question what is the total number of outcomes in each situation? picking a month of the year and tossing a coin

Answer:

105 cm³

Step-by-step explanation:

Given:

Formula:

\(\text{Area of triangular prism:} \ (\text{Area of triangle}) \times \text{Height of triangular prism}\)

Substitute the given measures in the formula to determine the volume.

\(\implies\text{Area of triangular prism:} \ (\frac{1}{2} \times 5 \times 7) \times 6\)

Simplify the expression as needed.

\(\implies\text{Area of triangular prism:} \ (17.5) \times 6\)

\(\implies\boxed{\text{Area of triangular prism:} \ 105 \ \text{cm}^{3}}\)

Answer:

105 cm³

Step-by-step explanation:

Given:

Height of triangular base: 7 cm

Base of triangular base: 5 cm

Height of triangular prism: 6 cm

Formula:

Substitute the given measures in the formula to determine the volume.

Simplify the expression as needed.

Answer:

part b (2,-1)

Part c the lines intersect at (-20,-45)

Step-by-step explanation:

Answer:

-3y+4x+4

Step-by-step explanation:

if you need the step-by-step explanation I can work it out for you just let me know

For the system of equations :

8x -2y = -16

y = 8 + 4x

has infinitely many solutions, and any value of x will give us a corresponding value of y that satisfies both equations.

For the system of equations :

7x - y = 2

-7x + y = 2

There are no solutions to this system of equations. The two equations are parallel and will never intersect.

To solve the system of equations, we can use the substitution method.

First, let's rearrange the second equation to isolate y: y = 8 + 4x

Now, we can substitute this expression for y into the first equation:

8x - 2(8 + 4x) = -16

Simplifying this equation gives us:

8x - 16 - 8x = -16

Simplifying further gives us:

-16 = -16

This is a true statement, but it does not give us a specific value for x or y. This means that the system of equations has infinitely many solutions, and any value of x will give us a corresponding value of y that satisfies both equations.

For the second system of equations, we can use the elimination method.

7x - y = 2

-7x + y = 2

Adding these two equations together gives us:

0 = 4 This is a false statement, which means that there are no solutions to this system of equations. The two equations are parallel and will never intersect.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

f(x) is linear

g(x) is exponential

Step-by-step explanation:

A linear function will always have the same rate of change between equally distant points, while an exponential function will have an increasingly large rate of change between equally distant points.

First, look at f(x). All these points are equally distant at 2 units apart on the x-axis, so they can be directly compared:

\((-38)-(-18)=-20\\(-58)-(-38)=-20\\(-78)-(-58)=-20\)

All of these points are the same distance apart on the y, so f(x) must be a linear function.

Now look at g(x). These are also all equally distant at only 1 unit apart.

\(30-10=20\\90-30=60\\270-90=180\)

These are very clearly not the same distance apart on the y, so g(x) must be the exponential function.

Answer:

Step-by-step explanation:

A

Generally when you're solving systems of equations like this you want one variable to be by itself and have no coefficient (it's not being multiplied by anything)

In question A, the x variable is by itself but it has a coefficient of 4 (not 1)

On solving the provided question we cans say that quadratic equation - x^2-5x-4 = 0 and x = 1 , 3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

quadratic equation -

x^2-5x-4 = 0

x(x-1) -3(x-3) =

(x-1)(x-3) = 0

x = 1 , 3

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Answer:

130

Step-by-step explanation:

120 - (-10)

120 + 10

change it to add then remove the negative

The  triangle is rotated 90° counterclockwise about the origin shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

we have to rotate 90° counterclockwise about the origin.

as, the rule for 90° counterclockwise about the origin is (x, y) becomes

(-y, x).

As, the coordinates after rotation are :

(-8, 3)---> (-3, -8)

(-2, 8)---> (-8, -2)

(-5, 7) -----> (-7, -5)

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The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

To estimate a population mean using a 99% confidence interval and a random sample of 35 individuals, you need to find the critical t-score.

Step 1: Determine the degrees of freedom. For a sample of 35 individuals, the degrees of freedom (df) = sample size - 1 = 35 - 1 = 34.

Step 2: Find the critical t-score using a t-table or an online calculator. For a 99% confidence interval and 34 degrees of freedom, the critical t-score is approximately 2.733.

Your answer: The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

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Answer:

Step-by-step explanation:

120

It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

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a) The complement of the set of pupils who do not jog or swim or cycle would be the set of pupils who do at least one of these activities.

b) 8% of pupils do both jog and cycle.

41% of pupils swim or cycle.

And, the percentage of pupils who do not jog, swim, or cycle is 15%.

We have to given that;

It is found that 15% of pupils at a school do not jog or swim or cycle, 8% do all three activities, 15% swim and cycle but do not jog, 15% do both jog and swim, 20% swim only, 18% cycle only and 42% do two or more activities.

Hence, The complement of the set of pupils who do not jog or swim or cycle would be the set of pupils who do at least one of these activities.

And, the percentage of pupils who do both jog and cycle, we look at the intersection of sets A and B, which is 8%.

