The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.
How to calculate the probability distribution?The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,
Z = (X - μ)/σ
Where X - random variable; μ - mean; σ - standard deviation;
Then the probability is calculated by P(Z < x), using the values from the distribution table.
Calculation:The given data has the mean μ = 120 and the standard deviation σ = 18
Z- score for X =150:
Z = (150 - 120)/18
= 1.67
Z - score for X = 156:
Z = (156 - 120)/18
= 2
So, the probability distribution over these scores is
P(150 < X < 156) = P(1.67 < Z < 2)
⇒ P(Z < 2) - P(Z < 1.67)
From the standard distribution table,
P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254
On substituting,
P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471
Rounding off to four decimal places,
P(150 < X < 156) = 0.0247
Thus, the required probability is 0.0247.
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50% is what percent of 40%?
Answer:
125%Step-by-step explanation:
[tex] \frac{50}{100} \times 40[/tex][tex] = 125\%[/tex]f(x)=x3 −4x even odd or neither
Answer:
The function would be odd
The answer is neither.
Let's take an odd number and substitute.
f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)Now, let's take an even number.
f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)Since both even and odd numbers are possible, it is neither.
Admission into an amusement park for 4 children
and 2 adults is $116.90. For 6 children and 3 adults,
the admission is $175.35. Assuming a different price
for children and adults, what is the price of the child's
ticket and the price of the adult ticket?
Answer:
A child ticket costs $16.50 and an adult ticket costs $25.45.
It is found that the child ticket costs $16.50 and an adult ticket costs $25.45.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that 4 children and 2 adults are $116.90. For 6 children and 3 adults, the admission is $175.35.
Assuming a different price for children and adults,
Let the children are x and the adult is y.
Therefore,
4x + 2y = 116.90
6x + 3y = 175.35
Hence, the child ticket costs $16.50 and an adult ticket costs $25.45.
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Which statement is not true for goodness-of-fit tests? Question content area bottom Part 1 A. Expected frequencies must be whole numbers. B. Observed frequencies must be whole numbers. C. The observed frequency is found from sample data values. D. The expected frequency is found assuming that the distribution is as claimed.
The statement that is not true for goodness-of-fit tests is: A. Expected frequencies must be whole numbers.
What is Goodness-of-fit tests?Goodness-of-fit tests can be defined as the test conducted to help find out whether the observe value work hand in hand with expected value or the observe value is different from the expected value.
The statement is not true because it is not must for expected frequencies to be whole number despite the fact that expected frequencies are whole numbers.
Therefore the statement that is not true for goodness-of-fit tests is: A. Expected frequencies must be whole numbers.
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219. There is a local maximum at x = 2, local minimum at x = 1, and the graph is neither concave up nor concave down.
Lisa is cutting a 14-inch piece of paper into 0.4-inch strips. How many strips of paper will she have when she is finished?
5.6
35
30
28
Answer:
take 14/0.4the multiply by ten both the denominator and .numerator then simplify by two your final answer will be 35
an employee at a factory is paid $9.25 per hour plus a $8.00 bonus for every 20 transformers assemble.
Answer:
Step-by-step explanation
Answer:
$13.47 per hour
Step-by-step explanation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
What’s the next 3 numbers 0 10 1011 1031 102113 10311213
The next three numbers here would be 0, 10, 1011, 1031, 102113, 10311213, 10411223, 1031221314, 1041222314.
What is a number sequence
The term number sequence is used to refer to the list of numbers that have the relationship of having a linked rule. The number that follows in the sequence has to be worked out from the previous numbers in that particular sequence. You have to follow the particular rule to be able to work out the number that has to follow in the sequence.
For example we have these numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 etc. We would have to understand the pattern of numbers that are in the sequence. We can see that there is a difference of 3 between the number that succeeds the previous one in the sequence.
How to get the next values in the sequenceThe first value here is given to be 0
Next we have the 1 0 = 10
The next that we have is 1 0 and 1 1 written as 1011
Next is 1 zero and three one = 1031
We continue to follow the pattern till we arrive at 1041222314. This is where the sequence would then have to stop.
Hence we have to conclude that the next numbers are 10411223, 1031221314, 1041222314.
