The sum of three numbers is 71. The third number is 2 times the first. The second number is 5 less than the first. What are the numbers?

Explanation:

Plug x = -2 into h(x)

h(x) = x+4

h(-2) = -2+4

h(-2) = 2

This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.

g(x) = 5x

g(2) = 5*2

g(2) = 10

Therefore, g[ h(-2) ] = 10

Answer:

2.2

Step-by-step explanation:

(1.85 x 2) - 1.50

...............

Answer:

B. 0.593

Step-by-step explanation:

Answer: True

Step-by-step explanation:

The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.

__________________________________________________________

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)

The correct answer is True.

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:

[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]

The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.

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The equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.

To find the equation of a line perpendicular to a line with a slope of 1/13 and passing through the point (-1, 3), we need to determine the slope of the perpendicular line.

The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the given slope. The negative reciprocal of 1/13 is -13/1, or simply -13.

Now that we have the slope (-13) and a point (-1, 3) that the line passes through, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.

The point-slope form is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

Substituting the values (-1, 3) and -13 into the point-slope form, we get:

y - 3 = -13(x - (-1))

Simplifying:

y - 3 = -13(x + 1)

Expanding the equation:

y - 3 = -13x - 13

To convert the equation to slope-intercept form (y = mx + b), we can isolate y:

y = -13x - 13 + 3

y = -13x - 10

Therefore, the equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.

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WU is the perpendicular bisector of TV and W is the midpoint of TV.

Statements:

WU is the perpendicular bisector of TV.

W is the midpoint of TV.

TW = VW.

∠ZTWU and ∠ZVWU are right angles.

∠ZTWU ≅ ∠LVWU.

WU = WU.

∠ATWU ≅ ∠AVWU.

TU = VU.

Reasons:

Given.

Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.

Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.

Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.

All right angles are congruent.

Reflexive property of congruence: Any segment or angle is congruent to itself.

Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.

Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.

Therefore, the correct statements and reasons are:

Statements:

WU is the perpendicular bisector of TV.

W is the midpoint of TV.

TW = VW.

∠ZTWU and ∠ZVWU are right angles.

∠ZTWU ≅ ∠LVWU.

WU = WU.

∠ATWU ≅ ∠AVWU.

TU = VU.

Reasons:

Given.

Definition of the perpendicular bisector.

Definition of midpoint.

Given.

All right angles are congruent.

Reflexive property of congruence.

CPCTC.

CPCTC.

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Answer:

V = (3.14)(4.25)²(6)

Step-by-step explanation:

a.  The investment to double in value take about 14 years for the funding to double in value.

b.  The genuine time it will take for the funding to double in fee is about 13.86 years.

(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.

Using the rule of 70, we can calculate the estimated doubling time:

Time to double ≈ 70 / boom rate

Time to double ≈ 70 / 5

Simplifying, we have:

Time to double ≈ 14 years

Therefore, it would take about 14 years for the funding to double in value.

(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:

Doubling time (exact) = ln(2) / (ln(1 + r))

where r is the increase fee as a decimal.

In this case, the increase charge is 5% per year, or 0.05 as a decimal.

Doubling time (exact) = ln(2) / (ln(1 + 0.05))

Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)

Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.

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Answer:

Samuel = 21 orders

Nicole = 31 orders

Miguel = 63 orders

Step-by-step explanation:

Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.

We know that the sum of their tree orders equals 115 as

N + M + S = 115

Since Miguel served 3 times as many orders as Samuel, we know that

M = 3S.

Since Nicole served 10 more orders than Samuel, we know that

N = S + 10

Samuel's Orders:

Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:

S + 10 + 3S + S = 115

5S + 10 = 115

5S = 105

S = 21

Thus, Samuel served 21 orders.

Nicole's Orders:

Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:

N = 21 + 10

N = 31

Thus, Nicole served 31 orders.

Miguel's Orders:

Now we plug in 19 for S in M  = 3S to determine how many orders Miguel served:

M = 3(21)

M = 63

Thus, Miguel served 63 orders.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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a : 10<x<=20

b: 20<x<=30

So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.

Answer:

The answer is 2400 cm^3

Step-by-step explanation:

You just need to multiply the dimensions

Answer:

2400 cm³

Step-by-step explanation:

Volume of cuboid = length × width × height

Volume = 8 cm × 15 cm × 20 cm

Volume = 2400 cm³

So, the volume of the cuboid is 2400 cm³

The linear function for this case is:

f(x) = 5,000*x + 7,000

The general linear function is written as:

f(x) = a*x + b

Where a is the slope and b is the y-intercept.

Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:

f(x)= a*x + 7,000

Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:

f(x) = 5,000*x + 7,000

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Step-by-step explanation:  

C

f(0) = -3

I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.

However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.

Hope this helps.

1) The probability that 5 will be working is: 0.187

2) The probability that at least one machine would be working is: 0.006

3) The probability that all would be working is : 1

We are given the parameters as:

Total number of machines = 200

Probability that a Machine is working = 12% = 0.12

1) Now, you want to pick 40 machines and want to find the probability that 5 will be working.

This probability is given by the expression:

P(5 working) = C(40,5) * 0.12⁵·0.88³⁵ ≈ 0.187

where C(n, k) = n!/(k!(n-k)!)

2) The probability that at least one machine would be working is:

0.88⁴⁰ ≈ 0.006

3) The probability that all would be working is the complement of the probability that all have failed. Thus:

P(all working) = 1 - 0.12⁴⁰ ≈ 1

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The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.

To find the total area of the garden beds, we can use the expression:

Total area = (length of one side)^2 * number of garden beds

Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:

Total area = (4)^2 * 3

Simplifying:

Total area = 16 * 3

Total area = 48 square feet

Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.

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,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.

To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.

Let's calculate the total amount of flour and butter each student brought:

Alice:

Flour: 2 cups

Butter: 1/4 cup

Maria:

Flour: 1 1/4 cups

Butter: 3/4 cup

Now let's compare the amounts with the required ingredients for a batch of cookies:

Required amount per batch:

Flour: 3/4 cup

Butter: 1/3 cup

First, let's see how many batches of cookies Alice can make:

Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.

Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.

Next, let's see how many batches of cookies Maria can make:

Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.

Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.

Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:

Alice: 2 and 2/3 batches

Maria: 1 and 2/3 batches

Raul: Not mentioned, so we assume he brought the required ingredients.

The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.

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The correct options to the questions posed are :

From the given table of f(x) and x, from which we have;

The minimum point for f(x) as it's vertex as (-3, -10) = -3

For the function g(x). represented by the graph, the axis of symmetry is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3

The y-intercept, is the point on the graph where the line intersects the y-axis or where x = 0. Here , the point is (0,8) = 8

Over the interval [-6, -3]

The average rate of change of f(x) is

(-10 - 8)/(-3 -(-6)) = -6

From the graph of g(x), we have;

The axis of symmetry is the line x = -3

The y-intercept = (0, -2) = -2

Over the interval [-6, -3]

The average rate of change = (6 - (-2))/(-3 -(-6)) = 8/3 = 2.67

Hence,

The functions f and g have the same axis of symmetry.

The y-intercept of f is greater than the y-intercept of g.

Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.

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Case 1: SE = s / √500

Case 2: SE = s / √5,000

Case 3: SE = s / √50,000

To find the standard error of the mean in each of the given cases, we can use the formula:

Standard Error (SE) = population standard deviation / square root of sample size

However, since the population standard deviation is not provided, we'll need to use an estimated value. We'll assume the population standard deviation is unknown and use the sample standard deviation as an estimate.

Given that the sample size is 44 and the population mean (μ) is 8, we'll calculate the standard deviation for each case:

Case 1: Sample size (n) = 500

The sample size (500) is larger than 5% of the population (44), so we can assume it's a large enough sample. In this case, we'll use the standard formula for the standard error of the mean without the finite population correction factor:

SE = sample standard deviation / square root of sample size

= s / √n

Case 2: Sample size (n) = 5,000

Similar to Case 1, the sample size (5,000) is larger than 5% of the population (44), so we'll use the standard formula without the finite population correction factor:

SE = s / √n

Case 3: Sample size (n) = 50,000

In this case, the sample size (50,000) is much larger than the population size (44), which means we have a large enough sample. Therefore, we'll also use the standard formula without the finite population correction factor:

SE = s / √n

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Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.

Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.

Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.

By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.

Therefore:

AB/EA = DC/ED

Substitute:

AB/18 = 4/6

Cross multiply:

AB = 18 * 4/6

AB = 12

Therefore, the radius of the circle B is: 12.

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Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.