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The equation of the line in slope intercept form is y = -x + 2

The equation of a line in slope intercept form can represented as follows.

y = mx + b

where

Therefore, let's find the slope of the line using (0, 2) and (-1, 3).

m = slope = 3 - 2 / -1 - 0

slope = 1/ - 1

slope = - 1

Therefore, let's find the y-intercept using (0, 2).

Hence,

y = -x + b

2 = -(0) + b

b = 2

Hence, the equation of the line is y = -x + 2

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Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = [tex]H_0\\[/tex] * D

where

v = velocity = 8254

[tex]H_0\\[/tex] = hubble constant = 70

D = v/[tex]H_0\\[/tex]

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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Answer:

57

Step-by-step explanation:

3(12 + 5) + 2(3) Use distributive property A(B + C) = AB + AC

36 + 15 + 2(3) = 57 Multiplication over addition

Answer:

57

Step-by-step explanation:

Do you remember PEMDAS?

first do the parentheses (12+5) = 17

then do the Multiplication 3x17= 51

and you have another multiplication 2x3= 6

so now you just need to add

51+6 = 57

Answer:

Rounded to the nearest 0.01 or the Hundredths Place. = 324.70

Step-by-step explanation:

As per the concept of simple interest,

OA. The 30-year 8.5% loan is more economical. The buyer will save approximately $182,436.76 in interest.

OB. The 15-year 8% loan is more economical. The buyer will save approximately $74,311.19 in interest.

Simple interest:

Basically, rate of interest calculated only on the principal amount, or on that portion of the principal amount that remains as known as simple interest.

Given,

In terms of paying less in interest, which is more economical for a $90,000 mortgage: a 30-year fixed-rate at 8.5% or a 15-year fixed-rate at 8%?

Here we need o find how much is saved in interest in these two years.

Here we have the formula,

[tex]PMT=\frac{P\frac{r}{n}}{1-[1 + \frac{r}{n}]^{-nt}}[/tex]

As per the given question we have identified that the value of

P = 90,000

R = 8.5%

n = 15

So, in decimal form, it can be written as,

r = 0.085

t = 30 years.

Now, we have to take the value of t as 30, then we get the value of PMT as,

[tex]PMT=\frac{90000\frac{0.085}{15}}{1-[1 + \frac{0.085}{15}]^{-15\times30}}[/tex]

When we simplify this one then we get,

The interest on a 30 year loan at 8.5% per year would be,

=> $182,436.76

And when we equate this one for 15 years, then we get the interest on a 15 year loan at 8.0% per year would be

=> $74,311.19

Therefore, the total interest you pay for the 30 year mortgage is substantially more than the total interest you pay for the 15 year mortgage.

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Answer:

C

Step-by-step explanation:

not enough info by i think its C

Estimate the sum of the lengths of ribbon. 7 One-eighth yards + 8.2 yards or: 7 1/8 yards + 8.2 yards

Which statements are true about the estimate? Check all that apply.

7 One-eighth can be rounded to 7.

8.2 can be rounded to 8.

The estimated sum is 2 yards.

The estimated sum is 15 yards.

To find the sum, subtract 8 – 7.

[tex]2x^2+20x+50[/tex]

[tex]2(x^2+10x+25)[/tex]

find two numbers than sum to 10 and multiply to 25:

5 + 5 = 10

5 * 5 = 25

so the factorization is:

[tex]2(x+5)(x+5)\\\\= 2(x+5)^2[/tex]

Answer: set up a proportion 7000 /3 yrs an 8.15% over 100 then cross multiply Step-by-step explanation:

The probability that a patient with a negative result is truly HIV-free is 0.999.

To find the probability that confirms that the result of the HIV test is negative, we must take into account the information provided in the information and perform the following mathematical operation.

The probability that No HIV and test positive is:

P = 0.85 * 0.985

P = 0.8372

The probability that HIV and test negative is:

P = 0.15 * 0.003

P = 0.00045

The probability that No HIV and negative test of HIV and negative test is:

P = 0.00045 + 0.8372

P = 0.8377

P = (NOT HIV / Test)

P = 0.8372 / 0.8377

P = 0.999

According to the above, the probability that a patient with a negative result is truly HIV-free is 0.999.

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Answer:

45 degrees

Step-by-step explanation:

angle AXD is equal to BXD plus AXB

95-x=(X+20)+(X+30)

95-x=2x+50

   +x.  +x

95=3x+50

-50.    -50

45=3x

/3.   /3

15=x

Now fill in X for bxd

15+30

45

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Answer:

Step-by-step explanation:

The solutes percentage to the solvent. =. 2\4 x 100

. = 50%

Answer:

Step-by-step explanation:

V₁ = 2 ml

V₂ = 4 ml

V = V₁ + V₂ = 2 + 4 = 6 ml

V₁ / V = 2 / 6 = 1 /3    or ≈ 33%

for given triangles ΔABC and ΔADC,

∠ABC ≅ ∠ADC

In this question, we have been given a quadrilateral ABCD with segment AC is the angle bisector of angle BAD.

We need to prove ∠ABC ≅ ∠ADC

AB ≅ AD                                     ......................(Given)

∠BAC ≅ ∠DAC                           ......................(Given)

AC ≅ AC                      .....................(Common side)

ΔABC ≅ ΔADC           ..................(SAS postulate of triangle congruence)

∠ABC ≅ ∠ADC           .............(corresponding sides of congruent triangles)

Hence proved.

Therefore, for given triangles ∠ABC ≅ ∠ADC

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Answer:

350

Step-by-step explanation:

1. Take 30% of 500

You can accomplish this by multiplying 500 by 0.3 to get 150

500 x 0.3 = 150

150 is 30% of 500

2. Subtract your findings (30%) from total price (500)

500 - 150 = 350

350 is the sale price with a 30% discount on a $500 bicycle

Answer:

$350

Step-by-step explanation:

You have to multiply 500 by 0.7 to find the discount price.

500*0.7=350

The three angles of the triangles are ∠A= 60°, ∠B = 75° and ∠C = 45°.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

The ∠5y + ∠7y = 180

∠12y = 180

y = 180/12 = 15

Hence the ∠CBA = 75° AND ∠ACB = 45°.

Now ∠A + 75+45 = 180

∠A = 180-120 = 60°

Hence, the three angles of the triangles are ∠A= 60°, ∠B = 75° and ∠C = 45°.

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When P(a) = 1/5, p(b) = 1/8 l, the value of p(a and b) is 1/40. This is the probability.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

Since P(a) = 1/5, p(b) = 1/8, the probability of P(a and b) will be

= P(a) × P(b)

= 1/5 × 1/8

= 1/40

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Work Shown:

[tex]a_n = a_{n-1} - 12\\\\a_1 = a_{1-1} - 12\\\\a_1 = a_{0} - 12\\\\a_1 = 84 - 12\\\\a_1 = 72\\\\[/tex]

After 1 minute, there are 72 gallons of water left.

[tex]a_n = a_{n-1} - 12\\\\a_2 = a_{2-1} - 12\\\\a_2 = a_{1} - 12\\\\a_2 = 72 - 12\\\\a_2 = 60\\\\[/tex]

After 2 minutes, there are 60 gallons left.

[tex]a_n = a_{n-1} - 12\\\\a_3 = a_{3-1} - 12\\\\a_3 = a_{2} - 12\\\\a_3 = 60 - 12\\\\a_3 = 48\\\\[/tex]

After 3 minutes, there are 48 gallons left.

[tex]a_n = a_{n-1} - 12\\\\a_4 = a_{4-1} - 12\\\\a_4 = a_{3} - 12\\\\a_4 = 48 - 12\\\\a_4 = 36\\\\[/tex]

After 4 minutes, there are 36 gallons left.

[tex]a_n = a_{n-1} - 12\\\\a_5 = a_{5-1} - 12\\\\a_5 = a_{4} - 12\\\\a_5 = 36 - 12\\\\a_5 = \boldsymbol{24}\\\\[/tex]

After 5 minutes, there are 24 gallons left.

------------------------

Table of values

[tex]\begin{array}{|c|c|} \cline{1-2}n & a_n\\\cline{1-2}0 & 84\\\cline{1-2}1 & 72\\\cline{1-2}2 & 60\\\cline{1-2}3 & 48\\\cline{1-2}4 & 36\\\cline{1-2}5 & \boldsymbol{24}\\\cline{1-2}\end{array}[/tex]

Answer:

81 and 100

Step-by-step explanation:

There is a pattern between each square number

For 1 and 4, the difference is 3

For 4 and 9, the difference is 5

For 9 and 16, the difference is 7

For 16 and 25, the difference is 9

For 25 and 36, the difference is 11

For 36 and 49, the difference is 13

For 49 and 64, the difference is 15

For 64 and 81, the difference is 17

For 81 and 100, the difference is 19

I would appreciate it if you mark my answer as brainliest.

Answer: 75 cups of giardia-laced lemonade

Step-by-step explanation:

       On the first day he sells 33 lemonades, so we will start with "33 +" for our equation. Then, he sells 6 additional lemonades each day further as the summer heats up. If x is equal to days, the next part will be "6(x-1)" for our equation.

       Lastly, we will plug in an 8 for x, number of days, and solve,

33 + 6(x - 1)

33 + 6(8 - 1)

75

             75 cups of giardia-laced lemonade

Step-by-step explanation:

What are these examples of? -Printer -Mouse -Moniter -Keyboard -Scanner

Answer:

90. 718 kg

Step-by-step explanation:

0.454x 200= 90.718

if u round it it's 90.8kg

Answer: 90.8

Step-by-step explanation:

200x0.454=90.8

Since 1 pound is 0.454 kg, you multiply the 200 with the 0.454 because there are 200 pounds!

the answer is zero

you should know how you read the question

15 is 5​% of 300. So 300 is the unknown number.

percentage, a relative value indicating hundredth parts of any quantity.

We need to find 15 is 5​% of what​ number

Let us convert 5% to decimal.

Divide 5 by 100

5/100=0.05

By given x is the number

0.05x=15

Divide both sides by 0.05

x=300

Hence, 300 is the unknown number.

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Answer:

5pi/12

105 degrees

Step-by-step explanation:

I can help with the first 2 too many answers in one will get my answer deleted

7pi/12  x 180/pi

7x15=105

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The probabilities are given as follows:

a) P(driver is female) = 0.486 = 48.6%.

b) P(driver is age 65 or over) = 0.1356 = 13.56%.

c) P(driver is age 65 or over and female) = 0.0661 = 6.61%.

d) The events are not mutually exclusive, as the intersection of the two events is different of zero.

e) The expected number of male drivers would be of 5,140.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

Hence, for a population, the probability of a single person having some characteristic is given by the percentage of people with this characteristic in the population.

The drivers that are 65 or over are composed as follows:

Hence the total percentage is:

6.61 + 6.95 = 13.56%.

For item d, the events “being 65 or over” and “female” are not mutually exclusive, as there are females that are 65 or over.

The expected value of an event over n people is the multiplication of n by the probability, hence:

10000 x 0.514 = 5,140.

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The binomial distribution in 3 decimal place value is 0.294

Binomial distribution:

Binomial probability distribution determines the probability of a discrete random variable that results from an experiment in which there are two possible independent outcomes and which is repeated n times.

The calculation formula is:

[tex]P(X) = \binom{n}{X} \cdot p^X \cdot (1-p)^{n-X}[/tex]

where

n  is the number of trials,

p  is the probability of success on a single trial, and

X  is the number of successes.

Given,

Here we have the following values,

n = 8

p = 0.2

Here we need to find the value of p(X = 2)

Here we know the values of

number of trials = 8

probability of success = 0.2

And the number of success = 2

Then the binomial distribution is calculated by applying these values on the formulas, then we get,

[tex]P(2) = \frac{8!}{2!(8-2)!} \cdot 0.2^2 \cdot (1-0.2)^{8-2}[/tex]

When we evaluating the expression, we have

P(2) = 0.29360128

Therefore, the resulting value is P(2) = 0.29360128

When we round of t into 3 decimal places then we get the value 0.294.

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