Therefore, 8% of pupils do both jog and cycle.

the percentage of pupils who swim or cycle, we add the percentages of sets B, C, and D (the parts of the circles that include swimming or cycling), which gives;

= 8% + 15% + 18%

= 41%.

Therefore, 41% of pupils swim or cycle.

the percentage of pupils who do not swim, we add the percentages of sets A, B, and D (the parts of the circles that do not include swimming), which gives;

= 15% + 8% + 18%

= 41%.

Therefore, 41% of pupils do not swim.

the percentage of pupils who do not jog, swim, or cycle, we look at the complement of the set of pupils who do at least one of these activities. This is given as 15%,

So the percentage of pupils who do not jog, swim, or cycle is 15%.

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Step-by-step explanation:

k(-5)= 6.(-5)+100

=30 + 100

=70

Answer:

70

Step-by-step explanation:

We can substitue -5 in for x:

k(-5) = 6(-5) + 100 = 70.

Answer:

RS.20

Step-by-step explanation:

1 pen costs R5.20 and is sold for RS5 so profit is RS.20 per pen

For an electric network with three switches ( two are in series and one in parallel), the probability that the system is working is equal to the 0.644 or 64.4 %.

We have, an electric network has 3 switches aligned as present in above figure. Switches present in upper side in network or in series are switch 1 and switch 2 and switch present in parallel is switch 3. The probability that one out of three is turn on = 60% = 0.60

We have to determine probability that the system is working. System is working when all switches are on. Letvus consider the events,

A = Switch 1 is turn on

B = Switch 2 is turn on

C= Switch 3 is turn on

Now, probability that switch 1 is turn on P( A) = 0.60

Probability that switch 2 is turn on P( B)

= 0.60

Probability that switch 3 is turn on P(C)

= 0.60

We know if two events A and B are independent then, we have P(A∩B) = P(A) × P(B)

Here, Switch 1 and switch 2 are independent so, P( A∩B) =0.60 × 0.60

= 0.36

Probability that the system is working =

[(switch 3 is turn on ) or (switch 1 is turn on and switch 2 is turn on)]

= P( C∪( A∩B))

= P(C) + P(A∩B ) - P ( C∩ (A∩B))

= 0.60 + 0.36 - P(C) × P(A∩B)

= 0.96 - 0.6 × 0.36

= 0.96 - 0.216

= 0.644

Hence, required probability is 0.644.

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Complete question:

the above figure completes the question.

an electric network has 3 switches aligned as shown in figure 1 and the probability that one of them is turned on is 60%, independently of the status of the other switches. what is the probability that the system is working? 8 points per problems

Answer:(5-3)=42

Step-by-step explanation:

Hello There!!

Your answer is 21.

First, You should do is (5 ₋ 3) = 2.

Then, You need to divide 42/2 =21.

\(\sqrt[HopeThisHelps}\)\(^{HopeThisHelps}\)

\(\frac{Loserbrazts}{}\)

The total perimeter will be 4x^+17 and length be 22.76 cm

As per the data given in the questions,

We have, the shape of the sandwich be rectangular.

We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),

where, l = length of the rectangle

and, b = breadth of the rectangle

The expression for the perimeter of the sandwich would be:

2 (2x^2 + 9) + 2 (2x^2 + 8)

= 4x^2 + 26

Now for finding the length of the crust,

we will put the value of x=1.2,

So, the value of the approximate length of the crust would be:

=4x^2 + 26

= 4 * 1.2^2 + 26

= 22.76 centimetres.

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Answer:A is correctly scientifically notated

B is incorrect

C is correctly notated

D is correct. 10 to the zero power simply means “1”

Step-by-step explanation:

Answer:

1a. n=7

2a. p=3

3a. m=48

4a. a=81

5a. a=8

6a. p=14

7a. s=60

8a. r=18

9a. n=65

---------------

1b. a=15

2b. b=5

3b. n=10

4b. d=13

5b. e=120

6b. n=45

7b. x=8

8b. x=56

9b. a=96

----------------

1c. b=36

2c. r=120

3c. s=11

4c. m=112

5c. i=272

6c. b=20

7c. a=42

8c. m=11

9c. p=21

Step-by-step explanation:

1. 2n+2= 16

Subtract 2 from each side

2n=14

Divide each side by 2.

n=7

2a. 11p-5=28

Add 5 to each side

11p=33

Divide each side by 11

p=3

3a. m/16 +7=10

Subtract 7 from each side

m/16 =3

multiply each side by 16

m=48

4a. a/9 -3 =6

Add 3 to each side

a/9=9

Multiply each side by 9

a=81

5a. 9a-11=61

Add 11 to each side

9a=72

Divide each side by 9

a=8

6a. 3p+12=54

Subtract 12 from each side

3p=42

Divide each side by 3

p=14

7a. s/15+1=5

Subtract 1 from each side

s/15=4

Multiply each side by 15

s=60

8a. 3r-11=43

Add 11 to each side

3r=54

Divide each side by 3

r=18

9a. n/5 -5=8

Add 5 to each side

n/5=13

Multiply each side by 5

n=65

1b. a/3-1=4

Add 1

a/3=5

Multiply by 3

a=15

2b. 8b+12=52

Subtract 12

8b=40

Divide by 8

b=5

3b. 6n+4=64

Suntract 4

6n=60

Divide by 6

n=10

4b. 5d+6=71

Subtract 6

5d=65

Divide by 5

d=13

5b. e/12-7=3

Add 7

e/12=10

Multiply by 12

e=120

6b. n/3+12=27

Subtract 12

n/3=15

Multiply by 3

n=45

7b. 6x+25=73

Subtract 25

6x=48

Divide by 6

x=8

8b. x/7+14=22

Subtract 14

x/7= 8

Multiply by 7

x=56

9b. a/6+4=20

Subtract 4

a/6=16

Multiply by 6

a=96

1c. b/4+2=11

Subtract 2

b/4=9

Multiply by 4

b=36

2c. r/20-3=3

Add 3

r/20=6

Multiply by 20

r=120

3c. 4s-5=39

Add 5

4s=44

Divide by 4

s=11

4c. m/8+5=14

Subtract 5

m/8=14

Multiply by 8

m=112

5c. i/4+5=73

Subtract 5

i/4=68

Multiply by 4

i=272

6c. 5b-7=93

Add 7

5b=100

Divide by 5

b=20

7c. a/3-3=11

Add 3

a/3=14

Multiply by 3

a=42

8c. 5m+13=68

Subtract 13

5m=55

Divide by 5

m=11

9c. 3p-15=48

Add 15

3p=63

Divide by 3

p=21

One or two may be wrong but that's because I was trying to do the answers quickly.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer: 7

Step-by-step explanation:

7

The following values represent the rollercoaster graph scenario most accurately:

is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6

Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5

Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)

For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6

The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.

The Latin word Datum, which meaning "something provided," is where the word data first appeared.

In the question, where at x = 0, Red(x) = 10,

at x = 5, Red(x) = 2.5

For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5       if    6 ≤ x < 10

Given, where at x = 10, Green (x) = 7,

So, at x = 6, Green (x) = 2.0

For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15

Given, where at x = 10, Purple (x) = 7,

at x = 15, Purple (x) = 0

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The complete question is:

The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.

Answer: The answer is C

Answer:

the anwer is c ig

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

there are 15 students , 9 of which are boys, then

number of girls = 15 - 9 = 6

ratio of boys : girls = 9 : 6 = 3 : 2 ← in simplest form

Answer:

A≈50.27

Step-by-step explanation:

Using the formulas

A=πr2

d=2r

Solving forA

A=1/ 4πd^2=1/ 4·π·82≈50.26548

Answer:

Area= 50.3cm^2

Step-by-step explanation:

Use the area of a circle formula A= πr²

Then plug in your radius which is half of your diameter.

A=π(4)² = 50.3 cm²

Answer:

x = 0

Step-by-step explanation:

\(\frac{1}{3} (6x-5)-x=\frac{1}{3} -2(x+1)\)

We will be using the Distributive Property shown below:

5(x+1) = 5x+5

Distribute 1/3 and -2:

\(\frac{6}{3} x-\frac{5}{3}-x=\frac{1}{3} -2x-2\):

Combine Like Terms:

\(x-\frac{5}{3} =-2x-\frac{5}{3}\)

Add 2x to both sides:

\(3x-\frac{5}{3} =-\frac{5}{3}\)

Add 5/3 to both sides:

\(3x=0\)

Divide both sides by 3:

\(x=0\)

To maximize profit, the company should produce 5 thousand of type A solar panels and 0.1875 thousand of type B solar panels per year.

To maximize profit, we need to find the values of x and y that will give us the maximum value of the profit function P(x,y) = R(x,y) - C(x,y).

First, let's find the profit function by subtracting the cost function from the revenue function:

P(x,y) = R(x,y) - C(x,y)
= (6x + 7y) - (x^2 - 4xy + 8y^2 + 16x - 61y - 2)
= -x^2 + 10x + 3y - 8y^2 + 2

Next, we need to find the partial derivatives of the profit function with respect to x and y:

∂P/∂x = -2x + 10
∂P/∂y = 3 - 16y

To find the critical points, we need to set the partial derivatives equal to zero and solve for x and y:

-2x + 10 = 0
x = 5

3 - 16y = 0
y = 0.1875

So the critical point is (5, 0.1875).

To determine if this is a maximum or minimum, we need to find the second partial derivatives and use the second derivative test:

∂^2P/∂x^2 = -2
∂^2P/∂y^2 = -16
∂^2P/∂x∂y = 0

The determinant of the Hessian matrix is (-2)(-16) - 0^2 = 32. Since this is positive and ∂^2P/∂x^2 is negative, the critical point is a local maximum.

Therefore, to maximize profit, the company should produce 5 thousand of type A solar panels and 0.1875 thousand of type B solar panels per year.

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