Heather and Marcus are
training for a marathon. Heather
ran 48.6 miles last week. Marcus
completed 90% as many miles as
Heather. How many miles did
Marcus run?​

Answer: f(x)=3x2+30x+65

Step-by-step explanation:

F(x)=3(x+5)2-10

Using bodmas

B= bracket

O=of

D= division

M= multiplication

A= Addition

S= subtraction

So we go with the bracket

(X+5)2

=(x+5)(x+5)

Open the bracket

=x2+5x+5x+25

=x2+10x+15

Substitute for (x+5)2

F(x)=3(x2+10x+25)-10

Open the bracket

F(x)= 3x2+30x+75-10

F(x)= 3x2+30x+65

For every 110 phones, 4 have defects, There's 5 sets of 110 in 550, so multiply 5 by 4.

5 × 4 = 20

20 out of the 550 may have defects.

Hope this helps :)

Final answer:

There are two portions of two-fifths in four-fifths; this is determined by dividing four-fifths by two-fifths, which simplifies to 2.

Explanation:

The student is asking how many portions of two-fifths fit into four-fifths. This is a basic division problem, which we can solve by dividing four-fifths [tex](\frac{4}{5})[/tex] by two-fifths ([tex]\frac{2}{5}[/tex]). The division of fractions is performed by multiplying the first fraction by the reciprocal of the second fraction.

To find the reciprocal of two-fifths ([tex]\frac{2}{5}[/tex]), we flip the numerator and denominator, resulting in five-halves ([tex]\frac{5}{2}[/tex]). Next, we multiply four-fifths ([tex](\frac{4}{5})[/tex]) by five-halves ([tex]\frac{5}{2}[/tex]).

 [tex]\frac{4}{5} \times \frac{5}{2}[/tex] =  [tex]\frac{4 \times 5}{5 \times 2}[/tex] = [tex]\frac{20}{10}[/tex] = 2

Therefore, there are two two-fifths in four-fifths.

Answer:

(26,65)

Step-by-step explanation:

We know that each package has 5 sheets of paper and 2 staples. So, to know how many sheets of paper and staples that will be used in 13 packages, we just need to multiply each quantity of material used by 13.

So, we have that:

Total sheets of paper = 13 * 5 = 65

Total staples = 13 * 2 = 26

So the ordered pair (x,y), where x is staples and y is sheets of paper is:

(26,65)

Answer:

The ordered pair is (26, 65).

Step-by-step explanation:

From the given information, a package has 5 sheets of paper and is held together with 2 staples.

13 packets contains 13 packages, so that:

Number of sheet of paper required = 13 × 5

                                                           = 65

Number of staples required = 13 × 2

                                              = 26

Therefore, the ordered pair is; staples (26) and sheets of paper (65) i.e (26, 65).

Answer:

1,350 mg.

Step-by-step explanation:

Multiply the amount of mg per kg by the number of kg to get the total amount of mg needed by the patient.

1350 milligrams pharmacist needs to fill the order for that patient.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

Given that,

The patient needs the drug according to his weight by multiplying of 15

Since the weight of the patient is 90 kg

So,

Amount of drug needed = 15 × 90 = 1350 miligram.

Hence "1350 milligrams pharmacist needs to fill the order for that patient".

For more information about multiplication,

brainly.com/question/14059007

#SPJ2

Answer:

[tex] - (x - 4 {)}^{2} [/tex]

Step-by-step explanation:

The given expresion is

[tex] - {x}^{2} + 8x - 16[/tex]

Factor -1;

[tex] - ( {x}^{2} - 8x + 16)[/tex]

Split the middle term with -4x-4x

[tex] - ( {x}^{2} - 4x - 4x + 16)[/tex]

Factor by grouping within the parenthesis:

[tex] - ( x({x} - 4)- 4(x - 4) )[/tex]

Factor further:

[tex] - (x - 4)(x -4 )[/tex]

[tex] - (x - 4 {)}^{2} [/tex]

This the opposite of the square of (x-4)

Answer:

e

Step-by-step explanation:

you do math

Answer:

$7,650.00

Step-by-step explanation:

5.5 x 5 = 27.5

turn 27.5 into a percent

6000 x 0.275 = $7,650.00

Answer:

3:10

Step-by-step explanation:

The question is asking the ratio of red cars to all the cars.

