The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
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Vector g is shown below.
Vector h is parallel to g, in the same direction and
half as long.
Work out h as a column vector.
9
Answer:
h = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
Step-by-step explanation:
g = [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] , then
h = [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
which expression is equivalent to....
Answer:
A^32
Step-by-step explanation:
Done
Answer:
Option D: a³²
Step-by-step explanation:
Powers in this case multiply, 8*4=32
therefore answer D a³² is correct
What is the perimeter in units ?
Answer:
12 + [tex]4\sqrt{5}[/tex] approximates to 20.944
Step-by-step explanation:
VU - 8 units
UW - 4 units
VW - [tex]\sqrt{64+16} = \sqrt{80} =4\sqrt{5}[/tex]
12 + 4sqrt(5)
Answer:
6 (2 + √5) units
Step-by-step explanation:
Finding the length of the 3rd side :
*Applying Pythagorean Theorem*
VW² = 4² + 8²VW² = 16 + 64VW = √80VW = 6√5The perimeter :
4 + 8 + 6√512 + 6√56 (2 + √5) unitsAn arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?
an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n
Answer:
an= -3+5(n-1)
Step-by-step explanation:
Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.
Answer:
A.) an = -3 + 5(n - 1)
Explanation:
Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)
Arithmetic Series: a + (n - 1)d
['a' is first term, 'n' determines term position, 'd' is common difference]
Determine the following:
a = -3d = second term - first term = 2 - (-3) = 5Putting into equation:
-3 + (n - 1)5-3 + 5(n - 1)Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.
A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.
Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2
Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
What is the iteration method?Iteration is the process of repeating a procedure in order to produce a series of results.
We have:
= √0.15
[tex]= \rm \sqrt{{\dfrac{15}{100}}}[/tex]
[tex]= \rm \sqrt{{\dfrac{3}{20}}}[/tex]
= (1.732)/(4.472)
= 0.3872
√0.15 is less than 0.4.
Thus, Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
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Answer:
C
Step-by-step explanation:
A certain field is a rectangle with a perimeter of 1030 feet. The length is 181 feet more than the width. Find the width and length of the rectangular field.
Step-by-step explanation:
the perimeter is
2×length + 2×width = 1030 ft
length + width = 515 ft
length = width + 181
now we use that in the first equation :
(width + 181) + width = 515
2×width + 181 = 515
2×width = 334
width = 167 ft
because of
length = width + 181
length = 167 + 181 = 348 ft
The width and length of the rectangular field are 165.5 ft and 346.5 ft respectively.
Concept: Perimeter is the sum of the length of all sides of a figure/solid.
Given: Length = 181+width
Let width be equal to 'width' ft
Perimeter= 1030 feet
In a rectangle there are 2 length and 2 width so the perimeter of a rectangle is equal to 2*(181+ width) + 2width = 362 + 2width + 2 width = ⇒362 + 4width =1030 ft
4width = 662 ( on transposing)
width= 165.5 ft
length= 181+ 165.5 ft
length = 346.5 ft
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Question 1
Kapoor Corporation uses the following activity rates from its activity-based costing to assign overhead costs to products.
Activity Cost Pools Activity Rate
Setting up batches $86.50 per batch
Assembling products $4.63 per assembly hour
Processing customer orders $52.16 per customer order
Data concerning two products appear below:
Product J00A Product S06U
Number of batches 34 43
Number of assembly hours 105 812
Number of customer orders 17 32
Required:
a. How much overhead cost would be assigned to Product J00A using the company's activity-based costing system?
b. How much overhead cost would be assigned to Product S06U using the company's activity-based costing system?
Overhead Cost:
There are some expenses incurred at the time of manufacturing of products and services that are not directly attributable to the finished products. These expenses are known as manufacturing overheads or indirect expenses.
The overhead cost would be assigned to Product J00A using the company's activity-based costing system is $4313.87.
How to calculate the cost?The overhead cost that would be assigned to Product J00A using the company's activity-based costing system will be:
= ($86.50 × 34) + ($4.63 × 105) + ($52.16 × 17)
= $2941 + $486.15 + $886.72
= $4313.87
The overhead cost would be assigned to Product S06U using the company's activity-based costing system will be:
= ($86.50 × 43) + ($4.63 × 812) + ($52.16 × 32)
= $3719.50 + $3759.56 + $1669.12
= $9148.18
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A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
The probability of getting a heart from the first deck and then a diamond on the second deck will be 6.25%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The probability of getting a heart from the first deck = 13/52.
And the probability of getting a diamond from the second deck = 13/52.
So, The probability of getting a heart from the first deck and then a diamond on the second deck will be,
Probability = (13/52) × (13/52) = 0.0625 = 6.25%
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Difficult one. Need help with work shown.
