Bilquis and Kayla are reading the same book. At the beginning of the month, Bilquis was on page 23 and Kayla was on page 2. Bilquis will read 7 pages per day and Kayla will read 14 pages per day. Let
B represent the page of the book that Bilquis is on at the end oftt days into the month, and let K represent the page of the book that Kayla is on at the end of t days into the month. Write an equation for each situation,in terms of t, and determine whether Bilquis or Kayla is farther along in the book after 4 days.

Answer:

C: She subtracted 15 from each side of the equation.

Step-by-step explanation:

30 = 15 - 3x

-15

   15 = -3x

The math operation Amanda did to apply in her first step is She subtracted 15 from each side of the equation, the correct option is C.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Equation is 30 = 15 - 3x

Now,

We can  check this by adding 15 to both sides of her first step and see that you get back the original equation.

15 = -3x 15 + 15 = -3x + 15 30 = 15 - 3x

Therefore, by the given equation answer will be  She subtracted 15 from each side of the equation.

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Answer:

Step-by-step explanation:

To solve for x in the equation 5 - 3(x + 1) = 4x - 40, we can simplify and rearrange the terms as follows:

5 - 3(x + 1) = 4x - 40

5 - 3x - 3 = 4x - 40 (distribute the -3)

2x = 32 (add 3x to both sides and add 40 to both sides)

x = 16 (divide both sides by 2)

Therefore, the value of x in the equation 5 - 3(x + 1) = 4x - 40 is 16.

Answer:

x = 6

Step-by-step explanation:

5 - 3(x + 1) = 4x - 40 ← distribute parenthesis and simplify left side

5 - 3x - 3 = 4x - 40

2 - 3x = 4x - 40 ( subtract 4x from both sides )

2 - 7x = - 40 ( subtract 2 from both sides )

- 7x = - 42 ( divide both sides by - 7 )

x = 6

Julie has $1,000 and wants to invest it. She has three options: 1-year Treasury note paying 4.4% interest, 1-year CD paying 3.9% interest, or money market mutual fund with an average yield of 3.7%. Pros of Treasury note are high interest rate but con is lack of flexibility. Pros of CD are lower risk and predictable return but con is lower interest rate. Pros of money market fund are liquidity and flexibility but con is lower interest rate.

The investment options available to Julie are 1-year Treasury note paying 4.4 percent interest This option offers the highest interest rate among the three options and is a low-risk investment as it is backed by the government. However, the money is locked in for one year, and there may be penalties for early withdrawal.

1-year CD paying 3.9 percent interest This option is also a low-risk investment, but the interest rate is slightly lower than the Treasury note. The money is also locked in for one year, and there may be penalties for early withdrawal.

Money market mutual fund with an average yield of 3.7 percent This option offers a slightly higher return than a savings account, but the risk level is slightly higher. The money can be withdrawn at any time without penalty, making it a more flexible option.

The pros of the Treasury note and CD options are higher interest rates and low-risk investments, while the cons are that the money is locked in for one year, and there may be penalties for early withdrawal.

The pros of the money market mutual fund are flexibility and slightly higher returns, while the cons are slightly higher risk and lower returns compared to the other two options. Julie should weigh the pros and cons of each option based on her personal financial goals and risk tolerance.

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The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.

Given that:

Rate, r = £1.28 per metre

The length of the fence is calculated as,

P = 10 + 6 + 8

P = 24 meters

Then the total cost of the fence will be calculated as,

Total cost = P x r

Total cost = 24 x £1.28

Total cost = £30.72

The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.

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The missing diagram is given below.

a) The proportion of the class with a midterm mark less than 75 is about 30.85%.

b) The probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.

a. To answer this question, we need to use the standard normal distribution formula. We convert the value of 75 to a z-score using the formula: z = (x - μ) / σ, where x is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation.

So, z = (75 - 78) / 6 = -0.5.

Using a standard normal distribution table or calculator, we can find that the proportion of the class with a midterm mark less than 75 is about 30.85%.

b. To answer this question, we need to use the central limit theorem, which states that the sample means of large samples (n ≥ 30) from any population will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ / √n).

