Answer:
x = 36
Step-by-step explanation:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
Subtract x and 36 from both sides.
[tex] -12\sqrt{x} = -x - 36 [/tex]
Divide both sides by -1.
[tex] 12\sqrt{x} = x + 36 [/tex]
Square both sides.
[tex] 144x = x^2 + 72x + 1296 [/tex]
Subtract 144x from both sides.
[tex] 0 = x^2 - 72x + 1296 [/tex]
Factor the right side.
[tex] 0 = (x - 36)^2 [/tex]
[tex] x - 36 = 0 [/tex]
[tex] x = 36 [/tex]
Since the solution of the equation involved squaring both sides, we musty check the answer for possible extraneous solutions.
Check x = 36:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
[tex] 36 - 12\sqrt{36} + 36 = 0 [/tex]
[tex] 36 - 12\times 6 + 36 = 0 [/tex]
[tex] 36 - 72 + 36 = 0 [/tex]
[tex] 0 = 0 [/tex]
Since 0 = 0 is a true statement, the solution x = 36 is a valid solution.
Mars Inc. claims that they produce M&Ms with the following distributions:
Brown 30% Red 20% Yellow 20%
Orange 10% Green 10% Blue 10%
How many M&Ms must be sampled to construct the 97% confidence interval for the proportion of red M&Ms in that bag if we want a margin of error of ± .15?
a) 33
b) 36
c) 34
d) 26
e) 25
f) None of the above
Answer:
C) 34
Step-by-step explanation:
1) Some definitions
By definition the margin of error (ME) is the error that tell to us how many percentage points your results will differ from the real population value, on this case our parameter of interest is pr = proportion of red M&M's
ME = Critical value x Standard error of the sample =0.15.
The proportion of red M&M's follows a normal distribution, and our critical value would be from the normal standard distribution on this case
2) Calculate the critical value
a) Compute alpha (α): α = 1 - (confidence level / 100) = 1- 0.97 = 0.03
b) Calculate the critical probability (p*): p* = 1 - α/2 = 1 - (0.03/2) = 0.985
c) Find the z-score using the cumulative probability obtained at step b)
On this case P(Z<z) = 0.985 , the value of z = 2.17 using the normal standard table
3) Calculate n from the formula of ME
The margin of error for a proportion is given by this formula
ME = z sqrt{{pr(1-pr)/n}}
Squaring both sides :
(ME/z) ^2 = (pr(1-pr))/n
And solving for n we got
n = (pr(1-pr))/(ME/z)^2 = (0.2x0.8)/ (0.15/2.17)^2 = 33.488
We need to round up the sample in order to ensure that the confidence level of 97% is meeted, and on this case the answer would be 34.
The number of M&Ms needed to construct a confidence interval for the proportion of red M&Ms with a margin of error of ± .15 is n = 36.
To construct a confidence interval for the proportion of red M&Ms with a margin of error of ± .15, we can use the formula for the sample size needed:
n = (Z² × p × (1-p)) / E²
Substitute Z = 2.17 (for 97% confidence), p = 0.20 (given proportion of red M&Ms), and E = 0.15 into the formula:
n = (2.17²× 0.20 × 0.80) / 0.15²
= 36
Therefore, the number of M&Ms that must be sampled to construct the 97% confidence interval for the proportion of red M&Ms with a margin of error of ± .15 is 36.
what does x and oe equal?
Answer:
œ=50
Step-by-step explanation:
Solve the equation: 120+œ+60+15+20 = 130+35+2œ
Simplifies as follows: œ+215 = 2œ+165
œ = 215 - 165 = 50
Angelica has been depositing $280 each month into a savings account with an APR of 2.76% for the last 3 years. If she continues depositing this amount for an additional 12 years, what will the balance in her savings account be?
Answer:
$62,490.65
Step-by-step explanation:
If we assume her deposits are at the beginning of the month, and that the interest is compounded monthly, the future value is that of an "annuity due." The formula is ...
FV = P(1+r/n)((1+r/n)^(nt)-1)/(r/n)
where r is the APR (.0276), n is the number of yearly compoundings (12), P is the monthly payment ($280), and t is the number of years (15). Putting the numbers into the formula and doing the arithmetic, we get ...