Answer:
the length of the fence = 420 ft
The total area = 8000 ft²
Step-by-step explanation:
the fence has the same length as the perimeter of the rectangle
then
the length of the fence = 2×(160+50) = 420 ft
………………………………………………………………
The total area enclosed by the fencing = the area of the rectangle
Then
The total area = 160×50 = 8000 ft²
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2(length + width)
= 2(160 + 50)
= 2 × 210
= 420 ft ← amount of fencing needed
the area (A) of a rectangle is calculated as
A = length × width = 160 × 50 = 8000 ft²
Liz earns a salary of $2,200 per month, plus a commission of 5% of her sales. She wants to earn at least
$2,500 this month. Enter an inequality to find amounts of sales that will meet her goal.your
variable represents. Enter the commission rate as a decimal.
Answer:
2200 + 0.5x >= 2500
Step-by-step explanation:
x is the amount of sales
The changes in account balances for Elder Company for 2021 are as follows:
Assets $ 480,000 debit
Common stock 250,000 credit
Liabilities 160,000 credit
Paid-in capital—excess of par 30,000 credit
Assuming the only changes in retained earnings in 2021 were for net income and a $50,000 dividend, what was net income for 2021?
The changes in account balances for Elder Company for 2021 are net income will be $160000
We have given debt common stock = $680000
Credit liabilities = 350000
Credit paid in capital = 190000
And an excess of par 30,000 credit Assuming the only changes in retained earnings
So 680000 = 350000+190000+30000+ retained earning
What is the net income?Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
So retained earning = $110000
Dividend paid = $50000
So Net income = dividend paid + retained earning
Net income = $110000+$50000
Net income = $160000
So option (c) will be the correct answer.
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What is the product?
(3a²b7)(5a³b³)
O 8a5b15
O 8a6b56
O 15a³b¹5
O 15a5b56
Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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Y=3x-7 complete the missing value in the solution to the equation (1,
Answer: (1, -4) or y = -4
Step-by-step explanation:
Given:
y = 3x - 7
Plug in the value of 1 for x - given to us by "(1, ?)
y = 3x - 7
y = 3(1) - 7
Multiply:
y = 3 - 7
Subtract:
y = -4
y = -4
According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ
Answer:
OD.(x-3)(x-2)
Step-by-step explanation:
we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.
so its OD
as -3×-2=6
and -3+-2=-5
A car travels 18 mile in 213 minutes. What is its speed in terms of miles per minute?
Answer:
[tex]\textsf {0.08 miles per minute}[/tex]
Step-by-step explanation:
[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]
[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]
[tex]\textsf {Speed = 0.08 miles per minute }[/tex]
Answer:
The speed in miles per minute is 0.0845 mpm.
Step-by-step explanation:
The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.
Speed = Distance ÷ Time
Speed = 18 m / 213 min
18 divided by 213 = 0.0845
speed = 0.0845 mpm
Therefore the speed in miles per minute is 0.0845 mpm.
Which of the following statements is true?
Answer:
Last choice, [tex]\sqrt{15}[/tex] is irrational and [tex]\sqrt{0.001}[/tex] is rational
Step-by-step explanation:
Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers, ex. 0.4
Irrational Numbers: A type of real number which cannot be represented as a simple fraction (non ending decimal), ex. 0.4161446
[tex]\sqrt{15} = 3.8729[/tex] making it irrational
First and third choice are INCORRECT as they state its rational[tex]\sqrt{0.001} = 1/1000[/tex] making it rational
Second choice is INCORRECT as they state its irrationalHence, the last choice is correct
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Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]
[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]
[ log (x) + log (y) = log (xy) ]
[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]
[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]
The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Okay last question, I’ll mark brainliest whoever gets it correct first
Answer:
Angle ABC = 112°
Step-by-step explanation:
THAT IS CORRECT TRUST ME
A rectangle has a side length of three and two sevenths centimeters and a side width of 4 centimeters. What is the area of the rectangle?ten and six sevenths cm2
thirteen and one seventh cm2
thirteen and five sevenths cm2
fifteen and one seventh cm2
The area of the rectangle is thirteen and one seventh cm2
What is the area of the rectangle?A rectangle is a four-sided object that has two widths and two lengths. The sum of angles in a rectangle is 360 degrees.
Area of a rectangle = length x width
3 2/7 x 4
23/7 x 4 = 92 / 7 = 13 1/7 cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
How to get the area of the rectangle?
For a rectangle of length L and width W, the area is:
A = L*W
Here we know that:
L = (3 + 2/7)cm
W = 4cm
Then the area is:
A = (3 + 2/7)cm*4cm = (12 + 8/7)cm² = (13 + 1/7) cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
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Question 1 of 10
What is the midpoint of the segment shown below?
