Find the indicated side of the
right triangle.
30°
X
60°
3

The graph the system of linear equations on a coordinate plane is added as an attachment and the solution is (2, 2)

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y=-1/2x+3 and y=2x-2

Rewrite the equations in the system of equations as follows:

So, we have the following representation

y = -1/2x + 3

y = 2x - 2

Next, we plot the graph of the system of equations

See attachment for the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (2, 2)

This means that the solution to the system of equations is (2, 2)

Recall that

y = -1/2x + 3

y = 2x - 2

Solution = (2, 2)

So, we have

2 = -1/2 x 2 + 3 = 2 --- true

2 = 2 x 2 - 2 = 2 --- true

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the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

given that

the combined perimeter of a circle and square is 16cm

let side length of the square is s

let radius of the circle with r

So, the perimeter (P) and the area (A) of the shape are:

P= 4s + 2[tex]\pi[/tex]r

A = [tex]s^{2}[/tex] + [tex]\pi[/tex][tex]r^{2}[/tex]

given that perimeter is 16

so, 4s +2[tex]\pi[/tex]r = 16

divide by 4

s +0.5[tex]\pi[/tex]r = 4

s = 4 - 0.5[tex]\pi[/tex]r

substitute s value in area

A =  [tex](4-0.5\pi r)^{2}[/tex] + [tex]\pi[/tex]r

A = 16 - 4[tex]\pi[/tex]r +0.25[tex](\pi r)^{2}[/tex] +[tex]\pi[/tex][tex]r^{2}[/tex]

A =16 - 4[tex]\pi[/tex]r + (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])[tex]r^{2}[/tex]

differentiate with respect to r

A' = 0 - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r

A' = - 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r

now A' =0

- 4[tex]\pi[/tex] +2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r =0

2 (0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r =  4[tex]\pi[/tex]

divide both sides by 2

(0.25 [tex]\pi ^{2}[/tex] + [tex]\pi[/tex])r = 2[tex]\pi[/tex]

r = [tex]\frac{2\pi }{0.25\pi ^{2} +\pi }[/tex]

r = [tex]\frac{2\pi }{\pi (0.25\pi +1)}[/tex]

substitute  [tex]\pi[/tex] =3.14

r = 2/(0.25(3.14)+1)

r = 1.12

substitute r value in s

s = 4 - 0.5 * 3.14 *1.12

s =2.24

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

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The mass of the Cougar is 70 Kg using the concept of equations.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It demonstrates the equal relationship between the expressions presented on the left and right sides. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved. If there is no "equal to" symbol, a statement is not an equation.

Let the mass of white-tailed deer = d

Mass of cougar = c

According to the question,

d = 1.4 × c                   ....(1)

d = 98 kg                   ....(2)

So,

1.4 × c = 98

c = 98/1.4

c = 70

So, the mass of the Cougar = 70 Kg

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Answer:

61

Step-by-step explanation:

hope this helps

for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, p value will be pchisq(8.4345,5)

To test a hypothesis' validity against actual data, a statistical calculation called a p-value is used. The probability of experiencing the results that were observed is calculated using a p-value, assuming that the null hypothesis is true. The p-value can be calculated by looking up the 8.4345 value in the Chi-Square distribution table with 5 degrees of freedom (6-1=5). The resulting p-value will depend on the significance level you choose.

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[tex]f(x)=(\dfrac{1}{4} )^x[/tex]

Please refer to the following graph below:

Answer:

You can write it like 25.20 x -2 = -50.40

Step-by-step explanation:

Answer:The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.

Step-by-step explanation:

The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.

Answer:

69.29 deg

Step-by-step explanation:

Recall that tan(x) = opposite/adjacent. This is helpful because we know the opposite and adjacent leg from the angle x! This gives us tan(x) = 43/18, so we can solve for x by taking tan^-1 of both sides, giving x = tan^-1(43/18), or 67.29 degrees.

In the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.

What is a polynomial?

'poly' means many and 'nominal' means term. A polynomial is a type of algebraic expression with many terms having variables and coefficients.

Given polynomial is,

[tex] {(x + y)}^{6} [/tex]

Expanding the given sixth-degree polynomial using binomial expansion we get the expression of the picture given.

Solving all expressions we get,

[tex] {(x + y)}^{6} = {x}^{6} + 6 {x}^{5} y +15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6x {y}^{5} + {y}^{6} [/tex]

The middle term is

[tex]20 {x}^{3} {y}^{3} [/tex]

The coefficient of the term is 20

The sum of all coefficients is 1+6+15+20+15+6+1= 64

Hence, in the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.

