If there is no picture for the spinner and we assume that it is completely fair, meaning that you have an equal chance of landing on any spot: You will expect to get a certain color every 3 spins because you have 3 different colors. In this case the answer would be 20 pupcakes.
A 12 inch line segment is divided into two parts. Which of the following lengths result in a ratio closest to the golden ratio, 1+√5/2 ?
The lengths of segment which is the part of a 12 inch line segment closest to the golden ratio, (1+√5)/2 are 7.4166 inch and 4.5834 inch.
What is the value of golden ratio?The value of golden ratio is equal to 1.618. It can also be given as (1+√5)/2.
A 12 inch line segment is divided into the two parts in a particular ratio. Let suppose the line segment is AC which is divided into AB and BC parts. Thus,
AB+BC=AC
AB+BC=12 ....1
The ratio of both segment is equal to golden ratio. Thus
[tex]\dfrac{AB}{BC}=\dfrac{AC}{AB}=\dfrac{1+\sqrt{5}}{2}\\\dfrac{12}{AB}=1.618\\AB=7.4166 \rm\; in[/tex]
Put this value in equation one as,
AB+7.4166=12
AB=4.5834
Hence, the lengths of segment which is the part of a 12 inch line segment closest to the golden ratio, (1+√5)/2 are 7.4166 inch and 4.5834 inch.
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It is said that once a Chinese emperor decided to divide a number of horses among his generals such that
(a) if they are divided equally among 3 of his generals, 2 horses will remain;
(b) if they are divided equally among 5 of his generals, 1 horse will remain;
(c) and if they are divided equally among 7 of his generals, 6 horses will remain.
I. Find the smallest number of horses that satisfies this condition.
II. Write an explicit rule for each of part (a), (b) and (c).
III. Write an explicit rule for the number of horses that can be divided in such a way.
IV. Write a recursive rule for the explicit rule found in part III.
Using the three conditions, the smallest number of horses that can be shared among the generals is 41
The smallest number of horsesThe conditions are given as:
A remainder of 2, if divided among 3 generalsA remainder of 1, if divided among 5 generalsA remainder of 6, if divided among 7 generalsThe numbers that can divide 5 and leave a remainder of 1 are:
11, 16, 21, 26, 31, 36, 41, 56, 61, 66, 71......
Of all these numbers, the smallest number that satisfy the three conditions is: 41
i.e.
41/3 = 13 R 2
41/5 = 8 R 1
41/7 = 5 R 6
Hence, the smallest number of horses is 41
The explicit rule for each conditionLet the number of horses a general gets be x.
The explicit rule for each condition can be represented as:
Condition (a): Total = 3x + 2Condition (b): Total = 5x + 1Condition (c): Total = 7x + 6The explicit and the recursive ruleUsing the condition (b), we have:
Total = 5x + 1
Rewrite as a function
f(x) = 5x + 1
When x = 0, we have:
f(0) = 1
For other values of x, we have:
f(1) = 6
f(2) = 11
f(3) = 16
Rewrite as:
f(0) = 1
f(1) = 5 + 1 = 5 +f(0)
f(2) = 5 + 6 = 5 + f(1)
f(3) = 5 + 11 = 5 + f(2)
Express 2 as 3 - 1
f(3) = 5 + f(3 - 1)
Express 3 as x
f(x) = 5 + f(x - 1)
Hence, the recursive function is f(x) = 5 + f(x - 1) where f(0) = 1
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The linear equation y = 30x describes how far from home Traci is as she drives from Dallas to Anchorage. Let x represent the number of hours and y represent the number of miles. How far from home is Traci in 12 hours? Is the equation linear, or not?
Traci will be 360 miles in 12 hours if the linear equation y = 30x describes how far from home Traci is as she drives from Dallas to Anchorage and the equation of the graph is linear.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation:
y = 30x
Here, x represent the number of hours and y represent the number of miles.
When x = 12 hours then
y = 30(12) = 360 miles
If draw the graph the equation y = 30x, it will be a linear equation.
(refer attached picture)
Thus, Traci will be 360 miles in 12 hours if the linear equation y = 30x describes how far from home Traci is as she drives from Dallas to Anchorage and the equation of the graph is linear.
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Which fraction correctly represents one whole? 1/7 3/7 7/7 and 7/1
WILL GIVE BRAINLIEST
Answer: 7/7
Step-by-step explanation:
7/7 simplifies to 1/1 which is equal to one. One is the same as one whole, so this is the answer to our question.
7/1 is also wholes but it is seven wholes, not one.
[tex]\displaystyle \frac{7}{7} =\frac{1}{1}=1[/tex]
Answer:
7/7
Step-by-step explanation:
If the numerator matches the denominator, then it is one whole.
Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for asparagus,S for Shrimp, B for Bacon, F for French, and V for Vinegrette. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: mushrooms, asparagus. Also you will addone of the following meats: Shrimp, bacon. Lastly, you will decide on one of the following dressings: French, vinegrette.
Answer: {(MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)}
Step-by-step explanation:
Sample space is a set that contains all the possible outcomes for an event.For salad:
Choices for extra toppings (mushrooms, olives) =2
Choices for meats (bacon, eggs) =2
Choices for dressings (vinaigrette, honey mustard.)= 2
By Fundamental counting principal .
The number of different salads can be made= (Choices for extra toppings) x (Choices for meats ) x (Choices for dressings)
= 2 x 2 x 2 = 8
All the possible outcomes = (MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)
Required Sample space would be : {(MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)}
Solve |7x +42| = 14x. Identify the solution and an extraneous solution.
A. Solution: x = -2;
extraneous solution: x = 6
B. Solution: x = 6;
extraneous solution: a = -6
C. Solution: x = 6;
extraneous solution: x = -2
D. Solution: x = = 2;
extraneous solution: a = -6
First Case
[tex]|7x+42|=14x\\\\7x+42=14x\\\\42=7x\\\\6=x[/tex]
Second case
[tex]-|7x+42|=14x\\\\-7x-42=14x\\\\-42=21x\\\\-2=x[/tex]
Verify into first case
[tex]|7(6)+42|=14(6)\\\\|84|=84\\\\84=84\\\\LS=RS[/tex]
[tex]|7(-2)+42|=14(-2)\\\\28\neq -28\\\\LS\neq RS[/tex]
The solution is 6 and the extraneous solution is -2, which makes the answer C.
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
A. [tex]\frac{x}{9} + \frac{x}{8} = 1[/tex]; 2.18 hours
B. [tex]\frac{1}{9} + \frac{1}{8} = \frac{1}{x}[/tex]; 3.73 hours
C. [tex]\frac{9}{x} + \frac{8}{x} = 1[/tex]; 8.5 hours
D. [tex]\frac{x}{9} + \frac{x}{8} = 1[/tex]; 4.24 hours
Answer:
D 4.24
Step-by-step explanation:
Assume the area of room be A
Irina painting speed be x, 8x = A
Paulo painting speed be y, 9y = A
Together painting speed = x + y = A/8 + A/9
Assume together painting time = t
(A/8 + A/9) t = A
(1/8 + 1/9)t = 1
17t = 72
t = 4.24
Which statement best describes the streams on either side of the Great Divide?
They feed different water sheds.
They channel rain to the Pacific Ocean.
They flow into the same drainage basin.
They have some of the same large rivers.
Explanation:
The Great Divide commonly refers to the continental divide of North America. The watersheds of the Pacific Ocean are separated from the Atlantic Ocean by the Great Divide. Green River watershed is located to the west of the endorheic basin, and it is drained to the Gulf of California/Pacific Ocean.
The water flowing to the Pacific Ocean is separated from the water flowing to the Southern and Indian Oceans. Various
water sheds can be efficiently fed through Great Divide.
