Which value of b satisfies both inequalities for b?
2b-8 > 5
3b-13 < 9
Use substitution to find the answer.
A 5
B7
C8
D10

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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Answer: the slop is 23

Step-by-step explanation:

Answer:

1) b,c

2) -3/2

3) y = -3/2x + 30

4) 16 min

5) 8

6) 90

Step-by-step explanation:

4) 6 = -3/2x + 30

-24 = -3/2x

-48 = -3x

x = 16

6) (0,50) (2,230)   slope = (230 - 50) / (2 - 0) = 180/2 or 90

Answer:

i think it is D  formation of groundwater

Step-by-step explanation:

After 30 years of continuous deposits of $2000 per year into an IRA account earning 5% interest compounded continuously, the account would have $8,966.60. The interest earned is -$51,033.40, indicating a loss. The value of the IRA, when you turn 65, is  $8,966.60.

To calculate the amount in the IRA account after 30 years, we can use the continuous compound interest formula. The formula for the future value (FV) of a continuous income stream is given by:

FV = P * \(e^{(rt)}\)

Where:

P = annual deposit amount

r = interest rate per year (in decimal form)

t = number of years

In this case, the annual deposit amount is $2000, the interest rate is 5% (0.05 in decimal form), and the number of years is 30.

FV = 2000 * \(e^{(0.05 * 30)}\)

Using a calculator, we can calculate the value of \(e^{(0.05 * 30)}\) to be approximately 4.483.

FV = 2000 * 4.483 ≈ $8,966.60

So, the amount in the IRA account after 30 years will be approximately $8,966.60.

To determine the interest earned, we subtract the total amount deposited from the final value:

Interest = FV - (P * t)

Interest = 8,966.60 - (2000 * 30) = 8,966.60 - 60,000 = -$51,033.40

The negative value indicates that the total amount deposited is greater than the final value, resulting in an overall loss of $51,033.40.

The value of the IRA, when you turn 65, is equal to the final amount, which is approximately $8,966.60.

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Yes, you can find the standard error now by taking the standard deviation divided by the square root of the sample size.

The standard deviation in a data set is the mean deviation of the data from their mean.

For sample size n for a data set with data points X1, X2, X3……..Xn for exact standard deviation:

1. Calculates the arithmetic mean M of the set data by adding them all and dividing by n.

M = ( X1+X2+ X3+…..+Xn) / n

2. Calculate the deviation (D) for each data point from the mean M

D = (Xi-M) for all

3. Squaring and sum of all deviations, sum of squares (SS)

4. Divide SS by n.This quantity is the sample variance V

5. Take the square root of V.

6. This quantity is the sample standard deviation, SD.

There are some specific terms and issues to consider. If you are estimating the standard deviation of a population from a sample and the population mean $ is not known, M serves as an unbiased estimate of $. Again, SS is divided by (n-1), not n.

The resulting standard deviation is an unbiased estimate of the population standard deviation based on the sample size, n. If the population mean is known, use that mean instead of the sample mean. , and the SD of the sample is only calculated for n through SS dives.

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Answer: 155°

because ∠a and ∠c are 2 opposing angles => m∠a = m∠c = 155°

Step-by-step explanation:

10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Cost per unit = Total manufacturing cost / Number of units produced = $1,663,240 / 6,400 = $259.88 per unit

To calculate the total manufacturing cost and cost per unit for the month of August, we need to determine the overhead cost for each activity:

1. Material handling: Number of parts used x Rate = 142,000 parts x $2.00 per part = $284,000
2. Assembly and inspection: Number of direct labor hours x Rate = 26,480 DLH x $25.00 per DLH = $662,000
3. Testing: Number of units tested x Rate = 6,400 units x $5.00 per unit = $32,000

Now, add up all the overhead costs: $284,000 + $662,000 + $32,000 = $978,000

Next, add direct material and direct labor costs:
Direct material cost = $208,600
Direct labor cost = 26,480 DLH x $18.00 per hour = $476,640

Total manufacturing cost = Direct material + Direct labor + Overhead costs = $208,600 + $476,640 + $978,000 = $1,663,240

Cost per unit = Total manufacturing cost / Number of units produced = $1,663,240 / 6,400 = $259.88 per unit

Manufacturing overhead cost = Number of direct labor hours x Rate = 26,480 DLH x $40.00 per DLH = $1,059,200

To calculate the total manufacturing overhead cost applied for the month of August using the $40.00 per direct labor hour rate.

Manufacturing overhead cost = Number of direct labor hours x Rate = 26,480 DLH x $40.00 per DLH = $1,059,200

The traditional method using a single predetermined overhead rate based on direct labor hours may not accurately capture the variation in overhead costs associated with different activities or products.

