The area of the actual office space is 36 yards if the scale is 1:6 yards.
An item is enlarged in a scale drawing. An expansion increases or decreases the size of an item by multiplying each of its lengths by a scale factor. A scale of 1:5, for instance, indicates that the size of 1 unit in the picture corresponds to the size of 5 units in the actual world.
The scale of office space is 1:6 yards. The scale drawing has an area of 6 square inches. This means that 1 scale represents 6 square inches of office. For the actual area multiply 6 by the area of the scale drawing which will give 36 yards.
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On a print-out of these slope fields, sketch for each three solution curves to the differential equations that generated them. Then complete the following statements: For the slope field in figure 1. a solution passing through the point (0.-1) has slope. For the slope field in figure 1. a solution passing through the point (-2.2) has slope. For the slope field in figure 2. a solution passing through the point (1.-3) has slope For the slope field in figure 2. a solution passing through the point (0.4) has a slope.
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
What is slope field?A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.
Here,
For figure 1 slope field=
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}[/tex]
For figure 2 slope field=
[tex]\frac{dy}{dx} = xy-3\\[/tex]
For figure 1 a solution passing through the point (0,-1)
therefore,
slope=
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2[/tex]
so slope comes out to be negative
For figure 1 a solution passing through the point (-2,2)
[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30[/tex]
so slope comes out to be negative
For the slope field in figure 2. a solution passing through the point (1.-3)
[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6[/tex]
so slope comes out to be negative
[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3[/tex]
so slope comes out to be negative.
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
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The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.
Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.
The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).
The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.
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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ...
Answer:
0.36
0.26
0.16
0.06
the answers doesn't come in -
A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area. HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters
How to determine the dimensions of the field that will allow for the maximum area.From the question, we have
Fencing available, Perimeter = 1600 meters
Number of sections, n = 3
Represent the dimensions with x and y
So, we have:
Area = Number of sections* x * y = 3xy
Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y
Recall that
Perimeter = 1600 meters
So, we have
6x + 4y = 1600
A = 3xy
Divide 6x + 4y = 1600 by 2
3x + 2y = 800
Make y the subject
y = (800 - 3x)/2
Substitute y = (800 - 3x)/2 in A = 3xy
A = 3x(800 - 3x)/2
So, we have
A = 1200x - 4.5x²
Differentiate and set to 0
1200 - 9x = 0
So, we have
9x = 1200
Divide by 9
x = 400/3
Recall that y = (800 - 3x)/2
So, we have
y = (800 - 3 x 400/3)/2
Evaluate
y = 200
Hence, the dimensions are 200 by 400/3
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an information technology company claims that a certain model of laptops have mean battery capacity of 5 hours. a consumer report firm wants to show that the actual mean is smaller than the company claims. what should be the null and alternative hypotheses?
The null and alternative hypotheses are-
Null hypothesis H₀; μ ≤ 9Alternative hypothesis Hₐ: μ > 9Explain the formulation of Hypotheses?The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.
This alternative hypothesis is a statement that contradicts the null and is the assertion that a sample research seeks to demonstrate. This null hypothesis can be accepted that represents the declaration of equality, the generally accepted presumption about the population.The intended relationship between the variables must be stated first. In order for researchers to determine whether such a hypothesis is true or untrue, it must also be able to be tested and falsified. Third, it must be consistent the with corpus of information already in existence. Last but not least, it should be said as briefly and simply as possible.A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.
For this assertion, we form:
Null hypothesis H₀; μ ≤ 9
Alternative hypothesis Hₐ: μ > 9
The assertion is represented by the alternative hypothesis in this right-tailed test.
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If the first equation is multiplied by 3 and then the equations are added, the result is _____. 3x + y = 3 x - 3y = -2 10 x = 7 10 x = 11 8 x = 7.
