Answer:
16.0%
16.0%
Step-by-step explanation:
Given that :
First $20,000 is exempt from tax
$20000 to $50000 = 12% tax rate
Over $50000 = 16% tax rate
Earning = $90000
Since earning is greater than $50000
Tax rate = 16% = 0.16
Average tax rate = tax paid / taxable income
Tax paid = 0.16 * 90,000 = $14,400
Average tax rate = 14,400 / 90,000
Average tax rate = 0.16 = 16%
Marginal tax rate :
Change in tax paid / change in earning
Suppose ; amount earned increases to 95,000
Tax paid = 95000 * 0.16 = 15200
Change in tax paid = (15200 - 14400) = 800
Change in earning = 95000 - 90000 = 5000
= 800 / 5000
= 0.16 = 16%
Marginal tax rate = 16%
Rewrite the equation in Standard Form: 2=y-2x
Answer:
Standard Form: 2x - y = -2
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
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
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
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
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.
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
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
what is the unit rate for $290 for 18
Answer:
16.1
Step-by-step explanation:
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
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
20. Find the slope of the line graphed below.
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]
Nora makes $3000 a month. If she spends 15% of that on medical bills each month, how much does she spend on medical bills?
127.86
+78.95
+23.09
Answer:
229.9
Step-by-step explanation:
Answer:
229.9
Step-by-step explanation:
Uh easyyyyy lol
Determine whether each ordered pair is a solution of the system.
5-7x+2y2 =-10
1-5x-2y =-22
a) (-4,-6)
b) (6,4)
According to the system:
5 – 7x + 2y² = -10
1 – 5x – 2y = -22
______________
a) No ; (4, 6) is not a solution to the
system. This point does not touch either equation.
b) No ; (6, 4) is not a solution to the system. This point does not touch either equation.
Solutions:
[tex]( \frac{122 - 3 \sqrt{101}}{25}, \frac{ - 7 +3 \sqrt{101}}{10}) ≈ (3.674, 2.315) \\ ( \frac{122 + 3 \sqrt{101}}{25}, \frac{ - 7 - 3 \sqrt{101}}{10}) ≈ (6.086, -3.715) [/tex]
x = ( 122 ∓ 3√101 ) / 25 ≈ 3.674 or 6.086
y = ( -7 ± 3√101 ) / 10 ≈ 2.315 or -3.715
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!!~~
Find the volume of the cube.
Answer:
60 cm & 60 mL
Hope this helps! Let me know if this is right or not.
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.
Plsss help ASAP!!!!!!
Answer:
Its either A or D because its reflection so that cancels out B and C
im not sure if this helps u or not but at lest it cancels out 2 of the options
The reflection of a horizontal line has the same result as a rotation of 90 degrees clockwise.
Step-by-step explanation:
When an image is rotated 90 degrees counterclockwise the shape is still congruent but in a different quadrant. The same is true when an image is reflected across a horizontal line.
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:
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 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.
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
help help HELP ASAP.
1 a negative
2 a positive
Answer:
a negative
Step-by-step explanation:
Answer:
Negative
Step-by-step explanation:
The fact that the market value falls below the maintenance cost, shows that the at the current value of the car is negative.
help meee plzzzzzzzz
Answer:
450 cm i think
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:
what is baal veer? give all the bad and good fairies names i will mark those people as b brainiest
Answer:
The story revolves around a boy, Baal Veer, who is blessed with the powers of 7 fairies. Gaal Pari (Cheek Fairy), Vijhdar Pari (Electric Fairy), Baal Pari (Tress Fairy), Atkaati Pari (Obstacle Fairy), Aarpar Pari (Across Fairy), Bhatkati Pari (Wander Fairy), Natkhat Pari (Naughty Fairy) and Rani Pari (Queen Fairy) give magical powers to Baal Veer to help them fight an evil fairy Bhayankar Pari (Frightening Fairy), who wants to become the queen of Pari Lok (Fairy Realm). Years ago, Maa Pari (Mother Fairy) gave Pari Lok's (Fairy Realm's) throne to Bahuroopi Pari (Disguise Fairy) instead of Bhayankar Pari, who, at that time was Bhali Pari (Good Fairy), so she returns to take revenge from Maa Pari and Rani Pari. Baal Veer is sent to Earth to help children and to save Earth from Bhayankar Pari and the wrath of other cunning and cruel, evil fairies. Baal Veer stays with the Dagli family on Earth as Ballu. The family has seven members who never lie, even at the time of difficult circumstances, including Manav and Meher, who later receive powers from Rani Pari (they were made Baal Mitra and Baal Sakhi, respectively) and help Baal Veer in his quests and adventures.
Step-by-step explanation:
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
Evaluate the function at x = –2.
y = 3
y = –2
y = 2
y = 0