Final answer:
The approximate square root of 48 is found by locating it between the perfect squares of 36 (6²) and 49 (7²), leading to a closer estimation of about 6.9 when considering 48 as 16 * 3 and simplifying.
Explanation:
The question asks to find the approximate square root of 48. To do this, we first recognize that the exact square root of 48 is not a whole number, and therefore, we need to find two perfect squares between which 48 lies. The perfect squares closest to 48 are 49 (7²) and 36 (6²). Since 48 is closer to 49, we can estimate that the square root of 48 is slightly less than 7. A more refined method involves thinking of 48 as 16 * 3, which then gives us √16 * √3 = 4√3. Knowing that √3 is approximately 1.732, we can multiply this by 4 to get an approximation of 6.928. Therefore, a good approximation for the square root of 48 is approximately 6.9.
Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one of the two cards is a face card (Jack, Queen, or King)? (Give the answer as a decimal rounded to three decimal places.)
The probability of drawing at least one face card when drawing two cards with replacement from a standard deck is approximately 0.407.
Explanation:The student is asking for the probability of drawing at least one face card (Jack, Queen, or King) when drawing two cards with replacement from a standard deck of 52 cards. To find this, we can use the complement rule: subtract the probability of not drawing a face card in both draws from 1. There are 12 face cards in a deck of 52 cards, so the probability of drawing a non-face card (event N) on one draw is 40/52 (since there are 40 non-face cards).
Using the complement rule:
Calculate the probability of drawing a non-face card both times: P(NN) = (40/52) * (40/52).Subtract the above probability from 1 to get the probability of at least one face card: P(at least one F) = 1 - P(NN).Now perform the calculations:
P(NN) = (40/52) * (40/52) = 0.5929 (approximately).
P(at least one F) = 1 - 0.5929 = 0.4071 (rounded to three decimal places).
Therefore, the probability of drawing at least one face card in two draws with replacement is approximately 0.407.
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!
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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You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 6 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer.
Answer:
try 45
Step-by-step explanation:
The water level rises at a rate of approximately 2.83 cm per minute. Therefore, the water level would be approximately 34 cm after 12 minutes.
Explanation:This problem involves the concept of linear relationships and slopes in mathematics. Given that the water level rises by 17 cm every 6 minutes, we can find the rate of increase per minute by dividing 17 cm by 6 minutes. This value, approximately 2.83 cm/minute, is the slope of the linear relationship.
This means each additional minute increases the water level by about 2.83 cm. If we denote the time as x and the water level as y, the linear equation expressing this relationship can be written as y = 2.83x.
To find the value of y when x (time) is 12 minutes, we substitute x = 12 into this equation. So, y = 2.83 * 12 = 33.96 cm. Therefore, the water level would be close to 34 cm after 12 minutes.
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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)
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:
1) y varies directly with x. If y = -4 when x = 2, find y when x = -6.
Answer:
-12
Step-by-step explanation:
2 - -4 = 6 --> y + 6 = x
x = -6, so subtract 6 from x to find y
-6 - 6 = -12
y = -12
Does that help?
To find y when x = -6, given that y varies directly with x and y = -4 when x = 2, we first calculate the proportionality constant k, and then use it to find the new value of y.
Explanation:If y varies directly with x, this means that y can be expressed as y = kx, where k is the proportionality constant. Given that y = -4 when x = 2, we can first find the value of k by substituting these values into the direct variation equation:
-4 = k(2)
From this, we can solve for k:
k = -2
Now, to find y when x = -6, we substitute -6 for x in the original direct variation equation y = kx, using our found value of k:
y = (-2)(-6)
y = 12
Therefore, when x = -6, y will be 12.
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PLEASE HELP !!!! Solve the system using either substitution or elimination: 3x+6y=6 x-5y=23
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: ( 8 , − 3 ) Equation Form: x = 8 , y = − 3
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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.
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]
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
Check whether (5,12,13) forms a pythagorean triplet.
Write each equation in logarithmic form.
Answer:
B) [tex]log_3 81=4[/tex]
Step-by-step explanation:
The definition of logarithm is the following:
The logarithm of a certain number x with respect to a certain base b is the exponent by which b should be raised in order to give x. Mathematically, given the equation
[tex]b^y = x[/tex] (1)
The logarithm of x to base b is defined as
[tex]y=log_b x[/tex] (2)
In this problem, we have the following equation:
[tex]3^4=81[/tex]
By comparing it with equation (1), we notice that:
b = 3
y = 4
x = 81
Therefore, by re-arranging the variables using equation (2), we can rewrite it as:
[tex]4=log_3 81[/tex]
Which corresponds to option B.
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:
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.
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
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
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:
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
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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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
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,
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.
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:
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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Half of m is greater than or equal to 50
Answer:1/2m>50
Step-by-step explanation:Put a line under the sign.
What is the answer please
Answer:
(-12, 9)
Step-by-step explanation:
Trina makes 3 retanglular quilts for her grandchildren. The first measures 70 inches by 90 inches. She enlarges these dimensions by a scale factor of 1.2 to make a second quilt. Then she enlarges the dimensions by a scale factor of 1.5 to make the third quilt. What are the dimensions of the third quilt?
Answer:
8.2, 105.00
Step-by-step explanation:
Take the first measures and add the enlargements to get the dimensions of the third quilt. This probably is wrong I just had to answer a question
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.
Assignment
Active
Applying Properties of Congruent Prisms
The volume of one prism is known, along with the height For the two prisms to be congruent, what must the area
of another prism. The values are shown below.
of the base be, given that the triangular bases are
congruent?
3 in 2
6 in?
12 in 2
15 in 2
15 in
V = 90 in.
Intro
Done
Answer: 6 in ^2
Step-by-step explanation:
The shapes are congruent, so all the given values have to apply to both shapes. Keeping this in mind, the only answer that works is 6in^2.