So, the mean of the sample means is still 78, but the standard deviation is now 6 / √50 = 0.848.

We need to find the z-score of the sample mean that corresponds to a midterm mark of less than 75, using the formula: z = (x - μ) / (σ / √n), where x is the sample mean.

So, z = (75 - 78) / (0.848) = -3.54.

Using a standard normal distribution table or calculator, we can find that the probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.

a. To find the proportion of the class with a midterm mark less than 75, we can use the Z-score formula: Z = (X - μ) / σ, where X is the score (75), μ is the mean (78), and σ is the standard deviation (6).

Z = (75 - 78) / 6 = -0.5

Now, we can look up the Z-score of -0.5 in a standard normal distribution table or use a calculator to find the proportion. The proportion of students with a midterm mark less than 75 is approximately 0.3085 or 30.85%.

b. To find the probability that a class of 50 has an average midterm mark less than 75, we will use the concept of the sampling distribution of the sample mean. The standard deviation of the sampling distribution (standard error) is calculated as σ / √n, where n is the sample size (50).

Standard error = 6 / √50 ≈ 0.85

Now, we can calculate the Z-score for the sample mean: Z = (75 - 78) / 0.85 ≈ -3.53

Using the standard normal distribution table or calculator, we find the probability to be approximately 0.0002 or 0.02%. So, there is a 0.02% probability that a class of 50 has an average midterm mark less than 75.

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The measure of angle C in the given triangle is approximately 37°

From the question, we are to determine the measure of angle C in the given diagram.

The diagram shows a triangle

From the Law of Sines, we know that

sin (A)/ a = sin (B) / b = sin (C) / c

Thus,

In the given triangle, we can write that

sin (C) / c = sin (B) / b

From the given information

c = 9

B = 70°

b = 14

Substitute the parameters into the equation

sin (C) / 9 = sin (70°) / 14

sin (C) = (9 × sin (70°)) / 14

sin (C) = 0.604088

C = sin⁻¹ (0.604088)

C = 37.16

C ≈ 37°

Hence, the measure of C is 37°

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Answer:

  0.464

Step-by-step explanation:

You want the probability that a student prefers afternoon classes, given that the student is a junior.

The conditional probability can be found using the formula ...

  P(A|J) = P(A&J)/P(J)

For the values on the right, we can use numbers of students. This gives ...

  P(A|J) = 13/(6+13+9) = 13/28 ≈ 0.464

The probability that a student prefers afternoon classes given they are a junior is about 0.464.

__

Additional comment

We can use numbers of students in the above calculation because the corresponding probability is that number divided by the total number of students. That "divided by" factor is common to numerator and denominator, so cancels. This simplifies the calculation.

We used A|J to signify "prefers afternoon" given "is a junior".

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Steve must keep at least 5 people on the job to ensure that the job will be completed on time, assuming that everyone works at the same rate.

This is because after 6 days, 8 people have already completed [tex]$\frac{1}{3}$[/tex]of the job, and the remaining job can be completed by 5 people working at the same rate in 24 days.

Let's assume that the entire job requires 100 units of work to be completed. After 6 days, 8 people have already completed [tex]$\frac{1}{3}$[/tex] of the job, which means they have completed [tex]$\frac{1}{3}\cdot[/tex]100= 33.33$ units of work in 6 days. Their combined rate of work is [tex]$\frac{33.33}{6\cdot 8}[/tex]=0.6944$ units per day per person.

Now, the remaining job that needs to be completed is 100-33.33=66.67 units of work. If we assume that x people need to be kept on the job to ensure that the job will be completed on time, then the equation becomes:[tex]$\frac{66.67}{(30-6)\cdot x}[/tex]=0.6944$

Simplifying this equation, we get: [tex]$x\geq \frac{66.67}{24\cdot 0.6944}[/tex]=4.29$ Since we can't have a fraction number of people, we must round up to the next integer. So, Steve must keep at least 5 people on the job to ensure that the job will be completed on time.

