marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors

Answer:

The slope is 5.

Step-by-step explanation:

[tex]m = \frac{1 - 6}{ - 1 - 0} = \frac{ - 5}{ - 1} = 5[/tex]

The total amount given the original price and tax rate is $33.59

From the question, we have the following parameters:

Original price = $31.69

Sales tax rate = 6%

In order to determine the total sales amount, we make use of the following total sales equation

Total sales = original price + original price * sales tax rate

Substitute the known values in the above equation

So, we have the following equation

Total sales = 31.69 + 31.69 * 6%

Evaluate

Total sales = 33.59

Hence, the total amount is $33.59

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a) The correct equation to represent the given condition is;

⇒ 4 (x + $3) = $36

Where, x represents the amount Pablo parents added in each day.

b) The amount to added by his parents in his account = $6

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;

For 4 days, Pablo put $3 into his account.

And, His parent also add the some money to his saving account.

In the end, there was a total $36 in his account.

Now,

Let the amount Pablo parents added in each day = x

So, We can formulate;

⇒ 4 (x + $3) = $36

Solve for x as;

⇒ 4x + $12 = $36

⇒ 4 x = $36 - $12

⇒ 4x = $24

Divide by 4 both side, we get;

⇒ x = $6

Thus,

a) The correct equation to represent the given condition is;

⇒ 4 (x + $3) = $36

Where, x represents the amount Pablo parents added in each day.

b) The amount to added by his parents in his account = $6

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Answer:

First option

Step-by-step explanation:

→ Define domain

The set of x values a function can take

→ Identify

2 to negative infinity

Answer; the  Negative of 12 is -12

Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12  

Answer:

2x-y=18

Step-by-step explanation:

y + 4 = 2(x - 7)     (open brackets)

y + 4 = 2x - 14      (re arrange)

4 + 14 = 2x - y

2x - y = 18

Answer:

1300 and 750

Step-by-step explanation:

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Answer:

150 Houses

Step-by-step explanation:

180/6=30. Every 1/6 is 30 houses. Therefore you multiply 30x5 to get 150. 150 is 5/6 of the houses sold.

Answer:

$6.50

Step-by-step explanation:

3.50(2)+2x+2.50(3)=26.50

6.00+2x+7.50=26.50

13.50+2x=26.50

2x=13.00

x=6.50

Answer:

$2.46

Step-by-step explanation:

7.38/3 = 2.46

2.46 x 3 = 7.38

Step-by-step explanation:

[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]

The probability that exactly 10 people will show up is 0.230

Let X measure the number of people (out of 12) who show up for a flight. For each passenger

we have a 90% chance of showing up, so X is a binomial random variable with n = 12 and p = 0.90.

(b) Everyone gets a seat when X ≤ 10. We have to find the probability when exactly 10 people show up for the flight , so we use the binomial probability for P(10)

∴ P(10) = [tex]C^{n} _{x} p^{x}(1-p)^{n-x}[/tex]

P(10) = 0.230

So , the probability that exactly 10 people show up for the flight is 0.230 .

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It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

Given that;

Finding the hourly cost of stamping parts for each machine is one way to approach this issue.

In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).

If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.

By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;

250t + 500t = 1000

750t = 1000

t = 1000/750

t = 1.333

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

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When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96

Option b. is correct

We have the following parameters:

sample, n=300

proportions of rooms reserved, p=6%

We first get the sample mean,

Sample mean=n*p

                       =300*6%

                        =18

Now, we get population mean according to binomial distribution, μ'

μ=n-sample mean

   =300-18

   =282

We get the standard deviation, σ

σ=(sample mean*(1-p))^1/2

 =(18*(1-6%))^1/2

 =4.11

We now, calculate z-score:

z=(x-μ)/σ, given x should be at least 275

z=(275-282)/4.11

 =-1.703

Now, we have p(x>275)=p(z>-1.703)

From z-score of probabilities, we have p(z>-1.703) as 0.95572

So, p(x>275)=0.95572

                    =0.96

Hence, the probability that at least 275 rooms are occupied is 0.96

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The equation which has exactly one solution is 6x - 6 = 15x + 15.

