we draw a random sample of size 64 from the normal population with variance 2.8. if the sample mean is 14.5, what is a 99% confidence interval for the population mean?

Answer:

b || c

Step-by-step explanation:

a can only be parallel to c is if c is parallel to either a or b as both a and b are parallel to each other. By the way || means that they are parallel lines.

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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The solution of the given trigonometric equation in the interval [0, 2π) is given by θ = 0.90, 5.39 (rounded off to two decimal places).

We need to solve for θ.

So, we can write cos(2θ) = 2/8 ⇒ cos(2θ) = 1/4

We know that cos(2θ) = 2

cos²θ - 1∴ 2cos²θ - 1 = 1/4⇒ 2

cos²θ = 5/4⇒ cos²θ = 5/8⇒ cosθ = ±(5/8)^(1/2)

Now, in the interval [0, 2π), cosθ is positive in the first and fourth quadrants only.

Hence, θ lies in the first and fourth quadrants and can be given as follows

:θ = cos⁻¹(5/8) and θ = 2π - cos⁻¹(5/8)

On evaluating, we get:θ = 0.896 and θ = 5.388

Therefore, the answer is 0.90, 5.39.

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We need to deal with sin^4(2x), which is equal to (sin^2(2x))^2. Applying the power reduction formula for sin^2(2x):
sin^4(2x) = ((1 - cos(4x))/2)^2
This expression does not contain any exponents greater than 1 and utilizes the power reduction formula as requested.

Using the power reduction formula for sin(2x), we have:
sin(2x) = 2sin(x)cos(x)
Substituting this into the expression sin^4(2x), we get:
sin^4(2x) = (2sin(x)cos(x))^4
Expanding this expression, we get:
sin^4(2x) = 16sin^4(x)cos^4(x)
Therefore, we can rewrite sin^4(2x) using the power reduction formula as:
16sin^4(x)cos^4(x)
the expression using power reduction formulas. Given the expression sin^4(2x), we can apply the power reduction formula for sin^2(x):
sin^2(x) = (1 - cos(2x))/2
Now, we need to deal with sin^4(2x), which is equal to (sin^2(2x))^2. Applying the power reduction formula for sin^2(2x):
sin^4(2x) = ((1 - cos(4x))/2)^2
This expression does not contain any exponents greater than 1 and utilizes the power reduction formula as requested.

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Answer:

The chemical element loses 4% of its weight everyday

Step-by-step explanation:

Here, we are interested in knowing the percentage weight loss of the chemical each day.

The key to answering this is looking at the expression inside the bracket.

We can express M(t) = 169•(0.96)^t as

M(t) = 169•(1-0.04)^t

So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here

Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%

Answer:

0.96

Step-by-step explanation:

The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.

The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.

Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.

Answer: 2

Step-by-step explanation:

Answer:

y = 7.2

Step-by-step explanation:

y ÷ 6 = 1.2

y ÷ 6 × 6 = 1.2 × 6

y = 7.2

a. Two populations.

b. Qualitative (categorical) data.

c. Proportion stats.

d. Null hypothesis: p1 = p2 (The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch). Alternative hypothesis: p1 > p2 (The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch).

e. Z-test for two proportions.

f. P-value.

g. A small P-value provides convincing evidence to support Phoebe's hunch that older students are more likely to bring a bag lunch than younger students.

h. 95% confidence interval to estimate the difference in proportions.

What is hypothesis?

A hypothesis is a proposed explanation or assumption that is tested through research and data analysis. It is a statement that suggests a relationship or difference between variables or phenomena and serves as a basis for scientific investigation.

a. There are two populations in this problem: the population of seniors and the population of sophomores.

b. This is a problem about qualitative (categorical) data since we are examining whether students bring a bag lunch or not.

c. We will use the proportion stats option in StatCrunch to complete this problem.

d. Null hypothesis (H0): The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch.

Alternative hypothesis (Ha): The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch.

e. The test statistic is the z-test for two proportions.

f. The P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

g. The strength of the P-value determines the level of evidence against the null hypothesis. If the P-value is small (below the significance level), it provides strong evidence against the null hypothesis. In this case, a P-value less than 0.05 (assuming significance level α = 0.05) would suggest convincing evidence to support Phoebe's hunch.

h. To construct a 95% confidence interval to estimate the difference in proportions, we use the formula:

Confidence interval = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the critical value corresponding to the desired confidence level (in this case, z value for a 95% confidence level).

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The cost of Eddie's entree was $2.66.

Let x be the cost of Eddie's entree.

We know that the total bill, including the cost of food and the tip, was split between Rita and Eddie. Therefore:

Rita's bill = cost of her food + her share of the tip

Eddie's bill = cost of his food + his share of the tip

Total bill = Rita's bill + Eddie's bill

We know that the total tip was $9, which is 18% of the total bill. Therefore, we can set up an equation:

0.18 × (Rita's bill + Eddie's bill) = $9

Simplifying this equation, we get:

Rita's bill + Eddie's bill = $50

We can now set up two more equations based on the cost of Rita and Eddie's meals:

Rita's bill = $8 (salad) + $20 (entree) + her share of the tip

Eddie's bill = $8 (salad) + x (entree) + his share of the tip

We know that Rita's share of the tip was $9, so her bill was:

Rita's bill = $8 (salad) + $20 (entree) + $9 (tip) = $37

We can now substitute this value into the first equation to solve for Eddie's bill:

Eddie's bill = $50 - Rita's bill = $50 - $37 = $13

We also know that Eddie's share of the tip was $9, so we can set up another equation:

0.18 × $13 = $2.34 (Eddie's share of the tip)

Finally, we can set up an equation based on the cost of Eddie's entree:

$8 (salad) + x (entree) + $2.34 (tip) = $13

Simplifying this equation, we get:

x = ($13 - $8 - $2.34) / 1 = $2.66

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True, all three parts of a whole, parts of a set, and division meanings of fractions involve the idea of partitioning.

Partitioning is a method of splitting numbers into smaller parts to make work easy. An example of Partitioning is when the child is taught to recognize that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4.

A fraction is defined as a part of the whole thing in mathematics, for example, when we say "1/2 of the pizza", we are partitioning the whole pizza into two equal parts and taking one of those parts. Types of Fractions are Proper Fractions, Improper Fractions, Mixed fractions, Like fractions, Unlike fractions, and Equivalent fractions

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It is accurate to say that Jayla biked the same speed but in the opposite direction as Sarah and Justin if they all cover the same distance at a given time.

Speed is used to measure the rate at which an object moves. The speed is based in the distance covered and the time used.

An individual may bike the same speed but in different direction if the time and distance covered is the same. But when there is a disparity, it not safe to say they run or bike the same speed.

To know if the bike the same speed, both Jayla, Sarah and Justin speed should be computed.

Therefore, It is accurate to say that Jayla biked the same speed but in the opposite direction as Sarah and Justin if they all cover the same distance at a given time.

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The information you gave was presented as a table with three columns: value, x-coordinate, and y-coordinate.

You would need to make a graph with the x-coordinate acting as the horizontal axis and the y-coordinate acting as the vertical axis in order to plot this data point. The size or colour of the data point would serve as a representation of the value.

Here is an illustration of a data point plot:

\(x | 12 | 14 | 14 | 34 \\ y | 1 | 1 | 3 | 3 \\ v | 1 | 1 | 3 | 3\)

The value at the position (12,1) will be 1, the value at the point (14,1) will be 1, the value at the point (14,3) will be 3, and the value at the point (34,3) will be 3. It's vital to remember that the values on the graph can be depicted by many colours or shapes.

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Answer:

False

Step-by-step explanation:

The line formed by a to b is right but you would need the same line as the same length as a to c soo

you would need 8 of 2 lines so you would not be incorrect

Answer:

Step-by-step explanation:

P=2975 + r and 4= p - 225

Answer:

21x^2-2x+1

Step-by-step explanation:

The area of shaded region= The area of the floor - area of the identical islands

The area of shaded region=(5x+1)^2-2*(2x)(x+3)=25x^2+1+10x-4x^2-12x=21x^2-2x+1

Answer:

The given expression P(√7-4; 4) represents the coordinates of a point P on a two-dimensional plane. The "P" stands for the point, and the "of" signifies that we're looking at the coordinates of that point.

In this case, the x-coordinate is √7-4 and the y-coordinate is 4. The x-coordinate tells us how far to the right or left of the origin (0,0) the point is located, while the y-coordinate tells us how far up or down from the origin it is. Together, these two coordinates give us the exact location of the point P on the plane.

The coordinates of point P are given as (√7-4, 4). Coordinates help to define a specific point on a plane using an ordered pair of numbers, typically written in the form (x, y). In this case, the x-coordinate is √7-4, and the y-coordinate is 4.

