Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The equation is [tex]ln (SALARY) = 1 + 0.02 ln(EDU)[/tex]
generally
[tex]ln (e) = 1[/tex]
=> [tex]ln (SALARY) = ln (e) + 0.02 ln(EDU)[/tex]
Apply log rules
=> [tex]ln (SALARY) = ln[ e(EDU)^{0.02} ][/tex]
=> [tex]SALARY = e(EDU)^{0.02}[/tex]
When EDU is increase by 1% we have that
[tex]\frac{1}{100} * EDU + EDU[/tex]
=> [tex]1.01 EDU[/tex]
So the new SALARY will now be
[tex]SALARY'' = e(1.01EDU)^{0.02}[/tex]
The ratio by which the new SALARY will increase is obtain by dividing the value of new SALARY (SALARY'' ) with that of the former SALARY (SALARY) and this mathematically represented as
[tex] \frac{SALARY'' }{SALARY} = \frac{e*1.01 (EDU)^{0.02}}{e (EDU)^{0.02}}[/tex]
=> [tex]\frac{SALARY ''}{SALARY} = 1.0002[/tex]
Generally the percentage increase of salary is mathematically evaluated as
[tex]k= (\frac{SALARY''}{SALARY} - 1 ) * 100[/tex]
=> [tex]k= (1.0002 - 1 ) * 100[/tex]
=> [tex]k= 0.02 \%[/tex]
Can you guys please help I don’t understand!! Please show steps if you can
Step-by-step explanation:
it may help you to understand.
Peter paid $79.80 for renting a tricycle for 6 hours. What was the rate per hour for renting the tricycle? (Input only numeric values and decimal point, and report prices to two decimal places, such as 12.30.)
$
per hour (10 points)
Answer:
$13.30
Step-by-step explanation:
To find the rate of change, simply just divide $79.80 by the number of hours, in this case 6, to find the amount of increase per hour. $79.80/6 = $13.30 was the starting value and increased the following hours, making $13.30 the answer.
If you earn $6 per hour, what is your time and a half overtime rate?
Answer:
Let the hours worked by you be x,
Your salary with time and half overtime will be,
=> x + x/2
If you worked for 1 and half overtime hour you will get,
6 + 6/2
=> 6 + 3
=> 9
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Thank You!!
Can somebody solve this?
Answer:
8 months
Step-by-step explanation:
if you can get 120 per month then 950/120 = ~8
Answer:
She needs $350.
Step-by-step explanation:
120 x 5 = 600
$950 - $600 = $350
Question
Find the slope of the line of (4,5) (0,-1)
Answer:
Slope=6/4
Step-by-step explanation:
Slope formula[tex]= \frac{y_{1} -y_{2}}{x_{1}-x_{2} }[/tex]
So we do : [tex]\frac{-1-5}{0-4}= \frac{-6}{-4} = \frac{6}{4}[/tex]
The slope is 6/4
In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points that Tyler scored, which equations are correct? Select all that apply.
c = t + 0.5t
c = t + 0.5
c = (1+0.5)t
c = t + 50
c = 1.5t
Which of the following is the least reduced equivalent of 243/729?
Answer:
1/9
Step-by-step explanation:
243/729 to it's equivalent fraction is
243/729 divide numerator and the denominator by 3 = 81/243
81/243 divide numerator and denominator by 3 =27/81
27/81 divide both numerator and denominator by 3 =9/81
9/81 divide both numerator and denominator by 9 =1/9
answer = 1/9
Therefore, 243/729 reduced to it's equivalent fraction is = 1/9
6 units to the right of 0
Use the distributive property to simplify 5(2x+3).
7x + 3
7x + 8
10x + 15
10x + 25
Answer:
the distributive property to simplify 5(2x+3)=10x+15
Need help with my geometry homework grade due to
The surface area of the base ball to the nearest whole number is 26 in²
What is surface area of a sphere?A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere is expressed as;
SA = 4πr²
where r is the radius and it's calculated as;
C = 2πr
9 = 2πr
r = 4.5/π =
SA = 4 π × (4.5/π)²
SA = 81/π
SA = 26 in²( nearest whole number)
Therefore the surface area of the sphere is 26 in²
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I need someone really good in math to help me please
Answer:
I
Step-by-step explanation:
This is the correct because it starts out by multiplying by 2, but in the second row, it multiplies it by -2, not 2.
