Sarah is 12 years old. Her sister, Emily, is 8 years less than 3 times Sarah's age. Write an expression for Emily's age in terms of Sarah's age, s.

Answer:

Step-by-step explanation:

Variables:

let x be the number of minutes

let y be the total number of pages read

Use the form y = mx + b

"b" is irrelevant in this context because the initial value is 0 (they have not read it before or it is not given)

m is the rate, how fast they can read, how many pages each minute

Alejandro:

28 = 1x   <=Simplify because any number multiplied by 1 is itself.

28 = x

Carly:

12 = 2x

Answer:

Nathan's estimate would be greater than the actual product.

Step-by-step explanation:

Let a, b, c, d be natural numbers such that a<c and b<d

Multiplying a positive number on both sides doesn't affect the inequality

⇒a×b < c×b and c×b < c×d

⇒a×b < c×d

Here 67<70 and 36<40

∴67×36<70×40

Hence, Nathan's estimate would be greater than the actual product.          

Answer:

x=17/150

Step-by-step explanation:

11x-4/50=70/60

11x-2/25=7/6

11x=7/6+2/25

11x=187/150

x=(187/150)/11

x=(187/150)(1/11)

x=187/1650

simplify,

x=17/150

Answer:

x=17/150

Step-by-step explanation:

Answer:

Step-by-step explanation:

∡ECD = 90°

∡DCA= 90°

∡BCA=90°

∡BCE =90°

⇔ ABC=DCE

Answer:

The value in box of circle B is 3 and the value in box which belongs in both circle B and S is 6 and value which belongs in circle S is 1 and the value of box outside both the circle is 2.

Step-by-step explanation:

In given Venn diagram

ε = class of 12 pupils

pupils who have brother B = 9

pupils who have sister S = 7

pupils who have neither brother nor sister = 2

Hence the Venn diagram is drawn in the attachment for your reference.

n(E) =12

n(neither B nor S) = 2

So, n(B or S)= n(E) - n(neither B nor S)= 12-2=10

n(B) = 9

n(S) = 7

Now, addition theorem,

n(B or S) = n(B) + n(S) - n(B and S)

[tex]10=9+7-n(B\ and \ S)\\n(B\ and \ S) = 6[/tex]

So the value in box which is in both circle B and S is 6.

So the Box which contains only brothers = n(B) - n(B and S)  = 9 - 6 = 3

Value in box of circle B is 3.

So the Box which contains only Sisters = n(S) - n(B and S)  = 7 - 6 = 1

Value in box of circle S is 1.

There are 12 pupils in a class so, the number of pupils having both brother and sisters are 6 and the pupils had either brother or sister are 10.

Given :

Given that there are pupils in a class that is, n(E) = 12

Pupils who have brother, n(B) = 9

Pupils who have sister, n(S) = 7

Pupils who have neither brother nor sister, n(neither B nor S) = 2

So,  n(B or S) = n(E) - n(neither B nor S)

                      = 12 - 2 = 10

n(B or S) = 10

Now, through the addition theorem:

n(B or S) = n(B) + n(S) - n(B and S)

10 = 9 + 7 - n(B and S)

n(B and S) = 6

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Answer:

106°

Step-by-step explanation:

For the equilateral ΔBCD all angles are 60° (180/3 = 60).

m∠ADB is 67° Since the triangle is isosceles the base angles are =.

m∠ ABD will be 180 - (67+67) = 46°.

m∠DBC = 60° so  m∠ABC = 46 + 60 = 106°

Answer:

For the equilateral ΔBCD all angles are 60° (180/3 = 60).

m∠ADB is 67° Since the triangle is isosceles the base angles are =.

m∠ ABD will be 180 - (67+67) = 46°.

m∠DBC = 60° so  m∠ABC = 46 + 60 = 106°

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Step-by-step explanation:

Final answer:

The system of linear inequalities for Kayla's fruit purchase is x + y ≥ 15 to represent the quantity of fruit, and 0.65x + 0.78y < 20 to represent the budget constraint.

Explanation:

The student's question is asking for a system of linear inequalities that would model the situation in which Kayla wants to buy at least 15 fruits consisting of apples and oranges, without spending more than $20. Given that apples (x) are $0.65 each and oranges (y) are $0.78 each, we can set up the following inequalities:

x + y ≥ 15

0.65x + 0.78y < 20

The first inequality represents the requirement that Kayla needs to buy at least 15 pieces of fruit. The second inequality represents the constraint that she needs to spend less than $20 on her purchase.

Answer:

B. $336.09

Step-by-step explanation:

Monthly payment = $876.09

Interest rate = 4.8%

Convert the annual interest rate to monthly rate = 4.8% / 12

Monthly rate = 0.4% or 0.004

Amount going towards interest payment = 0.004* loan amount

Interest = 0.004 * 135,000

Interest = $540

Therefore, from the monthly payment of $876.09 , $540 goes towards paying interest and the balance is the note reduction;

Note reduction = $876.09 - $540 = $336.09

Answer:

336.09

Step-by-step explanation:

this is the right anwser

Thus, a product that normally costs $20 with a 75 percent discount will cost you $5.00, and you saved $15.00. You can also calculate how much you save by simply moving the period in 75.00 percent two spaces to the left, and then multiply the result by $20 as follows: $20 x .75 = $15.00 savings.

Answer: $35

Step-by-step explanation:

20(75%)=15+20= $35

Answer:

28

Step-by-step explanation:

24-7-4=13

13+15=28

Answer:

7

Step-by-step explanation:

3(7)=21-5=16

To evaluate the given expression 5x−6y+20z4yz, for x = 5, y = 3, and z = 1/4, we substitute the given values and apply the order of operations to solve the problem.

The question requires us to evaluate the mathematical expression given as 5x−6y+20z4yz with provided values of x = 5, y = 3, and z = 1/4. Let us substitute the values into the expression as follows:

First, replace each 'x', 'y', 'z' in the expression with the given values:

= 5×5 - 6×3 + 20×(1/4) / (4×3×(1/4))

= 25 - 18 + 20 / (3)

= 7 + 20/3

Finally, you can calculate the exact numerical result depending on whether you are allowed to leave it as an improper fraction or if you need to convert it to a mixed number or decimal form.

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The edge of cube is: 2.5 cm

Step-by-step explanation:

Let V be the volume of cube

V = 15.625 cm^3

Let x be the side of the cube then

[tex]V = x^3\\15.625 = x^3[/tex]

Taking cube root on both sides

[tex]\sqrt[3]{x^3} = \sqrt[3]{15.625} \\x = 2.5\ cm[/tex]

The edge of cube is: 2.5 cm

Keywords: Volume, Cube

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Answer:

The graph in the attached figure

Step-by-step explanation:

Graph the solution of the inequality

[tex]t\leq -4[/tex]

we know that

The solution is the interval ---> (-∞,-4]

All real numbers less than or equal to -4

In a number line the solution is the shaded area at left of t=-4 (closed circle, because the number -4 is included in the solution))

using a graphing tool

The graph in the attached figure

Answer: 5:37

Step-by-step explanation:

The answer is d/5:37pm

Step-by-step explanation:

2:07+2:30=4:37

Cheyenne is 1 he ahead

4:37+1:00=5:37

This is a mathematics problem involving the calculation of the slope of a line graph. The machine produces 20 soda bottles per minute as concluded from the given coordinates (4,80) and (7,140).

The subject of this question falls under Mathematics, specifically the topic of linear relationships or functions. The task is to calculate the rate at which soda bottles are made per minute using the given coordinates of the graph, (4,80) and (7,140).

First, we need to calculate the slope of the line represented by these points since the slope corresponds to the number of soda bottles produced per minute. In a linear relationship, the slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, (x1, y1) is (4,80) and (x2, y2) is (7,140). Plugging these values into the slope formula, we get: slope = (140 - 80) / (7 - 4) = 60 / 3 = 20.

So, the machine produces 20 soda bottles per minute.

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Answer:

A= 24 ounces and B= 36 ounces.

Step-by-step explanation:

Given: Solution A contain 30% salt= 0.30 salt.

           Solution B contain 55% salt= 0.55 salt.

           New mixture should be of 60 ounces with 45% salt.

Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.

Scientist need to to obtain 60 ounce of mixture from solution A and B.

∴ [tex]x+y= 60\ ounces[/tex]

y= [tex]60-x[/tex]         equation 1

Now, solving to get final solution.

∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]

Substituting the value of y from equation 1

⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]

⇒ [tex]0.3x+33-0.55x= 27[/tex]

⇒ [tex]-0.25x= -6[/tex]

∴ x= 24 ounces

Next, finding y

y= 60-x

∴ y= [tex]60-24= 36\ ounces.[/tex]

y= 36 ounces.

Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.

Answer:

Yes

Step-by-step explanation:

312/3=104

She would have used 1200 messages in all by the month of August.

Step-by-step explanation:

Messages allowed per month = 150

There will be 8 months starting from January to August, therefore,

Time period = 8 months

Messages in 8 months = Messages per month * Time period

[tex]Messages\ in\ 8\ months=150*8\\Messages\ in\ 8\ months=1200[/tex]

She would have used 1200 messages in all by the month of August.

Keywords: Multiplication

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Answer:

20/3

Step-by-step explanation:

5/(3/4)=(5/1)(4/3)=20/3

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)

m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1

Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6

y = - x + 6 or y = 6 - x ⇒ B

Answer:

43+44+45

Step-by-step explanation:

X + X + 1 + X + 2 = 132

3X + 3 = 132

3X + 3 - 3 = 132 - 3

3X = 129

3X/3 = 129/3

X = 43

consecutive means numbers after

Answer:

(1,c) (2,b) (3,A)

Step-by-step explanation:

May be right or worng i just read thought it better.

Answer:

4x(2x+3)

Step-by-step explanation:

The answer is 4x(2x+3)

Answer:

54

Step-by-step explanation:

8*7-12/6=56-2=54

Answer:

56-2=54

Step-by-step explanation:

8×7 - 12÷6 =56 - 2= 54

Answer:

Cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.

Step-by-step explanation:

We are given the following in the question:

Plan A

A rate of 8 cents per minute.

Plan B

A 50​-cent minimum charge per completed​ call.

We have to find the​ cost, in cents per​ minute, for a 3​-minute call.

Cost according to plan A:

[tex]\text{Cost per minute}\times \text{Call length in minutes}\\= 8 \times 3\\=24 \text{cents}[/tex]

Cost according to plan B:

50 cents for a 3 minute call

Rate =

[tex]\displaystyle\frac{\text{Total cost}}{\text{Duration of call}} = \frac{50}{3} = 16.67 \text{ cents per minute}[/tex]

The company chooses the plan with greater cost, thus, it chooses plan B.

Thus, cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.

What is the minimum cuts  needed to cut a circle into 8  equal parts ?

A : 4 cuts

Answer:

Step-by-step explanation:

When we have a circle, each cut (supposing the curst are in the exact middle) which give use two haves. So, if we cut one time, we'll have two equal parts, if we cut a second time, we'll have 4 equal parts, a third time, we'll get us 6 equal parts, and if we cut a fourth time, we'll have 8 equal parts.

So, whenever we have this kind of problem dividing circles, we just say that each cut in the exact middle equals two equal haves, so if we have 4 cuts, we just multiply them by 2, 4(2)=8. Therefore, we have 8 equal parts.

Answer:

0.5

Step-by-step explanation:

0.5 x 4 = 2, 2 + 7 = 9

Answer:n=1/2

Step-by-step explanation:

4n+7=9

   -7   -7

4n=2

divide by 4 on both sides

n=1/2

an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon

The only type of polygon that must be regular if it is equiangular is a regular polygon.

Here, we have,

we know that,

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

an equiangular polygon is a polygon whose vertex angles are equal.

If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.

Hence, The only type of polygon that must be regular if it is equiangular is a regular polygon.

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