What is the greatest common factor of 88 and a 121

Answer:

c

Step-by-step explanation:

let the number be n then multiplied by itself gives n², thus

n² + 7 = 16 ( subtract 7 from both sides )

n² = 9 ( take the square root of both sides )

n = [tex]\sqrt{9}[/tex] = 3

Final answer:

The positive number that when squared and increased by 7 equals 16 is 3, which corresponds to option (c).

Explanation:

The student is asking to find a positive number which, when multiplied by itself (squared), and then 7 is added, equals to 16. To find this number, we can set up a simple equation where x is the positive number we are looking for: x2 + 7 = 16. To solve for x, subtract 7 from both sides to get x2 = 9. Taking the square root of both sides gives us x = 3, since 32 = 9. Therefore, the correct answer is (c) 3.

Answer:

one hundred million seven thousand and one

Answer:

One hundred million seven thousand and one

Step-by-step explanation:

Answer: 3

Step-by-step explanation: We found the factors and prime factorization of 21 and 27. The biggest common factor number is the GCF number. So the greatest common factor 21 and 27 is 3.

The greatest common factor of 21 and 27 is 3.

A set's greatest common factor (GCF) is the largest factor that all of the numbers share.

For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

We have the number 21 and 27.

Now, factories 21 and 27 as

21 = 3 x 7

27 = 3 x 3 x 3

So, the common factor of 21 and 27 is 3.

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The cafeteria can make 14 full stacks of milk cartons with 18 cartons in each stack.

To determine how many full stacks of milk cartons the cafeteria can make, we need to divide the total number of cartons by the number of cartons per stack. The total number of cartons is 269, and each stack is to contain 18 cartons.

We perform the division as follows:

[tex]\[ \text{Number of full stacks} = \frac{\text{Total number of cartons}}{\text{Number of cartons per stack}} \] \[ \text{Number of full stacks} = \frac{269}{18} \][/tex]

When we divide 269 by 18, we get 14 with a remainder. The quotient, 14, represents the number of full stacks, and the remainder indicates that there will be some cartons left over that will not form a full stack.

Since we are only interested in the number of full stacks, we disregard the remainder. Therefore, the cafeteria can make 14 full stacks of 18 cartons each. The remaining cartons will either form a partial stack or be set aside, depending on the cafeteria's policy for stacking.

-38(-3) = 114

-72/(-12) = 6

-9 x 23 = -207

-150/5 = -30

564 / -4 = -141

Given that, we have to find each product or quotient

-38(-3)

It is a product, so we have to find product value

[tex]-38(-3)=38 \times 3=114[/tex]

-72 / (-12)

It is division, so we have to find the quotient

[tex]\frac{-72}{-12}=\frac{72}{12}=6[/tex]

-9 x 23

It is a product, so we have to find product value

[tex]-9 \times 23=-207[/tex]

- 150 / 5

It is division, so we have to find quotient

[tex]\frac{-150}{5}=-30[/tex]

564 / -4

It is division, so we have to find the quotient

[tex]\frac{564}{-4}=-141[/tex]

Answer:

see explanation

Step-by-step explanation:

Sum the parts of the ratio, 2 + 3 + 3 = 8

Divide the sum to be shared by 8 to find the value of one part of the ratio

£96 ÷ 8 = £12 ← value of 1 part of the ratio, thus

David gets 2 × £12 = £24

Stephen gets 3 × £12 = £36

June also gets £36

The equality used is Subtraction property of equality

Option A is correct

Step-by-step explanation:

We need to identify which option best explains or justifies Step 1.

Step 1 is: [tex]-c = ax^2 + bx[/tex]

The given equation is: [tex]0 = ax^2 + bx + c[/tex]

To get the equation for step 1 we need to subtract c on both sides of equation i.e using subtraction property of equality

[tex]0-c = ax^2 + bx + c-c[/tex]

[tex]-c = ax^2 + bx [/tex]

So, The equality used is Subtraction property of equality

Option A is correct.

Keywords: Solving Quadratic Equations

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Answer:

26

Step-by-step explanation:

15 3/5=78/5

(78/5)/(3/5)=(78/5)(5/3)=78/3=26

There are 26 three-fifths in fifteen and three-fifths.

To find out how many times [tex]\frac{3}{5}[/tex] is in [tex]15 \frac{3}{5}[/tex], we follow these steps:

Convert the mixed number [tex]15 \frac{3}{5}[/tex] into an improper fraction.

[tex]15 \frac{3}{5} = 15 + \frac{3}{5} = \frac{15 \times 5}{5} + \frac{3}{5} = \frac{75}{5} + \frac{3}{5} = \frac{75 + 3}{5} = \frac{78}{5}[/tex]

Divide [tex]\frac{78}{5}[/tex] by [tex]\frac{3}{5}[/tex].

To divide fractions, we multiply by the reciprocal:

[tex]\frac{78}{5} \div \frac{3}{5} = \frac{78}{5} \times \frac{5}{3} = \frac{78 \times 5}{5 \times 3} = \frac{390}{15}[/tex]

Simplify [tex]\frac{390}{15}[/tex].

