Answer:
x = 0.5
Step-by-step explanation:
What is the area of the purple region? *
Answer:
49pi or about 153.94 square meters.
Step-by-step explanation:
Because the two semicircles together take up the 28m long edge of the rectangle, they each half that diameter and a quarter of that radius. This means that both semicircles have a radius of 28/4=7. Since two semicircle with the same radius form a full circle, we can just calculate the area of a full circle of radius 7. [tex]\pi \cdot 7^2=49\pi\approx 153.94[/tex]. Hope this helps!
a snowbank that is 6 inches deep is melting at the rate of 0.5 in per hour . what’s a linear function to model the scenario and identify the domain and range of the function
Answer: y = -0.5x + 6
Domain = 0≤x≤12
Range = 0≤y≤6
What is 145 divided by 788
Answer:
0.18401015
Step-by-step explanation:
You should use an online calculator
What is the answer please
Answer:
(-12, 9)
Step-by-step explanation:
Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.
The question is incomplete! Complete question along with answer and explanation is provided below.
Question:
Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.
The Probability is (2/12)(4/12) = 8/144
Answer:
P = (2/12)(4/11) = 2/33
Step-by-step explanation:
There are total 3 + 2 + 4 + 3 = 12 marbles
The probability of drawing a yellow marble is given by
P(yellow) = number of yellow marbles/total number of marbles
There are 2 yellow marbles and total 12 marbles
P(yellow) = 2/12
Then Francisco draws a red marble without replacing the first one so that means there are total 11 marbles left.
P(red) = number of red marbles/total number of marbles
There are 4 red marbles and total 11 marbles
P(red) = 4/11
Therefore, the overall probability is
P = (2/12)(4/11) = 2/33
Francisco made the error of calculating the probability with replacement whereas, in reality he did not replaced the marble after drawing the yellow marble, so he should have used total 11 marbles for the calculation of drawing red marble,
can somebody do this
6x²-x-2=0
Answer:
X= 1 + 7/12
x = 1 - 7/12
Step-by-step explanation:
Answer:
[tex]x=\frac{19}{12}\\ or\\x=\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]6x^2-x-2=0[/tex]
a=6
b=-1
c=-2
[tex]x=-b\frac{+}{}\frac{\sqrt[]{b^2-4ac} }{2a}[/tex]
[tex]x=-(-1)\frac{+}{}\frac{\sqrt[]{(-1)^2-4(6)(-2)} }{2(6)}[/tex]
[tex]x=1\frac{+}{}\frac{\sqrt[]{1+48} }{12}[/tex]
[tex]x=1\frac{+}{}\frac{\sqrt[]{49} }{12}[/tex]
[tex]x=1\frac{+}{}\frac{7}{12}[/tex]
------------------------------
[tex]x=1+\frac{7}{12}[/tex]
[tex]x=1-\frac{7}{12}[/tex]
------------------------------
[tex]1+\frac{7}{12}=\frac{(1*12)+(7*1)}{12} =\frac{12+7}{12} =\frac{19}{12}[/tex]
------------------------------
[tex]1-\frac{7}{12}=\frac{(1*12)-(7*1)}{12} =\frac{12-7}{12} =\frac{5}{12}[/tex]
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x)=(x-7)^2, S(x)=x^2+4x+31
(a) Equilibrium point: x = 1
(b) Consumer surplus at equilibrium: 0
(c) Producer surplus at equilibrium: 0
We have,
To find the equilibrium point, we need to set the demand (D(x)) equal to the supply (S(x)):
D(x) = S(x)
Given:
D(x) = (x - 7)^2
S(x) = x^2 + 4x + 31
(a) Equilibrium point:
Setting D(x) equal to S(x):
(x - 7)^2 = x^2 + 4x + 31
Expanding and rearranging the equation:
x^2 - 14x + 49 = x^2 + 4x + 31
Simplifying and rearranging further:
-14x - 4x = 31 - 49
-18x = -18
x = 1
Therefore, the equilibrium point is x = 1.
(b) Consumer surplus at the equilibrium point:
Consumer surplus represents the difference between the price consumers are willing to pay and the price they actually pay.
At the equilibrium point, the price consumers are willing to pay (D(x)) is equal to the price they actually pay (S(x)).