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Answer:

x - 16 = -3

Step-by-step explanation:

x - 16 = -3  Add 16 to both sides of the equation

x = 13

It was 13 degrees at noon

After solving the expression, the number is 5.

In the given question we have to answer twice the sum of five times a number increased by one is twelve.

We have to determine the number by solving the given statement.

To solve the question we have to read the statement carefully. Then write the expression according to the statement. Then solve the statement according the rules.

In the given statement given that five time a number.

Let the number be x. So the expression should be 5x.

Again says that five times a number increased by one. So the expression 5x+1.

Then says that twice the sum of five times a number increased by one. Now the expression should be 2(5x+1).

Then says that twice the sum of five times a number increased by one is twelve. Now the statement is 2(5x+1)=12

Now solving the expression.

Divide by 2 on both side, we get

5x+1=6

Subtract 1 on both side, we get

5x=5

Divide by 5 on both side, we get

x=1

Now the number is 5.

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The required hypothesis are as follows , H0: μ = 438 and Ha: μ ≠ 438

The null hypotheses for the above scenario will be the statement of no effect and it'll be the mean weight of the bag that filled will be 438grams.

H0: μ = 438

The alternative hypotheses for the above scenario will be that the bag isn't filled with 438grams. They are either underfilled below 438grams or overfilled above 438grams.

Ha: μ ≠ 438

Statistics is the study of surveys and research on numerical data. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.

The null hypothesis is a broad assertion or default condition that there is nothing happening. For instance, there is no relationship between two measured occurrences or a connection between groups.

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The probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given: An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight.

The airline sells 170 tickets for a flight that has only 165 seats.

The proportion of reservations that do not show up for the flight

P = 5% =  0.05.

Number of tickets sold n = 170

Number of seats in the flight = 165

If at least 5 people do not show up then we have enough seats for every person.

P(X ≥ 5) =  Σ (from 5 to 170)[tex]170C_x(0.05)^x(0.95)^1^7^0^-^x[/tex]

P(X ≥ 5) ≈ 0.9306

Hence, the probability that a seat will be available for every person holding a reservation and planning to fly s 0.9306.

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Answer:

Step-by-step explanation:

Pros: Lower rates: Insurance rates are reduced for most consumers. ✓ Rates match risk: Higher-risk policyholders may pay a higher rate that accurately reflects their higher risk of loss – so lower-risk policyholders don't have to subsidize the cost of insurance for higher-risk policyholders.

Cons: HIGHER rates.

Insurance companies justify the use of insurance scores by citing studies showing a positive correlation between credit scores and insurance claims

A higher credit score decreases your insurance rate, often significantly, with almost every company and in most states. Getting a quote, however, does not affect your credit. Your credit score is a key part of determining the rate you pay for insurance.

The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

The definition of an exponential function is given by the equation

y = aeᵇˣ, where a and b are constants.

The given function is f(x) = 87000(0.9)ˣ.

Given that x = 0 represents the year 2010.

Therefore, x= 5 represents the year 2015.

Substitute x = 5 into the given function:

f(5) = 87000(0.9)⁵

     ≈ 51373

Hence, the population of Orange country is about 51373 in 2015.

Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.

The population of Greene city after 5 years is given by:

78000(1-8%)⁵

= 78000(1 - 0.08)⁵

= 78000(0.92)⁵

= 51408

Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

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Answer:

(1,16),(2,32),(3,48),(4,64)

Step-by-step explanation:

so 1=16

2×16=32

3×16=48

4×16=64

The correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)

For this equation we have to "multiply" each number that makes scene.

We got to work with what is given in the question.

Given options:

(16, 1), (32, 2), (48, 3), (64, 4)

(1, 16), (2, 32), (3, 48), (4, 60)

(1, 16), (2, 32), (3, 48), (4, 64)

(1, 32), (2, 48), (3, 64), (4, 80)

Therefore, the equation is:

[tex]2*16\\3*16\\4*16[/tex]

Therefore, the correct answer is C. (1, 16), (2, 32), (3, 48), (4, 64)

The graph of the new function compared to the first one will be shifted down.

Vertical translation describes the movement of a function graph upward or below. The function's form is preserved in this case. The graph moving or shifting along the y-axis is another name for it. Each point on the graph moves k units vertically during vertical translation, and the graph is said to have translated k units.

The two functions are

f(x) = x + 2

g(x) = x - 1

You can see that all you need to do to transform f into g is just take 3 off of it.

f(x) - 3 = (x+2) - 3

= x + 2 - 3

= x - 1

= g(x)

Every transformation, such as f(x) f(x) + k, now produces a vertical translation, which is translated upward if k > 0 and downward if k 0. The correct response is C since the function is translated three units down in our situation where k = -3.

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The complete question is:

"If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?

A. It would be shifted up.

B. It would be shifted left.

C. It would be shifted down.

D. It would be less steep."

The number of pounds of strawberries sold and the number of pounds of blueberries sold are 50 and 23 respectively.

As in the question Keilantra runs a farm stand that sells strawberries and blueberries. Each pound of strawberries sells for $2.25 and each pound of blueberries sells for $4. Keilantra made $204.50 from selling a total of 73 pounds of strawberries and blueberries.

Let x be a number of strawberries and y is that of blueberries.

2.25x + 4y = 204.5-----------------------(1)

And

x + y = 73--------------------------------------(2)

On solving equation (1) and (2), we get,

x = 50 and y = 23

So, there are 50 pound strawberries and 23 pound  blueberries are sold.

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The square of the hypotenuse equals the square of the sum of the other two sides is 13.89ft

Definition Of Pythagoras Theorem :

The Pythagorean theorem states that the total of the squares on a right triangle's legs equals the square on the hypotenuse (the side opposite the right angle)—or, in popular algebraic form, a2 + b2 = c2.

Given:

Height of the Tent Pole = 6ft.

Base of the Pole of the Tent = 12ft.

Now we will use Pythagoras theorem to find how long the rope is.

Use of Pythagoras theorem

Hence, the length of the rope is 13.89ft.

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Answer: -3x2

Step-by-step explanation:

The question according to the equation will be a board that is 1/4 yard long cut into 2 equal pieces. Hence, option A is correct.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The given equation in the question is,

1/4 ÷ 2 = 1/8

It can be clearly seen that 1/4 divided by 2 is mentioned in the question and the product obtained is 1/8.

It means that 1/4 is divided into 2 equal pieces and the length of each piece is 1/8.

So, the question will be a board that is 1/4 yard long cut into 2 equal pieces. How long is each piece?

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Answer:

A. is the answer

Step-by-step explanation:

y as a function of x meaning:

Every x has a y, but the x value cannot repeat and every x has it's own y.

Example:

x: 1 2 3 4 5

y: 2 4 6 8 10

This is y as a function of x because the x values do not repeat and they each have a y value.

Example 2:

x:3 4 5 3 6

y: 1 2 3 4 5

This wrong because the 3 in the x value repeats twice which cause y not to be a function of x.

The reason why it wouldn't be B is because of -1

The reason why it wouldn't be C is because the y values repeat

The reason why it wouldn't be D is because all the x values are -7

Hope this helped!

Answer:

-3 is the answer.

Step-by-step explanation:

Given

(-12)3 + (24+9)----------^

= -12*3 + 33 ---------

= -36 + 33

= -3

The probability of committees contain 2 boys and 1 girl is 9.

In the given question,

A committee of 3 is selected from Jillian, Miles, Mark, and Nikia.

We have to find the how many committees contain 2 boys and 1 girl.

As we know that,

Simply put, probability is the likelihood that something will occur. If we don't know how such an occurrence will end out, we can discuss the possibility or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

There are total 3 selection.

Possibility of selecting 2 boys = [tex]^{3}C_{2}[/tex].

There are total 3 selection.

Possibility of selecting 1 girl = [tex]^{3}C_{1}[/tex].

So the probability of committees contain 2 boys and 1 girl is

P(C) = [tex]^{3}C_{2}\times^{3}C_{1}[/tex]

After solving

P(C) = 9

The probability of committees contain 2 boys and 1 girl is 9.

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As asked in the question the value of xz and y will be even ,

xz is even and y is also even

given

X = factor of Y

Y = factor of Z

Therefore,

z= mnz = mnx  , xz = even

because

either z even, so the answer is directly yes or x is even (or both) but if x is even and as then  z= mnz = mnx must be even too (one of the multiples of z is even, so z is even too).

(2) y=  even

because

as z=ny then as one of the multiples of z even then only  z  will be even

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.

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Answer:

5:8

Step-by-step explanation:

The ratio of dogs and cats is 5:8

The ratios always have a common multiple.

Let that common multiple is ‘a’

So dogs and cat are:

dogs=5a

cats=8a

total animals=5a+8a=13a

13a=52

a=52/13

= 4 ——- Means, the common multiple is ‘4’

So, number of cats = 8a

=8*4=32

Answer:

37

Step-by-step explanation: