Answer:
150
Step-by-step explanation:
We know that Scott's ratio of making the basket is 9/12. All we need to do is find out how many baskets he'll make if he attempts 200 shots.
So, 9/12 needs to become x/200. We don't know what x is yet, but there's a shortcut.
9/12 can be simplified by dividing 3 on the top and bottom.
9/12 ÷ 3/3 = 3/4
We can then see how many times 4 can go into 200.
200/4 = 50
So, we multiply 3/4 by 50 on both the top and bottom.
3/4 × 50/50 = 150/200.
So, if he attempts 200 shots then he'll make 150 of them.
Scott can expect to make approximately 150 baskets if he attempts 200 shots with his success rate being 9 out of 12, which equates to a 75% success rate.
Explanation:The question asks how many baskets Scott can expect to make if he tries 200 shots given that his average success rate is 9 out of 12. To find the answer, we can set up a proportion because Scott's shooting is a matter of probability and ratios. First, we determine Scott's success rate as a fraction: 9/12 which simplifies to 3/4 or a success rate of 75%.
Then, we apply this success rate to the new number of attempts (200) to find the expected number of successful baskets:
Expected number of baskets = Success rate x Total attemptsExpected number of baskets = (3/4) x 200Expected number of baskets = 150Therefore, if Scott attempts 200 shots, he can expect to make approximately 150 baskets.
A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?
The circumference of the circle is 23.89 ft
The circumference of a circle is the distance around it and it can be calculated by the formula:
Circumference = π x diameter
The circumference is therefore:
= 22/7 x 7.6
= 167.2 / 7
= 23.89 feet
The option given that is closest to 23.89 ft is the right answer.
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can you give a description of the relationship between the years since the tree was transplanted and its height in inches? if so what is it?
Answer:
The height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.Explanation:
Please, find attached an image with the table that accompanies this question.
1. Pattern
The table is:
Years: 2 4 5 8 9
Height (in.): 34 50 58 82 90
The most simple pattern is a linear pattern. A linear pattern has a constante rate of change.
The rate of change between two points is:
rate of change = change in the output / changee in the inputFind the rate of change for the data:
(50 - 34) in / (4 - 2) year = 16in / 2year = 8in/year(58 - 50) in / (5 - 4) year = 8in/1year = 8 in/year(82 - 58) in / (8 - 5) year = 24in / 3year = 8 in/year(90 - 82) in / (9 - 8) year = 8in / 1 year = 8 in/yearHence, the heigth and the years since the tree was transplantated show a linear relationship: every year the tree grew 8 inches.
2. Intial height:
You can find the initial height of the tree by using the rate of change of the height.
At year 2: height = 34 inchesAt year 1: height = 34 inches - 8 inches = 26 inchesAt year 0: height = 26 inches - 8 inches = 18 inches3. Relationship
You can describe the relationship in terms of the initial height and the numbers of years since the tree was transplantated.
Then, the height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.
You can even write an equation (function):
name H the height of the tree in inchesname y the number of years since the tree was transplantatedthe equation is: H = 18 + yWhen the turnpike littered the toll, traffic increased from 1,500 cars per day to 2,700
What was the percentage of the increase in traffic volume?
Answer:
80%
Step-by-step explanation:
The percentage change between two numbers can be calculated as ...
percentage change = ((new value)/(old value) -1) × 100%
= (2700/1500 -1) × 100% = (1.80 -1) × 100% = 80%
Traffic volume increased 80%.
Between the hours of 10PM and 6AM, the
temperature decreases an average of ¾ of a degree
per hour. How many minutes will it take for the
temperature to decrease by 5°F?
Final answer:
It will take 400 minutes for the temperature to decrease by 5°F, calculated by dividing 5°F by the rate of ¾°F/h, resulting in 6.6667 hours, which is then converted into minutes (6.6667 hours × 60 minutes/hour = 400 minutes).
Explanation:
To calculate the time it will take for the temperature to decrease by 5°F, knowing that the temperature decreases at a rate of ¾ of a degree per hour, we can use the following steps:
Divide the total desired temperature decrease (5°F) by the rate of temperature decrease per hour (¾°F/h).
Calculate the total hours required for a 5°F decrease.
Since we want to find the time in minutes, we multiply the hours by 60 (as there are 60 minutes in an hour).
Step 1: 5°F divided by ¾°F/h = 5 ÷ 0.75 = 6.6667 hours
Step 2: 6.6667 hours are needed.
Step 3: 6.6667 hours × 60 minutes/hour = 400 minutes
Therefore, it will take 400 minutes for the temperature to decrease by 5°F.