Answer:
the answer if i
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIEST
4 friends share 3 pizzas equally how much pizza did each friend get?
Answer:
3/4
Step-by-step explanation:
No matter how many pizzas there are, if we divide each pizza to 4 slices, each one gets one slice from each pizza, that is 1/4 of a pizza for each brother. Since there are 3 pizzas, simply multiply 3 x 1/4 = 3/4
Answer:
It depends on the amount of slices
Step-by-step explanation:
It depends on the amount of slices
If there are 8 slices on each pizza, than it's 6 slices per friend. If it's 6, than its 4.5. I assume you mean with 8 slices, so it's 6 slices per friends
8 • 10^4 is how many times as large as 4 • 10^-5
Answer:
D. 2 x 10^9
Step-by-step explanation:
The sum of three consecutive integers is 657. What are the three integers?
Answer:
218, 219, 220
Step-by-step explanation:
Which symbol makes the comparison true? 0.74 to 0.740
Answer:
=
Step-by-step explanation:
4. Sketch the graph of F(x) = 1 +x/x²-1
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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What is 478 divided by 72?
Answer:
6.638 repeating
Step-by-step explanation:
you just need to set up a long division problem and then solve.
Let A be a set of numbers.
• We say that A is closed under addition provided that x + y ∈ A for all x, y ∈ A.
• We say that A is closed under multiplication provided that xy ∈ A for all x, y ∈ A. For each of the following sets, determine whether or not it is closed under addition and whether or not it is closed under multiplication. Justify your answers.
a. The set of all integers divisible by 5.
b. {2n + 1 | n ∈ Z}.
c. {2, 5, 8, 11, 14, . . . }.
d. { 1 7n | n ∈ Z}.
e. The set of nonzero real numbers.
Answer:
a. closed under addition and multiplication
b. not closed under addition but closed under multiplication.
c. not closed under addition and multiplication
d. closed under addition and multiplication
e. not closed under addition but closed under multiplication
Step-by-step explanation:
a.
Let A be a set of all integers divisible by 5.
Let [tex]x,y[/tex]∈A such that [tex]x=5m\,,\,y=5n[/tex]
Find [tex]x+y,xy[/tex]
[tex]x+y=5m+5n=5(m+n)[/tex]
So, [tex]x+y[/tex] is divisible by 5.
[tex]xy=(5m)(5n)=25mn=5(5mn)[/tex]
So,
[tex]xy[/tex] is divisible by 5.
Therefore, A is closed under addition and multiplication.
b.
Let A = { 2n +1 | n ∈ Z}
Let [tex]x,y[/tex]∈A such that [tex]x=2m+1\,,\,y=2n+1[/tex] where m, n ∈ Z.
Find [tex]x+y,xy[/tex]
[tex]x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)[/tex]
So,
[tex]x+y[/tex] ∉ A
[tex]xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1[/tex]
So,
[tex]xy[/tex]∈ A
Therefore, A is not closed under addition but A is closed under multiplication.
c.
[tex]Let A=\{2,5,8,11,14,...\}[/tex]
Let [tex]x=2,y=5[/tex] but [tex]x+y=2+5=7[/tex]∉A
Also,
[tex]xy=2(5)=10[/tex]∉A
Therefore, A is not closed under addition and multiplication.
d.
Let A = { 17n: n∈Z}
Let [tex]x,y[/tex] ∈ A such that [tex]x=17n,y=17m[/tex]
Find x + y and xy
[tex]x+y=17n+17m=17(n+m)[/tex]
[tex]xy=(17m)(17n)=289mn=17(17mn)[/tex]
So,
[tex]x+y,xy[/tex] ∈ A
Therefore, A is closed under addition and multiplication.
e.
Let A be the set of nonzero real numbers.
Let [tex]x,y[/tex] ∈ A such that [tex]x=-1,y=1[/tex]
Find x + y
[tex]x+y=-1+1=0[/tex]
So,
[tex]x+y[/tex] ∈ A
Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.
Therefore, A is not closed under addition but A is closed under multiplication.
There are 292 people in the concert hall. The same number of people are seated in each of the 4 different sections of the concert hall. How many people are seated in each section?
