The maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s
What is centripetal force? For which motion does the centripetal force exists? Given a example?
The centripetal force is the force needed to keep a body moving in circular motion. It exists for circular motion. Example - rotation of earth around sun.
We have an athlete swings a 7.9 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.9 m at an angular speed of 0.27 rev/s.
[A] -
Tangential speed of ball = v = rω = 0.9 x 0.27 = 0.243 m/s
[B] -
Centripetal acceleration = a[c] = rω² = 0.9 x 0.27 x 0.27 = 0.06561
[C] -
Maximum tension = Maximum centripetal force = mrω² = 132.3
ω² = 132.3/mr
ω² = 18.60
v² = 18.60r²
v = 3.89 m/s
Therefore, the maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s
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The expression 0.12x + (x − 35) models the final price of a scooter with an instant rebate in a state that charges sales tax.
a) Which part of the expression represents the discounted price before tax?
b) Which part of the expression represent the amount of sales tax, in dollars (not the tax rate, the amount of sales tax paid)?
a. The part of the expression that represents the discounted price before tax is (x − 35).
b. The of the expression represent the amount of sales tax, is 0.12x.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the expression 0.12x + (x − 35) models the final price of a scooter.
It should be noted that 0.12x represented the sale tax. In this case, the sales tax is 12% which was depicted as 0.12.
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how many quarts of pure antifreeze must be added to 5 quarts of a 10% antifreeze solution to obtain a 30% antifreeze solution?
The number of quarts of pure antifreeze that must be add to obtain a 30% antifreeze solution would be = 15 quart.
What is an antifreeze?Antifreeze is defined as the solution that can be used to lower the freezing point of a liquid based substance.
The percentage solution of antifreeze 1 = 10
The quantity of quart of antifreeze 1 = 5
The percentage solution of antifreeze 2 = 30%
The quantity of quart of antifreeze 2 = x
Using the formula;
if 10% = 5
30% = X
make X the subject of formula:
X = 30×5/10
X = 150/10
X = 15 quarts.
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HELP PLEASE!
The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 2
y is less than negative one-third times x plus 1
Which ordered pair is included in the solution to this system?
(−6, −3)
(−6, −2)
(−6, 3)
(−6, 4)
The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).
The correct answer option is option B and C
How to solve the system of inequality?y ≥ 2/3x + 2
y < - 1/3x + 1
Check all that applies:
(x, y) = (−6, −3)
(x, y) = (−6, −2)
(x, y) = (−6, 3)
(x, y) = (−6, 4)
It can be seen that x = -6Use this to find the value of yy ≥ 2/3x + 2
substitute x = -6 into the inequality
y ≥ 2/3(-6) + 2
y ≥ -12/3 + 2
y ≥ - 4 + 2
y ≥ - 2
(x, y) = (-6, -2)
y < - 1/3x + 1
substitute x = -6 into the inequality
y < -1/3(-6) + 1
y < 6/3 + 1
y < 2 + 1
y < 3
(x, y) = (-6, 3)
So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).
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x^x=4
Find the solution
Answer: 2
x = 2
[tex]x^{2}[/tex] = 4
[tex]2^{2}[/tex] = 4
4 = 4
Determining the Regression Equation The table below shows the approximate height of a ball thrown up in the air after x seconds. A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150. Which quadratic model best represents the data? f(x) = –16x2 + 99x + 6 f(x) = –36x2 + 37x + 5 f(x) = 36x2 + 37x + 5 f(x) = 16x2 + 99x + 6
The equation of the quadratic model is f(x) = -16x^2+99x+6.
From the given table:
A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150.
we know that:
regression equation = ax^2 + bx + c.
a∑x^4+b∑x^3+c∑x^3 = ∑x^2y
a∑x^3+b∑x^2+c∑x = ∑xy
a∑x^2+b∑x+cn = ∑y
After substituting and solving these three equations we get:
a = -15.714
b = 98.857
c = 5.571
Approximate values
a = -16
b = 99
c = 6
substitute these values
f(x) = -16x^2+99x+6.
Therefore the equation of the quadratic model is f(x) = -16x^2+99x+6.
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Help now Which variables would the scatter plot at the right be most likely to represent?
a.The number of people at a concert and the total concession sales
b.The number of guests at a hotel and the total water consumption
c.The number of siblings a person has and the person's GPA
d.The total number of miles driven and the total gallons of gas used
The variables that the scatter plot is most likely to represent are:
c. The number of siblings a person has and the person's GPA.
What is shown on the scatter plot?A scatter plot is composed by a set of points in the following format:
(Input, Output).
Meaning that the objective of the scatter plot is to find a relation between the output variable and the input variable.
This relation, also classified as association, can be classified as follows:
Positive: as the input increases, so does the output.Negative: as the input increases, the output decreases.No association: the input neither increases nor decreases, it remains oscillating.in this problem, we have an oscillating scatter plot, meaning that it represents variables without any clear relation among themselves.
Hence, option c is correct, as there is no relation between the number of siblings that a person has and the GPA of the person.
For the other three options, they would have been represented by increasing scatter plots.
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Students were asked to bring their favorite fruit to class. 93% of the fruits consisted of bananas, apples, and oranges. If oranges were twice as popular as bananas, and apples were 19 percentage points less popular than bananas, what are the percentages of each individual fruit?
Answer:
apples 19%, bananas 38%, oranges 36%, and other fruits 7%
Question 10
An electronics retailer purchases a laptop for $430 per unit. Per unit, the expense is 19% of the selling price
and profit is 25% of the selling price. What is the regular selling price per unit?
(rounded to nearest cent)
The regular selling price per unit for the laptop is $298.6.
How to calculate the price?Let the regular price per unit be x.
The expense is 19% of the selling price and profit is 25% of the selling price. This will be illustrated as:
x + (19% × x) + (25% × x) = 430
x + 0.19x + 0.25x = 440
1.44x = 430
Divide
x = 430 / 1.44
x = 298.6
The price is $298.6
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algebraically manipulating the formula for finding the simple interest find the principal deposited in a savings account which earned $3500 in interest at a simple interest rate of 8.5% for 10 years
the portion of students taking summer classes decreased 6.3% from 2015 to 2016. if 38% of students took summer classes in 2015, what portion were taking summer classes in 2016
The portion that were taking summer classes in 2016 is 31.4%.
How to calculate the value?From the information, the portion of students taking summer classes decreased 6.3% from 2015 to 2016 and it was stated that 38% of students took summer classes in 2015.
In this case, the portion of the people taking dinner classes will be:
= Original percentage - Reduction in percentage
= 38% - 3.6%
= 31.4%
The percentage is 31.4%
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Rachel is a stunt driver, and she's escaping from a building that is about to explode!
The variable d models Rachel's distance from her exit (in meters) t seconds after the cameras
began recording the stunt.
d=-38t+220
What is Rachel's speed?
meters per second
As per the concept of distance-speed-time formula, the speed of Rachel is 38 meters per second
Distance-speed-time formula
The general time formula to calculate the distance-speed-time for any task is given as
[Time = Distance ÷ Speed].
And the SI unit of time is seconds (s).
Given,
Rachel is a stunt driver, and she's escaping from a building that is about to explode! And the variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.
The function of d=-38t+220
Now, we have to find the speed of Rachel.
We already know that the speed is calculated as,
=> v = dx/dt
Here we have the distance is a function of time,
Now, we have to apply it one the given formula then we get,
=> v = d/dt( 38t + 220)
After the differentiation we get the value of
=> v = 38 m/s
Here the derivative of a constant (here 220) is zero.
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What is the greatest Comon factor of 30,72,54?
The greatest common factor of 30, 72, and 54 would be 6.
You are driving (too fast) down a straight, country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road tracking vehicle speeds and are in contact with each other. At the first officer’s position, you drive by going 39 miles per hour. At the second officer’s position 63 seconds later, you drive by going 38 miles per hour. The second officer pulls you over and gives you a ticket. Were they justified in giving you a ticket, even though you were not caught speeding?
Hint: refer to the Mean Value Theorem to assist with your justification and reasoning.
Yes, they justified giving us a ticket, even though we were not caught speeding, because we drove at a speed higher than the posted speed limit.
It is given that we are driving down a straight country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road, tracking vehicle speeds, and are in contact with each other. At the first officer’s position, we drive by going 39 miles per hour. At the second officer’s position, 63 seconds later, we drive by, going 38 miles per hour.
The second officer pulls us over and gives us a ticket. We will use the mean value theorem to check whether getting a ticket was justified or not. Let the maximum speed be "v" that we reach between the officers at time "c". Let the function f(t) denote the distance at time "t".
f'(c) = [f(b) - f(a)]/(b - a)
v = (1 - 0)/(63 - 0)
v = 1/63 miles per second
We need to convert the speed into miles per hour.
v = 3600/63 = 57.143 miles per hour
The speed is higher than the posted speed limit. Hence, they justified giving us a ticket, even though we were not caught speeding.
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Show Me How
Question Content Area
Cost Flow Methods
The following three identical units of Item K113 are purchased during April:
Item Beta Units Cost
April 2 Purchase 1 $165
April 15 Purchase 1 169
April 20 Purchase 1 173
Total 3 $507
Average cost per unit $169 ($507 ÷ 3 units)
Assume that one unit is sold on April 27 for $210. Determine the gross profit for April and ending inventory on April 30 using the (a) first-in, first-out (FIFO); (b) last-in, first-out (LIFO); and (c) weighted average cost method.
Gross Profit Ending Inventory
a. First-in, first-out (FIFO) $fill in the blank 1
$fill in the blank 2
b. Last-in, first-out (LIFO) $fill in the blank 3
$fill in the blank 4
c. Weighted average cost $fill in the blank 5
$fill in the blank 6
Feedback Area
Feedback
The determination of the gross profit for April and the ending inventory on April 30, using the FIFO, LIFO, and weighted average cost methods, is as follows:
Gross Profit Ending Inventory
FIFO $45 $342
LIFO $37 $334
Weighted Average $41 $338
What is the gross profit?The gross profit is the difference between the net sales revenue and the cost of goods sold.
It is the first profit point in the income statement which measures the financial performance of an entity during a period.
What is the ending inventory?The ending inventory is the difference between the cost of goods available for sale and the cost of goods sold, depending on the inventory method in use.
Some of the inventory methods include FIFO, LIFO, Weighted Average, and Specific Identification.
Item Beta Units Cost
April 2 Purchase 1 $165
April 15 Purchase 1 169
April 20 Purchase 1 173
April 27 Sales 1 $210
Total 3 $507
Average cost per unit $169 ($507 ÷ 3 units)
Cost of goods available for sale = $507
a) First-in, First-out (FIFO):
Ending inventory = $342 ($169 + $173)
Cost of goods sold = $165 ($507 - $342)
Gross profit = $45 ($210 - $165)
b) Last-in, First-out (LIFO):
Ending inventory = $334 ($165 + $169)
Cost of goods sold = $173 ($507 - $334)
Gross profit = $37 ($210 - $173)
c) Weighted average cost method:
Ending inventory = $338 (2 x $169)
Cost of goods sold = $169 (1 x $169)
Gross profit = $41 ($210 - $169)
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At 10:00 a.m. han and Tyler both start running toward each other from opposite ends of a 10 mile path along the river how han can run at a pace of 12 miles per minute Tyler can run at a pace 15 miles per minute how far does han run after a half an hour
Answer: 2.5 miles
We are given that
Total length of path=10 mile
Han runs at a pace=12 minutes per mile
Tyler runs at a pace=15 minutes per mile
We have to find the distance run by Han after a half hour.
