A teacher allows her students to decide whether to use the mean, median, or mode to determine their test averages. One student determined that he will receive the highest average if he uses the mean. Which test scores are his?
A. 95, 82, 76, 95, 96B. 79, 80, 91, 83, 80C. 65, 84, 75, 74, 65D. 100, 87, 94, 94, 81

Answer: what trapezoid?

The probability that a randomly selected student drives to school is [tex]\( \frac{2}{45} \)[/tex].

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of sophomores who drive to school is 2, and the total number of sophomores is the sum of those who drive, take the bus, and walk: 2 + 25 + 3 = 30. Therefore, the probability for sophomores is [tex]\( \frac{2}{30} \)[/tex]. Similarly, for juniors, it is [tex]\( \frac{13}{35} \)[/tex], and for seniors, it is [tex]\( \frac{25}{35} \)[/tex]. To find the overall probability, we take the weighted average:

P(driver to school) = [tex]\frac{\text{(Number of sophomores)} \times P(\text{sophomores}) + \text{(Number of juniors)} \times P(\text{juniors}) + \text{(Number of seniors)} \times P(\text{seniors})}{\text{Total number of students}}[/tex]

[tex]\[ P(\text{driver to school}) = \frac{2 \times \frac{2}{30} + 13 \times \frac{13}{35} + 25 \times \frac{25}{35}}{30 + 35 + 35} \][/tex]

After calculating, the final answer is [tex]\( \frac{2}{45} \)[/tex], representing the probability that a randomly selected student drives to school. This approach considers the distribution of students across different grades, giving a more accurate representation of the overall likelihood.

Answer:

84,500

Step-by-step explanation:

8.45*10^4

8.45 * (10*10*10*10)

8.45 * 10000

84500

the decimal place moves to the right for however many zeros you have :)

i hope this helps :)

Answer:

.15 kilometers or 150 meters

Step-by-step explanation:

Answer:

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴ [tex]a_{1}[/tex] = 1

∵ He will double the amount he runs each day for the next

   6 days

- That means he multiplies each day by 2 to find how many miles

   he will run next day

∴  [tex]a_{2}[/tex] = 1 × 2 = 2 miles

∴  [tex]a_{3}[/tex] = 2 × 2 = 4 miles

∴  [tex]a_{4}[/tex] = 4 × 2 = 8 miles

∴  [tex]a_{5}[/tex] = 8 × 2 = 16 miles

∴  [tex]a_{6}[/tex] = 16 × 2 = 32 miles

∴  [tex]a_{7}[/tex] = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴ [tex]a_{1}[/tex] = 10

∵ She will increase the amount she runs by 3 miles each day for

   the next six days

- That means she adds each day by 3 to find how many miles

    she will run next day

∴  [tex]a_{2}[/tex] = 10 + 3 = 13 miles

∴  [tex]a_{3}[/tex] = 13 + 3 = 16 miles

∴  [tex]a_{4}[/tex] = 16 + 3 = 19 miles

∴  [tex]a_{5}[/tex] = 19 + 3 = 22 miles

∴  [tex]a_{6}[/tex] = 22 + 3 = 25 miles

∴  [tex]a_{7}[/tex] = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is [tex]S_{n}=\frac{a_{1}(1-r^{n})}{1-r}[/tex]

∵ [tex]a_{1}[/tex] = 1 , r = 2 and n = 7

∴  [tex]S_{7}=\frac{1(1-2^{7})}{1-2}[/tex]

∴  [tex]S_{7}[/tex] = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is [tex]S_{n}=\frac{n}{2}[a_{1}+a_{n}][/tex]

∵ n = 7,  [tex]a_{1}[/tex] = 10  and  [tex]a_{7}[/tex] = 28

∴ [tex]S_{7}=\frac{7}{2}(10+28)[/tex]

∴ [tex]S_{7}[/tex] = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

Answer: There are 96 green pens sold.

