Systems of Equations and Inequalities 2020-2021 / 5 of 18

Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought

2 spirals and 3 pens for $8. 66. Another student bought 4 spirals and 5 pens for $15. 20. Find the unit cost of a spiral.

1

The system of the equation is written as

x + y = 428

5x + 3y = 1674

the solution:

adult tickets is 195

students tickets is 233

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Janine sold 428 tickets for the school play

x + y = 428

Janine’s total ticket sales were $1674

Student tickets were $3 and adult tickets were $5

5x + 3y = 1674

The simultaneous equation

x + y = 428

5x + 3y = 1674

solving the equation  by elimination method

x + y = 428 * 3

3x + 3y = 1284

5x + 3y = 1674

subtraction gives

-2x = -390

x = 195

substitute x = 195 into x + y = 428

195 + y = 428

y = 428 - 195

y = 233

hence adult tickets is 195, while students tickets is 233

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Answer:

Step-by-step explanation:

23 barrels an 3 budgets

Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

The population of florida is d) a majority of the residents of florida were born elsewhere.

What is majority ?

A majority refers to a number or group that is greater than half of the total number or group. In a group of 10 people, a majority would be 6 or more people. In an election, a candidate who receives more than 50% of the vote is said to have won by a majority. In a legislative body, a majority vote is one where more than half of the members vote in favor of a motion or bill.

This statement is closest to describing the population of Florida. Florida is a popular destination for retirees and tourists, and many people move to Florida from other states and countries. According to the U.S. Census Bureau, Florida has the highest net in-migration of any state in the country, and as of 2020, about 57% of the state's population was born in another state or country.

The population of florida is d) a majority of the residents of florida were born elsewhere.

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The standard deviation of the weight of 4 men would be: 5 lbs.

The standard deviation of a sample of size 4 is the square root of the variance divided by the sample size. In this case, the standard deviation of the weight of 4 men would be:

√(100 / 4) = √(25) = 5 lbs

Please note that the standard deviation of a population is denoted by the Greek letter sigma (σ) and the standard deviation of a sample is denoted by the letter s.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{h}{2}=\cfrac{8}{h}\implies h^2=16\implies h=\sqrt{16}\implies h=4[/tex]

The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is presented as follows;

A linear relationship is a relationship that when plotted on the coordinate plane, produces a linear graph.

The first difference of the y-values in the data contained in the table for Function A are the same and equal to 6, therefore, the data for Function A is a linear relationship.

The slope of the graph of the values in Function A, [tex]m_A[/tex] is found as follows;

Slope of Function A, [tex]m_A[/tex] = (18 - 12)/(3 - 2) = 6

The slope of the graph of A is 6

The equation representing the relationship in function A in point-slope form is therefore;

y - 12 = 6·(x - 2)

y - 12 = 6·x - 12

y = 6·x - 12 + 12 = 6·x

The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x

The value c in the equation is 0 (c = 0). The y-intercept intercept of the graph of Function A is therefore, c = 0

The y-intercept of the graph of Function A is 0

The first difference of the data in the table of Function B is also a constant

The slope of Function B, [tex]m_B[/tex] = (5 - 1)/(1 - 0) = 4

The slope of the graph of B is 4

From the values in the table, the y-value at the y-intercept, which is the point where x = 0, is y = 1

The y-intercept of the graph of Function B is 1

The true statement is therefore;

The y-intercept of the graph of A is less than the y-intercept of the graph of B

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a. The first mentioned case is an Observational study, b. The second one is an Experiment, c. The same goes for the third case it is an observational study, d. And the fourth case is an Experiment.

In observational studies, researchers observe and record information about outcomes of interest without interfering with or controlling variables. Data on the proportion of community college students who successfully complete transfer-level English courses can be gathered and the data can be analyzed to provide answers to specific research questions.

The researcher must do this by contrasting her two sets of explanatory variables to see if there is a correlation between the explanatory and response variables.

If there is a causal relationship between two variables, researchers can observe plants and animals in new habitats and contrast them with their native habitats.

The relationship between consumption and LDL cholesterol oxidation is unclear, and experiments are required to determine whether eating simple carbohydrates increases LDL cholesterol oxidation.

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The question is -

For each of the following research questions, determine whether an observational study, an experiment, or neither should be used to answer the question. Note - each term on the right may be used more than once or not at all. Observational study What proportion of community college students successfully complete a transfer-level English course?

Experiment are non-elite soccer players less likely to develop arthritis of the hip or knee than elite soccer players. This is a question about the population of soccer players. The words "less likely in this research question require researchers to compare two groups of the explanatory variable to determine whether an association exists between the explanatory and response variables The researchers will then generalize the results to the population Observational study Does shifting flora and fauna to new habitats lead to the extinction of some species?

The word "lead" requires researchers to compare two groups of the explanatory variable to determine whether a cause-and-effect relationship exists between the explanatory variable and the response variables. Experiment Does the consumption of simple carbohydrates increase the oxidation of LDL cholesterol?

Answer:

2 cups of punch = 5 cups of juice

28cups of punch = 28/2 × 5

= 85 cups of juice

Answer: 1,302$ per month.

Step-by-step explanation: 125,000 divided by 8 = 15,625. 15,625 divided by 12 = 1302

(I'M SO SORRY FOR GETTING IT WRONG THE FIRST TIME, I FORGOT TO DIVIDE BY 12)

The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =[tex](1-p) / p^2[/tex]

By substituting the value of p = 0.80, we get:

Variance = [tex](1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125[/tex]

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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Answer:

no

Step-by-step explanation:

The possible rational zeros of ƒ(x) = 3x³ + 22x² +28x - 35 are the factors of -35 divided by the factors of 3. These are:

-35/1 = -35, -35/-1 = 35

-35/3 = -5, -35/-3 = 5

Using the Rational Root Theorem, we can now test these values to see if they are zeros of the function:

-35: 3(-35)³ + 22(-35)² + 28(-35) - 35 = -8,925 + 30,950 + -980 - 35 = -9,880 which is not a zero

35: 3(35)³ + 22(35)² + 28(35) - 35 = 42,875 + 30,950 + 980 - 35 = 74,770 which is not a zero

-5: 3(-5)³ + 22(-5)² + 28(-5) - 35 = -125 + -100 + -140 - 35 = -400 which is not a zero

5: 3(5)³ + 22(5)² + 28(5) - 35 = 125 + 100 + 140 - 35 = 330 which is not a zero

So the function ƒ(x) = 3x³ + 22x² +28x - 35 has no rational zeros.

С

To solve for b, we need to get b on one side of the equation and all the other numbers on the other side. To do this, we can start by adding 3 1/2 to both sides of the equation:

-3 1/2 + 3 1/2 = 1 1/4b + 3 1/2

This simplifies to:

0 = 1 1/4b + 3 1/2

Now we can subtract 3 1/2 from both sides of the equation:

0 - 3 1/2 = 1 1/4b

This gives us:

-3 1/2 = 1 1/4b

To solve for b, we can divide both sides of the equation by 1 1/4. To do this, we need to convert the mixed number to an improper fraction:

-14/2 = 1 1/4b

Now we can divide both sides of the equation by 1 1/4:

-14/2 ÷ 1 1/4 = b

This simplifies to:

-7/1 = b

So the value of b is -7

It is worth noting that the solution for b is a negative number, it is possible that the original problem is not well defined and it might not have a solution.

Answer:

b = -2 4/5

Step-by-step explanation:

-3 1/2 = 1 1/4 b

-7/2 = 5/4 b

b = -7/2 × 4/5

b = -28/10

b = -14/5

b = -2 4/5

If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not reliable. So the option 4 is correct.

A set of standardized tests or subtests created to measure human intellect result in a total score known as an intelligence quotient (IQ). When an intelligence test was given, a person's mental age score was calculated. This score was then divided by their chronological age, which was also expressed in years and months. The resulting fraction (quotient), which yielded the IQ score, was multiplied by 100.

Test results that measure intelligence are estimates of intelligence.

A vast range of item material can be found on the many distinct IQ test types. There are both verbal and visual test items. Test questions can range from being grounded on abstract reasoning issues to focusing on math, language, or general knowledge.

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If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not:

1. powerful.

2. accurate.

3. valid.

4. reliable.

The value of the mathematical statement 159.12 divided by 6.8 is 23.4

from the question, we have the following parameters that can be used in our computation:

159.12 divided by 6.8

When represented using numbers and expressions, we have

159.12/6.8

Using a calculator, the value of the quotient is

23.4

Hence, the solution is 23.4

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Answer:
m<1 = 135°
m<2 = 135°

Step-by-step explanation:

When solving for angles we know that the horizontal lines are both parallel. This means that 135° is equal to number 1.

For angle 2 we know that angles opposite are equal to the angle already given. This means that angle 2 is equal to angle 1.

The image I gave should help you understand this.

Total VAT imposed on the Hungarian Secret boxes by Hungarian Government during time of purchase is 6480 Hungarian Forint

A consumption tax known as value-added tax (VAT) is imposed on products and services at every step in the supply chain where value is added, from the point of initial production to the point of sale.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

The total cost of the Secret Boxes is 30480.

The VAT is 27 %

So, the price of the Secret Boxes without Taxex is x

Therefore ,

x + 27% of x  = 30480

⇒ x + 27x/100 = 30480

⇒ 127x/100 = 30480

⇒ x = 24000

Total VAT imposed on the boxes = 30480 - 24000 = 6480

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Answer: 25, 25, 50, 50

Step-by-step explanation: Hello! Because it is a parallelogram, there are two pairs of congruent sides.  This means that if one of the sides is twice the size of the other, then the side congruent to the side that is twice the size of the smaller side is also twice the size of the smaller side.  

Let's represent a as the two smaller sides and b as the two larger sides

2a = b, 2a + 2a = b + b, 1/2(b) = a

Since the parallelogram is 150 cm, you know that 100 + 50 = 150.

50 is half the quantity of 100 and both add up to 150.

You now know that a + a = 50 and b + b = 100

a = a and b = b.

Divide 50 and 100 by two to find the length of each side.

50/2 = 25, 100/2 = 50.

The lengths of each side of the parallelogram are: 25, 25, 50, 50.

The value of x when Sum of LHS = RHS is 4.

The letter "x" may be used in algebra to represent an unknown value. It might be called a "variable" or "unknown." If we make an effort, we can determine the value of x in the equation x + 2 = 7! The letter "x" is not required for a variable; it can also be "y," "w," or any other letter, name, or symbol.

The algebraic statement should typically take one of the following shapes: addition, subtraction, multiplication, and division. To find the value of x, first bring the variable to the left side, then shift every other value to the right side.

x + 5 + x+ 5+ x+ 5 = 27

3x + 15 = 27

3x = 27 - 15

x = 12/3

x = 4

Thus, The value of x when Sum of LHS = RHS is 4.

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Correct question:

Given both sides are equivalent expression and LHS sum = RHS. Find The value of x?

Using linear equation, Isaac saved $33.3 and June ran 20.25 miles in 3 days.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let Eve saved = $x

then Isaac saved= 5x+x=$6x

where x=$5.55

Hence,

           Isaac saved=$33.3

Let June ran y mile in one day

so, In three days she ran = 3y mile where y=6.75 miles

Hence,

           June ran 20.25 miles in 3 days.

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The problem has no solution, because gift card will have negative price .

A system of equations is a set of multiple equations with multiple variables, where the goal is to find the values of the variables that satisfy all the equations simultaneously. It can be solved using different methods such as substitution, elimination and graphing.

This problem can be solved by setting up a system of equations and solving for the variables.

Let x be the cost of each gift card and y be the cost of each gift wrap.

According to the problem statement, we know that:

20x + 40y = $160 (where 20 gift cards and 40 gift wraps sell for $160)

10x + 30y = $110 (where 10 gift cards and 30 gift wraps sell for $110)

We can use these equations to find the value of x and y. To solve the system of equations, we can use the method of substitution.

We can solve the first equation for x:

x = ($160 - 40y) / 20

Now we can substitute this expression for x into the second equation:

10(($160 - 40y) / 20) + 30y = $110

Simplifying this equation:

8y = $50

then we can divide both sides by 8 to get:

y = $6.25

So each gift wrap costs $6.25

We can check our answer by substituting it back into the first equation to make sure it is consistent with the given information.

20x + 40($6.25) = $160

20x + $250 = $160

20x = -$90

x = -$4.5

We can see that x is negative, which is not a possible solution.

Therefore, the problem has no solution, because it is not possible to have negative prices for the gift cards.

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The expression for the synthetic division is 10n³ + 8n² -10 - 0

Synthetic division can be defined as a mathematical way to divide a polynomial by a given binomial x - c

Given that, c is a constant.

The steps to take in synthetic division;

Given the polynomial;

(10n^3*18n^2-2n-10)/(n+1)

[tex]\sqrt[n + 1]{10n^3 + 18n^2 -2n - 10}[/tex]

- 1             coefficient of dividend

                10    18    -2    -10

                ____-10_-8__10_________

                10     8     -10    0

The quotient becomes;

10n³ + 8n² -10 - 0

Hence, the expression is 10n³ + 8n² -10 - 0

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The "dead spot" is 19.04 thousand miles from the center of the earth

To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.

We know that F = −K x2 + 0.012K (239 − x)2

So, we set F equal to 0 and solve for x:

0 = −K x2 + 0.012K (239 − x)2

0 = −K x2 + 0.012K (239 − x)2

K x2 = 0.012K (239 − x)2

x2 = 0.012 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 x2 - 676.8 x + 568.976

x2 - 2.888 x2 = 676.8 x - 568.976

-1.888 x2 = 676.8 x - 568.976

x2 = 361.6 x - 303.504

x = √(361.6 x - 303.504)

x = √(361.6 x - 303.504)

x = 19.04

So the "dead spot" is 19.04 thousand miles from the center of the earth

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Answer:

the price of each CD before tax is $10.70

Step-by-step explanation:

We can start by using algebra to set up an equation to represent the situation. Let x be the price of each CD before tax.

We know that:

The total price of the CDs before tax is 2x (because he bought 2 CDs that were the same price)

The total price of the CDs including tax is $23.80 (because that's what he paid)

The amount of tax is $2.40 (because that's what is stated in the problem)

So we can set up the equation as:

2x + 2.40 = 23.80

To find the price of each CD before tax, we can subtract the amount of tax from both sides of the equation:

2x = 21.40

And then divide both sides by 2:

x = 10.70

So the price of each CD before tax is $10.70

The measure of ∠G is 48°.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

From the figure,

∠G and 48° are alternate exterior angles.

Alternate exterior angles are equal.

So,

∠G = 48°

Thus,

∠G = 48°

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When a figure is rotated and reflected, the new figure will be congruent to the original one, but different coordinate axis. When a figure is translated, reflected and dilated the image will be similar, but the scales will be different.

The original figure we transform is the pre-image and after transformation it is called image. Rotation is the transformation of an image when it is rotated through the Centre of axis. Reflection creates a mirror image of the original figure/ pre-image. Translation means the image is moved to a certain distance in the coordinate axis. Dilation is making an image bigger or smaller, the sides will be in ratio and thee will be a scale factor.

So if a image is rotated, reflected and translated, there will be changes in the coordinate plane, but no change in the size of the image. During dilation the size is varied.

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He used 1/8 of the paint for the birdhouse. This was calculated by adding the 3/8 of paint used for the bookhelf and 1/4 of paint used for the wagon together and then subtracting this amount from the total amount of paint. The result was 1/8 of the paint that was left for the birdhouse.

1. We know that Mr. Riva used 3/8 of the paint for the bookhelf and 1/4 for the wagon.

3/8 + 1/4 = 5/8

2. Since he had 1/8 of the paint left, we can subtract the amount he used from the total amount of paint:

1 - 5/8 = 1/8

3. Therefore, Mr. Riva used 1/8 of the paint for the birdhouse.

Mr. Riva used 1/8 of the paint for the birdhouse. This was calculated by adding the 3/8 of paint used for the bookhelf and 1/4 of paint used for the wagon together and then subtracting this amount from the total amount of paint. The result was 1/8 of the paint that was left for the birdhouse.

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Answer:

An exponential decay function has the form y = a*b^(-kt) where a is the initial value, b is the base of the exponential function (in this case, 1 - the decay rate as a decimal), k is the decay rate and t is the time.

Given that the initial value is 980, the decay rate is 1% every 2 days and the time is 5 weeks. The first step is to convert the time to the same unit of time as the decay rate, in this case, days: 5 weeks * 7 days/week = 35 days.

The decay rate per day is 1/100 because 1% as a decimal is 0.01, so the decay rate per day is 0.01/2 = 0.005

Now we can plug in the values in the function:

y = 980 * (1 - 0.005)^(-0.005*35)

y = 980 * 0.995^(-17.5)

y ≈ 574.64

So, the value of the quantity after 5 weeks to the nearest hundredth is 574.64

It's worth noting that in this case, the base (1 - decay rate) is less than 1, which implies that the value of the quantity decreases over time.