The water is gathered and depleted into water bodies like waterway, lake or stream correct answer is option C i.e. They flow into the same drainage basin.
What is the purpose of drainage i the Great Divide??The land region which gathers water is likewise called a drainage bowl or catchment region. It monitors water, advances the proceeded with stream of the waterway. It helps in the amassing of groundwater, empowers solid soil and furthermore gives territory to untamed life and plants.
Here, we have,
A drainage bowl addresses the land region which is contributing water to a stream. The water commitment can be straightforwardly toward a solitary stream, or toward a few streams that stream into a bigger, focal stream.
Fundamentally, the drainage bowl has a stream going through it, in its least part. The land is getting on rise to the side structure the stream, and the edges of the slopes or mountains are making up its limits.
The water is gathered and depleted into water bodies like waterway, lake or stream correct answer is option C i.e. They flow into the same drainage basin.
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Use the t-distribution to find a confidence interval for a difference in means μ1−μ2 given the relevant sample results. Give the best estimate for μ1−μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.
A 99% confidence interval for μ1−μ2 using the sample results x⎯⎯1=535, s1=103, n1=380 and x⎯⎯2=465, s2=86, n2=200
Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.
The best estimate and the degree of freedom when the t-distribution is used to find a confidence interval is 7 and 56 respectively.
How to illustrate the research?The best estimate from the information given in the research will be:
= X1 - X2
= 53.5 - 46.5
= 7
The degree of freedom will be:
= 38 + 20 - 2
= 56
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A pet store has three fish tanks each holding a different volume of water in a different number of fish to a holds 4 L and five fish tank bee holds 100 L in office tanks tea or 108 L and 23 fish. order the tanks by volume per fish from least to greatest.
Write out the sample space for the given experiment. Use the letter R to indicate red, G to indicate green, and B to indicate blue. A die shows 3 different colors on it. Give the sample space for the next 2 rolls. separate your answers using commas
Answer:
{RR,RG,RB,BR.BB BG,GR,GB,GG}
Step-by-step explanation:
It can be calculated by,
[tex]n^2=3^2=9[/tex]
{RR,RG,RB,BR.BB BG,GR,GB,GG}
In June Gemma paid £68 for her electricity.
In July she will pay 5% more for her electricity.
Work out how much Gemma will pay for her electricity in July.
A company made a bar graph showing the amount of sales for each month in thousands of dollars. Which of the following is closest to the mean amount of sales for the four-month period?
A.
$5,250
B.
$6,250
C.
$6,375
D.
$5,750
Answer:
The answer is A.
In May, there were about 5,500 dollars in sales.
In June, there were 8,000 dollars in sales.
In July, there were about 2,500 dollars in sales.
In August, there were 6,000 dollars in sales.
To find the range, subtract the smallest amount from the largest amount.
$8,000 - $2,500 = $5,500
Therefore, the range is $5,500.
Answer: 6,375
Step-by-step explanation:
The HCF of 12, 8 ,32 is?
Answer:
4
Step-by-step explanation:
Prime factorizing all terms :
12 = 2² x 38 = 2³32 = 2⁵The highest common factor (HCF) shared by the 3 numbers is :
2²4Hence, HCF (12, 8, 32) = 4
Students at a school will sell hats to raise money. There are some hats left over from last year, and 20 boxes of hats will be ordered this year. When the order arrives, the total number of hats the student will have can be determined using the function f(x) = 48x + 37, where x represents the number of boxes ordered. If the number of hats per box changes so that the situation is modeled by the function h(x) = 24x + 37, then how many fewer hats will the students have available to sell if they still order 20 boxes?
A)517
B)480
C)997
D)365
Answer: A) 480
Step-by-step explanation:
x=20 substitute in the two equations
48(20)+37
24(20)+37
since the question said fewer , then you should subtract
48(20)+37 - 24(20)+37 = (960+37) - (480+37)
=923 - 443= 480
Students will have 517 hats to sell, that is 480 fewer than determined.
The correct option is B.
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Given,
Total hats = Left hats of last year + 20 boxes of hats newly ordered
Total hats
f(x) = 48x + 37
where x is number of boxes
But number of hats per box changes,
h(x) = 24x + 37
fewer no. of hats than determined
f(x) - h(x) = 48x + 37 - 24x - 37
f(x) - h(x) = 24x
No. of boxes = 20
No. of hats fewer than determined = 24 × 20 = 480
And no. of hats available
h(20) = 480 + 37
h(20) = 517
No. of hats available to sell = 517
Hence, 517 hats are available to sell that is 480 fewer hats than determined
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The rectangular prism shown below has a volume of 42 cubic meters what is the length of the prism
Answer:
3m
Step-by-step explanation:
From the diagram,
height = 7m
Width = 2m
Given that the volume of prism = 42 cubic meters = 42m³
Length of prism = ?
Inserting the values of the variables:
42 = l×2×7
42 = 14×l
l = 42/14
l = 3
The length of the prism = 3m
Help asap pleaseeeeeeeee
Answer:
√5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{5\div \sqrt{5}}[/tex]
Which can be rewritten as:
[tex]\displaystyle \large{\dfrac{5}{\sqrt{5}}}[/tex]
To find:
Simplified formTo find simplified form of the expression, keep in mind that surds should not remain as denominators. Therefore, what we have to do is to multiply both numerator & denominator by the surd itself so the denominator will be cleared as rational number.
[tex]\displaystyle \large{\dfrac{5\cdot \sqrt{5}}{\sqrt{5}\cdot \sqrt{5}}}[/tex]
We know that if same surds multiply each other, the surd will be canceled and remains only the insides. To express it in math, it can be as:
[tex]\displaystyle \large{\sqrt{a}\cdot \sqrt{a} = \left(\sqrt{a}\right )^2 =a}[/tex]
Therefore:
[tex]\displaystyle \large{\dfrac{5\sqrt{5}}{5}}[/tex]
Cancel 5:
[tex]\displaystyle \large{\sqrt{5}}[/tex]
Henceforth, the simplified expression is √5
Can y'all please help me with this? Thanks.
Answer:
j : 7327
Step-by-step explanation:
Split the figure into three parts 1 cylinder and hemispheres.
find the volume of each part and then in the end add them
Vol of cylinder =
[tex]\pi \times r {}^{2} \times h \\ 3.14 \times 10 \times 10 \times 10 \\ = 3140 \\ [/tex]
Find the volume of one hemisphere=
[tex] = \frac{2}{3} \pi \times r {}^{3} \\ 2093.33[/tex]
Vol of 2 hemispheres = 2×2093.33
= 4186.66667
Total volume= 3140 + 4186.6667 = 7326.66
= 7327
Find x. Round to the nearest tenth:
IMPORTANT!!!! PLS ANSWER FAST!!
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=-16x^2+198x+148
Answer:
yes i think
Step-by-step explanation:
What of the following functions is graphed below?
Answer:
Your answer is D. y = |x + 3| - 4
Step-by-step explanation:
Looking at the graph there seems to be only translations shift. There is no vertical stretch/shrink or Horizontal stretch/shrink
Absolute formula: y = |x - h| + k
Your (h,k) = (-3, -4) plug them into the absolute formula.
y = |x - (-3)| + (-4)
y = |x + 3| - 4
A survey of 100 high school students provided this
frequency table on how students get to school:
Drive to Take the
Grade
Walk
School bus
Sophomore 2
25
3
3
Junior
13
20
2
Senior
25
5
5
a
What is the probability that a randomly selected student
is a junior?
?