(PLEASE HELP THIS IS DUE IS 20 MINUTES, THERES ALSO TWO QUESTIONS)
1.) Micah has a garden. He constructs a scale model of the garden using the scale 1 inch: 2 feet. The garden has a length of 6 feet. What is the length of the garden in Micah’s model? (1 point show your work, 1 point correct answer)
2.)The figure on the left represents a scale drawing of the figure on the right. What is the scale? (2 pts. 1pt show work, 1 pt correct answer)
THE PICTURE IS FOR THE SECOND QUESTION
Answer:1. 3 inches
Step-by-step explanation:1 inch =2ft 2x3=6
To find the length of the garden in Micah's model, we need to set up a proportion using the given scale. The scale for the figure on the left to the figure on the right can be determined by comparing corresponding lengths.
Explanation:1.) To find the length of the garden in Micah's model, we need to use the scale 1 inch: 2 feet. Since the garden has a length of 6 feet, we can set up a proportion:
1 inch / 2 feet = x inches / 6 feet
Cross-multiplying, we get 2 feet * x inches = 1 inch * 6 feet
Simplifying, we have 2x inches = 6 inches, so x = 3 inches.
Therefore, the length of the garden in Micah's model is 3 inches.
2.) The scale of the figure on the left to the figure on the right can be determined by comparing the corresponding lengths. If we measure the lengths of a certain side of the left figure and the right figure, we can find the scale. For example, if the length of a side of the left figure is 2 cm, and the corresponding side on the right figure is 4 cm, the scale is 1 cm: 2 cm.
Therefore, the scale is 1 cm: 2 cm.
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which of the following is the graph of (g - f)(x)
Answer:
It's the third one
Guaranteed!!
Hence, the graph second is correct.
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here,
[tex]f(x)=-x\\g(x)=2x[/tex]
So,
[tex]g(x)-f(x)=2x-(-x)\\\\(g-f)(x)=2x+x\\\\(g-f)(x)=3x[/tex]
Draw the graph:-
Hence, the graph second is correct.
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Solve the equation 11x + 7 = 73?
Answer:
6
Step-by-step explanation:
11x + 7 = 73
- 7 - 7
11x = 66
divide 66 by 11 and you get 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Subtract 7 from both sides
11x + 7 - 7 = 73 - 7
11x = 66
Step 2: Divide both sides by 11
11x = 66
11x / 11 = 66 / 11
x = 6
Answer: x = 6
The farmer looks out in the barnyard and Cesar pigs and the chickens. He says to his daughter, “ I count 40 heads in 100 feet. How many pigs and how many chickens are out there?”
Answer:
There are 10 pigs and 30 chickens
Step-by-step explanation:
Let the number of pigs be x
let the number of chickens be y
Then there are 40 heads . So the total number of pigs and chickens is 40
x + y = 40-----------------------(1)
We know that pigs have 4 legs and chickens have 2 legs
4x + 2y = 100----------------------(2)
Solving (1) and (2)
multiply (1) by 2
2x + 2y = 80-------------------------(3)
subtract (3) from (2)
4x + 2y = 100
2x + 2y = 80
----------------------------
2x = 20
----------------------------
[tex]x = \frac{20}{2}[/tex]
x = 10
Now Substituting x in (1), we get
10 + y = 40
y = 40 - 10
y = 30
Find the volume of each figure
Mitchel owns a livestock trailer that can hold a maximum of 5,000 pounds. The average weight of each goat is 90 pounds, and the average weight of each calf is 360 pounds. Mitchel would like to know how many goats and calves he can transport in a single trip.
Mitchel can transport a 1:1 ratio of goats to calves in his livestock trailer, equating to 11 goats and 11 calves per trip, given their respective average weights of 90 and 360 pounds and the trailer's weight limit of 5000 pounds.
Explanation:Mitchel has a livestock trailer with a weight limit of 5,000 pounds. Given that each goat weights about 90 pounds and each calf about 360 pounds, we need to calculate how many of each animal the trailer can accommodate within its weight limit, while taking into account their average weights.
Let's look at one possible solution, using goats and calves in a 1:1 ratio. This would be 90 + 360 = 450 pounds per set of goat and calf. To fit within the trailer's weight limit, we then divide the total weight capacity by the weight of one set of animals: 5,000 / 450 = 11.11, which we round down to 11. This tells us that Mitchel can transport 11 goats and 11 calves in his trailer for each trip.
It's important to mention that this distribution can be adjusted according to need, as long as the total weight of the animals is kept below the trailer's weight limit.
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1/2 (5n-6) = -6(-2n-5)
a parking lot has total of 60 cars and trucks. the ratio of cars to trucks is 7:3 how many cars are in the parking lot. How many trucks are in the parking lot justify your anwsers
Which system of equations has no solutions...please help quick
For a system to have no solutions the lines must be parallel (they cannot intersect).
So the answer is the graph on the top right.
Answer: top right and bottom right
Step-by-step explanation:
For there to be a solution the lines have to cross at one time so when they are not touching there is no solution
Based on the given triangle, the cosine of the 30 degree angle is:
P.S.
It is not 1/3 (third option)
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Remember SOHCAHTOA
The cosine of an angle in a right triangle is the adjacent sides length divided by the hypotenuses length
In this case, for the angle 30 degrees, the adjacent length is [tex]\sqrt{3}[/tex] and the hypotenuse's length is 2
So, the cosine of the 30 degree angle is the first option:
[tex]\frac{\sqrt{3} }{2}[/tex]
evaluate 15/k when k=3 ?
15/k
15/3
5
Hope this helps! ;)
Answer:
5
Step-by-step explanation:
Since k=3 you would put 3 under 15. Now the equation would look like this: 15/3 instead of 15/k. Then you would divide 15 by 3 which is 5.
1.125 divided by (3/4) (3/4) +6(14/3)
What is the missing denominator in
the expression below?
Answer:
The denominator should be 3. Hope this helps.
the base of parellogram is twice its height . if the area is 648msq find its base and height
Answer:
h=18m, b=2m
Step-by-step explanation:
Let the base be b and height be h
Condition 1:
b=2h ----(1)
Condition 2:
Area=b*h
b*h=648 -----(2)
Putting (1) into (2)
2h*h=648
2h^2=648
Dividing both sides by 2
h^2=324
Taking sq root on both sides
h=18 m
Now
Putting value of h in eq (1)
b=2(18)
b=36 m
A car was purchased for $39150.00 and is expected to be worth $10800.00 in 9 years. Determine the rate at which the van depreciates in value.
Answer:
The annual rate of depreciation of the car is 8.05% or 72.41/9
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Price of the purchase of the car = $ 39,150
Price after 9 years = $ 10,800
2. Determine the rate at which the van depreciates in value.
Let's calculate what is the percentage of depreciation after 9 years, this way:
Percentage of depreciation after 9 years = [1 - (Price after 9 years/Price of the purchase of the car)] * 100
Replacing with the values we know:
Percentage of depreciation after 9 years = [1 - (10,800/39,150)] * 100
Percentage of depreciation after 9 years = [1 - 0.2759] * 100
Percentage of depreciation after 9 years = 72.41%
Annual rate of depreciation = 72.41/9 = 8.05%
-37=x-9.9 , what’s the value of x ?
Answer:
x= 3.73737373737......
Step-by-step explanation:
To find x, divide -9.9 to both sides.
-37 = x-9.9
-9.9 -9.9
3.73737373737...= x
This is a repeating decimal.
Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a. 1 and b.
1?
log,
logo
logna
logna
logo
log,
log,b
logo
logo
Save and
Next
Submit
Step-by-step explanation:
We have,
[tex]\log _{a}x[/tex]
To find, the value of [tex]\log _{a}x[/tex] = ?
∴ [tex]\log _{a}x[/tex] , where a, b and x are positive
a ≠ 1 and b ≠ 1
We know that,
The logarithm identity,
[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]
∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Where, b is the common base of logarithm
∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.
A store offers a discount of 30 % on all refrence of books. If a dictionary cost $12 before the discount what is the dollar amount of the discount.
Answer:
3.6
Step-by-step explanation:
30%×12= 3.6
30%=0.3
A rectangle has a perimeter of 25 meters. If the lengths of the sides of the rectangle are multiplied by 7 to make a new rectangle, what is the perimeter of the new rectangle?
Answer:
175 m
Step-by-step explanation:
We are given;
The perimeter of a rectangle as 25 mWe are required to determine the new perimeter if the sides of the rectangle are multiplied by 7.
We know that;
Perimeter of a rectangle = 2(L+W)
Therefore, initially;
2(L+W) = 25 m
Hence;
L + W = 12.5 m
if the sides are multiplied by 7, then;
New length = 7L
New Width = 7W
Thus;
New perimeter = 2(7L+7W)
= 14 (L + W)
but, L + W = 12.5
Thus;
New perimeter = 14 (12.5)
= 175 m
Therefore, the new perimeter will be 175 m
Answer:
The answer to the problem is 175
Step-by-step explanation:
Graph f(x)=3sin(12x)−5 . Use 3.14 for π .
Answer:
see attached
Step-by-step explanation:
The given function is a vertical expansion of the sine function by a factor of 3 and a translation downward by 5 units.
It will oscillate between -8 and -2, with a midline at y = -5. The multiplier 12 indicates the period of the function will be 2π/12 = π/6 ≈ 0.5233... for the given value of π.
A graphing calculator is a useful tool for creating the graph.
Answer:
Step-by-step explanation:
took the test
Choose the correct simplification of (xy2z)3.
xy2z3
x3y6z3
x3y8z3
x4y5z4
Answer:
[tex]x^3y^6z^3[/tex]
Step-by-step explanation:
we have
[tex](xy^2z)^3[/tex]
Applying the property of exponents
[tex](x^m)^n=x^{m*n}[/tex]
[tex](xy^2z)^3=(x^3)(y^2)^3(z^3)=x^3y^{2*3}z^3=x^3y^6z^3[/tex]
The correct simplification of [tex]\((xy^2z)^3\) is \(x^3y^6z^3\).[/tex]
To simplify the expression [tex]\((xy^2z)^3\),[/tex] you need to raise each component within the parentheses to the power of 3.
[tex]\(x^3\)[/tex] represents \(x\) raised to the power of 3, [tex]\(y^{2 \times 3}\)[/tex] represents [tex]\(y^6\)[/tex] (since you multiply the exponents when raising a power to a power), and [tex]\(z^3\)[/tex]represents \(z\) raised to the power of 3.
So, [tex]\((xy^2z)^3\) simplifies to \(x^3y^6z^3\).[/tex]
The given options are:
[tex]a) \(x^3y^3z^3\)\\b) \(x^3y^6z^3\)\\c) \(x^3y^8z^3\)\\d) \(x^4y^5z^4\)[/tex]
Comparing the simplified expression [tex]\(x^3y^6z^3\)[/tex] with the options, the correct answer is option (b) [tex]\(x^3y^6z^3\).[/tex]
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If 10% of 60 is 6, what is 5% of 60?
Explain how you found your answer
Answer:
3
Step-by-step explanation:
If we already know that 10% of 60 is 6 and that 5% is one half of 10%, we can just divide the 10% value by two to find the 5% of 60.
7/10×1/2 please help me
Answer:
7/20
Step-by-step explanation:
7/10 * 1/2
By multiplying
7/20
0.35
Answer: 7/20 or .35
Step-by-step explanation: .7 times .5 is .35
What is an equation of the line that passes through the point (3,6) and is parallel to the line 2x+3y=21
Answer: y= -2/3+8
Step-by-step explanation:
solve x+3y=-28
y=-5x using substitution
Answer:
Step-by-step explanation:
x + 3y = - 28
y = -5x
x + 3(-5x) = -28
x -15x = -28
-14x=-28
x=2
y = -5(2)
y=-10
An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, she can buy 2 stone spheres and 6 stone cylinders. If one stone cylinder costs $36.81, how much does each stone sphere cost?
The cost of each stone sphere is $ 36.81
Solution:
Given that,
An architect plans to buy 5 stone spheres and 3 stone cylinders
For the same amount, she can buy 2 stone spheres and 6 stone cylinders
Let "x" be that same amount
Let "a" be the cost of each stone sphere
Cost of each stone cylinder = $ 36.81
Therefore,
x = 5 stone spheres and 3 stone cylinders
x = 5a + 3(36.81)
Similarly,
x = 2 stone spheres and 6 stone cylinders
x = 2a + 6(36.81)
Equate both,
[tex]5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81[/tex]
Thus cost of each stone sphere is $ 36.81
By setting up and solving equations based on the given scenarios, we find that the cost of each stone sphere is also $36.81, the same as one stone cylinder.
Explanation:Let's denote the cost of one stone sphere as S and the cost of one stone cylinder as C. We know one stone cylinder costs $36.81. We are given two scenarios involving the purchase of stone spheres and cylinders with equal total cost. In the first scenario, 5 stone spheres and 3 stone cylinders are bought, and in the second, 2 stone spheres and 6 stone cylinders are purchased.
Formulating these scenarios into equations gives us:
5S + 3C = 2S + 6CConsidering C = $36.81Substituting the value of C into the equation simplifies it to:
5S + 3(36.81) = 2S + 6(36.81)
Simplifying further:
5S + 110.43 = 2S + 220.86
Subtracting 2S and 110.43 from both sides results in:
3S = 110.43
Dividing both sides by 3 gives:
S = $36.81
Therefore, each stone sphere also costs $36.81.