Answer:
Age of Anna = x years
Age of Jane i.e. Anna's sister = (x-y) years
a, What was the sum of their ages two years ago?
Solution,
Age of Anna two years ago = (x-2) years
Age of Jane two years ago = (x-y-2) years
Sum of their ages = x - 2 + x-y-2 = 2x - y -4
b. What will be the sum of their ages in 3 years?
Solution,
We have,
Present age of Anna = x years
Present age of Jane = (x-y) years
So,
Age of Anna after 3 years = (x+3) years
Age of Jane after 3 years = (x-y+3) years
Therefore,
Sum of their ages in 3 years = (x+3) +(x-y+3) = 2x - y+6
c. How old was Anna when Jane was born?
Solution,
Here,
According to question,
Jane is y years younger than Anna
So, Anna was y years when Jane was born.
[Suppose your age is 10 years and your brothers age is 14 years. You are 4 years younger than your brother. Also, his age was 4 years when you were born.]
An insurance company has written 100 policies for $75,000, 500 policies for $25,000, and 1000 policies for $10,000 for people of age 20. If experience shows that the probability that a person will die at age 20 is 0.0015, how much can the company expect to pay out during the year the policies were written? The company can expect to pay out _____ $ over the year after the policies were written.
Answer:
The company can expect to pay out $45,000 over the year after the policies were written.
Step-by-step explanation:
This can be determined as follows:
The probability that a person will die at age 20 = 0.0015
Revenue from 100 policies = 100 * $75,000 = $7,500,000
Revenue from 500 policies = 500 * $25,000 = $12,500,000
Revenue from 1000 policies = 1000 * $10,000 = $10,000,000
Total revenue from all policies = Revenue from 100 policies + Revenue from 500 policies + Revenue from 1000 policies = $7,500,000 + $12,500,000 + $10,000,000 = $30,000,000
Expected amount to pay out during the year the policies were written = Total revenue from all policies * The probability that a person will die at age 20 = $30,000,000 * 0.0015 = $45,000
Therefore, the company can expect to pay out $45,000 over the year after the policies were written.
The volume of a right circular cone is 300 cubic inches. What is the volume, in cubic inches, of a right cylinder th
has the same base and height as the cone?
Answer:
The volume of the cylinder is 900 cubic inches
Step-by-step explanation:
Given
Let V1 represent the volume of a cone and V2 represents the volume of a cylinder
[tex]V_1 = 300in^3[/tex]
Required
Determine the volume of a cylinder with same dimension
The volume of a cone is calculated as:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
The volume of a cylinder is calculated as:
[tex]V_2 = \pi r^2h[/tex]
Since, the cone and cylinder have the same dimensions, we can substitute [tex]\pi r^2h[/tex] for [tex]V_2[/tex] in [tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
So, we have:
[tex]V_1 = \frac{1}{3} * V_2[/tex]
Multiply both sides by 3
[tex]3 * V_1 = \frac{1}{3} * V_2 * 3[/tex]
[tex]3 * V_1 = V_2[/tex]
[tex]V_2 = 3 * V_1[/tex]
Substitute [tex]300in^3[/tex] for [tex]V_1[/tex]
[tex]V_2 = 3 * 300in^3[/tex]
[tex]V_2 = 900in^3[/tex]
Hence, the volume of the cylinder is 900 cubic inches
If 1st and 4tg terms of G.p are 500 and 32 respectively it's second term is ?
Answer:
[tex]T_{2} = 200[/tex]
Step-by-step explanation:
Given
Geometry Progression
[tex]T_1 = 500[/tex]
[tex]T_4 = 32[/tex]
Required
Calculate the second term
First, we need to write out the formula to calculate the nth term of a GP
[tex]T_n = ar^{n-1}[/tex]
For first term: Tn = 500 and n = 1
[tex]500 = ar^{1-1}[/tex]
[tex]500 = ar^{0}[/tex]
[tex]500 = a[/tex]
[tex]a = 500[/tex]
For fought term: Tn = 32 and n = 4
[tex]32 = ar^{4-1}[/tex]
[tex]32 = ar^3[/tex]
Substitute 500 for a
[tex]32 = 500 * r^3[/tex]
Make r^3 the subject
[tex]r^3 = \frac{32}{500}[/tex]
[tex]r^3 = 0.064[/tex]
Take cube roots
[tex]\sqrt[3]{r^3} = \sqrt[3]{0.064}[/tex]
[tex]r = \sqrt[3]{0.064}[/tex]
[tex]r = 0.4[/tex]
Using: [tex]T_n = ar^{n-1}[/tex]
[tex]n = 2[/tex] [tex]r = 0.4[/tex] and [tex]a = 500[/tex]
[tex]T_{2} = 500 * 0.4^{2-1}[/tex]
[tex]T_{2} = 500 * 0.4^1[/tex]
[tex]T_{2} = 500 * 0.4[/tex]
[tex]T_{2} = 200[/tex]
Hence, the second term is 200
y= p2 + qr write p in terms of y, q and r
Step-by-step explanation:
y=p²+qr
y-qr=p²
p=√y-qr
now, is it fine..
I need some assistance please
Answer:
2x + y = 20 . y=3x
2x + 3x = 20
5x = 20
x/5 = 20/5
x = 4
(4,0)
Angles 1 and 2 are supplementary. Angle 2 measures 50 degrees
MORE THAN angle 1. What is the measure of angle 2?
Answer: 115 degrees
Step-by-step explanation:
Give me the brainliest plz!
how do I know how many extraneous solutions there is
Answer:
how do u know how many extraneous solutions there is?
Step-by-step explanation:
To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.
Answer: To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes
Step-by-step explanation:
Please can I have brainliest I need one more to rank up
Which equation represents the graph of function j?
Answer:
Hi your answer is... B... Because The following radical phrase does not have to be negativeAnswer: C or j(x) = (-x + 4)^1/2
Step-by-step explanation:
Got it right on the test
(11 POINTS!! ) CAN SOMEONE PLEASE DO NUMBERS 19-22 FOR ME, I’LL MARK YOUR ANSWER BRAINIEST!! Thanks in advance❤️
Answer:
19. x=2
20. y= - 72
21. y=4
22.x= - 1
Step-by-step explanation:
What is the value of the expression, if p=42?
Then whats p+22
Answer:
64
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
p=42 and p+22=?
Substitute:
(42)+22=?
Add:
(42)+22=64
what is the answer 42 ounces to 5 pounds in simplest form
42 ounces is equivalent to 2.625 pounds.
To convert 42 ounces to pounds, we divide by the conversion factor of 16 ounces per pound, since there are 16 ounces in a pound:
= 42 ounces / 16 ounces per pound
= 2.625 pounds
Now, to express 2.625 pounds in simplest form.
Since it is in decimal form, so we don't need to simplify it further.
Therefore, 42 ounces is equivalent to 2.625 pounds.
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Which equation can be used to find 55 percent of 900?
StartFraction 55 times 1 Over 900 times 1 EndFraction = StartFraction 55 Over 900 EndFraction
StartFraction 100 times 16.36 Over 55 times 16.36 EndFraction = StartFraction 1636 Over 899.8 EndFraction
StartFraction 900 times 9 Over 100 times 9 EndFraction = StartFraction 8100 Over 900 EndFraction
StartFraction 55 times 9 Over 100 times 9 EndFraction = StartFraction 495 Over 900 EndFraction
Answer:
the answer is A
Step-by-step explanation:
igot a 100
Answer:
D
Step-by-step explanation:
Helpppp pleaseeeeeeeeeeeee
Answer:
$1.30
Step-by-step explanation:
91/14/5
find the missing angle of the triangle 42° 87° x
Answer:
X =51 is the best answer for this question
The midpoint of segment AB has the coordinates M(-4,2). If the coordinates of endpoint A are (-6, -7), find the coordinates of endpoint B.
Given:
The midpoint of segment AB has the coordinates M(-4,2).
The coordinates of endpoint A are (-6, -7).
To find:
The coordinates of B.
Solution:
Let the coordinates of point B are (a,b).
Formula for midpoint:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
The midpoint of segment AB has the coordinates M(-4,2), so by using the above formula we get
[tex]M=\left(\dfrac{-6+a}{2},\dfrac{-7+b}{2}\right)[/tex]
[tex](-4,2)=\left(\dfrac{-6+a}{2},\dfrac{-7+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-6+a}{2}=-4[/tex]
[tex]-6+a=-8[/tex]
[tex]a=-8+6[/tex]
[tex]a=-2[/tex]
And,
[tex]\dfrac{-7+b}{2}=2[/tex]
[tex]-7+b=4[/tex]
[tex]b=4+7[/tex]
[tex]b=11[/tex]
Therefore, the coordinates of point B are (-2,11).
If 5 workers complete one task in 7 days, then how many days will 7 workers take to complete the same task?
Answer: 5 days
Step-by-step explanation:
5*7=35 - means the total amount of the days to complete the job by 1 worker is 35 days
So 7 workers can do this job in
35:7=5 days
ctions and Models
Algebra I
Which of the following options results in a graph that shows exponential decay? (2 points)
Of(x) = 0.6(2)*
O f(x) = 3(0.7)
O f(x) = 0.4(1.6)*
O f(x) = 20(3)*
3. (04.03 LC)
Answer:
i need help
Step-by-step explanation:
I dont understand
The amount of money earned by bank customers based on the amount of principal in their savings account is _______________.
Answer:
interest
Step-by-step explanation:
A nursery has $55,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 29% and the profit on a red maple tree is 18%. The profit for the entire stock is 20%. How much was invested in each type of tree?
