HELP I'M BEING TIMED A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? A) The test contains 4 three-point questions and 20 five-point questions. B) The test contains 10 three-point questions and 14 five-point questions. C) The test contains 14 three-point questions and 10 five-point questions. D) The test contains 20 three-point questions and 8 five-point questions.

Answer:

The solution of the system of inequalities 3x > y and x + y ≤ 4 is graphed by the shaded region given.

a) The matrix representation of the given linear transformation T is:

A = [3/2, -3√3/2]

[3√3/2, 3/2]

b) The four transformed points represent the vertices of the image of the unit square under the transformation T.

c) The area of the image of the unit square under the transformation T is 9√3 square units.

a) Finding the matrix A of the linear transformation T:

To find the matrix representation of the given linear transformation, we need to consider the individual transformations involved and their effects on the standard basis vectors.

Rotation by θ = π/3 (anti-clockwise):

Rotation transformations preserve the length of vectors and change their direction. To find the effect of this rotation on the standard basis vectors, let's consider each basis vector individually.

The standard basis vectors are:

e₁ = (1, 0) (unit vector along the x-axis)

e₂ = (0, 1) (unit vector along the y-axis)

Applying the rotation transformation, we have:

T(e₁) = cos(π/3)e₁ + sin(π/3)e₂

= (cos(π/3), sin(π/3))

T(e₂) = -sin(π/3)e₁ + cos(π/3)e₂

= (-sin(π/3), cos(π/3))

Stretching by a factor of 3 along the x-axis:

Stretching transformations change the lengths of vectors while preserving their direction. We can directly apply the stretching transformation to the rotated basis vectors.

Applying the stretching transformation, we have:

T(T(e₁)) = 3T(e₁)

= 3(cos(π/3), sin(π/3))

= (3cos(π/3), 3sin(π/3))

T(T(e₂)) = 3T(e₂)

= 3(-sin(π/3), cos(π/3))

= (-3sin(π/3), 3cos(π/3))

Now, we can construct the matrix A using the resulting vectors as columns:

A = [3cos(π/3), -3sin(π/3)]

[3sin(π/3), 3cos(π/3)]

Simplifying the trigonometric values, we get:

A = [3/2, -3√3/2]

[3√3/2, 3/2]

b) Finding the image of the unit square under the transformation T:

To find the image of the unit square, we apply the transformation T to each of the four vertices of the unit square.

The vertices of the unit square are:

(0, 0), (1, 0), (1, 1), (0, 1)

Applying the transformation T to each vertex, we get:

T(0, 0) = (0, 0) (Origin remains unchanged)

T(1, 0) = (3/2, 3√3/2)

T(1, 1) = (3/2, 9√3/2)

T(0, 1) = (-3/2, 9√3/2)

c) Calculating the area of the image of the unit square under the transformation T:

To find the area of the image of the unit square, we can calculate the area of the parallelogram formed by the transformed vertices.

The lengths of the sides of the parallelogram can be determined by finding the differences between the transformed points. Let's label the transformed vertices as follows:

A = (0, 0)

B = (3/2, 3√3/2)

C = (3/2, 9√3/2)

D = (-3/2, 9√3/2)

The lengths of the sides are:

AB = BC = CD = DA = √((3/2)^2 + (3√3/2)^2) = √(9/4 + 27/4) = √(36/4) = 3

The height of the parallelogram is the difference between the y-coordinates of points C and B, which is 9√3/2 - 3√3/2 = 6√3/2 = 3√3.

The area of a parallelogram can be calculated by multiplying the base length by the height. In this case, the base length is 3, and the height is 3√3.

Area = base × height = 3 × 3√3 = 9√3 square units.

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For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.

The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.

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The number of scores above 18 in a sample of 1000 cases with a mean of 14 and a standard deviation of 2.5 is 2 or higher. This can be found using standard normal distribution and z-scores.

To find the number of scores above 18, we need to calculate the z-score that corresponds to 18 and then use a standard normal distribution table to find the proportion of scores that are above that z-score. The z-score can be calculated as (18-14)/2.5 = 2.

Next, we can look up the proportion of scores that correspond to a z-score of 2 or higher in a standard normal distribution table. This proportion represents the number of scores in the sample that are above 18, assuming a normal distribution.