There are 3 red cars, and the total of the cars (all the cars) is 10.

The ratio is asking red to all.

So it is 3:10.

We want to get the ratio of red toy cars to the total number of red cars, we will get: 3:10

Here we know that:

There are 2 black cars, 3 red cars, and 5 white cars.

We want to get the ratio (remember that the ratio a to b is a:b) of red toy cars to all the toy cars.

First, we can see that there are 3 red toy cars.

And the total number of toy cars is:

2 + 3 + 5 = 10

So the ratio is just 3:10

If you want to learn more, you can read:

https://brainly.com/question/25326254

Answer:

y = -5/4x+4

Step-by-step explanation:

We can use the slope intercept form of a line

y = mx+b

where m is the slope and b is the y intercept

y = -5/4x +b

Substitute the point into the equation

-1 = -5/4(4) +b

-1 =-5+b

Add 5 to each side

-1+5 = -5+5+b

4 = b

y = -5/4x+4

Answer:

the answer is D

Step-by-step explanation:

Answer:

30. [tex]x=5\\y=5\sqrt{3}[/tex]

31.  [tex]x=4\\y=4\sqrt{3}[/tex]

32. [tex]x=6\\y=6\sqrt{3}[/tex]

33. [tex]x=4.5\\y=\frac{9\sqrt{3} }{2}[/tex]

34. [tex]x=40\\y=40\sqrt{3}[/tex]

35. [tex]x=7.5\\y=\frac{15\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Use SOHCAHTOA to find one of the missing sides, then use the pythagorean theorem ([tex]x^{2}+ y^{2} =z^{2}[/tex]) to find the other one

[tex]sin=\frac{opposite}{hypotenuse}[/tex]

[tex]cos=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan=\frac{opposite}{adjacent}[/tex]

30.

First find [tex]x[/tex] using Sin

[tex]sin(30)=\frac{x}{10}[/tex]

[tex]10*sin(30)=x[/tex]

[tex]x=5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]5^{2}+ y^{2} =10^{2}[/tex]

[tex]25+y^{2} =100[/tex]

[tex]y^{2} =75[/tex]

[tex]\sqrt{y^{2}} =\sqrt{75}[/tex]

[tex]y=5\sqrt{3}[/tex]

32.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{8}[/tex]

[tex]8*sin(30)=x[/tex]

[tex]x=4[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]4^{2}+ y^{2} =8^{2}[/tex]

[tex]16+y^{2} =64[/tex]

[tex]y^{2} =48[/tex]

[tex]\sqrt{y^{2} } =\sqrt{48}[/tex]

[tex]y=4\sqrt{3}[/tex]

32.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{12}[/tex]

[tex]12*sin(30)=x[/tex]

[tex]x=6[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]6^{2}+ y^{2} =12^{2}[/tex]

[tex]36+y^{2} =144[/tex]

[tex]y^{2} =108[/tex]

[tex]\sqrt{y^{2} } =\sqrt{108}[/tex]

[tex]y=6\sqrt{3}[/tex]

33.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{9}[/tex]

[tex]9*sin(30)=x[/tex]

[tex]x=4.5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]4.5^{2}+ y^{2} =9^{2}[/tex]

[tex]20.25+y^{2} =81[/tex]

[tex]y^{2} =60.75[/tex]

[tex]\sqrt{y^{2} } =\sqrt{60.75}[/tex]

[tex]y=\frac{9\sqrt{3} }{2}[/tex]

34.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{80}[/tex]

[tex]80*sin(30)=x[/tex]

[tex]x=40[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]40^{2}+ y^{2} =80^{2}[/tex]

[tex]1600+y^{2} =6400[/tex]

[tex]y^{2} =4800[/tex]

[tex]\sqrt{y^{2} } =\sqrt{4800}[/tex]

[tex]y=40\sqrt{3}[/tex]

35.

First use Sin to find [tex]x[/tex]

[tex]sin(30)=\frac{x}{15}[/tex]

[tex]15*sin(30)=x[/tex]

[tex]x=7.5[/tex]

Then use the pythagorean theorem to find [tex]y[/tex]

[tex]7.5^{2}+ y^{2} =15^{2}[/tex]

[tex]56.25+y^{2} =225[/tex]

[tex]y^{2} =168.75[/tex]

[tex]\sqrt{y^{2} }=\sqrt{168.75}[/tex]

[tex]y=\frac{15\sqrt{3} }{2}[/tex]

Answer:

y = 3x-6

Step-by-step explanation:

First we need to find the slope of the line

2y-6x=4

Solve for y

Add 6x to each side

2y-6x+6x=4+6x

2y = 6x+4

Divide each side by 2

2y/2 =6x/2 +4/2

y = 3x +2

The slope is 3

We want a line parallel, so it will have the same slope

We have a slope and a point

y = 3m+b

Substitute in the point

6 = 3(4)+b

6 =12+b

Subtract 12 from each side

6-12 = 12-12+b

-6 =b

y = 3x-6

Answer:

y = 3x - 6

Step-by-step explanation:

2y = 6x + 4

y = 3x + 2

Slope = 3

y = 3x + c

6 = 3(4) + c

c = 6 - 12

c = -6

y = 3x - 6

Answer:

18 inches.

Step-by-step explanation:

Hope this helps! Would you like an explanation?

Answer:

9999

Step-by-step explanation:

Find the greatest value of x and the least value of x that satisfy the equation:

2x-2000 = 9999 (Yields the greatest solution)

2x + 2000 = -9999 (Yields the least solution)

Solve both equations and you get:

3999.5 (Greatest solution)

-5999.5 (Least solution)

That means the range of integer solutions is between 3999 and -5999 (inclusive). That means there are 9999 integral solutions

Answer:

20,000 integers

Step-by-step explanation:

By triangular inequality,

|x - 2000 + x| ≤ |x−2000|+|x|

|x−2000|+|x| ≤ 9999

|x - 2000 + x| ≤ 9999

|2x - 2000| ≤ 9999

|x - 10000| ≤ 4999.5

x - 10000 ≤ 4999.5

x ≤ 4999.5

x ≤ 14999.5

-(x - 10000) ≤ 4999.5

-4999.5 ≤ x - 10000

-5000.5 ≤ x

All solutions:

-5000.5 ≤ x ≤ 14999.5

No. of inyegers:

14999 - (-5000) + 1

20,000 integers

Answer:

252 7 x 3 x 2

Step-by-step explanation:

The boy can wear 252 different outfits to school.

To calculate the number of different outfits, you can multiply the number of choices for each clothing item.

In this case, he has 7 choices of pants, 3 choices of shirts, 2 choices of ties, and 6 choices of jackets.

To find the total number of outfits, simply multiply these choices together: 7 pants x 3 shirts x 2 ties x 6 jackets = 252 different outfits.

This calculation works because for each choice of one item of clothing, there are still all the other choices available for the remaining items.

So, for every pair of pants, he can choose from 3 different shirts, and for each shirt-pants combination, there are 2 tie options, and so on.

Multiplying these choices together gives us the total number of outfits he can create while wearing one of each item.

for such more questions on multiply

https://brainly.com/question/29793687

#SPJ2

Answer:

B) 24

Step-by-step explanation:

3 x 8 = 24

4 x 6 = 24

Answer:

24

Step-by-step explanation:

Answer: 3 ft

Step-by-step explanation: It is a ratio, the shadows are half the length of the original object .

Final answer:

The rate 6 + 4 2/3 in lowest terms is 32/3 or, as a mixed number, it is 10 2/3.

Explanation:

The student asked to express the rate 6 + 4 2/3 in lowest terms. To do this, we will first convert the mixed number 4 2/3 into an improper fraction. The mixed number 4 2/3 can be converted by multiplying the whole number 4 by the denominator 3 and then adding the numerator 2, which gives us 14/3. So now we have the expression 6 + 14/3.

