solve for the given variable
3(m + 7) =

The volume of the prism not occupied by the sphere is 704.69 cubic in.

Given that, the radius of the sphere=4 in. and the dimensions of a rectangular prism length=9 in. width=8 in. and height 10 in.

We need to find what is the volume of the prism not occupied by the sphere.

The formula to find the volume of the rectangular prism is Volume=Length×Width×Height.

The formula to find the volume of the sphere is Volume=4/3 πr³.

Now, the volume of the rectangular prism=9×8×10=720 cubic in.

The volume of the sphere=4/3×3.14×4³

V=15.31 cubic in.

Then, the volume of the prism not occupied by the sphere=The volume of the rectangular prism-The volume of the sphere

The volume of prism=720-15.31=704.69 cubic in.

Therefore, the volume of the prism not occupied by the sphere is 704.69 cubic in.

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The measure of the indicated angle in each triangle is ∠U=80° and ∠Q =93°

The measure of each triangle's specified angle.

Comprehensive explanation:

Calculate the indicated angle's measurement.

Given: The additional two triangle angles.

Solution:

We are aware that a triangle's three angles add up to 180 degrees.

So,

The measure of the indicated angle in each triangle.​

1st TRIANGLE

∠U+∠V+∠T =180°

∠U+63°37° =180°

∠U= 180°-100°

∠U=80°

2ND TRIANGLE

∠A+∠B+∠C=180°

46°+90°+∠C =180°

∠C=44°

The measure of the indicated angle in each triangle.​

3rd TRIANGLE

∠R+∠P+∠Q= 180°

36°+51°+∠Q =180°

∠Q =93°

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The required answer is she needs to number each plant from 1 to 60 and randomly select  10 plant. The correct option is C

Probability can be defined as a number that reflects the chance or likelihood that a particular event will occur.

As she has 60 seeds, firstly she must number each plant in order or randomly see the height, After that he can peek at random 10 plants to test the fertilizer.

The required answer is she needs to number each plant from 1 to 60 and randomly select 10 plant.

A greenhouse owner wants to test. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants and decides to use a random number table to select a simple random sample. Which of the following correctly labels the population of violets Is to be determined.

The correct option is C

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The correct conversion factors to indicate the number of feet in one mile is: 1 mi = 5280 ft.

To convert miles to feet, we must use the equality: 1 mi = 5280 ft.

Using the table of equalities, we can see that 1 mi = 5280 ft, so the correct conversion factor to indicate the number of feet in one mile is 1 mi = 5280 ft.

To convert miles to feet, we use the conversion factor of 1 mile being equal to 5280 feet. This means that for every 1 mile, there are 5280 feet. To convert a specific number of miles to feet, we multiply the number of miles by the conversion factor of 5280 feet/mile. For example, if we want to convert 2 miles to feet, we multiply 2 by 5280 to get 10560 feet. Hence, 2 miles is equal to 10560 feet. This conversion factor can be used to convert any number of miles to feet, as long as we use it consistently and accurately.

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Answer:

y = 2x

Step-by-step explanation:

We know

They earn $2 for each cup of lemonade they sell. So, the equation is

y = 2x

The dependent variable is the number of games and the independent variable is the number of months.

We know that Quincy was given 3 video games for his new game system and every month he saves enough to get 2 more video games.

Then the two variables are the number of months and the number of games.

We know that he starts with 3 games and each month he adds 2 more, then we can write the relation:

y = 3 + 2*x

Where y is the number of games and x the number of months.

Then the independent variable is the number of months, and the dependent variable (which depends on the other one) is the number of games.

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The domain of the function f(x) =  {- 3, - 1, 0 2, 4}.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

Given, The graph represents a relation where x represents the independent variable and y represents the dependent variable.

The ordered pairs are given by, (- 3, 4), (- 1, 1), (0, - 2), (2, 0), and (4, - 1).

We know the domain of the function are all the x coordinates.

Therefore, The domain of the function f(x) = {- 3, - 1, 0 2, 4}.

