This week Skyler got a promotion at work that came with a 3 % pay increase. If now his monthly salary is $ 2369 , how much was he making before the raise?Enter your answer as a decimal. If needed, round to the nearest penny. Do not use commas.
Answers
Answer
Skyler's original salary is was $2300
Solution
- We are told that Skyler got a promotion that led to a 3% increase in his monthly salary and this salary became $2369. We are asked to find his original salary before the 3% salary increase.
- We can let his initial salary be X. Thus, we can model this 3% increase in his salary as follows:
\(\begin{gathered} 3\text{ \% increase in salary of X dollars:} \\ \frac{3}{100}\times X=0.03X \end{gathered}\)
- Now that we know the expression for the 3% increase in salary, we can now simply add this value to X to get his new salary.
- Thus, we can say:
\(\begin{gathered} \text{Old Salary}+\text{ Salary increase}=\text{ New Salary} \\ \text{Old Salary}=X \\ \text{Salary increase}=0.03X \\ \text{New Salary}=2369 \\ \\ \therefore X+0.03X=2369 \end{gathered}\)- This has led us to the equation in terms of X, Skyler's initial salary, which is solvable.
- Solving for X, we have:
\(\begin{gathered} X+0.03X=2369 \\ 1.03X=2369 \\ \text{Divide both sides by 1.03} \\ \frac{1.03X}{1.03}=\frac{2369}{1.03} \\ \\ \therefore X=2300 \end{gathered}\)Final Answer
Skyler's original salary is was $2300
Related Questions
What is the product of 4.5 ⋅ 10^5 and 1.6 ⋅ 10^2?
Answers
Answer: 450000, 160
Step-by-step explanation:
4.5 ⋅ 10^5 =
4.5*100000=
4*100000+0.5*100000=
400000+50000=450000
1.6 ⋅ 10^2=
1.6*100=
1*100+0.6*100=
100+60=160
What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answers
The value of the discriminant for the quadratic equation –3 = –x2 + 2x is 16
What is the value of the discriminant for the quadratic equation?The quadratic equation is given as:
–3 = –x^2 + 2x
Rewrite the equation as:
x^2 - 2x - 3 = 0
A quadratic equation is represented as;
ax^2 + bx + c = 0
So, we have
a = 1
b = -2
c = -3
The discriminant is
d = b^2 - 4ac
So, we have
d = (-2)^2 - 4 * 1 * -3
Evaluate
d = 16
Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is 16
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Answer:
16
Step-by-step explanation:
if a runner finishes the 26.2. mille race in 4 hours and 37 mins and Wilson kipping finish in 4 minutes and 43 seconds per mile how much faster was kipsang then the average runner
Answers
Answer
a) Wilson Kipsang is 7.046 miles per hour faster than the average runner.
Solution is presented below under Explanation.
b) Wilson Kipsang is 2.24 times faster than the average runner.
c) When the average runner is at mile 6, Kipsang will be at mile 13.45.
d) Kipsang's record time = 2 hours, 3 minutes, 34.6 seconds
Explanation
To solve this, we will calculate the speed of the average runner and then the speed of Wilson Kipsang
Speed = (Distance/Time)
For the average runner
Distance = 26.2 miles
Time = 4 hours 37 mins = 4 hours + (37/60) = 4.617 hours
Speed = (Distance/Time)
Speed = (26.2/4.617)
Speed = 5.675 miles per hour
For Wilson Kipsang
Distance = 1 mile
Time = 4 minutes 43 seconds = (4/60) + (43/3600) = 0.0667 + 0.01194 = 0.0786 hour
Speed = (Distance/Time)
Speed = (1/0.0786) = 12.721 miles per hour
So, now, we are asked to find how much faster than the average runner is Wilson Kipsang
Wilson Kipsang's speed = 12.721 miles per hour
Average runner's speed = 5.675 miles per hour
Wilson Kipsang is faster than the average runner by
(12.721 - 5.676) = 7.046 miles per hour
b) We are asked to find how many times faster than the average runner Wilson Kipsang is.
Let the number of times he is faster than the average runner be x
Wilson Kipsang's speed = 12.721 miles per hour
Average runner's speed = 5.675 miles per hour
(5.675) (x) = (12.721)
Divide both sides by 5.675
x = (12.721/5.675)
x = 2.24 times
c) If the average runner is at mile 6, where would Kipsang be?
To do this, we will find the time it takes the average runner to be at mile 6, then use that time to find where Kipsang would be.
Speed = (Distance/Time)
By cross multiplying, we see that
Time = (Distance/Speed)
For the average runner
Distance = 6 miles
Speed = 5.675 miles per hour
Time = (Distance/Speed)
Time = (6/5.675) = 1.057 hours
For Wilson Kipsang,
Speed = (Distance/Time)
By cross multiplying
Distance = (Speed) (Time)
Speed = 12.721 miles per hour
Time = 1.057 hours
Distance = (Speed) (Time)
Distance = (12.721) (1.057)
Distance = 13.45 miles
d) We were told that for Kipsang
1 mile = 4 minutes 43 seconds
26.2 miles = 26.2 (4 minutes 43 seconds)
26.2 miles = 26.2 (283 seconds) = 7414.6 seconds
We can then convert this further
7414.6 seconds = 2 hours, 3 minutes, 34.6 seconds
Hope this Helps!!!
- 5 1/2 - 9 1/4 + 2 3/4
Answers
-12
Explanation:\(-5\frac{1}{2}-9\frac{1}{4}+2\frac{3}{4}\)first we convert to improper fraction:
\(=\frac{-11}{2}\text{ - }\frac{37}{4}\text{ + }\frac{11}{4}\)simplify:
\(\begin{gathered} =\text{ }\frac{2(-11)\text{ - 37(1) + 11(1)}}{4} \\ =\text{ }\frac{-22\text{ - 37 + 11}}{4} \\ =\text{ }\frac{-59\text{ + 11}}{4} \end{gathered}\)\(\begin{gathered} =\text{ }\frac{-48}{4} \\ =\text{ -12} \end{gathered}\)Tanvir applies the distributive property to the left-hand side of the equation 1/3(3q+15)=101 Which equation shows the correct application of the distributive property?
1: q+15=101
2:3q+5=101
3:3q+15=101
4:q+5=101
Answers
When Tanvir applies the distributive property to the left-hand side of the equation, 1/3(3q+15)=101, the equation that shows the correct application is equation 4: q+5=101.
What is distributive property?The distributive property applies basic mathematical operations, especially in equations.
This property is that when a value is multiplied or divided by a number to a set that will be added or subtracted, the result is the same, notwithstanding if the operation is done before the addition or subtraction.
1/3(3q+15) = 101
(3q/3+15/3) = 101
= q + 5 = 101
q = 96
Check of Distributive Property:
1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1 x 96 + 5 = 101
= 96 + 5 = 101
= 101 = 101
Or: 1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1/3(288 + 15) = 101
= 1/3(303) = 101
= 101 = 101
Thus, the equation that correctly applies the distributive property is equation 4: q+5=101.
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solve please hurry answer
Answers
Answer:
10 dollars for adult tickets and 6 dollars for student tickets
Step-by-step explanation:
a=adult tickets
s=student tickets
4a+2s=52 3a+5s=60
5(4a+2s=52) 2(3a+5s=60)
20a+10s=260 6a+10s=120
-6a+10s=120
14a=140
a=10
10 dollars per adult ticket
4(10)+2s=52
40+2s=52
2s=12
s=6
6 dollars per student ticket
HELP ASAP PLS SHOW WORK
Answers
Answer:
42
dnndndndndndnd
dndndndndj
You are given the following linear regression model fitted to 12 observations:
Y = β0 + β1 ∗ X +\epsilon
The results of the regression are as follows:
Parameter Estimate Standard Error
Bo 15.52 3.242
B1 0.40 0.181
Determine the results of the hypothesis test H0 : β0 = 0 against the alternative H1 : β1\not\equiv0
(A) Reject at α = 0.01
(B) Reject at α = 0.02, Do not reject at α = 0.01
(C) Reject at α = 0.05, Do not reject at α = 0.02
(D) Reject at α = 0.10, Do not reject at α = 0.05
(E) Do not reject at α = 0.10
Please I need the workings on how option D is the correct one, thank you.
Answers
The results of the hypothesis test H0:β0 = 0 against the alternative H1:β1 ≠ 0 is Reject at α = 0.10, Do not reject at α = 0.05. Hence, option D is the accurate solution.
To determine the results of the hypothesis test H0:β0 = 0 against the alternative H1:β1 ≠ 0, we will calculate the t-statistic and compare it to the critical values from the t-distribution at the desired significance level.
The t-statistic for the null hypothesis is given by -
t = (Bo - 0) / SE(Bo)
where Bo is the estimate of the intercept, SE(Bo) is its standard error, and 0 is the hypothesized value under the null hypothesis.
Substituting the given values, we get,
t = 15.52 / 3.242 = 4.785
The degrees of freedom for this test are n - 2 = 10, where n is the number of observations.
At a significance level of 0.10, the critical values for a two-tailed test with 10 degrees of freedom are ±1.812. Since our calculated t-statistic of 4.785 is greater than the critical value of 1.812, we reject the null hypothesis at α = 0.10.
Similarly, at a significance level of 0.05, the critical values for a two-tailed test with 10 degrees of freedom are ±2.228. Since our calculated t-statistic is less than the critical value of 2.228, we do not reject the null hypothesis at α = 0.05.
Therefore, the correct answer is (D) Reject at α = 0.10, Do not reject at α = 0.05.
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A survey in Men’s Health magazine reported that 39% of cardiologists said that they took vitamin E supplements. To see if this is still true, a researcher randomly selected 100 cardiologists and found that 36 said that they took vitamin E supplements. At α = 0.05, test the claim that 39% of the cardiologists took vitamin E supplements. A recent study said that taking too much vitamin e might be harmful how might this study make the results of the previous study invalid?
Answers
Answer:
\(z=\frac{0.36 -0.39}{\sqrt{\frac{0.39(1-0.39)}{100}}}=-0.615\)
The p value for this case would be:
\(p_v =2*P(z<-0.615)=0.539\)
For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39
Step-by-step explanation:
Information given
n=100 represent the random sample taken
X=36 represent the number of people that take E supplement
\(\hat p=\frac{36}{100}=0.36\) estimated proportion of people who take R supplement
\(p_o=0.39\) is the value that we want to test
\(\alpha=0.05\) represent the significance level
z would represent the statistic
\(p_v\) represent the p value
Hypothesis to test
We want to test if the true proportion is equatl to 0.39 or not, the system of hypothesis are.:
Null hypothesis:\(p=0.39\)
Alternative hypothesis:\(p \neq 0.39\)
The statistic is given by:
\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)
Replacing the info we got:
\(z=\frac{0.36 -0.39}{\sqrt{\frac{0.39(1-0.39)}{100}}}=-0.615\)
The p value for this case would be:
\(p_v =2*P(z<-0.615)=0.539\)
For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39
Look at the number line below.
Which expression represents the distance between T and U on the number line?
*please I need help!*
A). |-2+ -5|
B). |-2 - -5|
C). -5 - -2
D). |-2|+|-5|
Answers
B. is the ans hope you get a hundred
Rachel just purchased a homeowners insurance policy for her new home that costs $0.43 per $100. Her home is worth $387,500. What is Rachel’s annual homeowners insurance premium? a. $1,666.25 b. $2,208.75 c. $8,802.33 d. $9,011.63 Please select the best answer from the choices provided
Answers
Answer:
The answer is A.
Do you need an explanation?
387,500 /100 = 3,875
3,875 * 0.43 = 1,666.25
I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!
it's for todayyyyyyyyyyyyyyyy
Answers
hi
a) m = 2
b) m = 4
c) n = 5
d) n= 3
e) m = 6
f) n = 4
Create an equation modeling the scenario. Use the equation to solve for the missing number. In your final answer, include the equation and all necessary calculations.
Twice the sum of a number and seven is three times the number. 20 points
Answers
Answer:
Number = 14
Step-by-step explanation:
It is given that,
Twice the sum of a number and seven is three times the number
Let the number be x. Twice of the number is 2x. Three times of the number is 3x.
So,
2(x+7)=3x is the equation that models the given scenario
Opening brackets on LHS,
2x+14=3x
Subtracting 2x on both the sides
2x-2x+14=3x-2x
14=x
So, the number is 14.
The number is 14.
The calculation is as follows:
Let the number be x. Twice of the number is 2x. Three times of the number is 3x.
Based on the above information, the calculation is as follows:
2(x+7)=3x
2x+14=3x
x = 14
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a water snake in a well is 30 M below the ground level its lights 20 m upward and then slips down 10 M how far it is from the ground level
\( - 30 - + 20 - - 10\)
Answers
If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.
The graph shows the relationship between time and the distance a train travels.
What is the slope of the line?
?
Distance (mi)
200
150
100
50
0
ہے
Time (h)
3
Answers
Answer:
50
Step-by-step explanation:
i got it correct on the iready quiz
The graph of the line does not change except only in the y - intercept. The slope of the line remains same.
What is the general equation of the straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line is -y = mx + c
[m] : slope of line.
[c] : y - intercept
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a graph that shows the relationship between time and the distance a train travels.
From the graph, we can write the coordinates as -
(1, 60) and (2, 120)
So, we can write the slope of the line as -
m = (120 - 60)/(2 - 1)
m = 60/1
m = 60
Therefore, the slope of the line given in the graph will be 60 miles/hr.
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Dhani has 4 cards numbered 1 through 4. He removes 2 cards at random and adds their values.
What is the probability that the sum is less than or equal to 5?
7/12
2/3
3/5
3/4
Answers
Answer:
\(2/3\)
Step-by-step explanation:
The total number of sums (not distinct) is \(4\cdot 3=12\), because we're removing without replacement.
Count the sums that fit the stipulation (sum \(\leq\) 5):
\(1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2\)
There are 8 sums that work. Therefore, the desired answer is \(\frac{8}{12}=\boxed{\frac{2}{3}}\)
What is the value of 4³ pls help for quiz 10 points
Answers
Answer:
64
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
four times four , three times
4*4*4 = 64
Write the following number in words: 3 811 459
Answers
Answer: three million eight hundred eleven thousand four hundred fifty nine
1 000 000 = million
100 000 = hundred thousand
10 000 = ten thousand
1 000 = one thousand
100 = one hundred
10 = ten
1 = one
When I would look at questions like this I would use this chart and replace the numbers and I found that this really helped
Please answer this correctly without making mistakes
Answers
Answer:
1540 cm³
Step-by-step explanation:
V= blh= 14 cm * 22 cm * 5 cm = 1540 cm³
Answer:
1540 cm³
Step-by-step explanation:
This is because the formula for volume is l*w*h so 5*22*14 is 1540
brainliest please
4. Sketch the graph of F(x) = 1 +x/x²-1
Answers
The graph of the function is attached below.
What is the graph of a function?The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.
Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.
We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.
In the given problem;
The graph of the function f(x) = 1 + x / x² - 1 is attached below;
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If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.
Answers
Proving X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".
Given :
If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.
Take a computable surjection :
f : ω → W.
Defined G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.
here clearly, G ⊆ W .
And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.
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Simplify: 3√5⋅√10+11√5⋅√10−√5
26√50
14√15−√5
14√50−√5
6√35
Answers
Answer:
When multiplying radical expressions with the same index, we use the product rule for radicals. If a and b represent positive real numbers,
Example 1: Multiply:
√2⋅√6
Solution: This problem is a product of two square roots. Apply the product rule for radicals and then simplify.
Step-by-step explanation:
Hope this helps . ;)
Find the product of smallest natural number and the smallest whole number , 보라해
Answers
Answer:
smallest whole number is 0 so product of 0 is 0
smallest natural number is 1 so product of 1 is 1
For equation y= -x + 3 a) complete the table of valuesb) plot the points found in the above table using c) Graph the line represented by the given equation
Answers
The equation is given to be:
\(y=-x+3\)QUESTION A
We will make the necessary substitutions into the equations to get the missing values.
At x = 0:
\(\begin{gathered} y=-0+3 \\ y=3 \end{gathered}\)At x = 1:
\(\begin{gathered} y=-1+3 \\ y=2 \end{gathered}\)At x = 2:
\(\begin{gathered} y=-2+3 \\ y=1 \end{gathered}\)Therefore, the table is filled as shown below:
QUESTION B
The points are plotted as shown below:
QUESTION 3
The graph is shown below:
The median value is ____
Answers
Answer:
45
Step-by-step explanation:
Solving a word problem on proportions using a unit rate
Kala drove 315 miles in 5 hours.
At the same rate, how long would it take her to drive 693 miles?
Answers
Answer: It would take Kala 11 hours to drive 693 miles
Step-by-step explanation:
315/5=63 miles an hour
693/63=11 hours
It would take Kala 11 hours to drive 693 miles
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
Answers
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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Use what you know about intersecting lines to label the missing and
picture below.
35°
X
type of angle pair:
zoom in
X =
OManeuvering the Middle LLC, 2016, 2022
Answers
Answer:
x = 145
Step-by-step explanation:
x and 35° lie on a straight line and are supplementary angles , sum to 180°
x + 35 = 180 ( subtract 35 from both sides )
x = 145
77-y=5x Rewrite the equation in simplified slope-intercept form
Answers
Answer:
y = -5x +77
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
77 - y = 5x
Subtract 77 from each side
77-y-77 = 5x-77
-y = 5x-77
Multiply each side by -1
y = -5x +77
Answer:
y = - 5x + 77
Step-by-step explanation:
Slope intercept form means,
y = mx + cHere,
m - slope of the line
c - y intercept
And now to write the given expression in slope intercept form you can simply make y the subject in the equation.
Let us write it now.
77 - y = 5x
Subtract 77 from both sides.
-y = 5x - 77
To make y value positive multiply the whole equation by -1.
y = - 5x + 77
Choose the correct answer below
Answers
The correct statement is;
False, because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be x = 2π/3 + 2nx and x = 4π/3 + 2nx.
Option D
How to determine the statementFrom the information given, we have that;
All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx
There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx
Such that n is an integer.
This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.
The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.
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