Answer:
Range = 13
Mean = 8.3
Variance = 17.61
Step-by-step explanation:
Given the population dataset :
2, 9, 15, 4, 12, 9, 13, 6, 3, 10
1.) Range : (maximum - minimum)
Maximum = 15 ; minimum = 2
Range = (15 - 2) = 13
2.) population mean (μ) :
μ = ΣX / n
n = sample size
μ = (2 + 9 + 15 + 4 + 12 + 9 + 13 + 6 + 3 + 10) / 10
μ = 83 / 10
μ = 8.3
3.) Population variance (s²)
Σ(x - μ)² / n
=[(2 - 8.3)^2 + (9 - 8.3)^2 + (15 - 8.3)^2 + (4 - 8.3)^2 + (12 - 8.3)^2 + (9 - 8.3)^2 + (13 - 8.3)^2 + (6 - 8.3)^2 + (3 - 8.3)^2 + (10 - 8.3)^2] / 10
s² = 176.1 / 10
s² = 17.61
The soccer field at Mario’s school has an area of 6000 square meters how can Mario show the area has a whole number multiplied by a power of 10
Answer:
[tex]Area = 6 * 10^3\ m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 6000m^2[/tex]
Required
Write as a number by power of 10
[tex]Area = 6000m^2[/tex]
Split 6000 as 6 * 1000
[tex]Area = 6 * 1000m^2[/tex]
Express 1000 as 10^3 --- Law of indices
[tex]Area = 6 * 10^3\ m^2[/tex]
Find the x-coordinates of all local maxima using the second derivative test. f(x)=x3+4x2+10 If there are multiple values, give them separated by commas. If there are no local maxima, enter ∅.
Answer:
f(x) = x³ +4x²+10
f'(x) = 3x²+8x
the critical point is that x value that has zero to be the first derivative function
3x²+8x = 0
when we factorize
x(3x+8) = 0
x = 0
3x+8 = 0
3x = -8
x = -8/3
at critical point when f"(x)>0, that is our minima
when f"<0 that is the maxima
f'(x) = 3x²+8x
f''(x) = 6x + 8
f"(0) = 8>0
the point x = 0 is minima point
f"(x) = -8/3 = -8<0 is Maxima
x coordinate of maxima = -8/3
United Airlines' flights from Boston to Dallas are on time 80 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 3 flights are on time is
Answer: 14.5
Step-by-step explanation:
Given data:
Success rate = 80% = 0.8
No of flights = 7
No of failures = 1 – 0.8 = 0.2
Solution
at least 3 flights are on time is
= 7C3 * (0.80)^3 * (0.80)^1 + 7C7 * (0.80)^7 * (0.80)^1
= 35 * 0.512 * 0.8 + 1 * 0.21 * 0.8
= 14.336 + 0.168
= 14.5
Solve equation.
X^2-4x-12 = 0
Answer:
Step-by-step explanation:
x2 - 4x - 12 = 0
x2 - 6x + 2x - 12= 0
x(x - 6) + 2(x - 6) = 0
x + 2 = 0
x = - 2
x - 6 = 0
x = 6
Use the graph of f(x) provided to answer the question. What is f(f(-4)?
Answer:
f(f(-4) = -2
Step-by-step explanation:
f(f(-4))
First find the value of f(-4)
f(-4) = 2
Now find f(2)
f(2) = -2
How many units is -9 from zero on the number line?
Select one:
A. 9
B. - 9
C. 0
D. 18
Answer:
A
it is asking for its absolute value
Step-by-step explanation:
When three numbers are added two at a time, the sums are 29, 46, 53. What is the sum of all three numbers?
Answer:
[tex]Sum = 64[/tex]
Step-by-step explanation:
Let the three numbers be a, b and c; such that:
[tex]a + b = 29[/tex] ---- (1)
[tex]b + c = 46[/tex] --- (2)
[tex]a + c = 53[/tex] --- (3)
Subtract equation 2 from 3
[tex]a - b + c - c = 53 - 46[/tex]
[tex]a - b = 7[/tex] --- (4)
Add this equation to the (1)
[tex]a + a + b - b = 29 + 7[/tex]
[tex]2a= 36[/tex]
Solve for a
[tex]a = 36/2[/tex]
[tex]a = 18[/tex]
Substitute 18 for a in (1)
[tex]a + b = 29[/tex]
[tex]18 + b = 29[/tex]
Solve for b
[tex]b = 29 - 18[/tex]
[tex]b = 11[/tex]
Substitute 11 for b in (2)
[tex]b + c = 46[/tex]
[tex]11 + c = 46[/tex]
Solve for c
[tex]c = 46 - 11[/tex]
[tex]c = 35[/tex]
[tex]Sum = a + b +c[/tex]
[tex]Sum = 18 + 11 + 35[/tex]
[tex]Sum = 64[/tex]
Use the approach in Gauss's problem to find the sums of the arithmetic sequences below
(do not use formulas).
>
c. 3+ 6 + 9 + ... + 300
Answer:
15150 is the required sum.
Step-by-step explanation:
Gauss method of summing sequences like this is to add the first term to the last term, the second term to the second to the last term and so on until you get to the middle. By doing this, you will always get the same sum. Then you divide the number of terms by two, because you are technically adding the first half of the sequence to the second half. You then multiply the sum of each pair that gave the same number with the number of terms that has been divided by 2. For this problem we have:
3 + 300 = 303
6 + 297 = 303
9 + 294 = 303
and so on.
100÷ 2 = 50.
Therefore we have 50 * 303 = 15150 is the required sum.
Solve −3−4x≤21.
A
x≤−6
B
x≥6
C
x≥−6
D
x≤4
Answer: A
Step-by-step explanation:subtract then multipy the see which one is least to greaest
Please help!!
What is the range of y = sin 1x?
O f-1, 1]
[O, TI]
ol-
(_00,00)
Answer:
C
Step-by-step explanation:
C is what I get when I put it into desmos. someone else may be able to explain why
Barkery’s Bakery sold 20 dog cakes during Week 1 of operation, 27 dog cakes during Week 2, and 34 dog cakes
during Week 3.
a. If this pattern continues, represent the first five
terms of the sequence using a table of values.
Answer:
Week 1 - 20
Week 2 - 27
Week 3- 34
Week 4 - 41
Week 5 - 48
Etc, etc,...
Step-by-step explanation:
The values increase by 7 each week.
What’s the slope and y-intercept of y=-1/3x-3
Answer:
Step-by-step explanation:
y = mx + b
m = slope
b = y-intecept
Your equation is:
y= -1/3x - 3
So the slope is:
- 1/3
The y-intercept is:
-3
look at picture
look at picture
Answer:
point ??????? I think not sure
what is the slope of the line that passes through (37, -9) and (36, 81)
Answer:
m= -90 is your answer
Step-by-step explanation:
For future reference, you should try using Symbolab, it works really well and I use it ALL the time!
Find the difference.
2215 - 1489 =
Answer:
726
Step-by-step explanation:
Answer:
it is 726
Step-by-step explanation:
you subtract 2215 and 1489 and that gives you 726. :)
10. What is the greatest common factor of 500; 1,000 ;
and 12,500 ?
A. 5
B. 100
C.
125
D. 250
E. 500
Answer:
E. 500
Step-by-step explanation:
All 3 are divisible by 500
A recipe asks that the following three ingredients be mixed together as follows: add 1/2 of a cup of flour for every 1/2 of a teaspoon of baking soda, and every 1/4 of a teaspoon of salt.
Which of the following rates are unit rates equivalent to the ratios shown above? Select all that apply.
Answer:
Option 2: 1 teaspoon of baking soda per 1 cup of flour
Option 3: ½ teaspoon of salt per 1 teaspoon of baking soda
Step-by-step explanation:
The recipe has 3 ingredients mixed in the following ratio =>
½ of a cup of flour : ½ of a teaspoon of baking soda : ¼ of teaspoon of salt
Let's analyse each given options to see which rate is correct or not using the above ratio that makes a recipe:
Option 1 => 2 teaspoon of salt : 1 teaspoon of baking soda.
¼ salt : ½ baking soda
2 salt : x baking soda
Thus, ¼ / ½ = ²/x
Cross multiply
¼*x = ½*2
x/4 = 1
x = 4
Therefore, 2 teaspoon of salt will need 4 teaspoon of baking soda not 1.
Option 2 => 1 teaspoon of baking soda : 1 cup of floor.
½ baking soda : ½ flour
1 baking soda : x flour
Thus, ½ / ½ = ¹/x
Cross multiply
½*x = ½*1
x/2 = ½
Multiply both sides by 2
x = ½*2
x = 1
Therefore, 1 teaspoon of baking soda will need 1 cup of floor. This is correct.
Option 3 => ½ teaspoon of salt : 1 teaspoon of baking soda.
¼ salt : ½ baking soda
½ salt : x baking soda
Thus, ¼ / ½ = ½/x
Cross multiply
¼*x = ½*½
x/4 = ¼
Multiply both sides by 4
x = ¼*4
x = 1
Therefore, ½ teaspoon of salt will need 1 teaspoon of baking soda. This is correct.
Option 4 => 1 teaspoon of baking soda : 2 teaspoon of salt.
½ baking soda : ¼ salt
1 baking soda : x salt
Thus, ½ / ¼ = 1/x
Cross multiply
½*x = ¼*1
x/2 = ¼
Multiply both sides by2
x = ¼*2
x = ½
Therefore, 1 teaspoon of baking soda will need ½ teaspoon of salt not 2.
Option 5 => 2 teaspoon of salt : 1 cup of flour
¼ salt : ½ flour
2 salt : x flour
Thus, ¼ / ½ = ²/x
Cross multiply
¼*x = ½*2
x/4 = 1
x = 4
Therefore, 2 teaspoon of salt will need 4 cup of flour not 1.
The correct options are option 2 and option 3.
A banquet hall is divided into two sections that both have tables with chairs arranged around them. In the smaller section, there are 9 tables with 6 chairs each. In the larger section, there are currently 4 tables with 8 chairs each. More tables, each with 8 chairs, will be added to this larger section so that there will be 126 total chairs in the banquet hall. Which equation could be used to determine how many more tables, t, each with 8 chairs, are needed in the larger section?
Answer:
The equation that could be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section is
8t + 86 = 126 OR 8t = 40
Step-by-step explanation:
From the question,
In the smaller section of the banquet hall, there are 9 tables with 6 chairs each.
This means there are 9 × 6 chairs there
9 × 6 = 54
Hence, there are 54 chairs in the smaller section of the banquet hall.
Also, from the question,
In the larger section of the banquet hall, there are currently 4 tables with 8 chairs each.
This means there are 4 × 8 chairs there presently
4 × 8 = 32
Hence, there are currently 32 chairs in the larger section of banquet hall.
From the question,
More tables, each with 8 chairs, will be added to this larger section so that there will be 126 total chairs in the banquet hall.
If t more tables are to be added,
This means that t × 8 (8t) chairs will be added to the larger section so that there will be 126 total chairs in the banquet hall.
The total chair in the banquet hall will be = Total number of chairs in the smaller section + Current number of chairs in the larger section + Number of chairs to be added to the larger section
Therefore,
126 = 54 + 32 + 8t
126 = 86 + 8t
Then,
8t + 86 = 126
8t = 126 - 86
8t = 40
This equation can be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section.
Hence, the equation that could be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section is
8t + 86 = 126 OR 8t = 40.
If desired,
8t = 40
t = 40/8
t = 5
Hence, 5 more tables are needed in the larger section.
x^2-10x+27 in the form (x-a)^2+B
Answer:
(x-5)^2+2
Step-by-step explanation:
To convert between standard and vertex form, you have to complete the square (which, as a reminder, (a+b)^2 = a^2+2ab+b^2).
Since a^2 is x^2, and 2ab is -10x, then b must be -5, so b^2 is 25. Therefore, we add and subtract 25 from the expression:
(x-10x+25)+27-25
Then, we can make (x-10x+25) to (x-5)^2:
(x-5)^2+2
A ball is thrown with an initial velocity of 32 ft/s from a height of 4.5 feet. It’s height as a function of time is given by the equation h(t)=-16t2+32t+4.5. How long will the ball be in the air, and how high does the ball go?
Answer:
the ball will be in the air for possibly 2.5 seconds and it max hieght was 10 ft
Step-by-step explanation:
no clue
Whats 28,456 +92 / 2 * 8 + 3?
Answer:
37485947
Step-by-step explanation:
Answer:
I think that the answer is 28827
.............................
Someone bought a car for $5,000. During the first year, its value depreciated by 20%. What was the value of the car after one year?
Answer:
The value of the car after one year is $1000
Step-by-step explanation:
$5000 * 0.2 = 1000.
You can say the 20% = 0.2.
So it is depreciated by 0.2.
You multiply the number (5000) by 0.2
5000 * 0.2 = 1000.
Answer:
The answer is 1,000
Step-by-step explanation:
because 20% of 5000 is the answer which is 1,000
Suppose that the scores on a reading ability test are normally distributed with a mean of and a standard deviation of . What proportion of individuals score more than points on this test? Round your answer to at least four decimal places.
Answer:
The proportion of individuals score at most 74 points on this test is 70%.
Step-by-step explanation:
The complete question is:
Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 8. What proportion of individuals score at most 74 points on this test? Round your answer to at least four decimal places.
Solution:
Let X represent the scores on a reading ability test.
It is provided that [tex]X\sim N(70,8^{2})[/tex].
Compute the probability that an individuals score is at most 74 points on this test as follows:
[tex]P(X\leq 74)=P(\frac{X-\mu}{\sigma}\leq \frac{74-70}{8})[/tex]
[tex]=P(Z<0.50)\\=0.69146\\\approx 0.70[/tex]
Thus, the proportion of individuals score at most 74 points on this test is 70%.
Solve the compound inequality, then correctly fill in the blanks below.
-3 2-5 <2
I
Answer:
hold my picolr
Step-by-step explanation:
How many gallons of paint should be purchased to paint 10 motel rooms as shown in the illustration?
(Do not paint the floor.) It takes 1 gal to paint 240 square feet (ft 2).
10 ft
8 ft
20 ft
Andrew owns a food truck that sells tacos and burritos. He only has enough ingredients to make 113 tacos or burritos.Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.
Answer:
heres the actual answer.
Step-by-step explanation:
1 point) The joint probability mass function of XX and YY is given by p(1,1)=0.1p(2,1)=0.1p(3,1)=0.05p(1,2)=0.05p(2,2)=0.3p(3,2)=0.1p(1,3)=0.1p(2,3)=0.05p(3,3)=0.15 p(1,1)=0.1p(1,2)=0.05p(1,3)=0.1p(2,1)=0.1p(2,2)=0.3p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.15 (a) Compute the conditional mass function of YY given X=3X=3: P(Y=1|X=3)=P(Y=1|X=3)= P(Y=2|X=3)=P(Y=2|X=3)= P(Y=3|X=3)=P(Y=3|X=3)= (b) Are XX and YY independent? (enter YES or NO) (c) Compute the following probabilities: P(X+Y>2)=P(X+Y>2)= P(XY=3)=P(XY=3)= P(XY>1)=P(XY>1)=
Answer:
Step-by-step explanation:
The given information shows that X and Y are two variables with joint probability distribution as follows:
X/Y 1 2 3 Total
1 0.1 0.05 0.1 0.25
2 0.1 0.3 0.05 0.45
3 0.05 0.1 0.15 0.3
Total 0.25 0.45 0.3 1.00
Thus, the required probability is:
[tex]P(Y = 1|X=3) = \dfrac{P(Y=1,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 1|X=3) = \dfrac{0.05}{0.1}[/tex]
[tex]P(Y = 1|X=3) =0.5[/tex]
The calculated probability value of Y =1, given that X = 3 is 0.5
[tex]P(Y = 2|X=3) = \dfrac{P(Y=2,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 2|X=3) = \dfrac{0.1}{0.1}[/tex]
[tex]P(Y = 2|X=3) = 1.00[/tex]
The calculated probability value of Y =2, given that X = 3 is 1.00
[tex]P(Y = 3|X=3) = \dfrac{P(Y=3,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 3|X=3) = \dfrac{0.15}{0.1}[/tex]
[tex]P(Y = 3|X=3) =1.5[/tex]
The calculated probability value of Y =3, given that X = 3 is 1.50
B.
From the joint probability distribution table, we can see that the probability value of the intersection X = 3 and Y = 3 is 1.50
i.e
P(X =3, Y =3) = 1.5
However;
the marginal probability of X = 0.3
the marginal probability of Y = 0.3
P(X =3)(Y=3) = 0.3 × 0.3 = 0.09
∴
≠ P(X =3)(Y=3)
Thus;
NO, the random variables X and Y are not independent.
C.
P(X+Y > 2) = P(X =2, Y = 1) + P( Y =2, X=1) + P(Y = 3, X= 1) + P( Y =2, X=2) +
P(Y =3, X=2) + P(Y =1, X =3) + P( Y =2, X =2) +P(Y =3, X =3)
P(X+Y > 2) = 0.1 + 0.05 + 0.1 + 0.3 + 0.05 + 0.05 + 0.1 + 0.15
P(X+Y > 2) = 0.9
P(XY =3) = P(X =2, Y =1 ) + P( Y =1 , X = 2)
P(XY =3) = 0.10 + 0.05
P(XY =3) = 0.15
P(XY > 1) = 0.1 + 0.05 + 0.1 + 0.1 + 0.3 + 0.05 + 0.05 + 0.1 + 0.15
P(XY > 1) = 1.00
Convert 9% to a decimal.
Answer:
0.09
Step-by-step explanation:
:)
Answer: .09
9% converted to a decimal is .09
Plz mark brainliest:)
Is this a function or not a function? (Picture)
Answer:
a function
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The function has more than one point on one line of Y.
Toby works at an amusement park. He loads 10 new passengers onto the roller coaster every
3/4
of a minute. At what rate does Toby load passengers?
Pleaseeee
Answer:
13 1/3
Step-by-step explanation:
im sure this is right btw