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Answer:

Step-by-step explanation:

For b

[tex]9\sqrt{3} = 3^{2} 3^{\frac{1}{2} }[/tex]

add exponents

=[tex]3^{\frac{5}{2} }[/tex]

so b= 5/2

For c

[tex]\frac{1}{\sqrt{3} } = 3^{-\frac{1}{2} }[/tex]

so c= -1/2

The statistic typically used in the estimation of the population variance of a variable is the sample variance, denoted by s².

The sample variance is a measure of the spread or dispersion of a set of data around its mean. It is calculated by taking the sum of the squared differences between each data point and the sample mean, and then dividing by the sample size minus one.

The sample variance is an unbiased estimator of the population variance, which means that its expected value is equal to the true population variance. However, the sample variance is not the only statistic used in the estimation of the population variance. Other statistics, such as the z-score, Student's t-test, chi-squared test, and Thompson's tau, may also be used in certain contexts depending on the specific research question and data characteristics.

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The value of Sin W after calculating is 12/13.

The formula for calculating sin is perpendicular / hypotenuse. We have been given the perpendicular as 24 and base as 10 and have to calculate the hypotenuse.

Hypotenuse² = base² + perpendicular²

Hypotenuse² = 10² + 24²

Hypotenuse² = 100 + 576

Hypotenuse² = 676

Hypotenuse = √676

= 26

Sin W = perpendicular / hypotenuse

= 24 /26

= 12/13

The sine function in trigonometry is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.

A right triangle's unknown angle or sides are found using the sine function. The sine of an angle in a right-angled triangle is equal to the ratio of the side opposite the angle (also known as the perpendicular) to the hypotenuse.

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The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.

We have,

Let's call the smaller number "x".

Since the other number is 20% more than the smaller number, the larger number can be represented as:

x + 0.2x = 1.2x

We know that the sum of the two numbers is 196, so we can set up the equation:

x + 1.2x = 196

Simplifying the left side of the equation, we get:

2.2x = 196

Dividing both sides by 2.2, we get:

x = 89.09 (rounded to two decimal places)

Therefore,

The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.

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As per the standard deviation, the area of the shaded region is 0.7619 (option c).

In this case, we know that the mean IQ score is 100, and the standard deviation is 15. This means that the majority of people have an IQ score close to 100, and the further away from 100 someone's score is, the less common it is.

Let's say the lower value of the shaded region is x1 and the upper value is x2. We can find the z-scores for these values:

z1 = (x1 - 100) / 15

z2 = (x2 - 100) / 15

Without knowing the specific values of x1 and x2, we can't calculate the exact probability. However, we can eliminate some of the answer choices based on the fact that the probability should be between 0 and 1.

If one of the answer choices is greater than 1, we know that it's incorrect. Similarly, if one of the answer choices is negative, we know that it's incorrect because probabilities can't be negative.

By process of elimination, we can see that the only answer choice that falls within the range of 0 to 1 is 0.7619.

Therefore, the correct answer is option (c).

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Answer:

The correct answer is x = 1 and x = -3. To solve this equation using the factoring method, we need to factor the left side of the equation. This gives us (2x + 3)(x - 1) = 0. We then set each factor equal to 0 and solve for x. This gives us x = 1 and x = -3.

Is there anything else I can help you with?

Answer:

1. 1/2

2. 1/-1.5

3.1/-2

Step-by-step explanation:

Answer:

all of them apply

Step-by-step explanation:

Here is the completed table:

Outcome: Friends Family At Home

Probability: 0.27  0.35   0.38

Or

1) Friends = 0.27

2) Family = 0.35

3) Home = 0.38

The table shows the sample space for the spring break plans of the students surveyed. The sample space includes three outcomes: going out of town with friends, going out of town with family, and staying at home. The probabilities for each outcome are given in the table. The probability of an outcome represents the proportion of students who reported that outcome in the census.

a) A ∪ B = {1, 4, 7, 9, 10, 14, 17, 20}, b) A ∩ C =  {}, A ∪ C = {2, 3, 4, 7, 10, 14, 17, 20}, A ∩ B ∩ C =  {}( null set)

a) A ∪ B is union of two sets

= {1, 4, 7, 9, 10, 14, 17, 20}

b) A ∩ C is intersection between the sets A and C

= empty set (since they have no elements in common.)

