Answer:
E. 800%
Step-by-step explanation:
Since,
u = 8d/h² __________ eqn (1)
Now, density (d) is doubled and usage (h) is halved.
Hence the new life (u'), becomes:
u' = 8(2d)/(0.5h)²
u' = 8(8d/h²)
using eqn (1), we get:
u' = 8u
In percentage,
u' = 800% of u
In words, the percentage increase in useful life of the equipment is 800%.
Answer: E. 800%
Step-by-step explanation:
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h^2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment.
Assuming d = 1 and h = 1, then
u = (8 × 1)/1^2 = 8
If the density of the underlying material is doubled and the daily usage of the equipment is halved, it means that
d = 2 and h = 1/2 = 0.5, therefore,
u = (8 × 2)/0.5^2 = 16/0.25 = 64
64/8 = 8
The percentage increase in the useful life of the equipment is
8 × 100 = 800%
Given: ∆AKM, R = 2, m∠A = 33°, O∈ AM . Find: perimeter of ∆AKM
Answer:
∆AKM is a right triangle for it is inscribed in semicircle O.
AM = diameter of semi-circle O = 2R = 2(2) = 4
%22AK%22%2F%22AM%22=cos%2833%5Eo%29
AK+=+AM%2Acos%2833%5Eo%29
AK+=+4cos%2833%5Eo%29
%22KM%22%2F%22AM%22=sin%2833%5Eo%29
KM+=+AM%2Asin%2833%5Eo%29
KM+=+4sin%2833%5Eo%29
The perimeter of a triangle is the sum of the three sides.
perimeter=AK%2BKM%2BAM
perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4
Approximately 9.533238412
Step-by-step explanation:
Answer:
reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER AND POINTS!
Answer:
c
Step-by-step explanation:
The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 60
E. 90
Answer:
D.
Step-by-step explanation:
Let the number of stamps Kaye had be k and that of Alberto be a. Then we know that are in a ratio of 5 to 3.
Hence, k : a = 5:3
or 3k = 5a
Then Kaye gave Alberto 10 of her stamp to make the ratio 7:5
k - 10/a + 10 = 7/5
Cross multiply:
5(k - 10) = 7(a + 10)
5k - 50 = 7a + 70
5k - 7a = 120
Let us now solve the last equation simultaneously with the equation 3k = 5a
5k - 7a = 120
3k - 5a = 0
Multiply equation 1 by 3 and equation 2 by 5
15k - 21a = 360
15k - 25a = 0
Subtract 1 from 2, 4a = 360
and thus a = 90
We know 3k = 5a
3k = 5 * 90
k = 450/3 = 150
Now if we subtract 90 from 150, this yields 60
Given a positive integer N, find all of the positive integers from 1 to N that can be written as a sum of 2 cubic numbers (also have to be positive) in two different ways.
Answer:
There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:
1³+12³=9³+10³=17292³+24³=18³+20³=1383210³+27³=19³+24³=2068315³+945³=744³+756³=843912000Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.
for which values of x and y is line p parallel to line q?
x=5, y=3
x=1, y=5
x=3, y=5
x=3, y=6
Answer:
x=3, y=5
Step-by-step explanation:
(16x+2) and (45x-5) are co-interior angles and they sum up to 180 degrees.
To find x
(16x+2)+(45x-5)=180
16x+45x-5+2=180
61x-3=180
61x=180+3
61x=183
x=3
(45x-5) and (26y) are corresponding angles so their values are equal
(45x-5)=(26y), x=3
(45 (3)-5)=(26y)
135-5=26y
130=26y
5=y
WILL GIVE BRAINLIEST!!!! PLEASE HELP!!!
A function is shown: f(x) = 16x2 − 1. Choose the equivalent function that best shows the x-intercepts on the graph.
A. f(x) = (4x + 1)(4x − 1)
B. f(x) = (8x + 1)(8x − 1)
C. f(x) = 4(x2 + 1)
D. f(x) = 8(x2 − 1)
Answer:
it is option a
Step-by-step explanation:
. f(x) = (4x + 1)(4x − 1) is the correct answer overall you have the check it and just make sure you fully to your capability of those steps
The equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us that f(x)=16x²-1, therefore, the equivalent function that best shows the x-intercepts on the graph can be written as,
[tex]f(x)= 16x^2-1\\\\f(x)=16x^2-1^2\\\\f(x)=(4x-1)(4x+1)[/tex]
If we solve the roots of the given function,
(4x-1)=0
x = 1/4 = 0.25
(4x+1)=0
x = -1/4 = -0.25
Thus, the x-intercept of the function is 0.25 or -0.25.
Thus, the equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).
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In your own words, describe what happens when a line is reflected across the x-axis.
Answer:
Every point in the line would get reflected about the x axis and we would get a new line.
Step-by-step explanation:
When you reflect a point about the x-axis , the x-coordinate of the image remains the same but the y - coordinate changes to its negative value.
Now a line is a collection of points and we have to find out what happens when we reflect a line about the x-axis.
Reflecting a line about the line is same as keeping a mirror along the x-axis and the image we see in the mirror is the same as the image we obtain in the mirror.
So every point in the line would get reflected about the x axis and we would get a new line.
Final answer:
Reflecting a line across the x-axis inverts the y-coordinates of all points on the line, while the x-coordinates remain unchanged; the reflected line appears flipped over the x-axis, preserving distance but potentially changing orientation.
Explanation:
When a line is reflected across the x-axis, each point on the original line is flipped vertically to a new position on the opposite side of the x-axis, maintaining the same distance from the x-axis. Essentially, every point's y-coordinate is multiplied by -1, causing the line to appear as a mirror image of itself with respect to the x-axis. This transformation preserves the shape and size of the original line but changes its orientation relative to the x-axis.
Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
answer choices are:
-6
6
8
Answer:
-6Step-by-step explanation:
f(x)=3x-1 g(x)=-x+6f(-2)=3*(-2)-1 g(5)=-5+6f(-2)=-7 g(5)=1 f(-2)+g(5)=-7+1=-6How can you use the values of a, b, and c to write a quadratic function in vertex form?
Answer:
y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)
Step-by-step explanation:
We presume you're starting with ...
y = ax^2 +bx +c
As you would with numbers, factor the first two terms:
y = a(x^2 +b/a·x) +c
Add half the square of the x term inside and its opposite outside parentheses:
y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2
y = a(x +b/(2a))^2 +c -b^2/(4a)
You can combine the last two terms to a more familiar fraction:
y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)
To write a quadratic function in vertex form, use the values of a, b, and c. Find the coordinates of the vertex using h = -b/2a and k = f(h).
Substitute the values into the vertex form.
To write a quadratic function in vertex form, you can use the values of a, b, and c.
The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k,
where (h, k) represents the coordinates of the vertex.
To find h and k, you can use the formulas h = -b/2a and k = f(h).
Once you have the values of h and k, you can substitute them into the vertex form to obtain the quadratic function in vertex form.
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A 4-inch tall box with a square base is constructed in order to hold a set of 16 identical cupcakes, each with a diameter of 2 inches. What is the area of the base, in square inches, of the smallest box that can hold the cupcakes?
Answer:
64 square inches
Step-by-step explanation:
The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.
Each cupcake is 2 inches, so the base is 8 inches by 8 inches. Therefore, the area is 64 square inches.
Thirty elves would like to build a skating ring so they can all use it at the same time. Santa tells them, they need at least 40 square feet for each skater, so no one will bump into each other. If they build a rectangular rink, what are the possible dimensions (length and width)for the rink?
Answer:
The Possible dimension of the ring could be;
20 ft × 60 ft
25 ft × 48 ft
30 ft × 40 ft
60 ft × 20 ft
48 ft × 25 ft
40 ft × 30 ft
Step-by-step explanation:
Given:
Number of skaters = 30
Area for each skater = 40 sq ft
We need to find the dimension of rectangular ring the are going to build.
Now we know that they building the skating ring such that they all can use at same time.
Hence if the all use at same time then we will find the total area first.
Total area can be calculated by multiplying Number of skaters with area required for each skaters.
Framing the equation we get;
Total area = [tex]30\times 40 = 1200 \ ft^2[/tex]
Hence The total area of the rectangular ring would be 1200 sq. ft.
Now we know that Total area is equal to product of length and width.
[tex]length\times width =1200ft^2[/tex]
1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30
Hence the Possible dimension of the ring could be;
20 ft × 60 ft
25 ft × 48 ft
30 ft × 40 ft
60 ft × 20 ft
48 ft × 25 ft
40 ft × 30 ft
Which expression is equivalent to (64 y Superscript 100 Baseline) Superscript one-half?
8y10
8y50
32y10
32y50
Answer:
[tex]8y^{50}[/tex]
Step-by-step explanation:
This expression is equal :
[tex]{(64y^{100})}^{\frac{1}{2}}[/tex]
Here we can use this rule :
[tex](a^mb^n)^y=a^{my}b^{ny}[/tex]
Now, 64 we can write like : [tex]8^2[/tex]
[tex](8^2y^{100})^{\frac{1}{2}}[/tex]
Now we can use our rule :
[tex]8^{2*\frac{1}{2}}y^{100*\frac{1}{2}[/tex]
When we simplify, we have :
8y^{50}
Answer:
b
Step-by-step explanation:
There are twelve shirts in your closet: five blue, four green, and three red. You randomly select one to wear. What is the probability it is blue or green?
A)
5
36
B)
11
12
C)
2
5
D)
3
4
Joe wants to purchase a new skateboard. He already has $40 and can save $20 each week from his job. Write a linear equation to represent the total amount he has after ‘w’ weeks.
A) T = 20 + 40w
B) T = 60w
C) T = 40 + 20 + w
D) T = 40 + 20w
Answer:
D
Step-by-step explanation:
Joe already has $40 and can save $20 each week. the total amount he can save in a given number of weeks is $20 multiplied by the that number of weeks which in this case is w so 20w. To find the total T of the amount he has after w weeks, you add the amount he already has to the amount saved. So the equation would be T=40+20w
Answer:
D) T = 40 + 20w
Step-by-step explanation:
Trust me! i had this on my test/ exam, and it was correct!!
i really hoped this helped! Have a wonderful day!
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off. The regular ticket price was $9.00 and the tax is 6%. What would Charlie's total be?
Answer:
The Total of Charlie's will be $7.16.
Step-by-step explanation:
Given:
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.
Price of regular ticket = $9.00.
tax = 6%.
We need to find Charlie’s total.
So we will first find the price of regular ticket with 25% off.
25% percent of regular ticket = [tex]\frac{25}{100}\times 9 = \$2.25[/tex]
Discounted Price of regular ticket will be equal to Price of regular ticket minus Discounted amount.
Discounted Price of regular ticket = 9 - 2.25 = $6.75
Now, including tax :
Tax paid will be on discounted amount.
Hence Amount paid in tax = [tex]6\% \times 6.75= \frac{6}{100}\times 6.75 = \$0.405[/tex]
Total amount paid by charlie is equal to sum of Discounted Price of regular ticket and Amount paid in tax
Total Amount paid by charlie = [tex]6.75+0.405 =\$7.155 \approx \$7.16[/tex]
Therefore, the total of Charlie's will be $7.16.
Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
(1.5, 2.85)
O (1.05, 3.3)
(-1.2, -1.05)
O(-2.4, -2.1)
Answer:
[tex](1.5,2.85)[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
we have the endpoints:
Q(0.3, 1.8), R(2.7, 3.9)
substitute in the formula
[tex]M(\frac{0.3+2.7}{2},\frac{1.8+3.9}{2})[/tex]
[tex]M(\frac{3}{2},\frac{5.7}{2})[/tex]
[tex]M(1.5,2.85)[/tex]
A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by p = 45 / q 1.5
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
1) Express q as a function of p.
2) Find the price elasticity of demand when the price is set at $4.00 per serving.
Answer:
1. [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
2. [tex]E_d=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
The given demand equation is
[tex]p=\dfrac{45}{q^{1.5}}[/tex]
where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.
Part 1 :
We need to Express q as a function of p.
The given equation can be rewritten as
[tex]q^{1.5}=\dfrac{45}{p}[/tex]
Using the properties of exponent, we get
[tex]q=(\dfrac{45}{p})^{\frac{1}{1.5}}[/tex] [tex][\because x^n=a\Rightarrow x=a^{\frac{1}{n}}][/tex]
[tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]
Therefore, the required equation is [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex].
Part 2 :
[tex]q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}[/tex]
Differentiate q with respect to p.
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})[/tex]
[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})[/tex]
Formula for price elasticity of demand is
[tex]E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}[/tex]
[tex]E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}[/tex]
Cancel out common factors.
[tex]E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}[/tex]
Using the properties of exponents we get
[tex]E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})[/tex]
[tex]E_d=-\dfrac{2}{3}(p^{0})[/tex]
[tex]E_d=-\dfrac{2}{3}[/tex]
Therefore, the price elasticity of demand is -2/3.
To address the question, q as a function of p is q = (45/p)^(2/3), and the price elasticity of demand when p is $4 can be found by taking the derivative of q with respect to p and substituting the given values in the elasticity formula.
Explanation:The student has asked to express q as a function of p and to find the price elasticity of demand when the price is set at $4.00 per serving for a new roast chicken product. The given equation is p = 45 / q1.5.
To find q as a function of p, we rearrange the equation: q = (45/p)1/1.5 or q = (45/p)2/3.To find the price elasticity of demand, we use the formula Ed = (dq/dp) × (p/q). First, we calculate the derivative dq/dp of the function q(p), and then substitute p=4 to find Ed at that price.The derivative of q with respect to p is dq/dp = -2/3 × (45/p4/3). Substituting p=4, we get the quantity q = (45/4)2/3. Plugging these values into our elasticity formula gives us the price elasticity of demand at p=$4.00.
Twenty years ago, you began investing $3,000 a year. Because your investments earned an average of 8 percent a year, your investment portfolio has a current dollar value of $92,000. How much did you earn on your investments over the 20-year period of time? a.) $40,000
b.) $132,000
c.) $92,000
d.) $52,000
e.) $2,000
Answer:
$32,000
Step-by-step explanation:
Yearly investment = $3,000
Number of years = 20
Investments earned an average of 8 percent a year.
Total invested amount = $3,000 × 20 = $60,000
Current value of investment = $92,000.
We need to find the total earnings on the investment.
Earnings = Current value of investment - Total invested amount
Earnings = $92,000 - $60,000
Earnings = $32,000
Therefore, the total earnings is $32,000.
To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.
Explanation:This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.
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Let f(x) = x³+6x²+6x and let c be the number that satisfies the Mean Value Theorem for f on the interval [-6,0].Find the Mean Value Theorem.
Answer:
c = 0 or c = -4
Step-by-step explanation:
According to the Mean Value Theorem
[tex]f^{'}(c) = \frac{f(0) - f(-6)}{0 - (-6)} = \frac{0 - (-6)^3 - 6*(-6)^2 - 6*(-6)}{6} = 36 - 36 + 6 = 6[/tex]
By taking the first derivative of f
[tex]f^{'}(x) = 3x^2 + 12x + 6[/tex]
Since[tex]f^{'}(c) = 6[/tex]
We can solve for c
[tex]3c^2 + 12c + 6 = 6[/tex]
[tex]3c^2 + 12c = 0[/tex]
[tex]c(c + 4) = 0[/tex]
c = 0 or c = -4
You randomly guess the answers on a multiple choice test each question has three choices what is the probability that you will guess the correct answer
Answer:
If the question is single answer correct then the answer is [tex]\frac{1}{3}[/tex] and if it's multiple options correct than the answer is [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
There is a little ambiguity in the question, that whether one answer is correct or multiple options are correct, but let;s deal with both the cases.
Probability = [tex]\frac{TotalNo.OfFavourableOutcomes}{TotalOfNoOfOutcomes}[/tex]
Probability when one option is right=[tex]\frac{1}{3}[/tex]
If this is a question , where multiple options are right then the total no. of cases for it will be = TTT, TFF, FTF, FFT, TTF, TFT, FTT (FFF is not a valid case, because the question has to have at least one valid answer.)
Probability when more than one option can be right=[tex]\frac{1}{7}[/tex]
Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people who are not yet retired) who did not believe that the U.S. Social Security program will be able to pay them a retirement benefit when they retire. In the summer of 2010, the Gallup poll found that 60% of nonretirees thought that Social Security would not be able to pay a benefit. Five years later in the summer of 2015, Gallup asked the same question to 1,282 nonretirees and found that 51% of respondents did not think that Social Security would be able to pay a retirement benefit by the time that they retire. We would like to test the hypothesis that in 2015 there is a lower proportion of nonretirees who do not think that Social Security will be able to pay them a benefit. A z-test for the population proportion showed that z = -4.29, p < 0.001.
Which of the following is the best conclusion based on the output?
A. We have extremely strong evidence to reject H0.
B. We have extremely strong evidence to reject Ha.
C. We have moderately strong evidence to reject H0.
D. There is a probability of 0 that H0 is correct.
E. There is a probability of 0 that Ha is correct.
Answer:
A. We have extremely strong evidence to reject H0.
Step-by-step explanation:
Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.
According to the data null and alternative hypotheses should be:
[tex]H_{0}[/tex]: P=0.60[tex]H_{a}[/tex]: P<0.60Test statistics is -4.29 and p-value of the statistics is p<0.001
At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.
Madison spent 3 times as long on her social project as she did on her other project. If she spent a total of 8 hours on he projects how long did she spend on her social project
Answer:
6 hours
Step-by-step explanation:
Suppose Madison spent x hours on her social project,
then the number of hours spent on other project will be 1/3 of x=x/3
Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e
x + x/3 = 4x/3
It si given that this is 8 hours, therefore
4x/3=8
Multiplying both sides by 3:
4x=24
Dividing across board by 4:
x= 6 hours
Given ΔMNO, find the measure of ∠LMN.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
38°
52°
76°
104°
Answer:
104°
Step-by-step explanation:
Thinking process:
Let the triangle be:
ΔMNO
The angle be: ∠LMN.
From the description, NOP is 104°
If, segment MN and NO are marked congruent then the corresponding angle, ∠LMN is 104°
This property of congruency applies since the segments are equal.
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?(1) a^n = 64(2) n=6
Answer:
a=2
Step-by-step explanation:
Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320=[tex]2^{7}[/tex]*3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).
In (1) a^n=64 and in (2) n=6 so it can be written as 2^6=64 so a=2 and n=6. So the value of a is 2. a=2
In this Circular Flow example the Money Supply is reduced as the Fed ___________ $20 billion of Treasury bonds and bills from/to the banking system..
Answer:
Deduct/subtract
Step-by-step explanation:
Federal Reserve board uses different methods to increase or decrease the currency in circulation. This methods are known as Monetary policy. The Central bank, at its discretion, can print more currency to increase the flow of currency in circulation
The Federal Reserve Board, which is the governing body that manages the Federal Reserve System, oversees all domestic monetary policy. The Fed"s job is to increase and decrease paper currency in circulation. This effort is to curb inflation and hyperinflation, stabilize the economy and create room for ease of doing business with the international community
The Fed can increase the money supply by lowering the reserve requirements for banks, which allows them to lend more money.
Also, by raising the banks' reserve requirements, the Fed can decrease the size of the money supply.
The Central bank modify short-term interest rates by lowering or increasing the discount rate that banks pay on short-term loans from the Fed.
Modifying Reserve Requirements : they can moderate the amount of money banks can hold.
PLEASE HELP !!!
Give all angles of rotational symmetry less than 360°, listed from least to greatest.
The angles of rotational symmetry less than 360°, listed from least to greatest, are
°,
°,
°, and
°.
Answer: 60°, 72°, 90°, 120° and 180°
Step-by-step explanation:
To calculate the angle of rotational symmetry of a shape or polygon, you make use of this formula
[tex]\frac{360}{n} where n is the number of sides of the shape[/tex]
example for a Square with 4 sides. the angle of rotational symmetry is 360/4 =90°.
It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. She sells cups of the lemonade for $1.25.How many cups of lemonade will serine need to break even?
Answer: it will need 40 cups of lemonade to break even
Step-by-step explanation:
Break even represents the point at which there is neither profit nor loss.
It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. Assuming that she made x cups of lemonade, the total cost of making x cups would be
30 + 0.5x
She sells each cup of the lemonade for $1.25 . Assuming that she sold x cups of lemonade, therefore, the total amount would be 1.25×x = 1.25x
To break even,
30 + 0.5x = 1.25x
1.25x - 0.5x = 30
0.75x = 30
x = 30/0.75
x = 40
A long-distance phone company has a monthly fee of $7.95 and charges a rate of $0.05 per minute. Another long-distance company has a monthly fee of $9.95 and charges a rate of $0.03 per minute. At how many minutes would the two companies have equal charges?
Answer:
100 minutes
Step-by-step explanation:
Let the number of minutes required for the two Billings to be equal be x.
Now we write this in an equation form.
7.95 + 0.05x = 9.95 + 0.03x
0.05x - 0.03x = 9.95 - 7.95
0.02x = 2
x = 2/0.02 = 100 minutes
At the 100th minute, the amount of Billings would be equal
Assume that the probability of any newborn baby being a boy is one half and that all births are independent. If a family has three children (no twins), what is the probability of the event that they are all boys?
Answer:
1/8
Step-by-step explanation:
P(B) = 1/2
Now we are considering that the three children are all boys. This means we are considering that the first is a boy, the second is a boy and the third too is a boy. This brings us to the situation BBB
That is a boy and a boy and another boy. In probability, the word and means we multiply the three.
Hence:
P(BBB) = P(B1) * P(B2) * P(B3) = 1/2 * 1/2 * 1/2 = 1/8 or 0.125
The probability of a three-child family having all boys, given that each birth is independently a boy with a probability of one half, is 1/8 or 0.125 (12.5%).
Explanation:The subject of your question is based in
probability
, a key concept in mathematics. Specifically, you're asking about the
probability of a family having three boys
, with the probability of any birth resulting in a boy being given as one half. As the question indicates that all births are independent, we're dealing with independent events in probability. The probability of independent events is calculated by multiplying the probabilities of each individual event. In this case, the probability of having a boy is one half (or 0.5), and we have three independent events (the births of the three children). Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2), which simplifies to 1/8 or 0.125. So, assuming that all births are equally likely to result in a boy or a girl, the probability of a three-child family having all boys is 0.125, or 12.5%.
Learn more about Probability here:https://brainly.com/question/32117953
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AB = x + 4 DC = 12 AD = x + 2 BC = ? Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?
Answer:
AB = DC = 12
AD = BC = 10
Step-by-step explanation:
For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...
AB = DC
x+4 = 12 . . . . substitute expressions for length
x = 8 . . . . . . . subtract 4
Then the lengths of AD and BC must be ...
BC = AD = x+2 = 8+2 = 10
___
The figure will be a parallelogram when x=8 and sides have lengths ...
AB = DC = 12
AD = BC = 10
_____
Comment on the problem
Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.