50 POINTS

Question 5

The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

Determine P(2 tails).

12.5%
37.5%
50%
75%

Question 6
Which table shows the sample space for spinning the spinner twice?

spinner with 3 equal sections colored yellow, blue, and red


Blue Yellow Red
Red Red Red Red
Blue Blue Blue Blue
Yellow Yellow Yellow Yellow

Blue Yellow Red
Blue Blue, Blue Blue, Yellow Blue, Red
Blue Blue, Blue Blue, Yellow Blue, Red

Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Red, Yellow Blue, Yellow
Yellow Yellow, Red Yellow, Blue Yellow, Blue

Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Blue, Blue Yellow, Blue
Yellow Red, Yellow Blue, Yellow Yellow, Yellow

Question 7
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.

one third
two thirds
two sixths
four ninths

Answer:3 and 2 4th in a fraction

Step-by-step explanation:

Answer:

2 cups

Step-by-step explanation:

    6 and a 1/2 cups

-

    4 and a 1/2 cups

the 2 halfs would cross out and 6-4 is 2.

Answer:

Yes they are mutually exclusive

Step-by-step explanation:

Yes, both of the events are mutually exclusive because each student has only one major and therefore can't select both Maths and finance majors at the same time.

Thus, they are mutually exclusive of each other.

Answer:

x=12°

Step-by-step explanation:

property of triangles:

4x-2=180°-30°-100°=50°

\(4x+2=50\)

\(4x=50-2=48\)

\(x=\frac{48}{4} =12^{0}\)

I hope this help you

Answer:

Step-by-step explanation:

if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.

so, we do the rule of three:

x = (94900 * 100)/ 65

x = 146000

and that is the population in 2020.

Answer:

Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?

Answer:

Option 4: -6.1 - (-3.13)

Step-by-step explanation:

Let's solve each option individually to see if  -2.97 fits as the solution:

-6.1 - 3.13 = -9.23

-6.1 - (-31.3) = 25.2

-0.61 - (-3.13) = 2.52

-6.1 - (-3.13) =  -2.97

As you can see, -2.97 is the answer to Option 4.

So, the decimal -2.97 is the solution to the subtraction problem in Option 4.

Answer:

Its D

Step-by-step explanation:

Got it right brother

Answer:

77,5

Step-by-step explanation:

13

. 75

_____

65

71

_____

77,5

Answer:

\( {x}^{2} + 4x - 9 = 5x + 3 \\ {x }^{2} - x - 12 \\ {x}^{2} - 4x + 3x - 12 \\ x(x - 4) + 3(x - 4) \\ (x - 4)(x + 3) \\ x = 4 \: and - 3\)

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

it'd be (0, 5) it sits on the y line so it's the only y intercept

Answer:

y=-3x+5

Step-by-step explanation:

It start from its starts from 5 on the y axis, and goes down by 3 so its negitive. So y=-3x+5

Answer:

A. 2^20/3^8

Step-by-step explanation:

Hope this helped, have a good day <3

Answer:

2 20

3 8

Step-by-step explanation:

you times the exponent on the inside to the exponent on the outside

The meaning of the x-value on the line when y = 100 is the number of hours a student should spend on their homework to expect a score of 100 on the quiz.

1. The given information suggests that the math teacher plots student grades on the y-axis (vertical axis) and the number of hours they study on the x-axis (horizontal axis).

2. The teacher then draws a line of best fit, which represents the general trend or relationship between the quiz scores and the number of study hours.

3. We are asked to determine the meaning of the x-value on the line when y = 100, which implies finding the number of study hours required to expect a score of 100 on the quiz.

4. To find this value, we look for the point on the line where the y-coordinate is 100.

5. By observing the graph or equation of the line, we can determine the corresponding x-value or the number of study hours.

6. In this case, the x-value corresponding to y = 100 represents the number of hours a student should spend on their homework to expect a score of 100 on the quiz.

7. Therefore, the x-value on the line when y = 100 provides an estimate of the amount of time a student needs to allocate for studying in order to achieve a score of 100 on the quiz.

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Answer:

\(Length = 17\)

Step-by-step explanation:

Step 1:  Find the length of the rectangle

\(Area = Width * Length\)

\(\frac{51}{3} = \frac{3 * Length}{3}\)

\(17 = Length\)

Answer:  \(Length = 17 cm\)

The small business needs to produce 53 action figures on Friday

so that the mean number of action figures produced per day is 50.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Assuming that the small business needs to produce x number of action figures on Friday.

∴ (50 + 55 + 45 + 53 + 44 + x)/6 = 50.  (mean is average)

247 + x = 300.

x = 300 - 247.

x = 53.

So, On Friday they have to produce 53 action figures.

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The computer can occupy a maximum of 1200 bytes of memory.

To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.

If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.

The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.

Hence, the maximum memory capacity this computer can occupy would be 300 memory words.

To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:

300 memory words * 4 bytes per word = 1200 bytes.

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The answer is \(y^{4+6}\) = \(y^{10}\)

An isometric transformation is a transformation that preserves the distance and angles between a pre-image and its image. Examples are: translation, reflection, rotation.

Answer:

No, the side lengths are not preserved.

This is a non isometric transformation.

Answer:

The area of this figure is 31,29.

Step-by-step explanation:

We have to find also the area of the rectangle, then we will find the area of the circle and divide by 2 because here is a half circle.

area of the rectangle = b x h

area of the rectangle = 6 x 6

area of the rectangle = 36

diameter = 6

r = d : 2

r = 6 : 2

r = 3 ft

area of the circle = π x r²

area of the circle = 3,14 x 3 ft

area of the circle = 9,42 ft

area of half of circle = 9,42 : 2 = 4,71 ft

area of this figure = area of rectangle - area of half of the circle

area of this figure = 36 - 4,71

area of this figure = 31,29

So the area of this figure is 31,29.

I hope this is helpful. :)

The surface area of the rectangular prism is 1476 square units

From the question, we have the following parameters that can be used in our computation:

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

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The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

\(\[Tina = Kai + 4\]\)

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

\(\[16 = k + 4\]\)

This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

\(\[k + 4 = 16\]\)

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)

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Answer:

The novelist can write 4/15ths of a page in an hour.

Step-by-step explanation:

Just multiply 3/5 by the reciprocal of 9/4, which is 4/9. Multiply 3/5 and 4/9 to get 12/45 or 4/15. In conclusion, the writer can write 4/15th of a page in an hour.

The equations 3x + 4y = 24, x - 7y - 15 = 0, and y = -5x + 10, the constant amount that the function changes by over equal intervals is 1.333, 15, and -2, respectively.

An equation is a mathematical expression that uses symbols and numbers to represent two or more values and their relationship. It is used to show how different values are related and how they change in response to each other. Equations can be used to calculate the solutions to problems, and they are essential in understanding many scientific and engineering principles.

In order to determine the constant amount that the function changes by over equal intervals, we need to use the slope-intercept form of a linear equation. This form of the equation is written as y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope of the line (m) is the amount that the y-value changes by for every unit that the x-value changes by. To calculate the slope of the line, we will use the following equation: m = (y2 - y1) / (x2 - x1).

For the equation 3x + 4y = 24, the slope can be calculated as follows:

m = (4 - 0) / (3 - 0)
m = 4/3
m = 1.333

This means that for every unit increase in x, the y value will increase by 1.333.

For the equation x - 7y - 15 = 0, the slope can be calculated as follows:

m = (0 - (-15)) / (1 - 0)
m = 15/1
m = 15

This means that for every unit increase in x, the y value will increase by 15.

For the equation y = -5x + 10, the slope can be calculated as follows:

m = (10 - 0) / (0 - (-5))
m = 10/-5
m = -2

This means that for every unit increase in x, the y value will decrease by 2.

Therefore, for the equations 3x + 4y = 24, x - 7y - 15 = 0, and y = -5x + 10, the constant amount that the function changes by over equal intervals is 1.333, 15, and -2, respectively.