The correct answer option is option A

Check all that applies:

6x - 6 = 15x + 15

6x - 15x = 15 + 6

- 9x = 21

divide both sides by -9

x = 21/-9

x = -2.33

6x + 15 = 6x + 15

6x - 6x = 15 - 15

0 = 0

False

6x - 15 = 6x + 15

6x - 6x = 15 + 15

0 = 30

False

6x - 6 = 6x + 15

6x - 6x = 15 + 6

0 = 21

False

In conclusion, the 6x - 6 = 15x + 15 has only one solution.

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Answer: x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4

Step-by-step explanation:

2sin(x)-1=0

tan(x)-1=0

sin(x)=1/2

tan(x)=1

x=π/6

x=5π/6

x=π/4

x=5π/4

x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4

Answer:

−2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5

Step-by-step explanation:

The alternative hypothesis and null are:

H₀ : p = 0.31 vs H₁ : p > 0.31

Given that;

A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.

To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;

n = 900

P = 0.34

p = 0.31

α = 0.10

Claim: More than 31% do not malfunction within the first 1000 hours of operation.

The null and alternative hypothesis must be stated.

This is a right-tailed test because the claim is directional to the right side (> type).

Therefore, the alternative hypothesis and null are:

H₀ : p = 0.31 vs H₁ : p > 0.31

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Each function operation should be matched with what it is equivalent to as follows:

f(x) + g(x) = -2x² + x + 6.

g(x) - f(x) = -2x² - 5x + 2.

f(x) · g(x) = -6x³ - 10x² + 8x + 8.

h(x) - f(x) = 3x² - 7x - 2

f(x) · h(x) = 9x³ - 6x² - 8x.

f(x) + g(x) + h(x) = x² - 3x + 6.

In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.

From the information provided, we have the following functions:

f(x) = 3x + 2

g(x) = -2x² - 2x + 4

h(x) = 3x² - 4x

f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)

f(x) + g(x) = 3x + 2 - 2x² - 2x + 4

Next, we would rearrange the function by collecting like terms as follows:

f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)

f(x) + g(x) = -2x² + x + 6 (solution).

g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)

Opening the bracket, we have:

g(x) - f(x) = -2x² - 2x + 4 - 3x - 2

Next, we would rearrange the function by collecting like terms as follows:

g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)

g(x) - f(x) = -2x² - 5x + 2 (solution).

f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)

Opening the bracket, we have:

f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8

Next, we would rearrange the function by collecting like terms as follows:

f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8

f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).

h(x) - f(x) = 3x² - 4x - (3x + 2)

h(x) - f(x) = 3x² - 4x - 3x - 2

h(x) - f(x) = 3x² - 7x - 2 (solution).

f(x) · h(x) = (3x + 2) × (3x² - 4x)

f(x) · h(x) = 9x³ - 12x² + 6x² - 8x

f(x) · h(x) = 9x³ - 6x² - 8x (solution).

f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)

f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x

f(x) + g(x) + h(x) = x² - 3x + 6 (solution).

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The probability that there will be no repeats on the digits is 0.504.

What is meaning of probability?

The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.

The number of digits of the password is 4.

The numbers from 0 to 9 is 10.

If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.

The total number of ways is 10 × 10 × 10 × 10 =10000.

If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).

The total number of ways is 10 × 9 × 8 × 7 =5040.

The favorable outcomes for this event is 5040.

The total number of outcomes is 10000.

The required probability is 5040/10000 = 0.504.

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The slope of the line that passes through the given pair of points is, -3/7.

What is slope of the line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.

Given: (8, -2), (1, 1)

Since, if two points [tex](x_1, y_1), (x_2, y_2)[/tex] are given then slope (m) is defined as,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].

Here,

[tex](x_1, y_1) = (8, -2)\\(x_2, y_2)=(1, 1)[/tex]

So, the slope can be defined as,

[tex]m = \frac{1-(-2)}{1-8} \\m=\frac{3}{-7} \\m=-\frac{3}{7}[/tex]

Hence, the slope of the line that passes through the given pair of points is, -3/7.

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For a unimodal distribution which is symmetrical with a mean price of $2.11 and standard deviation of $0.56, a local grocer’s price of $3.50 in standard units would be 2.282 and it is unusually expensive.

A unimodal distribution refers to a distribution with one clear peak as the values increase to a single highest point after which they. It can be symmetrical or non-symmetrical. A symmetrical distribution refers to a distribution whose mean, mode, and median are all equal.

The standard score (z) is given by:

z = (x - µ)/σ where µ is the mean and σ is the standard deviation.

To determine the value of z for $3.50 price:

z = (3.5 – 2.11)/0.56 = 2.482

From the z-table, the probability of z ≥ 2.282

P (z ≥ 2.282) = 1 – P (z < 2.282) = 1 – 0.98876 = 0.0112 or 1.12%

Hence, the price of $ 3.50 is unusually high.

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The new price of the flight is $208.25

In this question, we have the following parameters

Discount proportion = 15%

Cost of flight = $245

This means that

New price = Cost of flight x (1 - Discount proportion)

Substitute the known values in the above equation, so, we have the following representation

New price = $245 x (1 - 15%)

Evaluate the product

New price = $208.25

Hence, th new price is $208.25

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The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.

Here,

The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.

=(1+2+3+4+5+6+7+8)/2

=18

Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.

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The perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

We need to find the perimeter of given figures.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

4) Now, sum of all the sides

= 5+3.5+1.5+3.5+5+3.5+1.5+3.5 m

= 27 m

5) Here, radius = Diameter/2 = 17 cm

Perimeter = 2 semicircles+2(17) cm

= 2 × 1/2 πr + 2×17

= 2 × 3.14 × 17 + 34

= 140.76 cm

6) In the given figure here, there are 4 similar triangles

= 4(4+3) inches

= 4 × 7

= 28 inches

Therefore, the perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

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The inequality that represents the quantity of bags of soil Sabrina needs is 1.75x >  42

The bags of soil needed is 24 bags

Inequality as used in math refers to relations that are not precisely equal

Sabrina needs more than 42 ft.³ of soil to top up her raised garden bed

> 42 ft³

each bag of soil contains 1.75 ft.³

let the number of bags of soil be x, such that

1.75x >  42

x > 42 / 1.75

x >  24

Sabrina needs at least 24 bags of soil

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The largest sample size required is 2886.4.

Here we have to calculate how large of a sample size is required.

The formula:

(Z ∝I2/ E)² × P( 1- P)

The given data:

Margin error (E) = 1.5%

=0.015

As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:

The level of significance(∝) = 1 - 0.90

= 0.10

The z value for the 90% confidence is 1.645

Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)

= 2886.4

The largest a sample size required is 2886.4

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Answer:

See below

Step-by-step explanation:

It is NOT a right triangle or the diagonal would measure 52 feet (instead of 54 feet) ....it is an OBTUSE triangle

The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:

Case D: 50.513

Case E: 46.165

Case F: 2.052

In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:

Case D

tan 29° = 28 / x

x = 28 / tan 29°

x ≈ 50.513

The missing side length is approximately 50.513 units.

Case E

tan 18° = 15 / x

x = 15 / tan 18°

x ≈ 46.165

The missing side length is approximately 46.165 units.

Case F

cos 70° = x / 46

x = 46 · cos 70°

x ≈ 2.052

The missing side length is approximately 2.052 units.

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The solution to the given set of systems of equations is (x, y) = (1, -4).

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let's determine the solution using the elimination Method

3x−2y=11  (Equation 1)

3x−y=7(Equation 2)

Multiply the second equation by 2.

6x - 2y = 14    (Equation 3)

Now subtract the first equation from third to eliminate the y.

6x - 2y - (3x - 2y) = 14 - 11

3x = 3

x = 1

Now to find the value of y,

3x−y=7

3(1) − y = 7

y = 7 - 3

y = -4

Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).

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