You pay off a debt of $300 by paying 70%

There are 0.857 quarts of pure antifreeze that must be added to 3 quarts of a 10% antifreeze solution to obtain a 30% antifreeze solution.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that there is 10% times 3 quarts or 0.3 quarts of antifreeze in the current mix and we want a 30% solution.

Let the amount of pure antifreeze to be added would be x

The equation to solve becomes,

⇒ (0.3 + x )/(3 + x) = 0.3

⇒ (0.3 + x ) = 0.3 × (3 + x)

⇒ (0.3 + x ) = 0.9 +0.3x

⇒ 0.7x = 0.6

⇒ x = 0.857

Therefore, we need to add 0.857 quarts of pure antifreeze to the current solution to make a 30% solution.

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Answers

P(U and V) = 0

P(U or V) = 0.67

========================================

Explanation:

P(U and V) = 0 since U and V are mutually exclusive. Such events cannot happen at the same time. Example: flipping a coin to get heads and tails at the same time.

-------

P(U or V) = P(U) + P(V) - P(U and V)

P(U or V) = 0.29 + 0.38 - 0

P(U or V) = 0.67

-------

I'm not sure about P(UV) since there doesn't seem to be enough information. Does your teacher mention if the events are independent or not?

y=1/2x-13/2 is equation of the line that satisfies the given conditions. Through (1, −6) and parallel to the line x + 2y = 6

y=mx+c

where m is the slope.

Firstly we need to find the slope of the line  x - 2y = 6 by using slope intercept form, y=mx+c.

-2y=6-x

2y=x-6

y=1/2 x-6

m=1/2 slope of the line  x - 2y = 6.

For parallel lines slope will be same.

Now Use y = mx + b and the point (1,-6) to find b, the y-intercept.

-6= (1/2)*1 + b

-6-1/2=b

-13/2=b

y=1/2x-13/2 is the equation of line.

Therefore y=1/2x-13/2 is the line parallel to x + 2y = 6.

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The number of people that must attend for him to break even

is 240.

Given that the owner charges $7 per ticket, every customer receives a brochure that costs the owner $2 for each person and the owner must pay his band $1200.

We are required to find the people must attend for him to break-even.

Break even point is the point at which there is not any profits or losses.

We have to first form the equation for the break even.

Suppose the number of people be x.

Cost to the owner will be 1200+2x.

Revenue will be 7x.

Break even point will be at the point where 7x=1200+2x

7x-2x=1200

5x=1200

x=240

Hence the number of people that must attend for him to break even

is 240.

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Question is incomplete. It should include the following line:

Calculate the break even level for the owner of local concert hall.

Answer:

( -6 , 0 )

Step-by-step explanation:

the other one would be ( 3 , 0 ) but hope this helps !!

The function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15

The given parameters are

Discount = $15

Value = d

The function f(d) that models this discount on an item that costs d dollars is

f(d) = Value - Discount

This gives

f(d) = d - 15

Hence, the function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15

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The attached graph represents the graph of the inequality x ≤ 1 or x > 8

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

x ≤ 1 or x > 8

When an inequality is represented with < or >, then we make use of the open circle to represent the inequality.

Otherwise, we make use of the closed circle to represent the inequality.

Using the above as a guide, we have the following representations:

x ≤ 1 -> Closed circle

x > 8 -> Open circle

See attachment for the graph of the inequality

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Answer:

  95

Step-by-step explanation:

You want the sum of 38 and 57 by making use of the GCF and the distributive property.

The GCF of two numbers can be found by looking at their difference (or their remainder when one divides the other). Here, that is ...

  57 -38 = 19

This value is a factor of both numbers, so is their GCF.

The distributive property tells us how to express the sum with the GCF factored out:

  38 +57 = 19(2 +3)

Then the sum is ...

  19(2 +3) = 19(5) = 95

The sum is 95.

Answer:

Step-by-step explanation:

-5 - 9x = 3-9x-8  (Used distributive property)

-5 - 9x = -9x-5  (-8+3 = -5)

- 9x = -9x  (Add 5 to both sides)

0 = 0 (Add 9x to both sides)

Answer: If i did it right it should be -0.866

Step-by-step explanation:

The required expression is 17x + 2124 which represents the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by adding,  subtracting, dividing, and multiplying built-in functions.