To understand the location of point P on a plane, you can follow these steps:
1. Start at the origin (0, 0).
2. Move √7-4 units in the horizontal (x) direction. If the value is positive, move to the right; if negative, move to the left.
3. Move 4 units in the vertical (y) direction. Since 4 is positive, move upward.

After following these steps, you will reach point P with coordinates (√7-4, 4) on the plane.

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Answer:

135 degrees

Step-by-step explanation:

180-90=90/2=45

180-45=135

Hope this helped:)

To sketch the region enclosed by the curves y = cos(x) and y = sin(2x) for the interval 0 ≤ x ≤ 2, we can follow these steps:

1. Plot the graphs of the two functions separately on the given interval.

For y = cos(x):

- Start by marking key points on the graph: (0, 1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1).

- Connect the points smoothly to create a curve that oscillates between 1 and -1.

For y = sin(2x):

- Start by marking key points on the graph: (0, 0), (π/4, 1), (π/2, 0), (3π/4, -1), (π, 0), (5π/4, 1), (3π/2, 0), (7π/4, -1), (2π, 0).

- Connect the points smoothly to create a curve that oscillates between 1 and -1, but with twice the frequency of the cosine curve.

2. Identify the region enclosed by the curves.

- The region enclosed by the curves is the area between the two curves from x = 0 to x = 2.

3. Shade the region enclosed by the curves.

- Shade the area between the two curves on the interval 0 ≤ x ≤ 2.

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There are a total of 600 Employees in the automotive company.

The total number of employees in the automotive company, we need to determine the proportion of employees working in each area.

Let's denote the total number of employees as "x". According to the given information:

- The proportion of employees working in auto parts assembly is 2/3 of the total. So, the number of employees in auto parts assembly is (2/3)x.

- The proportion of employees working in the washing area is 1/8 of the total. So, the number of employees in the washing area is (1/8)x.

- The proportion of employees working in the customer service area is 1/6 of the total. So, the number of employees in the customer service area is (1/6)x.

- The rest of the employees are executives, and the number of executives is given as 25.

We can set up an equation to represent the total number of employees:

(2/3)x + (1/8)x + (1/6)x + 25 = x

To solve this equation, we can simplify and solve for x:

[(16/24)x + (3/24)x + (4/24)x] + 25 = x

(23/24)x + 25 = x

25 = x - (23/24)x

25 = (1/24)x

x = 24 * 25

x = 600

Therefore, there are a total of 600 employees in the automotive company.

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The limit does not exist. As x approaches 0 from the left, x/|x| approaches negative infinity. As x approaches 0 from the right, x/|x| approaches positive infinity.

When we consider the expression x/|x|, we need to examine its behavior as x approaches 0 from both the left and the right. Let's first look at the left-hand limit as x approaches 0. In this case, x takes on negative values approaching 0. When x is negative and close to 0, the numerator x remains negative, but the denominator |x| becomes positive since the absolute value of a negative number is positive. Thus, x/|x| becomes a negative value divided by a positive value, resulting in a negative quotient. As x approaches 0 from the left, the quotient x/|x| approaches negative infinity.

Now let's consider the right-hand limit as x approaches 0. In this case, x takes on positive values approaching 0. When x is positive and close to 0, both the numerator x and the denominator |x| are positive. Therefore, x/|x| becomes a positive value divided by a positive value, resulting in a positive quotient. As x approaches 0 from the right, the quotient x/|x| approaches positive infinity.

Since the left-hand limit and the right-hand limit give different results (negative infinity and positive infinity, respectively), we conclude that the limit as x approaches 0 does not exist.

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Answer:

216

Step-by-step explanation:

6 * 6*6 = 216 possible outcomes

The number of outcomes for a rolling of cube three times = 216 outcomes

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

When rolling a six-sided number cube three times, we can calculate the total number of outcomes by considering the number of possible outcomes for each individual roll

Now , For each roll of the number cube, there are six possible outcomes

Since we are rolling the cube three times, we need to multiply the number of outcomes for each roll together:

Number of outcomes = 6 x 6 x 6 = 216

Hence , there will be 216 possible outcomes when rolling a six-sided number cube three times

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Answer: a set of all possible inputs for the function.

Step-by-step explanation:

Answer:  A domain of a function is all set of inputs that make the function definable.

Step-by-step explanation:

The teacher's goal in introducing students to a card game where they must find the missing addend could be to develop and enhance their algebraic reasoning skills.

