Answer:
(a) The standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Step-by-step explanation:
We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.
(a) It is stated that 5% of American households spend less than $1000 for daily transportation.
Let X = the amount spent on daily transportation
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312
[tex]\sigma[/tex] = standard deviation
Now, 5% of American households spend less than $1000 on daily transportation means that;
P(X < $1,000) = 0.05
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;
[tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]
[tex]\sigma=\frac{-\$5312}{-1.645}[/tex] = 3229.18
So, the standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)
P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)
P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)
= 1 - 0.5359 = 0.4641
P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex]
= 1 - 0.7642 = 0.2358
Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is given by;
P(X > x) = 0.03 {where x is the required range}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;
[tex]\frac{x-\$6312}{3229.18}=1.88[/tex]
[tex]{x-\$6312}=1.88\times 3229.18[/tex]
x = $6312 + 6070.86 = $12382.86
So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Write an algebraic expression to represents the verbal expression: the difference between the product of 4 and a number and the square of the number
Answer:
[tex]4n-n^2[/tex]
Step-by-step explanation:
I use 'n' as the unknown value, but you can use any letter you want as the variable.
The product of four and a number would be represented by '4 * n'. The ideal way to write this would be '4n', even though '4 * n' is also correct in value.
The square of the number would be n². Squaring a number is multiplying a number by itself.
The phrase 'difference between...' means subtraction.
Putting it together:
"The difference between the product of 4 and a number and the square of the number" would be:
[tex]4n-n^2[/tex]
Hope this helps.
3. Use completing square method to evaluate 6x2 + 11x +3 = 0
Answer:
-b+or-
[tex] - b - + \sqrt{a {}^{2} - 4ac } \div 2a[/tex]
Nearly x=-1.416
Or x=-0.416
Answer:
x=-1/3 or x = -3/2
Step-by-step explanation:
6x²+11x+3=0
divide through by 6
x² +11x/6 + 3/6 =0
collect like terms that is those with x should be left on one side nd the one without x should be on the other side
x² +11x/6 = -1/2
add the square of the half of the co efficient of B i.e 11x/6 to both sides
(x+11/12)² = 121/144 -1/2
(x+11/12)² = 121-72/144
square root of both sides
x+11/12 =+or - √49/144
x= -11/12 ± 7/12
x= -1/3 or x= -3/2
number added to the difference between triple the number and thirteen Translate into a variable expression. (Use x for your variable. Do not simplify.)
Answer:
[tex]4x - 13[/tex]
Step-by-step explanation:
Given
Represent the number with x
Required
Translate the statements to expression
First, we need to get triple of x:
[tex]Triple\ of\ x= 3 * x[/tex]
[tex]Triple\ of\ x= 3 x[/tex]
Next is to get the difference between 3x and 13
This is represented as [tex]3x - 13[/tex]
Lastly, Add x to the above:
[tex]x + 3x - 13[/tex]
[tex]4x - 13[/tex]
Hence, the variable expression is 4x - 13
A number is chosen at random from the set {1,2,3,4,5,6,7,8,9,10} find the probability that it is a perfect square
Step-by-step explanation:
Perfect squares = 1, 4,9
Probability = 3/ 10
draw a circle whose radius is 3 and centered at (1,2)
First graph the center at (1,2). Then use your given radius to graph four points around the center. One vertical point above and one below the center, and one horizontal point to the right and one to the left of the center. Those points should be:
• (1,5)
• (1,-1)
• (-2,2)
• (4,2)
Then, to the best of your ability, draw a circle connecting those points.
I hope this makes sense. Please let me know if you have any further questions!
The equation of the circle that has a center at (1, 2) and a radius of 3 units will be (x - 1)² + (y - 2)² = 9. The circle is drawn below.
What is the equation of a circle?Let r be the radius of the circle and the location of the center of the circle be (h, k).
Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The center of the circle is (1, 2) and the radius of the circle is 3 units. Then the equation of the circle is given as,
(x - 1)² + (y - 2)² = 3²
(x - 1)² + (y - 2)² = 9
The equation of the circle that has a center at (1, 2) and a radius of 3 units will be (x - 1)² + (y - 2)² = 9. The circle is drawn below.
More about the equation of the circle link is given below.
https://brainly.com/question/10618691
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Find the number which when added to 10 times itself gives 264
Answer: 24
Step-by-step explanation:
Let x=the number
x+10x=264
11x=264
x=24
Hope this helps!! :)
Does the function model exponential growth or decay f(x)=3*(7/4)^x
Answer:
Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.
Answer:
It models exponential growth.
Step-by-step explanation:
7/4 > 1, so f(x) grows at an exponential rate as x increases.
A graph of f(x) is attached below, showing the exponential growth.
The two triangles are similar. What is the value of x?
Answer:
x=5
Step-by-step explanation:
We can write ratios to help us solve
4x 12 +3
---------- = ------------
3x+1 12
Using cross products
4x*12 = (3x+1) * (15)
48x = 45x +15
Subtract 45x from each side
3x =15
Divide by 3
3x/3 =15/3
x=5
Round 4.028 to the nearest tenth.
Answer:
4.0
Step-by-step explanation:
Look at the decimal place next to the tenths place. It has a 2 in its place. The rule for rounding is that any number 4 or lower is rounded down. Any number 5 or above is rounded up. The number is 2, which is below 4, so we round down. The tenths place would stay the same because it can't get any smaller. Therefore, 4.028 is rounded down to 4.0
Tell whether the statement true or false. If it is false, give a counter example.
Can anyone help me with these? Thank you so much if you can!
Answer:
25) true
for example if x is -3 then x^2 will be +9
26) false
for example -3×-3×3 can give you positive answer 27
27) true
because any number when multiplied with 0 will only give you 0 answer
Step-by-step explanation:
Which numbers are rational.
3
1.8989
را با
0.5
2.0
Answer:
All of those numbers are rational
Janelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Let x represent the number of students in Janelle’s group.
3x = 23 + 5
3x = 23
3x – 5 = 23
3x + 5 = 23
Answer:
3x+5=23
Step-by-step explanation:
Answer:
D. 3x+5=23
Step-by-step explanation:
What concepts do you think belong in this branch of mathematics?
What is the perimeter of the given figure? A.19 pie symbol inches B. 24+ 5 pie symbol inches C.29 pie symbol inches D.14 + 5 pie Symbol inches
Answer:
Perimeter of the shape = (14+5π )inchesStep-by-step explanation:
The shape is made up of a semicircle and a right angled triangle.
Perimeter of the shape = perimeter of a semicircle + perimeter of the right angle triangle.
Since perimeter of a circle = 2πr
Perimeter of a semicircle = 2πr/2 = πr wherr r is the radius
r = 10in/2 = 5in
Perimeter of the semicircle = 5π in
Perimeter of a triangle = s1+s2+s3 where s1, s2 and s3 are the sides of the triangle.
We only have 2 sdies of the triangle, hence we need to get the third side using pythagoras theorem.
let s1 = 10in, s2 = 6in
10² = 6²+s3²
s3 = √10²-6²
s3 = √100-36
s3 = √64
s3 = 8in
Perimeter of the triangle = 10in+6in+8in = 24in
Perimeter of the shape = (24in + 5π in) - 10in (10 in was subtracted since it is common to both shapes)
Perimeter of the shape = (14+5π )inches
How does mass affect friction?
Plz help
An object of large mass is pulled down into the surface with a greater force than an object of low mass and as a consequence , there is greater friction between the surface of heavy objects than between the surface and the light object
Let f(x) = 5x + 12. Find f−1(x)
Answer:
(x-12)/5
Step-by-step explanation:
Answer:
f⁻¹(x) = (x - 12)/5
Step-by-step explanation:
To find the inverse of f(x), you have to switch the places of the x and y. You then have to rearrange the equation so that it is equal to y.
f(x) = 5x + 12
x = 5y + 12
x - 12 = (5y + 12) - 12
x - 12 = 5y
(x - 12)/5 = 5y/5
(x - 12)/5 = y
f⁻¹(x) = (x - 12)/5
Increase #500 in the ratio 16:10
Answer:
Answer is 900.
Step-by-step explanation:
To find:
Increase #500 in the ratio 16:10
Solution:
New Number: Old Number = 16:10
We are given the old number as 500.
Let the new number after increase = [tex]x[/tex]
Now, using the above ratio:
[tex]x[/tex]: 500 = 16:10
[tex]\dfrac{x}{500} = \dfrac{16}{10}\\\Rightarrow x = 500 \times \dfrac{16}{10}\\\Rightarrow x = 50 \times 16\\\Rightarrow x = 900[/tex]
Therefore, the increased value of 500 in the ration 16:10 is 900.
what is the greatest common factor of 61 and 77
Their GCF is 1. They don’t have any others that are the same
One pound of grapes cost a 1.55.Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes
Answer:
x times 1.55
Step-by-step explanation:
3.5 times 1.55 = 5.325
Answer:
5.325
Step-by-step explanation:
answer as soon as possible, please! !algebra! 2¹⁵ x 8¹⁹ x 2⁴ x 8¹⁰ a. 2¹⁹ x 8²⁹ b. 4⁶⁰ x 64¹⁹⁰ c. 2⁶⁰ x 8¹⁹⁰ d. 4¹⁹ x 16²⁹ and the x's are multiplication not variables
Answer:
The measure of angle B would be 100°
Step-by-step explanation:
Supplementary means two angles add up to 180 degrees. Let's say A+B=180. Since we know what A is, we can substitute that in, B+80=180. Now solve. B=100
Step-by-step explanation:
10-15 kinda hard for me
10 is 90 degrees as all angles on a straight line add up to 180
11 is 42 degrees as all angles on a straight line add up to 180
12 is 138 degrees as all angles on a straight line add up to 180
13 is 42 degrees as vertically opposite angles are the same
14 is 132 degrees as i added the other two angles
15 is 138 degrees as i added the other two angles
there you go hope this helped
The average third grade student can read
80 words in 5 minutes. What is the average
reading rate per minute?
write an expression to represent the problem.
Answer:
16x
Step-by-step explanation:
80 divided by 5 is 16, so the student can read 16 words per minute. X is the number of minutes.
The average reading rate per minute is 16 words/ min.
and its expression will be [tex]16x[/tex]
where, [tex]x[/tex] represents the minutes
What is proportion ?
A proportion is an equation based on the equality of two ratios.
It is given that the average third grade student can read 80 words in 5 minutes and it is to calculate the average words read by the student per minute :
[tex]\begin{aligned}5 \text{\:min}&\rightarrow 80 \text{\:words}\\1 \text{\:min}&\rightarrow \frac{80}{5}\text{\:words} \\&\rightarrow 16 \text{\:words}\end{aligned}[/tex]
Therefore, the average reading rate per minute is 16 words/ min.
Read more about ratio at:
https://brainly.com/question/17869111
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) I went from my house to a playground, 300
metres away in 10 minutes. I ran back and
reached in 2 minutes. What was my average
speed? give answer fast!
Answer:
v = 0.834 m/s or 3 km/h
Step-by-step explanation:
Given that,
Distance between house and playground is 300 meters
If you went 300 metres away in 10 minutes and ran back and reached in 2 minutes, it means total distance covered by you during whole journey is 300 m + 300 m = 600 m
Total time, t = 10 min + 2 min = 12 min = 720 seconds
Total distance covered divided by total time gives average speed. So,
[tex]v=\dfrac{600\ m}{720\ s}\\\\v=0.834\ m/s[/tex]
or
v = 3 km/h
So, the average speed is 0.834 m/s or 3 km/h.
Please solve, 1-2x= -1+8+8x-8x
Answer: [tex]x=-3[/tex]
Simplify both sides of the equation
[tex]1+-2x=-1+8+8x+-8x[/tex]
[tex]-2x+1=(8x+-8x)+(-1+8)[/tex] (Combine Like Terms)
[tex]-2x+1=7[/tex]
Subtract 1 from both sides
[tex]-2x+1-1=7-1\\-2x=6[/tex]
Divide both sides by -2
[tex]-2x/-2=6/-2\\x=-3[/tex]
Answer:
[tex]\Huge \boxed{x=-3}[/tex]
Step-by-step explanation:
[tex]1-2x= -1+8+8x-8x[/tex]
Combining like terms.
[tex]1-2x= 7[/tex]
Subtracting 1 from both sides.
[tex]-2x= 7-1[/tex]
[tex]-2x=6[/tex]
Dividing both sides by -2.
[tex]x=-3[/tex]
Given f(x) = x2 − 4x + 5, find each value. a. f(2) b. f(−6)
Answer:
This problem requires you to plug in the values to get an answer.
f(2)=1
f(-6)= 65
Step-by-step explanation:
You need to plug in each value in the equation.
[tex]f(2) = 2^{2} - 4(2) + 5[/tex]
[tex]f(2) = 4 - 8 + 5[/tex]
[tex]f(2) = - 4 + 5[/tex]
[tex]f(2) = 1[/tex]
For f(-6):
[tex]f( - 6) = ( - 6)^{2} - 4( - 6) + 5[/tex]
[tex]f( - 6) = 36 + 24 + 5[/tex]
[tex]f( - 6) = 65[/tex]
You received $112 in all selling paintings. You sold one painting for $27
and the rest for $17 each. Solve the equation below to find x, the number
of $17 paintings you sold.
17x + 27 = 112
Answer:
5
Step-by-step explanation:
17x = 85
17x/17 = 85/17
x = 5
The number of Liters remaining in a 100 Liter tank that is draining at a rate of 4 Liters per minute for m
minutes.
Answer:
Big fella
Step-by-step explanation:
100-4 x m
Five boys A, B, C, D,E
are sitting in a park in a circle. A is facing South-West, D is facing
South-East, B and E are right opposite A and D respectively and C is equidistant between
D and B. Which direction is C facing?
Answer:
C is facing North
Step-by-step explanation:
Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.
Answer:
Jackson is charitable.
Step-by-step explanation:
a stockbroker sold 70 shares of stock $14.52 each. what was the total amount of the sale?
Answer:
$1016.4 - if this is just a simple multiplication question