If I buy 20 LEGO bricks, it costs $4.20If I buy 55 LEGO bricks, it costs $11.55If I buy 100 LEGO bricks, it costs $28.10(1) Find a linear function that closely models the data. (2) What are the units of measurement on the slope of the line? (3) What are the unit of measurement of the vertical intercept?(4) What is the contextual pneaning of the slope?
Answers
Solution:
Given the values;
(a) The linear function that models the data is;
\(\)
Related Questions
The value of a piece of equipment is decreasing at a rate of 7,5% yearly. If the equipment
was valued at $930 when it was purchased, which function represents the value of the
equipment x years after it was purchased? Explain,
Answers
Answer:
y=930 x 075^x
Step-by-step explanation:
y is the price after the amount of years x being plugged into the equation. 930 is what you started with. 7.5 is what is being decreased so divide that by 100 and you get 0.075 plug in the amount of years into x and you have your equation
How do I verify: tan(x)+cot(x)=(2)/sin(2x)?
I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)
Answers
\(sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\)
\(tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}\)
now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.
let's recall something else, that same/same = 1, so
\(\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1\)
therefore
\(\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}\)
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.3 mm. Round values to 4 decimal places when possible.
The mean of this distribution is _____
The standard deviation is _____
The probability that the round off error for a jumper's distance is exactly 0.4 is P(x = 0.4) = ____-
The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.3 mm is P(1.2 < x < 3.4) = ____
The probability that the jump's round off error is greater than 4.16 is P(x > 4.16) = ____
P(x > 4.2 | x > 1.8) = ___
Find the 85th percentile____
Find the maximum for the lower quartile. ____
Answers
Using the uniform distribution, it is found that:
The mean is of 2.65 mm.The standard deviation is of 1.53 mm.P(X = 0.4) = 0.P(1.2 < x < 3.4) = 0.4151 = 41.51%.P(X > 4.16) = 0.2121 = 21.51%.P(X > 4.2|x > 1.8) = 0.3257 = 32.57%.85th percentile: 4.505 mm.Lower quartile: 1.325 mm.Uniform probability distributionThe uniform distribution has two bounds, a and b, and all outcomes in the distribution are equally as likely.
In this problem, the bounds are as follows:
a = 0, b = 5.3.
Hence the mean is:
M = (a + b)/2 = (0 + 5.3)/2 = 2.65 mm.
The standard deviation is of:
\(S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{5.3^2}{12}} = 1.53\)
The uniform distribution is continuous, hence the probability of an exact value is of 0.
The probability of finding a value between c and d is:
\(P(c \leq X \leq d) = \frac{d - c}{b - a}\)
Hence:
P(1.2 < x < 3.4) = (3.4 - 1.2)/(5.3 - 0) = 0.4151 = 41.51%.
The probability of finding a value above x is:
\(P(X > x) = \frac{b - x}{b - a}\)
Hence:
P(X > 4.16) = (5.3 - 4.16)/(5.3 - 0) = 0.2121 = 21.51%.
P(x > 4.2 | x > 1.8) makes the lower bound 1.8, hence:
P(X > 4.2|x > 1.8) = (5.3 - 4.16)/(5.3 - 1.8) = 0.3257 = 32.57%.
The 85th percentile is found as follows:
0.85 x (5.3 - 0) = 4.505 mm.
The lower quartile is the 25th percentile, hence:
0.25 x (5.3 - 0) = 1.325 mm.
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What is the measure of 23, in degrees, in the figure shown? 30° 137° 3
Answers
Answer:
73°
Step-by-step explanation:
This equation uses two supplementary angles. Supplementary angles are two angles that add up to 180 degrees.
The triangle has two angles implied, 30 degrees and (180-137) degrees.
(180 - 137) = 43 degrees
Now that we have two angles inside the triangle, we subtract them from 180 to find the last angle.
180 - 43 - 30 = 107
The angle with a measure of 107 degrees and angle 3 are supplementary
180 - 107 = 73 degrees
Answer:73.4° Fahrenheit.
Step-by-step explanation:
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
The coordinate of the point after transformation is: (3, -4)
What is the coordinate after moving of point?The coordinate initially is given as (0, -4).
Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:
(0 - 1, -4)
= (-1, -4)
Moving by 4 units to the right means an addition of 4 units to x coordinate to get:
(-1 + 4, -4)
= (3, -4)
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The following data are the daily number of minutes of smartphone use for a random sample of 8 students at your institution:
117, 156, 89, 72, 116, 125, 101, 100.
Required:
a. Test the null hypothesis according to which the true mean is greater or equal to 100 min against the alternative that it is less than 100. Use a significance level of 5% (state the null and the alternative hypothesis, the test statistic and the conclusion).
b. Compute a 90% confidence interval for the true mean number of minutes per day a student uses his or her smartphone. Is your finding consistent with your answer in (a) (Explain why or why not)
Answers
Answer:
We fail to reject the Null ;
(88.323, 130.677)
Step-by-step explanation:
Given the data :
117, 156, 89, 72, 116, 125, 101, 100
H0 : μ ≥ 100
H1: μ < 100
From the data: using calculator :
Mean, x = 109.5
Standard deviation, s = 25.33
The test statistic:
(x - μ) ÷ s/Sqrt(n)
(109.5 - 100) ÷ 25.33/sqrt(8)
Test statistic = 1.06
Since, same size is small, we use t test ;
Using the Pvalue calculator :
T at df = 8 - 1 = 7, α = 0.05
Pvalue = 0.161
Pvalue > α
0.161 > 0.05 ; Hence, we fail to reject H0.
B.)
C. I = mean ± Tcritical *s/√n
Tcritical = 2.365 at 95% and df = 7
109.5 ± 2.365(25.3264/√8)
109.5 ± 2.365(8.9542)
(109.5-21.1768 ; 109.5+21.1768)
(88.323, 130.677)
In conclusion true mean is in the confidence interval, so it is consistent.
The square below represents one whole.
Answers
Answer:
6 percent
Step-by-step explanation:
6/100 is shaded. This is the same thing as 0.06. Once I move the decimal two places to the right, I get 6. (I move the decimal place because percents are out of 100, so two decimal places.) This means 6 percent.
The following are the ages of 12 history teachers In a school district 29,30,32,32,39,41,46,49,50,51,52,53 minimum lower quartile median upper quartile maximum and interquartile range
Answers
The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
How does interquartile range work?Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.
According to the given information:To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.
Step 1: Find the median (Q2)
When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:
Median (Q2) = (41 + 46)/2 = 43.5
Step 2: Find the lower quartile (Q1)
The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:
Q1 = (32 + 32)/2 = 32
Step 3: Find the upper quartile (Q3)
The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:
Q3 = (50 + 51)/2 = 50.5
Now we have all the information we need to construct the five-number summary and interquartile range:
Minimum: 29
Lower quartile (Q1): 32
Median (Q2): 43.5
Upper quartile (Q3): 50.5
Maximum: 53
Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5
the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
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Identify the exponent in the term -3X²
Answers
Answer:
The 2 aka ²
Step-by-step explanation:
Because an exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression
Choose the table that represents g(x) = 3⋅f(x) when f(x) = x − 1
Answers
Are the two triangles congruent?
Choose 1 answer:
(Choice A)
A-Yes
B-No
C-There is not enough information to say.
Answers
(8x2 – 3x +9)
+ (4x2 + 8x - 2)
Answers
Answer:
x = 1
Step-by-step explanation:
16-12+8+8-2
Rewrite as a simplified fraction.1. 6 =?
Answers
Answer:
1 3/5
Step-by-step explanation:
CAN SOMEONE TELL ME IF I CLICKED THE RIGHT AWNSER PLEASE
Answers
Answer:
yes your absolutely right
Step-by-step explanation:
you just are
#5: Which ratio compares ginger ale to lemonade.
Answers
Answer:
how are we supposed to now if u didnt give the ratio
Step-by-step explanation:
Lilly likes to collect records. Last year she had 15 records in her collection. Now she has 18 records. What is the percent increase of her collection?
