please help! please provide step by step explanation :)

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.

If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,

P = 3/9

P = 1/3

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

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Answer:

762.24

Step-by-step explanation:

Rounded to the hundredth place

The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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Answer:

a 6,3 b 2,3 c 2,-1 d 6,-1

Step-by-step explanation:

flip the signs

Answer:

Rotation

Step-by-step explanation:

Answer:

rotation

Step-by-step explanation:

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:91

Step-by-step explanation:

Answer: 2288

Explanation:

26 x 88 = 2288

Answer: C /-6

Step-by-step explanation:

Answer: 60,000 cars would be sold at $17000.

Step-by-step explanation:

• first we find the slope of the function between two points

(50,000, 18000) and ( 55,000, 17500)

• Let the number of cars sold be the x axis coordinate.

and the price is the y axis coordinate.

• next we plot this points.

m= Change in y / Change in x = rise / run

The slope m = (18000 - 17500/ 50,000 - 55,000)

= -0.1

• The equation of the line in point slope form is m(x-x1)=(y-y1)

• substituting for the first point

-0.1 (X-50,000) = y-18000

-0.1x - 5000 = y - 18000

-0.1x = 18000 + 5000

y = -0.1x + 23000

our slope -0.1 is negative.

In order to find the number of cars to be sold at a price of $17000, substitute this value y in the equation such that:

17000 =-0.1x+23000

solve for x

-0.1x = 23000-17000

0.1x = 6000

divide both sides by 0.1

x = 60000

60,000 cars would be sold at $17,000

Answer:

2/35

Step-by-step explanation:

\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)

Given:-

Ages of sample students: 14, 7, 8, 5, 6, 10, 13, 9

Sample mean:-

The sample mean is a statistic obtained by calculating the arithmetic mean of the values ​​of the variables in the sample.

Formula= \(\frac{Sum of Observations}{Number of Observations}\)

Here,

= \(\frac{14+7+8+5+6+10+13+9}{8}\)

=\(\frac{72}{8}\)

=9

So, sample mean is 9.

Sample standard deviation:-

If you've got got a population, take limitless samples of n size, and plot their manner in a histogram, you get a possibility distribution. That possibility distribution is what we name the sampling distribution of the suggest, and prefer every other distribution, it has its personal suggest and well known deviation.

Formula = \(\frac{sigma}{rootover of n}\)

sigma is standard deviation.

sigma= √\(\frac{summation of ( X- sample mean)^{2} }{n-1}\)

Step-by-step explanation:

since it is geometric sequence we will use the formula

\(tn = {a \times r}^{n - 1} \)

a = 2

\(r = - \frac{1}{4} \)

The first term

T1(a) = 2

The second Term

\(t2 = {a \times r}^{2 - 1} = {a \times r}^{1} \)

\(t2 = {2 \times - \frac{1}{4} }^{1} = - \frac{1}{2} \)

The third term

\(t3 = {a \times r}^{3 - 1} = {a \times r}^{2} \)

\(t3 = {2 \times - \frac{1}{4} }^{2} = 2 \times - \frac{1}{16} = \frac{1}{8} \)

The fourth term

\(t4 = {a \times r}^{4 - 1} = {a \times r}^{3} \)

\(t4 = {2 \times - \frac{1}{4} }^{3} = 2 \times - \frac{1}{64} = - \frac{1}{32} \)

The fifth term

\(t5 = {a \times r}^{5 - 1} = {a \times r}^{4} \)

\(t5 = {2 \times - \frac{1}{4} }^{4} = 2 \times - \frac{1}{256} = - \frac{1}{128} \)

i hope all these helped

Answer:

\(2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

\(a_n=2\left(-\dfrac{1}{4}\right)^{n-1}\)

To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.

\(\begin{aligned}\implies a_1 & =2\left(-\dfrac{1}{4}\right)^{1-1}\\& =2\left(-\dfrac{1}{4}\right)^{0}\\& =2\left(1\right)\\&=2\end{aligned}\)

\(\begin{aligned}\implies a_2 & =2\left(-\dfrac{1}{4}\right)^{2-1}\\& =2\left(-\dfrac{1}{4}\right)^{1}\\& =2\left(-\dfrac{1}{4}\right)\\&=-\dfrac{1}{2}\end{aligned}\)

\(\begin{aligned}\implies a_3 & =2\left(-\dfrac{1}{4}\right)^{3-1}\\& =2\left(-\dfrac{1}{4}\right)^{2}\\& =2\left(\dfrac{1}{16}\right)\\&=\dfrac{1}{8}\end{aligned}\)

\(\begin{aligned}\implies a_4 & =2\left(-\dfrac{1}{4}\right)^{4-1}\\& =2\left(-\dfrac{1}{4}\right)^{3}\\& =2\left(-\dfrac{1}{64}\right)\\& =-\dfrac{1}{32}\end{aligned}\)

\(\begin{aligned}\implies a_5 & =2\left(-\dfrac{1}{4}\right)^{5-1}\\& =2\left(-\dfrac{1}{4}\right)^{4}\\& =2\left(\dfrac{1}{256}\right)\\& =\dfrac{1}{128}\end{aligned}\)

Therefore, the first 5 terms of the given geometric sequence are:

\(2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}\)

Answer:

Step-by-step explanation:

16x^4y^-3z^4 / 36x^-2yz^0

16x^4y^-3z^4 = 16x^4z^4/y^3

36x^-2yz^0 = 36x^-2y(1) =36x^-2y = 36y/x^2

16x^4y^-3z^4 / 36x^-2yz^0

= (16x^4z^4/y^3) / (36y/x^2)

= 16x^4z^4/y^3 * x^2/36y  

= (4/9)x^6z^4/y^4

or another way

fist multiply it out

f(x) = 4x^(3/5) - x^(8/5)

now differentiate knowing d/dx(x^n) = n x^(n-1)

to get

4*(3/5) x^(-2/5) - 8/5 x^(3/5)

simplify to get

12/5/x^(2/5) -   8/5 x^(3/5)

If this is what your looking for please give me brainiest, i have done this problem in the past so i know how to solve it :)

According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Before we find quartile, we have to arrange the data set in order first from least to greatest which this problem has already arranged the data for us.

Next, proceed with the calculation. The formula for finding position of quartile is:

\(\displaystyle{Q_r = \dfrac{r(N+1)}{4}}\)

Where \(\displaystyle{Q_r}\) means the rth quartile, N means number of data set. Since we want to find the third quartile, substitute r = 3 and there are 11 data so substitute N = 11:

\(\displaystyle{Q_3 = \dfrac{3(11+1)}{4}}\\\\\displaystyle{Q_3 = \dfrac{3(12)}{4}}\\\\\displaystyle{Q_3 = 3\cdot 3}\\\\\displaystyle{Q_3 = 9}\)

So the position of third quartile is at 9th position which is 37.

Henceforth, the third quartile is 37.

Answer:

37.

Step-by-step explanation:

The data is in ascending order, which is what we need to get the answer.

As there are 11 numbers the 9th number is the upper(third)  quartile.

The median ( middle) number is 29 and the upper quartile is the middle number of the 5 numbers to the right of the median.

It is 37.

Answer:

15

Step-by-step explanation:

Answer:

9.92 x 10⁷

Also, if you could label this brainliest that would be a great help!

Thanks xx 

-Dante

Answer:

Step-by-step explanation:

\((3.2*10^{5}})*(3.1*10^{2})=3.2*3.1* 10^{5+2}\\\\= 9.92*10^{7}\)

Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.

Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.

Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.

Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:

     |          /

     |        /

     |      /

     |    /  

     |  /    

     |/      

---------------

The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:

y = x - 7

y = (-1/2)x + 5/2

Substituting the first equation into the second, we get:

x - 7 = (-1/2)x + 5/2

Simplifying this equation, we get:

(3/2)x = 19/2

x = 19/3

Substituting this value of x into either of the original equations, we get:

y = 19/3 - 7 = 2/3

So the point that represents a solution to the system is (19/3, 2/3).

Step-by-step explanation:

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

A store sells 5 oranges and 10 apples.

What is the cost amount?

The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.

Here, we have

Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.

We have to determine how many of each type of fruit were sold.

We, let the oranges be x.

let the apples be y.

x + y = 15...(1)

1x + 2y = 25...(2)

We subtract equation(2) from equation(1), we get

y = 10

Now we put the value of y in equation (1) and we get

x + 10 = 15

x= 5

Hence, a store sells 5 oranges and 10 apples.

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Answer:

$667.80

Step-by-step explanation:

30% of 900 is 270, so the price of the TV would be 630 without the tax. 6% of 630 is 37.8, so in total, the price would be $667.80

The polynomial 9 · x² - 6 · x - 4 = - 5 has a discriminant equal to 0 and two same real roots.

Quadratic equations are polynomials of the form:

y = a · x² + b · x + c

Where:

The discriminant is a real number determined by the following formula:

D = b² - 4 · a · c

There are three cases for discriminants:

First, write the polynomial in standard form:

9 · x² - 6 · x + 1 = 0

Second, calculate the value of the discriminant:

D = (- 6)² - 4 · 9 · 1

D = 36 - 36

D = 0

The polynomial has two same roots.

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Answer:

32.5 feet

Step-by-step explanation:

This situation forms a right triangle. We are given the distance from the base of the tower (long leg of the triangle) and are asked to find the height (short leg of the triangle).

With this information, we can use the tan ratio, opposite over adjacent, to find the height of the tower.

tan 18 = \(\frac{x}{100}\)

Multiply each side by 100:

(100) tan 18 = x

Simplify and round to the nearest tenth:

32.49 = x

32.5 = x

So, the height of the tower is approximately 32.5 feet