Answer:
$15500
Step-by-step explanation:
10^3 x 12 = 12,000
10^2 x 35 = 3,500
12,000 + 3,500 = 15,500
20. Find the slope of the line graphed below.
The unshaded regions are quarter circles. Which choice best approximates the area of the shaded region? Use ≈3.14.
Answer:
123.6cm^2
Step-by-step explanation:
24^2=576
area of all four quarter circles combined: 144pi
576-122pi
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. 1)If a random sample of 16 cars is selected, a) what is the probability that the sample mean will be between 39 and 48 minutes? b) 95% of all sample means will fall between what two values? c) 90% of the sample means will be greater than what value? 2)What sample size is needed in order for the standard deviation of the mean to be one fifth of the population standard deviation?
Answer:
1a
[tex]P(39 < X < 48 ) = 0.8767[/tex]
1b
95% of all sample means will fall between [tex] 40.1 < \mu < 49.9 [/tex]
1c
[tex]\= x = 41. 795[/tex]
2
[tex]n = 25[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]n = 45[/tex]
The population standard deviation is [tex]\sigma = 10[/tex]
The sample size is n = 16
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{x} = \frac{ \sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{ 10 }{\sqrt{16 } }[/tex]
=> [tex]\sigma_{x} = 2.5[/tex]
Generally the probability that the sample mean will be between 39 and 48 minutes is
[tex]P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )[/tex]
=> [tex]P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )[/tex]
=> [tex]P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)[/tex]
From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is
=> [tex]P( Z< 1.2 ) = 0.88493[/tex]
and
[tex]P( Z< - 2.4 ) = 0.0081975[/tex]
So
[tex]P(39 < X < 48 ) = 0.88493 -0.0081975[/tex]
=> [tex]P(39 < X < 48 ) = 0.8767[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * 2.5 [/tex]
=> [tex]E =4.9 [/tex]
Generally the 95% of all sample means will fall between
[tex]\mu -E < and \mu +E[/tex]
=> [tex]45 -4.9\ and \ 45 + 4.9[/tex]
Generally the value which 90% of sample means is greater than is mathematically represented
[tex]P( \= X > \= x ) = 0.90[/tex]
=> [tex]P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90[/tex]
=> [tex]P( \= X > \= x ) = P( Z > z ) = 0.90[/tex]
Generally from the z-table the critical value of 0.90 is
[tex]z = -1.282[/tex]
[tex]\frac{\= x -45 }{ 2.5} = -1.282[/tex]
=> [tex]\= x = 41. 795[/tex]
Considering question 2
Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as
[tex]s = \frac{1}{5} \sigma[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]s = \frac{\sigma }{ \sqrt{n} }[/tex]
=> [tex]\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }[/tex]
=> [tex]n = 5^2[/tex]
=> [tex]n = 25[/tex]
Using the normal distribution and the central limit theorem, it is found that:
1)
a) 0.8767 = 87.67% probability that the sample mean will be between 39 and 48 minutes.
b) 95% of all sample means will fall between 40.1 and 49.9 minutes.
c) 90% of the sample means will be greater than 41.8 minutes.
2) A sample size of 25 is needed.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 45 minutes, hence [tex]\mu = 45[/tex].The standard deviation is of 10 minutes, hence [tex]\sigma = 10[/tex].Sample of 16 cars, hence [tex]n = 16, s = \frac{10}{\sqrt{16}} = 2.5[/tex].Item 1, question a:
The probability is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 39, hence:
X = 48:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48 - 45}{2.5}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a p-value of 0.8849.
X = 39:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{39 - 45}{2.5}[/tex]
[tex]Z = -2.4[/tex]
[tex]Z = -2.4[/tex] has a p-value of 0.0082.
0.8849 - 0.0082 = 0.8767
0.8767 = 87.67% probability that the sample mean will be between 39 and 48 minutes.
Item b:
The critical value for a 95% confidence interval is |z| = 1.96, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.96 = \frac{X - 45}{2.5}[/tex]
[tex]X - 45 = -1.96(2.5)[/tex]
[tex]X = 40.1[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 45}{2.5}[/tex]
[tex]X - 45 = 1.96(2.5)[/tex]
[tex]X = 49.9[/tex]
95% of all sample means will fall between 40.1 and 49.9 minutes.
