suppose that, in the base period, a college student buys 20 gallons of gasoline at $2 per gallon, 2 mugs for $13 each, and 4 movie tickets for $7 each. in the next month, the price of gasoline is $2.25 per gallon, mugs cost $12.50 each, and the price of a movie ticket is $7.50. the change in the price level from the first to the second month is:

By using distributive property, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

In order to quickly solve equations, a number is distributed across the integers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.

We have,

[tex]-3\left(7x^{2}+3x\right)[/tex]

Using Distributive Property, A(B+C) = AB+AC

[tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

Hence, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

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Step-by-step explanation:

it is a rectangle.

the area is a rectangle is

length × width

in our case

length × width = 55 ft²

length = 3×width + 4

we use that in the first equation :

(3×width + 4)×width = 55

3×width² + 4×width - 55 = 0

the general solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =

= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =

= (-4 ± 26))/6

width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft

width2 = (-4 - 26)/6 = -30/6 = -5

negative numbers for the size of a physical object don't make sense, so

11/3 = 3 2/3 ft is our solution.

length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft

so,

the length = 15 ft

the width = 3 2/3 ft (or 11/3 ft)

Answer:

(-3,6)----> (0,5)

(9,-8)----> (6,-9)

Step-by-step explanation:

The translation T(3,-1) shows that we need to add three units to the x-coordinates and -1 unit to the y-coordinates, as follows in the answer above.

To maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

Combinatorics is a branch of math focused on the arrangements of objects.

Estimates of the number of operations needed by a computer algorithm can be created using combinatorial approaches.

It is given that the number of persons in each circular table and the square table will be 10 and 4 respectively.

We now need to determine the largest multiple of 10 in order to maximize the number of circular tables.

Now, if we take 100, there will only be 2 seats left. However, 4 people are needed for square tables. Therefore, 100 is incorrect.

The circular tables utilized would be if we choose 90 as a multiple of 10 is,

= 90 / 9

= 10

Number of guests left,

=102 - 90

= 12

12 is a multiple of 4 as a result 3 square tables may therefore fit 12 people,

=4 × 3

=12

Thus, to maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

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[tex]5 \div 6 \times 2100 = 1750[/tex]

Answer:

1. How much did the 2 lb of the first type of candy cost the owner?

2x

2. How much did the 3 lb of the second type of candy cost the owner?

3*1.5 = 4.5

3. How much did the two types of candy cost the store owner in total?

2x + 4.5

4. How much money will the store owner get if she sells all of the new mixture?

(2 + 3)*2.5 = 12.5

5. Write an equation to find the cost per pound of the first candy

2x + 4.5 = 12.5

6. Solve the equation to find the owners cost of the first candy per pound

2x + 4.5 = 12.5

2x = 8

x = 4

Answer:

Step-by-step explanation:

The distance between two points is represented by the following equation;

Therefore, if the endpoints of WX are (-5,-1) and X(2,6):

Answer:

28

Step-by-step explanation:

2 x 7 = 14

Number should be in between 26 and 31

So,

14 x 2 = 28

28 has one of its prime factors as 2 and 7.

Hence,

28 is the number which is in between 26 and 31 it has the prime factors of 2 and 7.

Answer:

Step-by-step explanation: Given prime factors: 2, 7

 By multiplying, 2 X 7= 14

 Given, number is between 26 and 31

       therefore, 14 X 2= 28 (since 2 is a prime factor)

        ans: 28

Answer: C

Step-by-step explanation:

This is the definition of a negative exponent.

The formula for calculating simple interest is expressed as

I = PRT

where

I represents the interest

P represents the principal or initial amount invested

R represents the interest rate

T represents the time in years

From the information given,

P = 11750

R = 7.5%

Recall, percentage is expressed in terms of 100. Thus,

R = 7.5/100 = 0.075

T = 3

By substituting these values into the formula,

I = 11750 x 0.075 x 3

I = 2643.75

Total interest = 2643.75 rupees

Total amount = principal + total interest

By substituting the values,

Total amount = 11750 + 2643.75

Total amount =

Answer: 11750 + 2643.75

Step-by-step explanation:

The formula for calculating simple interest is expressed as

I = PRT

where

I represents the interest

P represents the principal or initial amount invested

R represents the interest rate

T represents the time in years

From the information given,

P = 11750

R = 7.5%

Recall, percentage is expressed in terms of 100. Thus,

R = 7.5/100 = 0.075

T = 3

By substituting these values into the formula,

I = 11750 x 0.075 x 3

I = 2643.75

Total interest = 2643.75 rupees

Total amount = principal + total interest

By substituting the values,

Total amount = 11750 + 2643.75

The Point-slop form for X is X = 5Y+15, and the Point-slop form for Y is [tex]\frac{X-5}{5}[/tex],  for the line with a slope 1/5 and passing through the point ​(-4​, -5​).