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What's the Value of X in 1/2 + X = 5/6
Answer:
x = 1/3
Step-by-step explanation:
1/2 + X = 5/6
collecting the like terms
X = 5/6 - 1/2
making one fraction on the left side by taking the common denominator
X = (5 - 3)/6
X = 2/6
devide the numerator and denominator by 2, you get
X = 1/3
Solve the system of equations algebraically and create a graphical model.
[tex]3x + 2y = 8 \\ x + 2y = 4[/tex]
Answer: [tex]x=2, y=1[/tex]
Step-by-step explanation:
Subtracting the second equation from the first yields [tex]2x=4 \longrightarrow x=2[/tex].
This means that [tex]y=1[/tex].
So, the solution is [tex]x=2, y=1[/tex]
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
y
=
−
10.51
x
+
15.05
and the
r
=
−
0.45
.
The proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
How to determine the proportion of the variation in y that can be explained by the variation in the values of x?The complete question requires that we calculate the proportion of the variation in y that can be explained by the variation in the values of x
The given parameters in the question are:
The regression equation is reported as
y = − 10.51x + 15.05
r = − 0.45
Take the square of both sides in the equation r = − 0.45
r^2 = − 0.45^2
Evaluate the squares
r^2 = 0.2025
This represents the proportion of the variation in y that can be explained by the variation in the values of x
Hence, the proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
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Which expression has a conflict of 10 and a constant of5
The expression that has a coefficient of 10 and constant of 5 is 10x + 5.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A coefficient is a number or any symbol representing a constant value that is multiplied by a variable. A constant is a value or number that never changes in expression.
The expression that has a coefficient of 10 and constant of 5 is 10x + 5.
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The average speed of a car on a stretch of interstate is 70 miles per hour. Convert this rate to feet per second.
Answer:
102. 66 feet / SecondStep-by-step explanation:
To do conversion change miles into feet and hour into second.
One foot is 5280 feet
And an hour is 3600sec
70 miles / Hour
70 * 5280feet / 3600 second
369600 feet / 3600seconds
Then simplify
102. 66 feet / Second
Speed given
70mph1 mi=5280ft
1h=3600s
So convert
70×5280ft/3600s7×528ft/36s102.67ft/sComplete each statement describing the transformations you observed for the graph of y = 2x + k.
When the value of k increases, the graph of the function:
When the value of k decreases, the graph of the function:
.
Using translation concepts, it is found that:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The translation y -> y + k represents:
A shift up if k > 0.A shift down if k < 0.Hence:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.More can be learned about translation concepts at https://brainly.com/question/4521517
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3,480
A)348 hundreds
B)3,480 ones
C)3 x 1,000+ 4 x 100 + 8 x 80
D)3 thousands and 80 tens
C)3 thousands and 48 tens
Answer
B
explanation
3480ones = 3480x1=3480
4. Find the value of x & y from the following equation 4x+5y=90, x+y=20 a. 10, 15 b. 10, 5 c. 10, 8 d. 10, 10
Answer:
d. 10, 10
Step-by-step explanation:
4(10)+5(10) = 40 + 50 = 90
10 + 10 = 20
Hope this helps
An equation is formed of two equal expressions. In the two of the given equations, the value of x and y are 10 and 10, respectively. The correct option is D.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two of the equation, which can be named as,
4x+5y=90 ...... equation 1
x+y=20 ............ equation 2
Solve the second equation for x,
x + y = 20
x = 20 - y ................ equation 3
In the first equation substitute the value of x from the third equation,
4x + 5y = 90
4(20 - y) + 5y = 90
Solving the equation for y,
80 - 4y + 5y = 90
y = 90 - 80
y = 10
Substitute the value of y in the second equation, to get the value of x,
x + y = 20
x + 10 = 20
x = 20 - 10
x = 10
Hence, In the two of the given equations, the value of x and y are 10 and 10, respectively.
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Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program? help pls
Answer: 4
Step-by-step explanation:
x - (1/3)x - (1/6)x = 2
(6x - 2x - x)/6 = 2
3x/6 = 2
x=4
what is the length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm?
