Solve the system of equations below graphically. Identify the graphs and the solution point on the Cartesian plane below.
x-y=0
5x+2y=7

Answer: Without a visual representation of the triangles, it's difficult to determine whether the statements are true or false.

However, in general, the side lengths of a triangle determine its shape and size. If two triangles have the same side lengths, then they are congruent, meaning they have the same shape and size. Therefore, if the triangles in question have different side lengths for x = 16, x = 27, and x = 31, then it's possible that the statements are either true or false, depending on the specific side lengths.

Without additional information, it's not possible to determine whether the statements are true or false.

Step-by-step explanation:

the ticket price needs to be lowered by approximately $8.33 in order to fill all seats in the stadium.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000.

Let's assume that if the ticket price is lowered by $x, the corresponding increase in attendance is 3000x.

Then, if the ticket price is lowered by $x, the new attendance will be:

33,000 + 3000x

We want to find the ticket price that will result in full capacity, which is 58,000 spectators.

So, we can set the new attendance equal to 58,000 and solve for x:

33,000 + 3000x = 58,000

3000x = 25,000

x = 25,000/3000

x ≈ 8.33

Therefore, the ticket price needs to be lowered by $8.33 to $1.67 in order to fill all seats in the stadium.

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Complete question:

A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. how much ticket price to be lowered so that all seats will be full?

Let's use the given information to set up equations to solve for the ages of the family members.

We know that the mean age of the family is 23 years, so we can write:

(sum of ages) / 7 = 23

sum of ages = 161

We also know that the median age is 16 years, which means that the ages of the family members can be arranged in order from smallest to largest, and the middle age (or the average of the two middle ages, if there are an even number of ages) is 16. We can use this information to set up an equation:

(3rd smallest age + 4th smallest age) / 2 = 16

3rd smallest age + 4th smallest age = 32

Next, we know that the range of the ages is 35 years, which means that the difference between the largest age and the smallest age is 35. We can use this information to set up another equation:

largest age - smallest age = 35

Finally, we know that the modes (the most common ages) are 12 years and 45 years. This means that there are two family members whose ages are 12 years and two family members whose ages are 45 years. We can use this information to set up two more equations:

number of 12-year-olds + number of 45-year-olds = 4

12 x number of 12-year-olds + 45 x number of 45-year-olds = sum of ages

We now have five equations and five unknowns (the ages of the seven family members). We can solve for these unknowns using algebra. One possible set of ages that satisfies all of the equations is:

2, 2, 12, 16, 20, 45, 64

(Note that the ages do not have to be integers, but this particular set of ages happens to be integers and satisfies all of the given conditions.)

Answer:

We should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

Step-by-step explanation:

This problem can be solved using the binomial distribution, which can tell us the probability of getting a certain number of successes in a given number of trials, each with a certain probability of success. In this case, the trials are the bonds, the probability of success is 50% (the chance that a bond will not default), and we want to know how many bonds we need to buy to have at least a 97% chance of getting 5 or more successes.

Let X be the number of bonds that do not default. We want to find the smallest value of n (the total number of bonds we buy) such that P(X ≥ 5) ≥ 0.97.

Using the binomial distribution, we can calculate that the probability of getting exactly k successes out of n trials with a probability p of success is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.

To find P(X ≥ 5), we can calculate the probabilities of getting 5, 6, 7, 8, 9, or 10 successes and add them up:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

We want this probability to be at least 0.97, so we can set up the following inequality:

P(X ≥ 5) ≥ 0.97

P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) ≥ 0.97

We can then use a spreadsheet or a binomial probability table to find the smallest value of n that satisfies this inequality. For example, using Excel's BINOM.DIST function, we can enter the following formula in a cell:

=BINOM.DIST(4,n,0.5,TRUE) + BINOM.DIST(5,n,0.5,TRUE) + BINOM.DIST(6,n,0.5,TRUE) + BINOM.DIST(7,n,0.5,TRUE) + BINOM.DIST(8,n,0.5,TRUE) + BINOM.DIST(9,n,0.5,TRUE) + BINOM.DIST(10,n,0.5,TRUE)

where n is the number of bonds we want to buy, and TRUE indicates that we want to calculate the cumulative distribution function (CDF) up to the given value of k.

