A spinner with equal sections labeled 1-3 is spun two times. A player wins if the sum of the spins is 4 or greater.
Which outcomes are winning outcomes, and what is the probability that a player will win?

Answer: $5

Step-by-step explanation: To calculate how much she spent on the 4 boxes of candy, we need to subtract 5 from 25, because we won't be including the cost of the magazine. So, therefore 25-5 is 20. So, now to find the cost for one, we need to set up a proportional relationship like this:

\(\frac{20}{4}\) = \(\frac{?}{1}\)

So, with that, we need to divide 4 by 20 to find the cost of 1. So, if you know, 20 divided by 4 = 5. So, therefore the cost of each candy box is $5. We can check our answer if we use the inverse operations, so our new equation would look like this:

5(4) + 5 = 25

We can check this, because we know 5 x 4 = 20, and 20 + 5 = 25. So 25 = 25, so it is $5.00

Answer: should be B

Step-by-step explanation:

The function g(x) = x(x - 4)^3 represents a cubic polynomial. It has a local minimum, intervals of increasing and decreasing behavior, concave up and concave down intervals, and possibly inflection points.

a) To find the intervals of increasing or decreasing, we need to examine the sign of the derivative. Taking the derivative of g(x), we get g'(x) = 4x^3 - 36x^2 + 48x.

We can factor this expression to obtain g'(x) = 4x(x - 4)(x - 3).

From this, we see that g'(x) is positive when x < 0 or x > 4 and negative when 0 < x < 3. Thus, g(x) is increasing on (-∞, 0) and (4, ∞) and decreasing on (0, 4).

b) To find the local maximum or minimum, we can set g'(x) = 0 and solve for x. Setting 4x(x - 4)(x - 3) = 0, we find x = 0, x = 4, and x = 3 as potential critical points. Evaluating g(x) at these points, we have g(0) = 0, g(4) = 0, and g(3) = -27. Therefore, the point (3, -27) is a local minimum.

c) The concavity of g(x) can be determined by analyzing the sign of the second derivative, g''(x). Taking the derivative of g'(x), we obtain g''(x) = 12x^2 - 72x + 48. Factoring this expression, we have g''(x) = 12(x - 2)(x - 4). From this, we observe that g''(x) is positive when x < 2 or x > 4 and negative when 2 < x < 4. Thus, g(x) is concave up on (-∞, 2) and (4, ∞) and concave down on (2, 4).

d) The inflection points occur when the concavity changes. Setting g''(x) = 0 and solving for x, we find x = 2 and x = 4 as potential inflection points. Evaluating g(x) at these points, we have g(2) = -16 and g(4) = 0. Therefore, the points (2, -16) and (4, 0) may be inflection points.

e) To sketch the graph, we can use the information obtained from the previous parts. The graph starts from negative infinity, increases on (-∞, 0), reaches a local minimum at (3, -27), continues to increase on (4, ∞), and becomes concave up on (-∞, 2) and (4, ∞). It is concave down on (2, 4) and potentially has inflection points at (2, -16) and (4, 0). The x-intercepts are at x = 0 and x = 4. Overall, the graph exhibits a downward concavity, increasing behavior, and a local minimum.

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a) Deposit around $6,825.23 annually for 12 years with a 12% interest rate compounded monthly to have $250,000.  b) For continuous compounding, deposit approximately $5,308.94 annually.

a) To calculate the annual deposit required with a 12% interest rate compounded monthly, we can use the formula for the future value of an ordinary annuity:\[ FV = P \times \left( \frac{{(1 + r/n)^{n \times t} - 1}}{{r/n}} \right) \]

Where:FV = Future Value ($250,000)

P = Annual deposit

r = Interest rate per period (12% or 0.12)

n = Number of compounding periods per year (12)

t = Number of years (12)

