Questiul 4 15 points)
Laurie and Maya sold at most $50 worth of get-well and friendship cards. The
friendship cards, x, were sold for $2 each and the get-well cards, y, were sold for
$1.50 each. Which point represents a reasonable number of cards sold?

Answer:

Option 4 - The solution of x is [tex]x=4\pm5i[/tex].

Step-by-step explanation:

Given : Equation [tex]x^2-8x+41=0[/tex]

To find : Solve for x in the equation ?

Solution :

Solving a quadratic equation [tex]ax^2+bx+c=0[/tex] solution is given by, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, a=1, b=-8 and c=41

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{-100}}{2}[/tex]

[tex]x=\frac{8\pm10i}{2}[/tex]

[tex]x=4\pm5i[/tex]

Therefore, the solution of x is [tex]x=4\pm5i[/tex].

Answer:

D

Step-by-step explanation:

trust meh

Answer:

D. The probability is 6/11, and the event is neither likely nor unlikely

Step-by-step explanation:

54% = 6/11

Answer:

D

Step-by-step explanation:

Answer:

Mean  = 45.178

Standard Deviation = 10.33

Step-by-step explanation:

class                m              frequency, f           m [tex]\times[/tex] f            f [tex]\times[/tex] [tex]m^{2}[/tex]      

25 - 34          29.5                22.1                   651.95         19232.525

35 - 44           39.5                31.5                  1244.25        49147.875

45 - 54           49.5                37.7                  1866.15        92374.425

55 - 64            59.5               25.3                 1505.35        89568.352

                                          116.6                    5267.7           250323.15

mean = [tex]\frac{5267.7}{116.6} = 45.178[/tex]      standard deviation  = [tex]\sqrt{\frac{250323.15 - \frac{(5267.7)^2}{116.6} }{(116.1 - 1)} } = 10.33[/tex]

The mean of a distribution is the average of the distribution ; it is the sum of observation divided by the count of the observation.

Given that:

[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64\\{Number}&22.1&31.5&37.7&25.3\end{array}[/tex]

First, we calculate midpoint of each class.

This is the sum of the class interval divided by 2.

So, we have:

[tex]x_1 = \frac{25+34}{2} = 29.5[/tex]

[tex]x_2 = \frac{35+44}{2} = 39.5[/tex]

And so on...

The table becomes:

[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64&{Number(f)}&22.1&31.5&37.7&25.3&{x}&29.5&39.5&49.5&59.5\end{array}[/tex]

The mean of the distribution is:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{29.5 \times 22.1 + 39.5 \times 31.5 + 49.5 \times 37.7 +59.5 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}[/tex]

[tex]\bar x = \frac{5267.7}{116.6}[/tex]

[tex]\bar x = 45.18[/tex]

The standard deviation is calculated as follows:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

[tex]\sigma= \sqrt{\frac{(29.5 - 45.1)^2\times 22.1 + (39.5 - 45.1)^2 \times 31.5 + (49.5 - 45.1)^2 \times 37.7 + (59.5 - 45.1)^2 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}}[/tex]

[tex]\sigma= \sqrt{\frac{12342.176}{116.6}}[/tex]

[tex]\sigma= \sqrt{105.85}[/tex]

[tex]\sigma= 10.29[/tex]

Hence:

Read more about mean and standard deviation at:

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Answer:

72 dollars

Step-by-step explanation:

Answer: 2.5

Step-by-step explanation:

Mean m = Sum s ÷ no of observation n

m = 2.5, n = 10

2.5 = s ÷ 10

s = 10 × 2.5

s = 25.

If one observation 2.5 is deleted from sum 25, new sum equals 25 — 2.5 = 22.5.

The no of observation becomes 9.

Therefore new mean = 22.5 ÷ 9

m = 2.5.

How this helps?

The question is about calculation of a new mean after deleting an observation from a data group. Despite deleting an observation of 2.5 from a data set with a mean of 2.5, the mean remains the same.

The subject matter is about computing the mean of a data set after a data point has been deleted. Starting off, we know we initially have 10 observations with a mean of 2.5. Therefore, the total sum of the observations can be calculated by multiplying the mean with the number of data points (2.5 * 10) to get 25.

Now, if we are to delete one observation worth 2.5, we have to subtract it from our total of 25 to get a new sum of 22.5. Then, we also decrease the number of data points by 1, which leaves us with 9 data points.

Finally, the new mean can be calculated by dividing the new sum by the new number of data points. In this case, it would be 22.5 divided by 9, which equals 2.5. Thus, the mean remains the same even after deleting the observation of 2.5.

