emma has 63 pencils noah has 49 penecils and michel has 77 pencils.Use the GCF and the distributive property to find the total number of pencils

say the numbers are "a" and "b", we know that they're in the ratio of 2:3, or namely that

[tex]\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}[/tex]

[tex]\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}[/tex]

The positive numbers for both the parts are obtained as 22,33 and 16,24 respectively.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

(a) As per the question, the numbers can be considered as 2x and 3x respectively.

Then, the equation for their sum can be written as follows,

3x + 2x = 55

⇒ 5x = 55

⇒ x = 11

The numbers are obtained as 2 × 11 = 22 and 3 × 11 = 33.

(b) Similarly, the equation for the product of numbers can be written as,

3x × 2x = 384

⇒ 6x² = 384

⇒ x² = 64

⇒ x = 8

The numbers are obtained as 2× 8 = 16 and 3 × 8 = 24.

The required number for both the cases are 22,33 and 16,24 respectively.

To know more about linear equation click on,

https://brainly.com/question/11897796

#SPJ5

Answer:

the value of x must be 71°

Step-by-step explanation:

180° - (38° + 33°) = 109°

x = 180° - 109°

x = 71°

Answer:

x = 71

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 38 + 33 = 71

Answer:

y= -x-6/2

Step-by-step explanation:

Given,

x+2y=-6

or,2y=-x-6 (cross multiplication)

or,y= -x-6/2

Answer:

x>3

Step-by-step explanation:

-5x+20<5

-5x<5-20

-5x<-15

5x>15

x>15/5

x>3

Answer:

A) x > 3

Step-by-step explanation:

[tex]-5x + 20 < 5\\\rule{150}{0.5}\\-5x + 20 - 20 < 5 - 20 \\\\-5x < -15 \\\\\frac{-5x < -15}{-5}\\\\\boxed{x > 3}[/tex]

Answer:

f = 14

Step-by-step explanation:

it is because skephalo and hot and poggers science and dnf

Answer:

-5+

Step-by-step explanation:

Slope of the line passing through the points (1, 4) and (3, 2) is -1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The line passing through the points (1, 4) and (3, 2)

Plug in the points in the slope formula.

Slope = 2-4/3-1

=-2/2

=-1

Hence, slope of the line passing through the points (1, 4) and (3, 2) is -1.

To learn more on slope of line click:

https://brainly.com/question/16180119

#SPJ7

Step-by-step explanation:

1/5 of 175

=1/5×$175

=$35

sale price = original price - discount price

= $175 -$35

= $140

Answer:

Option A is the correct answer

Step-by-step explanation:

We know that

1 yard = 3 foot

1 foot = 12 inch

1 yard = [tex]3\times12[/tex] inches

[tex]=36[/tex] inches

Option A is the correct answer

Answer:

81%

Step-by-step explanation:

200-38= 162

162/200= 81/100

81%

Answer:

Step-by-step explanation:

B

whether the negative sign is next to the fraction bar or next to the numerator, it doesnt matter.

A results in the last number being different from the one in the question.

answer is B

Answer:

64 degrees

Step-by-step explanation:

X equals 64 degrees because it shares a vertical angle pair with another angle which is 64 degrees. Since they are across from each other, x is 64 degrees.

Vertical angles are a pair of opposite angles formed by intersecting lines.

Answer:

they had 112 cookies

Step-by-step explanation:

14×8 = 112

Answer:

x= 12.5 or 25/2

Step-by-step explanation:

8x - 4 (+4) = 96 (+4)

8x (/8) = 100 (/8)

x= 12.5 or 25/2

Answer:

x=3

Step-by-step explanation:

What u should always do is look at the letters of the triangles given:

It will tell u that:

[tex] \frac{tu}{dc} = \frac{uv}{cb} [/tex]

Now we once again just sub in the values:

[tex] \frac{12}{9} = \frac{20}{4x + 3} [/tex]

we can simplify the fraction on the right

[tex] \frac{4}{3} = \frac{20}{4x + 3} [/tex]

And now we cross multiply

3×20=4(4x+3)

60=16x+12

60-12=16x

48=16x

Therefore :

x=3

The solutions are:

(a) Standard error is 957.04. (b) The probability is 50%. (c)The probability is 0.8491. (d) The probability is 0.8617.

To calculate the values, use the standard error formula for the sample mean:

(a)

The standard error is given by:

[tex]Standard\ error =\dfrac{ Population \ standard \ deviation}{\sqrt{sample\ size}}\\Standard\ error=\dfrac {\$ 7,400 }{ \sqrt60}\\Standard\ error =\ $957.04[/tex]

(b)

To find the probability that the sample mean will be more than $27,175, convert it into a z-score and then find the area under the normal distribution curve:

z = (sample mean - population mean) / standard error

z = ($27,175 - $27,175) / $957.04

z = 0

Since the z-score is 0, the area under the curve to the right of this point is 0.5 or 50%.

c. To find the probability that the sample mean will be within $1,000 of the population mean, we need to find the area between the range of $(27,175 - $1,000) and $(27,175 + $1,000).

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

Now, we calculate the z-scores for both limits:

lower = ($26,175 - $27,175) / $957.04 ≈ -1.045

upper = ($28,175 - $27,175) / $957.04 ≈ 1.045

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.045 and 1.045 is approximately 0.8491.

(d)

If the sample size were increased to 100.

[tex]Standard error = \dfrac{ \$7,400}{ \sqrt{100}} \\Standard error = \$740[/tex]

Find the probability that the sample mean will be within $1,000 of the population mean, did in part c:

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

lower = ($26,175 - $27,175) / $740

lower ≈ -1.351

upper = ($28,175 - $27,175) / $740

upper ≈ 1.351

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.351 and 1.351 is approximately 0.8617.

Hence,

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ12

Answer:

the answer is -21

Step-by-step explanation:

(4²-42)+(3²-4)

=16-42+(9-4)

=-26+5

=-21

Answer:

p=1

Step-by-step explanation:

[tex]\frac{4-p}{1-0}[/tex]=3

4-p=3

p=1

Answer:

51

Step-by-step explanation:

if there isn't such an answer tell me so that I can try again.goodbye

Step-by-step explanation:

the general line equation format is

y = ax + b

a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".

b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.

(i)

A (3, 5)

B (5, 9)

x changes by +2 (from 3 to 5).

y changes by +4 (from 5 to 9).

so, the slope (or gradient) is +4/+2 = 2

(ii)

the semi-finished equation is

y = 2x + b

let's use A to get b :

5 = 2×3 + b = 6 + b

b = -1

and the full equation is

y = 2x - 1

(iii)

for point (4, k) we get

k = 2×4 - 1 = 8 - 1 = 7

According to the given expected value, it is found that Josh's statement is correct.

In this problem, the expected amount donated by a given voter they call is $18.07.

You can learn more about expected value at https://brainly.com/question/25858347

Answer:

both correct :)

Step-by-step explanation:

ANSWERS:

[tex]1. False \\ 2. True \\ 3. False \\ 4. True \\ [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

answer will be a 1,208 square centimeters

Answer:

it's for sure option (B) cuz it's represented in the form of a straight line which means it's linear!

hope helpful~

Answer:

B

Step-by-step explanation:

I thinks its the best answer

Answer:

10$

Step-by-step explanation:

because 10$ + 10$ + 10$ equals 30$ so one is 30$

Answer:

BRO BRING THE PHONE CLOSER TO THE SCREEN WE CANT SEE ANYTING

Step-by-step explanation: