Leroy is 22 years old. His car averages 31 miles
per gallon. His car payments are $165.32 per
month, and he has 36 more payments to
make. How old will he be when he pays off his
car?
Answer:
he will be 25
Step-by-step explanation:
36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
A quadrilateral inscribed in a circle has its opposite angles adding up to 180°
So
<NOP + <M = 180
4x+8x-24 = 180
12x = 180+24
12x = 204
Dividing both sides by 12
x = 17
<NOP = 4(17)
= 68°
If f(x)=x³-2x², which expression equivalent to f(i)?
Answer:
f(x) = x³ - 2x²
=>
f(i) = i³- 2i²
Hope this helps!
:)
someone pls pls pls help me
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A, 2/3C, -8D, 4E, -1/6NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
~I will mark as BRANLIEST and give you 55 points if you answer correctly.
Answer:
The lines would intersect at: (6, -4)
Step-by-step explanation:
I graphed both lines.
Answer:
(4,-2)
Step-by-step explanation:
The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.
Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect
[tex]\frac{1}{2} x-4=-x+2[/tex]
First, we can add 4 to each side
[tex]\frac{1}{2} x=-x+6[/tex]
Then we can add x to each side
[tex]\frac{3}{2} x=6[/tex]
Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]
[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]
Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.
[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]
This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]
Please help. I’ll mark you as brainliest if correct!
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
Please help. I’ll mark you as brainliest if correct!!!!
Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]
This simplifies to:
[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]
This further simplifies to:
[tex]\frac{-3i +2}{5}[/tex]
Can be rewritten as:
[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]
a = 2/5
b = -3/5
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions
Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]
In this question:
[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 6328125}{11250}[/tex]
[tex]X - 6328125 = 1.28*11250[/tex]
[tex]X = 6342525[/tex]
The 90th percentile for the distribution of the total contributions is $6,342,525.
Sick computers: Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose
P(V) = 0.47, P(W) = 0.37, P(Vand W) = 0.01
(a) Find the probability that the computer contains either a virus or a worm or both.
(b) Find the probability that the computer does not contain a worm
Part 1 of 2
(a) Find the probability that the computer contains either a virus or a worm or both.
The probability that the computer contains either a virus or a worm or both is
Х
5
Part 2 of 2
(b) Find the probability that the computer does not contain a worm
The probability that the computer does not contain a worm is
Х
Answer:
0.83
0.63
Step-by-step explanation:
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
a. the probability that the computer contains either a virus or a worm or both is 0.83
b. The probability that the computer does not contain a worm is 0.63.
Calculation:(a)
The probability is
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
(b) The probability is
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
Learn more about the probability here: https://brainly.com/question/16096170
can someone please help me it’s urgent!!!!!
Answer:
6/4
Explanation:
If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.
Hope this helps!
from a deck of 52 cards, what is the probability of getting a four or diamond.
Answer:
4/13
Step-by-step explanation:
There are 13 diamonds in a deck and 3 fours that aren't diamond
13+3=16
16/52 = 4/13
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
Please answer this correctly
Answer: 363 cm squared
Step-by-step explanation:
So we can split the shape into 1 triangle and 3 rectangles.
We can start with the top right rectangle which is a 4 by 5.
4*5 = 20 cm squared
We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.
This means the dimensions are 27 by 9.
27 * 9 = 243 cm squared
Now the final square toward the bottom left will be a 10 by 7.
10 * 7 = 70 cm squared.
Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.
10 + 4 + 5 = 19
19 - 13 = 6
6 + 6 = 12
Now that we have the height and base of the triangle we solve for the area.
0.5 * 5 * 12 = 30 cm squared
Now we add all the areas together to find the total area.
20 + 243 + 70 + 30 = 363 cm squared
what is the midpoint of the segment shown below?
(1, 2) (1,-5)
A. (1, -3/2)
B. (2, -3/2)
C. (2, -3)
D. (1, -3)
Answer:
The answer is A (1,-3/2)
Step-by-step explanation:
Add both x coordinates, divide by 2
Add both y coordinates, divide by 2
Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges.
{(-1.00000005)^n}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. The sequence diverges by oscillation.
b. The sequence converges monotonically. It converges to:________
c. The sequence converges by oscillation. It converges to:________
d. The sequence diverges monotonic ally.
Answer:
a
Step-by-step explanation:
(-1.00000005)^n
as n becomes very large, the function increases in both positive and negative direction.
If n=1, -1.00000005
if n=2, 1.0000001
if n= 3, -1.00000015
if n=20, 1.000001
if n=21, -1.00000105
An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
Select all fractions that are equal to 3/4
3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..
I hope this is what you are looking for :)
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
hord
12 cm
5 cm
Resu
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
SUME
The volume of the space outside the pyramid but inside the prism is
cubic centimeters,
Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
What’s the correct answer for this?
Answer:
C
Step-by-step explanation:
Measure of Arc FED = 51+79
= 130°
Since the measures of arcs and angles are the same
Hence
<FED = 130°
Find the volume of the cone.
Please help
Answer:1232m^3
Step-by-step explanation:
1/3 *22/7*7^2*24
1232m^3
A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________
Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
Solve for m:
-3(1 – 5m) = — 38 + 8m
Answer:
m = - 5
Step-by-step Explanation:
[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]
Answer:
-5
Step-by-step explanation:
Show that an implicit solution of 2x sin2(y) dx − (x2 + 10) cos(y) dy = 0 is given by ln(x2 + 10) + csc(y) = C. Differentiating ln(x2 + 10) + csc(y) = C we get 2x x2 + 10 + dy dx = 0 or 2x sin2(y) dx + dy = 0. Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
Answer:
Step-by-step explanation:
[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]
Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.
Problem solved
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
To learn more about an equation visit:
https://brainly.com/question/1529522.
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Arlinda says there is a linear relationship between the price (p) of 500ml soft drink and the number sold (x). The formula is x = ap + b where a and b are constants. At N$20 she sells 1500 of the 500ml soft drinks but the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. At what price will 600 of the 500ml energy drinks be sold?
Answer: 600 of the 500ml energy drinks be sold be sold at $45
Step-by-step explanation:
The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as
x = ap + b
At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be
1500 = 20a + b - - - - - - - - -1
the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300
The price at which they were sold is
20 + (50/100 × 20) = $30
The second equation would be
1300 = 30a + b - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
200 = - 10a
a = 200/- 10 = - 20
Substituting a = - 20 into equation 2, it becomes
1300 = 10 × - 20 + b
1300 = - 200 + b
b = 1300 + 200 = 1500
The linear relationship becomes
x = - 20p + 1500
If x = 600, then
600 = - 20p + 1500
- 20p = 600 - 1500 = - 900
p = - 900/ - 20
p = $45