Answer:
P(45<X<81) = P(-3<z<3)=0.9974 or 99.74%
Step-by-step explanation:
Mean = 63
Standard Deviation =6
We need to find probability that X lies between 45 and 81 i.e P(45<X<81)
First we will find z-score for X=45 and X=81
For X=45 the z-score can be found using formula: [tex]z-score=\frac{X-\mu}{\sigma}[/tex]
Putting values and finding z-score
[tex]z-score=\frac{X-\mu}{\sigma}\\z-score=\frac{45-63}{6}\\z-score=-3[/tex]
For X=45, z-score is -3
For X=81 the z-score can be found using formula: [tex]z-score=\frac{X-\mu}{\sigma}[/tex]
Putting values and finding z-score
[tex]z-score=\frac{X-\mu}{\sigma}\\z-score=\frac{81-63}{6}\\z-score=3[/tex]
For X=81, z-score is 3
Now finding the probability of P(-3<z<3)
It can be solved as:
P(-3<z<3)=P(z<3)-P(z<-3)
Looking at the z-score table to find
P(z<3)= 0.9987
P(z<-3)=0.0013
So, P(-3<z<3)=P(z<3)-P(z<-3)
P(-3<z<3)=0.9987 - 0.0013
P(-3<z<3)=0.9974
or P(-3<z<3)= 99.74%
So, P(45<X<81) = P(-3<z<3)=0.9974 or 99.74%
Split the fraction using partial fraction decomposition;
Please see the attached image for your answer. Hope this helps! If you can't read something please let me know.
Solve |3x - 4| = 6
{-2/3, 10/3}
{-10/3, 10/3}
{-2/3, 2/3}
Answer:
{-2/3, 10/3}
Step-by-step explanation:
Let's solve your equation step-by-step.
|3x−4|=6
Solve Absolute Value.
|3x−4|=6
We know either3x−4=6or3x−4=−6
3x−4=6(Possibility 1)
3x−4+4=6+4(Add 4 to both sides)
3x=10
3x/3 = 10/3
(Divide both sides by 3)
x=10/3
3x−4=−6(Possibility 2)
3x−4+4=−6+4(Add 4 to both sides)
3x=−2
3x/3 = −2/3
(Divide both sides by 3)
x= −2/3
Solve for n.
n+m= 16
Answer:n=16-m
Step-by-step explanation:
n+m=16
Subtract m from both sides.
n=16−m
Write the ratio as a ratio of whole numbers in lowest terms
$0.60 to $0.80
A point is randomly selected on the surface of a lake that has a maximum depth of 140 feet. Let y be the depth of the lake at the randomly chosen point.
(a)
What are possible values of y?
all real numbers from 0 to 140
all positive integers from 0 to 140
all real numbers from 1 to 140
all positive integers from 1 to 140
(b)
Is y discrete or continuous?
discrete
continuous
Melinda is at tennis practice. She hits 32 tennis balls a minute. She hit 45 tennis balls before practice. If Melinda hit a total of 1,645 tennis balls, how long was she at practice?
A. 45 minutes
B. 50 minutes
C. 60 minutes
D. 52 minutes
Is the function of f(x) discontinuous or continuous ?
f(x) = 1/x at x = 3
Answer: Continuous at x = 3
The function is only discontinuous at x = 0 since it causes a division by zero error. Everywhere else the function is a continuous curve.
Rita’s recipe for berry pies requires blueberries, raspberries, and strawberries. The ratio of cups of blueberries to cups of raspberries is 1 : 3. The ratio of cups of raspberries to cups of strawberries is 4 : 3. A batch of eight berry pies has a total of 25 cups of berries. How many cups of strawberries are in each pie?
