The required probability is 0.0087 (approximately).Note: The probability is less than 0.05. Hence, we can say that the event is rare.
C = 260 (mean)Standard deviation, σ = 40Let X be the number of items returned on a given day.As the number of items returned follows a normal distribution with mean C and standard deviation 40,Therefore,X ~ N (260, 40^2)We have to find the probability that fewer than 165 items are returned on a given day.i.e. P (X < 165).
We can find the standard score, z as follows.z = (X - μ) / σz = (165 - 260) / 40z = -2.375Now, we can find the probability as follows.P (X < 165) = P (Z < -2.375) = 0.0087 (approximately)Therefore, the required probability is 0.0087 (approximately).Note: The probability is less than 0.05. Hence, we can say that the event is rare.
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Express the confidence interval (0.069.0.159) in the form of p-E
the confidence interval (0.069, 0.159) can be expressed as 0.114 ± 0.045
In a confidence interval, the lower bound represents the point estimate minus the margin of error, and the upper bound represents the point estimate plus the margin of error. In this case, the lower bound of the confidence interval is 0.069 and the upper bound is 0.159. To express it in the form of p ± E, we need to find the point estimate and the margin of error.
The point estimate, p, is the average or central value of the interval. In this case, it would be the midpoint between the lower and upper bounds:
p = (0.069 + 0.159) / 2 = 0.114
The margin of error, E, can be calculated by taking half the difference between the upper and lower bounds:
E = (0.159 - 0.069) / 2 = 0.045
Therefore, the confidence interval (0.069, 0.159) can be expressed as 0.114 ± 0.045.
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The integral [, sin(x - 2) dx is transformed into S1, g(t)dt by applying an appropriate change of variable, then g() is: g(t) = sin g(t) = cos (5) O This option O This option g(t) = -cos (3) g(t) = sin O This option
By introducing the appropriate change of variable x = t + 2, we transformed the given integral [, sin(x - 2) dx] into S1, g(t)dt = [, sin(t) dt], where g(t) = sin(t). (option a)
To transform the given integral [, sin(x - 2) dx] into the form S1, g(t)dt, we need to apply a suitable change of variable. In this case, we'll introduce a new variable, t, and express x in terms of t. Let's denote this change of variable as x = h(t), where h(t) represents the transformation of t to x.
To determine the appropriate change of variable, we can start by looking at the expression inside the sine function: x - 2. We need to find a suitable expression for x that can help us simplify the integral. Let's set x - 2 equal to t:
x - 2 = t.
Now, we solve this equation for x to express it in terms of t:
x = t + 2.
Next, we differentiate both sides of the equation x = t + 2 with respect to t to find dx/dt:
dx/dt = d(t + 2)/dt.
Differentiating t + 2 with respect to t gives us:
dx/dt = 1.
Now, we have dx/dt = 1, which means dx = dt. We can substitute this value into the original integral:
[, sin(x - 2) dx] = [, sin(t) dt].
As you can see, the original integral [, sin(x - 2) dx] has been transformed into the form [, sin(t) dt] using the appropriate change of variable x = t + 2. Therefore, the integral S1, g(t)dt is now:
S1 = [, sin(t) dt],
and g(t) = sin(t).
Hence the correct option is (a).
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Use synthetic division to evaluate (2x2 − 7x + 5) ÷ (x − 1).
1. 2x - 9
2. 2x - 5
3. 2x^2 - 5x
4. 2x^2 - 10
25% of x is 30
x=?
please help!!!
25% of 30 can be found by converting 25% to a decimal and multiplying it by 30.
25% = 0.25
30x0.25=7.5
So x is 7.5.
---
hope it helps
240g in the ratio 5:3:2
Answer:
120:72:48
Step-by-step explanation:
Remark
Whatever the answer is (call it x to begin with), the equation starts as
5x + 3x + 2x = 240
What this means is that when you solve for x the results when multiplied by the ratio, should add to 240
Equation
5x + 3x + 2x = 240
Solution
Combine all the terms on the left.
