The shortest distance from P(5, 1) to Q(8, -3) is (A) 25 (B) 185 (C) 3 (D) 173 (E) 5
Answers
Answer:
E
Step-by-step explanation:
calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = P (5, 1 ) and (x₂, y₂ ) = Q (8, - 3 )
d = \(\sqrt{(8-5)^2+(-3-1)^2}\)
= \(\sqrt{3^2+(-4)^2}\)
= \(\sqrt{9+16}\)
= \(\sqrt{25}\)
= 5
Related Questions
The coordinates triangle ABC are A (0, 2), B (-2, 6), and C (4, 0). Find the coordinates of the orthocenter of this triangle.
A. (8,6)
B. (-8,-6)
C. (-7,-6)
D. (-8,-5)
Please help!!! giving a lot of points
Answers
You are one of the retirement counselors at the Valley View Bank. You have been asked to give a presentation to a class of high school seniors about the importance of saving for retirement. Your boss has designed an example for you to use in your presentation. The students are shown five retirement scenarios and are asked to guess which yields the most money. Note: All annuities are ordinary annuities. Also, although some people stop investing, the money remains in the account and receives 10% interest compounded annually. Look over each scenario and make an educated guess as to which investor will have the largest accumulation of money invested at 10% over the next 40 years. Then for your presentation, calculate the final value for each scenario, how much each person actually contributed, and how much interest was earned. • Adam invests $1,200 per year and stops after 15 years (remember, the balance will remain in this account, earning 10% interest compounded annually for the remaining 25 years. • Becky waits 15 years, invests $1,200 per year for 15 years, and then stops (balance will earn int • Clare waits 15 years, then invests $1,200 per year for 25 years. • David waits 10 years, then invests $1,500 per year for 15 years, and then stops (balance will earn interest for the remaining 15 years). • Ellen waits 10 years, then invests $1,500 per year for 30 years.
Answers
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
\((1+10)^{15}\)Venus invests $1,200 per year and stops after 15 years.
He can get money : \(1200*\) \((1+10)^{15}\) at the first year,
We can use ,
Compound interest formula, S = \(P*(1+i)^{n}\)
Where,
P means the Principal
I means the interest
n means the year
S means the principal and interest
At the second year he can get,
= 1200 * [(1+\(\frac{10degrees}{1}\)) + (\(1+[\frac{10degrees}{1} ]^{2}\))
The money of first year has two years interest,
The money of second year has one year interest.
So, we can calculate the 15th year he can get :
= 1200 * [\((1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )\)
= 1200 * \(\frac{(1*1)*(1-1*1^{15} )}{1-1*1}\)
The sum of geometric progression,
\(S_{n} =\frac{a*(1-q)^{n} }{1-q}\) , q≠1
= $ 41939.67
The rest of years he can get money :
= 41939.67 * (\((1+10percent))^{40-15}\)
= $ 454404.053
Kevin can get money 1200* [\((1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )\)
= 41939.67 at 30th year
Finally he can get money = 41936.67 \((1+\frac{10degrees}{1}) ^{40-15*0}\)
= $ 108780.71
Rafael can get money : 1200 * [\((1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )\)
= $ 129818.11
$454404.05 > $129818.11 > $108780.71
Therefore,
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
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*NEED ANSWER ASAP* *GIVING AWAY 10 POINTS*
A horseshoe weighs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?
A. 1.64 oz
B. 6.56 oz
C. 9.84 oz
D. 16.4 oz
Answers
Answer: A horseshoe weighs 8.2 ounces The nails in the horseshoe weigh 0.12 ounces.
Step-by-step explanation: B should be your answer have a great day :)
Answer:
B
Step-by-step explanation:
i did 8.2 divided by 20 percent ( .2)
then subtracted
equal 6.56
Salina currently has an account balance of $1,047.69. Her initial deposit on the account was $630 and it earned 3.9% simple interest. How long has Salina held the account?
A - 17 years
B - 26 years
C - 10 years
D - 43 years
Answers
Answer:
A. 17 years
Step-by-step explanation:
Use the simple interest equation, I = prt, where I is the interest money gained, p is the starting amount of money, r is the interest rate in decimal form, and t is the time in years.
Plug in the values to solve for t:
417.69 = (630)(0.039)(t)
417.69 = 24.57t
17 = t
= 17 years
So, the correct answer is A, 17 years
Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may
apply.)
square root of -9
Select all descriptions that may apply.
