Answer:
42
Step-by-step explanation:
The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:
7! / (7 - 2)!
= 7! / 5!
= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1
= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)
= 42
Answer:
[tex]\boxed{42}[/tex]
Step-by-step explanation:
Apply the permutation formula.
[tex]P(n,r)=\frac{n!}{ (n-r)!}[/tex]
[tex]P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\[/tex]
[tex]n=7\\r=2[/tex]
Plug in the values and evaluate.
[tex]P(7,2)=\frac{7!}{ (7-2)!}[/tex]
[tex]P(7,2)=\frac{7!}{ (5)!}[/tex]
[tex]P(7,2)=\frac{5040}{120}[/tex]
[tex]P(7,2)=42[/tex]
What is x? The degree of the angle of x
Answer:
x = 60°
Step-by-step explanation:
All the angles in a triangle add up to 180°. So, you have this equation.
87° + 33° + x = 180°
120° + x = 180°
x = 60°
The measure of angle x is 60°.
Hope that helps.
answer asap, please :)
Answer:
[tex]\boxed{\sf 4.41}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can solve using trigonometric functions.
[tex]\sf cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]\sf cos(25)=\frac{4}{?}[/tex]
[tex]\sf ?=\frac{4}{cos(25)}[/tex]
[tex]\sf ?= 4.41351167...[/tex]
Need help solving hi
Answer:
See below.
Step-by-step explanation:
[tex]2 \ln(x+2)=6[/tex]
[tex]\ln (x+2)=3[/tex]
[tex]e^{\ln(x+2)}=e^3[/tex]
[tex]x+2=e^3[/tex]
[tex]x=e^3-2[/tex]
[tex]x\approx 18. 09[/tex]
whats a significant figure
Answer:
Significant figures are any digits that contribute to the number: In 02.400, only 2 and 4 are significant digits. However, in 2.4001, 2, 4, 0, 0, and 1 are significant digits, because the number would not be the same without them.
Step-by-step explanation:
Hope it helps <3
Nakashima Gallery had the following petty cash transactions in February of the current year. Nakashima uses the perpetual system to account for merchandise inventory. Feb 2 Write a $400 check to establish a petty cash fund. Feb 5 Purchased paper for the copier for $14.15 that is immediately used. Feb 9 Paid $32.50 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These costs are added to merchandise inventory. Feb 12 Paid $7.95 postage to deliver a contract to a client Feb 14 Reimbursed Adina Sharon, the manager, $68 for mileage on her car. Feb 20 Purchased office paper for $67.77 that is immediately used. Feb 23 Paid a courier $20 to deliver merchandise sold to a customer, terms FOB destination. Feb 25 Paid $13.10 shipping charges (transportation in) on merchandise purchased for resale, terms FOB shipping point. These cost are added to merchandise inventory. Feb 27 Paid $54 for postage expenses Feb 28 The fund had $120.42 remaining in the petty cashbox. Sorted the petty cash receipts by accounts affected and exchanged them for a check to reimburse the fund for expenditures. Feb 28 The petty cash fund amount is increased by $100 to a total of $500
Answer:
1. Debit Petty cash for $400; and Credit Cash for $400.
2. Total petty cash payment = $270.57
3(a) Cash reimbursement is $279.58; and Cash over and short is $9.01.
3(b) Debit Petty cash for $100; and Credit Cash for $100.
Step-by-step explanation:
Note: This question is not complete. The full complete question is therefore provided before answering the question. See the attached pdf file for the full question.
The explanations to the answers are now given as follows:
1. Prepare the journal entry to establish the petty cash fund.
Note: See the journal entry in the attached excel file
2. Prepare a petty cash payments report for February with these categories: delivery expense, mileage expense, postage expense, merchandise inventory (for transportation-in), and office supplies expense. Sort the payments into the appropriate categories and total the expenditures in each category.
Note: See the petty cash payments report in the attached excel file.
