Norma and Jane go to the store to buy stocking stuffers. Norma spends $8 more than Jane. Total, Norma and Jane spend $52. How much did each girl spend?

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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a) Mean, median, and mode are measures of central tendency that summarize a set of data by providing a single value that represents the middle or typical data value in a dataset.

Mean: The mean is calculated by adding up all the values in a dataset and dividing by the number of values in the set. The mean is sensitive to outliers and skewed distributions.

Median: The median is the middle value in a dataset when the values are arranged in order. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values. The median is not sensitive to outliers and is a good measure of central tendency for skewed distributions.

Mode: The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), multiple modes (bimodal or multimodal), or no mode (uniform distribution).

b) A good example of a situation in which the median would be the preferred measure of central tendency is income distribution in a country. In this case, the mean might be skewed by a small number of very high-income individuals, while the median would give a better representation of the typical income of the majority of the population.

Measures of central tendency (mean, median, and mode) belong to the field of statistics and mathematics. They are a basic concept in descriptive statistics, which is the branch of statistics that deals with summarizing, organizing, and presenting data.

In general, measures of central tendency are a useful tool for making sense of and communicating data, and they are widely used in many different fields and applications.

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Answer:

9

Step-by-step explanation:

6+x   x=3

6+3=9

Answer:

Shift down one unit

Step-by-step explanation:

Correct for e2020

The transformation applied to the graph of f(x) to produce the graph of p(x) is:

A). a shift down 1 unit and a shift left 7 units.

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

To determine the transformation applied to the graph of f(x) = x² to produce the graph of p(x) = –50 + 14x – x², we can compare the general forms of the two functions:

f(x) = x²

p(x) = –x² + 14x - 50

The function p(x) can be written as,

p(x) = –(x² - 14x + 49) - 1

p(x) = -(x - 7)² - 1

Therefore, the transformation applied to the graph of f(x) to produce the graph of p(x) is:

A). a shift down 1 unit and a shift left 7 units.

So, the correct answer is A).

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Answer:

\(Sum=4*[\frac{n^2-1}{n^2}]\)

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

\(\sum_{k=1}^n \frac{12k(k-1)}{n^3}\)

Rearranging the above formula:

\(\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)\)            Eq (1)

According to summation formula:

\(\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\\)

Putt these in Eq (1), and we will get:

\(=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\\)

Taking \(2(n+1)\) as common:

\(=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}\)

After more simplifying,

\(Sum=4*[\frac{n^2-1}{n^2}]\)

Now ,for n=10:

\(Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96\)

For n=100:

\(Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996\)

For n=1000

\(Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996\)

For n=10000:

\(Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996\)

Answer:

D shows no relationship between the variables

Answer:

It’s actually B.

Step-by-step explanation:

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:$15.40

Step-by-step explanation:

The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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\(\tt Step-by-step~explanation:\)

Since ∠4 and ∠8 are corresponding angles, then that means they are congruent.

PART 1

\(\tt Step~1:\)

m∠4: (12x + 3)

m∠8: (15x - 15)

Since they have the same measure, we can set up the equation like this:

\(\tt (12x+3)=(15x-15)\)

\(\tt Step~2:\)

Our goal is to isolate the variable x. To do that, we need to move everything to one side and keep x on its own on one side of the equation.

Let's subtract 12x from both sides to move it to the right.

\(\tt 12x(-12x)+3=15x(-12x)-15\\3=3x-15\)

\(\tt Step~3:\)

Then, we add 15 from the right side and on the left side of the equation.

\(\tt 3(+15)=3x-15(+15)\\18=3x\)

\(\tt Step~4:\)

Finally, we divide both sides by 3 to get our value for x.

\(\tt\frac{3x}{3}=x\\\frac{18}{3} =6\\x=6\)

PART 2

\(\tt Step~5:\)

Now, we have to plug in x in the expression for m4.

\(\tt 12(6)+3\\72+3\\75\)

\(\large\boxed{\tt Our~final~answer:~m~4=75}\)

**The numbers in parenthesis with a + or - tells you to add or subtract ONLY HERE. If you see this in another problem, they are most likely telling you to multiply.

Based on the distribution of data, the box and whisker plot displays the results of the scientific test for two classes. It is incorrect to say that both sections have the same value for the third quartile.

The formulation of partial differential equation solutions uses distribution generalized functions. The likelihood of a specific value or range of values for a variable is known as the probability distribution. Cumulative distribution function, where the likelihood of a value not exceeding a certain value depends on that value. A list of the values recorded in a sample, or a frequency distribution. In coding theory, there are two types of distribution: inner and outer. distribution of a portion of a manifold's tangent bundle.Term distribution: the state of having all members of a category present. The distributive law from elementary algebra is generalized by the property of binary operations known as distributivity. the distribution.

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Answer: The river rose

93

inches in five days.

Explanation:

Day 1:

3

Day 2:

6

Day 3:

12

Day 4:

24

Day 5:

48

Total:

3

+

6

+

12

+

24

+

48

=

93

OR

Total:

3

(

1

+

2

+

4

+

8

+

16

)

=

93

Step-by-step explanation: uh I am sorry

Answer:

2

Step-by-step explanation:

29 % 3 = 9

3x9 = 27

29 - 27 = 2

Answer:

number 5 is time 3 x 7,658 = the real answer is 549

Step-by-step explanation:

Answer:

The answer is 549

Step-by-step explanation:

Hope this helps!!!

Answer:

what do you need help with

Answer:

what do you need help with?

Step-by-step explanation:

I had to edit my answer bc it was wrong ignore this block teehee sorry

Answer:

99, 93, 87, 81

Step-by-step explanation:

Answer:

b. weight of a ball

Step-by-step explanation:

The weight of any thing is continuous

I hope this help you

Answer:

y=3x-5

Step-by-step explanation:

took the test yesterday and got it right

Answer:

\(\mathsf{y=3x-4}\)

Step-by-step explanation:

\(\mathsf{point \ slope \ form \ of \ linear \ equation: \ \ y-y_1=m(x-x_1)}\)

\(\mathsf{slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}}}\)

(where m is the slope and \(\mathsf{(x_1,y_1)}\) and \(\mathsf{(x_2,y_2)}\) are points on the line)

Given:

\(\implies \mathsf{slope=\dfrac{8--1}{4-1}}=3}\)

Substuting m = 3 and point (1, -1) into the point-slope form of a linear equation:

\(\implies \mathsf{y-(-1)=3(x-1)}\)

\(\implies \mathsf{y=3x-4}\)

33°

Since it's a right triangle that has an immediate 90° angle, we have 90°'s left to worry about. We have two angles to worry about it, and since one angle is bigger than the other by 24°, it means that the gap between them is 24°. After doing some mental math, you get 57° + 33°. The gap between them is 24°, and they add up to 90°. Finally, since you're looking for the smaller angle in this problem, then 33° would be your answer.

Answer:

D

Step-by-step explanation:

Its saying a line which is not two lines. Parallel lines contain 2 lines not 1.

The equations give values of 1/2 and -11/8

you should be aware that two equations are solved simultaneously if they are solved together

The given equations are

-8x+10y=16 .............................1

-4x-5y=13 ..................................2

Multiply equation 2 by 2 to have

-8x -10y=26

Subtract equation 1 from equation 2

-8x+10y=16

-(-8x-10y=26)  To get

The we have 20y = 10

Make y the subject of the relation

y=1/2

Put y = 1/2 in equation 1

-8x +10(1/2) = 16

-8x +5 = 16

-8x = 16-5

-8x = 11

Making x the subject of the formula we have

x=-11/8

In conclusion the values of x and y are -11/8 and 1/2 respectively

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Answer:

90°

Step-by-step explanation:

diagonals of a kite intersect each other at 90°

:)

ANSWER :

third option 90 degrees

Step-by-step explanation:

the opossite adjasent angle is 1 that is 90 so angle 3 is opposite adjacent angle of angle 1

*The opposite adjacent angles will always be same

Answer:

Do you mean: When lit, a candle loses 5% of its original height every hour. Jennifer lit a candle with an original height of 8 inches.

Until the candle has been burning for at least _____ hours, the height of Jennifer's candle will be more than 7 inches.

If so your answer is: 2.5!

Answer:

140

If that's wrong, try 147

Step-by-step explanation:

With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):

\(y=7x-28\\\),

where our m (slope) is 7, and our b (y-intercept) is -28.

If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.

Hope this helps!

The system of equations that could be used to determine how many of each item were sold is:

C.

x + y + z = 87

y = z + 5

4.5x + 6y + 7.5z = 489

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

87 items in total were sold, hence:

x + y + z = 87.

The total earned was of $489, hence:

4.5x + 6y + 7.5z = 489.

The vendor sold 5 more items for $6.00 than for $7.50, hence:

y = z + 5.

These three equations are given in option C.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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The value of y given the inverse proportional relationship between the variables is 16.

When two variables vary inversely, as one of the variable increases, the other variable decreases.

The equation that represents inverse proportion : x = k / y

where b = constant of proportionality

k = xy

k = 12 x 4 = 48

y = k / x

48 / 3 = 16

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