Using proportions, it is found that there are 1.125 cups of strawberries in each pie.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, from the ratios, we have that:
The ratio of cups of blueberries to cups of raspberries is 1 : 3, hence, for each 4 cups, 1 is blueberry and 3 is raspberry.The ratio of cups of raspberries to cups of strawberries is 4 : 3, hence, for each 7 cups, 4 are raspberries and 3 are strawberries.The least common multiple of 3 and 4 is 12, hence, multiplying 4 by 3, the ratio is:
Raspberries : Strawberries : Blueberries = 12 : 9 : 4
Meaning that our of 12 + 9 + 4 = 25 cups, we have that:
12 cups are of raspberries.9 cups are of strawberries.4 cups is of blueberries.There amounts are for 8 pies, hence, for a single pie:
9/8 = 1.125 cups.
There are 1.125 cups of strawberries in each pie.
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Part A
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more. Choose the explicit formula to represent the situation.
A. an = 14 + 9(n + 1)
B. an = 5 + 9n
C. an = 14 + 9n
D. an = 5 + 9(n + 1)
Part B
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more. Choose the recursive formula to represent the situation.
A. an = an – 1 + 5; a1 = 14
B. an = an – 1 + 23; a1 = 9
C. an = an – 1 + 14; a1 = 9
D. an = an – 1 + 9; a1 = 14
Answer:
C. an = 14 + 9n
Step-by-step explanation:
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more.
Let n= additional pizza
an = 14 + (9 × n)
an = 14 + 9n
i need help for a good grade thank youuu
Answer:
Here us the answer in the attachment
Answer:
the person above is correct
Step- by-step explanation:
I need help with this question
Answer:
Step One: Evaluate the Function for A and B
f(1) = -6
f(2) = -1.5
Step Two: Use the Average Rate of Change Formula
f(b) - f(a) / b - a
-1.5 - -6 / 2 - 1
4.5 / 1
4.5
The average rate of change is equal to 4.5
In short, use
[tex] \frac{f(2) -f(1) }{2 - 1} [/tex]
Step-by-step explanation:
To explain, substitute 1 and 2 for f(x) then divide the difference of the two answers by the difference of the two x coordinates above to find the average rate of change
Which of the following equations has no solutions?
4x - 4 = -4(-x + 1)
-9x + 2 = -3(3x + 2)
-6x + 1 = -3(2x + 1) + x
-5 + 14x = 7(2x) - 5
Answer:
-9x + 2 = -3(3x + 2).
Step-by-step explanation:
-9x + 2 = -3(3x + 2)
-9x + 2 = -9x - 6
0 = -8, which is absurd, so :-
No solutions.
what’s the distance between Y(3,0) and Z(-1,-2)
Exact Distance = [tex]2\sqrt{5}[/tex] units
Approximate Distance = 4.4721 units
=================================================
Let's use the distance formula
[tex](x_1,y_1) = (3,0) \text{ and } (x_2, y_2) = (-1,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-1))^2 + (0-(-2))^2}\\\\d = \sqrt{(3+1)^2 + (0+2)^2}\\\\d = \sqrt{(4)^2 + (2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.4721\\\\[/tex]
The exact distance is [tex]2\sqrt{5}[/tex] units.
That approximates to about 4.4721 units.
Find the distance between the points A (13, 2) and B (7, 10).
Answer:
[tex]\sqrt{89}[/tex]units
Step-by-step explanation:
[tex]\sqrt{(7-13)^2+(10-2)^2}[/tex]
(-5)^2+(8)^2=25+64
25+64=89
[tex]\sqrt{89}[/tex]
the answer would be [tex]\sqrt{89}[/tex]
The sum of the first 10 positive odd integers.
Answer:
1,3,5,7,9,11,13,15,17,19
add them all together
= 100
Step-by-step explanation:
hope this works :)
If Xi = 1,3,5,8,12,15,9. Find the mean and median of the data set
The mean of the given data is 7.57 and the median of the given data is 8
Given that a data set i.e. Xi= 1,3,5,8,12,15,9. asked to find the mean and median of the given data.
Mean:
The mean is the average of the supplied numbers and is computed by dividing the total number of numbers by the sum of the given numbers.
Mean= [tex]\frac{sum of observation}{number of observation}[/tex]
Mean=[tex]\frac{1+3+5+8+12+15+9}{7}[/tex]
Mean=[tex]\frac{53}{7}[/tex]
Mean=7.57
The mean of the given data is 7.57
Median:
The median is a statistical metric that identifies the midway value of an ascending-ordered dataset (i.e., from smallest to largest value). The metric separates the dataset's lower and upper halves.
Arranging in ascending-order⇒1,3,5,8,9,12,15.
Then median=8
Therefore,The mean of the given data is 7.57 and the median of the given data is 8
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Translate the sentence into an equation or formula.
The surface area SA of a rectangular prism is 2 times the sum of the width (w) times height (h), and length (
l
) times width, and length times height.
A translation of the equation for the surface area of this rectangular prism is given by: SA = 2(WH + LW + LH).
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
How to translate the sentence into an equation or formula?Mathematically, the surface area of a rectangular prism can be calculated by using this equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.In this context, we can reasonably and logically deduce that a translation of the equation for the surface area of this rectangular prism is given by:
SA = 2(WH + LW + LH).
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Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD).
The perimeter of a rectangular traffic sign is 134 inches.
Also, its length is 9 inches longer than its width.
Find the dimensions of this sign.
The dimensions of the rectangular traffic sign whose perimeter is 134 inches according to the task content are; 38in by 29in.
What are the dimensions of the rectangular traffic sign?It then follows that from the task content that the dimensions of the rectangular traffic sign are to be determined.
Since the perimeter of a rectangle is given by;
P = 2(l+b)
where the length, l = b +9.
So therefore; 134 = 2(b+9 +b)
134 = 4b + 18
4b = 134 - 18
4b = 116
b = 29
In conclusion, the length, l of the traffic sign is; 29 +9
l = 38.
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logs (20x + 5y) using the properties of logarithms to expand
The logarithmic expansion of logs(20x + 5y) by using the properties of logarithmic is log(5)+log(4x+y).
The basic logarithmic function is of the form f(x) = logₐx(r)n = logₐx, where a > 0. It is the inverse of the exponential function aⁿ = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic functions is very useful in various mathematical computations.
Given that, log(20x+5y) and we have to expand it by using the properties of logarithms. So, let's proceed to solve the question.
log(20x+5y)
we can write 20 in terms of powers like 20 = (2²)x5
log((2².5)x+5y)
log(5(2².5x/5+5y/5))
log(5(2²x+y))
log(5(4x+y))
∵ log(ab) = log(a)+log(b)
⇒log(5(4x+y)) = log(5)+log(4x+y)
Hence, on expanding log(20x+5y) by using the properties of logarithms we get log(5)+log(4x+y) as our required answer.
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Melanie receives a 9% commission on every house she sells. If she received a commission of $20,340, what was the value of the house she sold?
4. Given 6 (1-x) what is the value of the
expression when x = -8?
Answer:
let x be -8
6(1-8)
6(7)
6x7=42
answer=42
A brokerage company evaluated the three services its call centers provide for reliability. The results showed the following:
Service Reliability Percentage
Checking customer account status .85
Confirming orders .72
Stock quotes .96
Compute the over-all reliability of the call center (round to 2 decimals) _____________
Show computation:
If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
Over-all reliability of the call centerUsing this formula to calculate the over-all reliability of the call center
Over-all reliability of the call center=Checking customer account status × Confirming orders× Stock quotes
Where:
Checking customer account status =.85
Confirming orders= .72
Stock quotes= .96
Let plug in the formula
Over-all reliability of the call center=.85×.72×.96
Over-all reliability of the call center=0.58752
Therefore If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
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(3 + 16.4a) − (9 + 5.7a)
22.1a + (−12)
1.07a + (−12)
22.1a + (−6)
10.7a + (−6)
Answer:
10.7a + (−6)
Step-by-step explanation:
If x is an integer, which of the following is the solution set for 3|x|=15?