3. Prepare the journal entries for required 2 to both (a) reimburse and (b) increase the fund amount.
Note: See the journal entries (a) and (b) in the attached excel file
3(a) Reimburse Workings:
w.1: Calculation of Cash reimbursement
Cash reimbursement = Petty cash fund - Petty cash fund balance = $400 - $120.42 = $279.58
w.2: Calculation of the Cash over and short
Cash over and short = Cash reimbursement – Total expenses = $279.58 - $270.57 - $120.42 = $9.01
if the discrimant of a equation is equal to -8, which statement describes the roots? A. there are two complex roots B. there are two real roots C. there is one real root D. there is one complex root
Answer:
Option A
Step-by-step explanation:
If Discriminant < 0 , (Just as -8) the roots are imaginary (Complex) and there are two complex roots.
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that d=3.125, sd=2.911, and n=8, and that you wish to test the hypothesis below at the 10% level of significance. What decision rule would you use? H0: μd=0 against H1: μd>0
Answer:
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Step-by-step explanation:
We are given that the means of two populations using paired observations. Suppose that [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8, and that you wish to test the hypothesis below at the 10% level of significance.
Let D = difference between the two paired observations.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0
The test statistics that would be used here is Paired t-test for dependent samples;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_d}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8
The decision rule for rejecting the null hypothesis in the given hypothesis test would be;
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.Write an expression for each statement and then simplify it, if possible.
g
There are two numbers, that sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers ?
Answer:
If the smaller number is x, then the equation is
. The numbers are
,
.
Answer:
x = 18; y = 35
Step-by-step explanation:
This gives us the equation:
1. x+y=53
2. 3x=y+19
3. 3x-y=19
Add the first and last line together: x+y+3x-y=53+19
Simplifies to: 4x=72
Divide by 4 to get: x = 18
Plug your numbers into the first equation to get 18+y=53; y = 35.
Answer:
The numbers are 18 and 35.
Step-by-step explanation:
The smaller number is x.
Let the other number by y.
Three times the smaller number is equal to 19 more than the larger number.
3x = y + 19
The larger number is
y = 3x - 19
the numbers add up to 53
x + y = 53
x + 3x - 19 = 53
4x = 72
x = 18
y = 3x - 19 = 3(18) - 19 = 54 - 19 = 35
The numbers are 18 and 35.
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 216x + 3, [−4, 5]
Answer:
absolute minimum = -749 and
absolute maximum = 467
Step-by-step explanation:
To get the absolute maximum and minimum of the function, the following steps must be followed.
First, we need to find the values of the function at the given interval [-4, 5].
Given the function f(x) = 6x³ − 9x² − 216x + 3
at x = -4;
f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3
f(-4) = 6(-64) - 9(16)+864+3
f(-4) = -256- 144+864+3
f(-4) = 467
at x = 5;
f(5) = 6(5)³ − 9(5)² − 216(5) + 3
f(5) = 6(125) - 9(25)-1080+3
f(5) = 750- 225-1080+3
f(5) = -552
Then we will get the values of the function at the crirical points.
The critical points are the value of x when df/dx = 0
df/dx = 18x²-18x-216 = 0
18x²-18x-216 = 0
Dividing through by 18 will give;
x²-x-12 = 0
On factorizing the resulting quadratic equation;
(x²-4x)+(3x-12) = 0
x(x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x+3 = 0 and x-4 = 0
x = -3 and x = 4 (critical points)
at x = -3;
f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3
f(-3) = 6(-27) - 9(9)+648+3
f(-3) = -162-81+648+3
f(-3) = 408
at x = 4
f(4) = 6(4)³ − 9(4)² − 216(4) + 3
f(4) = 6(64) - 9(16)-864+3
f(4) = 256- 144-864+3
f(4) = -749
Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively
trang can test message about 38 words per minute. if she types at this rate for 20 minutes about how many words will she type?
Answer:
760 words for 20 minutes.
Step-by-step explanation:
38 words = 1 minute
1 x 20 = 20
38 x 20 = 760 words
Write an equation for the absolute value. PLEASE HELP I’m so confused on this!!!
Answer:
y = 3 |x − 8| + 1
Step-by-step explanation:
y = 3 |x|
Shift right 8 units:
y = 3 |x − 8|
Shift up 1 unit:
y = 3 |x − 8| + 1
Find local maximum or minimum of the function: f(x)= (x + 1)^2(x - 3) Local maximum point= ( , ) Local maximum value= Local minimum point = ( , ) Local minimum value=
Answer: Local Max = (-1, 0)
Local Min = (1, -8)
Step-by-step explanation:
f(x) = (x + 1)² (x - 3)
Step 1: Find the zeros
(x + 1)² = 0 --> x = -1 (multiplicity of 2)
(x - 3) = 0 --> x = 3
Step 2: Find the Vertices
x = -1 --> (multiplicity is even which means this is a vertex)
The midpoint between x = -1 and x = 3 is x = 1
Step 3: Find the Local Max and Local Min
Use the x-value above to find the y-values
f(-1) = 0 because it is a zero
f(1) = (1 + 1)² (1 - 3)
= 2²(-2)
= 4(-2)
= -8
Conclusion:
(-1, 0) is the Local Max bigger y-value
(1, -8) is the Local Min smaller y-value
Answer:
f ( x ) = ( x – 3) 2 – 4; the minimum value is –4
Step-by-step explanation:
Given the function f ( x ) = x 2 – 6 x + 5, write an equivalent form of the function that reveals the minimum or maximum value of the function and state the minimum or maximum value.
f ( x ) = ( x – 3) 2 – 4; the minimum value is –4
( This The correct question to answer?) can't deleted..
Rachel's waist circumference is 37 inches and her hip circumference is 39 inches. Based on this information, what does her waist-to-hip ratio tell you?
Answer:
[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
Step-by-step explanation:
The waist-to-hip ratio of Rachel is:
[tex]n = \frac{37\,in}{39\,in}[/tex]
[tex]n = \frac{37}{39}[/tex]
[tex]n = 0.949[/tex]
The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
The length of her waist circumference is 94.9% the length of her hip circumference.
From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.
Therefore, her waist to hip ratio will be calculated thus:
n = 37/39
n = 0.949
This implies that the length of her waist circumference is 94.9% the length of her hip circumference.
Learn more about ratio on:
https://brainly.com/question/13763238
which statement is true about the radical expression square root of 25
Answer:
5
Step-by-step explanation:
The square Root of 25 in its simplest form means to get the number 25 inside the radical √ as low as possible.
25 is a perfect square, which means that you can simply calculate the square Root of 25 to get the answer. 5 times 5 equals 25. Thus, the square Root of 25 in simplest radical form is = 5
Need answers!!!!! ASAPPP
Answer:
t
Step-by-step explanation:
Test the claim that the proportion of men who own cats is smaller than 70% at the 0.05 significance level. The null and alternative hypothesis would be:
Answer:
the null hypothesis would be: p = 70%/0.7
The alternative hypothesis would be: p < 0.7
Step-by-step explanation:
The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.
In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7
The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7
I really need help on this
Answer:
Congruent
Step-by-step explanation:
I am not 100% sure because there are no measurements but it looks like the two shapes are the same size.
If this helped, please consider giving me brainliest, it will help me a lot :)
Have a good day.
Matrixes and Matrix Operations
Please help. I’ll mark you as brainliest if correct.
Answer:
3 × 7
Step-by-step explanation:
The order of a matrix is the number of rows and columns that it has. Rows are listed first and columns are listed second. The matrix has 3 rows going across horizontally and 7 columns going down vertically.
Therefore, the order of the matrix is 3 × 7.
Hope that helps.
A car is purchased for $16,500. After each year, the resale value decreases by 35%. What will the resale value be after 3 years?
round your answer to the nearest dollar.
Answer: 16500(.65)^3 =4531.31
Step-by-step explanation:
cos(0)=√2/2, and 3π/2<0<2π, evaluate sin(0) and tan(0). Sin(0)?
Answer:
Option (2)
Step-by-step explanation:
In this question we have to find the values of Sinθ and tanθ where [tex]\frac{3\pi}{2}<x<2\pi[/tex].
Cosθ = [tex]\frac{\sqrt{2}}{2}[/tex] ⇒ θ = [tex]\frac{7\pi }{4}[/tex]
[Since [tex]\text{Cos}\frac{7\pi }{4}=\text{Cos}(2\pi-\frac{\pi}{4})[/tex]
[tex]=\text{Cos}\frac{\pi }{4}[/tex]
[tex]=\frac{\sqrt{2} }{2}[/tex] ]
Since Cosine of any angle between [tex]\frac{3\pi}{2}[/tex] and 2π is positive and Sine is negative in nature,
[tex]\text{Sin}\frac{7\pi }{4}[/tex] = [tex]-\frac{\sqrt{2}}{2}[/tex]
Since, tanθ = [tex]\frac{\text{Sin}\theta}{\text{Cos}\theta}[/tex]
tanθ = [tex]\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} }[/tex]
= [tex]-\frac{\sqrt{2}}{2}\times \frac{2}{\sqrt{2}}[/tex]
= -1
Therefore, Option (2) will be the answer.
Answer:
Step-by-step explanation:
option 2 is the correct answer
1. Identify the axis of symmetry for y = -3(x+3)^2-2. a. x = -2 b. x = 3 c. x = 2 d. x = -3 2. Choose the correct axis of symmetry for x = -4(y -4)^2+6 a. y = -6 b. y = -4 c. y =6 d. y = 4
Answer:
The answer is :
DDStep-by-step explanation:
Axis of symmetry is the equation where it cuts the middle of the quadratic graph.
For quadratic equation in the form of (x+a)² + b, the axis of symmetry will be (x+a) = 0 which is x = -a :
Question 1,
[tex](x + 3) = 0[/tex]
[tex]x = - 3[/tex]
Question 2,
[tex](y - 4 )= 0[/tex]
[tex]y = 4[/tex]
Answer:
[tex]\boxed{x=-3} \\ \boxed{y=4}[/tex]
Step-by-step explanation:
Axis of symmetry is a line that cuts the parabola in half touching the vertex.
Quadratic forms ⇒ y = ax² + bx + c or x = ay² + by + c
Axis of symmetry ⇒ x = [tex]\frac{-b}{2a}[/tex] or y = [tex]\frac{-b}{2a}[/tex]
First problem:
y = -3(x+3)²-2
Write in quadratic form ⇒ y = ax² + bx + c
y = -3(x² + 6x + 9) - 2
y = -3x² -18x - 27 - 2
y = -3x² -18x - 29
a = -3, b = -18
Find axis of symmetry.
[tex]x= \frac{-b}{2a}[/tex]
[tex]x=\frac{--18}{2(-3)}[/tex]
[tex]x=\frac{18}{-6}=-3[/tex]
Second problem:
x = -4(y -4)² +6
Write in quadratic form ⇒ x = ay² + by + c
x = -4(y² - 18y + 16) + 6
x = -4y² + 32y - 64 + 6
x = -4y² + 32y - 58
a = -4, b = 32
Find axis of symmetry.
[tex]y= \frac{-b}{2a}[/tex]
[tex]y=\frac{-32}{2(-4)}[/tex]
[tex]y=\frac{-32}{-8}=4[/tex]
doreen schmidt Is a chemist. She needs to prepare 36 ounces of a 16% hydrochloric acid solution. Find the amount of 18% solution and the amount of 9% solution she should mix to get this solution
Please help.
Answer:
Mixing two concentrations for known amount of mixture
Step-by-step explanation:
Let x = amount (ounces) of 18% solution
then
36-x = amount (ounces) of 9% solution
0.18x + 0.09(36-x) = .16(36)
0.18x + 3.24-.09x = 5.76
0.09x + 3.24 = 5.76
0.09x = 2.52
x = 28 ounces of 18% solution
amount of 9% solution:
36-x = 36-18 = 18 ounces
"prepare 36 ounces", means mass or weight.
