please help asap 25 pts

Answer:

Variance of the given data = 31.143

Explanation:

  Variance, [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2[/tex], where n is the number of observations, μ is the mean and [tex]x_i[/tex] is the observations made.

   Number of observations, n = 7

   Mean, μ = [tex]\frac{10+19+21+28+12+20+16}{7} = 18[/tex]

   [tex]\sum_{i=1}^{n}(x_i-\mu)^2=(10-18)^2+(19-18)^2+(21-18)^2+(28-18)^2+(12-18)^2+(20-18)^2+(16-18)^2\\ \\ \sum_{i=1}^{n}(x_i-\mu)^2=64+1+9+100+36+4+4=218[/tex]

  [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2=\frac{218}{7} =31.143[/tex]

  So variance of the given data = 31.143

Final answer:

The variance of the given data set {10, 19, 21, 28, 12, 20, 16} is calculated by finding the mean, squaring the deviations from the mean, summing these squares, and dividing by the number of data points minus one, resulting in a variance of approximately 36.33.

Explanation:

Calculating Variance of a Data Set

To calculate the variance, we first need to find the mean (average) of the data set. Then, we subtract the mean from each data point (deviation), square each deviation, sum them all up, and finally, divide by the total number of data points minus one to account for sample variance.

The given data set is {10, 19, 21, 28, 12, 20, 16}. Let's calculate the mean:

Mean = (10 + 19 + 21 + 28 + 12 + 20 + 16) / 7 = 126 / 7 = 18

Next, calculate each deviation from the mean, square it, and sum these squared deviations:

(10 - 18)² = 64

(19 - 18)² = 1

(21 - 18)² = 9

(28 - 18)² = 100

(12 - 18)² = 36

(20 - 18)² = 4

(16 - 18)² = 4

Sum of squared deviations = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218

The variance is then the sum of the squared deviations divided by n - 1 (where n is the number of data points in our sample):

Variance = 218 / (7 - 1) = 218 / 6 ≈ 36.33

The example is 1 x (9 x 5) = 45

Using the associative property of multiplication, we basically rearrange the parenthesis to group the first two terms like so: (1 x 9) x 5

So this is why choice D (1 x 9) x 5 = 45 is the answer

This means that 1 x (9x 5) = (1 x 9) x 5 is a true equation

Answer:

19.57

Step-by-step explanation:

100% of 19 is 19.

In order to find out what 1% of 19, move the decimal point two place to the left. 1% of 19= 0.19. To find 3% of 19, multiply .19 x 3. add 0.19 x 3 to 19, aka add 0.57 to 19 to get 19.57= 103% of 19

Answer:

19.57 is the answer

Step-by-step explanation:

Using a number line to show what -4 + 3 equals:

Start at the -4.  Move three spaces to the right (+3).  You land on -1.

Using a number line to show what 3 + (-4) equals:

Start at the 3.  Move four spaces to the left (-4).  You land on -1.

The commutative property of addition states that a + b = b + a.

First of all, let's get rid of the absolute values. If the number inside is positive, don't do anything. If it's negative, switch the sign. So, the expression becomes

[tex] 6 + 3\cdot 4 + 5 - 0 \cdot 6 [/tex]

We have to perform multiplications first:

[tex] 6 + 12 + 5 - 0 [/tex]

The last subtraction by 0 doesn't affect the number in any way, so we can ignore it:

[tex] 6 + 12 + 5 [/tex]

Now you can perform the sums just as they appear:

[tex] 6 + 12 + 5 = 18 + 5 = 23 [/tex]

|-6| + 3|4| + |-5| - 0 * 6    

Note: absolute value makes the number positive

 6  + 3(4) +  5   - 0 * 6      

Now, use the order of operations (multiply first)

 6   + 12  + 5   -   0        

Next, add and subtract

     18      + 5   -   0

            23      -   0

                    23

Answer: 23

Hello,

Please, see the attached files.

Thanks.

x and y are whatever you want them to be.

It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:

... x = # of cans of cola

... y = # of cans of root beer

Then the problem statement tells you ...

... x + y = 30 . . . . . . . 30 cans total were bought

... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer

_____

This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.