Substituting x = 1 into the demand function D(x):
D(1) = (1 - 7)^2
D(1) = (-6)^2
D(1) = 36
Consumer surplus at the equilibrium point is the difference between what consumers are willing to pay and what they actually pay:
Consumer surplus = D(x) - S(x)
Consumer surplus = 36 - S(1)
Consumer surplus = 36 - (1^2 + 4(1) + 31)
Consumer surplus = 36 - (1 + 4 + 31)
Consumer surplus = 36 - 36
Consumer surplus = 0
Therefore, at the equilibrium point, the consumer surplus is 0.
(c) Producer surplus at the equilibrium point:
Producer surplus represents the difference between the price producers are willing to accept and the price they actually receive.
At the equilibrium point, the price producers are willing to accept (S(x)) is equal to the price they actually receive (D(x)).
Substituting x = 1 into the supply function S(x):
S(1) = 1^2 + 4(1) + 31
S(1) = 1 + 4 + 31
S(1) = 36
Producer surplus at the equilibrium point is the difference between what producers are willing to accept and what they actually receive:
Producer surplus = S(x) - D(x)
Producer surplus = 36 - D(1)
Producer surplus = 36 - (1 - 7)^2
Producer surplus = 36 - (-6)^2
Producer surplus = 36 - 36
Producer surplus = 0
Therefore, at the equilibrium point, the producer surplus is also 0.
Thus,
(a) Equilibrium point: x = 1
(b) Consumer surplus at equilibrium: 0
(c) Producer surplus at equilibrium: 0
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The equilibrium point in the market occurs when the demand and supply are equal, which can be found by solving the given function equations. Consumer surplus and producer surplus at the equilibrium point are computed as the area between the demand/supply curves and the equilibrium price.
Explanation:The equilibrium point is when the demand and supply are equal, this happens i.e., D(x) = S(x). Therefore, we first equate (x-7)^2 = x^2 + 4x + 31. Solving this equation gives us the equilibrium quantity, x.
The consumer surplus is the area between the demand curve and the consumer's actual payment, i.e., the area under D(x) above the equilibrium price. This equals to the integral from 0 to x of D(x) minus the equilibrium price. The producer surplus is the area between the supply curve and the consumer's payment, i.e., the area under S(x) below the equilibrium price. This equals to the integral from 0 to x of the equilibrium price minus S(x).
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To write 11x2+17x−10 in factored form, Diego first listed pairs of factors of -10. (_+5)(_+-2) (_+2)(_+-5) (_+10)(_+-1) (_+1)(_+-10) Use what Diego started to complete the rewriting. Only one of the factored forms needs to be used and completed.
Answer:
The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2
Step-by-step explanation:
If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.
Therefore, we prove with negative values.
x = -1: 11*(-1)²+17*(-1) - 10 = -16x = -2: 11*(-2)² + 17*(-2) - 10 = 44-34-10 = 0Therefore, -2 is a root. We can find the other knowing that
p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)
The independent term is 11*2*(-r₂) = -22r₂ = -10
thus, r₂ = -10/-22 = 5/11.
Therefore, p(x) = 11*(x+2)*(x-5/11)
To write 11x2+17x−10 in factored form we find two numbers whose sum is 17 and product is -110. The correct pair is 2 and -55 which leads to the factored form (11x - 55)(x + 2).
Explanation:The question involves factoring a quadratic expression, 11x2+17x−10. To re-write this expression in factored form, one needs to find two numbers, such that their sum equals to the coefficient of x, 17, and their product equals to the product of the coefficient of x² and the constant term (11*(-10)=-110). Diego started by listing all pairs of factors of the constant term, -10. The correct pair here, considering the product and the sum, are 2 and -55, because 2*(-55)=-110 and 2+(-55)=17. Therefore, our factored form will be: (11x - 55)(x + 2).
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jackson's kitten weighed 2 punds and 3 ounces.a month later the kitten weighed 56 ounces . how much weight did the kitten gain in that month
Answer:
Jackson's kitten gained 21 ounces that moth, or 1.3125 pounds.
Step-by-step explanation:
56-35=21
Answer:
21 ounces
Step-by-step explanation:
2 pounds is equal to 32 ounces, plus the 3 ounces, so the kitten was originally 35 ounces. You subtract 56-35, and get 21 ounces.
Joan has saved 7 quarters from washing cars how many cents does Joan have?
Answer:
175 cents
Step-by-step explanation:
1 quarter is equal to 25 cents.
Since there are 7 of them,
7 times 25 cents = 175 cents
In Euclidean geometry, the sum of the lengths of 2 sides of a triangle is greater than the length of the third side. The lengths of 3 sides of a triangle are 3x, 7, and 12.
Answer:[tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]
Step-by-step explanation:
Given
length of three sides are
[tex]3x, 7\ and\ 12[/tex]
according to Euclidean geometry
[tex]7+12>3x[/tex]
[tex]19>3x[/tex]
[tex]\frac{19}{3}>x[/tex]
also
[tex]3x+7>12[/tex]
[tex]3x>5[/tex]
[tex]x>\frac{5}{3}[/tex]
therefore value of [tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]
If x is an integer then x can be [tex]2,3,4,5,6[/tex]
A cooler contains five bottles of lemonade four bottles of water and three bottles of juice. Each is likely to be chosen. Describe a model that can be used to simulate the situation
Answer:Since each type of drink (lemonade, water, and juice) is equally likely to be chosen, the probability of choosing a type of drink is 1 in 3 picks. Thus, in order to get all three types of drinks, one must pick 3
Step-by-step explanation:
Five thousand, three hundred twenty people are on a cruise. If each dinner table seats 10 people, how many dinner tables does the cruise line need to provide?
tables
Answer:
532
Step-by-step explanation:
divide 5,320 by 10
WILL GIVE BRAINLIEST!!!! HELP PLEASE!!!!!!
Pavel needs $1,600 to repair damage done to his boat by a storm, but he doesn’t have enough in savings to cover the cost right now. He compares the following options for getting a loan:
• a car title loan with a $173 charge that must be paid off in two weeks or he loses ownership of his car
• a personal installment loan from his bank that must be paid off in three equal monthly payments of $600
Finish calculating the installment loan finance charge for three months by calculating the total interest using the appropriate formula.
$800
$200
$400
$280
The table below shows all of the possible outcomes for rolling two six-sided number cubes.
A table containing 36 possible outcomes. There are 5 desired outcomes.
What is the probability of rolling a sum of 8?
a
StartFraction 1 over 12 EndFraction
b
StartFraction 1 over 6 EndFraction
c
StartFraction 5 over 36 EndFraction
d
StartFraction 7 over 36 EndFraction
Answer:
d
Step-by-step explanation:
hope this helps
Gavin is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.
The probability that a sandwich was made with raspberry jelly is 0.84, the probability that it was made with creamy peanut butter is 0.27, and the probability that it was made with raspberry jelly and creamy peanut butter is 0.19.
What is the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter?
Answer:
P(A∪B) = 0.92
Step-by-step explanation:
Let's call A the event that the sandwich was made with raspberry Jelly and B the event that the sandwich was made with creamy peanut butter.
So, the probability P(A∪B) that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is calculated as:
P(A∪B) = P(A) + P(B) - P(A∩B)
Where P(A) is the probability that a sandwich was made with raspberry jelly, P(B) is the probability that it was made with creamy peanut butter and P(A∩B) is the probability that it was made with raspberry jelly and creamy peanut butter.
So, replacing P(A) by 0.84, P(B) by 0.27 and P(A∩B) by 0.19, we get that P(A∪B) is equal to:
P(A∪B) = 0.84 + 0.27 - 0.19
P(A∪B) = 0.92
The probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%, computed using the formula for the probability of A or B happening in probability theory.
Explanation:
In probability, when we want to find the probability of event A or event B happening, we use the formula P(A U B) = P(A) + P(B) - P(A ∩ B). Here, event A is the event that a sandwich was made with raspberry jelly, and event B is the event that it was made with creamy peanut butter. Given P(A) = 0.84, P(B) = 0.27, and P(A ∩ B) = 0.19, we can substitute these values into the formula.
So, P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.84 + 0.27 - 0.19 = 0.92.
This means that the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%.
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3. JASON IS 4 YEARS OLDER THAN
ANNE. THREE TIMES THE SUM OF THEIR
AGES IS 114. WHAT IS JASON'S AGE?
If anyone can help me and show their work it would help a lot!
Answer:
I think the answer is 38.
I'm thinking of two number,12 and another number.12 and my other number have a greatest common factor of 6 and their least common multiple is 36 .What's the other number I'm thinking of
Answer:
18
Step-by-step explanation:
Normally, when you multiply two numbers, their product equal to the product of their greatest common factor and their least common multiple
Let the number be y
The product of 12 and y is 12 y
Also, the product of their greatest common factor and their least common multiple is 6*36=216
Now
12y=216
Divide both sides by 12 to obtain y as
Y=216/12=18
Therefore, the other number is 18.
To prove
Factors of
12=2*2*3
18=2*3*3
Common factors for both are 2*3=6 equal to given GCD
The multiplies are 2*2*3*3=36
A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year,how many times will it be on front cover for 5 years
Answer:
The correct answer is 25.
Step-by-step explanation:
A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year.
Number of publications by the magazine every year = 12.
Number of publications in 5 years = 12 × 5 = 60.
Out of these 12 magazines in a year, the photo of a main dish is on 5 magazines.
Therefore in 60 magazines, the photo of a main dish would be 5 × 5 = 25 magazines.
Thus in five years there would be 25 publications in which the front page will have a poster of a main dish.
Based on the number of times the photo appears per year, in 5 years it will appear 25 times.
Every year, the photo in question appears 5 out of 12 times.
If there were 5 years therefore, it would appear:
= Number of times per year x Number of years
= 5 x 5
= 25 times
In conclusion, the photo of a main dish will appear 25 times in 5 years.
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If sally has 50000 pennies and she gives 2 to her sister how much does she have left
Answer:
49998 pennies left
Step-by-step explanation:
50000 - 2 = 49998
Answer:
50000-2=49998
Step-by-step explanation:
Helena wants to paint a box in the shape of a cube with sides that are 18 inches long. what is the surface area that Helena will paint?
Answer:
1944 Inches Squared
Step-by-step explanation:
Surface area Formula for a Cube:
[tex]A = 6a^2[/tex]
The "edge", which is also the side, is 18 inches.
[tex]a = 18[/tex]
Solve the formula.
[tex]A= 6a^2 = 6(18)^2 = 6 * 18^2\\18^2 = 324\\324 * 6 = 1944\\A=1944[/tex]
The cube's surface area should be 1944 square inches.
Answer:
Step-by-step explanation:
1944 Inches Squared
Step-by-step explanation:
Surface area Formula for a Cube:
The "edge", which is also the side, is 18 inches.
Solve the formula.
A rectangular prism is 10.8 yards long and 10.1 yards wide. Its volume is 218.16 cubic yards. What is the height of the rectangular prism?
Answer:
2 yards
Step-by-step explanation:
[tex]\frac{218.16}{10.8\cdot 10.1}=2[/tex] yards. Hope this helps!
Answer:
get the brainliest duck
Step-by-step explanation:
6. Ruth is having hardwood floors installed in her living room. The cost for the material is $2840 plus an installation charge of $1.90 per square foot. If the total cost for the material plus installation is $5120, determine the area of her living room. 7. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal
Answer:
(6) 1200 square feet
(7) 49 months
Step-by-step explanation:
Let the area of the living room be x square feet. Since the material cost is fixed as $2840 and cost ler square feet provided as $1.9 while and the total cost is given as $5120 then the the problem can be represented as
1.9x+$2840=$5120
Putting like terms together then
1.9x=$5120-$2840=$2280
Making x the subject of the above, by dividing both sides by 1.9 then
X=2280/1.9=1200 square feet.
Therefore, area is 1200 square feet.
(7)
Let the number of months when cost are similar be y.
For satelite option, since fixed cost of $298.9 is charged then monthly rate is $68.7 it means after y months, the expenditure for this plan will be 68.7y+$298.9
For cable option, since it only charges monthly fee of $74.80 then after y months, the expenditure amounts to 74.80y
Since after y months the expenses are same, then we equate both options to be equal. Therefore,
74.80y=68.70y+298.90
Putting like terms together then
74.80y-68.70y=298.90
6.1y=298.90
Dividing both sides by 6.1 to make y the subject then
Y=298.9/6.1=49 months
In 2012 there were approximately 8950 public librarys in the United States a survey found that 76% of the library's offered free access to the electronic books based on this information how many public library offered free access electronic books in 2012
Answer:
6,802
Step-by-step explanation:
Our first step is to change 76% into a decimal:
76% -> [tex]\frac{76}{100}[/tex] -> 0.76
Next, lets multiply and solve for x:
[tex]x=8,950(0.76)[/tex]
[tex]x = 6,802[/tex]
There were 6,802 public libraries that offered free access electronic books in 2012.
Answer:
6802 Libraries offered free electronic books.
Step-by-step explanation:
The yearly income I, in dollars, for the dairy comes from milk production, which depends on the number C of dairy cows. Each dairy cow produces 3500 gallons of milk per year, and the dairy sells milk for 2.00 per gallon. Find a formula that gives I as a linear function of C
Answer:
[tex]I=7000C[/tex]
Step-by-step explanation:
Let C represent number of dairy cows.