10x = 240 Divide by 10
x = 240/10
x = 24
Check
5*24 = 1203*24 = 722*24 = 48Total = 240a dice was rolled 60 times what is the probability of rolling a 3
Answer: 2/15
Step-by-step explanation:
Experimental probability is the actual results of the experiment (not what should have happened, which is theoretical probability.
A 3 was rolled 8 times, so the results are 8/60=4/30=2/15
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided The top five test scores in Mr. Rhodes's class were 98, 92, 96, 97, and 97. What is the mean absolute deviation?
Step-by-step explanation:
mad = 98 + 92 + 96 + 97 + 97 / 5
= 480/5
= 96
mad = (98 -96) + (92 - 96) + (96 -96) + (97- 96) + (97 -96) / 5
= 2 + (-4) + 0 + 1 + 1 / 5
=0/5
mad = 0
brainliest is appreciated
Answer:
1.6
Step-by-step explanation:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
98+92+96+97+97=480
480/5 values=96 is the mean or average of the set of numbers
so we just find the absolute value of the data value minus the mean.
For the first one it would be |98-96|=2
then continue on and get a set of values
{2,4,0,1,1}
now find the average of that to get the mean absolute deviation
2+4+0+1+1=8
8/5 values
1.6
Hope that helps :)
Write the equation of the circle.
Circle C that passes through (-5, 1) with center C(1,-4).
Answer:
answer is on this page
Step-by-step explanation:
https://www.mathpapa.com/algebra-calculator.html
2.
A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.
A. 9p + $11.50 = $94.75; p = $11.75
B. 9p + 11.5p = $94.75; p = $4.62
C. 9(p + $11.50) = $94.75; p = $5.00
D. 9p + $11.50 = $94.75; p = $9.25
Answer:
D. 9p + $11.50 = $94.75; p = $9.25
Step-by-step explanation:
To answer this problem, let p be the price of each scrub. The total bill (t) is the sum of the price of the potting soil (s) and of the 9 scrubs (n). This is depicted in the equation,
$11.50 + 9p = $94.75
The value of p from the equation is 9.25. Thus, each scrub costs $9.25. The answer is letter D.
...................................................................................................................................................
Let
p---------> the price of each scrub
s----------> the price of the potting soil
T--------> total bill
we know that
in this problem
substitute the values in the formula above
solve for p
therefore
the answer is the option D
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Given that a^b = x, evaluate the following: a^2b
Help PLZ!!! Will give brainliest to the first correct answer!!!!!!!
Answer:
[tex] x^2 [/tex]
Step-by-step explanation:
[tex] a^{2b} = a^{b \times 2} = (a^b)^2 = x^2 [/tex]
Answer: [tex] x^2 [/tex]
Answer:
x² is the answer
Step-by-step explanation:
if a^b=x
and a^2b= (a^b)²
=x²
The measures of the angles of a triangle are in the extended ratio 7:14:15.
Find the measures of the angles of the triangle.
Please i need help
Can you post a picture?
It would make it so much easier.
In your answers below, for the variable λ type the word lambda; for the derivative d/dx X(x) type X' ; for the double derivative d^2/dx^2 X(x) type X''; etc. Separate variables in the following partial differential equation for u(x,t): t^2uxx+x^2uxt−x^2ut=0
The final answer of the question which is the specific form of the solution u(x, t) = X(x)T(t)
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
To separate variables in the partial differential equation t²uxx + x²ux²t - x²zzut = 0, we assume that the solution can be written as a product of two functions, u(x, t) = X(x)T(t).
Let's begin by substituting this into the given equation:
t²(X''(x)T(t)) + x²(X(x)T'(t)) - x^2(X(x)T(t)) = 0
Now, we divide the equation by t²X(x)T(t) to separate the variables:
(X''(x) / X(x)) + (x^2 / t^2)(T'(t) / T(t)) - (x^2 / t^2) = 0
Next, we rearrange the terms:
(X''(x) / X(x)) + ((x² / t²)(T'(t) / T(t))) - (x² / t²) = 0
To satisfy this equation for all x and t, the left-hand side and the right-hand side must be equal to a constant value. Let's call this constant -λ^2:
(X''(x) / X(x)) + ((x² / t²)(T'(t) / T(t))) - (x² / t²) = -λ²
Now, we have two separate ordinary differential equations:
1. X''(x) / X(x) - x² / t² = -λ²
2. T'(t) / T(t) = λ²
Solving each equation separately will give us the general solutions for X(x) and T(t).
The general solution for u(x, t) can then be obtained by taking the product of X(x) and T(t):
u(x, t) = X(x)T(t)
The specific form of the solutions will depend on the boundary conditions or initial conditions given for the problem.
Hence, the final answer of the question which is the specific form of the solution u(x, t) = X(x)T(t)
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50% of x is 19. *reamber is means divide*
Answer:
9.5
Step-by-step explanation:
p = 15
p
+4
3
please help thank you
Answer:
9
Step-by-step explanation:
15/3 simplified is 5.
5 + 4 = 9
How could you calculate the value of log11(9100) using a calculator? What does it equal (round to the nearest tenths place)?
As part of his science project, Steve recorded the number of eggs laid by several lizards from the local pet shop. The data Steve collected is provided below.
10, 7, 8, 8, 9, 10, 9, 10, 8, 11, 11, 9, 7, 10, 9
In his report, Steve should use the _____ as a measure of center since his data is ____
1. A cooler is in the shape of a rectangular
prism. What is the volume of the cooler?
Round to the nearest tenth if necessary.
I
Answer:
what is the answerrrrrrrrrrrrrrrrr
Step-by-step explanation:
The volume of the cooler is 2772 in³
What is a volume?Volume is the amount of space taken up by an object
What is the volume of a rectangle?The formula for calculating the volume of a rectangular prism is volume = length × width × height.
According to the question
Length= 22in.
breadth= 12 in.
width= 10 1/2 in. or 21/2 in.
So, the volume= 22× 12× (21/2)
=2772 in³
Thus the volume of a rectangular prism is 2772 in³
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mrs chambers is 62 years old and plans to retire. over her life she earned an average of $2,500 per month after adjusting for inflation the formula for calculating the full monthly social security benefits is 90% of the first $680 earned the 32% of the earnings over $680 what will her monthly benefit be if her full retirement benefit is reduced by 30% for retiring at 62 years old
Answer: 60
Step-by-step explanation:
help please i will give brainliest to first answer
Answer:
m<ADC= 117
Step-by-step explanation:
Estimate the answers of these:
1. 489+1210
2. 3694-2016
3. 5082×312
4. 761÷34
The table below shows the relationship between the number of teaspoons of baking powder in a mix and the height of fudge brownies in centimeters. Which equation represents the height of fudge brownies with x teaspoons of baking powder?
Making Fudge Brownies
Baking Powder (tsp) 5 6 7 8
Height of Brownies (cm) 2.15 2.43 2.71 2.99
A.
y = 0.28x + 0.75
B.
y = 0.75x +0.56
C.
y = 0.75x + 0.28
D.
y = 0.56x + 0.75
Answer:
A.
y = 0.28x + 0.75
Step-by-step explanation:
Check all that applies using teaspoons of baking powder, x = 5
A.
y = 0.28x + 0.75
When x = 5
y = 0.28x + 0.75
= 0.28(5) + 0.75
= 1.4 + 0.75
y = 2.15
B.
y = 0.75x +0.56
When x = 5
y = 0.75x +0.56
= 0.75(5) + 0.56
= 3.75 + 0.56
= 4.31
C.
y = 0.75x + 0.28
When x = 5
y = 0.75x + 0.28
= 0.75(5) + 0.28
= 3.75 + 0.28
= 4.03
D.
y = 0.56x + 0.75
When x = 5
y = 0.56x + 0.75
= 0.56(5) + 0.75
= 2.8 + 0.75
= 3.55
The equation represents the height of fudge brownies with x teaspoons of baking powder is
y = 0.28x + 0.75
rectangle has its vertices at M(1,1), N(6,1), O(6,5), P(1,5). The rectangle is translated to the left 4 units and down 3 units. What are the new coordinates? (Answer Format: M(#,#) N(#,#) O(#,#) P(#,#))
Answer:
7aabbbjdkdbdjdkxbsks n sbs
Martin recorded the low temperatures at his house for one week. The temperatures are shown below.
-7, -3, 4, 1, 2, 8, 7
Approximately what was the average low temperature for the week?
Α. 7
B. "1
C. 1
D "8
A recipe calls for 1/3 of a cup of butter. If Matthew is making 1/4 of the recipe, how much butter should he use?
Answer:
1/12 a cup
Step-by-step explanation:
1/3*1/4=1/12
Answer:
1/12
Step-by-step explanation:
1/3*1/4=1/12
Jazmin takes a ride share service home from the airport. The ride share service charges $5 as an initial cost to pick her up, and $2.25 for every mile to her final destination. Jazmin's ride home cost a total of $38.75. Write an equation to represent the situation. Let m represent the number of miles to her home.
Answer:
38.75 = 2.25 m + 5
Step-by-step explanation:
It is given that :
Jazmin took a ride share service from airport to home.
The total cost of the ride service from airport to home is = $ 38.75
The ride service charged an initial cost for picker Jazmin = $ 5
Cost of the ride service for every mile = $ 2.25 per mile
Let the number of miles = m
Therefore, the equation that represents the situation is :
38.75 = 2.25 m + 5
where, m represents the number of miles.
can anyone help me with this question?
Answer:
45 and 13…......
Step-by-step explanation:
devide
Working together, Daniel and Donnie can clean the llama pen in 45 minutes. On his own, Daniel can clean the pen in an hour. How long does it take Donnie to clean the llama pen on his own?
Answer:
It takes him 15 minutes.
Step-by-step explanation:
Donnie clean the llama pen in 180 minutes on his own.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Daniel and Donnie can clean the llama pen in 45 minutes.
And, On his own, Daniel can clean the pen in an hour.
Now,
Let time to clean the llama pen in on his own = x minutes.
Since, Daniel and Donnie can clean the llama pen in 45 minutes.
So, In 1 minute, Daniel and Donnie clean the pen = 1/45
And, In 1 minute Daniel to work = 1/60
Thus, We can formulate;
1/x + 1/60 = 1/45
Solve for x as;
(60 + x) / 60x = 1/45
60 + x = 60x / 45
60 + x = 4x/3
180 + 3x = 4x
180 = 4x - 3x
180 = x
Thus, Donnie clean the llama pen in 180 minutes on his own.
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hurry!!!! I need help
Find the surface area of the square pyramid shown below.
(15 points)
Answer:
340
Step-by-step explanation
Base=10x10=100
Sides= {(12x10)/2}x4=240
Add sides plus base, 240+100=340
Write a similarity statement comparing the three triangles in the diagram
P R S Q
Answer:
The answer is ΔJMK ≈ ΔMLK ≈ ΔJLM ⇒ answer (A)
Step-by-step explanation:
* Lets start with the equal angles i the three triangles
- In ΔJMK
∵ m∠JKM = 90°
∴ m∠KJM + m∠KMJ = 90 ⇒ (1)
- IN ΔMLK
∵ m∠MKL = 90°
∴ m∠KML + m∠KLM = 90° ⇒ (2)
∵ m∠KMJ + m∠KML = 90° ⇒ (3)
- From (1) , (2) , (3)
∴ m∠KJM = m∠KML
∴ m∠KMJ = m∠KLM
* Now lets check the condition of similarity in the 3 triangles
- At first ΔJMK and ΔMLK
- In triangles JMK , MLK
∵ m∠KJM = m∠KML
∵ m∠KMJ = m∠KLM
∵ m∠JKM = m∠MKL
∴ ΔJMK ≈ ΔMLK ⇒ (4)
- At second ΔJMK and ΔJLM
∵ m∠KJM = m∠MJL
∵ m∠KMJ = m∠MLJ
∵ m∠JKM = m∠JML
∴ ΔJMK ≈ ΔJLM ⇒ (5)
* If two triangles are similar to one triangle, then they are
similar to each other
- From (4) and(5)
∴ ΔJMK ≈ ΔMLK ≈ ΔJLM