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The total surface area of the triangular pyramid is 170.4 inches².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

A triangular pyramid has a triangular base and three triangular faces.

Given that, base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in².

Area of the base = 62.4 inches²

Slant height = 6 inches

Length of edge of each of the three triangular faces = 12 inches

Area of a triangular face = [tex]\frac{1}{2}[/tex] × 12 × 6 = 36 inches²

Area of three triangular faces = 3 × 36 inches² = 108 inches²

Total surface area = 108 inches² + 62.4 inches² = 170.4 inches²

Hence 170.4 inches² is the total surface area of the pyramid.

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Poisson distribution is a discrete probability distribution that describes the number of events that occur randomly in a fixed interval of time or space.

a. The probability that the number of drivers will be at most 10 is calculated as the cumulative distribution function of Poisson distribution at 10, which is

 [tex]P(X \leq 10) = \sum_{i}=0^{10 }e^{-\mu} *\frac{\mu^{i }}{i!}[/tex]

where i ranges from 0 to 10.

b. The probability that the number of drivers will exceed 20 is calculated as

[tex]P(X > 20) = 1 - P(X \leq 20) = 1 - \sum_i=0^{20} e^{(-\mu)} *\frac{ \mu^i }{i!}[/tex]

where i ranges from 0 to 20.

c. The probability that the number of drivers will be between 10 and 20, inclusive is calculated as

[tex]P(10 \leq X \leq 20) = \sum_i=10^{20} e^{(-\mu)} *\frac{\mu^i}{i! }[/tex]

where i ranges from 10 to 20. The probability that the number of drivers will be strictly between 10 and 20 is calculated as

[tex]P(10 < X < 20) = \sum_i=10^{19} e^{(-\mu)} * \frac{\mu^i }{i!}[/tex]

where i range from 10 to 19.

d. The standard deviation of Poisson distribution with parameter μ = 20 is [tex]\sqrt{(\mu)} = \sqrt{(20)} = 2\sqrt5[/tex]

The probability that the number of drivers will be within 2 standard deviations of the mean value is calculated as

[tex]P(\mu - 2 * \sqrt{(\mu)}\leq X\leq \mu + 2 * \sqrt{(\mu)}) = \sum_i=16^{24} e^{(-\mu)} * \frac{\mu^i}{i!}[/tex]

where i ranges from 16 to 24.

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The complete question is :

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ =20 (suggested in the article “Dynamic Ride Sharing: Theory and Practice,” J. of Transp. Engr., 1997: 308–312). What is the probability that the number of drivers will

a. Be at most 10?

b. Exceed 20?

c. Be between 10 and 20, inclusive? Be strictly between 10 and 20?

d. Be within 2 standard deviations of the mean value?

A joule is one unit of energy, while a kilojoule is 1000 joules.

KJ x 1,000 = J.

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limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.

We can use the limit laws of product to solve this limit.

limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x)

= 15 * (-1)

= -15

To solve this limit, we can use the limit laws of product. By the limit laws of product, the limit of a product is equal to the product of two limits. Therefore, limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.

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At time t=0 the signal value is 10, then it decreases to 3, increases to 25, decreases to 4, increases to 30, decreases to 2 and then increases to 17.

At time t=0 the signal value is 10. This is the starting point for monitoring the signal every second. After one second, the signal value decreases to 3. After another second, the signal value increases to 25. After another second, the signal value decreases to 4. After another second, the signal value increases to 30. After another second, the signal value decreases to 2. Finally, after the last second, the signal value increases to 17. As the signal is monitored every second, it is possible to track its changes over time. This example signal had some fluctuation, with both increases and decreases in the value. It started at 10, decreased to 3, then increased to 25, decreased to 4, increased to 30, decreased to 2, and then increased to 17. This example shows how a signal can fluctuate over time, and how its value can change with each second that passes.

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Answer:

C

Step-by-step explanation:

15mpg

$1.09/gallon

10.5 per day * 22 days = 231 miles

will need 231/15 gallons of gas = 15.4gallons

cost = 15.4*1.09 = $16.79

The investment in 2% rate of interest was $2800 and the investment in 3% rate of interest was $3200.

