The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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A government buys `x`fighter planes at `z` dollars each, and `y` tons of wheat at w dollars each. It spends a total of `B`dollars, where `B=xz+yw`. Write an equation whose solution is the given quantity:
2. The price of a ton of wheat, given that a fighter plane costs 100,000 times as much as a ton of wheat, and that the government bought 20 fighter planes and 15,000 tons of wheat for a total cost of $90 million.
The equation whose solution is the given quantity is 90,000,000 = 2,000,000w + 15,000w where w = $44.67
EquationB = xz + yw
Where,
B = Total cost = 90x = number of fighter plane = 20y = tons of wheat = 15,000w = cost of each tons of wheatz = cost of fighter planez = 100,000wB = xz + yw
90,000,000 = (20 × 100,000w) + (15,000 × w)
90,000,000 = 2,000,000w + 15,000w
90,000,000 = 2,015,000w
w = 90,000,000 / 2,015,000
= 44.6650124069478
Approximately,
w = $44.67
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the alexander family and jenkins family each used their sprinklers last summer. the water output rate for the alexander familys sprinkler was 20 L per hour. theh water output rate fro the jenkins familys sprinkler was 25 L per hour. the familes used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1450 L. How long was each sprinkler used?
Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.
Step-by-step explanation:
Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
[tex]20x=1450[/tex]
[tex]x= 72.5[/tex]
If we just used the Alexanders it would of took 72 hours and 30 minutes.
Now lets look at the Jenkins family sprinkler, lets define it as Y.
[tex]25y=1450[/tex]
[tex]y = 58[/tex]
With only the Jenkins it would of took 58 hours.
Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
[tex]20x= 725[/tex]
[tex]x=36.25[/tex]
Jenkins
[tex]25y=725[/tex]
[tex]y=29[/tex]
Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.
Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take [tex]\frac{5}{4}[/tex] hours. We know that 1 hour contains 60 minutes, which means [tex]\frac{1}{4}[/tex] of a hour contains 15 minutes.
So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.
So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.
Given IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, the proportion of people with IQs above 130 is
The proportion of people with IQs above 130 is 2.3%.
How to calculate the value?Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Here the mean is 100 and a standard deviation of 15.
µ = 100, σ = 15
P(X > 130) =
= P( (X-µ)/σ > (130-100)/15)
= P(z > 2)
= 1 - P(z < 2)
Using excel function:
= 1 - NORM.S.DIST(2, 1)
= 0.023 = 2.3%
The value is 2.3%.
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What is the length of BC?
Answer:
75/4
Step-by-step explanation:
Assuming BA and ED are parallel, we know thay the two triangles are similar.
So,
[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]
Is x – 5 a factor of the function f(x) = x3 – 5x2 + 7x – 35? Use the Remainder Theorem to justify your answer.
Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,
Remainder theoremIn order to determine whether x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35, we will show that f(5) = 0
Substitute x = 5 into the function to have;
f(5) = 5^3 – 5(5)^2 + 7(5) – 35
f(5) = 125 - 125 + 35 - 35
f(5) = 0
Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,
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Lesson Review
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Factorization implies the obtaining of the common factors in an expression.
What is factorization?The term factorization implies the obtaining of the common factors in an expression.
The factors of the expressions are as follows;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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how to find n if sn=969 of A.p,a1=9 and d=6
10) Find the mean of the data set.
O a.) 5
Ob.) 9
O c.) 10
O d.) 13
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
Answer:
b
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{5+8+12+6+7+10+14+6+13}{9}[/tex]
= [tex]\frac{81}{9}[/tex]
= 9
Answer:
9
Step-by-step explanation:
The mean is also known as the average. To find it, we add up all of the data and divide it by how many numbers were added.
5 + 8 + 12 + 6 + 7 + 10 + 14 + 6 + 13 = 81
81/9 = 9
Brainliest, please :)
What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.
A group of people were asked if they had run a red light in the last year. 150 responded yes and 185 responded no. Find the probability that if a person is chosen at random, they have run a red light in the past year
The probability that a person chosen at random have run a red light in the past year is 0.45.
Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.
Probability lies between 0 and 1. The value of probability can be find by :
Probability= Number items/total items.
Number of people who said that they have run red light=150
Number of people who said that they have not run red light=185
Total people=150+185
=335 people
Probability that a person chosen at random have run red light in the past year=
=Number of people who said that they have run red lights / total people
=150/335
=0.447
After rounding off it will be 0.45.
Hence the probability that a person chosen at random have run a red light in the past year is 0.45.
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Which is the graph of the function f(x) = 1/2x2 + 2x - 6?
Answer:i would need to see the graph but here is what i think you are talking about and it shows how to it popular- problems /Algebra/ 262080
Step-by-step explanation:
Answer: man i wish i knew
Step-by-step explanation:
Find the slope of the line passing through the points (6, 4) and (6, -3).
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 x_1)
slope = (-3 - 4)/(6 - 6)
slope = -7/0
Since division by zero is undefined, this line has undefined slope.
Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Answer:
8 2/5
Step-by-step explanation:
42/5
to find the improper fraction, divide the numerator by the denominator
and then find the remainder
42 / 5 = 8 ( 5*8) the remainder is 42-40 = 2
Put the remainder over the denominator
8 2/5
Hey there!
Question reads….
Which mixed number is equivalent to the improper fraction 42/5?
EQUATION:
42/5
The one that is equivalent to the fraction is:
8 2/5
Reason:
8 2/5
= 8 * 5 + 2 / 5
= 40 + 2 / 5
= 42 / 5
Therefore, your answer should be:
Option C. 8 2/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
If each of the numbers in the following data set were multiplied by 17, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
DEFG is a rumbus. Find the vaule
Step-by-step explanation:
in a rhombus (not rumbus !) all sides are equally long.
that means
7x - 4 = 3x + 12
4x = 8
x = 2
Answer:
Step-by-step explanation:
The sides of a square are equal to each other, it is with the same with rhombus.
With this information, we can Say that [tex]DE[/tex] is equal to line [tex]GD[/tex], with
[tex]DE =7x-4GD=3x+12[/tex]
[tex]7x-4=3x+12\\[/tex]
Take [tex]3x[/tex] from both sides.
[tex]4x-4=12[/tex]
Add 4 to isolate X
[tex]4x=16[/tex]
Divide by 4
[tex]x=4\\[/tex]
So we can say that the value of [tex]x[/tex] is 4
what is 73 divdied by 84,649
Answer:
0.000862
Hope this helps :) If you have anymore questions just comment
Answer:
0.000862384670817 that is the answer
How should I solve this?
Inscribed angles that are formed by segments which extend from one side of the hypotenuse to the other are right angles.
Therefore, angle PRQ is a right angle and is equal to 90 degrees.
53y - 16 = 90
53y = 106
y = 2
Hope this helps!
Answer:
y=2
Step-by-step explanation:
the angle is 90 degrees which is equal to (53y-16).therefore find a number which you can substitute to get 90 which is y=2
Solve for x in sin xtan x + tan x – 2sin x + cos x = 0 for 0 ≤ x ≤2π rads.
The value of x = 4.71, 0.41, or 5.89 radian value
Specification:
sinxtanx + tanx -2sinx + cosx = 0
tanx = sinx / cosx
sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0
cosx to remove the fraction
sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0
sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1
sinx -2sinxcosx + 1 = 0
sinx (1-2cosx) = -1
1-2cosx = -1 / sinx
-2cosx = -1 / sinx -1
2cosx = 1 / sinx + 1
cosx = 1 / 2sinx + 1/2
sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2
Squared on both sides
1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4
4sin ^ 2 (x) Multiply
4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)
4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0
y = sinx
4y ^ 4 -3y ^ 2 + 2y + 1 = 0
sinx = y = -1 or -0.3478
x = 270, 180-22.61 or -22.61 degrees
x = 270, 157.39 or 337 .39 degrees
or
x = 3pi / 2, 0.13pi or 1.87pi radians
or
x = 4.71, 0.41 Or 5.89 radians
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Ali says 2 + 3 = 5, so 0.2 + 0.03 = 0.5. Is he correct? Why?
Answer:
No he's not correct.
Step-by-step explanation:
If you look closely the 2 and the 3 in the decimals are in different sections so it would not equal 0.5
It would equal 0.23
Drag a statement or reason to each blank in the table to complete the proof that <1 is congruent to <7.
Step-by-step explanation:
<1 congruent to <5.
<5 congruent to <7.
<1 congruent to <7.
Answer:
don't know but i need thee points
Step-by-step explanation:
Which of the following characteristics describe the graph of an exponential function?
Answer:
A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION
f
(
x
)
=
b
x
An exponential function with the form
f
(
x
)
=
b
x
,
b
>
0
,
b
≠
1
, has these characteristics:
one-to-one function
horizontal asymptote:
y
=
0
domain:
(
−
∞
,
∞
)
range:
(
0
,
∞
)
x-intercept: none
y-intercept:
(
0
,
1
)
increasing if
b
>
1
decreasing if
b
<
1
Step-by-step explanation:
hope it helps you
The correct answer is a right?
We can see that a and b are parallel, and c and e are parallel, so the correct option is E.
Which line must be parallel?
On the diagram, we can see that the angles in the third quadrant of the intersections between a and c, and the intersections between b and c, are the same angle.
Then, lines a and b must be parallel.
For the intersections with line d, we can see that this time the angle is on the fourth quadrant, so c and d are not parallel.
Finally, for line e, we can see that the known angle is on the first quadrant.
Notice that the angle on the first quadrant will be equal to the angle on the third quadrant.
So for the intersections of a and e, and b and e, on the third quadrant we have the known angle (the same one as in the intersections of a and c, and a and b).
Then c and e are parallel.
Then A and C are true.
Thus, the correct option is E.
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What is the equation of the rational function g(x) and its corresponding slant asymptote?
Rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x – 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x – 2
The solution to the Questions are
The alternate hypothesis demonstrates that there are two possible outcomes for the test.Decision rule: If z > 2.05 or z<-2.05, reject H0z=2.59The two-tailed nature of the test is shown by the alternative hypothesis.The result of the test yields the following P-value: 0.0096What is the alternate hypothesis?(a)
The alternate hypothesis demonstrates that there are two possible outcomes for the test.
(b)
Here we have
[tex]n_{1}=40,\\\\ \bar{x}_{1}=102,\sigma_{1}=5,n_{2}=50,\bar{x}_{2}=99,\sigma_{2}=6[/tex]
(b)
Here the test is two-tailed. So for [tex]\alpha =0.04[/tex], the critical values of the z-test are -2.05 and 2.05.
Decision rule: If z > 2.05 or z<-2.05, reject H0
(c)
Test statistics will be
[tex]z=\frac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} \\\\\\z=\frac{(102-99)-(0)}{\sqrt{\frac{5^{2}}{40}+\frac{6^{2}}{50}}}[/tex]
z=2.59
(d)
The two-tailed nature of the test is shown by the alternative hypothesis.
(e)
The result of the test yields the following P-value: 0.0096
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What is the correct classification for each given angle?
Drag and drop the answer into the box to match each angle.
Answer:
∠AFB = Acute
∠DFB = Obtuse
∠CFD = Right
Step-by-step explanation:
∠AFB is acute b/c its less than 90°
∠DFB is obtuse b/c it more than 90°
∠CFD is right b/c it's exactly 90°
1) A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20
Based on the sample data, does the treatment have a significant effect.?
Use a two tailed test with α = 0.05
steps
a) State the Null and the Alternate Hypotheses
A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20. Based on the sample data, the treatment has a significant effect as per the deduced test statistic. Following are the statements for Null and the Alternate Hypotheses,
H₀: The treatment does not have a significant effect
Hₐ: The treatment has a significant effect
According to the given information,
Size of the sample, n = 12
Population Mean, μ = 70
Sample Mean, M = 74.5
Standard Deviation, S = 5.20
The Null hypothesis is given by,
H₀: The treatment does not have a significant effect (μ = 70)
The Alternate hypothesis is given by,
Hₐ: The treatment has a significant effect (μ ≠ 70)
Since the population standard deviation is unknown, we will use one-sample t-test here.
Test statistic, TS = (M-μ) / (s/√n)
Substituting the given values of M, μ, S, and n, we get,
TS = (74.5-70) / (5.20/√12)
TS = 4.5 / 1.5
TS ≈ 3
The t table now provides critical values of -2.131 and 2.131 at 15 degrees of freedom for a two-tailed test using α = 0.05 (significance level).
Since our test statistic, TS does not fall in the range of the critical values, it falls in the rejection region. Thus, we can reject the null hypothesis and say that the treatment has a significant effect.
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the domain of f(x)= logb x is the set of all real numbers true or false pls need now
Answer: False
Step-by-step explanation:
The only number that makes this impossible to solve is x = 0
A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r* ) is 2.75%. The average inflation premium is 2.05%, and the maturity risk premium is estimated to be 0.1 3 (t 2 1)%, where t 5 number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds
Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%
How is the default risk premium found?The default risk premium can be found as:
=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium
Solving gives:
= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)
= 0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)
= 1.2%
The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.
This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.
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Solve for xxx in the diagram below.
x=x=x, equals
^\circ
∘please help
Answer:
x = 34
Step-by-step explanation:
The angles x + 12, 100, and x add up to a straight angle, so the sum of their measures is 180°.
(x + 12) + (100) + (x) = 180
x + 12 + 100 + x = 180
2x + 112 = 180
2x = 68
x = 34
What is the inverse of the function f (x) = 3(x + 5)2 – 4, such that x ≤ –5?
inverse of f of x is equal to negative 5 plus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x plus 4 all over 3 end quantity
inverse of f of x is equal to negative 5 plus the square root of the quantity x over 3 plus 4 end quantity
inverse of f of x is equal to negative 5 minus the square root of the quantity x over 3 plus 4 end quantity
The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = 3(x + 5)^2 - 4
Express f(x) as y
So, we have
y = 3(x + 5)^2 - 4
Swap the positions of x and y
So, we have
x = 3(y + 5)^2 - 4
Add 4 to both sides of the equation
So, we have
x + 4 = 3(y + 5)^2
Divide through by 3
So, we have
1/3(x + 4) = (y + 5)^2
Take the square root of both sides
So, we have
√[1/3(x + 4)] = y + 5
Subtract 5 from both sides of the equation
So, we have
y = -5 + √[1/3(x + 4)]
Rewrite as
f-1(x) = -5 + √[1/3(x + 4)]
Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]
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100 Points! Which shorts should I get?