What's the difference between 5.4 x 10-7 and 7.1 x 10-8? Express your answer
using either standard notation or scientific notation.
Answer:
.76 x 10 or 7.6 x 10^0
Step-by-step explanation:
divide coefficients and subtract exponents
5.4 / 7.1 = .76
10^-7 / 10^-8 = 10
Find 3.5% of 950 g.
Answer:
33.25 g
Step-by-step explanation:
Answer:
33.25 g
plz refer to the picture
PLZ HELP!!
What quadrant is (0, 4)
A.1
B.2
C.3
D.4
E.x-axis
F.y-axis
Answer:
F.y-axis
Step-by-step explanation:
y axis is the answer because 0 is starting.
The given point
(0,4)
is on the positive segment of the y-axis.
The mean amount purchased by a typical customer at Churchill's Grocery Store is $27.50 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 68 customers, answer the following questions
a. What is the likelihood the sample mean is at least $30.00?
b. What is the likelihood the sample mean is greater than $26.50 but less than $30.00?
c. Within what limits will 90 percent of the sample means occur?
Answer:
a) 0.0016 = 0.16% probability that the sample mean is at least $30.00.
b) 0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00
c) 90% of sample means will occur between $26.1 and $28.9.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 27.50, \sigma = 7, n = 68, s = \frac{7}{\sqrt{68}} = 0.85[/tex]
a. What is the likelihood the sample mean is at least $30.00?
This is 1 subtracted by the pvalue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem, we have that:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 27.5}{0.85}[/tex]
[tex]Z = 2.94[/tex]
[tex]Z = 2.94[/tex] has a pvalue of 0.9984
1 - 0.9984 = 0.0016
0.0016 = 0.16% probability that the sample mean is at least $30.00.
b. What is the likelihood the sample mean is greater than $26.50 but less than $30.00?
This is the pvalue of Z when X = 30 subtracted by the pvalue of Z when X = 26.50. So
From a, when X = 30, Z has a pvalue of 0.9984
When X = 26.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{26.5 - 27.5}{0.85}[/tex]
[tex]Z = -1.18[/tex]
[tex]Z = -1.18[/tex] has a pvalue of 0.1190
0.9984 - 0.1190 = 0.8794
0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00.
c. Within what limits will 90 percent of the sample means occur?
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile, that is, Z between -1.645 and Z = 1.645
Lower bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = -1.645*0.85[/tex]
[tex]X = 26.1[/tex]
Upper Bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = 1.645*0.85[/tex]
[tex]X = 28.9[/tex]
90% of sample means will occur between $26.1 and $28.9.
You buy cheese in 1 pound bags. The recipe for burritos requires 1.7 ounces of cheese per serving. How many servings can you make?
Jenna wants to rent a mountain bike by the week. Identify the independent variables that affect the total rental cost.
Answer:
2845
Step-by-step explanation:
Please help me! (12 points)
Answer:
4
Step-by-step explanation:
25÷2= 12.50
So it would be 4 because you are trying to find the price (p) for the boots (b)
Answer:
c is correct answer is yes then please
The amusement park has two plans available for the school to choose from. Plan A is listed in the table below.
Cost (per vehicle) = $10
Cost (per person) = $30
The cost of Plan B can be calculated using the formula c = $15v + $28p, where c represents the cost, v represents the number of vehicles, and p represents the number of people. The school has a budget of $7200 for the cost of tickets and parking. If 241 students are going on the field trip, which plan should the school purchase? Explain your reasoning.
Answer:
the second plan should be purchased.
Step-by-step explanation:
school budget is $7200
plan 1: 241 students are $30 each is
241 × 30 = $7230 which is over budget with no money for parking for the vehicles.
plan 2: 241 students are $28 each is
241 × 28 = $6748
with a budget of $7200 for the trip the amount left for parking is
$7200 - $6748 = $452
plan 2: Parking is $15 per vehicle
Therefore the remaining $452 can be used to pay for 452 ÷ 15 = 30.13 vehicles
The school should purchase Plan 2 for the field trip.
The budget of $7200 can pay for 241 tickets for students and parking for 30 vehicles
The school should purchase the second plan.
School's budget = $7200
The cost for the first plan will be:
= 241 × $30
= $7230
This is more than the school budget of $7200
For the second plan, the cost will be:
= 241 × $28
= $6748.
This is below the school budget and therefore affordable.
The school should choose the second plan as there'll be more money available for parking.
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4(-3)(-2)
How do
I do this?
Answer:
4(-3)(-2) = 24
Step-by-step explanation:
first solve the numbers in parenthesis.
4(-3)(-2)
= 4(6)
the negative sign cancels out in the product, because both of the numbers you multiplied are negative, which makes the product positive.
now solve for 4(6).
4(6) = 24
EFGH is an isosceles trapezoid. If EG=3y+19 and FH=11y-21, find the value of y.
Answer:
y = 5
Step-by-step explanation:
The diagonals of the isosceles EFGH are equal. Therefore:
EG = FH
EG = 3y + 19
FH = 11y - 21
Thus:
3y + 19 = 11y - 21
Collect like terms
3y - 11y = -19 - 21
-8y = -40
Divide both sides by -8
y = 5
A bouncy ball is dropped such that the height of its first bounce is 6 feet and each successive bounce is 72% of the previous bounce's height. What would be the height of the 6th bounce of the ball? Round to the nearest tenth (if necessary).
Answer:1.2
Step-by-step explanation:
The height of the 6th bounce of the ball will be 1.2 feet.
What is geometric sequence?
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
[tex]T_{n} =ar^{n-1}[/tex]
Where,
[tex]T_{n}[/tex] is the nth term.
r is the common ratio
a is the first term
According to the given question.
During the first bounce, height of the ball from the ground, a = 6 feet
And, the each successive bounce is 72% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
= 72% of 6
= [tex]\frac{72}{100} (6)[/tex]
= 0.72 × 6
= 4.32 feet
During the third bounce, the height of ball from the ground
= 72% of 4.32
= [tex]\frac{72}{100} (4.32)[/tex]
= 3.11 feet
Like this we will obtain a geometric sequence 6, 4.32, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.72
Therefore,
The sixth term of the geometric sequence is given by
[tex]T_{6} = 6(0.72)^{6-1}[/tex]
[tex]T_{6} =6(0.72)^{5}[/tex]
[tex]T_{6} = 6 (0.193)[/tex]
[tex]T_{6} = 1.16 feet[/tex]
[tex]T_{6} = 1.2[/tex] feet
Hence, the height of the 6th bounce of the ball will be 1.2 feet.
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i really need help on this problem! reply asap!!!
Find the zeros for 2x2−24=26. What is the positive value of x?
Answer:
i think it is 12
Step-by-step explanation:
Need as soon as possible
Answer: 136 square feet
=======================================================
Explanation:
The front face is a triangle with base 6 and height 4.
The area is 0.5*base*height = 0.5*6*4 = 12 square feet
The back face is also 12 square feet since the front and back faces are identical triangles.
So far we have 12+12 = 24 square feet of surface area.
--------------------
The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.
To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.
This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.
So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.
in abc, ac=bc cd is perpendicular with ab, d belongs to ab ab=4and cd=sqar root 3 find ac
Answer:
The answer is root 7
Step-by-step explanation:
You can find out that ΔABC is isosceles, and CD bisects AB, so AD = 2 - and now you have 2 sides given in ΔADC
Use the Pythagoras Theorum to find the hypotenuse AC
The answer is the square root of 7
-4/7p + (-2/7p) +1/7
Answer:
-6/7p+1/7
Step-by-step explanation:
xy^2-x^2y
x= -1
y= -2
Answer:
xy(x-1y)
Step-by-step explanation:
xy^2-x^2y
=solution,
taking common
xy(x-1y)
Please help me I will give you 10 points
Answer
Multiply 8 and 4
Step-by-step explanation:
start from left to right so you wanna start by dividing and multiplying first in evaluating
Bananas sell for $0.44 pounds. How much will 6 pounds of bananas cost.
Answer:
$2.64
Step-by-step explanation:
0.44 times 6.
Answer:
2.64
Step-by-step explanation:
6*0.44=2.64
i hope it will help you
que porcentaje de 108 es 81?
The theoretical probability of an event occurring is 3/4. Fill in the blank with a
number to complete each statement so that it best describes the expected
chances of the event occurring in an experiment. Out of 400 trials, the desired
outcome will occur approximately
times. *
Answer:
300 times
Step-by-step explanation:
Answer:
The answer is out of every 5, the desired out come will be approximately 2 times.
Step-by-step explanation:
Suppose you saved $300 dollars from a summer job. If school starts September 1, can you afford a cell phone data plan of $29.95 per month for the next year(until next September 1)?
Answer:
No
Step-by-step explanation:
Given that:
Amount saved = $300
Monthly data cost = $29.95
Number of monthly data that can be done from saving :
= amount saved / monthly data cost
= $300 / $29.95
= 10.016694
Hence, saving can only last for 10 months of data subscription.
Hence it can't last till September 1, if the following year, which is about 12 months
Look at the arrows in the drawings below. Indicate whether the arrows are parallel, perpendicular, or neither.
Answer:
In A and D the arrows are perpendicular, in B they are parallel and in C they are neither parallel nor perpendicular.
Step-by-step explanation:
The point P is on the unit circle. Find P(x, y) from the given information. The x-coordinate of P is 12 13 , and the y-coordinate is negative.
This question is incomplete, the complete question is;
The point P is on the unit circle. Find P(x, y) from the given information. The x-coordinate of P is 12/13 , and the y-coordinate is negative.
Answer: P( x, y ) = ( -5/13, 12/13 )
Step-by-step explanation:
Given that;
p( x, y ) is on the unit circle,
Radius of the circle must be 1
so the equation x² + y² = r²
x = 12/13 and r = 1
(12/13)² + y² = 1²
y² = 1 - (12/13)²
y = √ [ 1 - (12/13)² ]
y = ±5/13
since the y-coordinate is negative y = -5/13
Therefore, P( x, y ) = ( -5/13, 12/13 )
The population of people in a town increases by 100 each year. Which equation represents the situation? Let p represent the amount the population has increased and t represent the number of years.
Question 22 options:
t = 100 + p
p = 100 + t
p = 100t
t = 100p
Answer: p = 100t
Step-by-step explanation:
Assume that it had been 6 years.
100(6) = p
p = 600
There are 600 people in the town.
what is the standard form of (6x^2-8x-7)+(8x^2-76x)
Answer: 14x^2 - 84x - 7
====================================================
Explanation:
The like terms 6x^2 and 8x^2 combine to 14x^2
The like terms -8x and -76x combine to -84x
Nothing pairs with the -7, so its stays as is.
Standard form is where we list the terms in decreasing exponent order. We can think of -84x as -84x^1 and the -7 as -7x^0. So 14x^2 - 84x - 7 would be the same as 14x^2 - 84x^1 - 7x^0. The exponents count down: 2,1,0.
The final answer is a trinomial since it has three terms. It is also a quadratic because the degree (highest exponent) is 2.
5. Following data indicates the number of vehicles arrived during past
100 days in a certain tolling station.
Vehicles
No. of days
0 - 10
3
10 - 20
14
20 - 30
53
30-40
20
40 - 50
10
Calculate average number of vehicles in a day,
Answer:
what are you supposed to do here?
Step-by-step explanation:
500 is 37% of what number
A 37
B 74
C 185
D 370
Answer:
C i guess
Step-by-step explanation:
9(x-4) -7x=32-2(x+8)
Answer:
x=13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
using distributive property:
9x-36-7x=32-2x-16
2x-36=16-2x
4x=52
x= 13
plz brainliesttt
A game of chance involves spinning a wheel with 4 number on it. The wheel is designed so that the result of each spin Xhas the following probability distribution. 2 3 Result of a spin .x Probability : 0.50
(a) Find and interpret the mean of X.
(b) Find and interpret the standard deviation of x.
(c) It costs a player $5 for a single spin. The player will receive (in dollars) three times the number that appears. So the profit for one play of this game is Yeur 5. What is the mean and standard deviation of 7
Distribution table :
X : ___ 1 _____ 2 _____ 3 ______ 4
P(x) __0.50 __0.25 __ 0.15 ____ 0.10
Answer:
1.85 ; 1.014 ;` 0.55 ; 3.042
Step-by-step explanation:
Probability distribution :
X : ___ 1 _____ 2 _____ 3 ______ 4
P(x) __0.50 __0.25 __ 0.15 ____ 0.10
The mean: E(x) = Σ(X * p(x))
(1*0.5) + (2*0.25) + (3*0.15) + (4 *0.10)
= 1.85
Standard deviation = sqrt(Var(x))
Var(x) = Σ(x²*p(x)) - E(x)²
Var(x) = ((1^2*0.5) + (2^2*0.25) + (3^2*0.15) + (4^2 *0.10)) - 1.85^2
= 4.45 - 3.4225
= 1.0275
Standard deviation = sqrt(1.0275)
Standard deviation = 1.0136567
Standard deviation(X) = 1.014
3.)
Cost of spin = $5
Amount, y to be received = 3 times the number that appears
y = 3x - cost of playing
y = 3x - 5
E(y) = E(3x - 5)
E(y) = E(3x) - 5
Recall :E(x) = 1.85
E(y) = 3(1.85) - 5
E(y) = 0.55
Standard deviation :Sd(y) =
Sd(3x - 5)
3(1.014)
= 3.042