... (2y) +y = 30 . . . . . put 2y where x was

... 3y = 30 . . . . . . . . collect terms

... y = 10 . . . . . . . . . divide by 3

... 2y = x = 20

You're not done yet. You need to answer the question the problem asks.

Jared bought 20 cans of cola and 10 cans of root beer.

_____

Comment on x and y

You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.

Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.

Comment on problems of this type

When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.

Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).

What is the value of the number 3 in the the number 12,532.628

Solution

Here we need to use the place chart. I have attached the place value chart.

According to the place chart 3 is in tens place.

Therefore, the value of the number 3 in the number 12,532.628 is   3 x 10 = 30.

The answer is 30.

In the number 12,532.628, the digit 3 is located in the hundreds place, which means its value is 300.

The value of the number 3 in the number 12,532.628 is located in the hundreds place. To determine the place value of this digit, we start from the rightmost digit after the decimal point and move towards the left before the decimal point, labeling each position as follows: tenths, hundredths, thousandths, then units, tens, hundreds, thousands, and so on.

In 12,532.628, there are 2 units, 5 tens, 3 hundreds, 2 thousands, and 1 ten-thousands. Hence, the value of the number 3 here is 300. The digit 3 represents three hundred because it is in the hundreds place value.

From the graph, we know the y-intercepts (look at the picture).

y = 2 → y = 3x + 2

y = 3 → y = -1/3x + 3

We have

y ≥ 3x + 2 (shadow up of a line)

y ≤ -1/3x + 3 (shadows down of a line)

the common region is D.

Answer:

Option (a) and (d) are correct.

region A and region D satisfies the given inequality y ≥ 3x + 2.

Step-by-step explanation:

Given :  The graph of the system of inequalities y ≥ 3x + 2.

We have to determine which region contains the solution to the system.

We will chose a test point in each region and  see which point satisfies the given inequality.

For region A)

(0,6) is in region A

Put x = 0 and y = 6 in given inequality

We get,

6 ≥ 3(0) + 2.

6 ≥  2 (True)

For region B)

(4,6) is in region B

Put x = 4 and y = 6 in given inequality

We get,

6 ≥ 3(4) + 2.

6 ≥  12 + 2 = 14 (False)

For region C)

(0,0) is in region C

Put x = 0 and y = 0 in given inequality

We get,

0 ≥ 3(0) + 2.

0 ≥  2 (False)

For region D)

(-2,2) is in region A

Put x = -2 and y = 2 in given inequality

We get,

2 ≥ -3(2) + 2.

2 ≥ -6+ 2 = -4  (True)

Thus, region A and region D satisfies the given inequality

Thus, Option (a) and (d) are correct.

An expression involving a variable is a way to express an idea, rather than a specific number. So, writing [tex] 5x-7 [/tex] means that there is a certain quantity, x, and you want to multiply it by 5, and then subtract 7.

Note that we don't want to know the value of x, we're only saying that we will multiply it by 5 and then subtract 7.

So, if we know that x=9, we will multiply it by 5 and then subtract 7:

[tex] 5x-7 = 5\cdot 9 - 7 = 45-7 = 38 [/tex]

If it is like in the picture, then:

Domain = [-3, 3] (we read from the x axis)

Range = [-3, 1] (we read from the y axis)

If there are no points at the ends of the segments, then:

Domain = all real numbers

Range = (-∞ , 1]

Carla

Amir

Carlo

Esther

From greatest to least!

Answer:

1. Carla

2. Amir

3. Carlo

4. Esther

Answer:

de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

[tex]11x-17=2(3x+4)[/tex]

[tex]11x-17=6x+8[/tex]

[tex]11x-6x=8+17=25[/tex]

[tex]5x=25[/tex]

[tex]x=\frac{25}{5}=5[/tex]

Then , substitute the value of x

[tex]ab=3(5)+4=19[/tex]

ac=[tex]11(5)-17=55-17=38=cd[/tex]

ce=cd+de

49=38+de

[tex]de=49-38[/tex]

de=11

The measure of segment DE is 11.

Given:

[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]

See image in the attachment below showing the information given in the question.