Answer:
if the first equation 3x - 3y = -2 is multiplication by 3
therefore, 3x - 3y = -2
multiplied by 3
:9x - 9y = -6
then the equations are added,
9x - 9y = -2 + 10x + 710x + 118x + 7
9x + 10x + 710x + 118x + 9y + 7
947x + 9y = 7
HELP…I SELECTED YES AND UHH YUP
Answer: 86.8 dollars per month
Matt's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon,
the cafe sold 50 espressos in all, 24 of which were single-shot. What percentage of the
espressos were single-shot?
Answer: 48%
Step-by-step explanation:
scale up,
24/50=x/100
multiply 24/50 by 2 to get 100
so you get 48/100 which is 48%
Answer:
57 I think I'm not entirely sure
She was the first swimmer to cross the
between the two countries.
If you want your complaint to be addressed, you need to go through the appropriate
.
Answer:
Step-by-step explanation:
The word ‘channel’ has multiple meanings which can be discerned based on the context.
What is the thesaurus entry for the channel?
According to the thesaurus, as a noun, the word channel has two meanings. They are-
A pathway that contains water - here the channel is a strait or a small stream of water. The synonyms of the word, in this case, would be - avenue, carrier, route, and tunnel.
A means to achieve something- The synonyms, in this case, are the instrument, medium, and vehicle.
As a verb, the word channel means to direct or to convey something. Thus the synonyms would be to carry and to transmit.
How is ‘channel’ used in the contexts above?
In the sentences above the word, 'channel' is used as follows
She was the first swimmer to cross the channel between the two countries.- Here, the channel is a water body.
If you want your complaint to be addressed, you need to go through the appropriate channel.- Here, the channel is a medium or a route.
A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3 uints and the smallest square achieving this length is [tex]38^2[/tex] = 1444.
All squares end in the digit 0, 1, 4, 5, 6, or 9. A square ending in 11, 66, 55, 99 would be congruent to 3, 3, 2, 3 mod 4, but squares are congruent to 1 mod 4 or 0. So for a length > 1, the square should end in 4. For example, [tex]12^2[/tex] = 144.
A square ending in 4444 would be congruent to 12 mod 16, but squares are congruent to 0, 1 mod 16, 4 mod 16, or 9 mod 16. So, the maximum length should be 2 or 3.
If [tex]n^2[/tex] ends in 4, then n should end in 2 or 8. [tex](100a + 10b + 2) ^2[/tex]= 10000[tex]a^2[/tex] + 1000 (2ab) + 100 (4a + [tex]b^2[/tex]) + 10 (4b) + 4. So, if this ends in 44, then b = 6 or 1.
If b = 1, then 4a + [tex]b^2[/tex] is odd, so the square will not end in 444. If b = 6, then the square would be 1000k + (4a + 38) 100 + 44. This would end in 444 if we take, a= 9 or 4.
Thus the smallest numbers that end in 2 and whose square ends in 444 are 462 (square 213444) and 962 (square 925444).
[tex](100a + 10b + 8)^2[/tex] = 1000k + 100 ([tex]16a^2 + b^2[/tex]) + 10 (16b + 6) + 4.
Now, if this ends in 44, then b = 3 or 8.
let us take b=3, then [tex](100a + 38)^2[/tex] = 1000k + 100 (76a) + 1444, so this ends in 444 if a = 0. Hence, this should be the smallest solution.
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question the range for a list of measurements equals the greatest measurement minus the least measurement. the two lists of measurements, x and y , combined consist of 30 measurements with a range of 25. what is the range for the measurements in list x ? (1) the range for the 12 measurements in list y is 20. (2) list x consists of 18 measurements.
The statements are insufficient to answer the question.
What is measurement?
Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.
So we are given 2 lists, x and y and we are given the
1. The total number of measurements is 30. x(n) + y(n) = 30.
2. Largest measurement - Smallest Measurement = 25
But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.
We need to find the largest measurement of x and the smallest measurement of x for our answer.
1)The range for the 12 measurements in list y is 20.
Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT
2) List x consists of 18 measurements.
We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA
Hence, the statements are insufficient to answer the question.
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problem 1. (12 points) light bulbs of a certain type are advertised as having an average lifetime of 800 hours. the price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. a random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested, resulting in the accompanying output: variable n mean st. dev se of mean z p-value lifetime 50 738.44 38.20 5.40 -2.14 0.016 a) what conclusion would be appropriate for a significance level of .05? b) what about at a significance level of .01? c) which significance level would you recommend? why?
the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
The following is a definition of the test's hypothesis:
H0: The actual average lifetime, which is > 750 hours, is not less than what is stated
Ha! The actual average lifespan, at 750 hours, is less than what is advertised.
The examination is left-tailed.
Making a decision:
The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.
The test's p-value is calculated as,
0.016 as the p-value
(a)
The level of significance is 0.05.
The p-value is equal to 0.016/0.05.
The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.
Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than
(b)
The level of significance is = 0.01.
The p-value is equal to 0.016 > = 0.01.
The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.
Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
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If Josh can run 1.5 miles in 12minutes, how long will it take him to run 4 miles?
Answer:
if he can run 1.5 miles in 12 min he can run 4 miles in 0.5
ASAP!!
define: A formula to calculate Average Rate of Change over the interval, x [x1, x2].
What are the next two numbers in this sequence? 0, 1, 3, 6, 10, ___, ___
A. 17, 25
B. 15, 21
C. 16, 23
D. 14, 19
Answer:
b
Step-by-step explanation:
your answer is b to be precise
What is the slope of a line perpendicular to the line whose equation is 6x+y=-5
Answer:
It would have a slope of a positive 6x
Step-by-step explanation:
Since the slope of the equation shown is -6x, we would just find the opposite which is -6x
if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?
8 ounce of yellow color required.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint.
So, we have the composition ratio as 2:3
Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.
Thus, yellow = 2/5 x 20= 8 ounce
Blue= 3/5 x20 = 12 ounce
Hence, 8 ounce of yellow color required.
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an iphone 13 is on sale for $519.35. it is on sale for 35 off the regular price. what is the original price of the phone?
Answer:
Step-by-step explanation:
$519.35 + $35
The original price of the iPhone 13 is $554.35
Tommy earned $62.40 in interest after 4 years on a principal of $400. His simple interest rate is 3.9%. Jane
earned $66.60 in interest after 3 years on a principal of $600. Her simple interest rate is 3.7%. Which bank would you rather
use, Tommy's or Jane's? Explain your reasoning.
Answer:
I would rather use Jane's bank because she earned more interest in a shorter amount of time. Jane's bank has a higher simple interest rate of 3.7%, which means she earned more money in a shorter amount of time than Tommy did with his 3.9% rate.
what is the answer for shrinking 6x-2(x-3)
Answer:
4x +6
Step-by-step explanation:
You want the simplified form of 6x -2(x -3).
SimplifyGenerally, the first step in simplifying an expression is elimination of parentheses. This is done using the distributive property.
6x -2(x -3) = 6x -2x -2(-3) = 6x -2x +6
Then, like terms can be combined:
6x -2x +6 = (6 -2)x +6 = 4x +6
The simplified expression is 4x +6.
__
Additional comment
We notice the terms have a common factor of 2, so we can use the distributive property to factor that out:
= 2(2x +3)
This form may be useful in some circumstances, but is generally not considered to be the simplified form.
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The odds in favor of Michael Jordan making a free throw were 21:4. Find the probability of Michael Jordan missing a free throw.
Give answer as a decimal rounded to the nearest hundredth.
The probability that he will miss is 25%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The odds in favor of Michael Jordan making a free throw were 21:4.
Total number of throw is 21+4 = 25
The number of time he will miss is 4
So the probability that he will miss is 4/25 = 0.25
Hence, the probability that he will miss is 25%.
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Samuel has been planting young trees in her garden. The maple tree that is 125 centimeters tall is growing 3 centimeters per month, whereas the oak tree that is 83 centimeters tall is growing 10 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?
It will take 6 month to reach the same height for both maple tree and oak tree.
