Given are the numbers of 10 test scores in this class of 25 students. Use the appropriate notation to answer the following: (10 points) 32, 69, 77, 82, 102, 68, 88, 95, 75, 80 a. Draw a 5-point summar

It will take them 2 hours to do the whole task if they work together.

If one person can do a task in 3 hours and another person can do the same task in 6 hours, then we can calculate their individual rates of work as follows:

The first person can do 1/3 of the task per hour (since it takes them 3 hours to do the whole task).

The second person can do 1/6 of the task per hour (since it takes them 6 hours to do the whole task).

When they work together, their rates of work will add up, so their combined rate of work is:

1/3 + 1/6 = 1/2

This means that working together, they can do 1/2 of the task per hour. To find out how long it will take them to do the whole task, we can use the formula:

time = work ÷ rate of work

Since the whole task is 1 unit of work, and their combined rate of work is 1/2 units per hour, we can plug in these values to get:

time = 1 ÷ (1/2) = 2 hours

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The correct option is (a) Gareth will choose the Brand R credit card for the freezer because it is $548.18 less expensive than the Brand S.

An annual percentage rate, or APR, is used to express the interest rate that is applied to the principal amount of a loan.

The credit card's yearly percentage rate is 9.31%.

Gareth takes four years to pay off a Brand R freezer compared to just 18 months for a Brand S freezer.

Overall, ten years have gone.

To determine which credit card has the lowest lifetime cost for a freezer, we must compare the APRs of the two cards.

Let's say there are 1000 freezers. As a result, the APR for 18 months will be lower because the interest rate's duration is shorter.

The B and R will therefore be $548.18 less expensive than Brand S, according to a comparison of the APR.

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Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Given:

The functions are:

\(f(x)=\log_4x\)

\(g(x)=f\left(\dfrac{1}{3}x\right)\)

The function f(x) is dilated to become g(x).

To find:

The effect on f(x).

Solution:

Transformation is defined as:

\(g(x)=f(kx)\)            ...(i)

Where, k is the factor of horizontal stretch and compression.

If 0<k<1, then the graph of f(x) stretched horizontally by factor \(\dfrac{1}{k}\).

If k>1, then the graph of f(x) compressed horizontally by factor \(\dfrac{1}{k}\).

It is given that

\(g(x)=f\left(\dfrac{1}{3}x\right)\)          ...(ii)

On comparing (i) and (ii), we get

\(k=\dfrac{1}{3}\)

Therefore, the graph of f(x) stretched horizontally by factor \(3\).

Answer:

Hope the picture helps you draw.

Step-by-step explanation:

Answer:

The elavator can handle 950 more pounds.

Step-by-step explanation:

Since the elevator can handle 2,000 lb, and there is currently 1,050 lb on it, you have to subtract the weight that the elevator can handle from the weight that's already on it. So in other words, do 2000 - 1050.

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Hope it helps!

0.148 is the probability that they are both democrats.

In one town, 39% of all voters are democrats.

If two voters are randomly selected for a survey, the probability that they are both democrats can be calculated as follows.

P(A) = 0.39 is the probability of selecting a democrat in the first draw.

P(B|A) = 0.38

is the probability of selecting a democrat in the second draw if the first draw selects a democrat.

P(B|A') = 0.39 is the probability of selecting a democrat in the second draw if the first draw does not select a democrat.

The probability that both voters are democrats is:

P(A) x P(B|A) = 0.39 x 0.38 = 0.1482

The result is 0.1482, which means the probability that two voters are both democrats in one town is 0.1482 to the nearest thousandth.

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The slope is \(\frac{dy}{dx}\) which means it's 100/40 which is 2.5 or 5/2

\(d\) has a full time job in defining difference :D

So basically the slope is defined as the difference in the \(y\) over the difference in the \(x\)

Answer:

5/2

Step-by-step explanation:

To find slope, we can see how much to rise and run from one point to another. In this example, the slope would be 5/2 because you rise 5 and run 2 to get to a different point.

Hope this helps! Have a nice day ^^

Answer: A rhombus i think

Step-by-step explanation:

Answer:

rhombus

Step-by-step explanation:

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

Answer:

Width is \(1 \frac{1}{4} m\) or 1.25m

Step-by-step explanation:

\(\frac{5}{6}\) ÷ \(\frac{2}{3}\) = 5/6 x 3/2 = 5/4

The real number √21 is an example of an irrational number. (Correct choice: C)

According to number theory, real numbers are formed by the following sets:

Then, by direct inspection we get the following conclusions:

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Line sense in Burgers vector refers to direction and orientation of the vector in relation to the crystal lattice structure of a material. In summary, line sense is an component of the Burgers vector, it represents the direction of a dislocation in a crystal lattice.

The Burgers vector represents the magnitude and direction of the lattice distortion caused by a dislocation in the crystal. Line sense is important in understanding the behavior and movement of dislocations within a crystal. The direction of the Burgers vector determines the slip plane and slip direction of the dislocation. Thus, understanding the line sense of the Burgers vector is crucial in predicting the mechanical properties and deformation behavior of materials.

Line sense is the direction associated with a dislocation in a crystal lattice, while Burgers vector is the vector that represents the magnitude and direction of the lattice distortion caused by a dislocation. To understand line sense in Burgers vector, follow these steps:
1. Identify the dislocation in a crystal lattice.
2. Determine the direction of the dislocation movement, which is the line sense.
3. Calculate the Burgers vector by tracing a closed loop around the dislocation and finding the difference between the starting and ending points.
4. The Burgers vector will include both the magnitude of lattice distortion and the direction (line sense) of the dislocation.

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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Step-by-step explanation:

Well. Let's call α the 120° angle, and β its supplementary angle (80°). Let's draw also the height of the triangle. We'll call it CH. We know, from goniometric relations, that BC * sinβ = CH and BC * cosβ = BH. We just apply the pythagorean theorem so we get: AC = \(\sqrt{(AB+BH)^2+CH^2}.\) By inserting all the values you'll get the result.

Given two events A and B with P(A) = 0.4 and P(B) = 0.7, the maximum and minimum possible values for P(A|B) can be calculated as follows: Minimum possible value of P(A|B):

The minimum possible value of P(A|B) occurs when A and B are independent events, which means that the occurrence of B does not affect the probability of A. Therefore, P(A|B) = P(A) / P(B) = 0.4 / 0.7 = 0.57

Maximum possible value of P(A|B): The maximum possible value of P(A|B) occurs when A is a subset of B, which means that whenever event B occurs, event A must also occur.

Therefore, P(A|B) = P(A ∩ B) / P(B) = P(A) / P(B) = 0.4 / 0.7 = 0.57

Therefore, the minimum and maximum possible values for P(A|B) are 0.57.

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Answer:

8. 15

9. D

10. A

Step-by-step explanation:

Answer:

Total number of pies make = 4

Step-by-step explanation:

Given - Mrs. Coote-Brown needed 1 gallon of sliced peaches to make

             peach pies for her family reunion.

To find - If each pie requires 4 cups of peaches, how many pies will  

               Mrs. Coote-Brown be making ?

Proof -

As we know 1 gallon = 16 cups.

Now given,

4 cups of peaches = 1 peach pie

⇒1 cup of peach = \(\frac{1}{4}\) peach pie

⇒16 cups of peaches = \(\frac{16}{4}\) peach pie

⇒1 gallon of peaches  = 4 peach pie

∴ we get

Total number of pies make = 4

The original price of the pair of jeans is equals to the $120.

We Jodi wants to buy a pair of jeans.

The purchase price of pair of jeans = $90

Discount on price of jeans = 75%

Let the original price of pair of jeans be equal to "$x". Percent is an important concept of mathematics. It is a number or ratio of fraction of hundred. It is denoted by symbol %. The formula is

% = ( part /whole )×100

Here, it is said that the price of pair of jeans, $90, is only 75% of the original price. So, we can write it as the following way 75% of x = 90

=> (75/100) of x = 90

=> (75/100) × x = 90

=> x = 90× 100/75

=> x = 9000/75

=> x = 120

Hence, required value of x is 120.

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

The z-transform of a discrete-time signal h[n] is a mathematical tool that allows us to analyze the frequency response of the signal. It is defined as:

H(z) = ∑h[n]z^(-n)

where z is a complex variable and h[n] is the discrete-time signal.

(b) The zero-points of the z-transform are the values of z for which H(z) = 0, and the pole-points are the values of z for which H(z) is infinite.

(c) To determine if h[n] is causal, we need to check if the z-transform has any poles at or inside the unit circle in the complex plane. A causal system is one in which the output depends only on present and past inputs, and not on future inputs. If the z-transform has any poles inside the unit circle, the system is not causal.

To determine if h[n] is stable, we need to check if the z-transform has any poles outside the unit circle. A stable system is one in which the output does not grow unbounded over time. If the z-transform has any poles outside the unit circle, the system is not stable.

f (x) = x2. The basic function f (x) is taken and "transformed" (or "translated"), which is a fancy way of saying that the formula is changed and the graph is moved as a result.

The approach known as the differential transform method is used to determine the coefficients of the Taylor expansion used to solve differential and integral equations. Therefore, it is possible to acquire the Taylor expansion of a solution of arbitrary order and, as a result, to accurately determine the solution to the given equation.

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the standard deviation of the sample means:

σ(x) = σ/\(\sqrt{n}\)

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.

For the random samples we take from the population, we can compute the mean of the sample means:

μ (x) = μ

and the standard deviation of the sample means:

σ(x) = σ/\(\sqrt{n}\)

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Answer:

10/3 and 23/4

Step-by-step explanation:

Answer:

9 1/12

Step-by-step explanation:

3 1/3 + 5 3/4

Get a common denominator of 12

3   1/3*4/4 +  5  3/4 *3/3

3 4/12 + 5 9/12

8 13/12

8 + 12/12 + 1/12

8+1+1/12

9+1/12

9 1/12

Changing to improper fraction

3 1/3 = ( 3*3+1)/3 =10/3

5 3/4 = ( 4*5+3)/5 =23/4

Getting a common denominator

10/3 * 4/4 = 40/12

23/4 *3/3 =69/12

                   -------------

                   109/12

12 goes into 109  9 times

9*12 = 108  and that leaves 1 left over

9 1/12

Answer:

25%

Step-by-step explanation:

Assuming that each child can only be a boy or a girl, then each child will have a probability of 0.5 or 50% of being either gender. Therefore, since we need to find the probability of at least 2 being boys then we simply need to multiply this probability twice.

0.50 * 0.50 = 0.25 or 25%

Using this data we can say that there is a 25% probability of there being at least 2 boys in the family.

Answer:

%35 of 200 is 70

Step-by-step explanation:

so it maybe 70

am i right

Answer:

70% percent of cards

Step-by-step explanation:

If I am wrong pls correct me

Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

\(w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5\)

The equation of the circle is x² + y² − 8x - 6y + 9 = 0.

(x - h)2+ (y - k)2 = r2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius. A circle touches the x-axis at (3,0) if it is tangent to the x-axis at that location.

From the graph,

It is clear that radius = 2 units and center = (4,3)

The standard equation of the circle is -

(x − a)² + (y − b)² = (r)²

where (a,b) represents the coordinates of the circle and r = radius

Now putting the values in the above equation,

(x − 4)² + (y − 3)² = (4)²

(x − 4)² + (y - 3)² = 16

If required for further work you can expand this to give:

x² - 8x + 16 + y²-6y+9-16= 0

x² + y² − 8x - 6y + 9 = 0

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To solve this problem, we multiply and divide the given expression by 2-i:

Recall that:

Therefore:

Finally, multiplying the factors in the numerator, we get:

Finally, simplifying the above result, we get:

If a scatterplot of standardized, bivariate data displays data that are mostly lying in the upper left and lower right-hand quadrants, then the Pearson correlation is typically going to be negative. The above statement is false.

Bivariate data involves studying and comparing two separate variables. For example, a researcher may record how long it takes people to complete a crossword puzzle while measuring the stress levels of the participants. In this example, the two variables that the researcher is examining are time and stress.

Scatterplots display these bivariate data sets and provide a visual representation of the relationship between variables. In a scatterplot, each point represents a paired measurement of two variables for a specific subject, and each subject is represented by one point on the scatterplot.

When the points on a scatterplot graph produce a lower-left-to-upper-right pattern, we say that there is a positive correlation between the two variables. This pattern means that when the score of one observation is high, we expect the score of the other observation to be high as well, and vice versa.

When the points on a scatterplot graph produce a upper-left-to-lower-right pattern, we say that there is a negative correlation between the two variables. This pattern means that when the score of one observation is high, we expect the score of the other observation to be low, and vice versa.

In statistics, the Pearson correlation coefficient ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).

The Pearson correlation method is the most common method to use for numerical variables; it assigns a value between − 1 and 1, where 0 is no correlation, 1 is total positive correlation, and − 1 is total negative correlation. This is interpreted as follows: a correlation value of 0.7 between two variables would indicate that a significant and positive relationship exists between the two. A positive correlation signifies that if variable A goes up, then B will also go up, whereas if the value of the correlation is negative, then if A increases, B decreases.

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The probability of either A or B occurring will be 0.8.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Being connected in a way that one excludes or prevents the other events from happening also: completely at odds despite the fact that their viewpoints did not conflict.

Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5.

Then the probability of either A or B occurring will be

P(AUB) = P(A) + P(B)

P(AUB) = 0.3 + 0.5

P(AUB) = 0.8

The probability of either A or B occurring will be 0.8.

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