Step-by-step explanation:

Since we have given that

Number of pens in each pack of black pens = 3

Number of pens in each pack of red pens = 5

Number of pens in each pack of green pens = 6

Ratio of number of packs sold of black, red and green pens = 7: 2: 4

Number of total pens sold = 220

So, ratio of pens in number of packs would be

[tex]7\times 3:2\times 5:4\times 6\\\\=21:10:24[/tex]

So, Number of green pens sold would be

[tex]\dfrac{24}{55}\times 220\\\\=24\times 4\\\\=96\ pens[/tex]

Hence, there are 96 green pens sold.

96 green pens were sold.

Since the number of packs sold of black, red and green pens are in the ratio  7 : 2 : 4

Also, a total 220 pens were sold. Let x represent the total number of packs, hence:

Number of black pens = 7x/13 * 3 = 21x/13

Number of red pens = 2x/13 * 5 = 10x/13

Number of green pens = 4x/13 * 6 = 24x/13

Hence:

21x/13 + 10x/13 + 24x/13 = 220

21x + 10x + 24x = 2860

55x = 2860

x = 52

Number of green pens = 24x/13 = 24(52)/13 = 96

Hence  96 green pens were sold.

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Answer:

Step 1: −8x2−15x+2

Step 2: (−8x+1)(x+2)

Step 3: Say thank you

The factors of quadratic equation are : (8x -1) and (x + 2)

Given ,

-8x² -15x + 2 =​ 0

Now,

Firstly multiply the equation with -1 to make the coefficient of x² positive .

8x² + 15x -2 = 0

Now taking the factors,

8x² + 16x - 1x -2 = 0

8x(x + 2) -1 (x + 2) = 0

(8x -1) (x + 2) = 0

Thus,

The factors are (8x -1) and (x + 2).

The values of x are 1/8 and -2 .

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If I had to guess that it mean -4x + 6y = -18 and y = -2x+21:

Since we have a y =, we can plug that in.

-4x + 6(-2x + 21) = -18

-4x  -12x + 126 = -18

-16x = -18 -126

-16x = -144

-16x/-16 = -144/-16

x = 9

The value of x is equal to 9 and the value of y is equal to 3

Data given;

To solve the linear equations above, we have to use substitution method.

from equation 1

[tex]-4x + 6y = -18[/tex]

Make x the subject of formula

[tex]-4x + 6y = -18\\x = \frac{9 + 3y}{2}[/tex][tex]-4x + 6y = -18\\-4x = -18 - 6y \\\frac{-4x}{-4} = \frac{-18-6y}{-4}\\ x = \frac{9 + 3y}{2}[/tex]

substitute the value of x into equation 2

[tex]y = -2x + 21\\y = -2(\frac{9+3y}{2})+ 21\\ y = {-9-3y} + 21\\y = -3y + 12\\4y = 12\\4y/4 = 12/4\\y = 3[/tex]

substitute the value of y into either equation 1 or 2

[tex]y = -2x + 21\\3 = -2x + 21\\2x = 21 - 3\\2x = 18\\2x/2 = 18/2\\x = 9[/tex]

From the calculations above, the value of x is 9 and y is 3

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Answer:

Its A.

Step-by-step explanation:

Answer:

Measure of <N = 60°

(angles in an equilateral triangle are all equall 60°)

the measure of ∠M= 60°

(angles in an equilateral triangle are all equall 60°)

Step-by-step explanation:

Sum of angles in a triangle is equall to 180....

And in equilateral triangle of all sides equall...all angles are equal to 60° because all sides are equal.

So <m= <n=<o=60°

Bonita have 12 dimes and 7 quarters in her pocket.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Bonita have with dimes and quarters in pocket = $2.95

Bonita have 5 more dimes than quarters.

Now,

Let number of dimes = x

Let number of quarters = y

Since, Bonita have 5 more dimes than quarters.

x = y + 5

Here,

Bonita have with dimes and quarters in pocket = $2.95

So, we can formulate;

0.1x + 0.25y = =$2.95

Substitute the value of x in above equation, we get;

0.1 (y + 5) + 0.25y = $2.95

0.1y + 0.5 + 0.25y = $2.95

0.35y + 0.5 = $2.95

Subtract 0.5 we get;

0.35y + 0.5 - 0.5 = $2.95 - 0.5

0.35y = 2.45

Divide by 0.35 we get;

y = 7

And, x = y + 5 = 7 + 5 = 12

Thus, Bonita have 12 dimes and 7 quarters in her pocket.

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Answer:

Hanna donated b/50 books

Step-by-step explanation:

In this problem, we have:

n = 150 number of students at Hanna's school

b = ? number of total books donated by the students

Also, Hannah has donated 3 times as many as the average number of books each student donated.

The average number of books each student donated can be written as:

[tex]\frac{b}{150}[/tex]

And calling

h = number of books donated by Hannah

This means that

[tex]h=3(\frac{b}{150})[/tex]

Simplifying, this can be rewritten as

[tex]h=\frac{b}{50}[/tex]

Answer:

b/50

Step-by-step explanation:

Answer:

  y +3 = -6(x +9)

Step-by-step explanation:

The point-slope form of the equation of a line is ...

  y -k = m(x -h)

for a line with slope m through point (h, k).

You want the line with slope -6 through point (-9, -3), so its equation is ...

  y -(-3) = -6(x -(-9))

  y +3 = -6(x +9) . . . . . matches the last choice

Answer:

he started fishing by 5:10pm

Step-by-step explanation:

just subtract 1:30 from 6:40

Answer:

5.64

Step-by-step explanation:

set up a ratio problem

5 ounces/2.35 = 12 ounces/x

5x = 28.2

x = 5.64

Answer:

5.64

Step-by-step explanation:

5x2.4=12

SO,

2.35x2.4=5.64

Answer:

2.9 radians.

Step-by-step explanation:

Please kindly check the attached file for explanation.

The radian measure of a central angle intercepting an arc length of 5.8 units in a circle with a radius of 2 units is 2.9 radians when rounded to the nearest tenth.

The question deals with finding the radian measure of a central angle in a circle with a given radius and arc length. The formula for this calculation is theta = arc length / radius. Given that the circle's radius (r) is 2 units and the arc length (l) is 5.8 units, we substitute these values into the formula to find the radian measure of the central angle.

theta = l / r = 5.8 units / 2 units

This gives us theta = 2.9 radians. However, we need to round this to the nearest tenth, resulting in theta = 2.9 radians as the final answer.

Steps to solve:

f(x) = 3x+5/x; x = 2

~Substitute

f(2) = 3(2)+5/2

~Simplify

f(2) = 6+5/2

~Add

f(2) = 11/2

~Simplify

f(2) = 5.5

Best of Luck!

Answer:

1.3 x 3.14 x 3 x 3 x 3 = 27 x 1.3 x 3.14 = 113.04

formula is 4/3 x pi x radius to the power of three

Step-by-step explanation:

I may have used google...

Answer:

It's 113.04 in. 3

Step-by-step explanation:

I used the formula from the person on top, credits to them ^^

Answer:

$R = $500 + $15(t)

Step-by-step explanation:

in this question, we are told to give a mathematical expression that would model the amount of money that is made by Hillel.

from the question, we were made to understand that the amount of money he makes is a front of his time t. that is noted.

and also, he has a base cost of $500.

now, let’s write an equation;

R = $500 + 15(t)

where t represents the length of the performance as suggested by women

Answer:

  10

Step-by-step explanation:

Ground level is where h = 0, so solve the equation ...

  h(x) = 0

  -5(x -4)^2 +180 = 0 . . . . substitute for h(x)

  (x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36

  x -4 = 6 . . . . . . . . . . . . . . positive square root*

  x = 10 . . . . . . add 4

The object will hit the ground 10 seconds after launch.

_____

* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.

The object modeled by the quadratic equation h(x)=-5(x-4)²+180 will hit the ground 10 seconds after being launched.

The equation given is a quadratic equation which models the height of an object after being launched from a platform. To find out when the object will hit the ground, we need to determine when the height h(x) is equal to zero. The equation can be written as h(x) = -5(x - 4)² + 180.

To find the time when the object hits the ground, we set the height equal to zero and solve for x:
0 = -5(x - 4)² + 180
Solving the quadratic equation, we divide both sides by -5:
(x - 4)² = 36
Taking the square root of both sides gives two solutions: x - 4 = [tex]\pm6[/tex]. The positive root gives us the time after launch when the object hits the ground:
x - 4 = 6
x = 10

Therefore, the object will hit the ground 10 seconds after being launched.

Answer:

To find the radius diameter circumference and area, The area of a circle =  π x radius^2, Circumference of a circle = π x diameter, Remember that the diameter = 2 x radius.

Step-by-step explanation:

Answer:

log5(125)=3 The 5 should be smaller and a little lower.

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

The solution is,  138 divided by 2 is 69.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

138 divided by 2

i.e. 138/2

= 69

Hence, The solution is,  138 divided by 2 is 69.

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Answer:

38

Step-by-step explanation:

Answer:

38 packs

Step-by-step explanation:

Answer:

3.4 miles

Step-by-step explanation:

60 × 3 = 180

she has to drive 180 miles

180 ÷ 50 = 3.4

3.4 miles

In this problem, we need to understand the relationship between rate, time and distance. Here, we establish that Maria's aunt's house is 180 miles away. When Maria drives at a rate of 50 miles per hour, it takes her 3.6 hours to reach her aunt's house.

This is a problem of rate, time, and distance, specifically about understanding how changes in rate (or speed) affect time. Here, Maria drives to her aunt's house at a rate of 60 miles per hour, which takes 3 hours. The distance to her aunt's house, then, is 60 miles/hour times 3 hours, or 180 miles. We know that distance = rate times time (D = rt).

Now, when Maria drives at a rate of 50 miles per hour, the time will change. To find the new time, we rearrange the formula to t = D/r. Plugging the values in, t = 180 miles / 50 miles/hour, we get 3.6 hours. So, it would take Maria 3.6 hours to reach her aunt's house if she drives at a rate of 50 miles per hour.

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Answer:

35.36 cm

Step-by-step explanation:

The diagonal of a square will be given by

[tex]D=\sqrt {a^{2}+b^{2}}[/tex]

Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows

Given that a is 25 then

[tex]D=\sqrt {25^{2}+25^{2}}[/tex]

D=35.3553390593274

Rounding off the nearest two decimal place

D=35.36 cm

The length of the diagonal (c) of the square paper that measures 25 cm on a side can be found using the Pythagorean Theorem (a² + b² = c²). In this case, a = 25cm, b = 25cm, and by solving for c we get c = √(25² + 25²) ≈ 35.36 cm.

In order to answer your question about the length of the diagonal of a square, you would need to use the Pythagorean Theorem. The Pythagorean Theorem is a mathematical principle which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as: a² + b² = c².

In a square, all sides are equal, so we can consider the given measurement of 25 cm for both 'a' and 'b'. Hence, a = 25cm and b = 25cm. That would make our equation: 25² + 25² = c². When you calculate it, we get 625 + 625 = c², summing them up you get 1250 = c². To find 'c', you will take the square root of 1250 which equals approximately 35.36 cm. So, the length of the diagonal of the square paper is around 35.36 cm.

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Answer:

470(32 - n)

Step-by-step explanation:

Here are the given:

> 32 volunteers

> n volunteers who didn't donate

> 470 mL each

So your expression is: 470(32 - n).

Why?

Subtract the 32 volunteers who want to donate blood from the volunteers who were not able to donate then multiply it by 470.

Hope this helps!

Answer: 83 inches

Step-by-step explanation:

1 foot = 12 inches

In the mane, she used 6 feet of ribbon. 6×12 = 72 inches

 She used an additional 11 inches of ribbon around her front right leg

Altogether she use 72 + 11 = 83 inches

Answer:

397

Explanation: 9+7 =16 and 3 is odd

Answer:

397

Step-by-step explanation:

379 or 397 with fit the criteria