{0,5}
{−5,5}
{−5,0,5}
{0,45}
y = x – 2
y = –3x – 2
Answer:
y=3x-2
Step-by-step explanation:
if for y=-3x-2 is being solved for x your answer would be:
y=3x-2
3x-2=y
3x=y+2
3x/3=y+2/3
so your final answer for this question is: x=y+2/3
and for the first one y=x-2 there is no answer for it
There are 40 students in a class. 24 of those students are men. What percent of the class are women?
Answer: 40%
Step-by-step explanation:
c=class. m=men. w=women.
c=m+w
40=24+w
40-24=24-24+w
w=16
16/40=
4/10=
4*100%/10=
400%/10=40%
How many times larger is 5.025 x 1010 than 1.5 x 108?
335
299
29.9
3.35
[tex]\frac{5.025 \times 10^{10}}{1.5 \times 10^{8}} \\ \\ =\frac{5.025}{1.5}(100) \\ \\ =\boxed{335}[/tex]
Option A is correct, 5.025 x 10¹⁰ is 335 times larger than 1.5 x 10⁸.
To determine how many times larger one number is than another, we divide the larger number by the smaller number.
In this case, we want to find how many times larger 5.025 x 10¹⁰ is than 1.5 x 10⁸.
Dividing the larger number by the smaller number:
(5.025 x 10¹⁰) / (1.5 x 10⁸)
To simplify, we can divide the coefficients (5.025 / 1.5) and subtract the exponents (10¹⁰ - 10⁸):
(5.025 / 1.5) x 10¹⁰⁻⁸
Evaluating the division of the coefficients:
(3.35) x 10²
Therefore, 5.025 x 10¹⁰ is 3.35 x 10² times larger than 1.5 x 10⁸.
In decimal form, this can be expressed as:
3.35 × 10² = 335
Therefore, 5.025 x 10¹⁰ is 335 times larger than 1.5 x 10⁸.
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Solve 19×50 numerically
The solution of expression 19×50 is found as 950.
What is defined as the distributive property?This property states that multiplying the product of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.
The distributive property holds true for division the same way that it holds true for multiplication. However, with division, the concept of "breaking apart" or "distributing" can only be applied by dividing the numerator into lesser numbers that are exactly divisible even by divisor.In other words, the distributive property requires a phrase of the form:
A (B + C) can be simplified as A (B + C) = AB + AC.
This same applies foe the subtraction;
Thus, for the given numerical;
= 19×50
Using distributive property.
= (20 - 1)×50
Open the braces;
= 20×50 - 1×50
= 1000 - 50
= 950
Therefore, the solution of the numerical 19×50 is 950.
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find three consecutive integers such that the sum of the first and twice the second is 98 minus three times the third
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let the numbers be : x, x + 1 and x + 2 ~
now, according to given condition :
[tex]\qquad \sf \dashrightarrow \: x + 2(x + 1) = 98 - 3(x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: x + 2x + 2 = 98 - 3x - 6[/tex]
[tex]\qquad \sf \dashrightarrow \: x + 2x + 3x = 98 - 6 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 90[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 90 \div 6[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 15[/tex]
So, tge required numbers are : 15, 16 and 17
In a study of bird migration, a researcher
recorded on a certain day a total of 262
birds, consisting of 65 geese, 84 ducks,
and 113 robins in the skies. Show
a possible equation for calculating the
probability that a random bird chosen
from among these is NOT a duck.
The probability that a random bird chosen from among these is NOT a duck is 0.67
Given the total number of birds = 262
No of geese = 65
No of ducks = 84
No of robins = 113
We need to find the probability that a random bird chosen from among these is not a duck is
P ( not a duck ) = (total number of birds - no of ducks) / total number of birds
= 262 - 84 / 262
= 178 / 262
= 0.67
The probability that a random bird chosen from among these is NOT a duck is 0.67.
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