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Answer:

4 ounces

Step-by-step explanation:

Mean = 62 kilobits per second

Standard deviation = 4 kilobits per second

We use the Z-score formula to solve the given question, where Z = (x-μ)/σ where x = random variable, μ = Mean, σ = Standard deviation We use the Z-score table which is available in the statistics book to find the probability that corresponds to the Z-score.

(a) Find the probability that the file will transfer at a speed of 70 kilobits per second or more?

The probability that the file will transfer at a speed of 70 kilobits per second or more is 0.023.

The probability that the file will transfer at a speed of 70 kilobits per second or more? Z-score formula Z = (x-μ)/σZ = (70-62)/4Z = 2P (Z > 2) = 1- P(Z < 2) = 1- 0.9772 = 0.0228

So, the probability that the file will transfer at a speed of 70 kilobits per second or more is 0.023. (Round to 3 decimal places)

(b) Find Probability that the file will transfer at a speed of less than 58 kilobits per second?

The probability that the file will transfer at a speed of less than 58 kilobits per second is 0.16.

Probability that the file will transfer at a speed of less than 58 kilobits per second: Z-score formula Z = (x-μ)/σZ = (58-62)/4Z = -1P (Z < -1) = 0.1587So, Probability that the file will transfer at a speed of less than 58 kilobits per second is 0.16. (Round to 2 decimal places)

(c) If the file is one megabyte, what is the average time (in seconds) it will take to transfer the file?

The time it will take to transfer one megabyte of file is 0.13 seconds.

Time (in seconds) it will take to transfer one megabyte of file at 8 bits per byte. One megabyte = 8 Megabits (1 byte = 8 bits) Mean = 62 kilobits per second. So, 1 Megabit will take (1/62) seconds, similarly 8 Megabits will take 8*(1/62) = 0.129 seconds. So, the time it will take to transfer one megabyte of the file is 0.13 seconds. (Round to 2 decimal places)

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Step-by-step explanation:

well what is the question??

Answer:theres no q

Step-by-step explanation:

Probability P(D and C) is (C) 1/2.

To find the probability P(D and C):

According to the task content;

On this note, the probability, P(D and C) is given as;

Therefore, probability P(D and C) is (C) 1/2.

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The correct question is given below:
300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a dog, 180 have a cat, and 150 have a cat and a dog. Using this information, answer each of the following questions.

Let D be the event that a randomly selected student has a dog and C be the event that a randomly selected student has a cat.

What is P(D and C), the probability that a student in the class has a dog and a cat?

A) 2/3

B) 3/5

C) 1/2

D) 5/6

Given that:

Total number of fish = 140

Fish are green swordtails female = 44

Fish are green swordtails male = 36

Fish are orange swordtails female = 36

Fish are orange swordtails male = 24

Solution:

A. We have to find the probability that the selected fish is a green swordtail.

\(\text{P(green swordtail)}=\dfrac{\text{Total green swordtail fish}}{\text{Total fish}}\)

\(\text{P(green swordtail)}=\dfrac{80}{140}\)

\(\text{P(green swordtail)}=\dfrac{4}{7}\)

Therefore, the probability that the selected fish is a green swordtail is \(\dfrac{4}{7}.\)

B.  We have to find the probability that the selected fish is male.

\(\text{P(Male fish)}=\dfrac{\text{Total male fish}}{\text{Total fish}}\)

\(\text{P(Male fish)}=\dfrac{36+24}{140}\)

\(\text{P(Male fish)}=\dfrac{60}{140}\)

\(\text{P(Male fish)}=\dfrac{3}{7}\)

Therefore, the probability that the selected fish is a male, is \(\dfrac{3}{7}.\)

C. We have to find the probability that the selected fish is a male green swordtail.

\(\text{P(Male green swordtail)}=\dfrac{\text{Total male green swordtail fish}}{\text{Total fish}}\)

\(\text{P(Male green swordtail)}=\dfrac{36}{140}\)

\(\text{P(Male green swordtail)}=\dfrac{9}{35}\)

Therefore, probability that the selected fish is a male green swordtail is \(\dfrac{9}{35}.\)

D.

We have to find the probability that the selected fish is either a male or a green swordtail.

\(\text{P(Male or green swordtail)}=\dfrac{\text{Total male or green swordtail fish}}{\text{Total fish}}\)

\(\text{P(Male or green swordtail)}=\dfrac{44+36+24}{140}\)

\(\text{P(Male or green swordtail)}=\dfrac{96}{140}\)

\(\text{P(Male or green swordtail)}=\dfrac{24}{35}\)

Therefore, the probability the selected fish is either a male or a green swordtail is \(\dfrac{24}{35}.\)

Always check the quantity in each package to determine the appropriate number of hotdog bun packages needed for the given number of hotdog packages.
The dependent variable in this situation is the number of packages of hotdog buns needed, as it relies on the number of packages of hotdogs (the independent variable).

We want to know the dependent variable when considering the number of packages of hotdog buns needed for a certain number of packages of hotdogs.

Let me explain this relationship:
First, let's define the terms involved.

The dependent variable is the variable that depends on another variable (called the independent variable).

In this case, we are examining the relationship between the number of packages of hotdogs and the number of packages of hotdog buns needed.
The independent variable is the number of packages of hotdogs.

This is because the number of hotdog buns needed depends on the number of hotdogs you have.
The dependent variable, in this case, is the number of packages of hotdog buns needed.

This variable depends on the number of packages of hotdogs, as you need a certain amount of buns to accommodate the hotdogs.

To determine the relationship between these two variables, we would likely use a proportion or a ratio.

For example, if one package of hotdogs contains 10 hotdogs and one package of hotdog buns contains 10 buns, then the ratio is 1:1, meaning you need one package of hotdog buns for every package of hotdogs.
This relationship may vary depending on the number of hotdogs and buns in each package.

Remember to examine the proportion between the two variables to ensure you have the correct amount of buns for the hotdogs.

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Answer:

C.10 units

Step-by-step explanation:

To find the distance between two points in the coordinate plane, i use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

In this case, we have two points: (5, 2) and (-3, -4). We can plug these coordinates into the distance formula:

distance = sqrt[(-3 - 5)^2 + (-4 - 2)^2]

distance = sqrt[(-8)^2 + (-6)^2]

distance = sqrt[64 + 36]

distance = sqrt[100]

distance = 10

Therefore, the distance between (5, 2) and (-3, -4) on the coordinate plane is 10 units.

12.03% is the approximate amount rate of return earned.

We can use the formula for the future value of an annuity to solve this problem. The formula is:

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

where FV is the future value of the annuity, P is the payment (in this case, $250), r is the annual interest rate, and n is the number of years.

Using the information given in the problem, we know that:

P = $250

n = 5

FV = $1,750

Substituting these values into the formula, we get:

$1,750 = $250 * ((1 + r)^5 - 1) / r

Multiplying both sides by r and dividing both sides by $250, we get:

7 = ((1 + r)^5 - 1) / r

Multiplying both sides by r, we get:

7r = (1 + r)^5 - 1

Expanding the right side using the binomial theorem, we get:

7r = 1 + 5r + 10r^2 + 10r^3 + 5r^4 + r^5 - 1

Simplifying and rearranging, we get:

r^5 + 5r^4 + 10r^3 + 10r^2 - 7r = 0

We can solve this equation numerically using a calculator or a computer. One way to do this is to use the Newton-Raphson method, which is an iterative method that starts with an initial guess and refines it until it converges to a solution. Using this method with an initial guess of r = 0.1, we get:

r ≈ 0.1203

So the annual interest rate that you earned on the account is approximately 12.03%.

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Answer:

-4721613632.87 or -4721613632.9 or -4721613633

Step-by-step explanation:

10x9.2^-13 = 10x-472161363.287 = -4721613632.87 or you can round -4721613632.9 or -4721613633

Slope if distance time graph represent velocity or speed.

Yes, it can be parallel to time axis if the object is at rest position

The LCM of the given numbers have been determined.

LCM stands for Least Common Multiple .

For two numbers , LCM is the number that is the smallest number of which they both are a factor.

It is asked to determine

LCM of 6 and 9

6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}

9 = { 9 , 18 ,27 .....}

The LCM of 6 , 9 is 18

LCM of 8 and 12

8 = { 8,16,24,32....}

12 = {12 , 24 ,36....}

The LCM of 8 and 12 is 24

LCM of 4 , 6 and 8

4 = {4 , 8 , 12 , 16 , 20,24,28 ....}

6 = { 6 ,12 ,18,24......}

8 = {8 , 16,24 .....}

The LCM of 4,6 and 8  is 24

The LCM of 6 and 15 is 30  

The LCM of 20 and 30 is  60

The LCM of 25,30 and 75 is 150

The image of the solution is attached .