The activity-based costing (ABC) method is likely to provide better information for manufacturing managers because it allocates overhead costs based on specific cost drivers related to each activity. This allows for a more accurate representation of the resources consumed by each product or process. In contrast, the traditional method using a single predetermined overhead rate based on direct labor hours may not accurately capture the variation in overhead costs associated with different activities or products.

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Answer:

-8

Step-by-step explanation:

(-2)2+9(-2)+14

-4+-18+14

-22+14

=-8

Hope this helps

Answer:

0

Step-by-step explanation:

f(x) = x^2 + 9x + 14, when x = -2.

f(x)=(x+7)(x+2)

f(x)=(-2+7)(-2+2)=0

Answer:

x = - 2

Step-by-step explanation:

using the rules of exponents

\(a^{m}\) ×\(a^{n}\) = \(a^{(m+n)}\)

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\)

given

\(\frac{9^{3}(9^{1}) }{9^{6} }\)

= \(\frac{9^{(3+1)} }{9^{6} }\)

= \(\frac{9^{4} }{9^6} }\)

= \(9^{(4-6)}\)

= \(9^{-2}\) = \(9^{x}\)

then equating exponents

x = - 2

Answer:

-3x = 7 .  

Step-by-step explanation:

-3x - 6 - 1 =

-3x - 7

Hope that helps!

Answer:

-3x-7

Step-by-step explanation:

Combine like terms

Answer:

STEP n1:

Equation at the end of step 1

 (g•(5c+4))-((((5c+4)2)+8•(5c+4))-2)  = 0

STEP 2:

Equation at the end of step 2

 g • (5c + 4) -  (25c2 + 80c + 46)  = 0

STEP 3:

Equation at the end of step 3

 5gc + 4g - 25c2 - 80c - 46  = 0

STEP 4:

Solving a Single Variable Equation

4.1     Solve   5gc+4g-25c2-80c-46  = 0

Answer:  (5c+4)^2+40c+8 over 5c+4

Step-by-step explanation:

Answer:

(-6,2)

Step-by-step explanation:

\(x = - 6 \\ x - y = - 8\)

Substitution

Substitute x = -6 from the first equation in the second equation.

\( - 6 - y = - 8 \\ - 6 + 8 = y \\ 2 = y\)

Normally, we have to substitute either x-term or y-term in one of the equation to get another term. For this situation, we already know the value of x so It is not necessary to substitute the y-value.

Answer Check

We have to check the answer to make sure that we have got the right answer.

We can check the answer by substituting both x-value and y-value in the equation.

\(x - y = - 8\)

Substitute x = -6 and y = 2 in the equation.

\( - 6 - 2 = - 8 \\ - 8 = - 8\)

The equation is true. Therefore, our answer is (-6,2)

Yes, if "a" is an uncountable set and "zb" is a countable set, then "a-b" must be uncountable.

To prove this statement, we first need to understand what it means for a set to be countable or uncountable. A set is countable if its elements can be put in one-to-one correspondence with the natural numbers (1, 2, 3, ...). On the other hand, a set is uncountable if it cannot be put in one-to-one correspondence with the natural numbers.

Now, suppose "a" is an uncountable set and "zb" is a countable set. Let "b" be the subset of "zb" that is contained in "a". Then, since "zb" is countable, "b" is also countable. Now, consider the set "a-b". This set consists of all the elements in "a" that are not in "b". Since "a" is uncountable and "b" is countable, it follows that "a-b" must be uncountable.

Therefore, we can conclude that if "a" is an uncountable set and "zb" is a countable set, then "a-b" must be uncountable.

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To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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Answer:

Company B follows linear profit function while company A follows exponential profit function. Company B has more profit after 4 months while company A has more monthly profit after year-end. Option A is correct.

Given information:

Company A earns monthly profit based on the profit function,  where t is the number of months.

Company B earns profit based on a linear function. The data in the below table shows the profit after each month:

Month 3 4 7

Profit 5 10 25

Now, the profit earned by company A after 4 months will be,

Also, the profit earned after a year will be,

Now, the linear function which represents the profit of company B is,

So, the profit earned after 4 months and 1 year (by company B) will be,

Now, comparing the profit of companies A and B:

After 4 months, company B has more monthly profit which is 10 hundred dollars or 1 thousand dollars. After the year-end, company A earns more monthly profit as it is 102.04 hundred dollars. This is because company A follows an exponential function to predict the profit while company B uses a linear profit function.

Therefore, option A should be correct.

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Company B follows linear profit function while company A follows - 1

The profit of the company was decreasing in the year interval 2010 to 2015.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given that,

A company’s profit, P(t) , in thousands of dollars, from 2000 to 2015 , is represented by the graph provided.

Here  t=0 corresponds to the year 2000.

