Katherine is younger than Alexandra. Their ages are consecutive integers.
square of Katherine's age and 5 times
Find Katherine's age if the sum of the
if the sum of the
Alexandra's age is 109.

[tex]\displaystyle n=\frac{25}{2}[/tex]

A proportion is a set of equal ratios.

Cross Multiplication

The most common (and easiest) way to solve a proportion is cross multiplication. To cross-multiply, multiply the numerators by the opposite denominators. So, you are multiplying across the proportion.

After cross multiplying you get 10*10 = 8n.

Solving For n

Now, we can use algebra to find n.

Just, divide both sides by 8.

Then, simplify.

Checking The Answer

To check your answer all you have to do is plug n back into the equation.

This can be rewritten as

Then, the right side can be solved.

Answer:

32 oz

Step-by-step explanation:

Given the ratio 8 ounces to 1 cup, how many ounces are in 4 cups?

4 * 8 oz = 32 oz

Answer:

{YH, YT, BH, BT, TH, TT}

where Y = yellow, B = blue, T = turquoise

H = heads, T= tails

6 possible outcomes

Step-by-step explanation:

There are 2 independent events

Spinner which can land on one of three colors - Yellow(Y), Blue(B) and Turquoise(T)

Flipping a coin which has two outcomes Heads(H) and Tails(T)

Both events are independent of each other

So the sample space is:
{YH, YT, BH, BT, TH, TT}

Total of 6 outcomes

Answer:

30

Step-by-step explanation:

The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}[/tex]
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get [tex]\frac{f(3)-f(1)}{3-1}[/tex].

3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.

Answer:

-7-63a

Step-by-step explanation:

-7(1 + 9a)

(use the distributive property of multiplication to simplify)

-7-63a

Answer:

c) Propability of rolling doubles=6

Propability of rolling a sum grrater then or equal to 8 = 15

(Together add up to 21)

d)6 ->(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)

e)9 ->(1,6)(3,4)(5,2)(3,5)(5,3)(3,6)(5,4)(5,5)(5,6)

The percent increase with the additional baggage fee for airline would be $125 / $220 x 100% = 56.82%.

A number can be expressed as a fraction of 100 using a percentage. It may be computed by dividing the number by the total and multiplying by 100. It is commonly represented by the sign "%". The percentage of men, for instance, would be 25/100 x 100, or 25%, if there were 100 persons in all.

In a variety of areas, including statistics, finance, and education, percentages are often employed. For instance, in finance, percentage increase in stock prices are used to gauge a market's or company's success. In education, grades are frequently given as percentages to represent class marks.

How to solve?

The increase in the cost of the ticket is $295 - $220 = $75

The percent increase is $75 / $220 x 100% = 34.09%.

If the airline charges an additional $50 baggage fee, the new ticket price would be $295 + $50 = $345.

The increase in the cost of the ticket with the additional baggage fee would be $345 - $220 = $125.

The percent increase with the additional baggage fee would be $125 / $220 x 100% = 56.82%.

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Wdym by definition Answer:

Step-by-step explanation:

Answer: 4,375.

Step-by-step explanation: If your team is able to produce 1,250 widgets in one week, then in 3 1/2 weeks, they will be able to produce 3 1/2 * 1,250 = <<3.5*1250=4375>>4,375 widgets.

Answer: 7 years

Step-by-step explanation:  

We make the assumption that 8000 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $10\%=8000$.

Step 4: In the same vein, 100%=8000$.

So divide that by 5% 0.05%

Then multiply it by 5   0.0025%

Then convert it into money  26$

The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 41,842.71

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The estimated regression equation was determined to predict salary based on years of experience is,

⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)

Now,

Since, The equation is,

⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)

Hence, The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 22,717.59 + 2732.16 × 7

⇒ Estimated Salary = 22,717.59 + 19,125.12

⇒ Estimated Salary = 41,842.71

Thus, The estimated salary for an employee with 7 years of experience will be;

⇒ Estimated Salary = 41,842.71

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Step-by-step explanation:

xy/5

.........

....................

The required inequality model for this situation is 12x + 15.5y ≥ 390.

What are inequalities?

The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. The equal sign is substituted between by the less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">,"< "," <="," or ">=."

For instance, x>3 (x should be greater than 3)

If there is just one variable, the inequality is said to have an open sentence.

Instance: x 6 (x is less than 6)

Double Inequalities: If the statement demonstrates a double relation between the expressions or the numbers, the inequality is said to be a double inequality.

Instance: 3 x 8 ( x is greater than or equal to 3 and less than 8)
Given, the gas station pays $12 an hour and delivers groceries for $15.50 an hour.

And, x be the number of hours he works at the gas station and let y be the number of hours he works delivering groceries.

Then, total earnings in gas station = 12x

total earnings for delivering groceries = 15.5y

So, based on the given inequality condition

12x + 15.5y ≥ 390

Hence, the required inequality model for this situation is 12x + 15.5y ≥ 390.

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For the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters is the right triangle.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that, A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters.

We have to verify whether it is a right-angle triangle or not.

A right-angle triangle must follow the Pythagoras theorem.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

If the longest side is the hypotenuse.

h²=p²+b²

LHS

68² = 1424

RHS

60²+25²

3600+625

4225

L.H.S=R.H.S

Thus, the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters in the right triangle.

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Answer: 6 years old.

Step-by-step explanation:

Chris: 5+4a

c + a<40

5 + 4a + a < 40

5a<35

a<7

For the oldest, let's assume Arin is 6, because it is the highest number that is less than 7.

Arin can be maximum of 6 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let the Arin's age be x.

So, Chris age is 4x + 5

Now, the sum of their ages is less than 40.

x+ 4x+ 5 < 40

5x < 35

x < 7

Hence, Arin can be maximum of 6 years old.

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Find the area of a Shaded portion.

D. 68

In 0.02 seconds, the mortar shell will make contact with the target.

The formula for velocity, which is equal to distance / time, is used to calculate how long it will take to hit the target.

In the problem, the distance is 3 feet, and the velocity is given to be 150ft/s

therefore

150 = 3 / time

time = 3 / 150

time = 0.02 seconds

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Answer: The cost will be a total of $142.05. That is $125.80 for a Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.

Step-by-step explanation:

Given: Watermelons are 0.68 / lb and tomatoes are 3.25 / lb.

Let w = watermelon weight

Let t = tomato weight.

An equation would be:

.68w + 3.25t = Total cost

For 185 lb of Watermelon and 5 lbs of tomatoes:

.68(185) + 3.25(5) =

$125.80 + $16.25 = $142.05

Answer: 46 miles

Step-by-step explanation: according to my calculations i minus te total mileage gas times the current philosphy of the number of gallons with 50 - 30

Answer: Yeah

Step-by-step explanation: Multiplication can be done in any order, so using parenthesis to denote which numbers to multiply first should not matter.

The value of the inequality equation is x ≤ 7

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

4x ≤ 28   be equation (1)

Now , on simplifying the equation , we get

Divide by 4 on both sides of the inequality equation , we get

x ≤ 7

Therefore , the value of x is less than or equal to 7

All the numbers less than or equal to 7 satisfies the condition for x

The value of the equation x ≤ 7 is shown in the graph below

Hence , The value of the inequality equation is x ≤ 7

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Answer:

The combined amount of chocolate and regular milk sold was 52 cartons.

Step-by-step explanation:

1. Divide

36 ÷ 9 = 4

(This means that the ratio has a unit rate of 4. That means):

2. Second ratio rate

4 x 4 = 16

(Because the unit rate is 4).

3. Add

(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).

36 + 16 = 52 cartons.

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The perimeter of a square with a length of 5x can be represented by the expression 45x. This is because the perimeter of a square is equal to the length of any side of the square multiplied by the total number of sides, which is 4 for a square. So, for a square with a length of 5x, the perimeter would be 45x, or 20x.

Notice that the order the numbers are written on both sides is the same:

   n, then 2.9, then 0.3

Because the order is the same and all that changed were the parentheses (the way the numbers were grouped), this is the associative property of addition.

The associative property is about the groupings.  You can remember this by thinking about that fact that associations are groups.

The two possible ways to find the area are -

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

We have a trapezoid.

Now, we can find the area in two ways -

[1] -

A = (1/2) × {a + b} × {h}

[2] -

A = {b x h} - (1/2) x {(b - a} x h}

Therefore, the two possible ways to find the area are -

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Answer:

Zeg can buy a candy stick and a Popcorn ball.

Step-by-step explanation:

After calculating the total based on the following:

Candy bars are $0.99, Candy sticks are $0.45, Giant lollipops are $1.75, and Popcorn balls are $0.50.

the total was $8.24. [tex]9.20[/tex] [tex]-8.24 = 0.96[/tex] The only two items that can fit into this are a popcorn ball, and a candy stick.

The range of a function f(x)=3ˣ⁻¹-2 is (-2, ∞)

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability. The range of possibilities for variation or the distances between them: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.

Given,

f(x)=3ˣ⁻¹-2

Range=(-2, ∞)

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Answer:

Step-by-step explanation:

Answer:

try socratic

Step-by-step explanation: