A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and A score that is the same as the mean is 0.
What is normal distribution?A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
Given that, a normal distribution of BMCC MAT51 scores has a standard deviation of 1.5.
At above 1.5
Z = (μ + 1.5 - μ)/2 = 1
At below 1.5
Z = (μ -1.5 - μ)/2 =-1
At above 1.36
Z = (μ + 1.36 - μ)/2 = 0.90
At same as the mean
Z = (μ - μ)/2 = 0
Hence, A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and A score that is the same as the mean is 0.
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Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −36? Show your work.
A. −3x − 6 > −33 and −3x − 6 ≥ −36
B. −3x − 6 < −33 and −3x − 6 ≥ −36
C. −3x > −33 and −6 ≥ −36
D. −3x − 6 < −33 and −3x − 6 ≤ −36
Option (B) is the correct one and -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality
Given, a compound inequality
−33 > (−3x − 6) ≥ −36
Now, we can interpret the given inequality separately also,
−33 > (−3x − 6)
On simplifying, we get
-33 > -3x - 6
-33 + 6 > -3x
-27 > -3x or -3x - 6 < -33
also, (−3x − 6) ≥ −36
On simplifying, we get
-3x - 6 ≥ −36
-3x ≥ −36 + 6
-3x ≥ −30 or -3x - 6 ≥ −36
So, -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality.
Hence, Option (B) is the correct one and -3x - 6 < -33 and -3x - 6 ≥ −36 is an equivalent form of the given compound inequality.
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8(6 +4) what is the answer to this question
Answer: " 80 " ; that is, the number: "eighty."
____
Step-by-step explanation:
Note the order of operations:
PE MD AS ;
Please Excuse My Dear Aunt Sally.
____
in which:
Parentheses are the first priority; if they occur.
then:
Exponents are the second priority if they occur.
followed by:
Multiplication and
Division; if any of these occur; and the priority is from the left-hand side to the right-hand side—if they occur. So; multiplication does not necessarily take priority over division. Rather, "Multiplication and Division" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur;
followed by:
Addition and
Subtraction; of any of these occur; and the priority is from the 'left-hand side to the right-hand side—if they occur. So; addition does not necessarily take priority over subtraction. Rather, "Addition and Subtraction" are treated equally, as the "next priority", from "left to right"—as they occur/if they occur.
____
So: For our given problem; we can solve:
" 8(6 + 4) " ; which is the same as:
" 8 * (6 + 4) ";
We have a "multiplication" and a "parentheses" ;
So: The "parentheses" take first priority:
____
"(6 + 4) = 10 " ;
now: " 8 * (6 + 4) " ;
= 8 * 10 = 80 ; which is our answer:
____
Alternate method:
Note the distributive property of multiplication:
→ a(b + c) = ab + ac ;
So: 8 (6 + 4) = (8*6) + (8*4) ;
= 48 + 32;
= 80 ; which is our correct answer!
____
Hope this answer was helpful to you!
Please reply if you have any questions! Wishing you well!
____
if y=7 when x=-4, find y when x=2
equation y= ?
solution y= -14
Value of y is -14
According to the expressions "" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. The constant of proportionality, k, sometimes known as yx = k, or y = k/x (they are essentially identical though.)
Therefore, in order to solve for either y or x in the future using the knowledge provided, we must first determine the constant k.
As y varies inversely as x
then,
[tex]y=k/x\\\7=k/-4\\\k=-28[/tex]
To find the value of y at x =2
[tex]y=k/x\\\y=-28/2\\\y=-14[/tex]
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The triangle above is a right triangle with side lengths a = 7 in., b = 24 in., and c = 25 in. Which statement is true? A. The sum of the squares of the two smaller sides is equal to the third side. B. The difference between the squares of the two smaller sides is equal to the square of the third side. C. The difference between the squares of the two smaller sides is equal to the third side. D. The sum of the squares of the two smaller sides is equal to the square of the third side.
Answer: D is the correct answer.
Step-by-step explanation:
The pythagoras theorum states that in a right angled triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse ( the largest side.)
What is the value of x?
Hint --> The two triangles add up to 180°
The value of x for the given triangle is 12.
According to the question,
We have the following information:
We have a figure of two triangles joined together and some of the angles are marked.
Now, we observe the figure carefully then the base of both triangles are parallel to each other.
Now, 45° will be the angle of triangle on right hand side because they are vertically opposite angles.
We know that the sum of three angles of triangle is 180°.
For the RHS triangle, let's take third angle to be y:
45+65+y=180
110+y =180
y =180-110
y = 70°
Now, y will be equal to (6x-2) because they are vertically opposite angles.
6x-2 = 70
6x = 70+2
6x = 72
x = 72/6
x = 12
Hence, the value of x for the triangle is 12.
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Use technology to find the P-value for the hypothesis test described below.
The claim is that for 12 AM body temperatures, the mean is μ> 98.6°F. The sample size is n=8 and the test statistic is
t = 1.692
P-value=
(Round to three decimal places as needed.)
Answer:
Approximately, 0.067.
Step-by-step explanation:
Now we have to find the p-function.
The excel function:
TDIST (1.021, 32, 1) = 0.1575
Context:
1.021 is the test statistic32 is the degrees of freedom1 stands for one tailed alternative hypothesisGiven from the calculations, it can be said that the P-value is equal to approximately 0.067.
x² -2(x-y), for x = 7 and y = 4
The value of given expression for x = 7 and y = 4 is 43
In this question, we have been given an expression x² -2(x - y)
We need to find the value of given expression for x = 7 and y = 4
x² -2(x - y)
= 7² -2(7 - 4)
= 49 - 2(3)
= 49 - 6
= 43
Therefore, the value of given expression for x = 7 and y = 4 is 43
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Simplify n!/( n-1 )!
Answer: n
Step-by-step explanation: n!=(n-1)!*n
(n-1)!*n/(n-1)!=n
Why the given linear function f(x) = x is called Identity Function? Justify.
It is called an identity function because the image of a domain element is identical to the range output.
Why is it called identity function?It is called an identity function because the image of a domain element is identical to the range output. As a result, an identity function translates every real number to itself. An identity function's output is the same as its input.In the context of the code in your question, an identity function is just a function that returns the same argument that was supplied to it: In mathematics, it is represented as f(x) = x.In given liner function on the Graph, domain element is identical to the range
hence the function we can call Identity Function.
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It is called an identity function because the image of a domain element is identical to the range output.
Why is it called identity function?It is called an identity function because the image of a domain element is identical to the range output. As a result, an identity function translates every real number to itself. An identity function's output is the same as its input.In the context of the code in your question, an identity function is just a function that returns the same argument that was supplied to it: In mathematics, it is represented as f(x) = x.In given liner function on the Graph, domain element is identical to the range.Hence the function we can call Identity Function.
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Given f(10)=4 , f′(10)=8 , g(10)=−1 , and g′(10)=9 , find the values of the following.
(fg)'(10)=
(f/g)'(10)=
im stumped. please help
Answer:
(fg)'(10)= 3 and the other one is 1.5
Step-by-step explanation:
fg and 10 with the 4x- 10 as the fraction of values of the followings of G-9 so its (fg)'(10)= 3 and the other one is 1.5
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
The equation of circle that have diameter of 12 cm is x2+(y-3)2=36
What is equation of circle?
The standard equation of a circle is given by:
(x-h)2 + (y-k)2 = r2
Where (h, k) is the coordinates of center of the circle and r is the radius.
Given, diameter = 12 cm
radius = 6 cm
Hence, center is on y-axis hence, x = 0
the point we get (h,k) =(0,3)
Put in equation we get
x2+(y-3)2=36
which is equation of circle.
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What is the image of (0, -3) after a dilation by a scale factor of 1/3 centered at the origin?
The image of (0, -3) after dilation by a scale factor of 1/3 centered at the origin is : (0, -1)
Given point P (0, -3)
The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.
Therefore, the new point is given by :
P' = (0×(1/3), (-3)×(1/3))
P' = (0, -1)
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Image of (0,-3) after dilation is (0,-1).
Scale factor = 1/3
Given point = (0,-3)
To find image of a point, we multiply the co-ordinates of the given point by scale factor.
Therefore, image = (0*(1/3),-3*(1/3))
= (0,-1)
Hence, image of point (0,-3) is (0,-1).
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A box is 45cm long and 32cm wide when 36000cm^3 of sand is put into it what is the height of the sand
The height of the sand is 25cm
How to calculate height?
First the volume formula is height × long × wide. So, we can calculate height by dividing the volume by the long and wide.
= 36,000 ÷ 45 ÷ 32
= 25cm
Thus, the height of the sand is 25cm
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8/10 as a fraction written in thousands
8/10 as a fraction written in thousands is 8000/10000
What is equivalent form of fractions?This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator
Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.
In the given problem, 8/10
8 is the numerator10 is the denominator8/10 is an equivalent form of 8000/10000 in thousands this means that they are equal.
8/10 is shown to be equal to 8000/10000 by dividing, this reduces the fraction to 8/10. Using calculator can still show it that both numbers equal
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Doug deposits $4,998 into an interest-bearing account that is compounded continuously. He decides to not deposit or withdraw any money after the initial deposit. The following function represents the balance of the account, which is compounded continuously at a rate of r, after t years.
Which expression approximately represents the rate, r, at which the account is continuously compounded if the account balance is $6,614 after 7 years?
A.
B.
C.
D.
Answer:
interest rate = 0.0400215403 or 4.00215403% or 4%
Step-by-step explanation:
formula
final amount =
initial amount times e^(interest rate times time)
6614 = 4998 times e^(interest rate times 7)
(6614 ÷ 4998) = e^(interest rate times 7)
1.32332933173 = e^(interest rate times 7)
ln means natual log
ln(1.32332933173) = ln(e^(interest rate times 7))
0.28015078214 = interest rate times 7
0.28015078214 ÷ 7 = interest rate
0.0400215403 = interest rate
utub dr ashley godbold
investopedia
Using the properties of logarithms, rewrite In (x5). Answers: A.) x5 B.) 5(logx) C.) e5 D) 5In x
The given logarithmic expression [tex]ln(x^5)[/tex] can be expressed as 5*lnx.
so option (D) is correct.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
The given logarithmic expression is [tex]ln(x^5)[/tex]
Property of logarithms: [tex]ln(x^n) = nln(x)[/tex]
So by using the above property, we can rewrite the given expression as
[tex]=ln(x^5)\\=5ln(x)[/tex]
Hence, the given logarithmic expression [tex]ln(x^5)[/tex] can be expressed as 5*lnx.
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write the following as unit rate 1200 words to 40 minutes
Answer:
30 Units
Step-by-step explanation:
1200 units ÷ 40
40 units ÷ 40
=
30 units
1 unit
=
30 units
unit
= 30 units per unit
How many numbers less or equal to 300 are divisible by 3, 4, or both, but not by 9?
By definitions of composite numbers and prime numbers, a total of 117 whole numbers that are less or equal to 300, are divisible by 3, 4 or both, but not by 9.
How to find all numbers less or equal to 300 such that are divisible by 3 and 4 but not by 9
In this problem we must look for all composite numbers that are divisible by 3, 4 or both, but not by nine. Composite numbers are products of prime numbers, that is, whole numbers that are only divisible by themselves. The set of numbers are formed by three subsets:
Subset 1
n = 3 × x, n ≤ 300, n ≠ 9 · i, i ≥ 1
The elements of the subset are: 3, 6, 12, 15, 21, 24, 30, 33, 39, 42, 48, 51, 57, 60, 66, 69, 75, 78, 84, 87, 93, 96, 102, 105, 111, 114, 120, 123, 129, 132, 138, 141, 147, 150, 156, 159, 165, 168, 174, 177, 183, 186, 192, 195, 201, 204, 210, 213, 219, 222, 228, 231, 237, 240, 246, 249, 255, 258, 264, 267, 273, 276, 282, 285, 291, 294, 300. (67 numbers)
Subset 2
n = 4 × x, n ≤ 300, x ≠ 9 · i, i ≥ 1
The elements of the subset are 4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48, 52, 56, 60, 64, 68, 76, 80, 84, 88, 92, 96, 100, 104, 112, 116, 120, 124, 128, 132, 136, 140, 148, 152, 156, 160, 164, 168, 172, 176, 184, 188, 196, 200, 204, 208, 212, 220, 224, 228, 232, 236, 240, 244, 248, 256, 260, 264, 268, 272, 276, 280, 284, 292, 296, 300. (50 numbers)
Subset 3
n = 12 × x, n ≤ 300, n ≠ 9 · i, i ≥ 1
The elements of the subset are 12, 24, 48, 60, 84, 96, 120, 132, 156, 168, 204, 228, 240, 264, 276, 300.
There are 117 whole numbers less or equal to 300.
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A gardener uses a roller to flatten a bowling green of length 29 m. The roller has a diameter of 1.3 m. The gardener says the roller makes 8 full turns in travelling the length of the green. Is the gardener correct? Explain your answer.
The gardner is correct Because the total distance traveled by the roller is greater than the length of the bowling green.
What is a diameter?A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
For the gardener to be correct,
8×Perimeter of the roller = Length of the bowling green
Therefore,
8πd = 29 (for the gardener to be correct)Let use first find the perimeter of the roller
P = πd....... Equation 1Where:
P = Perimeterd = diameter of the roller = 1.3 mSubstitute these values into equation 1
P = 1.3×22/7P = 4.09For 8 full rotation,
8×4.09 = 32.72 mComparing the distance for 8 revolution of the roller with the length of the bowling green,
The total distance traveled by the roller is greater than the length of the bowling green.Therefore, the gardner is correct
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you are currently scheduled to work monday through friday of next week. I need you to try to assist 9 more customers per day to hit your goal for the week. i currently assist 52 customers per day. so the total of customers i assist per week would be
The total number of customers you will assist per week would be 366
Let Total number of customer you assist per week be variable "x"
We have to calculate the value of this variable now,
Given ,
you work Monday to Friday,
Total working days = 6
Number of customer you usually assist = 52 customers per day
This week to hit your goal you have to assist more customers
Number of more customer you need assist = 9 customers per day
So, Total customer you'll assist per day to hit goal = 52 + 9
=> 61 customers per day
Customer you will assist per week = customer assist per day × 6
x = 61 × 6
x = 366
Hence , you will assist 366 customers per week.
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jared has $50 to spend on some new clothes for school. if the sales tax rate in his state is 6% the pretax total comes to $48.92, determine both the sales tax and the total due.will he have enough money to the purchases?
The sales tax is $2.935, and the total due is $51.855 ,Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.
Given:
jared has $50 to spend on some new clothes for school. if the sales tax rate in his state is 6% the pretax total comes to $48.92.
sales tax = 6% = 6/100 = 0.06.
= 0.06 * 48.92
= $2.935.
Total due = sales tax + pretax total
= $48.92 + $2.935
= $51.855
Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.
Therefore The sales tax is $2.935, and the total due is $51.855 ,Jared has $50 but the cost is $51.855 so he does not have enough money to the purchases.
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Solve the equation. Leave answer(s) in exact simplified form and use a solution set to express your
answer. Show work to determine if a potential solution is extraneous.
log₂ (x+2)+log₂ (x+3)=1
The solution for the given logarithmuc function is x = -1 or x = -4.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
Property of logarithms: log(a) + log(b) = log(ab)
The given function is
[tex]log_{2}(x+2) + log_{2}(x+3)=1[/tex]
By using the property of logarithms, we get
[tex]log_{2}(x+2) + log_{2}(x+3)=1\\\\log_2{[(x+2)(x+3)]}=1\\\\(x+2)(x+3)=2\\\\x^2+2x+3x+6=2\\\\x^2+5x+6-2=0\\\\x^2+5x+4=0\\\\(x+1)(x+4)=0[/tex]
Simplifying, we get
x = -1 (or) x = -4
Hence, the solution for the given logarithmuc function is x = -1 or x = -4.
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One month Kaitlin rented 2 movies and 12 video games for a total of $71. The next month she rented 5 movies and 3 video games for a total of $29. Find the
rental cost for each movie and each video game.
Rental cost for each movie: $
Rental cost for each video game: $
Answer:
rental cost of each movie is $2.5
rental cost of each video game is $5.5
Step-by-step explanation:
use x for movie and y for video game. Then you get the equations
2x+12y=71 and 5x+3y=29
then you solve each equation for either x or y.
when you solve for y you will get
y = (71 -2x) / 12 and y = (29 -5x) / 3
because y is the same, you put those equations together
(71-2x) / 12 = (29 -5x) / 3
then solve for x and you get x = 2.5
then you put 2.5 for x in either of the original equations and solve for y.
for both equations you will get y = 5.5
How many nonreal complex nineteenth roots of 1 exist?
The number of nonreal complex nineteenth roots is 1
What does it mean to have complex roots?The roots of equations that are represented as complex numbers are known as complex roots. The roots of the quadratic equations with discriminant values less than zero are fictitious or complicated. The real part and the imaginary part of the complex roots are of the type = a + ib and = c + id.
Here we have to find the nonreal complex nineteenth roots of 1
we know that nth root ⇒ n roots
Therefore,
[tex]1^{1/19}[/tex] ⇒ -1,1
[tex]-1^{19}[/tex] ⇒ -1
[tex]1^{19}[/tex] ⇒ 1
we get 1 real root exist.
The number of non real complex nineteenth roots is 1.
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What is the rate of change (slope) of this graph? Explain how you found the answer.
The rate of change(slope) of the graph is 7 / 5.
How to find the rate of change(slope)?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The slope(rate of change) is change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
Therefore, let's find the slope of the graph as follows:
slope = y₂ - y₁ / x₂ - x₁
Therefore, using (0, -7) and (5, 0)
slope = 0 - (-7) / 5 - 0
slope = 7 / 5
Therefore, the slope of the graph is 7 / 5.
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Help please I need to finish this IXL
If the equation for a line "u" be represented as [y = (-2x + 10)], then the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)].
As per the question statement, the equation for a line "u" can be represented as [y = (-2x + 10)],
And we are required to determine the equation of another line "v", which is parallel to line "u" and passes through the point (-1, 2).
To solve this question, first we need to know about a property of parallel lines, which is, "Any straight line parallel to a line of known slope will also have the same slope"
Now, the formula to determine the equation of a straight line having a known slope, say "m" and a y-intercept of "c" goes as, [y = (mx + c)], also known as the slope-intercept form of line. Comparing the equation of line "u" with this slope-intercept form, we get, [m = (-2)] and [c = 10].
That is, the slope of line "u" is (-2), and hence, the slope of line "v" must also be (-2) since they are parallel to each other.
Also, the formula to determine the equation of a straight line having a known slope, say "m", and passing through a known point, say (x₁, y₁), goes as, [(y - y₁) = {m(x - x₁)], and using [m = (-2)] and [(x₁, y₁) = ((-1, 2)] in this formula, we get,
[(y - 2) = (-2){x - (-1)}]
Or, [(y - 2) = (-2)(x + 1)]
Or, [(y - 2) = (-2x - 2)]
Or, [y = (-2x - 2 + 2)]
Or, [y = (-2x)]
That is, the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)]
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Convert the decimal to a percent. 0.12573 Question 4 options: 0.0012573% 1.2573% 12.573% 12573%
Answer:
12.573%
Step-by-step explanation:
Percent means "parts per 100".
Therefore, to convert a decimal to a percent, multiply the decimal by 100.
When multiplying a decimal by a multiple of 10, simply move the decimal point to the right the same number of places as there are zeros.
Therefore, to multiply a decimal by 100, simply move the decimal point 2 places to the right.
⇒ 0.12573 × 100 = 12.573%
#p is invested at 10% and#q is invested at 12% . The annual income from these investment is #3800.if these investments are interchanged the annual income will be#3900. find p and q
Suppose $7000 is invested at an annual interest rate of 4% compounded daily for 3 yr. What is the accumulated amount in the account at the end of the 3 yr?
The accumulated amount in the account after 3 years, if $7000 was invested is $7892.43.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
To calculate the the accumulated amount in the account at the end of the 3 years, we use the formula below.
Formula:
A = P(1+R/n)ⁿˣ................ Equation 1Where:
A = Accumulated amount in the accountP = PrincipalR = Raten = Number of times the interest is compounded per yearx = Number of yearsFrom the question,
Given:
P = $7000R = 4% = 0.04x = 3 yearsn = 365Substitute these values into equation 1
A = 7000(1+0.04/365)³ˣ³⁶⁵A = 7000(1.12749)A = $7892.43Hence, the accumulated amount in the account is $7892.43.
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Which expression correctly shows how to rewrite log521 using a log base of 7?
log75log721
fraction numerator log subscript 7 end subscript 5 over denominator log subscript 7 end subscript 21 end fraction
log721log75
, fraction numerator log subscript 7 end subscript 21 over denominator log subscript 7 end subscript 5 end fraction,
log217log57
, fraction numerator log subscript 21 end subscript 7 over denominator log subscript 5 end subscript 7 end fraction,
log57log217
Answer: log7 21 / log7 5
I took one for the team and guessed, and got it right.
You are welcome future students.
The expression that correctly shows how to rewrite the logarithm [tex]\log_5{21}[/tex], using a logarithm of base 7, with change of base, is given as follows:
[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]
How to change the base of a logarithm?To change the base of a logarithm, a new fraction is written, in which:
The numerator is the logarithm of the new base of the number that the previous logarithm was calculated.The denominator is the logarithm of the new base of the base of the previous logarithm was calculated.In this problem, the logarithm that will be calculated is:
[tex]\log_5{21}[/tex]
Hence the number and the base of the logarithm are presented as follows:
The number is of 21.The base is of 5.With the change of the base to base 7, the numerator and the denominator of the fraction are given as follows:
Numerator: [tex]\log_7{21}[/tex]Denominator: [tex]\log_7{5}[/tex]Hence the simplified logarithm is presented as follows:
[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]
Meaning that the correct option is the second option.
More can be learned about the change of base of a logarithm at https://brainly.com/question/25588990
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