Rearranging the formula and plugging in the values, we have:

\[ P = \frac{{FV \times (r/n)}}{{(1 + r/n)^{n \times t} - 1}} \]

\[ P = \frac{{250,000 \times (0.12/12)}}{{(1 + 0.12/12)^{12 \times 12} - 1}} \]

\[ P \approx \$6,825.23 \]Therefore, you would need to deposit approximately $6,825.23 annually.

b) If the interest is compounded continuously, we can use the formula for continuous compounding:\[ FV = P \times e^{r \times t} \]

Where:FV = Future Value ($250,000)

P = Annual deposit

r = Interest rate per year (12% or 0.12)

t = Number of years (12)

Rearranging the formula and substituting the given values:

\[ P = \frac{{FV}}{{e^{r \times t}}} \]

\[ P = \frac{{250,000}}{{e^{0.12 \times 12}}} \]

\[ P \approx \$5,308.94 \]Thus, you would need to deposit approximately $5,308.94 annually.



Therefore, a) Deposit around $6,825.23 annually for 12 years with a 12% interest rate compounded monthly to have $250,000.  b) For continuous compounding, deposit approximately $5,308.94 annually.

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The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

-1024

Step-by-step explanation:

multiply each number by 2

A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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Answer:

Three

Step-by-step explanation:

Minus 60 from both side

255=85x

Divide both sides by 85

3=x

The possible number of person is 5.

Linear equation: an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution

Let,

The total amount of coffee= c

The total amount of milk = m

Total number of person = p

according to the question, c and m can't be .

Given,

Total amount of milk and coffee is 8 oz.

so,

\(\frac{c}{4} +\frac{m}{6} =8\\\)

\(\frac{3c+2m}{12} =8\)

So, this is linear equation.

3c+2m=8×12

\($$ \\$3 \mathrm{c}+2 \mathrm{~m}=96$\)

and

\(\eq\)\(c+m=8p\)

2(c+m) = 8p×2

\(2c+2m=24p\) ...(2)

By equation 1 and 2

\(3c+2m=96\\ 2m=96-3c\\ 2c+2m=16p\\ 2c+96-3c=16p\\96-c=16p\\96=16p+c\\\)

16p and 96 both are divisible by 16

So, let c =16k

Now 3c+2m =96

3(16k) +2m= 96

48k =2m= 96

k can't be 0, otherwise c is 0 and k cannot be 2, otherwise m is 0. Therefore k must be 1,

\(48+2m=96\\2m=96-48\\2m=48\\m=\frac{48}{2} \\m=24\)

BY putting m=24 in equation (1)

\(3c+2m=96\\3c+2(24)=96\\3c+48=96\\3c=96-48\\3c=48\\c=\frac{48}{3} \\c=16\)

Therefor, the number of person is 5

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Answer:

Blonde: 54 for mountains

Brunette: 100 for total

Red: 70 for total

Black: 41 for beach

Total: 162 for beach, 197 for mountains, 360 for total

Step-by-step explanation:

add and subtract as needed

Answer:

Step-by-step explanation:

Total Hours = 30 h

Total Pay = $240

Work at movie theater = $9/h

Work at babysitting = $6/h

Tm = hrs work at movie theater

Tb = hrs work as babysitting

Total hours = Tm + Tb = 30

So,

Tm = 30 - Tb

Total pay = Tm * 9 + Tb * 6 = 240, substitute Tm

(30 -Tb) * 9 + Tb * 6 = 240, solve for Tb

270 - 9Tb + 6Tb = 240

270 - 3Tb = 240

3Tb = 270 - 240 = 30

Tb = 10

Tm = 30 - Tb = 30 - 10 = 20

Hours work at movie = 20 hrs

Hours work as babysitter = 10 hrs

The tests average for your math class after completing test 2 is f(2)=81

The test average for your science class after completing test 2 is g(2)=83

The test average for maths class after test 2 is greater

Given linear function f(x)= 0.5x+80

x↔g(x)

1↔81

2↔83

3↔85

Solving (a): f(2)

We have:

f(x)= 0.5x+80

f(2)= 0.5*2+80

f(2)=81

Solving (b): g(2)

From the table:

g(x)=83 when x=2

So   g(2)=83

Solving (c): Which is greater f(2) or g(2)

In (a) and (b),

f(2)=81

g(2)=83

Hence, the test average for maths class is greater

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Answer: The answer is 0.8

Step-by-step explanation: Every gram is 0.001 of a kilogram

The amount of interest Judith will pay in the 40th month is $401. Thus, the correct answer is option A.