c) A ∪ C is  union of two sets

= {2, 3, 4, 7, 10, 14, 17, 20}

d) A ∩ B ∩ C is intersection between the sets A, B, and C

= empty set (since they have no elements in common)

e) B ∪ C is union of two sets

= {1, 2, 3, 4, 7, 9, 10, 14, 17, 20}

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As the length of confidence interval for population mean decreases, degree of confidence in interval's actually containing population mean is option b. increases.

This is because the length of the confidence interval is determined by the level of confidence and the sample size.

With a larger sample size leading to a narrower interval.

As the interval becomes narrower, it becomes more precise and therefore more likely to contain the population mean.

So, if keep the same level of confidence and increase the sample size.

The confidence interval will become narrower, increasing our degree of confidence in its ability to contain the population mean.

Conversely, if keep the same sample size and decrease the level of confidence, the interval will also become narrower.

But will be less confident in its ability to contain the population mean.

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The length BC is 13.86 units and the length of segment QP is 6 units

Given that

arc AXB = 240 degrees

OA = 8 units

This means that

∠AOB = 360 - 240

∠AOB = 120

The length AC is

tan(∠AOB/2) = AC/OA

So, we have

tan(60) = AC/8

This gives

AC = 8 * tan(60)

Evaluate

AC = 13.86

So, we have

BC = AC = 13.86

This is calculated as

QP² = OP² - OQ²

So, we have

QP² = (8 + 2)² - 8²

Evaluate

QP² = 36

So, we have

QP = 6

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The surface area of the cylinder is approximately 43,098.41 square yards.

The first step is to find the radius of the cylinder, which can be calculated by dividing the circumference by 2π

radius = circumference / (2π) = 516.24 yards / (2 × 3.14) ≈ 82.27 yards

Once we have the radius, we can use the formula for the surface area of a cylinder

surface area = 2πr² + 2πrh

where r is the radius and h is the height.

Plugging in the values we have

surface area = 2 × 3.14 × 82.27² + 2 × 3.14 × 82.27 × 10

Do the arithmetic operation

surface area ≈ 43,098.41 square yards

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The correct graph to display the data is the first one: a bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44.

We are given that;

The four graphs of the data

Now,

A bar graph is appropriate for categorical data, such as sport, where each category is distinct and has no inherent order. A histogram is appropriate for numerical data, such as height or weight, where the data is grouped into intervals that have equal width and are ordered from lowest to highest. A histogram has no gaps between the bars, while a bar graph has gaps to show that the categories are separate.

The order of the bars in a bar graph does not matter, as long as they match the labels. The order of the bars in a histogram does matter, as they reflect the order of the intervals. The second and fourth graphs are histograms and not suitable for this data. The third graph is a bar graph but has the wrong labels for the bars, so it does not match the data either.

Therefore, the graph will be of option 1.

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The length of an edge of the cube is, 17.3 inches

Given that;

A diagonal of a cube measures 30 inches

And, diagonal of a face measures the square root of 600 inches i.e √600 inches

Now, Consider the right angled triangle formed by the two diagonals and a side of the cube.

Now, lets use Pythagoras theorem,

(Side)² + (Face Diagonal)² = (Inner Diagonal)²

(Side)² = (30)² - (√600)²

(Side)² = 900 - 600

Length of the side = √300 = √3 × 100

Length of the side = 10√3 = 10 x 1.732 = 17.3

Thus, the length of an edge of the cube is, 17.3 inches

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A florist will used a several different types of flowers to make bouquet. Lilies 8, roses 1, and daffodils 13. Then, the probability of randomly selecting a lily from the bouquet is 4/11.

The total number of flowers in the bouquet is;

Total number of flowers = lilies + roses + daffodils = 8 + 1 + 13 = 22

The probability of randomly selecting a lily is the number of lilies in the bouquet divided by the total number of flowers;

P(lily) = number of lilies / total number of flowers = 8 / 22

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

P(lily) = 4 / 11

Therefore, P(lily) =  4 / 11

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The point it must contain is (4, 2), the correct option is D.

We are given that;

Slope=-1/2

Point= (2,3)

Now,

The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept. We know that the slope of this line is -1/2 and it passes through (2, 3). So we can substitute these values into the equation to get:

y = (-1/2)x + b

3 = (-1/2)(2) + b

3 = -1 + b

b = 4

So the equation of the line is y = (-1/2)x + 4.

To find which point lies on this line, we can substitute each of the given points into this equation and see which one satisfies it.

Let's start with point A (-2, 6):

6 = (-1/2)(-2) + 4

6 = 5

This point does not satisfy the equation of the line.

Let's try point B (0, 5):

5 = (-1/2)(0) + 4

5 = 4

This point does not satisfy the equation of the line.

Let's try point C (1, 2):

2 = (-1/2)(1) + 4

2 = 3.5

This point does not satisfy the equation of the line.

Finally, let's try point D (4, 2):

2 = (-1/2)(4) + 4

2 = 2

This point satisfies the equation of the line.

Therefore, if a line has a slope of -1/2 and contains the point (2, 3), then it must also contain point D (4, 2).

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The probability that a student has a brother or a sister is: 92%

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

We are given the parameters as:

Percentage that have a brother = 75%

Percentage that have a sister = 82%

Percentage that have a brother and a sister = 65%

Thus:

P(Brother or Sister) = 0.75 + 0.82 - 0.65

P(Brother or Sister) = 0.92 = 92%

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Answer:

Sales tax is a tax levied by the government on the sale of goods and services. It is usually calculated as a percentage of the sale price and added to the total cost of the transaction. The tax revenue generated from sales tax is often used to fund public services such as schools, roads, and public safety.

To calculate the amount of taxes you would pay on a $15.00 meal with a 7% sales tax, you would follow these steps:

Step 1: Convert the percentage tax rate to a decimal by dividing it by 100. In this case, 7% divided by 100 equals 0.07.

Step 2: Calculate the amount of taxes by multiplying the price of the meal by the tax rate in decimal form. In this case, $15.00 multiplied by 0.07 equals $1.05.

Step 3: Add the amount of taxes to the original price of the meal to find the total cost. In this case, $15.00 plus $1.05 equals $16.05.

Therefore, if you buy a meal from a restaurant that costs $15.00, and the tax is 7%, you would pay $1.05 in taxes, and the total cost of the meal would be $16.05.

Answer:

105

Step-by-step explanation:

Multiply .15 by 700=105

The point (-7,4) is the farthest from the point and the distance is 11 units away, the correct option is (d).

We have to find that which point is the farthest from the point (4,4),

The distance(d) between two points (x₁, y₁) and (x₂, y₂) can be calculated by the distance formula : √((x₂-x₁)² + (y₂-y₁)²);

Using this formula, we can find the distance between each of the points and (4, 4):

⇒ For point (-7, 4):

d = √((4 - (-7))² + (4 - 4)²)

d = √(11²)

d = 11 units

⇒ For point (4, 4):

d = √((4 - 4)² + (4 - 4)²)

d = 0 units

⇒ For point (4, -5):

d = √((4 - 4)² + (-5 - 4)²)

d = √(9²)

d = 9 units,

Therefore, the point farthest away from (4, 4) is (d) Point (-7, 4), and the distance is 11 units.

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The given question is incomplete, the complete question is

A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10. A point is plotted at (-7, 4), at (4, 4) and at (4, -5).

Which of the points plotted is farther away from (4, 4), and what is the distance?

(a) Point (4, -5), and it is 9 units away

(b) Point (4, -5), and it is 11 units away

(c) Point (-7, 4), and it is 9 units away

(d) Point (-7, 4), and it is 11 units away

Answer:

7/3  or 2 1/3.

Step-by-step explanation:

7/8 / 3/8

We invert the divisor and multiply, so we have:

7/8 * 8/3

= 7/3.