Let the number of MP3 players TechWiz sold last week would be x.

Here TechWiz Electronics makes a profit of $35 for each MP3 player sold.

Last week, TechWiz sold a combined total of 118 MP3 and DVD players.

As per the condition,

So the required expression for the combined total profit would be:

= 35x + 18(118-x)

= 35x + 2124 - 18x

= 17x + 2124

Hence, the required expression is 17x + 2124 which represents the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.

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Answer:

Step-by-step explanation:

So lets turn this into a ratio

-252/84

so now we need to know

y/74

So, -252/84= -3

so y/74 needs to be equal to -3

74*-3 =  222

-222/74=-3

So our answer is y = -222

Hope this helps!!^^

Answer:

More fruit for the new design.

Step-by-step explanation:

120 times 2/3 is 80.

1/5 of 80 is 16.

1/8 of 120 is 15.

15 < 16, so the second design has more fruit.

The measure of the angles shown is 90 degrees

A line is defined as the shortest distance between two points while the point where two lines meet is known as an angle.

From the given diagram, the sum of both adjacent angles is supplementary to have:

x + 96 + 96 + x = 180

2x + 192 = 180

2x = 180 - 192

2x = -12

x = -6

Substitute the value of x into the expression

<d = x + 96

<d = -6 +96

<d = 90 degrees

Hence the measure of the angles shown is 90 degrees

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The Total amount after 4 years will be $3000 and interest will be $500.

The rate at which you borrow or lend money is called the simple interest. If a borrower takes money from a lender, an extra amount of money is paid back to the lender. The borrowed money which is given for a specific period is called the principal. The extra amount which is paid back to the lender for using the money is called the interest.

You calculate the simple interest by multiplying the principal amount by the number of periods and the interest rate. Simple interest does not compound, and you don’t have to pay interest on interest. In simple interest, the payment applies to the month’s interest, and the remainder of the payment will reduce the principal amount.

The simple interest calculation's mathematical formula:

A = P (1+rt)

P = Principal Amount

R = Rate of interest

t = Number of years

A = Total accrued amount (Both principal and the interest)

Interest = A – P.

Total amount after 4 years

⇒ $2,500 (1+5%×4)

⇒ $2,500 ×1.2\

⇒ $3000

interest= $3000 - $2,500=  $500.

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Domain and range of [f(x) =-2(x+3)2 -5] are as follows: x in RR, y in [-∞, -5].

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f are contained in this collection (x). A function's range is the range of values that it can accept as input. The function produces this list of values once we enter an x value.

according to given information;

This is a polynomial of degree 2, "domain is x in RR," and "to determine the range, we require the vertex and if maximum" or "minimum turning point," the equation of the polynomial's vertex and range."" a parabola in "color(blue)"vertex form" is.

•(x)y=a(x-h)²+k

"where "(h,k)" are the coordinates of the vertex and a"

"is a multiplier"

f(x)=-2(x+3)²-5" is in this form"

"with "(h,k)=(-3,-5)" and "a=-2

"since " a <0" then maximum turning point"

"range is "y in(-oo,-5]

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The expression (128 + 32) when rewritten using factoring is 4(32 + 8)

The expression in the question s given as

(128 + 32)

Express the numbers 128 and 32 as the product of their factors

i.e. we factor out 4 from the expression

So, we have

(128 + 32) = (4 * 32 + 4 * 8)

Next, we factor out the common factor (i.e. 4) from the expression

So, we have

(128 + 32) = 4 * (32 + 8)

Rewrite the above expression as follows

(128 + 32) = 4(32 + 8)

Hence, the expression (128 + 32) when rewritten using factoring is 4(32 + 8)

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The radius of the large circle would just be the diameter of one of the smaller circles, so 14 inches.

In order to solve this, we will need to find the area of the large circle and subtract the area of two smaller circles.

I'll be using pi as 3.14 for this.

Large Circle:

[tex]A = \pi r^{2}\\A = \pi (14)^{2}\\A = 196\pi \\A = 615.44[/tex]

Smaller Circle:

[tex]A = \pi r^{2}\\A = \pi (7)^{2}\\A = 49\pi \\A = 153.86[/tex]

Now we just simply subtract them.

615.44 - (2 * 153.86)

= 307.72 inches

You might've noticed that is exactly half of the area of the larger circle.

That's because if you halve the radius of a circle, you will get one fourth of original area.

Answer:

See explanation

Step-by-step explanation:

The range is the set of y values.

Answer:

: integers

1.

a number which is not a fraction; a whole number.

Answer:

6.32

Step-by-step explanation:

They gave you everything you need in the question - just plug the x and y values in where they showed you. (2, 5) is your (x1, y1) and (-4, 7) is your (x2, y2)

The jump of the athlete to 40 inches, (1.016 m) is obtained using an initial velocity and time calculated as follows;

1) The initial velocity of the athlete is approximately 4.475 m/s

2) The time of flight which is the time to reach 40 inches and back is approximately 0.91 seconds

The height achieved by the athlete, h = 40 inches

Required;

1) The initial velocity

Solution;

From the kinematic equation of motion, for a free fall, we have;

Where;

v = The velocity at the final point = 0 (The athlete stops upward motion at the 1.016 m height and starts downward motion

u = The initial velocity

g = Acceleration due to gravity ≈ 9.81 m/s²

h = The height = 1.016 m

Which gives;

0² = u² - 2 × 9.81 × 1.016

u² = 2 × 9.81 × 1.016 ≈ 19.93392

u = √(19.93392) ≈ 4.465

2) The flight time;

The flight time can be found using the equation;

Which gives;

t = (u - v)/g

Where;

t = The time taken to reach maximum height.

Therefore;

t ≈ (4.465 - 0)/9.81 ≈ 0.455

The time taken to reach the record height is the same as the time to land back on the ground, which gives;

Time of flight = t + t = 2•t

The time of flight ≈ 2 × 0.445 ≈ 0.910

The time of flight is approximately 0.91 seconds.

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Answer: c: 52

Step-by-step explanation:

the angles are congruent as shown by the hashmarks in the arks so you just need to double it

Answer:

c. 52°

Step-by-step explanation:

Since part of the angle is given (26°) and both parts of the angle are equal. 26° + 26° = 52°

Answer:

0

Step-by-step explanation:

We just add left to right:

- 5 and -7 is -12

-12 plus 12 is 0.

Step-by-step explanation:

adding 93 to itself 6 times

dividing 558 by 6

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

564 is divided by 3 = 4

Answer:

Step-by-step explanation:

Given equation:

Divide both sides by - 4:

Answer:

The value of v is 6.

Step-by-step explanation:

Solving for the value of v,

→ -4v = -24

→ v = (-24)/(-4)

→ v = 24/4

→ [ v = 6 ]

Hence, the value of v is 6.

Answer:

Step-by-step explanation:

Based on the calculations, the IQR of this data is equal to 2.

How to determine the IQR of this data?

IQR is an acronym for interquartile range and it is a measure of the middle 50% of data values when they are ordered from lowest to highest.

Next, we would order the data from lowest to highest and then determine the median as follows:

Data = {1, 4, 4,} 4, {4, 6, 5}

Median = 4.

For Q₁ of the lower half of the data, we have:

Lower half = {1, 4, 4,}

Q₁ = 4.

For Q₃ of the upper half of the data, we have:

Upper half = {4, 6, 5}

Q₃ = 6.

Mathematically, IQR is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

IQR = 6 - 4

IQR = 2.

Answer by

Lanuel

The results of those seven rolls that are shown shows that the range is 5.

The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data.

Given that a six-sided die is rolled 7 times, to give 1, 4, 4, 4, 4, 6, 5, we need to find the range,

The numbers that are gotten include:

1, 4, 4, 4, 4, 6, 5.

It should be noted that range is calculated as:

R = Highest value - Lowest value

R = 6 - 1

R= 5

Therefore, the range from the numbers given is 5.

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