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Answer:

$15606000

Step-by-step explanation:

17,000,000*.15 (15% off)

$ 2550000 off

17,000,000

-2550000

$14450000 (15% off)

*1.08 (sales tax)

$15606000

sorry if it is incorrect

Answer:

if the sale tax comes first before the 15% off,

Sales Tax: 1360

so the price became 18360

Price Off: 2754

18360 - 2754 = 15606

if the sale tax comes after the 15% off,

Price Off: 2550

17000-2550 = 14450

eight percent of 14450 is 1156

14450+1156 = 15606

anyways, the price is the same no matter if the sales tax comes first or the discount comes first

The answer to (-4.7)⁰ is 1

How to solve the exponent

We have a rule of thumb that Any non-zero number raised to the power of 0 is equal to 1.

This is a fundamental rule in mathematics and is consistent across all real numbers.

So, when you have (-4.7)⁰, you're essentially raising the number -4.7 to the power of 0.

Even though -4.7 is negative, it's still a non-zero number. Therefore, according to the rule, (-4.7)⁰ equals 1.

Answer:24π feets

Step-by-step explanation:

Since the circumference C= 2πr and r=12

C= 2x12xπ

C=24π

Answer:

4a+20

Step-by-step explanation:

Answer:4a + 20

Step-by-step explanation:

Basically 45% of 360.

45/100 * 360

45/360 * 100

16,200 / 100

162

Answer:

162

Step-by-step explanation:

There are 360 seventh graders and 45% of this 360 ride the school bus

All we need to do is find 45% of 360

we have;

45 / 100 X 360

= 162

Hence 162 seventh graders ride the school bus

Answer:

x+3

Step-by-step explanation:

Since the number of cookies in the jar could be anything we'll use a variable to represent it, x.  so three more than x is what?

Well, what's thee more than 5? 8, so you add 3.

So x+3

Answer:

B: 0.449 secs

A, C, and D: y=2sin(pi/5x), y=2sin(pi/10x), y=2sin(10pi x)

B: y=2sin(2pi/3x)

Answer:

B. y=2sin(2pi/3x)

Step-by-step explanation:

Answer:

0.4 and alot of other 4's

Step-by-step explanation:

Answer:

.44444444 repeating

Any number less than 9 over 9 will be itself forever after a decimal point

Step-by-step explanation:

Answer:

[tex]\frac{13}{6}[/tex] or [tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:3/2 x 3= 9/6

2/3 x 2= 4/6

9/6 + 4/6 = 13/6

13/6=2 1/6

Answer:

s=12

Step-by-step explanation:

Since we know that triangle ABC is similar to XYZ, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of s.

[tex]\frac{XY}{AB}=\frac{XZ}{AC}\\\\\frac{9}{6} =\frac{s}{8}\\\frac{8*9}{6} =s\\s=72/6=12\\s=12[/tex]

Answer:

r=-11

Step-by-step explanation:

Solve for r:

2 (3 r + 11) = 7 r - 3 r

7 r - 3 r = 4 r:

2 (3 r + 11) = 4 r

Expand out terms of the left hand side:

6 r + 22 = 4 r

Subtract 4 r from both sides:

(6 r - 4 r) + 22 = 4 r - 4 r

6 r - 4 r = 2 r:

2 r + 22 = 4 r - 4 r

4 r - 4 r = 0:

2 r + 22 = 0

Subtract 22 from both sides:

2 r + (22 - 22) = -22

22 - 22 = 0:

2 r = -22

Divide both sides of 2 r = -22 by 2:

(2 r)/2 = (-22)/2

2/2 = 1:

r = (-22)/2

2 | 1 | 1

| 2 | 2

- | 2 |  

| | 2

| - | 2

| | 0:

Answer: r = -11

Answer:

18.9 units to 1 decimal Place

Step-by-step explanation:

You need the diameter so do 3 X 2 = 6

Circumference is pi X diameter so

Do 6 X pi = 6pi or 18.9 to 1 dp

Answer:

14.28 ft squared

Step-by-step explanation:

The formula for the area of a parallelogram is base times height.

Add 3.2 to 1.9 to get the base, and 2.8 is the height.

(3.2 + 1.9) x 2.8

5.1 x 2.8 = 14.28

14.28

Answer:

x=4, y=0. (4, 0).

Step-by-step explanation:

x+3y=4

2x-6y=8

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

x=4-3y

2(4-3y)-6y=8

8-6y-6y=8

8-12y=8

12y=8-8

12y=0

y=0/12

y=0

x+3(0)=4

x+0=4

x=4-0

x=4

Answer:

3)  A

4)  D

Step-by-step explanation:

3)

Find any four points where y intersects with x on graph A

(-4 , 2)        (-2 , 1)          (4, - 2)           (2 , -1)    

Find the relationship(s) between x and y

(-4 , 2)        (-2 , 1)          (4, - 2)           (2 , -1)    

x = -2y       x = -2y        x = -2y           x = -2y

It is shown that there is a direct proportional relationship between x and y, (x = -2y)

Repeat for graphs B, C, and D

Find any four points where y intersects with x on graph B

(3 , 2)           (5 , 4)          (-3 , -4)              (-4 , -5)

Find the relationship(s) between x and y    

x = 1.5y         x =  1.25y       x =  0.75y       x =  0.8y

As you can see, there is not a constant direct proportional relationship between x and y. B is not the correct answer

Graph C

Find any four points where y intersects with x on graph C

(-5 , -3)         (-1 , -3)      (1 , -3)          (5 , -3)

Find the relationship(s) between x and y    

x = 1.67y    x = 0.3y   x = -0.3y        x = -1.67y

Once again, there is not a constant direct proportional relationship between x and y, so C is not the correct answer

Graph D

Find any four points where y intersects with x on graph D

(2 , 1)      (2 , 2)      (2 , 3)          (2 , 4)

Find the relationship(s) between x and y    

x = 2y    x = y      x = 0.67y     x = .5y

There is no direct constant relationship between x and y in this graph either.

Graph A is the only graph with a direct proportional relationship between x and y.

4) Allison wants to know whom seventh-grade students will vote for in the upcoming class president election.

A) Every member of the student council

Asking every member of the student council who they are voting for will not help Allison, because it is likely that there are multiple grades involved in the student council, when Allison just wants to know the opinions of seventh-graders. The student council also might have a different opinion than the general seventh-graders.

B) All 12 girls in Allison's homeroom class

It is likely that the girls at Allison's school have a very different opinion than the boys at her school, making this a bad data set.

C) Every tenth student who arrives at school on Monday

Allison only want to know the opinions of seventh-graders, not every tenth student at her school, which would consist of more than seventh-graders.

D) Every tenth name on a roster of all of the seventh-graders at the school

This data set would be the most useful to Allison because it is multi-gender, only seventh-grade, and consists of the general seventh-graders (not part of a special group).

D

Hope this helps :)

Solution:

Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14)

To find:  Equation of the line in slope - intercept form

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

From given,

[tex](x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)[/tex]

Therefore,

[tex]m = \frac{14-(-2)}{3-(-5)}\\\\m = \frac{14+2}{3+5}\\\\m = \frac{16}{8}\\\\m = 2[/tex]

Thus slope of line is 2

Substitute m = 2 and (x, y) = (-5, -2) in eqn 1

-2 = 2(-5) + c

-2 = -10 + c

c = -2 + 10

c = 8

Substitute c = 8 and m = 2 in eqn 1

y = 2x + 8

Thus the equation of line is found

Answer:

the answer is y=2x+8

Step-by-step explanation:

Question:

Solve the inequality:

5.1 – r ≥ 5

Answer:

r ≤ 0.1

Solution:

Step 1: Given inequality:

5.1 – r ≥ 5

Step 2: Subtract 5.1 from both sides of the inequality

⇒ 5.1 – r – 5.1 ≥ 5 – 5.1

⇒ – r ≥ – 0.1

Step 3: To reverse the inequality, multiply both sides by –1.

⇒ (–r) × (–1) ≥ – 0.1 × (–1)

Negative × Negative = Positive

⇒ r ≤ 0.1

Hence the solution to the given inequality is r ≤ 0.1.

Answer:

D, 28, 45, 53

Step-by-step explanation:

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

Answer:

A. 250

B.40

C.225

D.24

Step-by-step explanation:

20/0.08 = 250

30/0.75 = 40

45/0.2 = 225

36/1.5 = 24

Answer:

a. 8% of 250 = 20

b. 75% of 40 = 30

c. 20% of 225 = 45

d. 150% of 24 = 36

Step-by-step explanation:

20×100÷8

=250

30×100÷75

=40

45×100÷20

=225

36×100÷150

=24

Answer:

35

Step-by-step explanation:

4 x 4+4(5-2)+7

4 x 4+4(3)+7

16+12+7

28+7

35

Answer:

25

Step-by-step explanation:

Given data

(4/5)x = -16

x = -16 (5/4)

x = -20

Now,

-2x-15 = ?

putting the value of x

-2(-20)-15 = 25

Answer:

Distrbutive Property

Step-by-step explanation:

The equation -4x - 1/4 = 1 illustrates the addition property of equality.

The property illustrated by the equation -4x - 1/4 = 1 is the addition property of equality. According to this property, if you add the same number to both sides of an equation, the equality of the equation is maintained. To isolate the variable, we need to get rid of the constant term (-1/4) on the left side of the equation by adding 1/4 to both sides. This simplifies the equation to -4x = 1 + 1/4. Then, divide both sides by -4 to solve for x.

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Answer:

56 per hour

Step-by-step explanation:

168 divided by 3

Answer: x^2-9x+20

Step-by-step explanation:

Answer:

x² - 9x + 20

Step-by-step explanation:

Given

(x - 5)(x - 4)

Each term in the second factor is multiplied by each factor in the first factor, that is

x(x - 4) - 5(x - 4 ) ← distribute both parenthesis

= x² - 4x - 5x + 20 ← collect like terms

= x² - 9x + 20