Half hour=30 minutes
Using unitary method
Han runs distance in 12 minutes=1 mile
Han runs distance in 1 minute= mile
Han runs distance in 30 minutes= miles
Hence, Han runs 2.5 miles after half hour.
Step-by-step explanation:
Which value es NOT defined
Answer:
It is B
Tangent theta is undefined when cosine theta equals zero. Remember that identity.
Write the quadratic equation whose roots are 2 and −6, and whose leading coefficient is 4.
Answer:
4x^2 + 16x - 48
Step-by-step explanation:
A quadratic equation with roots 2 and -6 has to have factors of (x - 2) and (x + 6) since both equal 0 when either 2 or 6 are plugged in. To get a leading coefficient of 4, multiply the product of the two factors by 4. When the 4 is distributed it becomes the leading coefficient:
4(x - 2)(x + 6)
4(x^2 + 4x - 12)
4x^2 + 16x - 48
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
first brand: ?
Second brand ?
please dont answer if you dont know it.
The gallons of first brand is 102 gallons and that of the second brand is 68 gallons.
According to the question,
We have the following information:
The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. 170 gallons of a mixture contains 80% pure antifreeze.
Now, let's take the amount of first brand to be x gallons and that of the second brand to be y gallons.
So, we have the following expressions:
x+y = 170
x = 170-y ....(1)
70x/100 + 95y/100 = (80*170)/100
70x+95y = 13600
Now, putting the value of x from equation 1:
70(170-y)+95y = 13600
11900-70y+95y = 13600
11900+25y = 13600
25y = 13600-11900
25y = 1700
y = 1700/25
y = 68
Now, putting this value of y in equation 1:
x = 170-68
x = 102
Hence, the gallons of first brand is 102 gallons and that of the second brand is 68 gallons.
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Multiply.
0.01 x 4066.61
OA. 4066.61
OB. 406.661
OC. 40.6661
OD. 4.06661
The solution after the multiplication of 0.01 x 4066.61 is 40.6661
Multiplication
Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. And the word multiply means the repeated addition of groups of equal sizes.
Given,
Here we have the operation 0.01 x 4066.61
Now we have to perform the multiplication operation in it.
While we looking into the given operation, we have identified that there are 4 total decimal places in both numbers.
First, we have to ignore the decimal places and complete the multiplication as if operating on two integers.
The the calculation for the multiplication is shown in the following image.
Now, we have to rewrite the product with 4 total decimal places.
Then we get the answer is 40.6661
Therefore, 0.01 × 4066.61 = 40.6661
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Help please Iekika is 3/2m tall, which is 4/5 as tall as Shanika. What does 3/2 divided by 4/5 represent in this situation?
Choose 1 answer:
(A) Shanika's height
(B) 4/5 of lekika's height
(C) lekika's height
(D) 3/2 of Shanika's height
Answer:shanikas height
Step-by-step explanation:
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 11 people, while each carton
of clothing will help 4 people. Each 20-cubic-foot box of food weighs 40 pounds and each 5-cubic-foot box of clothing
weighs 20 pounds. The commercial carriers transporting food and clothing are bound by the following constraints:
The total weight per carrier cannot exceed 23,000 pounds.
- The total volume must be no more than 9000 cubic feet.
Use this information to answer the following questions.
...
Through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.
It is given to us that -
Each carton of food will feed 11 people
Each carton of clothing will help 4 people
Each 20-cubic-foot box of food weighs 40 pounds
Each 5-cubic-foot box of clothing weighs 20 pounds
The total weight per carrier cannot exceed 23,000 pounds
The total volume must be no more than 9000 cubic feet
We have to find out the number of cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped.
Let us say that -
The number of cartons of food = x
The number of cartons of clothing = y
According to the given information, the constraints on weight and size can be represented as -
Constraints on weight:
[tex]40x+20y\leq 23000\\= > 20y\leq 23000-40x\\= > 20y\leq -40x+23000\\= > y\leq -2x+1150[/tex]------ (1)
Constraints on size:
[tex]20x+5y\leq 9000\\= > 5y\leq 9000-20x\\= > 5y\leq -20x+9000\\= > y\leq -4x+1800[/tex]----- (2)
We also know that
[tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]
The equation for the help that will be provided with each carton of food and clothing can be represented as -
[tex]11x+4y[/tex] ---- (3)
From equation (1), for weight graph, we have
[tex]y\leq -2x+1150[/tex]
For [tex]x=0[/tex], [tex]y\leq 1150[/tex]
For [tex]y=0, x\leq 575[/tex]
From equation (2), for size graph, we have
[tex]y\leq -4x+1800[/tex]
For [tex]x=0, y\leq 1800[/tex]
For [tex]y=0, x\leq 450[/tex]
For (0,1150), the equation (3) becomes
[tex]11x+4y[/tex]
[tex]= 11*0+4*1150\\= 4600[/tex]
For (360, 550), the equation (3) becomes
[tex]11x+4y\\= 11*360 + 4*550\\= 6160[/tex]
For (450,0), the equation (3) becomes
[tex]11x+4y\\= 11*450 + 4*0\\= 4950[/tex]
Thus, through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.
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what is the common denominator of 5, 12, 3 , 8
Answer:
i think the denominator of 5,12,3,8, is 24
wich car take 9 gallons of gas and drives 252 miles
The car which covers 28 miles on 1 gallon of gas that car will take 9 gallons of gas and drives 252 miles.
We know that the relation between distance, speed, and time is given by:
distance = speed * time
speed = distance / time
We are given;
Distance covered by the car = 252 miles
Gas used to cover 252 miles = 9 gallons
We will solve the given problem using the unitary method.
Since for 9 gallons of gas, the car covered a distance of 252 miles.
So, for 1 gallon of gas, the car covered a distance of 252 / 9 miles = 28 miles.
So, the car will drive 28 miles per gallon.
Thus, a car which covers 28 miles on 1 gallon of gas that car will take 9 gallons of gas and drives 252 miles.
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Please help I was sick and missed out on class.Thank you
Answer:
-1/2
Step-by-step explanation:
(-1-(-5)/(1-9)
(-1 + 5)/-8
4/-8
- 1/2
To calculate the distance between two points, we have to:
We have that the points are: (x₁ = 9, y₁ = -5) and (x₂ = 1,y₂ = -1). To calculate the slope, we apply the following formula:
[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]
Substitute data into the formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{-1-(-5) }{1-9 }=\dfrac{4}{-8}=-0.5000 }}[/tex]
Slope of the line that passes through the points (9,-5) and (1,-1) is 4/-8.To learn at:https://brainly.com/question/29402342To learn at:https://brainly.com/question/28865634To learn at:https://brainly.com/question/28121859To learn at:https://brainly.com/question/17004654To learn at:https://brainly.com/question/28922474To learn at:https://brainly.com/question/25243069Please provide as much explanation as you can! TYSM
a) This is a discrete probability distribution because the sum of the probabilities is of 1 and each probability is positive.
b) The distribution is represented by Graph A.
c) The mean is of: 1.559.
d) The standard deviation is of: 1.4
e) The probability that a student is involved in three activities is of 0.151.
f) The probability that a student is involved in three or four activities is of 0.28.
What is the probability distribution?From the table, the distribution is presented as follows:
P(X = 0) = 0.332.P(X = 1) = 0.186.P(X = 2) = 0.202.P(X = 3) = 0.151.P(X = 4) = 0.129.The sum of these probabilities is of:
0.332 + 0.186 + 0.202 + 0.151 + 0.129 = 1.
Since the sum is of one and none of the probabilities is negative, this is a valid discrete distribution shown by Graph A, as it associates each valeu of the input with it's respective probability.
The mean of the distribution is the sum of each outcome multiplied by it's probability, hence:
E(X) = 0 x 0.332 + 1 x 0.186 + 2 x 0.202 + 3 x 0.151 + 4 x 0.129 = 1.559.
The standard deviation is the square root of the sum of the differences squared between each outcome and the mean, multiplied by it's probability, hence:
S(X) = sqrt((0-1.559)² x 0.332 + (1-1.559)² x 0.186 + (2-1.559)² x 0.202 + (3-1.559)² x 0.151 + (4-1.559)² x 0.129) = 1.4.
The probabilities are given as follows:
Three activities: P(X = 3) = 0.151.Three or four activities: P(X = 3) + P(X = 4) = 0.151 + 0.129 = 0.28.A similar problem, also featuring a discrete distribution, is presented at brainly.com/question/27899440
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Avery is designing a large rectangular sign. They want the sign to have an area of 2 m² and a width of 4/5m.
How tall should the sign be?
The rectangular design should be 2.5 m tall.
What is area of rectangle?
A flat surface of a specific shape can be thought of as the area it occupies in space. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is known as the area of a rectangle. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes. To determine the area that these items occupy, use the formula for a rectangle's area.
Here area of rectangle = 2[tex]m^2[/tex]
And width of the rectangle w= 4/5 m .
Using area of rectangle formula ,
=> A = h*w
=> 2= h*4/5
=> h = 10/4 = 2.5 m.
Therefore the rectangular design would be 2.5 m tall.
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Supervisor: "If you switch to the late shift, you will receive a 10% wage increase."
Employee: "Great! I make $12.00 per hour now, and that extra 10% would put me at __________ per hour."
Employee: "Great! I make $12.00 per hour now, and that extra 10% would put me at $13. 20 per hour."
How to find the new wage rate?The supervisor says that should an employee work the late shift, they would be paid 10% more than they are paid now.
This increase in the wage rate is:
= Current wage rate x Increase for late shift
= 12 x 10 %
= $1. 20
The new wage rate for the employee would therefore be:
= Wage rate per hour + Extra if late shift is worked
= 12 + 1. 20
= $13. 20
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Make d the subject of this formula:
d+x=V
Answer:
d = V- x
Step-by-step explanation:
To make 'd' as the subject, isolate 'd'.
To isolate d, subtract 'x' from both sides,
d +x = V
d + x - x = V - x
d = V - x
The formula using d as the subject is d = V-x.
The formula is d+x = V
The subject of the formula is nothing but a variable that is being worked out. Here, we have to convert the given formula to describe d as the subject.
According to the property of equality, the two sides of the equation should be balanced. To solve the given expression, we use the subtraction property of equality.
The subtraction property of equality refers to balancing an equation by using the subtraction operation on both sides of the equation.
Therefore, subtract x on both sides of the given formula,
[tex]\begin{aligned}d+x&=V\\d+x-x&=V-x\\d&=V-x\end{aligned}[/tex]
Therefore, the final answer is d=V-x.
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Last year, Lisa opened an investment account with $6600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year?
Increase in amount:
Year-end amount:
Answer: $429
Step-by-step explanation:
$6600 + 6.5% = $7029
$7029 - $6600 =$ 429
solve the file please
By taking the difference between the final distance and the initial distance we will see that the change in the distance is -23/24 feet.
How to get the change in the distance?
First, we should define the system we will use.
Notice that "distance" is defined positive, then when you are behind your friend and when you are ahead, the distances are in both cases positive.
First, you are at (4 + 5/8) feet from your friend, and then you are at (3 + 2/3) feet from your friend.
The difference is given by the final distance minus the initial distance, so we have:
d = (3 + 2/3) ft - (4 + 5/8) ft
We can decompose the mixed numbers into wholes and fractions, so we get:
d = (3 + 2/3)ft - (4 + 5/8) ft
d = (3 - 4)ft + (2/3 - 5/8)ft
d = (-1)ft + (16/24 - 15/24)ft
d = -1 ft + 1/24ft = -23/24ft
So the change in the distance between the end and the beginning is:
d = -23/24ft
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