To calculate the amount of interest Judith will pay in the 40th month, we need to determine the remaining mortgage balance at that time. With an amortization period of 22 years (264 months), after 40 months, there will be 264 - 40 = 224 months remaining.

Using the formula for mortgage balance, we can find the remaining balance:

Remaining Balance = Principal * [((1 + r)^n) - ((1 + r)^m)] / [((1 + r)^n) - 1]

Where Principal = $175,000 (initial loan amount), r = 3.2% / 2 = 1.6% (semi-annual interest rate), n = 22 * 2 = 44 (total number of semi-annual periods), and m = 224 / 2 = 112 (remaining number of semi-annual periods).

Substituting the values into the formula, we find:

Remaining Balance = $175,000 * [((1 + 0.016)^44) - ((1 + 0.016)^112)] / [((1 + 0.016)^44) - 1] = $147,334.89

The interest paid in the 40th month is the difference between the previous month's balance and the remaining balance:

Interest = Previous Balance * Monthly Interest Rate = $175,000 - $147,334.89 = $27,665.11

Therefore, Judith will pay approximately $401 in interest in the 40th month. Thus, the correct answer is option A.

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Answer:

y=x+1

hope this helps

Answer: B and E

Step-by-step explanation:

Answer:

B C and E

Step-by-step explanation:

have a great day :D

The algorithm is correct and can be proven using the loop invariant theorem. The loop invariant for this algorithm is that at the start of each iteration of the loop, the value of j is a divisor of m.

To prove the correctness of the algorithm using the loop invariant theorem, we need to establish three properties: initialization, maintenance, and termination.

Initialization: Before the loop starts, j is initialized to 0. At this point, the loop invariant holds because 0 is a divisor of any positive integer m.

Maintenance: Assuming the loop invariant holds at the start of an iteration, we need to show that it holds after the iteration. In this algorithm, j is incremented by 1 in each iteration. Since j starts as a divisor of m, adding 1 to j does not change its divisibility property. Therefore, the loop invariant is maintained.

Termination: The loop terminates when j becomes greater than m. At this point, the loop invariant still holds because j is not a divisor of m. Thus, the loop invariant is maintained throughout the entire execution of the algorithm.

Since the initialization, maintenance, and termination properties hold, we can conclude that the algorithm is correct. The loop invariant, in this case, is that at the start of each iteration, the value of j is a divisor of m.

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The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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Answer:

should be C

Step-by-step explanation:

Answer:

C

Step-by-step explanation: took the test

False. You only flip when the number you are multiplying/dividing is negative.

Answer:

Length of pipe = 21 cm

Internal diameter = 4 cm

Internal radius = \frac{4}{2} = 2 cm24=2cm

Thickness = 0.5 cm

Outer radius = 2+0.5=2.5 cm

Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h

Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3

=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3

Hence The volume is 148.5 cubic cm.

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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm

Answer:

Yes

Step-by-step explanation:

From the origin means from the centre or middle but about a vertex is from a named point.

Answer:

200

Step-by-step explanation:

order of operations

Answer:

Dependent

Step-by-step explanation:

Two events are said to be dependent when the outcome of the first event is  related to the other.

When two events, A and B are dependent, the probability of occurrence of A and B is:

P(A and B) = P(A) · P(B|A)

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Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.

If two events A and B depend on each other, then the probability  of A and B occurring is

P(A and B) = P(A)  P(B|A)

Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.

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The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.

Annie rounds $ 280.05 to the nearest hundred

$ 280.05 will be equal to $ 300

Bobby rounds $ 280.05 to the nearest ten

$ 280.05 will be equal to = $ 280

Ciro rounds $ 280.05 to the nearest integer

$ 280.05 will be equal to = $ 280

Denise rounds $ 280.05 to the nearest tenth

$ 280.05 will be equal to = $ 280.1

Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280  + $ 280.1 = $ 1140.1

Therefore,

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

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Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.

Let's define the decision variables:

Let C represent the number of chairs produced.

Let T represent the number of tables produced.

Objective function:

The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:

Profit = 150C + 750T

Constraints:

Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:

5C + 3T ≤ 240

Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:

4C + 20T ≤ 700

Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:

C ≥ 0

T ≥ 0

Now, we can solve the linear programming problem to find the optimal solution:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

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If the material used for the half-spheres are three times more expensive than the material used for the part cylindrical, then the radius of the cylindrical part should be (125/3π)^(1/3) meters and the length of the cylindrical part should be 11.99 meters.

The radius and length of the cylindrical part that will minimize the cost of building the tank, can be determined by considering the cost of the materials used for the half-spheres and the cylindrical part.

Let's start by finding the volume of the cylindrical part. The volume of a cylinder is given by the formula

V = πr²h, where r is the radius and h is the height or length of the cylindrical part.

In this case, we want the volume to be 1000m³, so we can write the equation as:

1000 = πr²h ...(1)

Next, let's find the surface area of the two half-spheres. The surface area of a sphere is given by the formula:

A = 4πr².

Since we have two half-spheres, the total surface area of the half-spheres is:

2(4πr²) = 8πr².

The cost of the half-spheres is three times more expensive than the cost of the cylindrical part. Let's say the cost per unit area of the cylindrical part is x, then the cost per unit area of the half-spheres is 3x.

The total cost, C, is the sum of the cost of the cylindrical part and the cost of the half-spheres. It can be expressed as:

C = x(2πrh) + 3x(8πr²) ...(2)

Now, we can minimize the cost by differentiating equation (2) with respect to either r or h and setting it equal to zero. This will help us find the values of r and h that minimize the cost. To simplify the calculations, we can rewrite equation (2) in terms of h using equation (1):

C = x(2πr(1000/πr²)) + 3x(8πr²) C = 2x(1000/r) + 24xπr² ...(3)

Now, differentiating equation (3) with respect to r:

dC/dr = -2000x/r² + 48xπr

Setting dC/dr equal to zero:

0 = -2000x/r² + 48xπr

Simplifying the equation:

2000x/r² = 48xπr

Dividing both sides by 4x: 500/r² = 12πr

Multiplying both sides by r²: 500 = 12πr³

Dividing both sides by 12π: 500/(12π) = r³

Simplifying: 125/3π = r³

Taking the cube root of both sides: r = (125/3π)^(1/3)

Now, we can substitute this value of r back into equation (1) to find the value of h:

1000 = π((125/3π)^(1/3))^2h

Simplifying: 1000 = (125/3π)^(2/3)πh

Dividing both sides by π and simplifying:

1000/π = (125/3π)^(2/3)h

Simplifying further:

1000/π = (125/3)^(2/3)h

Now we can solve for h: h = (1000/π) / ( (125/3)^(2/3) )

Simplifying: h = 11.99 m

To summarize, to minimize the cost of building the tank, the radius of the cylindrical part should be (125/3π)^(1/3) meters and the length of the cylindrical part should be approximately 11.99 meters.

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Answer: x= 95° ;  y= 35°

Step-by-step explanation:

If J II K (symmetrical), then x°= 180°- 85°

                                            x°= 95°

In addition to this, because the J II K lines are symmetrical:

                               (5y-90)°= 85°

                              5y°- 90° = 85°

                                       5y°= 85°+ 90°

                                      5y° = 175°

                                  5y°/ 5 = 175°/5

                                          y°= 35°

Answer:

i can't see the file can u share it to me