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Part A: Each block will have an area of 128 square inches (8 in. x 16 in.), but the outside border of each block will be covered with blue paint.

Area is the measurement of the space contained within a two-dimensional surface.

The outside border of each block is 8 in. long and 16 in. high, for a total of 128 square inches of each block that is covered in blue paint.

Part B: The entire mural will have 25 identical blocks, so the total number of square inches of the entire mural that will be covered by white paint is 3,200 square inches (25 blocks x 128 square inches per block).

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Answer:

The answer might be \(\frac{1}{4}\)

Step-by-step explanation:

Answer:

the answer is -1/4

Step-by-step explanation: i took the test bro

Answer:

I didn't study that

Step-by-step explanation:

Answer: 135 degrees

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

sum of triangle angles = 180

then JLK =. 180 -(70+65) = 180 - 135 = 45

then JLK = 45

since JLM = 180

then KLM = 180 - 45 = 135

The  probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:

P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
     = 7 * 0.65^6 * 0.35^1
     = 0.3052

Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

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Answer:

x = 16 units

Step-by-step explanation:

∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.

If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.

Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.

Since side BC is part of BCD.

Side opposite of 90° [∆BCD] = BC = 32.

Since x is opposite of 30° [∆BCD].

x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.

Answer:

x = 2 and y = 3

Step-by-step explanation:

given:

using elimination rule:

 2x - 3y = -5

- 2x - y = - 7

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

-4y = -12

y = 3

Find x:

2x - 3y = -5

2x - 3(3) = -5

2x - 9 = -5

2x = - 5+9

2x = 4

x = 2

Answer:

\(y=3\\x=2\\\)

Step-by-step explanation:

\((2x-3y)-(2x+7)\\=-4y=(-5)-(7)\\-4y=-12\\y=12/4\\y=3\)

Insert y=3 into any one equation in the system of equations:

\(2x-3(3)=-5\\2x-9=-5\\2x=4\\x=4/2\\x=2\)

or

\(2x+(3)=7\\2x=4\\x=4/2\\x=2\)

Answer:

1- \(\frac{1}{2}\)

2- 1

3- -2

Step-by-step explanation:

1-

Add the numbers : \(\frac{5}{10}\)

Reduce the fraction with 5 : \(\frac{1}{2}\)

Solution : \(\frac{1}{2}\)

2-

Calculate the difference: \(\frac{-3}{-3}\)

Divide: 1

Solution: 1

3-

Subtract the numbers: \(\frac{6}{-3}\)

Reduce the fraction : -2

Solution: -2

Answer:

1. 1/2 or (2,1)

2. 1 or (-3,-3)

3. -2/1 or (-3,6)

Step-by-step explanation:

1. 2-(-3) = 2 + 3 =5

   6-(-4)= 6 +  4= 10

so 1/2 or (2,1)

2. 1-4 = 1 + (-4) = -3

  -2-1 = -2 + (-1)= -3

so 1 or (-3,-3)

3.  12-6 = 12 + (-6) = 6

    2-5 = 2 + (-5) = -3

so  -2/1 or (-3,6)

Answer:

The answer is C. $3.825. that is what i got

Answer:

The cost of the 250 bales of order is $4,250. So the its D.

Step-by-step explanation:

Based on the table, we can take any one and try to calculate the order of 1 bale. Eg., The first row states the cost of 150 bales of hay is $2550. So lets find how much is the cost of 1 bale which can be obtained by dividing 2550 by 150.

   1 bale = $2550 ÷ 150 bales = $17 per bale.

So now the question says what is the cost of 250 bales, which is nothing but 250 × $17 = $4250.

Answer:

Step-by-step explanation:

The median of the given set of data is 24.

We have a set of data given in the figure.

We have to determine its median.

The median is defined as the middle number in an ordered data set.

According to question, we have the following data set -

0, 12, 20, 28, 33, 40

The total number of elements (N) = 6 - which is even

The Median of a set of even number of elements is the average of the two middle values.

The two middle values are -  X[3] = 20 and X[4] = 28

Therefore -

Median = \(\frac{X[3]+X[4]}{2}\)= \(\frac{20+28}{2}\) = 24

Hence, the median of the given set of data is 24

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