Let u = ounces of 16%
Let v = ounces of 18%
(16u + 18v)/36=9
and u + v = 36
based on the above findings....
Mixing two concentrations for known amount of mixture
High Fructose Corn Syrup (HFCS) is a sweetener in food products that is linked to obesity and type II diabetes. The mean annual consumption in the United States in 2008 of HFCS was 60 lbs with a standard deviation of 20 lbs. Assume the population follows a Normal Distribution.
a. Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.
b. Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.
c. Find the 80th percentile of annual consumption of HFCS.
d. In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.
e. Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?
f. Find the quartile and Interquartile range for this population.
g. A teenager who loves soda consumes 105 lbs of HFCS per year. Is this result unusual?
Answer:
Explained below.
Step-by-step explanation:
X = annual consumption in the United States in 2008 of HFCS
[tex]X\sim N(60, 20^{2})[/tex]
(a)
Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.
[tex]P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-60}{20})=P(Z>-0.50)=P(Z<0.50)=0.6915[/tex]
P (X > 50) = 0.6915.
(b)
Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.
[tex]P(30<X<90)=P(\frac{30-60}{20}<\frac{X-\mu}{\sigma}<\frac{90-60}{20})\\\\=P(-1.5<Z<1.5)\\\\=0.93319-0.06681\\\\=0.86638\\\\\approx 0.8664[/tex]
P (30 < X < 90) = 0.8664.
(c)
Find the 80th percentile of annual consumption of HFCS.
P (X < x) = 0.80
⇒ P (Z < z) = 0.80
⇒ z = 0.84
[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-60}{20}\\\\x=60+(20\times 0.84}\\\\x=76.8[/tex]
80th percentile = 76.8.
(d)
In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.
P (X > 50) = 0.6915
Number of American who consume more than 50 lbs = 40 × 0.6915
= 27.66
≈ 28
Expected number = 28.
(e)
Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?
According to the Empirical rule, 95% of the normally distributed data lies within 2 standard deviations of mean.
[tex]P(\mu-2\sigma<X<\mu+2\sigma)=0.95\\\\P(60-2\cdot20<X<60+2\cdot20)=0.95\\\\P(20<X<100)=0.95[/tex]
Range = 20 < X < 100.
(f)
Find the quartile and Interquartile range for this population.
1st quartile: Q₁
P (X < Q₁) = 0.25
⇒ P (Z < z) = 0.25
⇒ z = -0.67
[tex]z=\frac{Q_{1}-\mu}{\sigma}\\\\-0.67=\frac{Q_{1}-60}{20}\\\\Q_{1}=60-(20\times 0.67)\\\\Q_{1}=46.6[/tex]
3rd quartile: Q₃
P (X < Q₃) = 0.75
⇒ P (Z < z) = 0.75
⇒ z = 0.67
[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\0.67=\frac{Q_{3}-60}{20}\\\\Q_{3}=60+(20\times 0.67)\\\\Q_{3}=73.4[/tex]
Inter quartile range:
[tex]IQR=Q_{3}-Q_{1}=73.4-46.6=26.8[/tex]
(g)
Compute the z-score for x = 105 lbs as follows:
[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\z=\frac{105-60}{20}\\\\z=2.25[/tex]
Z-scores greater than +2.00 or less than -2.00 are considered as unusual.
Thus, the result unusual.
Find the maximum and minimum values
Answer:
2 and 10 are the in and max
Answer:
Min = 2
Max = 10
Step-by-step explanation:
C = 2(x+y)
x ≥1
y ≥0
y ≤5 -x
The smallest y can be is zero
The smallest x can be is 1
The minimum is
C = 2 ( 0+1) = 2 ( 1) = 2
Looking for the max
y ≤5 -x
Add x to each side
x+y ≤5
The max is 5 for x+y
Substituting that into the equation for C
C = 2(5)
C = 10
Min = 2
Max = 10
Mary is 2 times older than Bob and Bob is 5 years older than Sally. Sally is 10 years old how old is Bob
Answer:
Bob is 15 years old.
Step-by-step explanation:
If Sally is 10 years old and Bob is five years older than Sally then we just need to add 10+5=15.
Hope this helps!!
Michelle Duncan wants to know what price home she can afford. Her annual gross income is $45,000. She owes $790 per month on other debts and expects her property taxes and homeowners insurance to cost $340 per month. She knows she can get an 10.00%, 30-year mortgage so her mortgage payment factor is 8.78. She expects to make a 20% down payment. What is Michelle's affordable home purchase price? (Round your answer to the nearest dollar amount.)
Group of answer choices
$43,870
$635
$655
$41,999
$39,784
Answer:
$41,999
Step-by-step explanation:
Annual income = 45000
monthly income = $45000/12 months = $3750
mandatory expense at 38% rule = $3750 x 0.38 = 1425
other debt = 790
tax and insurance = 340
= 1425 - 790 - 340
= 295
balance left = 295
mortgage payment = (295/8.78) x 1000
= $33,599
purchase price = monthly payment/ 1- % of down payment
= $33599/1 - 0.20
= 33599/0.80
= $41,999
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the temperature reading that separates the bottom 4% from the others. Round to two decimal places.
Answer:
the temperature reading that separates the bottom 4% from the others is -1.75°
Step-by-step explanation:
The summary of the given statistics data set are:
Mean [tex]\mu[/tex] : 0
Standard deviation [tex]\sigma[/tex] = 1
Probability of the thermometer readings = 4% = 0.04
The objective is to determine the temperature reading that separates the bottom 4% from the others
From the standard normal table,
Z score for the Probability P(Z < z) = 0.04
P(Z < -1.75) = 0.04
z = -1.75
Now, the z- score formula can be expressed as :
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]-1.75 = \dfrac{X-0}{1}[/tex]
-1.75 × 1 = X - 0
X = -1.75 × 1 - 0
X = -1.75
Therefore, the temperature reading that separates the bottom 4% from the others is -1.75°
If x is 6, What is X+4
Answer: 6 + 4
Step-by-step explanation:
6 is the x
Answer:
if X=6
meaning,when you add X+4 it will give you 6+4 which is equal to 10
Suppose that the functions g and h are defined for all real numbers x as follows.
gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).
Answer:
Step-by-step explanation:
Given the functions g(x) = x − 3x and h(x) = 5x + 2, we are to calculatae for the expression;
a) (g - h)(x) an (g * h)(x)
(g - h)(x) = g(x) - h(x)
(g - h)(x) = x − 3x -(5x+2)
(g-h)(x) = x-3x-5x-2
(g-h)(x) =-7x-2
b) (g * h)(x) = g(x) * h(x)
(g * h)(x) = (x − 3x )(5x+2)
(g * h)(x) = 5x²+2x-15x²-6x
(g * h)(x) = 5x²-15x²+2x-6x
(g * h)(x) = -10x²-4x
c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;
(g + h)(x) an (g * h)(x)
(g + h)(x) = g(x) +h(x)
(g + h)(x) = x − 3x + (5x+2)
(g+h)(x) = x-3x+5x+2
(g+h)(x) =3x+2
Substituting x = -2 into the resulting function;
(g+h)(-2) = 3(-2)+2
(g+h)(-2) = -6+2
(g+h)(-2) = -4
123=0
4235=0
656=2
5390=2
8890=6
1001=2
19235=1
What is 123456789?
Answer:
4
Step-by-step explanation:
I suppose this is a trick question.
The answer is equal to the "circular hole" in the numbers. (except 4, which does not contain circular hole).
So by counting the holes,
123456789 = 4
Answer:
4
Step-by-step explanation:
This is a trick/pattern
We have to count the number of holes in each number
1-0
2-0
3-0
4-0
5-0
6-1
7-0
8-2
9- 1
1+2+1 =4