Let the amount invested in 2% interest rate be x. So, the remaining invested amount = (6000 - x). The simple interest will be calculated by the formula -

S.I. = P×R×T/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.

Also, the sum of interest in each is $152. So, finding the individual interest first.

SI = x × 2 × 1/100

SI = 2x/100

SI = (6000 - x) × 3 × 1/100

SI = (18000 - 3x)/100

Finding the value of x.

2x/100 + (18000 - 3x)/100 = 152

Multiplying the equation with 100

2x + 18000 - 3x = 15200

3x - 2x = 18000 - 15200

x = 2800

Investment in 3% rate = 6000 - 2800

Investment in 3% rate = $3200

Thus, the investment was $2800 and $3200.

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The graph shows the discontinuity of the function at x = -1 and x = 1. Therefore, the values of x at which the function is not continuous are -1 and 1.

The graph shows that at x = -1 and x = 1, the graph has a sharp jump in the value of the function. This means that the function is not continuous at those points, and thus the values of x at which the function is not continuous are -1 and 1. The graph represents a mathematical function, and the concept of continuity is crucial in mathematical analysis. A function is considered continuous at a specific point if the value of the function at that point exists and the limit of the function as the input approaches that point is equal to the value of the function at that point. In this particular graph, the function experiences a sharp increase or decrease in its value at the points x = -1 and x = 1. This sudden change in the function's value indicates that the function is not continuous at these points, meaning that its value does not approach a single limiting value as the input approaches these points. Thus, the points -1 and 1 are the values of x at which the function is not continuous.

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The following values, when rounded to one significant figure in accordance with the stated statement, are 3*10⁴, 3, and 1*10⁴ m.

True figures are the number of digits that increase a value's accuracy, often a measurement. Starting with the first semi-digit, we count actual numbers. All the decimal places to the right of the next non-zero digit after the calculation are significant. The number 0.0079800, for instance, includes five significant digits. If a measurement includes the noughts to the side of the last non-zero digit, they are all significant.

As stated in the preceding sentence:

a). 25637 ≈  3*10⁴

b). 2.51 ≈ 3

c). 9877m ≈ 10000m = 1*10⁴m

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The correct statement regarding the linear function is given as follows:

a) The slope of the function is 85, and it represents the change in net profit per product sold.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is given as follows:

P(x) = 125x - (40x + 1200).

In slope-intercept format, it is obtained as follows:

P(x) = 125x - 40x - 1200

P(x) = 85x - 1200.

Hence the slope is of 85, representing the rate of change, and option a is the correct option.

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The probability that at most 8 of 9 students take the bus to school is approximately 0.9538.

To find the probability of at most 8 students taking the bus, we can use the cumulative distribution function (CDF) of the binomial distribution.

The CDF gives the probability of getting a certain number or fewer of successes in a fixed number of trials, where each trial has a fixed probability of success.

The CDF of a binomial distribution with parameters n (number of trials) = 9 and p (probability of success) = 0.75 is given by:

F(k) = Σ(i = 0 to k) (9 choose i) * (0.75)^i * (0.25)^(9-i)

where (9 choose i) is the binomial coefficient, which gives the number of ways to choose i successes from n trials.

Thus, to find the probability of at most 8 students taking the bus, we compute the CDF at k = 8:

F(8) = Σ(i = 0 to 8) (9 choose i) * (0.75)^i * (0.25)^(9-i)

Using a binomial calculator or programming language, we can find the value of F(8) which is approximately 0.9538.

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The horizontal distance jade she covered is approximately 2.0 km.

Let x be the horizontal distance,

Given,

Viola drives 2 kilometers up a hill that makes an angle of 9 with the horizontal.

Thus, the angle between the horizontal and the direction of his walking = 9°, and The angle between the horizontal and vertical = 90°

By making the diagram of the given situation,

The angle between vertical and the direction of his walking = 180°(9+90°)=180° - 99° = 81°

By the law of sine,

[tex]\frac{sin90}{2}=\frac{sin 81}{x}[/tex]

x*sin 90°=2*sin 81°

x= 1.97537668119 ≅ 2.0

Hence, the horizontal distance jade she covered is approximately 2.0 km.

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The first six terms of the given sequence are 0, 3, 8, 15, 24, 35

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given is a formula for a sequence aₙ = n²-1, we need to find the first six terms of the sequence,

Put n = 1 for first term,

a₁ = 1²-1

= 0

Put n = 2, for second term,

a₂ = 2²-1

= 3

Put n = 3, for third term,

a₃ = 3²-1

= 8

Put n = 4, for fourth term,

a₄ = 4²-1

= 15

Put n = 5, for fifth term,

a₅ = 5²-1

= 24

Put n = 6, for sixth term,

a₆ = 6²-1

= 35

Hence, the first six terms of the given sequence are 0, 3, 8, 15, 24, 35

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Answer: A: 120

Step-by-step explanation:

When adding all sides of a triangle it should always equal 180 degrees so by adding 30+30=60 after you do 180-60=120 or the proper way is 30+30+x=180

60+x=180

-60     -60

x=120

To achieve a 95% confidence level and ±1.5% precision, you would need a sample size of approximately 3845 people.

To estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ±1.5%, you would need to determine the sample size necessary to achieve this level of precision.

The formula for sample size estimation in proportion estimation is given by:

[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]

Where:

[tex]n = (1.96^2 * 0.5 * 0.5) / 0.015^2 = 3844.83[/tex]

Therefore, to achieve a 95% confidence level and ±1.5% precision, you would need a sample size of approximately 3845 people.

In conclusion, to estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ±1.5%, a sample size of approximately 3845 people is necessary. This calculation assumes that the estimated proportion of people in favor of expanding unemployment compensation is 0.5, and that the Z-score for a confidence level of 95% is 1.96.

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The height of the water tank given the volume, length and width is 40 cm

Volume of the water tank= 40 liters

Length of the water tank= 50 cm

Width of the water tank= 20 cm

Height of the water tank= x

convert liters to centimeters

1 liter= 1000 cm

40 liters= 40,000 cm

Volume of the water tank= length × width × height

40,000 = 50 × 20 × x

40,000 = 1000x

divide both sides by 1000

x = 40,000 / 1000

x = 40 cm

Therefore, the height of the water tank is 40 cm

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Answer: The probability of Hans winning and taking no more than three shots can be calculated using the principle of total probability and the law of total probability.

Let's call the event of Hans winning and taking no more than three shots "A". Then, the probability of event A can be broken down into several cases:

Case 1: Hans wins in one shot: P(A|Hans wins in one shot) = P(Hans wins in one shot) = 0.4.

Case 2: Hans wins in two shots: P(A|Hans wins in two shots) = P(Franz misses in the first shot) * P(Hans wins in the second shot) = (1 - 0.4) * 0.4 = 0.24.

Case 3: Hans wins in three shots: P(A|Hans wins in three shots) = P(Franz misses in the first two shots) * P(Hans wins in the third shot) = (1 - 0.4)^2 * 0.4 = 0.144.

Finally, the probability of event A can be calculated using the law of total probability as follows:

P(A) = P(A|Hans wins in one shot) + P(A|Hans wins in two shots) + P(A|Hans wins in three shots) = 0.4 + 0.24 + 0.144 = 0.784.

So, the probability of Hans winning the competition and taking no more than three shots is 0.784.

Step-by-step explanation:

The inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)

An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of the function produces the output x. x. A function that has an inverse is called invertible, and the inverse is denoted by f⁻¹.

Given that, a set of ordered pairs defines a function.

{(-49,7), (-56,8), (-63,9), (-70,10)}

We need to find its inverse function,

Since, we know that,

The inverse of a function means that the input becomes the output of the function and the output becomes input.