Since B is the midpoint of AC, therefore:

[tex]AB = AC[/tex]

[tex]2(AB) = AC[/tex]

Substitute

[tex]2(3x+4)=11x-17[/tex]

Solve for x

[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]

Divide both sides by 5

[tex]5 = x\\x=5[/tex]

Find DE:

[tex]DE = CE - CD[/tex] (Segment Addition Postulate)

[tex]AC = CD = 11x-17[/tex]

Plug in the value of x

[tex]CD = 11(5) -17 = 38[/tex]

[tex]CE = 49 (given)[/tex]

Substitute

[tex]DE = 49 - 38\\DE = 11[/tex]

Therefore the length of DE = 11.

Learn more about segments here:

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Algebraic expression:

x-5/5+10

Solution:

                                                                                                 ∴-1 + 10 = 9

Answer:

m∠SVT= 79

Step-by-step explanation:

8y-33= 5y+9

Subtract 5y from both sides

8y-33= 5y+9

8y-33= 5y +9

-5y     -5y

3y - 33= 9

Then add 33 to the other side

3y-33 = 9

   +33  +33

= 3y= 42

Side by Side need to divide (divide by 3 on each side)

3y= 42

/3    /3

y= 143

m∠SVT = 5y + 9

m∠SVT = 5(14) + 9

m∠SVT = 70 + 9

m∠SVT =  79

You can't simplify this equation anymore.

Answer:

None of the above. (Ask your teacher to show you how to work this problem.)

Step-by-step explanation:

Since the results are identical, the matrix of the next three rolls will look exactly like this matrix. (A)

The matrix of all 6 rolls will look like a 6-row matrix with the bottom 3 rows identical to the top 3 rows.

Adding or multiplying A by a constant will not produce these results.

_____

You can replicate columns using matrix multiplication, so you can transpose A, multiply it by a suitable version of an identity matrix, then transpose the result:

((A^T)·[I | I ])^T will turn the 3-row matrix to a 6-row matrix where I is a 3x3 identity matrix. I've used [I | I] here to mean the 3x3 identity matrix is itself replicated horizontally to make a 6-column matrix. ^T indicates transpose.

To represent the results of repeating die rolls in a matrix, each entry in the initial results matrix A is multiplied by the scalar value of the experiment repetition. If matrix A reflects 6 die rolls, the matrix for repeating these results would be 2A.

The student's question pertains to outcomes from rolling a six-sided die and recording the results in a matrix. To find the matrix representation of repeating the same die rolls, we would need to multiply the matrix A by the scalar value that represents the number of times the experiment is repeated. For example, if we denote matrix A as the initial 6 results and they repeated the experiment for the same number of times, then we would just need to multiply each entry in matrix A by 2 (since the results were repeated once more).

If matrix A is represented as:

Divide total students by the size of the group:

35 / 5 = 7 groups.

Do 35 divided by 5 and it will give you 7. So Mr. Brown will have 7 teams of 5.

2c + 4d = 92

substitute the given values into the expression and evaluate

2c + 4d = (2 × 30) + (4 × 8) = 60 + 32 = 92

The answer is 92. First substitute in 30 for c and multiply it by 2, and you get 60. Then, substitute in 8 for d and multiply it by 4 to get 32. Add 60 + 32 and it equals 92.

Answer:

In this case, the answer is $88.00. Have a nice day! <3

Step-by-step explanation:

Answer: The 3,8,13,18 and 23 the actual common difference of this sequence.

Explanation:

The given terms of the sequence are 3,8,13,18 and 23.

Where first term is 3, second is 8, thirst term is 18, fourth term is 18 and fifth term is 23.

The difference between second and third term is 5.

[tex]8-3=5[/tex]

The difference between third and fourth term is 5.

[tex]13-8=5[/tex]

So, the common difference of the sequence is 5. Since the difference between terms are same, therefore it is an arithmetic progression.

The formula to find the nth term is ,

[tex]a_n=a+(n-1)d[/tex]

Where a is the first term and d is the common difference.

The distance traveled by Davis family = 35 miles

Time taken to cover the distance = [tex]\frac{1}{2}[/tex] hour

Speed = Distance [tex]\div[/tex] Time

Speed = [tex]35 \div \frac{1}{2}[/tex]

Speed = [tex]35 \times 2[/tex]

So, speed = 70 miles/hour.

At 2:00 pm, the family destination was 245 miles away.

So, the number of hours, when the family was 245 miles away = [tex]245 \div 70[/tex]

=  3.5 hours

So, after 3.5 hours,  that is at 5:30 pm, the Davis family will be 245 miles away.