Answer:
73 people/section
Step-by-step explanation:
We want "number of people seated in each section," which is a rate.
Find this rate as follows:
292 people people 292
-------------------------- = x------------ = --------- people/section = 73 people/sect
4 sections section 4
Please help, I’ll give brainlyist
FIND THE MEASURE OF A
Answer:
18°
Step-by-step explanation:
The m∠A ≅ x+32
The angle opposite 36° is 36° & the angle opposite x+126 is x + 126: Vertical angles theorem
The three angles in the triangle with m∠A are 36°, x+126°, and x+32°(m∠A)
36+x+126+x+32 = 180 : Angles in a triangle theorem
194+2x = 180
2x = -14
x= -7
m∠A ≅ -14+32
m∠A≅ 18°
I hope this helps!!!
Which choice is equivalent to the expression below?
-18
A. 187
B. 3./21
C. -3/2
D. 3;
E. -181
Answer:
B i believe
Step-by-step explanation:
An airplane is heading north at an airspeed of 750 km/hr, but there is a wind blowing from the southeast at 50 km/hr.
The plane will end up flying
degrees off course
The plane's speed relative to the ground will be
km/hr
The plane's speed relative to the ground will be approximately 750.62 km/hr.
To determine the plane's heading off course and its speed relative to the ground, we can use vector addition.
Given:
Airspeed of the plane: 750 km/hr
Wind speed from the southeast: 50 km/hr
First, let's analyze the effect of the wind on the plane's course.
The wind is coming from the southeast, which is at a 45-degree angle to both north and east directions. Since the plane is heading directly north, the wind will have a component that pushes the plane off course.
To find the heading off course, we can use trigonometry. The component of the wind that affects the plane's course is the eastward component. We can calculate it using the cosine function:
Component off course = Wind speed * cos(45°)
Component off course = 50 km/hr * cos(45°)
Component off course ≈ 35.36 km/hr
The plane will end up flying at speed of approximately 35.36 km/hr off course.
Next, let's calculate the plane's speed relative to the ground. We can use vector addition to find the resultant velocity.
The northward velocity of the plane remains unchanged at 750 km/hr. The eastward velocity caused by the wind is the wind speed itself, which is 50 km/hr.
Using the Pythagorean theorem, we can find the resultant velocity:
Resultant velocity = √(750^2 + 50^2)
Resultant velocity ≈ 750.62 km/hr
The plane's speed relative to the ground will be approximately 750.62 km/hr.
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Drag each tile to the correct box. These equations take their y-values from the set {4, 5, 6, 7, 8}. Arrange the equations in decreasing order of the values of y that make them true. 4y + (y − 1) = 29 4y − y + 1 = 13 (2y + 3) − 4 = 9 , ,
Arranging the equations in decreasing Order of the values of y that make them true, we have:
4y + (y - 1) = 29
4y - y + 1 = 13
(2y + 3) - 4 = 9
To arrange the equations in decreasing order of the values of y that make them true, we need to solve each equation for y and evaluate the resulting expressions for the given set of y-values {4, 5, 6, 7, 8}.
Let's solve each equation one by one:
1. 4y + (y - 1) = 29
Simplifying the equation, we get:
5y - 1 = 29
Adding 1 to both sides, we have:
5y = 30
Dividing both sides by 5, we find:
y = 6
2. 4y - y + 1 = 13
Simplifying the equation, we get:
3y + 1 = 13
Subtracting 1 from both sides, we have:
3y = 12
Dividing both sides by 3, we find:
y = 4
3. (2y + 3) - 4 = 9
Simplifying the equation, we get:
2y - 1 = 9
Adding 1 to both sides, we have:
2y = 10
Dividing both sides by 2, we find:
y = 5
Now, let's evaluate the expressions for the given y-values:
For y = 8:
4y + (y - 1) = 4(8) + (8 - 1) = 32 + 7 = 39
For y = 7:
4y + (y - 1) = 4(7) + (7 - 1) = 28 + 6 = 34
For y = 6:
4y + (y - 1) = 4(6) + (6 - 1) = 24 + 5 = 29
For y = 5:
4y + (y - 1) = 4(5) + (5 - 1) = 20 + 4 = 24
For y = 4:
4y + (y - 1) = 4(4) + (4 - 1) = 16 + 3 = 19
Arranging the equations in decreasing order of the values of y that make them true, we have:
4y + (y - 1) = 29
4y - y + 1 = 13
(2y + 3) - 4 = 9
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Candle Burning
10
y
9
8
The slope of the graph is -1. Which statement
describes how the slope is related to the burning of a
candle?
O candle height increases 1 cm per hour
O candle height decreases 9 cm per hour
O candle is 1 cm tall
O candle burns down 1 cm per hour
7
Candle Height (cm)
1
2 3 4 5 6 7 8
Hours Burned
101
Answer:
Candle burns down 1 cm per hour
I’m doing the assignment!
The correct statement that describes how the slope is related to the burning of a candle is "Candle burns down 1 cm per hour."
The correct option is D.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The statement "The slope of the graph is -1" indicates that for each unit of increase in the horizontal variable (e.g. time), the vertical variable (e.g. height of the candle) decreases by 1 unit.
Therefore, the correct statement that describes how the slope is related to the burning of a candle is "Candle burns down 1 cm per hour."
Option A ("Candle height increases 1 cm per hour") and option C ("Candle is 1 cm tall") are not consistent with a negative slope.
Option B ("Candle height decreases 9 cm per hour") is not consistent with a slope of -1, as it implies a steeper slope.
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Enrique drives 108 miles before stopping to get gas. He then continues driving for 18 more miles before reaching his destination. How many total miles did Enrique drive?
90
126
216
288
Answer:
126 miles
Step-by-step explanation:
A rectangular garden plot has an area of 36ft if the width plot is 4 ft what is the length
Answer:
9 ft
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
36 divided by 4
=9
What is equivalent ratio in lower terms of 55:30?
Answer:
11:6
Step-by-step explanation:
Both values are divisable by 5 as their greatest common factor.
Andrew drew a square with each side measuring 3 inches. Lindsay drew a triangle with each side measuring 4 inches. Which shape has a greater perimeter? Write an equation to help explain your answer.
Select the correct answer below, and fill in the answer boxes to complete your choice.
(Use the operation symbols in the math palette as needed.)
A.
The square has a greater perimeter of
nothing inches. An equation for the perimeter of the shapes is
nothing.
B.
The triangle has a greater perimeter of
nothing inches. An equation for the perimeter of the shapes is
nothing.
C.
Both shapes have a perimeter of
nothing inches. An equation for the perimeter of the shapes is
nothing.
Answer:
C.
Both shapes have a perimeter of
12 inches. An equation for the perimeter of the shapes is 3 + 3 + 3 + 3 = 4 + 4 + 4.
Step-by-step explanation:
Since a square has 4 sides, we need to multiply 3 by 4 which is 12. Since a triangle has 3 sides, we need to multiply 4 by 3 which is 12. Therefore, both shapes share the same perimeter.
According to the Census Bureau, 3.29 people reside in the typical American household. A sample of 16 households in Arizona retirement communities showed the mean number of residents per household was 2.76 residents. The standard deviation of this sample was 1.29 residents. At the 0.05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.29 persons?
(a) State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)
H0: μ ≥
H1: μ <
(b) State the decision rule for .05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 if t <
(c) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic
(d) Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.29 persons
(Click to select)Fail to rejectReject H0. Mean number of residents (Click to select)is necessarilyis not necessarily less than 3.29 persons.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Alpha = 0.05
Sample size (n) = 16
Population mean(σ) = 3.29
Sample mean (m) = 2.76
Sample standard deviation (sd) = 1.29
(1)
Null hypothesis : μ ≥ 3.29
Alternative hypothesis : μ < 3.29
(2)
From the t distribution table :
The Null hypothesis should be rejected if
t < - t0
To obtain t0:
Degree of freedom (df) = n - 1 = 16 - 1 = 15 at alpha = 0.05
t0 = 1.753 ( left tailed) = - 1.753
(3)
Value of test statistic:
t = (m - σ) / (sd / √n)
(2.76 - 3.29) / (1.29 / √16)
-0.53 / 0.3225
t = - 1.643
Comparing t < - t0
But : -1.643 > - 1.753
Hence,
t > - t0
Hence, we fail to reject the null hypothesis