Divide the numerator and the denominator by their greatest common divisor (GCD), which is 15:

[tex]\frac{390 \div 15}{15 \div 15} = \frac{26}{1} = 26[/tex]

You invested 11000 in in 2st fund and 9000 in 2nd fund

Given that, You invested money in two funds.  

Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.  

This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.

Let the amount in Fund I be $x and amount in Fund II be $ y

Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)  

And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)  

Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660  

Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500

Subtract the two equations  

(2) ⇒ 0.6x + 0.1y = 7500

(1) ⇒ 0.16x + 0.1y = 2660

(-) --------------------------------

0.44x + 0 = 4840

x = 11000

Now, from eqn (2)  

0.12(11000) + 0.02y = 1500  

0.02y = 1500 – 1320  

0.02y = 180  

y = 9000

Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund

Answer:

(-36/6)+(-6)

Step-by-step explanation:

Answer:

[tex] \frac{ - 36}{6} + ( - 6)[/tex]

-12

Step-by-step explanation:

-36/6 = - 6

-6 + (-6) = -12

Answer:

0.46 repeating 6

Step-by-step explanation:

plug it into a calculator

The amount he will be spending now is : 0.65q

Using the information given ;

The amount which would be reduced from his spending would be :

Now we have ;

q × 35%

= 0.35q

The amount he will be spending now is :

Now we have;

q - 0.35q = 0.65q

Hence, the amount he will be spending now is : 0.65q

Answer:

13

Step-by-step explanation:

26 * 50/100 = 26 * 1/2 = 13

Answer:

13

Step-by-step explanation:

50% = 50/100 = 1/2

That means that 1/2 of the children have blue eyes.

26*(1/2) or 26/2 = 13

Using the normal distribution, it is found that:

a) 64.8% of years will have an annual rainfall of less than 44 inches.

b) 68.4% of years will have an annual rainfall of more than 39 inches.

c) 31.1% of years will have an annual rainfall of between 37 inches and 42 inches.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The proportion is the p-value of Z when X = 44, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{44 - 41.8}{5.8}[/tex]

[tex]Z = 0.38[/tex]

[tex]Z = 0.38[/tex] has a p-value of 0.648.

0.648 x 100% = 64.8%

64.8% of years will have an annual rainfall of less than 44 inches.

Item b:

The proportion is 1 subtracted by the p-value of Z when X = 39, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{39 - 41.8}{5.8}[/tex]

[tex]Z = -0.48[/tex]

[tex]Z = -0.48[/tex] has a p-value of 0.316.

1 - 0.316 = 0.684

0.684 x 100% = 68.4%

68.4% of years will have an annual rainfall of more than 39 inches.

Item c:

The proportion is the p-value of Z when X = 42 subtracted by the p-value of Z when X = 37, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{42 - 41.8}{5.8}[/tex]

[tex]Z = 0.035[/tex]

[tex]Z = 0.035[/tex] has a p-value of 0.514.

X = 37:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37 - 41.8}{5.8}[/tex]

[tex]Z = -0.83[/tex]

[tex]Z = -0.83[/tex] has a p-value of 0.203.

0.514 - 0.203 = 0.311

0.311 x 100% = 31.1%

31.1% of years will have an annual rainfall of between 37 inches and 42 inches.

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To calculate the percentage of years with an annual rainfall between 37 inches and 42 inches, we need to use the standard normal distribution. First, we can convert the rainfall values to z-scores, and then use a z-table or calculator to find the area under the curve between the corresponding z-scores.

To calculate the percentage of years with an annual rainfall between 37 inches and 42 inches, we need to use the standard normal distribution. First, we can convert the rainfall values to z-scores using the formula:

z = (x-mu)/sigma.

So, for 37 inches, the z-score is (37-41.8)/5.8 = -0.8276, and for 42 inches, the z-score is (42-41.8)/5.8 = 0.0345.

Now, we can use a z-table or calculator to find the area under the curve between these two z-scores. The percentage of years with an annual rainfall between 37 inches and 42 inches is the difference between these two areas.

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Answer:

1. -16

2. 1 (12 x 0 = 0 but its not the right)

3. 43

4.80

5. 5 4 (5 x 5 x 5 x 5 = 625)

Answer:-16 and 1

Step-by-step explanation:

Answer:

960 cubic cm.

Step-by-step explanation:

We have to find the volume of a solid figure as detailed in the attached photo.

The topmost part of the solid is a pyramid with a square base.

The square base has a dimensions 6 cm by 6 cm and the height of the pyramid is 4 cm, then the volume is  

[tex]\frac{1}{3} \times (\textrm {Area of base} \times {\textrm {Height}}) = \frac{1}{3} \times 4 \times 6^{2} = 48[/tex] cubic cm.

Now, the volume of the bottom cuboid of the pyramid is  

= Height × Length × Width

= 12 × 6 × 6

= 432 cubic cm.

And finally, the volume of the other cuboid = 10 × 8 × 6 = 480 cubic cm.