To add the whole number and the fraction, we can convert the whole number 6 into a fraction with the same denominator as 14/3. This means converting 6 to 18/3 (since 6 times 3 equals 18). Now we can add the fractions directly: 18/3 + 14/3 equals 32/3. Therefore, the rate 6 + 4 2/3 expressed in lowest terms is 32/3 or 10 2/3 when represented as a mixed number.

Answer:

B. He added 5 to each side of the equation.

Step-by-step explanation:

B. He added 5 to each side of the equation.

Answer:

12x/(4+x)

Step-by-step explanation:

The algebraic expression for 'the product of 12 and x divided by the sum of 4 and x' is written as (12  imes x) / (4 + x). This expression follows the order of operations and uses parentheses to ensure clarity.

The algebraic expression for 'the product of 12 and x divided by the sum of 4 and x' can be written as:
(12 x x) / (4 + x).

To write this expression, first, recognize the terms that signify mathematical operations. 'Product' signifies multiplication and a 'sum' signifies addition. The given statement involves both these operations, with 12 being multiplied by the variable x and then divided by the sum of 4 and x.

Using parentheses clarifies that the division applies to the entire sum of 4 and x, rather than just 4 or x. Without parentheses, it may lead to confusion about the order of operations. To represent division, we use the '/' symbol.

The correct algebraic expression (12  imes x) / (4 + x) follows the order of operations and ensures accurate representation of the mathematical relationship described in the problem.

3 + 1.75m

This represents 1.75 per mile plus a one time 3 charge.

Another way this can be written is

(1.75m + 6) - 3

This is a less efficient way, but represents the same. It is 1.75 per mile, this is plus 6, therefore we add the -3 outside the parenthesis so it evens out to +3 as the base charge.

Example: Lets say its 3 miles.

3 + 1.75 (3) = 8.25

(1.75 (3) + 6) - 3 = 8.25

Answer:

When m= 0,25

(8m-m ) + 3

3+ 8m-1/4m

With the first one you can add any number of miles infront of the brackets; ie) 4 miles

4(8m-m) +3 = 0.25t

32m-4m /28 (+3) = 0.25t x 28

28m +3 = 0.25t x 28

28m + 3 = 7t + 3t

31m = 10t

Step-by-step explanation:

To calculate the probability of a spinner landing on a yellow section, specific information about the spinner is required. For instance, with 5 sections where 1 is yellow, the probability would be 20%. Without such information, however, the correct percentage cannot be determined from the choices provided.

To determine the probability of the spinner stopping on a yellow section, we need specific information about the spinner such as the number of sections and the number of yellow sections. Without this information, we are unable to calculate the exact percentage. Assuming a student is given this type of probability question, they would typically be provided with a diagram or description of the spinner. For example, if there are 5 equal sections and 1 of those is yellow, then the probability (in percentage) would be 20%, calculated as (1 yellow section / 5 total sections) × 100%. However, since we do not have this information here, the correct option cannot be determined from the choices provided (A. 20%, B. 30%, C. 40%, D. 80%).

As for the probability of a randomly chosen student not living within five miles of the campus, this would typically be based on specific data provided in the context of the problem. Without the data, we cannot determine the correct percentage for this scenario as well, thus the correct answer is "Cannot be determined."

Answer:

1) biased sample

2) random sampling

Step-by-step explanation:

Since the results are based on feedback of students in only one class, it's not a good representative of the entire student body.

Also, since it's a math class there will be a bias.

Better method would be randomly selecting students from the entire school students list and take their feedback

Answer:

2 out of 20 chance you will roll a 1 or a 2.

Answer: 36 in²

Step-by-step explanation:

A=length times width

4.5 times 8 = 36

Answer:

[tex] 36.0 \: {inches}^{2} [/tex]

Step-by-step explanation:

[tex]area = l \times w = 8 \times 4.5 \\\hspace {65 pt} = 36.0 \: {inches}^{2} \\ [/tex]

Answer:

Step-by-step explanation:

*It's an isosceles triangle so 2 of the angles are going to be the same degrees

*Every triangle is 180 degrees

(48)+(48)=96 then 180-96=84

Answer:

The legs are 12 cm each, so the hypotenuse is

√(144+144)=12√2

So it would be the last one

Answer:

12√2

Step-by-step explanation:

Answer:

B

Step-by-step explanation: