Answer:
Variance for a total of 150 games is 20.67
Step-by-step explanation:
If x follows binomial distribution with parameters n and p then the probability distribution of [tex]\frac{x-np}{\sqrt{npq}}[/tex] tends to N (0.1)
As [tex]n\rightarrow \infty[/tex] where E(x)= np, var (x) = npq
[tex]\therefore[/tex] var (x) = 150[tex]\times[/tex]0.165 [tex]\times[/tex] (1-0.165)
(since, n= 150, p=0.165,
q = 1-p = 1-0.165)
= 20.66625
var (x) = 20.67
[tex]\therefore\\[/tex] variance for a total of 150 games is 20.67
Given to us:
Mark uses the normal approximation of the binomial distribution to model the number of home runs. Therefore,
Probability, p=0.165;
Number of samples, n=150;
Chances of failure, q = 1-p = 1-0.165 = 0.835;
According to binomial distribution,
Variance, var(x) = npq;
var (x) = npq
= 150 x 0.165 x 0.835
= 20.66625
Hence, the variance for a total of 150 games is 20.66625.
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an elastic band. which is 72cm
Initial length = 72 cm
Stretched length = 90 cm
Find the increased in length:
increase = 90 - 72 = 18
Find the percentage increase:
Percentage increase = change/original x 100
Percentage increase = 18/72 x 100 = 25%
Answer: The elastic band's length is increased by 25%
What are two integers whose sum is -2 and product is -80?
Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060
Answer:
Option (D)
Step-by-step explanation:
Sum of interior angles of a polygon is represented by the expression,
Sum of interior angles = n(n - 1)×180°
Here n is the number of sides of a polygon
If n = 18,
Sum of 18 sided polygon = (18 - 1) × 180°
= 7 × 180°
= 3060°
Therefore, sum of interior angles of a 18 sided polygon will be 3060°.
Option (D) will be the answer.
Answer:
2880
Step-by-step explanation:
SUM=_-2=
18-2=16
16*180 = 2880 OR
18*160 = 2880 degrees
pllllllease help me asap
Answer & Step-by-step explanation:
When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, let's use this equation to solve for the rate of change of each question.
Problem 1:
[tex]Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}[/tex]
The rate of change of this equation is 2/3
Problem 2:
[tex]Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2[/tex]
The rate of change for this equation is 2
Problem 3:
[tex]Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6[/tex]
The rate of change for this equation is 6
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Step-by-step explanation:
68$53++83(-$(7(3($++$
please help meeeeeee!
Answer:
2x^2+x-1/x^2-1
x^2+11x+18/x^2-11x+18
2x^2-5x+3/x^2+4x+3
Step-by-step explanation:
1.2 and 5
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Help ASAP please .
Which expression represents the volume of the sphere,
in cubic units?
3/4pi(6)^2
4/3pi(6)^3
3/4pi(12)^2
4/3pi(12)^3
Answer:
second option
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )
Here r = 6 , thus
V = [tex]\frac{4}{3}[/tex]π(6)³
Answer:
Second option
Step-by-step explanation:
Volume of a sphere = [tex]\frac{4}{3}*\pi *r^{3}[/tex]
→ Substitute in the value of radius
Volume of a sphere = [tex]\frac{4}{3}*\pi *6^{3}[/tex]
A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.
Answer:
0.5
Step-by-step explanation:
Let D be the event of selecting a marble with dots.
Let P be the event of selecting a purple marble.
The probability of selecting a marble with dots, P(D)=0.2
The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]
We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)
By the definition of conditional probability:
[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]
The probability of selecting a purple marble given that the marble has dots on it is 0.5.
Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?
Answer:
[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]
Step-by-step explanation:
In the attached diagram
CA=CO+OA
CO=DB
Therefore:
5=2+OA
OA=3 Units
The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:
OB=12 units
OA=3 units
Using Pythagoras theorem
[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]
The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
There are 100 sophomores at a school. 85% of them are good students. What would the percent of good students be at school if (round the answer up to the nearest ones) ten “F” students would come to this school?
Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer
Step-by-step explanation:
Answer:
77% (rounded)
Step-by-step explanation:
1. Find 85% of 100
100 x 0.85 = 85
SO 85 students out of 100 students are good students.
2. Add the 10 more students to the total number.
100 + 10 = 110 total students
3. Find the percent of good students in the total number of current students.
85/110 = 0.77 * 100 (to convert to percent) = 77%
Solve the equation 2q – 4 = 26 for q.
Answer:
q = 15
Step-by-step explanation:
2q – 4 = 26 (add 4 to both sides)
2q = 26 + 4
2q = 30 (divide both sides by 2)
q = 30/2
q = 15
A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?
Answer:
the slope of the perpendicular bisector is -2/3
Step-by-step explanation:
The slope of the line joining the two points P1(0,3), P2(6,12) is given by
m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5
The slope m2 of a line perpendicular to the previous line is given by
m1*m2 = -1
solving
m2 = -1/m1 = -1/ (3/2) = -2/3
THerefore the slope of the perpendicular bisector is -2/3
Calculate the slope of the line going through A(-4,3) and B(0,6) PLEASE ANSWER
Answer:
6-3/0-(-4)
=3/4
Step-by-step explanation:
Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3
Pls answer this question....
Answer:
2310cm³
Step-by-step explanation:
volume= πr²h
22/7× radius of circle × height
circumference= πd
44cm=22/7×d, diameter= 7 cm, radius= 3.5cm
v= 22/7× 3.5× 21 = 2310cm³
A box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted. A pair of contact lenses is drawn at random from the box.Find the probability that it is not tinted.What is the answer:2/3 2/5
Answer:
[tex]\dfrac{2}{3}.[/tex]
Step-by-step explanation:
It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.
1 dozen = 12 units
Total pairs of contact lenses [tex]=2\times 12 = 24[/tex]
Tinted pairs of contact lenses = 8
Pairs of contact lenses not tinted = 24 - 8 = 16
If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.
[tex]P(\text{Not tinted})=\dfrac{\text{Pairs of contact lenses not tinted}}{\text{Total pairs of contact lenses}}[/tex]
[tex]P(\text{Not tinted})=\dfrac{16}{24}[/tex]
[tex]P(\text{Not tinted})=\dfrac{2}{3}[/tex]
Therefore, the required probability is [tex]\dfrac{2}{3}.[/tex]
‼️10 points‼️
9. Match the graph with its equation.
A. x= 4
B. y= 4
C. x= -4
D. y= -4
━━━━━━━☆☆━━━━━━━
▹ Answer
C. x = -4
▹ Step-by-Step Explanation
The line passes through the point -4, and a vertical line represents x. Therefore, the answer is x = -4.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
x= -4
Step-by-step explanation:
The graph shows that the line crosses -4 and stays paralell with y-axis so the equation is x=-4
Find the value of x in each case:
Answer:
45
Step-by-step explanation:
From the figure given, TV and RS are parallel.
Therefore, angle VTS and angle RST equal (Alternate angles)
Thus, angle VTS = angle RST = x
Angle T + angle S + angle R = 180° (sum of angles in a triangle)
2x + x + x = 180
4x = 180
Divide both sides by 4 to solve for x
x = 180/4
x = 45
The value of x in each case is 45
If we input 45 as a value of x in the angles in the triangle, the sum of what we have will give us 180°.
Answer:45
Step-by-step explanation:
Problem P(x)=x4−3x2+kx−2P(x)=x^4-3x^2+kx-2P(x)=x4−3x2+kx−2P, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 3, x, squared, plus, k, x, minus, 2 where kkkk is an unknown integer. P(x)P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x−2)(x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis has a remainder of 10101010. What is the value of kkkk? K=k=k=
Answer: k = 4
Step-by-step explanation:
For this division, to determine the value of k, use the Remainder Theorem, which states that:
polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)
Knowing the degree of quotient is
degree of Q = degree of p(x) - degree of (x-a)
For this case, Q(x) is a third degree polynomial.
Using the theorem:
[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]
[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]
a = 1
b - 2a = 0 ⇒ b = 2
c - 2b = -3 ⇒ c = 1
-2d + 10 = -2 ⇒ d = 6
d - 2c = k ⇒ k = 4
Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
Solve for x. − 6 ≥ 10 − 8x.
Answer:
2</x or x>/2
Step-by-step explanation:
-6>/10-8x
-10 -10
-16>/-8x
divide both sides by -8
2</x or x>/2
the reason the sign is bc u r dividing by a - number.
Answer:
x ≥ 2
Step-by-step explanation:
-6 ≥ 10 - 8x
Subtract 10 on both parts.
-6 - 10 ≥ 10 - 8x - 10
-16 ≥ -8x
Divide both parts by -8 remembering to reverse sign.
-16/-8 ≤ (-8x)/-8
2 ≤ x
Switch parts.
x ≥ 2
A cyclist travels at an average speed of 12 mph for 4 hours. How far did she travel in miles?
Answer:
48 miles.
Step-by-step explanation:
Her average speed was 12 miles per hour. She traveled for 4 hours. We can set up a proportion that shows that she traveled 12 miles over 1 hour, so she traveled x miles over 4 hours.
[tex]\frac{12}{1} =\frac{x}{4}[/tex]
1 * x = 12 * 4
x = 48
So, the cyclist traveled 48 miles.
Hope this helps!
Answer: 48 miles
Explanation: Well obviously if you've been on the road for 4 hours and you're traveling at 12 miles per hour, you end up going 48 miles.
Mathematically speaking we get that
by multiplying 12 × 4 to equal 48.
This 12 represents our rate.
This 4 represents the number of hours or our time.
The 48 represents the 48 miles or our distance we've travelled.
So our rate × time = distance.
This formula is a very popular one in algebra.
5 3/4 divided by 1 1/2
Answer:
[tex] \frac{23}{6} [/tex]Solution,
[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{23}{4} \div \frac{3}{2} [/tex]
To divide by a fraction, multiply by the reciprocal of that fraction
[tex] \frac{23}{4} \times \frac{2}{3} [/tex]
Reduce the numbers with the GCF 2
[tex] \frac{23}{2} \times \frac{1}{3} [/tex]
Multiply the fraction
[tex] \frac{23}{6} [/tex]
Hope this helps...
Good luck on your assignment...
A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h
Answer:
d) 405 = 15 times 4.5 times h
The height of the prism 'h' = 6 inches
Step-by-step explanation:
Explanation:-
Given Volume of prism
V = 405 cubic inches
Given length of the prism
L = 15 inches
Given width of the prism
W = 4.5 inches
The volume of the prism
V = l w h
405 = 15 ×4.5× h
405 = 67.5 h
Dividing '67.5' on both sides , we get
h = 6 inches
Final answer:-
The height of the prism 'h' = 6 inches
Answer: V = l w h. 405 = 15 times 4.5 times h
Step-by-step explanation:
Given the following :
Volume of prism = 405 in^3
Length = 15 inches
Height = h
Width = 4.5 inches
Recall :
The volume of a prism is the product of the Base and the height.
That is;
Volume = Base × height
However, Base of prism is given by the area of the base shape of the prism.
From our parameters Base shape of the prism is a rectangle.
Therefore, Area of rectangle = Length × width
= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism
Therefore, Volume of prism equals ;
Volume = 15 × 4.5 × h
Volume = 405in^3
Volume = Base × height
405 = 15 × 4.5 × h
The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10
Step-by-step explanation:
This is an arithmetic sequence. The common difference is -6, and the first term is 52.
a = 52 − 6(n − 1)
When n = 8:
a = 52 − 6(8 − 1)
a = 52 − 42
a = 10
I need help please answer quick
Answer:
c/3, the sequence is NOT geometric because 2/3 was added to each term to get the next term.
Step-by-step explanation:
geometric sequences are multiplying, arithmetic sequences are addition.
1/3
1/3+2/3= 1 (or 3/3)
3/3+2/3= 5/3
5/3+2/3= 7/3
this is arithmetic, not geometric
Simplify by combining like terms: 5x + 3x + 10x
Answer:
answer is 8x+10x
18x
is the answer
help if you can but this is kinda urgent any help is welcome tho
Answer:
(Change in y)/(change in x) is defined as the average rate of change.
For a linear equation:
y = a*x + b
A is the average rate of change, and is called the "slope" of the linear equation, and this is a constant.
Then the sentence will be:
"The average change between two ordered pairs (x,y) is the ratio (change in x)/(change in y)
In a linear function, this is called the slope, and it is constant"