We have been given that each dairy cow produces 3500 gallons of milk per year. So amount of milk produced by C cows in 1 year would be [tex]3500C[/tex] gallons.
We are also told that the dairy sells milk for 2.00 per gallon. So yearly income I, in dollars for the dairy milk production would be 2.00 times the yearly milk production.
Since yearly milk production from C cows is [tex]3500C[/tex], so Income would be:
[tex]I=2.00(3500C)[/tex]
[tex]I=7000C[/tex]
Therefore, the formula [tex]I=7000C[/tex] represents yearly income (I) as a linear function of C.
Are the two cylinders similar? The diagrams are not drawn to scale.
a) no
b) yes
c) impossible to tell
for search: 8.32 10.192 2.6 3.64
thank you!
Answer:
a) no
Step-by-step explanation:
-The diagrams can be said to be mathematically similar if the dimensions of their corresponding sides enlarge or reduce by the same factor.
-We therefore determine the enlargement factor for both the radius and height as below:
-Let k be the scale factor
[tex]k_r=\frac{R}{r}\\\\=\frac{3.64}{2.6}\\\\=1.4\\\\k_h=\frac{H}{h}\\\\=\frac{10.192}{8.32}\\\\=1.225\\\\k_r\neq k_h[/tex]
Hence, the cylinders are not mathematically similar since the enlargment factors for the radius and height are not equal.
Answer:
Surface Area and Volume Unit Test
1. 14
2. hexagon
3. 224 m2
4. 896 pi in.2
5. 405 in.2
6. 49,009 m2
7. 4,910.4 yd3
8. 3.6 in
9. 4,608 cm3
10. 1,296 cm3
11. 1,442.0 yd3
12. 2,158 m2
13. no
14. 7 : 10
15. 100 m2
16. one-point perspective
17. 18.3 cm
Alice Jones worked 32 hours this week. She paid $4.00 per hour. She also earned $250 in tips. What is Alices gross pay for this week?
Answer:378
Step-by-step explanation:32 times 4=178 +250=378
Alice Jones's gross pay for the week is the sum of her hourly earnings ($128 from working 32 hours at $4.00 per hour) and her tips ($250), totalling $378.
To calculate Alice Jones's gross pay, we need to consider both her hourly wage and her tips. Alice worked 32 hours this week and was paid $4.00 per hour. This means her earnings from her hourly wage are:
32 hours times $4.00/hour = $128
Alice also earned $250 in tips. To find her gross pay for the week, we add her hourly earnings to her tips:
$128 + $250 = $378
Therefore, Alice's gross pay for the week is $378.
Half of m is greater than or equal to 50
Answer:1/2m>50
Step-by-step explanation:Put a line under the sign.
I need the coordinates for these
3x-2y=2
5x=5y+10
Answer:
solution is (-2, -4)
Step-by-step explanation:
I assume you want the solution?
so we want to find the intersection.
3x - 2y = 2
5x = 5y + 10
simplify the last equation
x = y + 2 by dividing out the 5
substitute
3*(y + 2) - 2y = 2
3y + 6 - 2y = 2
y + 6 = 2
y = -4
x = -4 + 2 = -2
solution is (-2, -4)
At the 2010 Winter Olympics in Vancouver, the top 8 countries got a total of 60 gold medals. Of the 60, Russia got 3 gold medals. Write and solve an equation to find what percent of the total gold medals, for the top countries, Russia got.
Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.
Let's denote the total number of gold medals obtained by Russia as [tex]\( x \)[/tex]. Since we know Russia got 3 gold medals, we have [tex]\( x = 3 \)[/tex].
Now, let's denote the total number of gold medals obtained by the top 8 countries (including Russia) as T. We're told that the total number of gold medals obtained by all top 8 countries combined is 60. Since Russia got 3 gold medals, the gold medals obtained by the other top 7 countries is [tex]\( T - 3 \)[/tex].
So, the percentage of gold medals obtained by Russia can be calculated as:
Percentage of gold medals obtained by Russia = [tex]\frac{\text{Number of gold medals obtained by Russia}}{\text{Total number of gold medals obtained by the top 8 countries}} \times 100\%\][/tex]
Substituting the known values:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{T} \times 100\%\][/tex]
We know that the total number of gold medals obtained by the top 8 countries is 60, so [tex]\( T = 60 \).[/tex] Substituting this into the equation:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{60} \times 100\%\][/tex]
Solving this equation:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{1}{20} \times 100\% = 5\%\][/tex]
So, Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.