Explain the term rate of growth?the country, region, or geographic area's yearly average rate of change in population size over a certain time period.
The given data is -
Present height of maple tree = 125 cmRate of growth = 3 centimeters per month.Present height of oak tree = 83 cmRate of growth of oak tree = 10 centimeters per month.Let the number of months when both will have the same height be 'x'.
Thus,
For maple tree,the final height be-
125 + 3x
For oak tree,the final height be-
83 + 10x
Equating both
125 + 3x = 83 + 10x
7x = 125 - 83
7x = 42
x = 6 months
Thus, it will take 6 month to reach the same height for both maple tree and oak tree.
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the telephone lines serving an airline reservation office are all busy about 60% of the time. a if you are calling this office, what is the probability that you will complete your call on the first try? the second try? the third try? b if you and a friend must both complete calls to this office, what is the probability that a total of four tries will be necessary for both of you to get through?
The probability that a total of four tries will be necessary for both of you to get through is 0.1728.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
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after constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
By using the concept of confidence interval, it can be concluded that-
To reduce confidence interval, it is needed to increase sample size.
Option c is correct
What is confidence interval?
Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.
Formula for percentage confidence interval
[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]
We have to reduce the size of the confidence interval
Confidence interval has no effect on mean, directly proportional to standard deviation and inversely proportional to sample size
So to reduce confidence interval, it is needed to increase sample size.
Option c is correct
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Complete Question
After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
Select one:
a. increase the population standard deviation
b. increase the level of confidence
c. increase the sample size
d. increase the sample mean
e. none of these would help
someone please help, thank you.
Step-by-step explanation:
it seems the questions 8., 9. and 10. demonstrate exactly what is the asked via variables in 11., 12. and 13.
you only need to apply the principles of equal angles of crossing lines again.
11.
to be parallel
50 + (x + 30) = 180
x + 80 = 180
x = 100.
12.
135 = 2y + 15
120 = 2y
y = 60
13.
70 = 4x - 10
4x = 80
x = 20
14.
yes, because
142 + 38 = 180°
15.
yes, because
112 + 68 = 180°
16.
no, because
146 + 44 = 190° <> 180°
17.
to be parallel, angle 1 = angle 2
88 = 2x
x = 44
18.
to be parallel, angle 1 = angle 3
88 = 2x + 10
2x = 78
x = 39
A customer leaves a tip of $3.00 on a $20 meal. At the same rate, what tip would they
leave for a $50 meal? What is the percentage the customer is leaving for a tip?
Answer: $7.5 tip
Step-by-step explanation:
divide 3 an 20 then get 0.15
then multiply 0.15 to 50 get 7.5
3x+4/2=9.5 what is x
Answer:
x = 2.5
Step-by-step explanation:
Answer:
[tex]\boxed{\boxed{\tt x=5}}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{3x+4}{2}=9.5[/tex]
Multiply both sides by 2:-
[tex]\tt \cfrac{2\left(3x+4\right)}{2}=9.5\times\:2[/tex]
[tex]\tt 3x+4=19[/tex]
Subtract 4 from both sides:-
[tex]\tt 3x=15[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}=\cfrac{15}{3}[/tex]
[tex]\tt x=5[/tex]
__
Hope this helps you!
Have a nice day!
What is the correct factorization of the following quadratic expression: x² - 7x - 60
a. (x-12) (x + 5)
b. (x+12) (x - 5)
c. (x-10) (x+6)
d. (x+10) (x-6)
hi help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a=3/4
Step-by-step explanation:
1) add 1/6 on both sides
-> 2/3a= 1/3+1/6
->2/3a = 1/2
2) isolate a by multiplying 3/2 on both sides
-> 2/3 x 3/2 a = 1/2 x 3/2
-> a=3/4
3 2/3 divided by 2/5
Answer:
9 1/6
Step-by-step explanation:
3 2/3 divided by 2/3
First convert 3 2/3 into a whole number
3 2/3 = 11/3
11/3 x 2/3 = 55/3
55/3 into a mixed number is 9 1/6