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Answer:

14

80

Step-by-step explanation:

Answer:

Step-by-step explanation:

35% of 40 is 14

55% of 80 is 44

Miguel will need to deposit approximately $3,261.25 into the annuity each year for 8 years in order for the annuity to have a total value of $24,000.

What is the annuity?

An annuity is a contract between you and an insurance company that requires the insurer to make payments to you, either immediately or in the future. You buy an annuity by making either a single payment or a series of payments.

We can use the formula for the future value of an annuity:

FV = PMT * \(((1 + r)^n - 1) / r\)

where FV is the future value, PMT is the regular payment, r is the interest rate per compounding period, and n is the number of compounding periods.

In this problem, we want to solve for PMT, given that FV = $24,000, r = 6.6%, n = 8, and payments are made at the end of each year.

First, we need to calculate the interest rate per year, since the annuity is compounded annually:

i = r / 100 = 6.6% / 100 = 0.066

Next, we can plug in the values and solve for PMT:

24000 = PMT *\(((1 + 0.066)^8 - 1) / 0.066\)

24000 = PMT * 7.3605

PMT = 24000 / 7.3605

PMT ≈ $3,261.25

Hence, Miguel will need to deposit approximately $3,261.25 into the annuity each year for 8 years in order for the annuity to have a total value of $24,000.

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Thanks to the other user

To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, the decimal equivalent to 2/5 is 0.4.

Answer:

The expected value of X, E(X), for the given probability distribution is 1.2

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E(x).

Hope is the sum of the product of the probability of each event and the value of that event. That is, it is the sum of the probability of each possible event multiplied by the frequency of said process, this indicates that if you have a discrete quantitative variable X with "n" possible events x₁, x₂, x₃... xₙ and probabilities P (X = xi) = Pi the mathematical expectation is:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + ... + xₙ*Pₙ

In this case:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + x₄*P₄

Being:

and replacing:

E(x)= 0* 0.5 + 1* 0.1 + 2*0.1 + 3*0.3

you get:

E(x)= 1.2

The expected value of X, E(X), for the given probability distribution is 1.2

Answer:

j=−9i+v

Step-by-step explanation:

Let's solve for j.

v=9i+j

Step 1: Flip the equation.

9i+j=v

Step 2: Add -9i to both sides.

9i+j+−9i=v+−9i

j=−9i+v

a. The probability that you will be accepted in both universities is 0.0875.

b. The probability that you will be accepted to at least one graduate program is 0.5125.

c. The probability that one and only one of the universities will accept you is 0.3875.

d. The probability that neither university will accept you is 0.4875.

a. The probability of being accepted in both universities is the product of the probabilities of being accepted in each university, since the events are independent:

P(accepted in A and accepted in B) = P(accepted in A) × P(accepted in B) = 0.25 × 0.35 = 0.0875

b. The probability of being accepted to at least one graduate program is the complement of the probability of being rejected by both universities:

P(accepted in A or accepted in B) = 1 - P(rejected by A and rejected by B) = 1 - P(not accepted in A) × P(not accepted in B) = 1 - 0.75 × 0.65 = 0.5125

c. The probability of being accepted in one and only one of the universities is the sum of the probabilities of being accepted in A and not in B, and being accepted in B and not in A:

P(accepted in A and not in B) + P(not accepted in A and accepted in B) = P(accepted in A) × P(not accepted in B) + P(not accepted in A) × P(accepted in B) = 0.25 × 0.65 + 0.75 × 0.35 = 0.3875

d. The probability of neither university accepting you is the product of the probabilities of not being accepted in each university:

P(not accepted in A and not accepted in B) = P(not accepted in A) × P(not accepted in B) = 0.75 × 0.65 = 0.4875

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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The average speed over the entire two hours will be 25 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The speed will be:

= Total distance / Total time taken

= (30 × 1) + (40 × 0.5) + (0 × 0.5) / 1 + 0.5 + 0.5

= 50 / 2

= 25 miles per hour.

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