Answer:
180
Step-by-step explanation:
Given the cost (in dollars) of buying x pounds of a party product is given by the function
C(x) = 10x + 300.
Suppose, for budgetary reasons; you can't spend more than $2100 on this product. You can spend less, but you have to buy at least 50 pounds.
To get the domain of the function, substitute C(x) =2100 and find x
2100 = 10x + 300
10x = 2100 - 300
10x = 1800
x = 1800/10
x = 180
Hence the domain of the function is 180
Will give brainliest answer
Answer:
Below.
Step-by-step explanation:
log 10 ( 100 ) = 2
Answer:
First one: log_10 (100) = 2 OR log (100) = 2
Second one: 5^-3 = 1/125
Step-by-step explanation:
Let's say the formula for a basic exponent equation is this:
a = b^x
a is the answer when you calculate b^x
b is the base
x is the exponent
Here's the log formula using those variables:
log_b (a) = x
As long as you know how to rearrange the numbers/variables, you are good to go:
100 = 10^2
a = 100
b = 10
x = 2
log_10 (100) = 2
You can also write this one as log (100) = 2 because when you put log by itself, it's assumed that the base thing already equals 10.
log_5 (1/125) = -3
a = 1/125
b = 5
x = -3
5^-3 = 1/125
Hope it helps (●'◡'●)
need help please help
Answer:
∆ ADB = ∆ ADC
Step-by-step explanation:
A point is selected at random from a line segment of length l, dividing it into two line segments. What is the probability that the longer line segment is at least three times as long as the shorter segment
Answer:
3/4
Step-by-step explanation:
Let a be the length of the shorter line segment and b be the length of the longer line segment.
Since the length of the line segment is l, we have that the length of the line segment equals length of shorter line segment + length of longer line segment.
So, l = a + b
Since we require that the longer line segment be at least three times longer than the shorter line segment, we have that b = 3a
So, l = a + b
l = a + 3a
l = 4a
The probability that the shorter line segment will be a(or 3 times shorter than b) is P(a) = length of shorter line segment/length of line segment = a/l
Since l = 4a.
a/l = 1/4
So, P(a) = 1/4
The probability that a will be less than 3 times shorter that b is P(a ≤ 1) = P(0) + P(a) = 0 + 1/4 = 1/4
The probability that b will be 3 times or more greater than a is thus P(b ≥ 3) = 1 - P(a ≤ 1) = 1 - 1/4 = 3/4
Think about tossing two coins.
What is
P (H on first coin)? ………………………….
P (H on second coin)? ……………………..
List the paired outcomes for tossing two coins: ………………………………
How many ways are there for two coins to land? ………………………
What is P (HH)? …………………………
Given:
Two coins are tossed.
To find:
1. P(H on first coin)?
2. P(H on second coin)?
3. List the paired outcomes for tossing two coins.
4. How many ways are there for two coins to land?
5. What is P(HH)?
Solution:
If a a coin is tossed, then we have to possible outcomes, i.e., heads (H) and tails (T).
It is given that two coins are tossed.
1. The probability of getting a heads on first coin is:
[tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. The probability of getting a heads on second coin is:
[tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. If two coins are tossed, then the total possible outcomes are:
[tex]\{HH,HT,TH,TT\}[/tex]
4. The number of ways for two coins to land is 4.
5. The probability of the heads on both tosses is:
[tex]P(HH)=\dfrac{1}{4}[/tex]
Therefore, the required solution are:
1. [tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. [tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. List of possible outcomes is [tex]\{HH,HT,TH,TT\}[/tex].
4. Number of possible outcomes is 4.
5. [tex]P(HH)=\dfrac{1}{4}[/tex]
A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.
