Answer:
3.6
Step-by-step explanation:
1/9+1/6
1/3^2+1/2x3=1/x
2+3/3^2x2=1/x
5/3^2x2=1/x
x.5=18
5x=18
5x/5= 18/5
x=18/5
x=3.6
To paint the room if they worked together in 4 hours 14 min.
To find time if they work together.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.An arithmetic sequence is a sequence where the difference between each successive pair of terms is the same. The explicit rule to write the formula for any arithmetic sequence is this:
an = a1 + d (n - 1).
Given that:
(1 room/Sally's time) + (1 room/Steve's time) = (1 room)/(time working together)
1/9+1/6+=+1/x
Multiply both sides by 54x
6x+9x=54
15x=54
x=3.6hours
Working together, they can paint the room in 3 hours 6 min.
So, to paint the room if they worked together in 3 hours 6 min.
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Which transformation is needed to be used on x^2, to get the graph of f(x) = 2x2 - 12x + 22?
Select one:
O a. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 13 units
O b. Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O c. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O d. Shift right by 3 units and shift upwards by 4 units
Please I need help
Answer: A
Step-by-step explanation:
The required transformation is Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units. Hence option B is correct.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Since, both curve of x² and 2x² - 12x + 22 is in the graph.
Now, the steps of transformation of x² into 2x² - 12x + 22 is as follows.
1) Shift left by 3 units.
2) Stretch vertically by a factor 2.
3) Shift upward by 4 units
Thus, the required result will be seen graph.
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what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
The result of a biology test was collected, and the grades and gender are summarized below A B C Total Male 5 4 17 26 Female 6 2 15 23 Total 11 6 32 49 Let p p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents).
Answer:
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Step-by-step explanation:
| A | B | C | Total
Male | 5 | 4 | 17 | 26
Female | 6 | 2 | 15 | 23
Total | 11 | 6 | 32 | 49
If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
All female students = 23
Female students that score an A = 6
p = (6/23) = 0.2608695652 = 0.261
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (6/23) = 0.261
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.
we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 23 - 1 = 22.
Significance level for 99.5% confidence interval
(100% - 99.5%)/2 = 0.25% = 0.0025
t (0.0025, 22) = 3.119 (from the t-tables)
Standard error of the mean = σₓ = √[p(1-p)/N]
p = 0.261
N = sample size = 23
σₓ = √(0.261×0.739/23) = 0.091575
99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.261 ± (3.119 × 0.091575)
CI = 0.261 ± 0.2856
99.5% CI = (-0.0246, 0.5466)
99.5% Confidence interval = (-0.025, 0.547)
= -0.025 < p < 0.547
Hope this Helps!!!
Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.)
sinh(0.4) ≈ 1 − (0.4)^2 / 2! + (0.4)^2 / 4!
R4 ≤
R4 =
Specifically what does R4 equal.
Answer:
R4 ≤ 0.00008
R4 = 0.00001
Step-by-step explanation:
Given: sinh( 0.4 ) ≈ [tex]1 - \frac{(0.4)^2}{2!} + \frac{(0.4)^2}{4!}[/tex]
using Taylor's Theorem
R4 ≤ 0.00008
R4 = 0.00001
attached is the detailed solution
MATH HELP ASAP :( Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive integer coefficient. Polynomial of lowest degree with lowest possible integer coefficients, and with zeros 9-41 and 0 (multiplicity 2).
Answer:
[tex]f(x)=((x-9)^2+16)x^2[/tex]
[tex]f(x)=x^4-18x^3+97x^2[/tex]
Step-by-step explanation:
If you want to, I could add the explanation as well. Just notify me.
Something really important I want to note is that since 9-4i is a zero, then 9+4i must must also be a zero.
The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
5 (u + 1) -
7 = 3
3 (u - 1) + 2u
Correct Question:
5 (u + 1) - 7 = 3 (u - 1) + 2u.
Solve for u
Answer:
See explanation below
Step-by-step explanation:
In this given question, we are required to find u.
Given the equation:
5 (u + 1) - 7 = 3 (u - 1) + 2u
Required:
Solve for u
To find u, first simplify both sides individually.
Simply 5 (u + 1) - 7:
Expand the parenthesis:
5u + 5 - 7
Collect like terms:
5u - 2
Simplify 3 (u - 1) + 2u:
Expand the parenthesis:
3u - 3 + 2u
Collect like terms:
3u + 2u - 3
5u - 3
Bring both simplified equations together:
5u - 2 = 5u - 3
5u - 5u - 2 = -3
-2 = -3
Since -2 ≠ -3, there is no solution.
Therefore, we can say the equation is invalid.
Jack is doing a test launch of his hovercraft for the upcoming STEM competition.
Answer:
The answer is missing.
I think there is something wrong with the equation on its own
Step-by-step explanation:
Equation for the hovercraft
F(x)= X²+6x+2
Olivia catapult equation
F(x)= √2x
Differential of the both equation will give the velocity at x time
F(x)= X²+6x+2
DF(x)/Dx= 2x +6
F(x)= √2x
F(x)= (2x)^½
DF(x)/Dx= (2x)^-½
So the differential is the velocity of the both equation.
Let's equate both equation to find the value of x at which they have same velocity.
(2x)^-½=- 2x+6
(2x)^-1= (-2x+6)²
(2x)^-1= 4x² -24x +36
0= 8x³ - 48x² +72x -1
An amount of $18,000 is borrowed for 13 years at 4% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
Use the calculator provided and round your answer to the nearest dollar
Answer:
Total amount to be paid back = $29971
Step-by-step explanation:
Formula used to calculate the final amount of the loan to be paid,
Total amount to be paid = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Where P = Principal amount of loan taken
r = rate of interest
n = Number of compounding in a year
t = duration of investment
By substituting the values in the formula,
Total amount to be paid after loan maturity = [tex]18000(1+\frac{0.04}{1})^{13\times 1}[/tex]
= [tex]18000(1.04)^{13}[/tex]
= 18000(1.66507)
= $29971.32
≈ $29971
Total amount to be paid after loan maturity will be $29971.
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
Which of the following steps indicates the distributive property when solving –3(x + 2) = 21?
Question 4 options:
A)
–3x + 2 = 21
B)
–3x – 6 = 21
C)
D)
–3x – 6 = –63
Answer:
B) –3x – 6 = 21
Step-by-step explanation:
Well the distributive property is the multiplying of a number by more numbers in parenthesis.
For example -3(x + 2) by using the distributive property we get,
-3x - 6
Thus,
the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.
Hope this helps :)
When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.
What is distributive property?Distributive property explains us how to solve expressions in the form of a(b + c).
After apply distributive property this term convert as ab+ac.
The given expression is,
3(x + 2) = 21
To solve the expression, use distributive property,
According to distributive property,
a(b + c) changes in the form of ab+ac.
Solve for the given expression,
3x + 2×3 = 21
3x + 6 = 21
Solve for the value of x,
3x = 21 - 6
3x = 15
x = 5
Hence, option (C) is correct.
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2.CommerceThe weight distribution of parcels sent in a certain manner is normal with meanvalue 12 pounds and standard deviation 3.5 pounds. The parcel service wishes to establish aweight valuecbeyond which there will be a surcharge. What value ofcis such that 99% ofall parcels are under the surcharge weight
Answer:
the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
Step-by-step explanation:
Given that :
The mean value [tex]\mu[/tex] = 12
The standard deviation [tex]\sigma[/tex] = 3.5
Let Consider Q to be the weight of the parcel that is normally distributed .
Then;
Q [tex]\sim[/tex] Norm(12,3.5)
The objective is to determine thewight value of c under which there is a surcharge
Also, let's not that 99% of all the parcels are below the surcharge
However ;
From the Percentiles table of Standard Normal Distribution;
At 99th percentile; the value for Z = 2.33
The formula for the Z-score is:
[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]
2.33 × 3.5 = X - 12
8.155 = X - 12
- X = - 12 - 8.155
- X = -20.155
X = 20.155
the weight value of c under which there is a surcharge = X + 1 (0) since all the pounds are below the surcharge
c = 20.155 + 1(0)
c = 20.155
Thus ; the value of c is 20.155 such that 99% of all parcels are under the surcharge weight.
The length of human pregnancies from conception to birth varies accordingly to a distribution that is approximately normal with mean 266 days and standard deviation 16 days. a study enrolls a random sample or 16 pregnant women. what are the mean and standard deviation of the sampling distribution of Xbar? What is the probability the average pregnancy length exceed 270 days?
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.
a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:
[tex]\mu_x=\mu=266\ days[/tex]
The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]
b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x > 270 days:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]
The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%
Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about the origin? A. (x,y)→(y,−x) B. (x,y)→(−y,−x) C. (x,y)→(y,x) D. (x,y)→(−x,−y)
Hey there! I'm happy to help!
If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒ (-x,-y).
Have a wonderful day! :D
Chapter: Simple linear equations (Answer in steps)
Step-by-step explanation:
5) a. x/2 = 7-5
x/2 = 2
x = 2×2
x=4
b.4x - 2 = 3x +7
4x - 3x = 7 + 2
x = 9
c. x+2 = 42 × 3
x+2 = 126
x = 124
d. 13x + 260 = 39
13x = 39 - 260
13x = -221
x = -17
6) a. 6x / 7 = 4 +2
6x = 6 × 7
6x = 42
x = 7
b. -49 = 7x + 7
-49 - 7 = 7x
7x = - 56
x = -8
c. -7 + 7x - 21 = 0
7x - 28 = 0
7x = 28
x = 4
d. 8x - 32 + 2 = 42
8x - 30 = 42
8x = 42 + 30
8x = 72
x = 9
e. 5x + 7 = 18
5x = 11
x = 2.5
What is the value of 3/4 increased by 2 1/6?
Answer:
2 11/12
Step-by-step explanation:
3/4 + 2 1/6
Add the fractions.
35/12
= 2 11/12
Answer:
[tex]2\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]
Rewrite the equation by completing the squares x^2-x-20
Answer: x = ¹/₂ ± √⁸¹
------------
2
Step-by-step explanation:
First write out the equation
x² - x - 20
Now we now write the equation by equating to 0
x² - x - 20 = 0
We now move 20 to the other side of the equation. So
x² - x = 20,
We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes
x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²
x² - ( ¹/₂ )² = 20 + ¹/₄
( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction
( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4
Taking the square root of both side to remove the square,we now have
x - ¹/₂ = √⁸¹/₄
x - ¹/₂ = √⁸¹/₂
Therefore,
x = ¹/₂ ± √⁸¹
-----------
2
SAT Scores Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of these high school seniors, those who are in the National Honor Society, is selected, would you expect the distribution of scores to have the same mean and standard deviation? Explain your answer.
Answer:
The distribution of scores would not have the same mean and standard deviation
Step-by-step explanation:
According to the given data we have the following:
mean=456
Standard deviation=100
mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed
Therefore, we can conclude that a subgroup of these high school seniors would not to be a perfect representation, hence, the distribution of scores would not have the same mean and standard deviation.
evaluate 4! +!3 /2 8 10 or 15
Answer:
15
Step-by-step explanation:
4! +3! /2
4!=4*3*2*1=24
3!=3*2*1=6
24+6/2=30/2=15
Combine like terms: 10 + 6y + 2x - 3
Answer:
6y +2x +7
Step-by-step explanation:
10 + 6y + 2x - 3
The only like terms are the constant
6y+2x +10-3
6y +2x +7
Answer:
2x + 6y + 7.
Step-by-step explanation:
10 + 6y + 2x - 3
= 2x + 6y - 3 + 10
= 2x + 6y + 7.
Hope this helps!
Almost there, then everything is set! Thanks guys
Answer:
x = 50°
Step-by-step explanation:
Step 1.
180° - 80° (because there are 180 degrees in a triangle) = 100°
Step 2.
100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)
Step 3.
Answer: x = 50°
PLS HELP ...... Urgently
Answer:
18+18 as point XYZ is in centroid of Q
Step-by-step explanation:
so it's equal.
36.which is option A.
Find the distance between the points X and Y shown in the figure.
Answer:
XY ≈ 14.87 units
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)
d = [tex]\sqrt{(8+6)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{14^2+(-5)^2}[/tex]
= [tex]\sqrt{196+25}[/tex]
= [tex]\sqrt{221}[/tex]
≈ 14.87 ( to 2 dec. places )
h(6)= ? I don't even know what the question is asking me to do
Answer:
h(6) = 8
Step-by-step explanation:
h(6) is find the value of the function when x=6
What is the y value ( the value of the blue line) when x=6
Go to x=6 and go up to the blue line
y =8
h(6) = 8
Answer:
8At X = 6 , h(X) = 8
plug the value of x
h (6) = 8
please see the attached picture..
Hope this helps...
Good luck on your assignment...
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?
[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]
Answer:
1/13
Step-by-step explanation:
Find the value of x. Give reasons to justify your solution. D ∈ AC
Answer:
x = 25°
Step-by-step explanation:
From the picture attached,
Since AE║BC and AC is a transverse,
Therefore, ∠EAC ≅ ∠BCA [Alternate interior angles]
m∠EAC = m∠BCA = x°
∠BCD = ∠DCB + ∠DBC [Since ∠BCD is an exterior angle of ΔBDC]
m∠BCD = m∠DCB + m∠DBC
50° = x° + x°
2x = 50
x = 25°
Therefore, value of x is 25°.
Answer: 25 degrees
Step-by-step explanation:
a hat contains 2 red apples and 3 green apples. a bucket contains 7 red apples and 3 green apples. a container is selected at random and an apple is drawn out. what is the probability that it will be a red apple
Answer:
15
Step-by-step explanation:
A new city Mayor would like to determine the proportion of community voters who are ages 18 to 20 years. He has heard it is 10%. To test this prediction, he surveys 1000 random community voters and found that 111 of them are aged 18 to 20. The following is the setup for this hypothesis test: H0:p=0.10 H0:p≠0.10 The p-value for this hypothesis test is 0.04. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer: He should reject the null hypothesis.
Step-by-step explanation: When using P-Values to decide if you accept or not the alternative hypothesis, compare the p-value with the chosen significance level (α).
In the Mayor's survey:
p-value = 0.04
α = 5% or 0.05
If the p-value is less than α, reject the null hypothesis and accept the alternative. If p-value is greater than or equals α, fail to reject the null hypothesis and don't accept the alternative.
Analysing the Mayor's survey:
p-value = 0.04 < α = 0.05
In conclusion, the Mayor should reject the null hypothesis and accept that the proportion of voters who are aged 18 to 20 is not equal to 10%, i.e., accept the alternative hypothesis: [tex]H_{a}[/tex]: p≠0.10
find the lowest common denominator of 3/x^3y and 7/xy^4
[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]
It's xy.
t the end of the past month the cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500. What was the balance in the Cash account at the beginning of last month?
Answer:
In this question it is given that:
The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.
And we have to use the formula
Substituting the values , we will get
Therefore beginning cash balance is