Item c:
Greater than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.28 = \frac{X - 45}{2.5}[/tex]
[tex]X - 45 = -1.28(2.5)[/tex]
[tex]X = 41.8[/tex]
90% of the sample means will be greater than 41.8 minutes.
Item 2:
This is n for which [tex]s = \frac{10}{5} = 2[/tex], hence:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = \frac{10}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 10[/tex]
Simplifying both sides by 2:
[tex]\sqrt{n} = 5[/tex]
[tex](\sqrt{n})^2 = 5^2[/tex]
[tex]n = 25[/tex]
A sample size of 25 is needed.
A similar problem is given at https://brainly.com/question/14789302
What is the slope of the line that passes through the points (5, -4) and (7, -4)?
Write your answer in simplest form.
Answer:
hey so the answer is m=-4
hope this helps!!~~
Please help answer 2 and 3 the best you possibly can
Answer:
2. x = 3
3. x = 5
Answer:
Below.
Step-by-step explanation:
(2). 6x + 51 + 111 = 180
6x = 180 - 162 = 18
x = 3.
(3). 6x = 30
x = 5.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circle. Given and , ° and
Answer:
The answer for the question is 11 and 12 I just got a test back and it was correct
Step-by-step explanation:
Answer:
32 and 146
Step-by-step explanation:
Parallelograms pre test on edg 2020
!ANSWERS !
1.c
2.c
3.a
4.b
5.c
6.c
7.d
8.d
9.d
10.c
You’re welcome ;)
QUICKLY!!!!!!!!!!
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions. Online Content: Site 1 When graphing inequalities, where can the solutions be found?
Answer:
what do u need help with
resolver
4×3
____
7+5
Answer:
THEY ARE EQUAL =
Step-by-step explanation:
what is the unit rate for $290 for 18
Answer:
16.1
Step-by-step explanation:
Rewrite the equation in Standard Form: 2=y-2x
Answer:
Standard Form: 2x - y = -2
2. Which of these sets of measurements represents the lengths of the sides of a right triangle?
a. (10, 24, 26)
b. (5, 12, 24)
C. (12, 18, 30)
d. (1, 2,9)
The answer is B because it has to have a right angle in it
HELPPP PLEASE IM FAILING MATHHHH !!!
Answer:
increases
Step-by-step explanation:
on on the side, it looks like you need to enter stuff into the table. All you need to do is copy the numbers from the table and transfer them to the empty one.
also this answer just makes sense. If you look at the table, you can see for the x values, they are always increasing. For The y values they are also increasing. Therefore, is the number of hours studying increases the corresponding test scores also increase
What is the equation in slope-intercept form of the line that passes through the points (0,-4) and (2,0)
Answer:
m=2
Step-by-step explanation:
if that's not how you write it then try y=2x
6x = 9 + x^2
A.-3,3
B.3
C.no solution
D.-3
Answer: b
Step-by-step explanation:Step 1: Simplify both sides of the equation.
6x=x2+9
Step 2: Subtract x^2+9 from both sides.
6x−(x2+9)=x2+9−(x2+9)
−x2+6x−9=0
Step 3: Factor left side of equation.
(−x+3)(x−3)=0
Step 4: Set factors equal to 0.
−x+3=0 or x−3=0
given the endpoint (-9,3) and (1,8) partition the segment into the ratio 2:3
Answer:
[tex]P = (-5,5)[/tex]
Step-by-step explanation:
Let the segments be A and B
[tex]A = (-9,3)[/tex]
[tex]B = (1,8)[/tex]
[tex]m:n = 2:3[/tex]
Required
Determine the endpoints after it is divided into ratios.
Let the point be represented with P
The formula to use is:
[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
Where
[tex]A = (-9,3)[/tex] ----- [tex](x_1,y_1)[/tex]
[tex]B = (1,8)[/tex] ------ [tex](x_2,y_2)[/tex]
So:
[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
[tex]P = (\frac{2 * 1 + 3 * -9}{2 + 3},\frac{2 * 8 + 3 * 3}{2 + 3})[/tex]
[tex]P = (\frac{-25}{5},\frac{25}{5})[/tex]
[tex]P = (-5,5)[/tex]
At the local harvest festival Marty bought 2 pumpkin pie slices and 2 cups of hot chocolate $10.00. Patty bought 4 slices of pie and 5 cups of hot chocolate for $22.50. How much is a slice of pumpkin pie and how much is a cup of hot chocolate?
Answer:
1 cup of hot chocolate is $2.5
1 slice of pumpkin pie is $2.5
Step-by-step explanation:
Represent Pumpkin Pie with P and Hot Chocolate with C:
Marty:
[tex]2P + 2H = 10[/tex]
Patty:
[tex]4P + 5H = 22.5[/tex]
So, we have the following set of equation:
[tex]2P + 2H = 10[/tex] -------- (1)
[tex]4P + 5H = 22.5[/tex] -------- (2)
Multiply the first equation by 2
[tex]2(2P + 2H = 10)[/tex]
[tex]4P + 4H = 20[/tex] -------- (3)
Subtract (3) from (2)
[tex]4P + 5H = 22.5[/tex]
[tex]4P + 4H = 20[/tex]
--------------------------
[tex]5H - 4H = 22.5 - 20[/tex]
[tex]H = 2.5[/tex]
Substitute 2.5 for H in [tex]2P + 2H = 10[/tex]
[tex]2P + 2 * 2.5 = 10[/tex]
[tex]2P + 5 = 10[/tex]
[tex]2P = 10 - 5[/tex]
[tex]2P = 5[/tex]
Divide through by 2
[tex]P = \frac{5}{2}[/tex]
[tex]P=2.5[/tex]
Hence, 1 cup of hot chocolate is $2.5 and 1 slice of pumpkin pie is $2.5
f(a) = a^4- 6a² - 10a - 4 at a=-2
Step-by-step explanation:
I'm sorry I don't know the answer i know your mad because I'm writing this
Which is better 32 miles or 12.7 kilometers and why
Answer:
32 miles
Step-by-step explanation:
32 miles is equal to 51.499008 Kilometers
12.7 kilometers is equal to 7.891414 miles
The perimeter of a rectangle is 138
meters and the area is 1080 square
meters. Find the length and the width of
the rectangle.
127.86
+78.95
+23.09
Answer:
229.9
Step-by-step explanation:
Answer:
229.9
Step-by-step explanation:
Uh easyyyyy lol
what is (d^1 3^1 d^3)^2
Answer:
Simplify the solution: 13^1d^3
Step-by-step explanation:
Any expression raised to the power of one equal itself.
Solve: 2y - 3.1 when y = 3.41
Answer:
3.72
Step-by-step explanation
2x3.42=6.82
6.82-3.1=3.72
Answer:
First, substitute y by the value
2(3.41)-3.1
Multiply the bracket by 2
It will be 0.58651026393, so you’ll round it up to make it shorter to make it easy for calculation
0.59-3.1=-2.51
-2.51 is the answer to your question
Step-by-step explanation:
I hope this helped, please give me brainliest
By which rule are these triangles congruent?
Answer:
AAS (Angle-Angle-Side)
Step-by-step explanation:
Topic: congruence and similarity
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Answer:
Angle Angle Side
Step-by-step explanation:
You can see you have two angles next to each other and one side next to that so just see which proof it fits
Hope This Helps
Evaluate the function at x = –2.
y = 3
y = –2
y = 2
y = 0
Find the y-intercept of the following equation. Simplify your answer.
y = –10x − 8
Answer: -8
Step-by-step explanation: because the formula is mx+b=y and the -8 is the b
The sum of two fractions is 1. If one fraction is 3/8 greater than the other, what are the two fractions?
Answer:
Well it could be a number of fractions. It could be 1/8 and 4/8, or 2/8 and 3/8.
Trevor made this number pattern 2,9,16,23,30,37 if the pattern continues what will be the eight number be
Answer:
44
Step-by-step explanation:
Can someone please help me with this?!!
Answer:
x=19
Step-by-step explanation:
x+8=2x-11
-11+11=0
8+11=19
x-x=0
2x-x=x
x=19
Please please help me
Answer: it would be g because if you distribute 9, you end up with x+72 and the bottom one is 9•8 (also 72)+x