Answer:
[tex]x =10[/tex]
Step-by-step explanation:
Given
[tex]AB = 12[/tex]
[tex]BC = 18[/tex]
[tex]AC = 3x[/tex]
Required
Solve for x
Since B is in between both points, then:
[tex]AC = AB + BC[/tex]
This gives
[tex]3x = 12 + 18[/tex]
[tex]3x = 30[/tex]
Divide by 3
[tex]x =10[/tex]
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Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist. b. What are the speeds of the two cyclists? _______________
Answer:
4r + 4(r + 3) = 68
r = 7 miles per hour
r + 3 = 10 miles per hour
Step-by-step explanation:
distance = rate * time
a)
4r + 4(r + 3) = 68
Distribute
4r + 4r + 12 = 68
8r + 12 = 68
8r = 56
r = 7 miles per hour
r + 3 = 10 miles per hour
The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is
Answer:
-1
Step-by-step explanation:
1-2=-1
y=mx+b
b= y intercept
Answer:
-1
Step-by-step explanation:
Plsss help Get brainiest if right!!
Anita can paint 25 wooden slats in 5.5 hours. If she continues to
work at the same speed without any breaks, how many slats can
she paint in 9.9 hours?
Hello!
25 wooden ..... 5.5 hours
x wooden ..... 9.9 hours
_____________________
25/x = 5.5/9.9
25 × 9.9 = x × 5.5
247.5 = x × 5.5
x × 5.5 = 247.5
x = 247.5 : 5.5
x = 45 wooden
Good luck! :)
Answer:
45
Step-by-step explanation:
In questions such as these it is implied Anita can and does work at a constant rate. Therefore, we can set up the following proportion:
[tex]\frac{25}{5.5}=\frac{x}{9.9}[/tex], where [tex]x[/tex] represents the number of wooden slats she can paint in 9.9 hours.
Multiplying both sides by 9, we get:
[tex]x=\frac{9.9\cdot 25}{5.5},\\x=\boxed{45}[/tex]
I need a fast help please
Answer:
(5) c
(6) c
(7) b
(8) a
Step-by-step explanation:
(5) The multiplicative inverse of a number n, is the number which when multiplied by n will give a result of 1 which is a multiplicative identity. The multiplicative inverse of a number is actually the reciprocal of that number. For example, the multiplicative inverse of n is 1/n. The multiplicative inverse of 5 is 1/5. The multiplicative inverse of 5/6 is 6/5.
Therefore, the multiplicative inverse of [tex]\frac{-11}{15}[/tex] is [tex]\frac{-15}{11}[/tex]
(6) To solve 7m + 12 = -4m + 78, follow these steps;
i. Collect like terms by putting terms with m on the left hand side and the terms without m on the right hand side as follows;
7m + 4m = 78 - 12
ii. Now solve both sides;
11m = 66
iii. Divide both sides by 11;
[tex]\frac{11m}{11} = \frac{66}{11}[/tex]
m = 6
(7) Let the number be x;
10 more than twice number is 22 implies that
10 + 2x = 22
Now solve the equation;
2x = 22 - 10
2x = 12
x = 6
(8) The interior angles of a given polygon are the angles of its vertices that are within or inside of the polygon.
The sum of the interior angles of a polygon is given by;
(n-2) x 180°
where;
n = number of sides of the polygon.
For example;
For a triangle, which has n = 3 sides, the sum of these interior angles is (3 - 2) x 180° = 180°
For a rectangle/square, which has n = 4 sides, the sum of these interior angles is (4 - 2) x 180° = 360°.
For a pentagon, which has n = 5 sides, the sum of these interior angles is (5 - 2) x 180° = 540°
Therefore, depending on the number of sides n, the sum of the interior angles of a given polygon is given by;
(n-2) x 180°
How many degrees are in a quarter circle? 25° 40° 90° 100°
Answer:
90
Step-by-step explanation:
360 ÷ 4 = 90
Which expression is equivalent to -28xy + 35y?
o 7y(-4xy + 5y)
O 7x{-4x+ 5y)
o 7xl-4y+54)
O 7y(-4x+5)
Answer:
[tex]-28xy+35y[/tex]
[tex]GCF ~is~ 7y[/tex]
[tex]=7y(-4+5)[/tex]
The equivalent expression: [tex]7y(-4x+5)[/tex]
-------------------------
hope it helps...
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You can afford a $950 per month mortgage payment. You've found a 30 year loan at 8% interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?
Answer:
129469.3194
342000
212530.6806
Step-by-step explanation:
Going to assume that the 8% is a nominal, montly rate
which means the effective monthly rate is .08/12= .006667
using the annuity immediate formula...
a.)
[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]
b.) we would pay 950*30*12= 342000
c.) the amount in interest would be 342000-129469.3194=212530.6806
a) The loan one can afford is $1,29,460.2
b) The total amount of money paid to the loan company over the life of the loan is $342,000.
c) $212539.8 of the total amount paid is interest.
To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:
[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual interest rate divided by 12),
and n is the total number of payments (number of years multiplied by 12).
Given:
Monthly payment (M) = $950
Loan term = 30 years
Interest rate = 8% per year
a) How big of a loan can you afford?
Let's calculate the principal loan amount (P):
First, we need to convert the annual interest rate to a monthly interest rate:
r = 0.08 / 12
= 0.00667
n = 30 years × 12 months
n= 360
Using the formula and plugging in the values we have:
[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]
[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]
[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]
[tex]950\times9.948 = 0.0730P[/tex]
Divide by 0.073:
Now we can solve for P:
[tex]P=\frac{9450.6}{0.0730}[/tex]
[tex]P = 1,29,460.2[/tex]
Therefore, you can afford a loan amount of $1,29,460.2
b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total amount = Monthly payment × Total number of payments
Total amount =[tex]$950 \times 360[/tex]
Total amount = [tex]342,000[/tex]
Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.
c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:
Interest = Total amount - Principal loan amount
Interest = [tex]342,000 - 129460.2[/tex]
=$212539.8
Therefore, $212539.8 of the total amount paid is interest.
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A bag has 6695 blue marbles and 6696 red marbles. We repeatedly remove 2 marbles from the bag. If the two chosen marbles are of the same color then we put 1 new red marble in the bag (after removing the 2 chosen marbles). If the two marbles are of different colors then we put one new blue marble in the bag. What will be the color of the last marble in the bag
9514 1404 393
Answer:
blue
Step-by-step explanation:
If two red marbles are removed, 1 red is returned. The number of reds is reduced by 1, and the number of blues is unchanged.
If two blue marbles are removed, 1 red is returned. The number of reds is increased by 1, and the number of blues is decreased by 2.
If one of each is removed, one blue is returned. The number of reds is reduced by 1, and the number of blues is unchanged.
So, at each step, the number of blue marbles is unchanged or reduced by 2. That is, it only changes by an even number. The number of blues is initially odd, so can never reach zero.
The last marble in the bag is blue.
True or False? The total surface area of a cube can be calculated using its volume.
Answer: false
Step-by-step explanation:
Surface Area Formula Surface Area Meaning
SA=2B+Ph Find the area of each face. Add up all areas.
SA=B+12sP Find the area of each face. Add up all areas.
SA=2B+2πrh Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height.
What is the measure of e?
Answer:
[tex] \theta = 4~radians [/tex]
Step-by-step explanation:
[tex] s = \theta r [/tex]
[tex] 20~cm = \theta \times 5~cm [/tex]
[tex] \theta = 4~radians [/tex]
help pls I need it badly
9514 1404 393
Answer:
22
Step-by-step explanation:
For calculators without a cube root key, you can use the 1/3 power. The attached shows the quotient to be about 22.
what is the slope of the function, represented by the table of values below?
A. -2
B. -3
C. -4
D. -6
Answer:
B. -3
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
Slope: 2/3
Y-intercept: 6
At a coffee shop, the first 100 customers'
orders were as follows.
Medium Large
Small
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a small given that he or she ordered a hot
drink?
Rounded to the nearest percent, [? ]%
Well formatted distribution table is attached below :
Answer:
7%
Step-by-step explanation:
The probability that a customer ordered a small Given that he or she ordered a hot drink ;
This is a conditional probability and will be represented as :
Let :
P(small drink) = P(S)
P(hot drink) = P(H)
Hence, the conditional probability is written as :
P(S|H) = P(SnH) / P(H) = 5 / (5+48+22) = 5/75 = 0.0666 = 0.0666 * 100% = 6.67%
Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company's return on equity (ROE) is 16%. Assuming the plowback ratio and the ROE are expected to remain constant forever:
If you believe that the company's required rate of return is 10%, what is your estimate of the price of the company's stock?
Answer:
$250
Step-by-step explanation:
according to the constant dividend growth model
price = d1 / (r - g)
d1 = next dividend to be paid
r = cost of equity
g = growth rate
Sustainable growth rate is the rate of growth a company can afford in the long term
sustainable growth rate = plowback rate x ROE
b = plowback rate. It is the portion of earnings that is not paid out as dividends
g = 0.50 x 0.16 = 0.08 = 8%
5 / (10% - 8%)
5 / 2%
5 / 0.02 = $250
how do you find the angle?
2 The product of two numbers is 5425. If one of them is 25. What is the other 2 number
Answer:
217
Step-by-step explanation:
5425/25 = 217
A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with mean 30% and standard deviation 10%.
(a) Find the probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
(c) What is the expected value of the return?
(d) Find the 75th percentile of returns.
Answer:
a) 0.0062 = 0.62% probability that the return will exceed 55%.
b) 0.3085 = 30.85% probability that the return will be less than 25%
c) 30%.
d) The 75th percentile of returns is 36.75%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean 30% and standard deviation 10%.
This means that [tex]\mu = 30, \sigma = 10[/tex]
(a) Find the probability that the return will exceed 55%.
This is 1 subtracted by the p-value of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 30}{10}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
p-value of Z when X = 25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 30}{10}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085
0.3085 = 30.85% probability that the return will be less than 25%.
(c) What is the expected value of the return?
The mean, that is, 30%.
(d) Find the 75th percentile of returns.
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 30}{10}[/tex]
[tex]X - 30 = 0.675*10[/tex]
[tex]X = 36.75[/tex]
The 75th percentile of returns is 36.75%.
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $2000. What is the probability of randomly selecting one employee who earned less than or equal to $45,000
Answer:
The probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621
Step-by-step explanation:
We are given that
Mean,[tex]\mu=50000[/tex]
Standard deviation,[tex]\sigma=2000[/tex]
We have to find the probability of randomly selecting one employee who earned less than or equal to $45,000.
[tex]P(x\leq 45000)=P(\frac{x-\mu}{\sigma}\leq \frac{45000-50000}{2000})[/tex]
[tex]P(x\leq 45000)=P(Z\leq-\frac{5000}{2000})[/tex]
[tex]P(x\leq 45000)=P(Z\leq -2.5)[/tex]
[tex]P(x\leq 45000)=0.00621[/tex]
Hence, the probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621
A right rectangular prism has a length of 2 1/4 cm, width of 8 cm, and height of 20 1/2 cm.
What is the volume of the prism?
Enter the answer in the box.
cm³
Answer:
369 cm^3
Step-by-step explanation:
you just multiply all the numbers together
Answer:
369 cm³.
Step-by-step explanation:
Volume of a rectangular prism is just length × width × height. So:
2.25 × 8 = 18
18 × 20.5 = 369
So, the volume is 369 cm³.
Parallel lines
What is the segment
Answer:
Step-by-step explanation:
The factorization of (x+y)^2+2(x+y)+1 is
please answer
Answer:
[tex](x + y+ 1)^2[/tex]
Step-by-step explanation:
[tex]Using : (a + b)^2 = a^2 + 2ab + b^2\\\\(x+ y)^2 + 2(x +y) + 1 , \ where \ a = (x+y) , \ b = 1 \\\\= (x +y)^2 + ( 2 \times 1 \times (x+y)) + 1^2\\\\= (x +y+ 1)^2[/tex]
Step-by-step explanation:
Using:(a+b) ² =a²+2ab+b²
Hope it is helpful to you
The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
Is a linear model or a quadratic model a better fit? Quadratic model graph quadratic model linear model
B
13 ft.
5 ft.
A
C
12 ft.
Find the value of Cos (B) =
Answer: the answer is 12/13