We can then use Excel's Goal Seek tool to find the smallest value of n that makes this formula equal to 0.97. For example, if we set the target value to 0.97 and the "Set cell" to the formula cell, and we vary the "To value" of n, Goal Seek finds that the smallest value of n that satisfies the inequality is 19. Therefore, we should buy at least 19 bonds to have at least a 97% chance of getting 5 or more bonds that do not default.

The slopes of the points are computed below

The slope of any two points is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Using the above as a guide, we have the following slopes in set 2

For set 3, we have the following slope values

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Answer:

The slope of a line parallel to Y-axis is zero.

Answer: Here you go.

Step-by-step explanation:

To calculate the volume of excavation needed for the water line, we first need to calculate the cross-sectional area of the trench.

The trench has a width of 18 inches and a depth of 3 feet, or 36 inches. So the cross-sectional area of the trench is:

18 inches x 36 inches = 648 square inches

Next, we need to subtract the cross-sectional area of the water line from the cross-sectional area of the trench to get the area of the excavation. The water line has a 3.5 inch outside diameter, so the radius is 1.75 inches. The cross-sectional area of the water line is:

π x (1.75 inches)^2 = 9.62 square inches

The area of the excavation is therefore:

648 square inches - 9.62 square inches = 638.38 square inches

To convert square inches to cubic feet, we need to multiply by the length of the trench in feet. The length of the trench is 500 feet. So the volume of excavation needed for the water line is:

638.38 square inches x 500 feet = 1,909,140 cubic inches

To convert cubic inches to cubic feet, we divide by 12^3 (12 inches per foot, cubed):

1,909,140 cubic inches ÷ (12 x 12 x 12) = 11.04 cubic feet

Therefore, the volume of excavation needed for the water line is approximately 11.04 cubic feet.

Answer: Let's define the events:

A: a proposal is judged worthy of funding by the first panel

B: the decision to fund a proposal is reversed by the second panel

We want to find the probability of the intersection of events A and B (i.e., a worthy proposal is disapproved by both panels). We can use the formula:

P(A and B) = P(B|A) * P(A)

We know that P(A) = 0.22 (the probability that a proposal is judged worthy of funding by the first panel). We also know that when a proposal is judged worthy of funding by the first panel, the probability that the decision to fund is reversed by the second panel is 0.74 (i.e., P(B|A) = 0.74).

Plugging in these values, we get:

P(A and B) = 0.74 * 0.22 = 0.1628

Therefore, the probability that a worthy proposal is disapproved by both panels is 0.1628, or approximately 16.28%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.

The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.

The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.

The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:

30x + 35(75 - x) = 2425

Expanding the equation:

30x + 2625 - 35x = 2425

Simplifying:

-5x = -200

x = 40

Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.

Answer: Car 1 used 40 gallons and car 2 used 35 gallons.

Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.

x+y=75

x=75-y                   Isolating a variable

30x+35y=2425    

30(75-y)+35y=2425            Substituting the variable we isolated

2250-30y+35y=2425

2250+5y=2425

5y=175

y=35

x+(35)=75

x=40

y=35 and x=40

Car 1 used 40 gallons and car 2 used 35 gallons.

Hope this helps!

Answer:

First, if it's a simple interest problem, convert R percent to r a decimal, r = R/100 = 9%/100 = 0.09 per year, then, solving our equation

I = 4000 × 0.09 × 2

I = 4000 × 0.18

I = $720.00

The simple interest accumulated on a principle of $4,000.00 at a rate of 9% per year for 2 years is $720.00.

Hope this helps. (Compound interest will be added if the equation needs it)

The answer to this question is as follows It's vital to keep in mind that equation while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

The formula to calculate Theodore's overall spending is:

3x + 4.50

This is due to the fact that he purchased three waters at a cost of x each, for a total cost of x, and a bag of popcorn at a cost of $4.50. The entire amount of money he spent may be calculated by adding these two expenses.

By condensing the formula 3x + 4.50, we obtain:

7.50x

It's vital to keep in mind that while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.

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The logical form of this argument in " If Russia invades the Ukraine, America will impose trade sanctions upon Russia" is c. Hypothetical Syllogism.

A hypothetical syllogism is a logical argument that uses two conditional statements, or "if-then" statements, to draw a conclusion. The general form of a hypothetical syllogism is:

If A is true, then B is true.

If B is true, then C is true.

Therefore, if A is true, then C is true.

Here's an example of a hypothetical syllogism:

If it rains, then the ground is wet.

If the ground is wet, then the grass is slippery.

Therefore, if it rains, then the grass is slippery.

Therefore, option C is correct.

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The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.

In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

It is said that there are 10 balls in a bag, labelled 1-10.

Now,

The number of ways the ball labelled 1 is picked is 1

The number of ways the ball labelled 2 is picked is 2

So the number of ways a ball labelled certain number is picked is 1.

Now there is no replacement.

So the total number of balls decreases by 1 when 1 ball is taken.

Then,

The probability of choosing the ball numbered 1 = 1/10

The probability of choosing 2 = 1/9

The probability of choosing 3 = 1/8

.

.

.

the probability of choosing 10 = 1

Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

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The total area of the composite figure is 107/216 square yards.

What is Area?

Area is a measure of the size of a two-dimensional shape or surface. It is the amount of space inside the boundaries of a flat object, measured in square units such as square meters, square feet, or square inches.

To find the total area of the composite figure, we need to first convert the dimensions from inches to yards, since the given scale is in inches per yards.

Since 1 yard is equal to 3 feet, which is equal to 36 inches, we have:

The height of the triangle is 6/36 = 1/6 yards.

The base of the triangle is 9 times the height, which is 9/6 = 3/2 yards.

The length of the rectangle is 7/9 yards.

The width of the rectangle is 6/9 = 2/3 yards.

The area of the triangle is:

(1/2) x (1/6) x (3/2) = 1/8 square yards.

The area of the rectangle is:

(7/9) x (2/3) = 14/27 square yards.

Therefore, the total area of the composite figure is:

1/8 + 14/27 = 107/216 square yards.

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Answer:

Class A: 87, 93, 96, 88, 92, 90, 100, 93, 91, 96

Mean: 92.6

Median: 92.5

Mode: 93 and 96

Class B: 72, 69, 54, 66, 63, 74, 59, 64, 70, 68

Mean: 65.9

Median: 67

Mode: No mode or 0

Step-by-step explanation:

You're welcome.

Answer: A great white shark can grow up to 20 feet in length, while a horn shark can grow up to 3 feet in length. Therefore, a great white shark is 17 feet larger than a horn shark.

Bamboo sharks can grow up to 5 feet in length. Therefore, to equal the length of a great white shark, you would need 4 bamboo sharks (since 4 x 5 = 20).

Step-by-step explanation:

oh my God cr7 ans messi are running

The vertex of the parabola is ( 0, -4). The correct option is F.

A vertex of a parabola is the point at which the parabola changes direction. It is the point on the parabola where the curve reaches its minimum or maximum value, depending on whether the parabola opens upward or downward.

A parabola is a type of conic section, a geometric shape formed by the intersection of a plane and a cone. In particular, a parabola is formed when a plane intersects a right circular cone parallel to one of its generating lines.

From the given graph the vertex of the parabola is,

Vertex = ( 0, -4 )

Therefore, the vertex is (0,-4).

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Answer:

0.05%

Step-by-step explanation:

Answer:45

Step-by-step explanation: see how if you cut off that spike and you plug it in the non-shaded part it fits. Now you’ve got yourself a rectangle so the area is 3+2= 5 x 9= 45

Answer:

520

Step-by-step explanation:

So you multiply 650 by 0.8 and you get 520. 0.8 is 80% but in a decimal form.

Answer:

If the house price is $250,000, then 1% of the appraised value is:

0.01 x $250,000 = $2,500

So Marisa can expect to pay $2,500 in annual property taxes.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

plug in 7 for "P"

so 10 - [7+3]

solve the inside first, which is 10, therefore 10-[10] leaving you with no solution or 0 as answer

Answer:

19

y = 6x - 11 it says the input is 5 so you input 5 as x

y = 6(5) - 11

y = 30 - 11

y = 19

1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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The principal amount of the loan is $1,200,000.

What is simple interest?

Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.

To find the principal amount of a loan, we need to use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.

Substituting these values into the formula, we get:

3150 = P * 0.105 * 0.25

Solving for P, we get:

P = 3150 / (0.105 * 0.25) = $1,200,000

Therefore, the principal amount of the loan is $1,200,000.

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Answer:

x is greater than or equal to 3

Step-by-step explanation:

I'm gonna assume you meant 3x-8

Treat it as an equation

3x-8 =1, 3x=9, x=3

If its x^3 -8

x^3 -8 =1, x^3=9, x is greater than or equal to the cubed root of 9

Therefore, John is incorrect, as buying a 2-liter bottle of orange juice is actually slightly more expensive per liter than buying a 1.5-liter bottle of cola.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

2.1.1 To determine how many packets of patties Julia should buy, we need to know the total number of patties needed for the school function. Let's assume that each person will eat one patty.

If there are 300 people attending the function, then Julia needs to buy:

300 x 1 = 300 patties

Each packet of patties contains 12 patties, so the number of packets needed can be calculated as follows:

300 patties ÷ 12 patties/packet = 25 packets

Therefore, Julia should buy 25 packets of patties.

2.1.2 To justify Julia's calculation, we can use algebra. Let's assume that the number of packets of patties she buys is x. We know that there are 12 patties in each packet, so the total number of patties is 12x. We also know that if she buys 42 packets, there will be a leftover of 4 patties.

This can be represented as the following equation:

12x + 4 = 42 x 12

Simplifying this equation:

12x = 500 - 4 = 496

x = 496/12 = 41.33 (rounded to two decimal places)

Since we can't buy a fractional number of packets, Julia would need to buy 42 packets of patties. This would give her a total of:

12 x 42 = 504 patties

She would then have 4 leftover patties, as calculated earlier. Therefore, Julia's calculation is correct.

2.2.1 To determine whether buying a 2-liter bottle of orange juice is cheaper than buying a 1.5-liter bottle of cola, we need to compare the price per liter of each drink.

For orange juice, the price per liter is:

R18.95 ÷ 2 liters = R9.475/liter

For cola, the price per liter is:

R14.50 ÷ 1.5 liters = R9.67/liter

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The journal entries for the aforementioned transactions in May are as follows:

1. a $48,000 profit from the selling of ordinary stock:

Cash 48,000

Stock 48,000

2. Paid $880 in rent for the office for the month:

Rent Expense 880

Cash 880

3. $1,750 worth of supplies were bought on credit:

Supplies 1,750

Accounts Payable 1,750

4. Paid fees, cash received, $12,600:

Cash 12,600

Fees Earned 12,600

5. $1,000 creditor account payment:

Accounts Payable 1,000

Cash 1,000

6. Spent $375 in transportation expenses for the month as well as $250 in other expenses:

Automobile Expense 375

Miscellaneous Expense 250

Cash 625

7. $3,900 in office salaries were paid for the month:

Salaries Expense 3,900

Cash 3,900

8. $2,400 in earned fees that the client will pay the next month:

Accounts Receivable 2,400

Fees Earned 2,400

9. determined that the $280 cost of the supplies used:

Supplies Expense 280

Supplies 280

10. Dividends paid, $2,400:

Retained Earnings 2,400

Cash 2,400

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