A. Nonreal complex
B. Real
C. Pure imaginary
D. Complex
Answers
Answer:
acxdddhdhxhhh sax skskskkkkkddffffffrrkel sssddjeeeeerrjrrjtjjj
The American customer satisfaction index scores of McDonalds restaurants grew from 61 in 2002 to 71 in the year 2014. Find the average rate of change for the data. Show work.
Answers
Answer:
\(\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}\)
Step-by-step explanation:
Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:
In order to solve for the average rate of change, we could simply use the average rate of change formula:
Average rate of change = Change in output/Change in input
\(\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}\)
Let (x₁, y₁) = (61, 2002)
(x₂, y₂) = (71, 2014)
Substitute these values into the average rate of change formula:
\(\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}\)
\(\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}\).
The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.
Required:
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?
d. What is the probability that all three of the meals will exceed the cost covered by your company?
Answers
Answer:
a. P(x=0)=0.2967
b. P(x=1)=0.4444
c. P(x=2)=0.2219
d. P(x=3)=0.0369
Step-by-step explanation:
The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).
The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants) by the total amount of restaurants from where we can pick (15 restaurants):
\(p=\dfrac{5}{15}=0.333\)
Then, we can model the probability that k meals cost more than $50 as:
\(P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\\)
a. We have to calculate P(x=0)
\(P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\\)
b. We have to calculate P(x=1)
\(P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\\)
c. We have to calcualte P(x=2)
\(P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\\)
d. We have to calculate P(x=3)
\(P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\\)
What is the volume of a sphere with a radius of 24 units?
A. 92167 units
O B, 230477 unite 3
O c. 18A324 units
D. 13,8247 units
Answers
Answer:
18A324 units
Step-by-step explanation:
The volume of a sphere is given by where r is given: The raduis of sphere =24 units
Then the volume of the given sphere will be
Hence, the volume of given sphere
find the number for which 200% is b mins PLZ HELP QUICK
Answers
Answer:
200
Step-by-step explanation:
is -92 a rational number
Answers
Answer: Yes
Step-by-step explanation: A rational number is a number that can be described as a fraction. -92 can be a fraction, therefor it's rational.
No
A rational number is any number that can be expressed as a ratio of two integers. For example, 1.5 is rational since it can be written as 3/2, 6/4, 9/6 or another fraction or two integers. Pi is irrational since it cannot be written as a fraction.
Craig is considering four loans. Loan L has a nominal rate of 8.254%, compounded daily. Loan M has a nominal rate
of 8.474%, compounded weekly. Loan N has a nominal rate of 8.533%, compounded monthly. Loan O has a nominal
rate of 8.604%, compounded yearly. Which of these loans will offer Craig the best effective interest rate?
a. loan L
b. loan M
c. loan N
d. loan O
Answers
The loan that will offer Craig the best effective interest rate is a) Loan L with a real percentage rate of 8.6%.
What is an effective interest rate?An effective interest rate is the real percentage rate on an interest-paying investment which removes the effects of compounding over time.
The formula for computing the effective interest rate is as follows:
Effective Interest Rate, r = (1 + i/n)^n - 1.
Nominal Interest Rates Compounding Periods
Loan L 8.25% 365 days
Loan M 8.47% 52 weeks
Loan N 8.533% 12 months
Loan O 8.604% Yearly
Effective Interest Rates:Loan L = (1 + 0.0825/365)^365 - 1
= 1.08598 - 1
= 0.086
= 8.6%
Loan M = (1 + 0.0847/52)^52 - 1
= 1.0883 - 1
= 0.0883
= 8.83%
Loan N = (1 + 0.08533/12)^12 - 1
= 1.0887 - 1
= 0.0887
= 8.87%
Loan O = (1 + 0.08604/1)^1 - 1
= 1.08604 - 1
= 0.08604
= 8.604%
Thus, we advise Craig to take Loan L because it offers the least-costly effective interest rate.
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PLEASE HELP. Mr. Washington made several purchases for his printing business. The mean price of the purchases was $150, and the mean absolute devlatlon was $30 . Based on this informaton, which statement must be true?
Answers
Answer:
the 4th statement
Step-by-step explanation:
The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.
Answers
the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.
A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.
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At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons
Answers
Answer:
1/12 gallons
Step-by-step explanation:
We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.
Step 1: Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2
(1/6) * (2/2) = 2/12
Step 2: Now we can subtract 1/12 from 2/12:
2/12 - 1/12 = 1/12
Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.
There are 3 types of PercentProblems.
a) Number compared to the Base is unknown: x/100 = ?/b
b) Base Number is unknown: a/?= x/100
c) Percent is unknown: a/b = ?/100
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8?
Answers
Answer:A. x= .100
Step-by-step explanation:because of the distance in miles
Can someone help me with the this
Answers
Answer:
x=4
Step-by-step explanation:
Because the bases are equal, you can set the exponents equal to each other
3^4x=3^2x+8
4x=2x+8
2x=8
x=4
f (x)=-3×^2-6x, find f(-4)
Answers
The value of function at x= -4 is f(-4) = -24.
We have the function,
f(x) = 3x² - 6x
Now, to find f(-4), we substitute -4 for x in the given function f(x) = -3x² - 6x:
f(-4) = -3(-4)² - 6(-4)
= -3(16) + 24
= -48 + 24
= -24
Therefore, the value of function at x= -4 is f(-4) = -24.
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Describe the transformation in each function as it relates to the graph of g (x) = ( -1/2 x)
Answers
Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?
–2
–1
1
2
Answers
The value for x that is a double root of this function is x = -1
How to determine the double root?The function is given as:
f(x) = x^3 - 3x - 2
From the graph of the above function (see attachment), we have the following highlights:
The curve crosses the x-axis at x = 2The curve touches the x-axis at x = -1The point that it touches the x-axis is the double root point
Hence, the value for x that is a double root of this function is x = -1
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An advertiser claims that 80% of people stream their TV, 10% have cable, and the rest do not watch TV. To evaluate this claim, they take a sample and calculate a test statistic of
. If their rejection region is, what would their conclusion be?
Answers
The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.
What is the rejection region?This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.
This happens when the rejection region is found to be around the area that is in the critical value.
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Of the pets in the pet show, 10/12 are cats. 6/10 of the cats are calico cats. What fraction of the cats are calico cats?
Answers
Answer:
6/10, simplified 3/5
Step-by-step explanation:
kinda tricky, but the fraction is stated right out.
Answer:
3/5
Step-by-step explanation:
My dance lesson starts at 11:40 am. It always 1 your and 10 minutes what time does it end?
Answers
Answer:
Step-by-step explanation:
This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?
*
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
O
0
A tree decays 10% every six weeks.
The height of a diver after jumping from a high dive into the water.
The height of a ball rolled down a hill.
A gym charges $15 perfitness class.
An ant bocid eliminates 50% of bacteria every 24 hours
The height of a rocket after it is Bunched
Answers
Answer:
Option 2 and 5 are correct. Look down for my explanation↓:
Step-by-step explanation:
So We need to tell which one of them is quadratic function.
Option 1 is exponential decay so, it is not quadratic.
Option 2 is quadratic because the diver will take the parabolic shape when jumps.
Option 3 is not quadratic. Option 4 is not quadratic it is linear.
Option 4 is again exponential not quadratic.
Option 5 is quadratic because it takes the parabolic shape again.
8. Find the slope between (-5, 4) & (0,3). * O m = 1/5 O O m = -5 m = 5 O m = -1/5
Answers
We can determine the slope using the following expression:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Now, using the two points given, we have:
\(m=\frac{3-4}{0-(-5)}\Rightarrow m=-\frac{1}{5}\)From this, we have that the slope(m) equals -1/5.
Solve for v. 2/5v = 10
Answers
On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answers
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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the sum of 2 times a number (x) and -2 is atleast 8
Answers
Answer: x ≥ 5
Step-by-step explanation:
2x - 2 ≥ 8
2x ≥ 10
(hi) :-)
Which point would NOT be a solution to the system of linear inequalities shown below?
Answers
It's asking would not be a solution soo
(-10, -9) as you can see
You're welcome thank me later
How do I make -25/176 in decimal form?!?!I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS:)
Answers
divide.
-25/176 is -.142
Answer:
you divide -25 by 176
-25 on the inside of the "dog house" and 176 on the outside because if you did it the other way it would be a whole number.
It would equal -0.14204545454
I hope this is good enough for you:
solve for b n+3xGb=qb
Answers
Answer:
0
Step-by-step explanation:
Answer:
x=\frac{q-n}{3G};\quad \:b\ne \:0
Step-by-step explanation:
bn+3xGb=qb
bn+3xGb-bn=qb-bn
3bn+3xGb-bn=qb-bn
\frac{3xGb}{3Gb}=\frac{qb}{3Gb}-\frac{bn}{3Gb};\quad \:b\ne \:0