To find the Davis family's arrival time, you calculate the average speed, find the time needed for the remaining distance, and then add it to the current time of 2:00pm. Their arrival time is calculated to be 5:30pm.

The student asked: The Davis family traveled 35 miles in 1/2 hour. If it is currently 2:00pm and the family destination is 245 miles away, at what time will they arrive? To solve this, we need to calculate the total travel time based on their average speed and the remaining distance to the destination.

First, we find their speed by dividing the distance traveled by the time taken: 35 miles / 0.5 hours = 70 miles per hour. Next, we calculate the remaining distance to travel, which is 245 miles.

To find the time needed to cover the remaining distance, we divide the distance by the speed: 245 miles / 70 miles per hour = 3.5 hours.

Now, we add the travel time to the current time. Since it's 2:00pm, adding 3.5 hours gives us 5:30pm, which is the arrival time.

The numbers -9 and -3 are 3 units from −6 on this number line.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Given a number line,

The 3 units left to the -6 is ⇒ -6 - 3 = -9

The 3 units right to the -6 ⇒ -6 + 3 = -3

Hence "The numbers -9 and -3 are 3 units from −6 on this number line".

To learn more about the number line,

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The numbers that are 3 units from -6 on the number line are determined as: -9 and -3.

What is a number line?

A number line is a visual tool that displays numbers in a linear sequence, extending endlessly in both positive and negative directions, illustrating their comparative sizes and positions.

To find numbers that are 3 units from -6 on the number line, you need to consider both numbers that are 3 units to the right and 3 units to the left of -6.

To the right of -6: -6 + 3 = -3

To the left of -6: -6 - 3 = -9

So, the correct numbers are:

D. -3

B. -9

Place them on the number line accordingly.

28 miles

increasing by 40% = original + increase = 100 + 40 = 140% = 1.4

multiplying 20 by 1.4 gives total he will run

miles run = 1.4 × 20 = 28

Answer:

28 miles

Step-by-step explanation:

Just multiply (20 miles per week) by 1.40:    1.40(20 mpw) = 28 miles

the answer you are looking for is not c or b or a the answer is 4/11 you can not simplify it any lower.

Isaiah would have to put 10 one-hundred gram weights to balance it out because there are 1000 grams in a kilogram.

Given

A triangle.

with vertices at (−2, 1) , (2, 1) , and ​ (3, 4) ​

Find out  the area of a triangle.

To proof

Formula

[tex]Area\ of\ triangle = \frac{1}{2}[ x_{1} (y_{2} -y_{3} ) + x_{2} (y_{3} - y_{1})+x_{3}(y_{1}-y_{2})[/tex]

As given the vertices at (−2, 1) , (2, 1) , and ​ (3, 4)

put in the above equation

we get

[tex]= \frac{1}{2} [-2(1-4)+ 2 (4-1) + 3 ( 1-1) ][/tex]

solving

[tex]= \frac{1}{2} [6 + 6][/tex]

thus

[tex]=\frac{1}{2} [12][/tex]

area of the triangle is 6 units².

Hence proved

The area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) is; Area = 6 units²

The formula for the area of a triangle when given the 3 vertices is;

Area = ½[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]

In this question, the vertices coordinates are; A(−2, 1), B(2, 1), and C(3, 4)

Thus;

Ax = -2

Bx = 2

Cx = 3

Ay = 1

By = 1

Cy = 4

Plugging in the relevant values into the area equation gives;

Area = ½[-2(1 - 4) + 2(4 - 1) + 3(1 - 1)]

Area = ½(6 + 6 + 0)

Area = ½ × 12

Area = 6 units²

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The third side is 9 cm long

Let [tex]x[/tex] represent one of the equal sides. Then the` other side will be [tex]2x-5[/tex].

Adding all the length of the sides should give 23. Thus,

[tex]x+x+2x-5=23[/tex]

This implies that,

[tex]4x-5=23[/tex]

We group like terms and simplify to obtain.

[tex]4x=23+5[/tex]

[tex]4x=28[/tex]

Divide through by 4 to get

[tex]x=7[/tex]

Hence the length of the other side is

[tex]2(7)-5=9[/tex]