By presenting the problem as a puzzle or game, the teacher aims to engage the students in a fun and interactive way while fostering their ability to think critically and solve mathematical problems. The game helps students practice identifying the missing addend and applying algebraic thinking to find the solution. Additionally, it promotes the development of problem-solving strategies, logical reasoning, and the ability to generalize mathematical patterns, which are foundational skills in algebraic reasoning.

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Answer:

m<-3 or m>5

Step-by-step explanation:

-2m+7<13

-2m<6

m<-3

5m+12>37

5m>25

m>5

The solution of the two expressions will be m<-3 or m>5.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the two inequalities are -2m + 7 < 13 or 5m + 12 > 37. The inequalities will be solved as,

-2m+7<13

-2m<6

m<-3

5m+12>37

5m>25

m>5

Hence, the solution for the inequalities will be m<-3 or m>5.

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After 10 minutes, there will be 130 kg of salt in the tank.

The initial amount of salt in the tank is 0.3 kg. We need to find the amount of salt in the tank after 10 minutes of adding and removing brine solution.

During each minute, 5 gallons of brine solution with 0.4 kg of salt per gallon is added to the tank. So, the amount of salt added per minute is:

0.4 kg/gallon x 5 gallons/minute = 2 kg/minute

At the same time, 5 gallons of the mixture containing salt is removed from the tank. So, the amount of salt removed per minute is:

(0.3 kg + amount of salt added) / 200 gallons x 5 gallons/minute = (0.3 + 2t) / 200 kg/minute

where t is the number of minutes.

The change in the amount of salt in the tank after 1 minute is the difference between the amount of salt added and the amount of salt removed:

2 kg/minute - (0.3 + 2t) / 200 kg/minute = (400 - 3 - 4t) / 200 kg/minute

After 10 minutes, the amount of salt in the tank will be:

0.3 kg + integral from t=0 to t=10 of [(400 - 3 - 4t) / 200] dt

= 0.3 kg + [200t - 2\(t^2\) - 3t] evaluated from t=0 to t=10

= 0.3 kg + [200(10) - 2\((10)^2\) - 3(10)] - [200(0) - 2\((0)^2\) - 3(0)]

= 0.3 kg + 160 - 30

= 130 kg

Therefore, after 10 minutes, there will be 130 kg of salt in the tank.

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The domain of a function are the values for which the function is defined or in the other words, it is the set of all possile values that the function accepts.

Therefore:

The solution is: : 9(4 + 5), is the distributive property of the GCF of 36 and 45 to rewrite the sum.

Here, we have,

given that,

36 and 45

we have,

The GCF of 36 and 45 is

36: 2 * 2 * 3 * 3

45: 3 * 3 * 5

The GCF of 45 and 36 is 9

9(4 + 5) would be how the distributive property would be written.

Hence, The solution is: : 9(4 + 5), is the distributive property of the GCF of 36 and 45 to rewrite the sum.

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complete question:

What is the distributive property of the GCF of 36 and 45 to rewrite the sum

Lines 2 and 3 are perpendicular, while Lines 1 and 2, and Lines 1 and 3 are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to examine their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If two lines have the same slope, they are parallel. If the product of their slopes is -1, they are perpendicular. Otherwise, they are neither parallel nor perpendicular.

Line 1: 10x - 4y = -4 can be rewritten in slope-intercept form as y = 2.5x + 1. This means its slope is 2.5.

Line 2: y = 5x + 7 is already in slope-intercept form. Its slope is 5.

Line 3: 5y = 2x + 4 can be rewritten in slope-intercept form as y = 0.4x + 0.8. This means its slope is 0.4.

Now we can compare the slopes of each pair of lines:

Lines 1 and 2: The slope of Line 1 is 2.5 and the slope of Line 2 is 5. These slopes are not equal and their product is not -1, so these lines are neither parallel nor perpendicular.

Lines 1 and 3: The slope of Line 1 is 2.5 and the slope of Line 3 is 0.4. These slopes are not equal and their product is not -1, so these lines are neither parallel nor perpendicular.

Lines 2 and 3: The slope of Line 2 is 5 and the slope of Line 3 is 0.4. Their product is -1, so these lines are perpendicular.

Therefore, Lines 2 and 3 are perpendicular, while Lines 1 and 2, and Lines 1 and 3 are neither parallel nor perpendicular.

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Answer:

Herman is wrong.  Latoya got the better deal.

Step-by-step explanation:

Latoya bought 8 pounds of potatoes for $18.

    ► 18 / 8 = $2.25 per pound

Herman bought 6 pounds of potatoes for $15.

    ► 15 / 6 = $2.50 per pound

Cheaper per pound is better!