Answers
diag d = √(6²+6²) = 6√2 in
The diagonal is also the diameter of the circle! So the radius of the circle is half of that:
radius r = d/2 = 3√2 in
The area of the circle is πr² = π(3√2)² = 18π in²
Related Questions
Coffee with sugar and milk added to it can contain up to calories. To consume a maximum of 600 mg if caffeine per day, how many full eight-ounce servings of a name-brand coffee with 330 mg of caffeine per 16-ounce serving could someone drink in a day and still stay below this limit? full 8-ounce servings
Answers
330 mg : 2 = 165 mg
Also we have to consume a maximum of 600 mg.
165 mg * 3 = 495 mg < 600 mg
165 mg * 4 = 660 mg > 600 mg
Answer: Someone could drink 3 full 8-ounce servings in a day and still stay below the limit.
Answer:
A) 500
B) 3
Right on edge
Step-by-step explanation:
Megumi earned a salary of $39,312 last year. How much did she earn per month
Answers
2 months in a year
39312/12 = 3276 per month
Answer:
She earned $ 3,276 per month.
Step-by-step explanation:
We know that,
1 year = 12 months,
Given,
Megumi earned a salary of $39,312 last year
⇒ His salary of one year = $ 39,312
⇒ Salary of 12 months = $ 39,312
[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]
Hence, she earned $ 3,276 per month.
HELP!! PLEASE A carpenter is framing a window with wood trim where the length of the window is 9 and 1/3 feet. If the width of the window is 6 and 3/ 4 feet, how many feet of the wood is needed to frame the window? Write your answer as a proper or improper fraction
Answers
The window is in the shape of a rectangle with the height of [tex]9 \frac{1}{3} [/tex] feet and width of [tex]6 \frac{3}{4} [/tex]. The diagram of the shape is shown below
The perimeter of a shape is obtained by adding up the length of all the sides that form the shape.
The perimeter of the window is [tex]9 \frac{1}{3}+9 \frac{1}{3}+6 \frac{3}{4}+6 \frac{3}{4} [/tex] = [tex]18 \frac{2}{3}+12 \frac{6}{4} [/tex]
We have two whole numbers 18 and 12 and two fractions [tex] \frac{2}{3} [/tex] and [tex] \frac{6}{4} [/tex]
Adding the two fractions that have different denominator
[tex] \frac{2}{3}+ \frac{6}{4} = \frac{8}{12}+ \frac{18}{12}= \frac{26}{12} [/tex], which is an improper fraction which we can change into a mixed number [tex]2 \frac{1}{6} [/tex]
So the perimeter of the window is
[tex]18+12+2 \frac{1}{6} =32 \frac{1}{6} [/tex]
and the length of wood needed for the frame is [tex]32 \frac{1}{6} [/tex] feet
Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).
A. y + 3 = −5(x − 2)
B. y − 2 = −5(x + 3)
C. y + 3 = −one fifth(x − 2)
D. y − 2 = −one fifth(x + 3)
Answers
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=2\\ x_1=-3\\ m=\boxed{?} \end{cases} \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}[/tex]
For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. 115 128 107 109 116 124 135 127 115 104 118 126 129 133
Answers
STEP 1: Work out the mean of data set
μ = Sum of values in the set ÷ Number of values in the set
μ = 1686 ÷ 14
μ = 120.4 (rounded to one decimal place)
STEP 2: Subtract the mean from each value in the data set, and then square each answer. The table attached below shows the details of the calculation
STEP 3: Add the answers in STEP 2, then divide by 13.
Note: we divide by 13 instead of 14 because our data set is a sample set.