Hence, the total volume of the solid is (48 + 432 + 480) = 960 cubic cm. (Answer)

Answer:

55 m  she is far from the beginning of the track

Explanation:

The linear track begins at  0 m

Since She is at the 10 m mark while practicing for the race so the initial point becomes 10 m further from the 0 m point

After running she is at 45 m from the 10 m meter  

Therefore, from the beginning of the track which is 10 m beyond from the initial point

Distance = (45m + 10m ) = 55 m

She is  55 m away from the beginning of the track.

Answer: I think that the answer is 55 meters.

Final answer:

After 64 sessions, the cost of both of Kendall's plans would be the same, which would be $2149.

Explanation:

Kendall's two pricing plans can be represented by linear equations. Plan 1 is $37 + $33 per session, while Plan 2 is $101 + $32 per session. To find out after how many sessions the cost would be the same, we set the two equations equal to each other:

37 + 33x = 101 + 32x

This simplifies to:

33x - 32x = 101 - 37

x = 64

So, after 64 sessions, the cost of both plans would be equal. To find that cost, we substitute x back into either equation:

Total cost for Plan 1 = 37 + 33(64) = $2149

Therefore, the cost for 64 sessions is $2149 using either plan.

Rs 100 of the average total cost is made up of variable costs.

Step-by-step explanation:

Given:

Number of output the firm produces= 7 units

Average cost of the output= Rs. 150

fixed factors of production = Rs.350

To Find:

How much of the average total cost is made up of variable costs=?

Solution:

we know that,

Average total cost= total cost/ number of output units produced

substituting the values, we get

[tex]150=\frac{\text{Total cost}}{7}[/tex]

Total cost= 1050

we know that Total fixed cost = 350

Total cost = Total fixed cost + Total variable cost

plug in the known values.

1050= 350 + Total variable cost

Total variable cost = 1050-350

Total variable cost =700

For 7th unit [tex]\frac{700}{7}[/tex] = 100

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

Note : Figure given is for reference to understand better.

Where redline is for given line and blueline for new line

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

[tex]8x-4y=5[/tex]

[tex]8(0)-4y=5[/tex]

[tex]y=\frac{-5}{4}[/tex]

When y=0, x=?

[tex]8x-4y=5[/tex]

[tex]8x-4(0)=5[/tex]

[tex]x=\frac{5}{8}[/tex]

We get points [tex]A(0,\frac{-5}{4}), B(\frac{5}{8},0)[/tex]

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B  will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point [tex]A(0,\frac{-5}{4})[/tex] from origin is [tex]( \frac{-5}{4})[/tex]  unit in x-direction and zero [tex]\frac{-5}{4})[/tex]  unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is [tex]A'(0,-10)[/tex]

For point B:

Distance of point [tex]B(\frac{5}{8},0)[/tex] from origin is [tex](\frac{5}{8})[/tex] unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is [tex]B'(5,0)[/tex]

Step 3: Find Equation of new line.

Points [tex]A'(0,-10)[/tex] and [tex]B'(5,0)[/tex] make a new line

The equation of given as

[tex]\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}[/tex]

[tex]\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}[/tex]

[tex]\frac{y+(10)}{x} = 2[/tex]

[tex]\frac{y+(10)}{x} = 2[/tex]

[tex]y+10= 2x[/tex]

[tex]y= 2x-10[/tex]

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

Answer:

A

Step-by-step explanation:

if you multiply the top by 2 the coefficients for x will be the same in both equations

4*2=8

The equations have equal x-coefficients is to A. Multiply both sides of the top equation by 2.

Multiplying both sides of the top equation by 2 results in:

8x + 4y = 8

This makes the x-coefficients equal in both equations, as they are both now 8x.

Option B would not work, as dividing both sides of the top equation by 4 would result in an x-coefficient of 1x in the first equation and 8x in the second equation.

Option C would also not work, as dividing both sides of the top equation by 2 would result in an x-coefficient of 2x in the first equation and 8x in the second equation.

Option D would work, as multiplying both sides of the top equation by 4 would result in an x-coefficient of 8x in both equations. However, option A is the simplest and most direct way to achieve the desired result.

Therefore, the correct answer is A. Multiply both sides of the top equation by 2.

Answer:

7 + n

Step-by-step explanation:

Answer:

2(5a+2)

Step-by-step explanation:

10a+4=2(5a+2)

Answer:

1500 students

600 boys

Step-by-step explanation:

40% are boys, so 60% are girls.

Writing a proportion:

900 / 60% = x / 100%

x = 1500

There are 1500 students in the school, which means there are 600 boys in the school.

this is the answer of question 4x-9/ 12

Answer:

4+1.25x(number of rides)=total cost

Answer:

Given: entrance is a flat fee of $4, and each ride costs $1.25

Treat the rides as x

$4 + x*$1.25 = the total cost of going to the carnival

Answer:

- v

Step-by-step explanation:

Given

(- 2 - 5v) - (- 4v - 2) ← distribute parenthesis, noting second is multiplied by - 1

= - 2 - 5v + 4v + 2 ← collect like terms

= (- 5v + 4v) + (- 2 + 2)

= - v + 0

= - v

(- 2 - 5v) - (- 4v - 2) =

= - 2 - 5v + 4v + 2

= - 5v + 4v - 2 + 2

= - v + 0

= - v