Answer:
The number of students that would have a test score between 61 and 71 are 154 students
Step-by-step explanation:
The given information are;
The mean test score, μ = 61
The standard deviation, σ = 10
The sample size, n = 450
The z score is given as follows;
[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]
We therefore have at x = 61,
[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]
P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5
For x = 71, we have;
[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]
P(x < 71) = P(Z < 1) = 0.84134
The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134
Given that the probability is equivalent to the proportion of the students that would have a test score between 61 and 71, we have;
The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.
Max and Sven bike away from home in the same direction starting at noon. They bike at constant speeds. Max bikes at xmph and he is ymph faster than Sven. By 4pm, how far ahead of Sven would Max be?
Answer:
Max would be 4y meters ahead by 4pm
Step-by-step explanation:
What we want to calculate here is the difference in the distance they have covered by 4pm given the speed at which they traveled.
Mathematically, distance = speed * time
The time is just the difference between 12 noon and 4pm which is 4 hours
Let’s tackle Max’s
He’s biking at x km/h, so the distance he would have covered by 4pm would be 4 * x = 4x meters
Now let’s tackle Sven
Sven is biking at a speed which is y mph less than Max’s x mph
Thus his speed would be (x-y) mph
His distance covered would be 4(x-y) meters
Now the difference between their bikes distance at 4pm would be;
4x - [4(x-y)]
= 4x -(4x -4y)
4x -4x + 4y
= 4y
Hence, Max would be 4y meters ahead by 4pm
What is the margin of error for 95% confidence for a sample of size 250 where p = 0.45?
A. 0.0541
B. 0.0775
C. 0.0706
D. 0.0617
Answer:
0.0617
Step-by-step explanation:
so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!
This method applies to any problems with the same basic format. Good luck!
If f ( x) = 4x
2 and g( x) = 5x , what is
g( f (2x)) ?
Answer: 40x
First, let's find f(2x)
[tex]f(2x)=4(2x)=8x[/tex]
Using this, let's find g(f(2x)):
[tex]g(f(2x))=g(8x)=5(8x)=40x[/tex]
That's the answer. Let me know if you need any clarifications, thanks!
Answer:
80x²
Step-by-step explanation:
f(x) = 4x², g(x) = 5x
f(2x) = 4(2x)² = 16x²
g(f(2x)) = 5(16x²) = 80x²
Solve.
y=x - 7
5+2y=7
Answer:
[tex]\huge\boxed{x=8;\ y=1\to(8;\ 1)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}[/tex]
[tex]\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}[/tex]
Answer:
(8, 1).
Step-by-step explanation:
y = x - 7
5 + 2y = 7
5 + 2(y) = 7
5 + 2(x - 7) = 7
5 + 2x - 14 = 7
Subtract 5 from both sides
2x - 14 = 2
Add 14 to both sides
2x = 16
Divide both sides by 2
x = 8
Since x = 8...
y = x - 7
y = 8 - 7
y = 1.
To check our work...
5 + 2y = 7
5 + 2 * 1 = 7
5 + 2 = 7
7 = 7
Since it works out, your answer is (8, 1).
Hope this helps!
The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)7 B. 5(7)(0.06) C. 5(1.06)7 D. 5(7)(1.06)
Complete Question:
The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)^7 B. 5(7)(0.06) C. 5(1.06)^7 D. 5(7)(1.06)
Answer:
C. 5(1.06)^7
Step-by-step explanation:
The volume of a tree increases by 7% every year
The formula we would be using is
V(t) = Vo (1 + r)t
Where V(t) = Volume after t years
Vo = Present of initial volume
r = rate of increase
t = time
From the question,
V(t) = Volume after t years = unknown
Vo = Present of initial volume = 5m³
r = rate of increase = 6% = 0.06
t = time = 7 in years
V(t) = 5 × ( 1 + 0.06)^ 7
V(t) =(5)(1.06)^7
Therefore, its volume be after 7 years if its volume is 5 cubic meters now is
Option C: (5)(1.06)^7
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
h(x) = -15.6(x - 3.8)² + 241
Step-by-step explanation:
if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.
or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)
the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.
Which algebraic expression represents the phrase below?
five times the sum of a number and eleven, divided by three times the sum of the number and eight
5(x + 11) + 3(x + 8)
5x+11
3X+8
5(X+11)
3(x+8)
5x + 11 + 3x + 8
Answer:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Step-by-step explanation:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Five times the sum of a number and eleven, divided by three times the sum of the number and eight
Five times the sum= 5(_+_)
a number and eleven= x+11
divided= ÷ or /
3 times the sum of= 3(_+_)
the number and eight.
Together it will be
[tex]the \: \: one \: written \: in \: the \: answering \: section[/tex]
Hope this helps ;) ❤❤❤
Find side AC and round your answer to the nearest hundredth, help please.
Answer:
Step-by-step explanation:
Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:
[tex]tan(70)=\frac{?}{3}[/tex] and
3tan(70) = ? so
? = 8.24
If c cars can be parked in each of the four main rows of the parking lot, what is the expression gor the maximum number of cars that can be parked in the parking lot?
Answer:
4c
Step-by-step explanation:
We can say that the maximum number of cars can be represented as:
Maximum number of cars = Total of rows × Number of cars per row
In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:
Maximum number of cars = 4c
Your sister asks you to pick out one of her CDs to listen to. She has 6 rock, 4 country, and 4 rap CDs. If you pick one at random, what is the probability that you pick a country CD?
Hey there! I'm happy to help!
We have 6 rock, 4 country, and 4 rap CDs. If we add these all together ,we have 14 total CDs.
Since there are 4 country CDs, we have a 4/14 chance of picking one, which simplifies to 2/7 chance.
Have a wonderful day!
which of the following is the Pythagorean theorem
Answer:
[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
The Pythagorean Theorem is used to find a missing side length in a right triangle, and the formula [tex]a^2+b^2=c^2[/tex] is used to find the missing side, assuming a and b are legs, while c is the hypotenuse.
Answer:
in a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length
What the correct answer now fast
Answer:
y = 12.9
Step-by-step explanation:
To find the value of the side y, simply apply the law of cosines.
y^2 = (14)^2 + (9)^2 - 2(14)(9)cos(64)
y^2 = 196 + 81 - 110.47
y^2 = 166.53
y = 12.9
Therefore, your solution should be y = 12.9
Cheers.
Please help me with this question!!!!!
Answer:
B. [tex]H(x)=-.008(x-82)^{2}+83[/tex]
Step-by-step explanation:
Well lets graph the following equation first,
H(x) = -.011(x - 82)^2 + 75
Then lets graph all the other equations.
Look at the image below↓
So A.
The purple line does not go farther or higher,
so A. is incorrect
B.
The black line goes higher and farther,
meaning it is correct.
C.
The red line goes farther but not higher.
So it is incorrect
D.
Again the blue line does not go farther of higher.
So its wrong.
Thus,
answer choice B. [tex]H(x)=-.008(x-82)^{2}+83[/tex] is correct.
Hope this helps :)
Ama has a rectangular garden measuring 12m and 25m.He wants to divide it into square plots of equal sizes .What is the largest sized square he can use?
In a class Vidya ranks 7th from the top. Divya
is 7 ranks ahead of Medha and 3 ranks
behind Vidya. Sushma who is 4th from the
bottom is 32 ranks behind Medha. How many
students are there in the class?
Answer:
52 students
Step-by-step explanation:
From the question above, we have the following information:
a) Vidya ranks 7th from the top.
Mathematically,
Vidya = 7th student
b) Divya 3 ranks behind Vidya.
Divya = Vidya + 3
Hence, Mathematically:
Divya = 7 + 3 = 10
Divya = 10th student
c) Also, Divya is 7 ranks ahead of Medha.
Mathematically,
Medha = 10 + 7= 17
Medha= 17th student
d)Sushma is 32 ranks behind Medha
Mathematically,
Sushma = Medha + 32
= 17 + 32 = 49
Sushma is the 49th student
Therefore, since, Sushma is 4th from the bottom, total number of students is:
49 + 3 = 52 students
A student in a statistics class asks students in a long lunch line about their opinions about the school cafeteria. The sample that results is most likely __________________.
A. quota
B. symmetric
C. large
D. biased
Answer:
The correct option is;
D. Biased
Step-by-step explanation:
A sampling method in which the members of the sample are not representative of the population, such that some members of the population have a higher or lower probability within the sample which is indicative that not all members of the population are sampled
A biased sample is a non random sample and the can lead to misleading data conclusion
In the question, the sampling of student opinion about the school cafeteria among students who are on the lunch line and so prefer the school cafeteria leaves out the portion of the population that get their lunch from alternative sources.
Answer:
biased
Step-by-step explanation:
please heellllpppp ....
Answer:
x ≈ 2.3 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos55° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] ( multiply both sides by 4 )
4 × cos55° = x , thus
x ≈ 2.3 cm ( to 1 dec. place )
Brandon mows his lawn once every 4 days. Thomas mows his lawn once every 8 days. Celena mows her lawn once every 6 days. If they are all mowing the lawn today, in how many days will they be mowing their lawns together again? A. 72 B. 24 C. 18 D. 12
Answer: B
Step-by-step explanation:
4,8 and 6 all go into 24
Sudhir bought an almirah for RS 13600 and spent RS 400 on its transportation . He sold it for RS 16800 . find the his gain percent
Answer:
His gain percent is 20%
Step-by-step explanation:
In this question, we want to find the percentage gain of the business.
We need the following parameters;
The cost price which is the sum of the amount she bought the goods + the amount spent on transport
Using the values we have in the question;
The cost price will be;
13,600 + 400 = Rs 14,000
The selling price = Rs 16,800
Mathematically the percentage gain will be;
% gain = (selling price- cost price)/selling price * 100%
% gain = (16,800-14,000)/14,000 * 100/1
% gain = 2800/14,000 * 100/1 = 1/5 * 100/1 = 20%
Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice
Answer:
1/216
Step-by-step explanation:
When a pair of dice is rolled, there are 36 possible different outcomes.
Of those 36 different outcomes, a sum of 3 is obtained in 2 different ways: 1, 2 and 2, 1.
Of those 36 different outcomes, a sum of 10 is possible in 3 different ways: 6, 4; 5, 5; 4, 6.
p(3 followed by 10) = p(3) * p(10) = 2/36 * 3/36 = 1/18 * 1/12 = 1/216
II NEED HELP!!!!!!!! Are the graphs of the lines in the pair parallel? Explain. y = 2/3x– 17 4x – 6y = –6 4x-6y=-6 Yes, since the slopes are the same and the y-intercepts are the same. A )No, since the y-intercepts are different. B)No, since the slopes are different. C)Yes, since the slopes are the same and the y-intercepts are different.
Answer:
A
Step-by-step explanation:
Can somebody please help me with this & show work ?? :)
Answer:
s = 116°, q and t are 64°
Step-by-step explanation:
isoceles so r and s are the same and q and t are the same. therefore q and t are 180-116 = 64
HELP please!!!
Jeanie wants a $100 000 mortgage. She arranged payments for the next 15 years. The bank charges 4.8%/a interest, compounded monthly.
a) how much is each monthly payment
b) how much interest is jeanie paying?
Answer:
in one month : 13676.57/12=1139.71
the interest on 100000 is: 205148.48-100000=105148.48
Step-by-step explanation:
A=P(1+r)^t (p is the mortgage, t is the time and r is the rate)
p=100000,t=15*12 month,r=4.8%( or 0.048)
A=100000(1+0.048/12)^(12*15)
A=205148.48 (the number rounded to the nearest hundredth)
205128.48 is the amount she has to pay it after 15 years
in one year : 205128.48/15=13676.57 ( rounded to nearest hundredth)
in one month : 13676.57/12=1139.71
the interest on 100000 is: 205148.48-100000=105148.48
MATH PLEASE HELP ME. WILL GIVE BRAINLIEST
Answer:
The answer is - 17Step-by-step explanation:
g(x) = 2x³ - 3x + 5
To find g(- 2) substitute the value of - 2 into g(x)
That's
g(- 2) = 2(-2)³ - 3(-2) + 5
= 2(-8) - 3(2) + 5
= - 16 - 6 + 5
= - 17Hope this helps you
Explain how to get the volume of this figure
Answer:
350 meters cubed.
Step-by-step explanation:
If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.
The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.
The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.
(5 * 7 * 3) + (7 * 7 * 5)
= (35 * 3) + (49 * 5)
= 105 + 245
= 350
So, the volume of the figure is 350 meters cubed.
Hope this helps!
NEEEED HELPPPPP PLEASEEEEEE Use long division to find the quotient below.
(8x^2 + 4x^2 + 100) - (2x + 5)
Answer:
[tex]4x^2 - 8x + 20[/tex]
Step-by-step explanation:
The correct equation is:
[tex]8x^3 + 4x^2 + 100[/tex]
We want to divide that by (2x + 5)
To do the long division, divide each term by 2x and then subtract the product of the result and (2x + 5) from the remaining part of the equation.
When you get to 0, you have reached the end of the division.
Whatever term you get from each step of division is part of the quotient.
Go over the steps above carefully while following them below:
Step 1:
Divide [tex]8x^3[/tex] by 2x. You get [tex]4x^2[/tex].
Step 2
Multiply [tex]4x^2[/tex] by (2x + 5) and subtract from [tex]8x^3 + 4x^2 + 100[/tex]:
[tex]8x^3 + 4x^2 + 100[/tex] - ([tex]8x^3 + 20x^2[/tex]) = [tex]-16x^2 + 100[/tex]
Step 3
Divide [tex]-16x^2[/tex] by 2x. You get [tex]-8x[/tex].
Step 4
Multiply -8x by (2x + 5) and subtract from [tex]-16x^2 + 100[/tex]:
[tex]-16x^2 + 100[/tex] - ([tex]-16x^2 - 40x[/tex]) = 40x + 100
Step 5
Divide 40x by 2x. You get 20.
Step 6
Multiply 20 by (2x + 5) and subtract from 40x + 100:
40x + 100 - (40x + 100) = 0
From the three steps of the division, we got [tex]4x^2[/tex], -8x and 20.
Therefore, the quotient is [tex]4x^2 - 8x + 20[/tex]
Determine the equation for a line perpendicular to y=1/3+4 and has an x-intercept of 2.
Answer:
y = -3x + 6
Step-by-step explanation:
Any line perpendicular to
y = (1/3)x + 4
has a slope of -1/(1/3) = -3
and equation
y = -3x + b .................(1)
If the line has an x intercept of 2 at (0,2), then
0 = -3(2) + b
solving
b = 6
By substituting b=6 into (1), the line required
y = -3x + 6
Answer:
y = -3x + 2
Step-by-step explanation:
y= [tex]\frac{1}{3}x +4[/tex]
Slope [tex]m_{1}=\frac{1}{3}[/tex]
slope of the perpendicular line [tex]m_{2}[/tex] = [tex]\frac{-1}{m_{1}}[/tex] = [tex]\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\[/tex]
b= 2
Slope intercept form of required line: y = mx + b
y = -3x + 2
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
C
Step-by-step explanation:
Line of symmetry
Can someone please help me?
Answer:
( - 1 , - 1 )Option D is the correct option.
Step-by-step explanation:
y = - 2x - 3 → Equation ( i )
y = 3x + 2 → Equation ( ii )
Using elimination method
y + 2x = - 3
y - 3x = 2
---------------------
5x = - 5
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{ - 5}{5} [/tex]
Calculate
[tex]x = - 1[/tex]
Again, Putting the value of x in equation ( ii ) in order t get the value of y
[tex]y = 3x + 2[/tex]
plug the value of x
[tex] = 3 \times ( - 1) + 2[/tex]
Any expression multiplied by ( - 1 ) equals it's opposite
[tex] = - 3 + 2[/tex]
Calculate
[tex] = - 1[/tex]
Therefore, The possible solution of the system is the ordered pair ( x , y )
[tex](x \:, y \: ) = ( - 1 \:, - 1)[/tex]
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex] - 1 = - 2 \times ( - 1) - 3[/tex]
[tex] - 1 = 3 \times ( - 1) + 2[/tex]
Simplify the equation
[tex] - 1 = - 1[/tex]
[tex] - 1 = - 1[/tex]
Since all the equalities are true, the ordered pair is the solution of the system.
( x , y ) = ( - 1 , - 1 )Hope this helps..
Best regards!!
U
480
S
d
T
b
R.
C
P
1549
Q
Answer:
a = 26°
b = 48°
c = 26°
d = 106°