When the function is given in the form of ordered pairs, the first element of each ordered pair represents the input and the second element represents the output.

Therefore,

The inverse will be:

{(7, -49), (8,-56), (9,-63), (10, -70)}

Hence, the inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)

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The central angle of the sector to the nearest tenth of a square inch is 473.2 sq.

To find the area of the sector, we can use the formula:

Area = (θ/360) * π * r²

where θ is the central angle of the sector in degrees, and r is the radius. To find the central angle, we can use the formula:

Arc length = (θ/360) * 2 * π * r

So,

Arc length = (θ/360) * 2 * π * 12 = 9

θ/360 * 2 * π * 12 = 9

θ/360 = 9 / (2 * π * 12)

θ = (9 / (2 * π * 12)) * 360

Approximating π as 3.14, we get:

θ = (9 / (2 * 3.14 * 12)) * 360 = 75.39

To the nearest tenth of a degree, this is 75.4 degrees.

Next, we can use the first formula to find the area:

Area = (75.4 / 360) * 3.14 * 12² = 473.2 sq in

To the nearest tenth of a square inch, this is 473.2 sq in.

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The central angle of the sector to the nearest tenth of a square inch is 473.2 sq.

To find the area of the sector, we can use the formula:

Area = (θ/360) * π * r²

where θ is the central angle of the sector in degrees, and r is the radius. To find the central angle, we can use the formula:

Arc length = (θ/360) * 2 * π * r

So,

Arc length = (θ/360) * 2 * π * 12 = 9

θ/360 * 2 * π * 12 = 9

θ/360 = 9 / (2 * π * 12)

θ = (9 / (2 * π * 12)) * 360

Approximating π as 3.14, we get:

θ = (9 / (2 * 3.14 * 12)) * 360 = 75.39

To the nearest tenth of a degree, this is 75.4 degrees.

Next, we can use the first formula to find the area:

Area = (75.4 / 360) * 3.14 * 12² = 473.2 sq in

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The geometric relation between the vectors v and w are:

The vectors are in the same direction.

Now, According to the question:

Geometrical Interpretation of Scalar Product

From the scalar product formula, we have a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → ) , that is, the scalar product of vectors a and b is equal to the magnitude of vector a times the projection of a onto vector b.

Vectors describe movement with both direction and magnitude. They can be added or subtracted to produce resultant vectors. The scalar product can be used to find the angle between vectors.

Now, vw =-||v|| ||w||

a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → )

vw =-||v|| ||w|| cos θ = |v| proj →w(→v) proj w → ( v → )

Hence, The vectors are in the same direction.

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Peter's gross semi-monthly earnings are P7,717.5 and each of his men's gross semi-monthly earnings are P6,150.

To calculate Peter's gross earnings,

We need to find the commission he earns on his own sales and the override commission he earns on his men's sales.

Peter's Commission on his own sales:

2.5% of P5,500 = P137.5

Peter's Override Commission on his men's sales:

0.5% of (number of men * P4,000) = 0.5% of (number of men * 4000)

Let's assume he has 4 men.

Then the total override commission would be:

0.5% * 4 * 4000 = P80

So Peter's gross semi-monthly earnings would be:

P5,500 + P137.5 + P80 + P2,000 = P7,717.5

To calculate the gross earnings of each of Peter's men, we need to find their basic semi-monthly salary, their commission on their own sales, and their transportation allowance.

Each man's basic semi-monthly salary: P4,000

Each man's Commission on their own sales will be:

3.75% * P4,000 = P150

So each man's gross semi-monthly earnings would be:

P4,000 + P150 + P2,000 = P6,150

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The actual distance in miles between the campsite and the trail is 9 miles.

Map can be defined as  a symbolic depiction emphasizing relationships between elements of some space such as objects and regions.

To convert from centimeters on the map to miles, we use the scale of 1 centimeter represents 5 miles.

So, 1.8 centimeters on the map represents 1.8 * 5 = 9 miles in real life.

Therefore, The actual distance in miles between the campsite and the trail is 9 miles.

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