a large percent increase in mileage can increase the risk of injury, so it's important to gradually increase mileage over time to prevent injury and ensure a successful training program.

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Step-by-step explanation:

I will assume the candle burns 1 inch per hour  ( you left that out of your post)

Length of candle remaining = 9 - 1 x      where 'x' = hours

     amount of candle remaining =   0   =  9 - x

                                           x = 9 hrs  

If it is NOT one inch per hour ....put that number where '1' is and solve for x

For each bag, BALLIO  would have needed 2.25 (or 2 1/4) yards of fabric.

"A way to find a multiple unit value from a single unit value as well as the reverse."

In every case, we first count the unit or amount value before figuring out the more or less amount value.

This method is referred to as a unified procedure for this reason.

By dividing the set value by the quantity of sets, one can find numerous set values.

By dividing several set values by the total number of sets, one can determine a set value.

According to our question-

9 bags you are making

must be the same

divide the nine bags by the four yards

2.25 yards per bag

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We can start by finding how much money Anastasia saves each week.

The difference between her starting balance and ending balance after 11 weeks is:

$665 - $225 = $440

So, over 11 weeks, Anastasia has saved a total of $440.

To find how much money she saves each week, we can divide the total savings by the number of weeks:

$440 ÷ 11 weeks = $40 per week

This means that Anastasia saves $40 each week.

To find out how much money she will have in her account after 24 weeks, we can multiply the amount she saves each week by the number of weeks:

$40 per week × 24 weeks = $960

Therefore, after 24 weeks, Anastasia will have $960 in her savings account.

Therefore, P(A|BC) = 4/7.

a. P(A|B)

We can use Bayes' theorem to calculate P(A|B):

P(A|B) = P(A ∩ B) / P(B)

We are given that P(A ∩ B) = 0.2 and P(B) = 0.3, so:

P(A|B) = 0.2 / 0.3 = 2/3

Therefore, P(A|B) = 2/3.

b. P(AC ∩ BC)

Using the complement rule, we can rewrite AC ∩ BC as (A ∪ B)C:

AC ∩ BC = (A ∪ B)C

Using De Morgan's laws, we can further rewrite this as:

AC ∩ BC = A'C ∩ B'C

Now, we can use the distributive property to write:

A'C ∩ B'C = (A ∪ B)'

Using the complement rule again, we have:

A'C ∩ B'C = 1 - P(A ∪ B)

We can use the inclusion-exclusion principle to calculate P(A ∪ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We are given that P(A) = 0.6, P(B) = 0.3, and P(A ∩ B) = 0.2, so:

P(A ∪ B) = 0.6 + 0.3 - 0.2 = 0.7

Therefore:

A'C ∩ B'C = 1 - 0.7 = 0.3

Hence, P(AC ∩ BC) = 0.3.

c. P(A ∩ BC)

Using the complement rule, we can write BC as 1 - B:

A ∩ BC = A ∩ (1 - B)

We can distribute the intersection over the complement:

A ∩ BC = A - (A ∩ B)

We are given that P(A) = 0.6 and P(A ∩ B) = 0.2, so:

A ∩ BC = 0.6 - 0.2 = 0.4

Therefore, P(A ∩ BC) = 0.4.

d. P(A|BC)

We can use Bayes' theorem again to calculate P(A|BC):

P(A|BC) = P(A ∩ BC) / P(BC)

Using the complement rule, we can write BC as 1 - B:

P(A|BC) = P(A ∩ (1 - B)) / P(1 - B)

We can distribute the intersection over the complement:

P(A|BC) = P(A) - P(A ∩ B) / P(1 - B)

We are given that P(A) = 0.6, P(A ∩ B) = 0.2, and P(B) = 0.3, so:

P(A|BC) = 0.6 - 0.2 / (1 - 0.3) = 0.4 / 0.7

Therefore, P(A|BC) = 4/7.

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The numbers that would make the inequalities given true are 3 (first inequality) and 5 (second inequality).

To begin, an inequality is a mathematical expression that uses symbols such as < less than or > greater than. In the case presented, we need to find two numbers.

Based on this, some possible numbers are:

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