O A. (6,3)
O B. (6,5)
O C. (3,5)
OD. (3, 3)
Answer:
[tex]\textsf{C.} \quad \left(3,\dfrac{5}{2}\right)[/tex]
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints of the line segment:
[tex]\textsf{Let }(x_1,y_1)=(-1,2)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(7,3)[/tex]
Substitute the defined endpoints into the midpoint formula and solve:
[tex]\implies \textsf{Midpoint}=\left(\dfrac{7+(-1)}{2},\dfrac{3+2}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(3,\dfrac{5}{2}\right)[/tex]
Midpoint
(-1+7/2,2+3/2(6/2,5/2)3,5/2)graph g(x) = -8|x| +1
Answer:
look the attachment in the above
Cells B1, C1, and D1 contain the values Seat1Row1, Seat2Row1, and Seat3Row1. If cells B1, C1, and D1 were selected, and autofill
used to fill E1, F1, and G1, what would be the auto-filled values?
Seat1Row2, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row3, Seat4Row4
Seat 1Row1, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row2, Seat4Row2
In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.
What values would be in E1, F1, and G1?When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.
If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.
When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.
If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.
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Which of the following is the conjugate of the expression below when x>-2?
6+√x+2
OA. 6+√x+2
B. 6-√x-2
C. 6-√√x+2
D. 6+√x-2
Please Hurry !!!!!!!A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answer:
(–2, 0) and (2, 5)
(2, –1) and (10, 9)
Step-by-step explanation:
1. Find the slope of the what is considered perpendicular to -4/5. To do this, we simply use the reciprocal and multiply it by -1. Therefore, a perpendicular line would have a slope of 5/4.
2. Next, we can plug each of the ordered pairs into [tex]\frac{y2-y1}{x2-x1}[/tex] to see whether or not they have a slope of 5/4. We must do this to all of the ordered pairs until we find 2. Keep in mind that coordinates give you (x, y) in that order, so don't get the x's and y's confused. Additionally, it does not matter which coordinate goes first, just make sure that you get y2 and x2 from the same coordinate, and y1 and x1 from the same coordinate.
[tex]\frac{0-5}{-2-2}=\frac{-5}{-4}=\frac{5}{4}[/tex] The first answer![tex]\frac{5-(-5)}{-4-4}=\frac{0}{-8}[/tex] Not an answer[tex]\frac{4-0}{-3-2}=\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-(-5)}{1-6} =\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-9}{2-10} =\frac{-10}{-8}= \frac{5}{4}[/tex] The second answer!Solve −x+5≤4 or 2x+3≥−1 and write the solution in interval notation.
Answer:
Step-by-step explanation:
[tex]\left \{ {{-x+5\leq 4} \atop {2x+3\geq -1}} \right.[/tex] ⇒ [tex]x\geq 1\\2x\geq 4\\x\geq -2[/tex]
or
[tex]x \geq -2\\(-2,+ { \infty} )[/tex] (Answer)
why f is not differentiable at x = 0 , where f(x) is x ^1/3
Therefore the f is continuous on R , i.e. real numbers and f is not differentiable at 0 ,Option A and D is the correct answer.
What is a Function ?A function is a mathematical statement which find relation between independent variable and dependent variable.
It always comes with a defined range and domain.
It is given that :
[tex]\rm f(x) = x^{1/3}\\\\LHD (at\; x = 0) = RHD (at \; x = 0)\\\\\= \lim_{x\rightarrow 0}\dfrac{f(x)-f(0)}{x-0}\\\\=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0}[/tex]
[tex]=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0} \\\\= \lim_{h\rightarrow 0}\dfrac{(-h)^{1/3}}{-h}\\\\\lim_{h\rightarrow 0}\dfrac{(-1)^{1/3}(h)^{1/3}}{-1*h}\\\\\lim_{h\rightarrow 0} (-1)^{-2/3}h^{-2/3}[/tex]
if we substitute h = 0 ,
Here, LHD and RHD does not exist at x = 0 So, f(x) is not differentiable at x = 0 .
Therefore the f is continuous on R , i.e. real numbers
and f is not differentiable at 0
Option A and D is the correct answer.
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-11-(-5)
————-
2x3
is an example of
A. a numerical equation
B. a numerical expression
C. an algebraic expression
D. an algebraic equation
Answer:
B.a numerical expression
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answer:
Or if you don't want any rounding it will be 115.38461538461
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. If you connect a 2 megohm resistor (2× 10^6 ohms) across a 2.4 kilovolt voltage source (2.4×10^3 volts),what would be the current in amps?
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.
What is Ohm's Law?Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.
The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)
= 1.2 × 10⁻³ amp
Hence, the current in the amp is 1.2 × 10⁻³.
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