Solve the system of equations by elimination. Express the solution as an ordered pair.
-3x+y = -13
4x - 2y = 16

The amount of money an account with simple interest at an annual rate of 3% would be $750 after 5 years.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that deposit amount is $5,000 in an account that earns simple interest at an annual rate of 3%.

Amount = $5,000

Rate = 3%

Time = 5 years

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 5,000 × 3% × 5

Simple Interest = 5,000 × 3/100 × 5

Simple Interest = 750

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Answer:

Step-by-step explanation:

.....-_-.....-__-....-___-_--____--_--_____--_--______________--_________________-u streched ma face dude.

We know that the store sells nuts for $2 per pound and chocolate for $0.95 per pound. We also know that x represents the total pounds of nuts, and 32 represents the total pounds of chocolate.

In order to write an equation that represents a mixture that costs $1.48 per pound, we first need to find an expression to represent the total pounds in this situation, which would be (x + 32).

Now that we have this, let's just combine everything we know into one equation:

2x + 0.95(32) = 1.48(x + 32)

Therefore, the correct answer choice is option B.

The value of the number 88 in the ratio of 1:7 will be 11:77.

The ratio is defined as the division of the numbers into two parts according to the requirements. The ratio generally compares one value is how many times the other value.

Given that the £88 is distributed in the ratio of 1:7. The distributed form of the number will be calculated as:-

x + 7x = 88

8x = 88

x = 11

The two values will be,

x = £11

7x = 7 x 11

7x =£77

Therefore, the value of the number 88 in the 1:7 ratio is 11:77.

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On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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The length of x is given as follows:

x = 3.6.

Similar polygons share these two features listed as follows:

In the context of this problem, the proportional relationship for the side lengths of the polygons is given as follows:

x/3 = 2.4/2 = 4.8/4 = 6/5.

The relationship can be simplified as follows:

x/3 = 1.2.

Applying cross multiplication, the value of x is obtained as follows:

x = 3 x 1.2

x = 3.6.

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Answer:

Since each ticket cost $6.25, then to find the total they spent on tickets you will multiply 6.25 by itself 4 times:

6.25 * 4 = 25

They spent $25 on movie tickets.

You can subtract that from the $37 to find the total they spent on the snacks:

37 - 25 = 12

Th spent $12 in total on movie snacks. Now to find how much they cost each, yo will divide that total by the 4 friends:

12/4 = 3

The movie snacks cost $3 each.

Step-by-step explanation:

Hope it helps! =D

The coordinates of Casper which lies exactly in the middle of Denton and Beacon are (-4, -1).

Coordinates are defined as the set of points in a coordinate plane or space, which describes the position of that point in that plane or space.

In a coordinate plane, the midpoint of two points (x₁, y₁) and (x₂, y₂) is the point (x, y) such that their measures are,

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

First, we can write the given measures.

Coordinates of Albion = (5, 5)

Coordinates of Denton = (-7, -3)

Given that, Beacon is lying exactly in the middle of Albion and Denton.

Let the coordinates of Beacon be (x, y).

Using the formula above,

x coordinate of Beacon = (5 + -7) / 2 = -1

y coordinate of Beacon = (5 + -3) / 2 = 1

Coordinates of Beacon are thus (-1, 1).

Casper is lying exactly in the middle of Denton(-7, -3) and Beacon (-1, 1).

Let (x' , y') be the coordinates of Casper.

Using the same formula,

x' = (-7 + -1) / 2 = -4

y' = (-3 + 1) / 2 = -1

Hence the coordinates of Casper are (-4, -1).

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Gloria walked  500500 Miles from nearest bus stop to home.

How to convert yards into miles ?

To convert a yard measurement to a mile measurement, divide the length by the conversion ratio.

Since one mile is equal to 1,760 yards, you can use this simple formula to convert:

miles = yards ÷ 1,760

The length in miles is equal to the yards divided by 1,760.

Given:

Gloria traveled : 888 miles

1 Mile = 1760 yards

880880880 yards = 500500 Miles

So she walked  500500 Miles from nearest bus stop to home.

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Answer:

a. 0.81

b. 0.81

Step-by-step explanation:

Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.

So if he makes 90% of his free throws, then:

a. The probability that he will make both free throws is (90/100)^2 = 0.81.

b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.

The answers to the questions rounded to 4 decimal places are:

a. 0.81

b. 0.81

1) The probability of picking more than 1 apple is 0.8. 2) the expected number of apples you can pick each year is 2.65. 3) the expected number of apples you can pick each year is 2.65.

To find the probability of picking more than 1 apple, we need to find the sum of the probabilities of picking 2, 3, and 4 apples. Using the table, we have P(N>1) = P(2) + P(3) + P(4) = 0.15 + 0.35 + 0.3 = 0.8. So, the probability of picking more than 1 apple is 0.8. The expected number of apples you can pick each year can be calculated using the formula: E(N) = ∑N * P(N), where the sum is taken over all possible values of N. Using the table, we have E(N) = (1 * 0.1) + (2 * 0.15) + (3 * 0.35) + (4 * 0.3) = 0.1 + 0.3 + 1.05 + 1.2 = 2.65. So, the expected number of apples you can pick each year is 2.65. To find the probability of picking 3 apples, given that your father picked more than 1 apple, we need to use the conditional probability formula. We have P(3|N>1) = P(3 and N>1) / P(N>1) = P(3) / P(N>1) = 0.35 / 0.8 = 0.4375. So, the probability of your father picking 3 apples, given that he picked more than 1 apple, is 0.4375

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Complete Question

Imagine you have an apple tree, and you pick apples from it each fall. Empirically, the number of apples (N) that you can harvest and the corresponding probability (P) can be summarized in the following table,  the table =  N - O, 1, 2, 3, 4 And P = 0.1, 0.15, 0.35, 0.3, 0.1

1) What is the probability that you can pick more than 1 apple? 2) What is the expected number of apples you can pick each year? 3) Your father told you that he picked more than 1 apple this year. What is the probability that he picked 3 apples, given that information?

The currect option is (b) H0: p = 0.5; Ha: p > 0.5

p represents the population proportion.

A null hypothesis is a statement from the population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.

An alternate hypothesis is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. a commentator believes that more than half of all adults favor such a ban. the null and alternative hypotheses you would use to test this claim are

a) H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p≠0.5

(e) H0:p>0.5;Ha:p=0.5

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Answer:

you cannot cancel (5-5) because it is multiplied to 5 and 4 if the question was 5+(5-5)=4+(5-5) you can cancel 5-5

The reason that we can't cancel out the (5 - 5) is because it is attached to different numbers and as such they must be multiplied first with distributive property.

According to the distributive property of algebra, multiplying the sum of two or more addends by a number will give us the same result as when each addend is multiplied individually by the number and the products are added together.

This also applies to addition as well.

We are given;

5(5 - 5) = 4(5 - 5)

Now, according to the distributive property, we will have to first multiply out the bracket to get a solution. Thus, we can't cancel out the (5 - 5) because it is attached to different numbers and as such they must be multiplied first with distributive property in mind.

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The two numbers, then, are 86 and 61.The two numbers can be found by using basic algebra.

The two numbers can be found by using basic algebra. To solve for the two numbers, we can set up two equations, one for the sum and one for the difference. For the sum, we can set up the equation: x + y = 147. For the difference, we can set up the equation: x - y = 25. We can then solve for x by adding y to both sides of the equation for the difference, so x = 25 + y. We can then substitute this value for x in the equation for the sum, so 25 + y + y = 147, or 2y = 122, and y = 61. We can then substitute this value for y in the equation for x, so x = 25 + 61, or x = 86. The two numbers, then, are 86 and 61.

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Answer:

Step-by-step explanation:

Let's call the length of the winning jump "w".

Sarah's best jump is 12% more than her first jump, which was 4.25m. So her best jump was 4.25m * 1.12 = 4.77m.

However, her best jump is 15% lower than the winning jump, so we can set up an equation to solve for w:

4.77m * 1.15 = w

Solving for w:

w = 4.77m * 1.15 = 5.51m

So the winning jump was 5.51m.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

Shrub $7

Rose Bush $8

Step-by-step explanation:

First, write them as equations

10r + 4s = $108

5r + s = $47

Next, multiply

10r + 2s = $94

10r + 4s = $108

Then, Subtract

2s = $14

After, Divide

s = $7

Then, plug in and solve

5s + $7 = $47

$40/5s = 8$

$8 = r

$7 = s

Answer: The bushes cost $8 and the shrubs cost 7$

Step-by-step explanation:

For this question you must use system of equations, trial and error will take a very long time.

So yeah, here is how you solve it-

First set up equations (b represents the amount of bushes and s represents the amount of shrubs):

5b + 1s = 47

10b+4s=108

Next you can either solve via elimination or the substitution method. I will show elimination here. Elimination works by slightly modifying one of the equations so that it cancels when it is added to the other equation:

(I modified the first equation)

-4(5b+1s = 47) = -20b-4s=-188

(Then add)

     -20b-4s=-188

  +    10b+4s=108

This equals: -10b=-80

Next you just solve for b:

b=-80/-10

b=8

To then find s, plug b into one of the original equations and solve for s:

(I plugged it into the first equation)

5(8)+1s=47

40+s=47

s=7

So the bushes cost $8 and the shrubs cost 7$

Hope this helps :)

If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition. Hence, option a. is the right answer.

According to the definition, we know that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition.

Let us consider two triangles △ABC and △QRP as shown below -

So, in △ABC and △QRP, we have,

∠B=∠R

∠C=∠P

BC=RP

∴ By ASA congruence test for triangles, we get △ABC ≅ △QRP

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The complete question is -

If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

a. ASA

b. AAA

c. SAS

d. RHS

Answer:

The price of the desk in the furniture store is $202.8

1. The value of line EF is 14.3

2. not enough info to get angle ECB

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

EF is congruent to AB

GB is congruent to EH

Therefore AG will be congruent FH

therefore FH = 12

tan 40 = 12/EF

EF = 12/tan40

EF = 12/0.839

EF = 14.3

There is not enough info to get angle ECB

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Answer:

13 months

Step-by-step explanation:

(b)

let C(x) = 431.5 and solve for x , that is

29x + 54.5 = 431.5 ( subtract 54.5 from both sides )

29x = 377 ( divide both sides by 29 )

x = 13

that is cable service for 13 months

The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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The probability of exactly 5 patients having kidney-related problems is approximately 0.253 or 25.3%.

The probability of a given number of patients having kidney-related problems can be found using the binomial distribution. The binomial distribution models the number of successful outcomes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each hospital admission is a trial, and the probability of success (having a kidney-related problem) is 0.3 (30%). The number of trials is 10, and we want to find the probability of exactly 5 patients having kidney-related problems.

We can use the formula for the probability mass function of the binomial distribution to find this:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where:

n = 10 (number of trials)

k = 5 (number of successful outcomes)

p = 0.3 (probability of success)

Using the formula, we have:

[tex]P(X = 5) = (10 choose 5) * 0.3^5 * (1-0.3)^(10-5)= 252 * 0.3^5 * 0.7^5[/tex]

= approximately 0.253

So, the probability of exactly 5 patients having kidney-related problems is approximately 0.253 or 25.3%.

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Thirty percent of hospital admissions for diabetic patents are related to problems with the kidneys. in a sample of 10 diabetic hospital admissions, what is the probability that exactly five patients will have kidney related problems?

Answer:

Step-by-step explanation:

The exponential equation in the form y= a[tex](b)^x[/tex] that can model is y= 500[tex](1.06)^x[/tex].

In mathematics, an exponential function is a relationship of the type

y = [tex]a^x[/tex], where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

Given:

Britney invested $500 in stocks.

After one year, the value of her stocks has increased to $530.

We know the Exponential Function y= a[tex](b)^x[/tex]

As, a= 500, y= 530, x= 1

So, y= a[tex](b)^x[/tex]

530 = 500 [tex](b)^1[/tex]

530 / 500 = b

b= 1.06

So, the exponential equation is y= 500[tex](1.06)^x[/tex]

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Answer:

2. More time spent on homework results in higher grades.

Step-by-step explanation:

The more time spent on homework pays off in higher grades. If this is incorrect my apologies.

More weight on one side of a balance scale will tip the scale in that direction is relationship is an example of causation.

Causation is the capacity of one variable to influence another.

Causation means that a change in one variable results in a change in another variable.

More weight on one side of a balance scale will tip the scale in that direction.

In this case, adding more weight to one side of the scale will directly cause it to tip in that direction.

There is a correlation between the variables, but it's not necessarily a direct cause-and-effect relationship.

The more education a person has, the more they read suggests that education and reading are correlated, but having more education doesn't necessarily cause a person to read more.

Hence,  More weight on one side of a balance scale will tip the scale in that direction is an example of causation.

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The parabola's shape is influenced by the separation between its focus and vertex. The parabola becomes wider as the vertex is focused further away (flatter).

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line. The parabola's directrix serves as the fixed line, while the focus, represented by the letter F, serves as the fixed point. The line through the F and perpendicular to the directrix is the parabola's axis.

2. As illustrated here, the parabola's shape is influenced by the separation between its focus and vertex.

The parabola becomes wider as the vertex is focused further away (flatter).

The parabola becomes thinner as the vertex comes into focus (steeper).

3. If a > 0 in the quadratic equation the parabola opens upward and if a< 0 then the parabola opens downward.

4. The vertex of the parabola is the location where it crosses the axis.

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Answer:

4 and -2

Step-by-step explanation:

4 + -2 = 2

4 x -2 = -8

The total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

The formula for calculating the number of unique ways to form three groups comprising of 3, 3, and 2 students is given by:

Number of ways = Number of ways to select 3 first-year students from 5 first-year students x Number of ways to select 3 second-year students from 3 second-year students x Number of ways to select 2 students from 8 students

=[tex]5C3 x 3C3 x 8C2[/tex]

= 10 x 1 x 28

= 280

Therefore, there are 280 unique ways to form three groups comprising 3, 3, and 2 students. This can be seen by considering the total number of possible arrangements of the 8 students into 3 groups of 3, 3 and 2. First, we need to select 3 students from 5 first-year students in 5C3 ways, which is equal to 10. Second, we need to select 3 students from 3 second-year students in 3C3 ways, which is equal to 1. Finally, we need to select 2 students from 8 students in 8C2 ways, which is equal to 28. Therefore, the total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

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Answer:

-4

Step-by-step explanation:

Answer:

f(0) = 4

Step-by-step explanation:

[tex]f(x) = {2x}^{2} + 4[/tex]

- When x = 0, then f(x) = f(0)

[tex]f(0) = 2(0) {}^{2} + 4 \\ f(0) = 4[/tex]