(∑x₁-μ)/13 = 1253.44÷13 = 96.42
The value obtained in STEP 3 is the variance. To obtain the standard deviation, we square root the variance
s = √96.42 = 9.819 (rounded to three decimal places)
----------------------------------------------------------------------------------------------------------------
We want to test the claim that the standard deviation of IQ scores of college students is less than 15. Putting this in the form of hypotheses we get:
H₀: σ=15
H₁: σ<15
The significance level, α, is 0.10
The degrees of freedom, v, is 14 - 1 = 13
Reading from the Chi² table for α = 0.1 and degree of freedom = 13, we have the critical value ≥19.812
The value of the test statistic is given as [(n-1)²s²] ÷ σ²
We have n = 14, s = 9.819, and σ = 15
test statistic = [(13)²(9.819)²] ÷ 15² = 72.417
72.417 is in the critical region (which is values ≥ 19.812) so the result is significant and H₀ is rejected. The standard deviation of IQ scores of college students is less than 15.
To test if the standard deviation of college students' IQ scores is less than 15, we must calculate the sample standard deviation and then perform a chi-square test for variance. Comparing the test statistic to the chi-square distribution at a 0.10 significance level allows us to accept or reject the null hypothesis.
Explanation:To test the claim that the standard deviation of IQ scores of college students is less than 15, we first need to calculate the sample standard deviation. The scores provided are 115, 128, 107, 109, 116, 124, 135, 127, 115, 104, 118, 126, 129, 133. We find the mean of these scores and then use the formula for sample standard deviation.
Step 1: Calculate the mean of the IQ scores.
Step 2: Find the sum of the squared deviations of each score from the mean.
Step 3: Divide by the number of scores minus one (n-1) to get the variance.
Step 4: Take the square root of the variance to find the sample standard deviation.
Once we have the sample standard deviation, we use the chi-square test for variance since we are testing about the population variance. Under the null hypothesis, we assume that the population standard deviation is 15. At a significance level of 0.10, we compare the test statistic to the corresponding chi-square distribution to determine if we can reject the null hypothesis.
Which is the graph of 2x – 4y > 6?
Answers
Answer:
Its the last graph
The graph of 2x – 4y > 6 is in the far-right graphic image.
Further explanationLet us first arrange the equation of the line followed by making a graph of a linear inequality.
Step-1: the x-intercept and the y-intercept
2x - 4y = 6
For y = 0, we get the x-intercept.2x - 4(0) = 6
2x = 6, and then divide by two on both sides.
Hence, the x-intercept is [tex]\boxed{x = 3} \rightarrow \boxed{ \ (3, 0) \ }[/tex]
For x = 0, we get the y-intercept.2(0) - 4y = 6
-4y = 6, and then divide by -4 on both sides.
Hence, the y-intercept is [tex]\boxed{y = -1\frac{1}{2}} \rightarrow \boxed{ \ (0, -1\frac{1}{2}) \ }[/tex]
Step-2: graph the inequality
2x - 4y = 6 is the boundary line and we draw the line dashed since the equality symbol is " > ".Test the point (0, 0), as origin, in 2x - 4y > 6, i.e., [tex]\boxed{2(0) - 4(0) > 6} \rightarrow \boxed{ \ 0 > 6, false \ }[/tex]So we shade the region which does not contain the test point.- - - - - - - - - -Notes:
To graph a linear equality in two variables, follow the steps.
Draw the boundary line using a dashed line if the inequality symbol is " < or > ", or a solid line if the inequality symbol is " ≤ or ≥ ".Choose a test point which is not on the boundary line and substitute it into the equality.Shade the region which includes the test point if the resulting inequality is true, and shades the region which does not contain the test point if the resulting inequality is false.Learn moreFinding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38? https://brainly.com/question/1626676 When the x-axis and y-axis have different units of measure the slope can be interpreted as a rate https://brainly.com/question/4858319Keywords: linear inequality, the equation of the line, shaded region, x-intercept, test the point, the line dashed
A rectangular container 20 cm long and 15 cm wide contains sone water. When an iron ball was put in the water level rose by 3cm, find the the volume of the iron ball
Answers
The volume of the iron ball in the rectangular container that is 20 cm long and 15 cm wide is 900cm³.
How to calculate volume?The volume of a rectangular cuboid can be calculated by multiplying the length, breadth and the height of the shape.
According to this question, a rectangular container 20 cm long and 15 cm wide contains sone water. When an iron ball was put in the water level rose by 3cm.
Volume of the iron ball = 20cm × 15cm × 3cm
Volume of the iron ball = 900cm³
Therefore, the volume of the iron ball in the rectangular container that is 20 cm long and 15 cm wide is 900cm³.
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Which polygon has an interior angle sum of 1080°?
Answers
The polygon which has an interior angle sum of 1080° is an Octagon
Interior angles of a PolygonFrom the question, we are to determine which polygon has an interior angle sum of 1080°
To find that, we will determine the number of sides the polygon has.
From the formula for sum of the interior angles in a polygon
Sum of interior angles = (n-2)180°
Where n is the number of sides
Then,
1080° = (n-2) 180°
1080° ÷ 180° = n-2
6 = n-2
n = 6 + 2
n = 8
A polygon with 8 sides is called an Octagon
Hence, the polygon which has an interior angle sum of 1080° is an Octagon
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Suppose a tax is added to each flight. dollars is added to every flight, no matter how long it is. the table shows the new data. what happens to the correlation coefficient when a constant is added to each number?
Answers
The correlation coefficient in both cases is 0.961.
9 x 3? Help me please lol I don't have a clue.
Answers
9 x 3 =
9 + 9 +9
9+9 = 18, 18+9 = 27
so 9x3 = 27
The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?
Answers
3x + 4x + 5x = 240 and solve for x.
which is: 12x = 240
x = 20
The longest side is 5x, so the longest side is 100.
Salun is assembling floor lamps. After 3 hours, there are 75 lamps available for shipment. After 5 hours, there are 97 lamps available for shipment. How many lamps are available at the end of an 8-hour shift?
Answers
Answer:
130 lamps are available at the end of an 8-hour shift
Step-by-step explanation:
Salun is assembling floor lamps. After 3 hours, there are 75 lamps available for shipment. After 5 hours, there are 97 lamps available for shipment
LEt x be the number of hours and y be the lamps available
(3,75) (5,97)
Make the equation y=mx+b
m is the slope and b is the y intercept
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{97-75}{5-3} =\frac{22}{2} =11[/tex]
y=11x+b
Now solve for b using (3,75)
75 = 11(3) +b
75 = 33 + b
Subtract 33 from both sides
42= b
So equation becomes y= 11x + 42
To find available lamps at the end of 8 hours, plug in 8 for x
y= 11(8) + 42= 130
x+3menor que 8 qual o resultado
Answers
x+3<8
8-3 =5
X<5
any number less than 5 will work
If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years
Answers
May has 31 days
there are 365 days in a year
31/365 probability someone has a birthday in May
The probability of the event A that represents that the man's birthday is in May is 0.084.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomely selected.
Assume that the Event A represents that the man's birthday is in may.
Total number of days in the month of may = n(A) = 31
Total number of days in a year = n(S) = 365
Therefore, the probability that the man's birthday is in may will be -
P(A) = n(A)/n(S)
P(A) = 31/365
P(A) = 0.084
Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.
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determine the heat energy received per kilogram of steam produced
Answers
Note : this value varies greatly with pressure and temperature.
Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money
Answers
2. C
3. B
4. E
5. A
6. F
Answer:
The correct matches are:
1. impulse - a sudden stirring to do something
2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.
3. naught - nothing, nonexistence
4. renown - fame ; the condition when you are known or talked about by many people.
5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.
6. thrifty - careful with money . Like a person is thrifty about his own time.
An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').
Answers
that is P(E)+P(E')=1, where E' is "not E".
The event E can happen in 4 ways, because there are four 2's that can be drawn.
P(E)=n(E)/52=4/52=0.08
P(E')=1-P(E)=1-0.08=0.92
Answer: 0.92
Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (6, 6, 3) and use it to approximate the number 6.022 + 5.972 + 2.992 .
Answers
[tex]f(x,y,z)\approx f(6,6,3)+f_x(6,6,3)(x-6)+f_y(6,6,3)(y-6)+f_z(6,6,3)(z-3)[/tex]
where the subscripted [tex]f[/tex]'s refer to the corresponding partial derivatives.