Finding the slop form using the formula  [tex]m=\frac{Y_{1} - Y_{2} }{X_{1} -x_{2} }[/tex]

The equation for x.

Here m=1/5.

∴  [tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4)

[tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X=5Y+20-5

X=5Y+15

∴Point-slop for X is X=5Y+15.

Solving for Y.

[tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

Simplifying and Solving.

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4), Taken  0n  X-(-5) the right side.

       [tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X+5-20=5Y

X-15=5Y

Taking 5 0n the right side.

[tex]\frac{X-15}{5}[/tex] = Y

∴ Point-slop form for Y is [tex]\frac{X-5}{5}[/tex]

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omg what is the......................

Answer: 7.3 < 12

Step-by-step explanation:

The number of times the value 1.5 exceeds the value 0.15 is 10, which is obtained by dividing both values.

We divide a by b to find how many times greater a number is than b; thus, to calculate how many times greater a number is, we use a division operation.

To determine how many times greater a number is than b, we compare them, i.e. divide them.

As an example:

50/10 = 5, indicating that 50 is five times greater than ten.

We must determine how many times the value 1.5 is greater than the value 0.15.

For this , let us divide 1.5 by 0.15

Number of times the value is greater = 1.5/0/15

                                                              = 10

Therefore, the number of times the value 1.5 is greater than the value 0.15 is 10.

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Answer:

b

Step-by-step explanation:

because you need ti 2x +

Answer:

10

Step-by-step explanation:

486-466 = 20

1/2 x 20 = 10

:]

Answer:

an expression that equals 10

Step-by-step explanation:

486 - 466 = 20

1/2 of 20 is 10

You don't list choices.

You need an expression that equals 10.

We are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

Given that, n=550 (Sample size, Number of trials), p=0.6 (Sample proportion) and 1−α=0.9 (Confidence level).

The confidence interval is one of the most used for estimating population parameters in statistics. It is common to perform an interval with a known confidence level to find a range of values that show us information about the population.

Using the standard error of the sample proportions [tex]ME=z_{\alpha /2}.\sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]=z_{0.9/2}.\sqrt{\frac{0.6(1-0.6)}{550} }[/tex]

[tex]=z_{0.45}.\sqrt{\frac{0.6(0.4)}{550} }[/tex]

= 0.1736 × √(0.24/550)

= 0.1736 × 0.0208

= 0.00361

Confidence interval = 0.6±0.00361

= (0.6+0.00361, 0.6-0.00361)

= (0.6036, 0.5963)

Therefore, we are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

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

Work Shown:

[tex]\frac{n^2+n-6}{n-2}\\\\\frac{(n+3)(n-2)}{n-2}\\\\n+3[/tex]

---------------

Explanation:

Often when simplifying, it's a good idea to factor and see what cancels (if anything does cancel).

To factor the numerator, think of two numbers that

Through trial and error, you should find the two numbers to be 3 and -2

So that's how [tex]n^2+n-6[/tex] factors to [tex](n+3)(n-2)[/tex].

After this point, the (n-2) terms cancel leaving n+3 behind

We can say [tex]\frac{n^2+n-6}{n-2}=n+3 \ \ \text{when } n \ne 2[/tex]

The [tex]n \ne 2[/tex] is to avoid a division by zero error.

Answer:

Perimeter

P = 24.2

Step-by-step explanation:

Perimeter

P = 9 + √(6^2 + 6^2) + √(3^2 + 6^2) = 24.2

The correct option is A, the system of inequalities is:

On the graph, we can see two lines.

One is a dashed line (so we need to use the symbols > or < ) and it is horizontal, such that the line is:

y = -3

And the shaded region is above that line, so the inequality is:

y > -3.

The other inequality is below a line y = -x, and we can see that the line is solid (so we use the symbols ≤ or ≥).