Answer:
On dogwood $45,000 was invested
On red maple tree , $10,000 would be invested
Step-by-step explanation:
Let the amount invested on dogwood tree be d and the amount invested on red maple be r
Total is 55,000
Thus;
d + r = 55,000 ••••••(i)
Total profit is;
20/100 * 55,000 = 11,000
Profit on dogwood is;
29/100 * d = 0.29d
Profit on red maple is;
18/100 * r = 0.18r
Both equals 11,000
0.29d + 0.18r = 11,000 •••••••(ii)
From equation i, d = 55,000 - r
substitute into ii
0.29(55,000-r) + 0.18r = 11,000
15950- 0.29r + 0.18r = 11,000
4950 = 0.11r
r = 4950/0.11
r = 45,000
d = 55,000 - r
d = 55,000 - 45,000
d = 10,000
Can anyone please help anyone bro
3p- 2c^3- 3c^3p +2 Write as a product
Answer:
[tex] (3p + 2) (1 - c)(1 + c + {c}^{2} )[/tex]
Step-by-step explanation:
[tex]3p- 2c^3- 3c^3p +2 \\ \\ = (3p - 3 {c}^{3} p) +( 2 - 2c^3) \\ \\ = 3p(1 - c^3) + 2(1 - c^3) \\ \\ = (1 - c^3)(3p + 2) \\ \\ = (1 - c)(1 + c + {c}^{2} )(3p + 2) \\ \\ = \bold{ \red{(3p + 2) (1 - c)(1 + c + {c}^{2} )}}[/tex]
HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!
Answer: AEC = 80
X=30
YW ;)
archilles ordered a pizza with 16 slices every hour he ate half of the remaining slice
Answer:
so there is 8 slice left
Step-by-step explanation:
factor 2x^2-9x+9=0 and please show ur steps
Answer:
♡ hi there, madi here! ♡
hope your having a great day.
I did the math so here's your answer.
2x−3)(x−3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2x-3=0. x-3=0
Set the first factor equal to 0 and solve.
x=3/2
Set the next factor equal to 0 and solve.
x=3
Therefore, the final solution is all the values that make (2x-3) (x-3)=0 true. x=3/2,3♡
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What number divided by 6 leaves a remainder of 5, divided by 5 leaves a remainder of 4, divided by 4 leaves a remainder of 3, and divided by 3 leaves a remainder of 2?
Answer:
59
Step-by-step explanation:
If a number is divided by [tex]n[/tex] and leaves a remainder [tex](n-1)[/tex], then the number [tex](n+1)[/tex] will be completely divisible by [tex]n[/tex].
Therefore, when we say a number [tex]x[/tex], when divided by 6, it leaves a remainder 5, then ([tex]x+1[/tex]) will be a multiple of 6.
When we say a number [tex]x[/tex], when divided by 5, it leaves a remainder 4, then ([tex]x+1[/tex]) will be a multiple of 5.
When we say a number [tex]x[/tex], when divided by 4, it leaves a remainder 3, then ([tex]x+1[/tex]) will be a multiple of 4.
When we say a number [tex]x[/tex], when divided by 3, it leaves a remainder 2, then ([tex]x+1[/tex]) will be a multiple of 3.
So, [tex]x+1[/tex] is a common multiple of 3, 4, 5 and 6.
Taking LCM of 3, 4, 5 and 6, we get 60.
So, the number 60 - 1 = 59 is the least such number.
Henry reads 20 pages in 10 minutes. Rotha reads 30 passes in 12 minutes. Who reads at a quicker rate?
Answer:
Rotha
Step-by-step explanation:
20 divided by 10 is 2
30 divided by 12 is 2.5
So Rotha is quicker
help me please click link to go to question
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Answer:
okay thank you. ummmm yes well it's not loading
Find the variable :
4t + 5.25 = 35.25
Follow the steps below to choose an equivalent expression for 15n – 20 using the distributive property. Use the work below to help you.
1. Find the GCF of the terms.
The GCF of 15n and 20 is 5.
2. To factor out the GCF, divide each term in the expression by the GCF.
15n ÷ 5 = 3n and 20 ÷ 5 = 4
Which expression is equivalent to 15n – 20?
2(8n – 6)
6(2n – 9)
5(3n – 4)
5(4n – 3)
PLS HELP MEEEEHHHH
Answer:
5(3n - 4)
Step-by-step explanation:
The GCF of 15 and 20 is 5, so 5 is on the outside of the parentheses. 15/5 = 3, so the term is 3n. 20/5 = 4, so the other term is 4. Put it all together and you have 5(3n - 4)
Answer:
5(3n - 4)
Step-by-step explanation:
Edge 2020
The number of passengers in the bus double every minute. The bus was full of
passengers at 7.45am. When was it one quarter full?
Answer:
7:43 am.
Step-by-step explanation:
it was 1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.
Knowing how the bus fills, we want to find the time where the bus is one-quarter full.
The bus is one-quarter full at 7:43 am.
We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.
Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.
One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.
Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.
And if N is the people in a full bus, then N/4 represents the buss a quarter full.
Then we can answer the question as:
The bus is one-quarter full at 7:43 am.
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