[tex]f(x,y,z)=x^2+y^2+z^2[/tex]
[tex]\implies\begin{cases}f_x(x,y,z)=2x\\f_y(x,y,z)=2y\\f_z(x,y,z)=2z\end{cases}[/tex]
So
[tex]f(6.02,5.97,2.99)\approx80.8288[/tex]
Compare to more precise value,
[tex]f(6.02,5.97,2.99)\approx80.8214[/tex]
Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?
Answers
Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.
Answers
A circular pond is to be surrounded by a gravel path. Use the diagram to find the square feet of gravel needed if we know the pond has a radius of 200 ft and the radius of the whole space is 250 ft?
Answers
Claire has received scores of 85,88,87,and 85 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 88?
Answers
88*5 = 440
so all 5 tests need to equal at least 440
85 +88 +87 +85 = 345
440-345 = 95
she needs at least a 95 to have an 88 average
95 is the minimum score she must receive on the fifth test to have an overall test score average of at least 88.
88*5 = 440
All 5 tests need to equal at least 440.
85 +88 +87 +85 = 345
440-345 = 95.
What is average in maths?In Maths, an average of a list of records is the expression of the primary price of a set of statistics. Mathematically, it's far described as the ratio of summation of all the facts to the range of units present inside the listing. In phrases of records, the common of a given set of numerical records is also called the mean.
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Leon watched a beetle and a spider on the sidewalk the beetle crawled 2 yards and the spider crawled 1/6 of the yard how much further did the beetle crawled in the spider
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2yards - 1/6 yards = 1 5/6 yards
This means that the beetle crawled 1 whole yard and 5/6 of another yard further than the spider.
The beetle crawled 11/6 yards, or 1 and 5/6 yards, further than the spider.
The question asks how much further the beetle crawled compared to the spider. The beetle crawled 2 yards, and the spider crawled 1/6 of a yard. To find out how much further the beetle crawled, we subtract the distance the spider crawled from the distance the beetle crawled.
Step 1: Convert the distances to the same unit, if necessary. Here, both distances are already in yards, so no conversion is needed.
Step 2: Subtract the spider's distance from the beetle's distance: 2 yards - 1/6 yard.
Step 3: Calculate the difference: 2 yards - 1/6 yard = 12/6 yards - 1/6 yard = 11/6 yards.
Therefore, the beetle crawled 11/6 yards, or 1 and 5/6 yards, further than the spider.
Rita borrowed 8000 at a rate of 10.5% compounded monthly assuming she makes no payments how much willshe owe after8 years
Answers
How do you convert numbers to percents
Answers
Example: 23 (×100) = 2300%
0.23 (×100) = 23%
Hope it helped!
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
Answers
(1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.
A total of
644
tickets were sold for the school play. They were either adult tickets or student tickets. There were
56
fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
s = a - 56
a + (a - 56) = 644
2a - 56 = 644
2a = 644 + 56
2a = 700
a = 700/2
a = 350 <=== adult tickets
s = a - 56
s = 350 - 56
s = 294 ...student tickets
martin brought 30 shares of microsoft at the close price of $24.53. In a few years, Martin sells all of his shares at $33.71. How much money did martin make?
Answers
9.18*30 = 275.4
Of course, we can't take into account inflation, because nothing is said, I mean that the $24 a few years ago are not the same as today ...
Answer:
Money did martin make = 275.4 $
Step-by-step explanation:
Martin brought 30 shares of Microsoft at the close price of $24.53.
Number of shares = 30
Cost per share = 24.53 $
Total cost = 30 x 24.53 = 735.9 $
Martin sells all of his shares at $33.71
Selling price per share = 33.71 $
Total selling price = 30 x 33.71 = 1011.3 $
Gain for Martin = 1011.3 - 735.9 = 275.4 $
Money did martin make = 275.4 $
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
Answers
all you have to do is divide the muscle weight by the total weight which is...60/140=
ANSWER: about 42.86%
p/100=60/140 multiply both sides by 100
p=6000/140
p=300/7 %
p≈42.86% (to nearest hundredth of a percent)
A company has a sales revenue of $10,000, cost of goods sold of $4500, and other operating expenses of $1500. what is this company's pre-tax income?