Answers
Neal invested $120,000 in stocks and bonds. He earned 18% on his stock investments and 12% on his bond investments. If Neal's combined profits on both types of investments were $17,400, how much did he invest in stocks?
Answers
Answer:
$50,000
Step-by-step explanation:
The given relations can be used to write and solve an equation for the amount invested in stocks.
SetupLet s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...
0.18s +0.12(120,000 -s) = 17,400
SolutionSimplifying the equation, we have ...
0.06s +14,400 = 17,400
0.06s = 3000 . . . . . . . . . . subtract 14,400
s = 50,000 . . . . . . . . . . . . divide by 0.06
Neal invested $50,000 in stocks.
__
Additional comment
The amount invested in bonds was 70,000. The profit earned was ...
0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400
Lester worked 12 hours last week at the grocery store and earned $93.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $62.00?
A. 9 hours
B. 10 hours
C. 11 hours
D. 8 hours
Answers
Answer:
8 hours
Step-by-step explanation:
We can use a ratio to solve
12 hours x hours
---------- = ------------
93 dollars 62 dollars
Using cross products
12 * 62 = 93x
Divide each side by 93
12*62/93 = 93x/93
8 = x
8 hours
15. This table shows the average high temperature, in °F, recorded in Savannah, GA and Atlanta, GA, over a seven day period.
Day
1
2
3
4
5
6
7
Temperature in °F, in Savannah, GA
85
87
81
79
80
91
90
Temperature in °F, in Atlanta, GA
76
73
80
78
77
81
79
Which conclusion can be drawn from the data?
A. The lower quartile for the temperatures in Savannah is lower than the lower quartile for the temperatures in Atlanta.
B. The inter-quartile range of the temperatures is the same for both cities.
C. The mean and median temperatures of Savannah were higher than the mean and median temperatures of Atlanta.
D. The upper quartile for the temperatures in Atlanta was higher than the upper quartile for the temperatures in Savannah.
16. This table shows prices for four different rides at the county fair.
Ferris Wheel
TeaCups
Ring of Fire
Bumper Cars
$2. 40
$1. 35
$3. 85
$2. 00
Which is the mean absolute deviation for this set of data?
A. 2.90 B. 0.725 C. 0 D. 1.35
17. Which of the following describes the histogram provided?
A. Symmetric
B. Skewed Left
C. Skewed Right
D. Uniform
18. Which of the following sets of data is represented by the given histogram of the frequency distribution?
Histogram
5
4
y
c
n
e
u
q
e
r
F
A.
3
2
1
0
0 5 10 15 20 25 30 35 40 45 50 Miles Per Gallon
Value
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
Frequency
1
2
4
4
2
2
1
1
0
0
B.
Value
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
Frequency
0
1
2
4
4
2
2
1
1
0
C.
Value
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
Frequency
0
5
10
15
20
25
30
35
40
45
D.
Value
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
Frequency
0
1
2
3
4
5
4
3
2
1
19. A linear regression was done to relate the age of a person, x, and the number of optimal hours of sleep, y. The equation was found to be �� = −0.12�� + 11.5 with a correlation coefficient of �� = −0.86.
a) Explain what each of the parameters in the linear model represent, i.e. the -0.12 and the 11.5. b) How do you interpret the fact that the correlation coefficient is negative?
Answers
Answer:
1.35
Step-by-step explanation:
Show ur work and check jt
Answers
Answer: 15
Step-by-step explanation:
m-5=10
m-5+5=10+5
m=15
Hi, can someone please help me out with this problem? thanks in advance.
Construct Income Statement(s) for a firm with an accounting break-even point of $1,000,000 and a degree of operating leverage of 3. Assume a corporate income tax rate of 10%. Show calculations that prove that the accounting break-even point is $1,000,000 and the DOL is 3 for your statement(s).
Answers
Answer:
The following is an income statement using the Contribution format.
...........................Income Statement for Rivieremia Corp................................
Sales ........................................................................$1,500,000
Less Variable Costs................................................($1,200,000)
Contribution Margin..............................................$300,000
Less Fixed Costs....................................................($200,000)
Operating Income .................................................$100,000
Less Tax....................................................................($10,000)
Net Income...............................................................$90,000
Tax = 10% * 100,000 = $10,000
Proving breakeven is $1,000,000.
The breakeven point for a company can be calculated by dividing the Fixed cost by the contribution margin ratio.
Contribution margin ratio = Contribution margin / Sales
= 300,000/1,500,000
= 20%
= Fixed Cost/ Contribution Margin ratio
= 200,000/20%
= $1,000,000
Degree of Operating Leverage = Contribution Margin/ Operating Income
= 300,000/100,000
= 3
A pair of shoes is on sale for 15% off. With this discount the customer saves 9$ if they buy the shoes. How much did the shoes cost?
Answers
1500 = 25x
60 = x
The original price was $60.
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
I'LL MARK THE BRAINLIEST
The length of a radius of a circle, measured in feet, is represented by the expression z + 3.6. The diameter of the circle is 11 4/5 ft.
What is the value of z?
Enter your answer as a decimal or mixed number in simplest form in the box.
Answers
The value of z in the circle is 2.3 units
How to determine the value of z in the circleIn the question, the following statements represents the given parameters
The length of a radius of a circle is represented by the expression z + 3.6. The given circle diameter is 11 4/5 ft.As a general rule, the diameter of a circle is the radius doubled
So, we have
2 * (z + 3.6) = 11 4/5
Express as decimal
2 * (z + 3.6) = 11.8
So, we have
z + 3.6 = 5.9
Evaluate the like terms
z = 2.3
Hence, the value of z is 2.3
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Two particles travel along the space curves r_1(t) = (t, t^2, t^3) r_2(t) = (1 + 4t, 1 + 16t, 1 + 52t). .Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) (x, y, z) = ()(smaller x-value) (x. y, z) = ()(larger x-value).
Answers
The paths intersect twice, at the point (1 ,1 ,1 ) when s=0 and t = 1
and at ( 3 , 9 , 27) when s = 1/2 and t = 3
The particles collide provided r₁(t) = r₂(t) <=>
< t , t² , t³ > = < 1+4t , 1+16t , 1+52t >
Comparing the both sides
=> t = 1+4t , t² = 1+16t and t³ = 1+52t
Solving first equation,
=> t = 1+4t
=> t = -1/3
Putting this value in other two,
=> (-1/3)² = 1+16(-1/3)
This doesn't satisfy these two
Therefore, the particles doesn't collide.
For the paths to intersect, We need to find a value for t and a value for s where r₁(t) = r₂(s) <=>
< t , t² , t³ > = < 1+4s , 1+16s , 1+52s >
Equating these with each other
=> t = 1+4s , t² = 1+16s and t³ = 1+52s
Solving these we will get s = 1/2 and t = 3
All these point satisfy all three equation
Thus , The paths intersect twice, at the point (1 ,1 ,1 ) when s=0 and t = 1
and at ( 3 , 9 , 27) when s = 1/2 and t = 3
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help me please
dont even need a full explanation
Answers
5x + 10 = 3x + 5
5x - 3x = 5 - 10
2x = -5
X = -5/2
let g (x) = 3x + 2 and f (x) = x-2/4. find the value f (g(0))
Answers
Answer: g (x - 2/4) = 3x + 1/2
Step-by-step explanation:
Y=-2/3x+4 Solve for x
Answers
Answer:
answer should be x = -3y/2 + 6
hope it helps :D
A company received orders for 1.500
erasers, and then a batch of orders
came in for 3,200 more. The company
has 800 erasers in stock, but 5,500 are
due in next week. How many erasers
will the company have in stock after
this shipment comes in and has
fulfilled all orders?
Answers
Answer:
0
Step-by-step explanation:
36/(x-3)=4 thank uu :>
Answers
Answer:
12
Step-by-step explanation:
36 / (x - 3) = 4
multiply both sides by (x - 3):
(x - 3)(36 / (x - 3)) = 4(x - 3)
36 = 4(x - 3)
expand right side:
36 = 4x - 12
add 12 to both sides:
36 + 12 = 4x - 12 + 12
48 = 4x
divide both sides by 4:
48/4 = 4x/4
x = 12