FV = $280(1.0023)(1.0023^180 -1)/(.0023) ≈ $62,490.65
Angelica's account balance after 15 years will be $62,490.65.
_____
If her deposits are at the end of the month, the balance will be $62,347.25.
Jack went out for dinner at Red Lobster, his meal was $45, jack wants to leave an 18% tip, list three different calculations jack can use to determine his bill including the tip
Answer:
Step-by-step explanation:
Jack went out for dinner at Red Lobster and his meal was $45, This is the amount that he needs to pay if there was no tax or tip.
jack wants to leave an 18% tip, The amount of tip that jack wants to leave is 18/100 × 45 = 0.18×45 = $8.1
To determine how much jack needs to pay including the tip,
Amount that jack would pay is bill + tip = 45 + 8.1 = $53.1
Another way of calculating it is,
Since the tip is 18% and his bill was 100%, we will add the percentages and multiply by the bill. It becomes
118/100 × 45 = $53.1
(x^2–x–4)multiplied by(x–5)
Answer:
x³ -6x² +x +20
Step-by-step explanation:
The distributive property is useful for making sure you have all of the partial products.
(x^2–x–4)(x–5) = x(x^2–x–4) -5(x^2–x–4)
= (x^3 -x^2 -4x) +(-5x^2 +5x +20)
= x^3 +(-1-5)x^2 +(-4+5)x +20
= x^3 -6x^2 +x +20
In the last math test andrew answered 80% of all the questions correctly.If he answered 32 questions correctly, what was the total number of questions in the math test?
Answer:
The total number of questions are 40
Step-by-step explanation:
let the total number of questions be "x".
percent of questions answered correctly are 80.
In fractions 80% is [tex]\frac{4}{5}[/tex]
The total number of correctly answered questions are 32.
the equation is,
[tex](\frac{4}{5})(x) = 32[/tex]
thus , x = [tex]\frac{(5)(32)}{4}[/tex]
x= 40
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = x + 1 intersect the circle with radius 6 and center (0, 1)?
Answer:
(3√2, 1+3√2) ≈ (4.243, 5.243)
Step-by-step explanation:
The line has a slope of 1 and goes through the center of the circle, so will intersect the circle at the point ...
(6, 6)/√2 +(0, 1) = (3√2, 1+3√2) ≈ (4.243, 5.243)
The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3 . Round your answer to three decimal places.
Answer:
0.093 ft/min
Step-by-step explanation:
V = 4/3 π r³
Take derivative with respect to time:
dV/dt = 4π r² dr/dt
Plug in values:
141 = 4π (11)² dr/dt
dr/dt = 141 / (484π)
dr/dt ≈ 0.093
The radius is increasing at 0.093 ft/min.
The increasing rate of the radius is equal to 0.093 ft/min.
What is the volume?Volume is defined as the space occupied by the object in a three-dimensional space. The sphere is the shape of a circular ball.
The volume is calculated by the formula below,
V = 4/3 π r³
Take the derivative with respect to time:
dV/dt = 4π r² dr/dt
Solve the equation for the rate of change of radius of the sphere,
141 = 4π (11)² dr/dt
dr/dt = 141 / (484π)
dr/dt ≈ 0.093
Therefore, the increasing rate of the radius is equal to 0.093 ft/min.
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help me QUICK, plz! 15 points!
Answer:
t=8
Step-by-step explanation:
Subtract 12t from both sides
(12t-12t) + 16 = (13t-12t) + 24
16 = 1t (or just t) + 24
Then subtract 16 from both sides, and bring "t" over the equals sign making it a negative integer.
-t = 8
t = 8
A five-digit number is represented by ABCDE. If we add the number 1 in front of ABCDE, then the product of 1ABCDE and 3 will be the six-digit number ABCDE1. What is the original five-digit number ABCDE?
Answer:
ABCDE = 42857
Step-by-step explanation:
First, we will use logic. The only number that when it's multiplied by 3, gives 1 at the end is 7, so E should be 7, so:
1ABCD7 * 3 = ABCD71
If 3 times 7 is 21, we carry two, so, the next number by logic, cannot be 1, because 3*1 = 3 + 2 = 5, it's not 7, so, it should be another number, like 5.
5*3 = 15 + 2 = 17 and we carry one. So this number fix in the digit, and D = 5.
We have now: 1ABC57 * 3 = ABC571
Letter C, we have to get a number that when it's multiplied by 3 and carry one, gives 5. In this case 8, because: 3 * 8 = 24 + 1 = 25 and carry two. D = 8.
So far: 1AB857 * 3 = AB8571
Now, the same thing with B. If we multiply 3 by 2, and carry two we will have 8 so: 3 * 2 = 6 + 2 = 8. B = 2
1A2857 * 3 = A28571
Finally for the last number, a number multiplied by 3 that hold the 1 as decene, In this case, the only possibility is 4, 3 * 4 = 12 so:
142857 * 3 = 428571
Is 27/50 closer to 1/2, 1 or 0
Answer:
I think it's closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{27}{50} = 0.54\\[/tex]\\
i do know that 1/2 is < 27/50
A large insurance company wanted to estimate u, the mean claim size (in 5) on an auto insurance policy. A random sample of 225 claims was chosen and it was found that the average claim size was $2875. From past experience the population standard deviation is assumed to be $1350.
Which of the following is the point estimate for u?
A. $225
B. $2875
C. $1350
D. None of the above.
Answer: B. $2875
Step-by-step explanation:
We know that best point estimate of population mean[tex](\mu)[/tex] is the sample mean[tex](\overline{x})[/tex] .
Given : A large insurance company wanted to estimate [tex]\mu[/tex], the mean claim size (in 5) on an auto insurance policy.
A random sample of 225 claims was chosen and it was found that the average claim size was $2875.
i.e. Sample mean [tex]\overline{x}=\$2875[/tex]
That means , the point estimate for [tex]\mu=\$2875[/tex]
Hence , the correct answer is option B . $2875.
The point estimate of u, the mean claim size, is $2875 as determined by the average claim size of a random sample of 225 claims.
Explanation:In statistics, a point estimate is often the best guess that one can make for an unknown parameter. In this case, we are looking for the mean claim size, denoted as u. When the question states that a random sample of 225 claims showed an average claim size of $2875, they are giving you the point estimate of u, because the calculated average is our best estimate of the population mean in this context. Therefore, the point estimate of u is $2875.
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Brandon is an amateur marksman. When he takes aim at a particular target on the shooting range, there is a 0.1, point, probability that he will hit it. One day, Brandon decides to attempt to hit 10 such targets in a row.
Assuming that Brandon is equally likely to hit each of the 10 targets, what is the probability that he will hit at least one of them?
Answer:
.65
Step-by-step explanation:
Strategy:
In this situation it is much easier to calculate the probability of the event we are looking for (he hits at least one target) by calculating the probability of its complement (he misses every target), and subtracting from 1.
In other words, we can use this strategy:
P(at least one hit)=1-P(miss all 10)
Calculations:
P(at least one hit)
=1-P(miss all 10)
=1-(0.9)^10
≈1-0.349
≈0.65
Answer:
P(at least one hit)≈0.65
I hope this helps!!!
The probability that Brandon will hit at least one of them is 0.65 approx.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
For the considered case, as each hit is independent of each other, and there is either hit or not hit, so this situation can be modeled by binomial distribution.
For this case, we get:
n = 10p = probability of success(we call it success if hit occurs) = 0.1X = count of successes in those 10 attemptsThen, we get: [tex]X \sim B(n=10,p=0.1)[/tex]
The probability that Brandon will hit at least one of them is written symbolically as:
[tex]P(X \geq 1)[/tex]
We can rewrite it as:
[tex]P(X \geq 1) = 1 - P(X < 1) = 1 - P(X = 0)[/tex]
Using the probability function of binomial distribution, we get:
[tex]P(X \geq 1) = 1 - \: ^{10}C_0(0.1)^0(1-0.1)^{10} = 1 -0.9^{10} \approx 0.65[/tex]
Thus, the probability that Brandon will hit at least one of them is 0.65 approx.
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Jera and Bipu are friends. Jera’s age 5 years ago was 20 less than Bipu’s age in 8 years. Bipu’s age 5 years ago was 34 years less than twice Jera’s age in 8 years. How old are they at present?
Answer:
Jera is 20Bipu is 27Step-by-step explanation:
Let j and b represent Jera's and Bipu's current ages.
j-5 = (b +8) -20 . . . . . Jera's age 5 years ago was 20 less than Bipu's age in 8 years
b-5 = 2(j+8) -34 . . . . .Bipu's age 5 years ago was 34 less than Jera's age in 8 years
__
Solving the first equation for j gives ...
j = b + 8 -20 + 5
j = b -7
Using that in the second equation, we get ...
b -5 = 2((b -7)+8) -34
0 = b -27 . . . . . . . subtract (b-5) and simplify
b = 27
j = 27 -7 = 20
Jera is 20; Bipu is 27.
Which domain restrictions apply to the rational expression? 14–2x / x^2–7x
Answer:
3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]
2C. [tex]\displaystyle III.[/tex]
2B. [tex]\displaystyle I.[/tex]
2A. [tex]\displaystyle II.[/tex]
1. [tex]\displaystyle Set-Builder\:Notation: {x|7, 0 ≠ x} \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
Step-by-step explanation:
3. See above.
2C. The keyword is ratio, which signifies division, so you would choose "III.".
2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".
2A. The keyword is total, which signifies addition, so you would choose "II.".
1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:
[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: {x|7, 0 ≠ x} \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]
I am joyous to assist you anytime.
Answer:
\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]
Step-by-step explanation:
Given expression is \[14 - 2x / x^{2} - 7x\]
For this rational expression to be valid it must satisfy the constraint that the denominator is not equal to 0.
This implies that \[x^{2} - 7x = 0\] should be false.
In order words \[x*(x-7) = 0\] should be false.
Or, x=0, x=7 must be false.
Hence the domain restriction that applies is as follows :
\[(-\infty ,0)\cup (0,7)\cup (7,\infty )\]
find the value(s) of the missing variables
Answer: x = 9
y = 13
Step-by-step explanation:
Toby and Marcus both collect stamps. Toby has 10 stamps and collects 4 new stamps every week. Marcus has 60 stamps and collects 2 new stamps every week. After how many weeks will Toby and Marcus have the same number ?
Answer:
25 weeks will Toby and Marcus have the same number of stamps
Explanation:
No of stamps collected by Toby initially= 10
No of stamps Toby collects every week= 4
No of stamps Marcus has initially= 60
No of stamps Marcus collects each week=2
Suppose the no of week when Toby and Marcus have the same number of stamps are x
Hence no of stamps collected by Toby after x weeks
=10+4x
No of stamps collected by Marcus after x weeks
=60+2x
Therefore to calculate the same of stamps collected by Toby and Marcus
No of stamps collected by Toby after x weeks= No of stamps collected by Marcus after x weeks
10+4x =60 +2x
4x-2x= 60-10
2x=50
x=25
Hence after 25 weeks Toby and Marcus will have the same number of stamps
You can travel to New York San Francisco, or Miami during June July or August. How many possible outcomes are illustrated in the tree diagram?
a. 3
b. 6
c. 9
d. 18
Answer:9
Step-by-step explanation:
You would count the possible outcomes on the right side of the diagram
The number of possible outcomes is 9.
Given that,
You can travel to New York San Francisco, or Miami during June July or August.Based on the above information, the calculation is as follows:
From NewYork = 3
From San Francisco = 3
From Miami = 3
Total = 9
Therefore we can conclude that the number of possible outcomes is 9.
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Consider the sequence:
5, 7, 11, 19, 35,....
Write an explicit definition that defines the sequence:
Group of answer choices
a_n=2n+3 a n = 2 n + 3
a_n=3n+2 a n = 3 n + 2
a_n=3n^2 a n = 3 n 2
a_n=2^n+3
Answer:
[tex]a_{n}=2^{n}+3[/tex]
Step-by-step explanation:
The given sequence is not arithmetic, it's a geometric sequence, that means the sequence is obtain using powers. The faster way to find the answer is to try options that fist with a geometric sequence. If we try the last one, we'll find that's the answer.
We need to try for n=1, n=2, n=3, n=4 and n=5:
a_{1}=2^{1}+3=5
a_{2}=2^{2}+3=4+3=7
a_{3}=2^{3}+3=8+3=11
a_{4}=2^{4}+3=16+3=19
a_{5}=2^{5}+3=32+3=35
Therefore, the right answer is the last choice, because as you can observe, it fits perfectly with the given sequence.
Alex was biking along a 48 mile trail. First half of the time he was biking twice as fast as the second half of the time. If he spent 4 hours on the road, how fast was he biking at first?
Answer:
The speed in the first part is 16 mph.
Step-by-step explanation:
The total distance is 48 miles. The total time is 4 hours.
In the second part of the trip, he was traveling at speed s for distance d for 2 hours.
In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.
speed = distance/time
distance = speed * time
First part of trip:
48 - d = 2s * 2
d + 4s = 48 Equation 1
Second part of the trip:
d = s * 2
d = 2s Equation 2
Equations 1 and 2 form a system of equations in two unknowns, d and s.
d + 4s = 48
d = 2s
Substitute 2s for d in equation 1.
2s + 4s = 48
6s = 48
s = 8
The speed in the second part is 8 mph.
The speed in the first part is 2s = 2(8) = 16.
The speed in the first part is 16 mph.
Check:
d = 2s = 2(8) = 16
48 - d = 48 - 16 = 32
The second part is 16 miles. The first part is 32 miles.
16 miles at 8 mph takes 2 hours.
32 miles at 16 mph takes 2 hours.
2 hours + 2 hours = 4 hours.
Our answer is correct.
Answer: The speed in the first part is 16 mph.
Answer:
The speed in the first part is 16 mph.
Step-by-step explanation:
The total distance is 48 miles. The total time is 4 hours.
In the second part of the trip, he was traveling at speed s for distance d for 2 hours.
In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.
speed = distance/time
distance = speed * time
First part of trip:
48 - d = 2s * 2
d + 4s = 48 Equation 1
Second part of the trip:
d = s * 2
d = 2s Equation 2
Equations 1 and 2 form a system of equations in two unknowns, d and s.
d + 4s = 48
d = 2s
Substitute 2s for d in equation 1.
2s + 4s = 48
6s = 48
s = 8
The speed in the second part is 8 mph.
The speed in the first part is 2s = 2(8) = 16.
The speed in the first part is 16 mph.
Check:
d = 2s = 2(8) = 16
48 - d = 48 - 16 = 32
The second part is 16 miles. The first part is 32 miles.
16 miles at 8 mph takes 2 hours.
32 miles at 16 mph takes 2 hours.
2 hours + 2 hours = 4 hours.
Our answer is correct.
Answer: The speed in the first part is 16 mph
A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 36 cm3. If nickel plating costs $1 per cm2 and silver plating costs $2 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length _______ cm and a height of________ cm
Answer:
The box which minimizes the cost of materials has a square base of side length 4.16 cm and a height of 2.08 cm
Step-by-step explanation:
The cost is minimized when the cost of each pair of opposite sides is the same as the cost of the top and bottom. Since the top and bottom are half the cost of the sides (per unit area), the area of the square top and bottom will be double that of the sides. That is, the box is half as tall as wide, so is half of a cube of volume 72 cm³.
Each side of the square base is ∛72 = 2∛9 ≈ 4.16 cm. The height is half that, or 2.08 cm.
_____
If you want to see this analytically, you can write the equation for cost, using ...
h = 36/s²
cost = 2(1)(s²) + (2)(4s)(36/s²) = 2s² +288/s
The derivative is set to zero to minimize cost:
d(cost)/ds = 4s -288/s² = 0
s³ = 72 . . . . . multiply by s²/4
s = ∛72 = 2∛9 ≈ 4.16 . . . . . cm
h = 36/(2∛9)² = ∛9
The box is 2∛9 cm square and ∛9 cm high, about 4.16 cm square by 2.08 cm.
To minimize the cost of materials, the dimensions of the box that minimize the cost of materials are approximately: Square base side length: 4.18 cm, Height: 2.05 cm.
Explanation:To minimize the cost of materials, we need to consider the areas that need to be plated with silver and nickel. Let's assume the side length of the square base is x cm, and the height of the box is h cm. The cost of silver plating the sides is $2 per cm², and the cost of nickel plating the bottom and top is $1 per cm².
The area of each silver-plated side is 4xh cm², and the area of each nickel-plated bottom and top is x² cm². The total cost of materials can be calculated using the formula:
Total cost = 4xh * $2 + 2x² * $1 = 8xh + 2x²
To minimize the cost, we need to find the values of x and h that will minimize this expression.
Since the volume of the box is given as 36 cm³, we have the equation x²h = 36.
Using the equation for the volume, we can solve for h in terms of x:
h = 36 / x².
Substituting this into the expression for the total cost:
Total cost = 8x(36 / x²) + 2x² = 288 / x + 2x²
To find the values of x and h that minimize the cost, we need to find the critical points of the expression. Taking the derivative of the total cost with respect to x, and setting it to zero:
d(Total cost) / dx = -288 / x² + 4x = 0
Simplifying this equation:
288 = 4x³
x³ = 72
x = ∛72 ≈ 4.18 cm
Substituting this value of x back into the equation for h:
h = 36 / (4.18)² ≈ 2.05 cm.
Therefore, the dimensions of the box that minimize the cost of materials are approximately:
Square base side length: 4.18 cm
Height: 2.05 cm
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Scenario: The market for used cell phones is very popular in Barylia. However, several phones available in this market are of inferior quality and it is often impossible to differentiate between a good-quality phone and a poor-quality phone. Refer to the scenario above. Based on the given information, we can conclude that the market for used cell phones in Barylia: is perfectly competitive. has only one seller. is monopolistically competitive. has asymmetric information.
Answer:
D: has asymmetric information.
Step-by-step explanation:
Several phones available in Barylia market are of inferior quality and it is often impossible to differentiate between a good-quality phone and a poor-quality phone.
So, we can conclude that the market for used cell phones in Barylia: has asymmetric information.
Asymmetric information or often called information failure shows the decision in transactions where one market or party has got better information than the others.
Katie keeps a record of her transactions in a notebook. Looking over her records for the past two weeks, Katie finds that her bank statement does not match her notebook, and she actually has more money than she thought she did. These are the relevant entries in Katie’s notebook:
Transaction
Debit ($)
Credit ($)
Beginning Balance
889.23
Fence repair
75.86
---
Dry cleaning
32.38
---
Paycheck
---
140.91
Gift from cousin
---
35.00
Car payment
178.66
---
Tax refund
---
66.18
New chair
161.55
---
Ending Balance
682.87
However, Katie’s bank statement says that her ending balance is $707.10. Which of the following is a possible explanation for the discrepancy?
a.
Katie’s neighbor paid for half of the fence repair, which Katie forgot to record.
b.
Katie transposed the digits in the cost of the dry cleaning, which actually cost $23.38.
c.
Katie’s new chair was on sale for 15% off, making it cost $137.32, but Katie wrote down the before-sale price.
d.
Katie’s tax refund came in two equal-sized checks, but Katie only recorded one of them.
Answer: C
Step-by-step explanation:707.10-682.87= 24.23. Similar difference can also be found in only chair which is. 161.55-137.32=24.23
Answer:
The correct answer is C on edge :) i just did the test
Step-by-step explanation:
Assume a circle of radius r has the same area as a square with side length s. Express the radius of the circle in terms of the length of a side of the square (i.e. write r as a function of s)
Final answer:
To express the radius of a circle in terms of the length of a side of a square, use the formula: r = s/√π.
Explanation:
A circle of radius r has the same area as a square with side length s. We can express the radius of the circle in terms of the length of a side of the square using the formula for the area of a circle: A = πr², where π is approximately 3.14159. Similarly, for the square, the area is given by A = s². Equating these two areas gives us the equation:
s² = πr²
Now, we can solve for r by rearranging the equation:
r = s/√π
Final answer:
To express the radius of a circle in terms of the side length of an equal-area square, use the formula r = s / √π.
Explanation:
To express the radius r of a circle in terms of the length of a side of the square s, where the circle and square have the same area, we start by setting the area formulas for both shapes equal to each other. The area of the circle is πr^2 and the area of the square is s^2. By equating the two areas, we have πr^2 = s^2. To solve for r, we need to take the square root of both sides of the equation divided by π, which gives us r = s / √π.
You select a family with three children. If M represents a male child, and F represents a female child, the set of equally likely outcomes for the children's genders is { MMM, MMF, FFM, MFF, FFM, FMF, FFM, FFF }. Find the probability of selecting a family with nothing 6 male children.
Answer:
1/8
Step-by-step explanation:
This is actually pretty easy.
First, you have the sample of the children.
You know that the family with 3 children, can only have the following children:
MMM: all males
MMF: 2 males, 1 female
MFF: 1 male, 2 females
MFM: 2 males, 1 female (different order)
FMM: 1 female, 2 males
FFM: 2 females, 1 male
FMF: 2 females, 1 male
FFF: 3 females
If you count all of these possibilities, we have 8 possible cases of family with the childrens.
In only one of them, we have only females and no males, which is the last one, all 3 females.
Therefore, the probability to select a family with no male, is only 1/8.
In the set of all possible sets of genders for three children, which is {MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF}, the event of having no male children is 'FFF'. As there are 8 possible outcomes in total, the probability of selecting a family with no male children is 1/8, or 0.125.
Explanation:It seems like there is a typo in your question. It asks about the probability of selecting a family with 'nothing 6 male children', which doesn't quite make sense. However, if the question is to find the probability of selecting a family with no male children, we can certainly answer that. In your given set of outcomes, { MMM, MMF, FFM, MFF, FFM, FMF, FFM, FFF }, there seems to be a mistake as FFM is repeated three times. The correct set of equally likely outcomes for a family with three children should be { MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF }.
Each outcome is equally likely, hence, the probability of any particular outcome is 1 divided by the total number of outcomes. The total unique outcomes for the genders of three children is 2^3, or 8. The event of having no male child corresponds to the outcome 'FFF'. Since there is only one such outcome, the probability of a family with no male children is 1/8 or 0.125.
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A builder wishes to construct a ramp 21 feet long that rises to a height of 5 feet above level ground. What angle should the ramp make with the horizontal? Decimal approximations will be marked incorrect. Symbolic trigonometric expressions such as arctan(5) are accepted. 1/ 5 21 α cos radians
Answer:
α = 13.39249775
Step-by-step explanation:
Length of the vamp = 21 ft long
Height of the vamp= 5 ft
using SOHCAHTOA
tanα = opposite /adjacent
Tan α = 5/21
α = arctan(5/21)
α = 13.39249775
Supppose A is an invertible n\times n matrix and v is an eigenvector of A with associated eigenvalue -3. Convince yourself that v is an eigenvalue of the following matrices, and find the associated eigenvalues:
1. \ A^6, \ eigenvalue = ,
2. \ A^{-1}, \ eigenvalue = ,
3. \ A + 5 I_n, \ eigenvalue = ,
4. \ 6 A, \ eigenvalue = .
Answer:you will an app go to =567
Given the functionf ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20
Describe where the function has a vertical asymptote and how you found your answer. Remember that an asymptote is represented by an equation of a line and not just a single value.
x = -4 is a vertical asymptote for the function.
Explanation:The graph of [tex]y=f(x)[/tex] is a vertical has an asymptote at [tex]x=a[/tex] if at least one of the following statements is true:
[tex]1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty[/tex]
The function is:
[tex]f(x)=\frac{x^2+7x+10}{x^2+9x+20}[/tex]
First of all, let't factor out:
[tex]f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq 5[/tex]
From here:
[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty[/tex]
[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty[/tex]
Accordingly:
[tex]x=-4 \ is \ a \ vertical \ asymptote \ for \\ \\ f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20}[/tex]
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5:3 =n:7 Solve for n.
(there fractions but i have to write them with : because i cant write fractions)
[tex] \frac{5}{3} = \frac{x}{7} [/tex]
you them cross multiply
5×7=35
3×X= 3x
35=3x
x(n)= 11.6
Answer:
n = 35/3 or 11 2/3.
Step-by-step explanation:
5/3 = n/7
Cross multiply:
3n = 5*7
3n = 35
n = 35/3
Samantha is the best middle manager the company has. She constantly puts countless hours into her job and is one of the best and brightest around. Samantha has not received a raise or promotion for many years and believes it is because she is a woman experiencing unseen discrimination. It is clear that Samantha is feeling the effects of a_____.
Answer:Glass ceiling
Step-by-step explanation:
Samantha is feeling the effect of glass ceiling .A glass ceiling is a term used to describe an unseen barrier that prevents a particular demographic (usually applied to minorities) from increasing in a hierarchy beyond a certain level.
Here The phrase “glass ceiling” is used to describe the difficulties faced by women when trying to move to higher roles in a male-dominated hierarchy.