Then here the inequality is.

y ≤ -x

Then the system of inequalities is:

y > -3.

y ≤ -x

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[tex] = 9( - 6 + 8i) - 3i( - 6 + 8i) \\ = - 54 + 72i + 15i - 24 {i}^{2} \\ = - 54 + 87i - 24 {i}^{2} [/tex]

ATTACHED IS THE SOLUTION

The approximate height of the door is 84in

A rectangle is a polygon with 4 sides and 4 right angles.

It has 2 lines of symmetry and one of that lines is called a diagonal.

Rectangles are cut into two to form right angled triangles.

The rectangle is divided into two right angled triangles

with a diagonal of 94 inches, base = 42 inches.

The height of the rectangle, the base and the diagonal form a right angled triangle.

By Pythagoras,

[tex](94)^{2}[/tex] = [tex](42)^{2}[/tex] + [tex](height)^{2}[/tex]

8836 = 1764 + [tex](height)^{2}[/tex]

[tex](height)^{2}[/tex] = 8836 - 1764 = 7072

height = [tex]\sqrt{7072}[/tex] = 84 inches

In conclusion, the height of the rectangular door is 84 inches approximately.

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Answer: B is the answer to the question

Step-by-step explanation:

Given:

The lengths of time spent in the store are normally distributed and are represented by the variable X

The survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store.

so, the mean = μ = 43

And the standard deviation = σ = 12 minutes

We will find the probability that supermarkets between 31 and 58 minutes

We will use the following formula to convert to the z-scores

So, we will find Z when x = 31 and When x = 58

So, we will find the probability of P (-1 < z < 1.25)

From the tables of the z-score:

The probability that x is less than or equal to 38 is 0.9861.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 38

μ = mean = 5

σ = standard deviation = 15

z-score = (38 - 5) / 15

z-score = 33 / 15

z-score = 2.2

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score =  2.2

probability = 0.9861

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Answer:

52 yards across

Step-by-step explanation:

Hakim drew a scale drawing of a neighborhood park. he used the scale 5 inches : 2 yards. a soccer field in the park is 130 inches wide in the drawing. how wide is the actual field?

130/5 = 26

26*2 = 52 yards across

1/2 is the factor which converts right angled triangles ΔRPQ to ΔVAQ

Triangle: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Both the triangles are right angled triangles at ΔVAQ and ΔRPQ

side AV=3 units and AQ=4 units

side RP=6 units and PQ=8 units

AV is half of RP and AQ is half of PQ

AV=1/2(RP) and AQ=1/2(PQ)

1/2 factor converts ΔRPQ to ΔVAQ

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The value of the given monomial, -8[tex]m^{4}n^{4}[/tex], when m = 0.5 and n = 2 is -8.

According to the question,

We have the following monomial:

-8[tex]m^{4} n^{4}[/tex]

We have m = 0.5 and n = 2.

Now, putting these values of m and n in the monomial:

-8 [tex](0.5)^{4} (2)^{4}[/tex]

(Please note that when a power is there on a number then it means that to solve the expression we have to multiply the base as many times as the given power. For example, in this case, we will multiply 2 four times and the result will be 16. This concept is applicable to every expression we are solving whether the base is in decimal or in fraction or a integer.)

-8*0.0625*16

-128*0.0625

-8

Hence, the value of the given monomial is -8.

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Answer:

x=1

Step-by-step explanation:

3x−1+2=4

Add −1 and 2 to get 1.

3x+1=4

Subtract 1 from both sides.

3x=4−1

Subtract 1 from 4 to get 3.

3x=3

Divide both sides by 3.

x=

3

3

​

Divide 3 by 3 to get 1.

x=1

The total mass of sugar used is 1.7 kg.

The mass of sugar he has left is 0.3 kg.

In mathematics, a fraction is a numerical value that represents a portion of a whole. The entire can be any number, a specific value, or an item. Fractions are written as p/q.

Given:

Total mass of sugar Mr tan has = 2 kg

Fraction of sugar used to make dessert = 1/4 kg

Fraction of sugar used to bake some cakes = 3/5 kg

The total mass of sugar used is calculated as,

= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes

Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg

Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg

Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg

Mass of sugar left =  Total mass of sugar - Total mass of sugar used

                             = 2 kg - 1.7 kg  = 0.3 kg

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