P(Junior)
=
Probability helps us to know the chances of an event occurring. The probability that a randomly selected student is a junior is 0.35.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability that a randomly selected student is a junior will be,
P(Junior) = [(Number of Juniors)\(Number of total students)]
P(Junior) = 35/100 = 0.35
Hence, The probability that a randomly selected student is a junior is 0.35.
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The sum of two numbers is negative thirty-two. One number is two less than the other.
Call the numbers m and n
Answer:
-17 + -15 = -32
Step-by-step explanation:
-15 is two less than -17
-17 can be m and -15 can be n and vice versa.
*REMEMBER WHEN ADDING NEGATIVE NUMBERS, ADD THEM BUT MAKE SURE THE OUTCOME IS NEGATIVE*
What value is an irrational number
Answer: Choice A
Explanation:
The number [tex]\sqrt{8}[/tex] is irrational. We cannot write it as a ratio or fraction of two integers. This is because 8 isn't a perfect square.
Multiplying any irrational number with a rational one leads to an irrational product.
In short:
irrational*rational = irrational
Therefore, the perimeter [tex]4\sqrt{8}[/tex] is also irrational.
Jessie finishes 2/5
of the problems on her homework before dinner. She finishes
another 3/10
of the problems on her homework after dinner. What fraction of the
problems on her homework does Jessie still have left to do?
Answer: Jessie still has 3/10 left.
Step-by-step explanation:
Convert 2/5 into tenths by multiplying by 2.
2/5 x 2 = 4/10
3/10 + 4/10 = 7/10
The entirety of her homework is 10/10 so do
10/10 - 7/10 = 3/10
She has 3/10 left.
What are the values of a, and r of the geometric series?
2-2 + 2-2 +2
-
O a = 2 and r=-2
a
O a = -2 and r= 2
O a = -1 and r= 2
O a = 2 and r=-1
The values of a and r is 2 and -1 respectively in the geometric series.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given geometric series is 2-2 + 2-2 +2-
A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index.
In the given series the first term is a and common ration is r
The common ratio is the number you multiply or divide by at each stage of the sequence.
r=-2/2 = -1
a , first term is 2
Hence, the values of a and r is 2 and -1 respectively in the given geometric series.
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NO LINKS!! Please help me with this problem. Part 2.
Answer:
g(x) = 10(x +1)² +5
Step-by-step explanation:
When a point is translated 3 units down, its y-value is 3 less than it was. The graph of f(x) is translated 3 units down by subtracting 3 from the value of f(x).
g(x) = f(x) -3 . . . . . translates f(x) 3 units down
__
For f(x) = 10(x +1)² +8, we want ...
g(x) = f(x) -3 = (10(x +1)² +8) -3
g(x) = 10(x +1)² +5
Translation of 3units down means change in y axis
y is decreased by 3
Hence new equation
g(x)=10(x+1)²+8-3g(x)=10(x+1)²+5Solve 2x+4<6
I have no clue
Why did you delete my answer
17) Which property is represented below?
6. (3 + 8) = 6:3+ 6.8
A. Commutative property of multiplication
O B. Distributive property
O C. Zero product property
D. Additive identity property
Answer:
Distributive Property
Step-by-step explanation:
It looks like you are multiplying the 6 to both the 3 and 8.
Blake was born in Minnesota, but now he lives in lowa, close to where lowa,
Wisconsin, and Illinois meet. He works in Illinois, but he buys all of his clothes
at a store in Wisconsin. If the sales tax rates for the four states are as shown
in the following table, which sales tax rate does Blake pay on the clothes he
buys?
The sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%
What is sales tax rate?The sales tax rate is the rate at which the sales tax is applied.
Total payable amount = Original amount + sales tax on that amount.
We are given that:
He(Blake) works in Illinois, but he buys all of his clothes at a store in Wisconsin.
So, the sales tax rate will be applied according to the rate of Wisconsin.
From the table, we see that the sales tax rate of Wisconsin is 5%.
Thus, the sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%
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Answer:
5%
Step-by-step explanation: