By solving for the number of employees, there were 70 employees at the party.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. An equation typically consists of two sides, with an equals sign (=) in between.
what is linear equation?A linear equation is an equation in which the highest power of the variable is 1. In other words, a linear equation is an equation that can be written in the form:
ax + b = 0
where a and b are constants and x is the variable.
To find out how many employees attended the party, you can set up the following equation:
Number of employees * $30 per employee = $1000 for space + $850 for food + $250 for decorations
You can then solve for the number of employees by dividing both sides of the equation by $30 per employee:
Number of employees = ($1000 for space + $850 for food + $250 for decorations) / $30 per employee
= $2100 / $30
= 70 employees
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Eliot and William go running. Eliot ran for 8 mile, and William ran for 12 mile. Eliot finihed hi run in 40 fewer minute than William. If they run at the ame peed, for how long did William run?
William ran for 48 minutes since Eliot ran for 8 miles in 40 fewer minutes than William. They were running at the same speed.
Eliot and William both went running and ran for 8 miles and 12 miles respectively. Eliot finished his 8 mile run in 40 fewer minutes than William. This means that if the two of them were running at the same speed, it would take William 40 minutes longer than Eliot to finish his 12 mile run. To calculate how long William ran for, we can add 40 minutes to the time it took Eliot to run 8 miles. Since Eliot ran 8 miles in 40 fewer minutes than William, this means that Eliot ran 8 miles in the amount of time that William ran 12 miles. The total time William ran for is therefore 8 miles plus 40 minutes, which is 48 minutes.
Eliot: 8 miles ÷ 40 minutes fewer
= 0.2 miles/minute
William: 12 miles ÷ (0.2 miles/minute x 40 minutes)
= 48 minutes
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Please help me answer this question
Answer:
Divide 5 to both side.
Step-by-step explanation:
Original Equation:
[tex]5(x-3)=5[/tex]
2nd Equation:
[tex](x-3)=1[/tex]
Single Steps:
Divide 5 to both side on Original Equation to get 2nd Equation.
it takes 10 seconds to fill a one-quart jar with water from your kitchen faucet. what is the flow rate, in gallons per minute, from the faucet? group of answer choices 40 10 1.5 4
1.5 litres of water are released from the faucet per minute.
It is given to us that -
There is a one quart jar
Water from the kitchen faucet fills the 1-quart jar in 10 seconds.
We need to ascertain the faucet's flow rate in gallons per minute.
We know that -
1 quart = 0.25 gallon ---- (1)
We also know that -
1 minute = 60 seconds
=> 60 seconds = 1 minute
=> 10 seconds = 10/60 = 0.16 minutes ----- (2)
Now, the flow rate can be calculated as -
Flow rate = Amount of water filled/Time taken ----- (3)
Substituting the values from equation (1) and (2) in equation (3), we have -
Flow rate = Amount of water filled/Time taken
=> Flow rate = 1 quart water/10 seconds
=> Flow rate = 0.25 gallons/0.16 minutes
=> Flow rate = 1.5 gallons per minute
Therefore, the flow rate of water from the faucet is 1.5 gallons per minute.
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Use the following table of 2010 exchange rates to solve the problem.
You wish to exchange 100 British pounds for Japanese yen. How many yen do you receive?
Answer:
aproximantly 131.1701yen
Step-by-step explanation:
Answer:
15430 Japanese yen
Step-by-step explanation:
To find out how many Japanese yen you receive for 100 British pounds, we need to find the exchange rate between British pounds and Japanese yen in the table. From the table, we can see that the exchange rate between British pounds and Japanese yen is 154.43. Therefore, if you exchange 100 British pounds, you will receive 100 * 154.43 = 15430 Japanese yen.
The length of a rectangle i meter longer than the width. If the area i quare meter, find the rectangle' dimenion. Round to the nearet tenth of a meter. The width i _____ meter
enter your repone here meter
The dimensions of the rectangle are, length = 5 inch and width = 6 inch.
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.
Let, the length of a rectangle is 7 inches less than twice the width, w, of the rectangle.
Suppose,
width = w = x, then,
length = l = 2x - 7
Since the area of the rectangle is 30 square inches.
We know that.
Area of rectangle = length x width
30 = (2x - 7) x (x)
30 = 2x^2 - 7x
2x^2 - 7x - 30 = 0
2x^2 - 12x + 5x - 30 = 0
2x(x - 6) + 5(x - 6) = 0
(2x + 5)(x - 6) = 0
⇒ 2x + 5 = 0, x - 6 = 0
⇒ x = -5/2, x = 6
Since length is not negative.
Therefore, w = 6.
So, l = 2(6) - 7 = 12 - 7 = 5
Hence, the length is 5 inches and the width is 6 inches.
complete question
The length of a rectangle i 7 inche le than twice the width, w, of the rectangle. Find the dimenion if the area i 30 quare meter
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the house trevor's family lives in has 6 people (including trevor) and 333 bathrooms. in the past month, each person showered for an average of 480480480 minutes and used an average 727272 liters of shower water (over the entire month). water costs 0.200.200, point, 20 dollars per liter. how much money did trevor's family spend, in total, on shower water in the past month?
The amount Trevor's family spent, in total, on shower water in the past month = 0.03 dollars per minute
In this question we have been given there are 6 people in Trevor's house.
There are 3 bathrooms in the house.
Each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month)
We need to find the amount of money Trevor's family spent, in total, on shower water in the past month.
By unitary method,
72 * 6 = 432 liters of shower water used by the entire family over the month
Each liter costs $0.2
so by unitary method,
the total amount paid:
A = 432 * 0.2
= 86.4 dollars
Each person showered for an average of 480 minutes.
So, total minutes would be 6x480 = 2880 minutes.
So, the required amount would be,
86.4/2880 = 0.03 dollars per minute
Therefore, Trevor's family paid $0.03 per minute on shower water.
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If a credit card has an average daily balance of $1250 and the
annual interest rate is 18%, what will the total bill for the month be?
If a credit card has an average daily balance of $1250 and the annual interest rate is 18%, the total bill for the month will be $1,268.75.
What Is Average Daily Balance?The average daily balance is the quotient resulting from the summation of the card's daily balances and the division by the number of days in the billing cycle.
The finance charge, which represents the interest and other fees for the use of the credit card, is computed by applying the monthly percentage rate (MPR) on the average daily balance.
Average daily balance = $1,250
Annual interest rate = 18%
Monthly percentage rate = 1.5% (18% ÷ 12)
Finance charge = $18.75 ($1,250 x 1.5%)
Total bill for the month = Average daily balance + Finance charge
= $1,268.75 ($1,250 + $18.75)
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Solve each equation by taking the square root.
7x2 +32 = -10
x= {___, ___}
Answer: x=(10-sqrt(128))/14=(5-4sqrt(2))/7=-0.094
Step-by-step explanation: (7x2 - 10x) - 1 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 7x2-10x-1
The first term is, 7x2 its coefficient is 7 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 7 • -1 = -7
Step-2 : Find two factors of -7 whose sum equals the coefficient of the middle term, which is -10 .
-7 + 1 = -6
-1 + 7 = 6
Jack brought a lunch box for $8 and 7 forks. He spent a total of $105. How much did each fork cost?
Answer:
13.85$
Step-by-step explanation:
105$-8$=97$
97$/7$=13.85$
Answer: About $13.86
Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:
105 - 8 = 97
So, now since he bought 7 forks, we need to divide 7 by 97. So:
97 / 7 = 13.857142857142858
So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:
13.86(7) + 8
97.02 + 8
= 105.02
This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)
how many terms in 3x ?
Answer:
3x is a single term
Step-by-step explanation:
The "3" is a coefficient. The "x" is the variable. is also a single term.
hope this helps
a bicycle wheel has a diameter of 24 inches. there are 32 spokes evenly distributed around the wheel. how far apart is each spoke?
The diameter of a bicycle wheel is 24 inches. Around the wheel, there are 32 spokes that are spaced 48 meters away from one another.
The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d . The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.
The diameter of the circle is the measurement at issue. The distance between the circle's center and its periphery can be measured.
far apart is each spoke (distance) = radius = diameter / 2
distance = 24/2
distance = 12
Since a wheel has 4 parts. so, 12*4 = 48 m
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brandon has two summer jobs. during the week he works in the grocery store, and on the weekend he works at a nursery. he gets paid $15 per hour to work at the grocery store and $20 per hour to work at the nursery. how many total hours does he work if he does 14 hours at the grocery store and 13 hours at the nursery? how many total hours does he work if he does gg hours at the grocery store and nn hours at the nursery?
If Brandon does 14 hours at the grocery store and 13 hours at the nursery the the total working hours = 96 hours
And if Brandon does g hours at the grocery store and n hours at the nursery then total working hours = (5g + 2n) hours
In this question we ahve been given Brandon has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery.
He gets paid $15 per hour to work at the grocery store and $20 per hour to work at the nursery.
We need to find the total working hours if he does 14 hours at the grocery store and 13 hours at the nursery.
Also, we need to find total working hours if he does g hours at the grocery store and n hours at the nursery.
We know that the number of week days = 5 and the number of weekend days = 2
if he does 14 hours at the grocery store during 5 days, then by unitary method he will work for 14 * 5 = 70 hours
Similarly, if he does13 hours at the nursery for 2 days, this means by unitary method he is working for 13 * 2 = 26 hours
So, the total number hours of working during a week,
70 + 26 = 96 hours
Let he does g hours at the grocery store
During week days total working hours would be,
= number of weekdays * number of working hours
= 5 * g
= 5g
and n hours at the nursery.
= number of weekend days * number of working hours
= 2n
so, the total hours would be 5g + 2n
Therefore, a) the total hours does he work if he does 14 hours at the grocery store and 13 hours at the nursery = 96 hours
b) the total hours does he work if he does gg hours at the grocery store and nn hours at the nursery = (5g + 2n) hours
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answer for bottom one
Answer:
Step-by-step explanation:
good luck lol
TRUE/FALSE. to cut the standard error of the mean in half, the sample size must be increased by a factor of
To cut the standard error of the mean in half, the sample size must be increased by a factor of four.
Therefore, the answer is False.
The formula to determine the standard error of the mean is
SE = SD/ √n
where SD is the standard deviation
n is the sample size
Therefore the standard error of the mean is inversely proportional to the square root of the sample size. Thus in order to decrease the standard error of the mean to half, we should increase the sample size by a factor of 4.
SE' = SD/ √(4n)
SE' = SD/ 2n
SE' = SE/ 2
--The question is incomplete, answering to the question below--
"To cut the standard error of the mean in half, the sample size must be increased by a factor of two. True or False."
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the smaller triangle has a perimeter of 31 ft and an area of 40 ft2. if the larger triangle has a perimeter of 62 ft, what will it's area be?
If the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.
We know that the perimeter of the smaller triangle is 31 feet, which means that the sum of the lengths of its three sides is 31 feet. We also know that the area of the smaller triangle is 40 square feet. We can set up the following equation to calculate the length of each side of the smaller triangle:
Side 1 + Side 2 + Side 3 = 31
We can then use the formula for the area of a triangle, A = bh/2, to calculate the length of the base and height of the smaller triangle. Since we know the area is 40 square feet, we can set up the following equation:
40 = (b)(h)/2
We can then solve this equation for b and h. We know that b + h = 31, so we can set up the following equation and solve for h:
h = 31 - b
Now that we know b and h for the smaller triangle, we can use the same formula to calculate the area of the larger triangle. Since we know that the perimeter of the larger triangle is 62 feet, we can set up the following equation to calculate the length of each side of the larger triangle:
Side 1 + Side 2 + Side 3 = 62
We can then use the following formula to calculate the area of the larger triangle:
A = (b)(h)/2
We know that b + h = 62, so we can set up the following equation and solve for h:
h = 62 - b
Now that we know b and h for the larger triangle, we can plug those values into the area formula and calculate the area of the larger triangle. The area of the larger triangle is 120 square feet. Therefore, if the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.
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Solve by using elimination
x + 3y = 12
-5x + +y = -12
(Please explain how to get the answer if possible.)
Step-by-step explanation:
what equations do we really have here ?
there seem to be typos in the equations.
I assume you truly have
x + 3y = 12
-5x + y = -12
now, elimination means that we multiply the equations (both sides to keep the equations in their information unchanged) by applying factors and then add the resulting equations.
the result should have "eliminated" one of the variables, so that we can solve for the remaining variable.
and then we use that result and one of the original equations to solve for the second variable.
in our case I suggest we try to eliminate x first.
so, we multiply the first equation by 5. the second equation can stay as it is.
and then we add both :
5x + 15y = 60
-5x + y = -12
-----------------------
0 16y = 48
y = 48/16 = 3
using e.g. the original first equation :
x + 3y = 12
we put in the already calculated value for y (3) and solve for x :
x + 3×3 = 12
x + 9 = 12
x = 12 - 9 = 3
x = 3
y = 3
you understand the principle ? please let me know, if you have further questions.
if your actual equations are different to my assumptions, you need to apply this in the same way as I showed you here to whatever the real equations are.
Answer:
(x, y) = (3, 3)
Step-by-step explanation:
You want to solve by elimination the system of equations ...
x +3y = 12-5x +y = -12EliminationThe point of the elimination method is to combine the equations in a way that causes the coefficient of one of the variables to become zero. In general, this can be accomplished by multiplying each equation by the coefficient of the chosen variable in the other equation, then subtracting the results one from the other.
Considering the x-coefficients, we can multiply the first equation by -5, the second by 1 and subtract the first product from the second. This eliminates the x-variable.
1(-5x +y) -(-5)(x +3y) = 1(-12) -(-5)(12)
-5x +y +5x +15y = -12 +60 . . . . . . . . . . eliminate parentheses
16y = 48 . . . . . . . . . . . . . . . . . . . collect terms
y = 3 . . . . . . . . . . . . . . . . divide by 16
Complete the solutionNow, we need to find x. We can do this by substituting for y in either equation. We choose to use the first equation:
x + 3(3) = 12
x = 3 . . . . . . . . . . subtract 9
The solution to the system of equations is (x, y) = (3, 3).