Simplify. ‒36 ÷ (27 ÷ 3 ∙ 2)
The simplified value of expression -36/(27/3*2) is -8.
Given an expression -36/(27/3*2).
We are required to find the simplified value of given expression. To simplify the expression we need to use addition,subtraction,multiplication, division, brackets, etc. We can say that we have to use BODMAS in order to find the simplified value of expression.
Expression is combination of numbers, symbols, coefficients, determinants, indeterminants, fraction,algebraic operations,etc. usually not found in equal to form.
The given expression :
=-36/(27/3*2) (Multiplying 3 and 2 first)
=-36/(27/6)
=(-36*2)/9 (Invert the fraction given in denominator)
=-72/9 (Multiplying -36 to 2)
=-8
Hence the simplified value of expression -36/(27/3*2) is -8.
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Copy the proof, mark the givens in the diagram and fill in the blanks to complete the proof
Answer:
Step-by-step explanation:
Draw UT Construction
UT = UT Reflexive Property
BT = EU Given
BU = ET Given
ΔUBT = ΔEUT SSS = SSS
<B = <E CPCTC
The bolded parts are the blanks you need to fill in.
Answer:
Draw UT construction
UT = UT reflexive property
BT = EU given
BU = ET given
ΔUBT = ΔEUT SSS = SSS
<B = <E CPCTC
hope this helps!
Definition of economic costs Gilberto lives in San Diego and runs a business that sells pianos. In an average year, he receives $701,000 from selling pianos. Of this sales revenue, he must pay the manufacturer a wholesale cost of $420,000; he also pays wages and utility bills totaling $247,000. He owns his showroom; if he chooses to rent it out, he will receive $9,000 in rent per year. Assume that the value of this showroom does not depreciate over the year. Also, if Gilberto does not operate this piano business, he can work as a financial advisor, receive an annual salary of $32,000 with no additional monetary costs, and rent out his showroom at the $9,000 per year rate. No other costs are incurred in running this piano business.
The wholesale cost for the pianos that Tim pays the manufacturer, wages and utility bills that Tim pays are counted as explicit cost. On the other hand, the salary that Tim could earn if he worked as an accountant and the rental income that Tim could earn from renting his showroom fall under implicit cost.
Difference between Implicit Cost and Explicit Cost:
These two expenses, implicit cost and explicit cost, both represent company activity. The connection between cost and business is what distinguishes these two.
An explicit cost is one that the owner bears directly; an implicit cost is one that the owner bears indirectly without paying or utilizing its own resources. However, the organization or corporation takes into account both expenses while making management decisions.
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which graph represents -5x+3y is equal to or greater than 9
Answer:
First, transform the given equation into the slope intercept form.
-5x + 3y >= 9
3y >= 5x + 9
y >= 5/3x + 3
Then graph the line y = 5/3x + 3. Draw a solid line with y intercept 3 and slope of 5/3.
Finally, shade everything that is above the line.
Find the inverse of function f. F(c) = 9x + 7
Answer:
(x-7)/9
Step-by-step explanation:
F(c) = 9x + 7
y = 9x + 7 Now switch the y and the x and solve for y
x = 9y + 7 Subtract 7 from both sides
x - 7 = 9y Divide both sides by 9
(x-7)/9
What is the domain of the relation graphed below?
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
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What is the length of CG?
Answer:
19
Step-by-step explanation:
63÷21=3
21 was multiplied by 3 to get 63
CG by 3 should give 57
How many pairs of two digit natural numbers have a difference equal to 50
The number exists 99, then 99 - 49 = 50
Therefore, the pair of two-digit numbers exist between 99 and 49.
What is the difference?In math, the word difference exists as the outcome of subtracting one number from another.
Let the first pair of two-digit numbers be xy and the second pair of numbers be yx.
we want a two-digit number, a two-digit number begins from 10 and ends with a two-digit number that exists 99.
Let the difference of 50 exists possible when we take the biggest two-digit number
Therefore, the number exists 99
99 - 49 = 50
Therefore, the pair of two-digit number exists 99 and 49.
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NO LINKS! Please help me with this problem
Answer:
x=70, y=55
Step-by-step explanation:
Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.
So using this we can derive the equation: [tex]y+2x-15=180[/tex]
The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.
So using these we can derive the equation: [tex]x+2y=180[/tex]
So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.
Original Equation:
[tex]x+2y = 180[/tex]
Subtract 2y from both sides
[tex]x = 180-2y[/tex]
Now let's plug this into the first equation
[tex]y+2x-15=180[/tex]
Plug in 180-2y as x
[tex]y+2(180-2y)-15=180[/tex]
Distribute the 2
[tex]y+360-4y-15=180[/tex]
Combine like terms
[tex]-3y + 345 = 180[/tex]
Subtract 345 from both sides
[tex]-3y = -165[/tex]
Divide both sides by -3
[tex]y=55[/tex]
So we can plug this into either equation to solve for x
[tex]x+2y=180[/tex]
Substitute in 55 as y
[tex]x+2(55)=180[/tex]
[tex]x+110=180[/tex]
Subtract 110 from both sides
[tex]x=70[/tex]
Answer:
x = 70°
y = 55°
Step-by-step explanation:
The angle sum theorem and the definition of a linear pair can be used to write two equations in the two unknowns. Those can be solved for the angle values.
Setupx + y + y = 180° . . . . . . angle sum theorem
y + (2x -15) = 180° . . . . definition of linear pair
SolutionWe can use the first equation to write an expression for x that can be substituted into the second equation:
x = 180 -2y
y +(2(180 -2y) -15) = 180 . . . . substitute for x
345 -3y = 180 . . . . . . . . . . . collect terms
115 -y = 60 . . . . . . . . . . . . .divide by 3
y = 55 . . . . . . . . . . . . . . add (y-60)
x = 180 -2(55) = 70
The values of the variables are ...
x = 70°
y = 55°
exterior angle = 125°
Find the area of the rhombus 12 5
Pls answer these questions ASAP
From the given descriptions and dimensions, we have;
6. 2000 cm²
7. 81 m²
8. a. 138 m²
b. 538 m²
c. 62 cm²
9. $107.25
Which method can be used to calculate the surface areas and cost?6. Type of box = Open box with no lid
Side length of the box = 20 cm
Therefore;
Number of faces of the box, painted = 5
Area of a face of the box = 20² = 400
Area of the surface painted, A = 5 × 400 cm² = 2000 cm²7. Area of the plastic to cover one book, A, is found as follows;
A = 2 × 20 × 15 + 2 × 3 × 15 + 2 × 20 × 3
Which gives;
A = 600 + 90 + 120 = 810The area of plastic needed to cover 1000 books is therefore;
Total area = 1,000 × 810 cm² = 810,000 cm²
Conversion of cm² to m² gives;
1 m² = 10,000 cm²Therefore;
A = 810,000 cm² = 810,000 cm² × 1/10,000 m²/cm² = 81 m²
The area of plastic needed to cover 1000 books is A = 81 m²8. The surface areas are;
a. A = 2 × 3 × 6 + 5 × 6 + 7 × 6 + 2×3×(3+7)/2 = 138
The surface area is 138 m²b. A = 2 × 15 × 5 + 2×(10×5 + (6×8)/2) + 2×8×15 = 538
A = 150 + 148 + 240 = 538
The surface area is 538 m²c. From the congruent marks, we have;
A = 5 × 3 × 3 + 5×1×3 + 2×1×1 = 62
The surface area is 62 cm²9. From the congruent markings, we have;
A = 2 × (1.5 × 1.5 + (1.5 × 1.3)/2) + 5×2×1.5
A = 6.45 + 15 = 21.45
Surface area of a the canvas, A = 21.45 m²
Cost per unit area of the canvas, c = $5
Cost of the canvas for the tent, C, is therefore;
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Choose the number (X) that should come next in this series (1, 2, 6, 15, X, 56, 92)
Answer:
31
Step-by-step explanation:
The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31
The unknown number(x) in the series is 31.
The given series 1, 2, 6, 15, x, 56, 92.
We need to find the value of x.
What is a series?In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.
The numbers in the series increase by (n+1)².
So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.
Therefore, the unknown number(x) in the series is 31.
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