The X axis has been marked from 0 to 15, which corresponds to the year from 2000 to 2015.

It is clear that from 0 to 10, the profit is increasing. So from 2000 to 2010 the graph is increasing.

From 10 to 15, the graph is decreasing or the profit is decreasing and finally the profit is 0.

So the graph is decreasing in the interval 2010 to 2015.

Hence the interval where the graph is decreasing is 2010 to 2015.

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The derivative of (sec(x)) / (1 + sec(x)) is [tan(x)] / [(1 + sec(x))^2].

To find the derivative of the given function, we can use the quotient rule:

Let u = sec(x) and v = 1 + sec(x).

Then, we have:

f(x) = u/v

Using the quotient rule, we have:

f'(x) = (v × u' - u × v') / v^2

where u' and v' are the derivatives of u and v with respect to x, respectively.

To find u' and v', we can use the chain rule:

u' = sec(x) × tan(x)

v' = sec(x) × tan(x)

Substituting u', v', u, and v into the quotient rule formula, we get:

f'(x) = [(1 + sec(x)) ×sec(x) × tan(x) - sec(x) × sec(x) × tan(x)] / (1 + sec(x))^2

Simplifying the numerator and denominator, we get:

f'(x) = [tan(x)] / [(1 + sec(x))^2]

Therefore, result of the derivative is [tan(x)] / [(1 + sec(x))^2]

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer: it the answer it so ez

Answer:

y=3

Step-by-step explanation:

as perpendicular to y axis so it means parallel to x-axis and we measure slope with positive x axis

The general solution includes both terms with c1 and c2, we cannot eliminate c1 and c2 completely. However, we have found the DE relating the second derivative and the first derivative of the given function: d²y/dt² - 2 * dy/dt = 15 * c2 * e^(-3t)Finding the differential equation (DE) whose general solution is given by y = c1 * e^(2t) + c2 * e^(-3t).

To find the DE, we will differentiate the general solution with respect to time 't' and then eliminate the constants c1 and c2.

First, find the first derivative, dy/dt:
dy/dt = 2 * c1 * e^(2t) - 3 * c2 * e^(-3t)

Next, find the second derivative, d²y/dt²:
d²y/dt² = 4 * c1 * e^(2t) + 9 * c2 * e^(-3t)

Now, we will eliminate c1 and c2. Multiply the first derivative by 2 and subtract it from the second derivative:
d²y/dt² - 2 * dy/dt = (4 * c1 * e^(2t) + 9 * c2 * e^(-3t)) - (4 * c1 * e^(2t) - 6 * c2 * e^(-3t))

Simplify the equation:
d²y/dt² - 2 * dy/dt = 15 * c2 * e^(-3t)

Since the general solution includes both terms with c1 and c2, we cannot eliminate c1 and c2 completely. However, we have found the DE relating the second derivative and the first derivative of the given function:

d²y/dt² - 2 * dy/dt = 15 * c2 * e^(-3t)

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Answer:

(2x−1)(x+4)

Step-by-step explanation:

2x2+7x−4=(2x−1)(x+4)

Answer:

It is wrong

Step-by-step explanation:

What we have is as follows;

9x + 2 = 8x^2 + 6x

Bringing 9x + 2 yo the right hand side, we have;

8x^2 + 6x -9x -2 = 0

8x^2 -3x -2 = 0

So what is used here is the quadratic formula and we want to try to see if it was used correctly.

The form we have in the question is however;

-8x^2+ 3x + 2 = 0

which is obtained by taking the right hand side of the equation to the left

Now;

using the quadratic formula;

x = -b ± √(b^2 -4ac)/2a

where a is -8

b = 3

c = 2

Thus we have

-3 ± √(9 - 4(-8)2)/2(-8)

-3 ± √(9 + 64)/(-16)

So where is wrong is in the square root

what we are supposed to have is 9 + 64 = 73 and not otherwise

Answer:

Step-by-step explanation:

No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.

Answer:

4

Step-by-step explanation:

i think i am correct but if im not sorry

The time William would arrive in town B IS 1 : 47 pm.

The first step is to determine the distance and the time of Dennis's travel.

Time = 14 hours (2 pm + 12) - 10 hours = 4 hours

Distance = time x average speed

4 x 52 = 208 miles

The second step is to determine the time of William's travel:

Distance / average speed = time

208 / 40 = 5.20 = 5 hours 12 minutes

Time William left for the trip = 10 am - 1 hour 25 minutes = 8 :35am

Time he would reach town B = 8 : 35am + 5 hours 12 minutes = 13 hours 47 minutes = 1 : 47 pm

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Answer:

0

Step-by-step explanation:

If the slope is a horizontal line it is 0

Answer:

66

Step-by-step explanation:

11 - 9 + 8^2

11 - 9 + 64

= 66