__
Additional comment
We chose to explain the elimination in terms of subtraction. That subtraction can be done in either order:
-5(equation 1) -1(equation 2)
or
1(equation 2) -(-5)(equation 1)
We chose the latter order so the coefficient of y would end up positive. We find fewer mistakes are made when the signs are positive.
Your curriculum materials may explain the elimination process in terms of addition. You may have noticed that subtracting -5 times the first equation is the same as adding 5 times the first equation. When you do this using addition, one of the multiplier coefficients needs to be the opposite of the coefficient of the variable in the other equation.
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Calculate the force required to accelerate a 0.50kg ball at 2000m/s².
The force required to accelerate a 0.50kg ball at 2000m/s² is 100 N
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Motion is described in physics as a change in position with respect to time. Motion, to put it simply, is the movement of a body. Motion is typically characterized as:
Variation in speed
Change of course
In the given problem the force required to change the body's state is calculated by the formula
F = mass * acceleration
= 0.5 * 200
= 100 N
the force is 100N
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2√5 times √8 plus 2√5 times √2 divide by 2. Any surds in the answer in their simplest form.
Answer:
The area of the compound shape is 5√10 cm²
Step-by-step explanation:
In the given shape, there is a rectangle and a right angle triangle.
i.e.,
Compund shape = Rectangle + Triangle
So,
Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle
For Rectangle;Length (l) = 2√5 cmWidth (w) = √8cm = 2√2 cmFormula;
A = l × wA = 2√5 × 2√2 cm
A = 4√10 cm²
For Triangle;Base (b) = 2 cmHeight (h) = 2√5 cmFormula;
A = ½ × base × heightA = ½ × √2 × 2√5 cm
A = 1 × √2 × √5 cm
A = √10 cm²
Now,
Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle
A = 4√10 cm² + √10 cm²
A = 5√10 cm²
Thus, The area of the compound shape is 5√10 cm²
please help me with this
Answer:
Because when you divide 100 by 4 and 50 by 2, you will get the same value
Hassan rings up an item that costs
$6,400. After sales tax, the total is
$6,848. What is the sales tax
percentage?
Answer: 7%
Step-by-step explanation:
Take 6848 divided by 6400, then times 100 = 107%
Then take 107% - 100% = 7%
The sales tax percentage is 7%
A boat, sailing downstream, has traveled the same distance in 4.5 hours as it has traveled upstream in 5 hours. Calculate the speed of the boat if the speed of the current is 3 km/h.
EQUATION REQUIRED!!!
The speed of the boat in still water is - 37 km/h
let, the distance be 'x' km/hr.
And the speed of the boat in still water is 'S' km/hr.
According to the question,
In downstream,
x = ( S + 3 ) * 4.5 ..........(1)
Similarly,
In Upstream,
x = ( S - 3)* 5 ........... (2)
From equations (1) and (2),
( S + 3 ) * 4.5 = (S - 3) * 5
or, 4.5 S + 13.5 = 5S - 15
or, 5S - 4.5S = 15 + 13.5
or, 0.5S = 18.5
divide both sides by 0.5,
0r, S = 37
So, the speed of the boat in still water is - 37 km/h
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Write 0.302 repeating as a fraction. show your work.
he area of a square is 121 ft2. what is the length of a diagonal of the square? round to the nearest foot.
What are the domain and the range of this graph?
a) The domain is {x∈R|x≤0} and the range is {y∈R|y≤0}.
b) The domain is {x∈R|x≤0} and the range is {y∈R|y≥0}.
c) The domain is {x|x∈R} and the range is {y∈R|y≤0}.
d) The domain is {x|x∈R} and the range is {y∈R|y≥0}.
Answer:
d) The domain is {x|x∈R} and the range is {y∈R|y≥0}--------------------------------------
Given is the graph of an absolute value function.
It has no domain restrictions, so x can be any real number.
There is a restriction on its range, it has a minimum at y = 0 and the rest of the values are positive real numbers.
It is correctly described in option d).
Cara earn a bae pay of $1,800 per month at a car dealerhip plu a commiion of 6% of her ale. What are Cara' total earning in a month in which he ale $40,000 worth of merchandie?
Using the concept of percentages the total earning of Cara can be found to be $4200.
What are percentages?Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.
How to solve percentages?Cara's earning = commission + basic salary
basic salary = $1800 (this is constant)
commission = 6% of $40000
= (6/100)*40000
= $2400
Cara's earning = 1800 + 2400
Hence, her earning is $4200
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Find the values of x and y.
1) x = 19.6; y = 12.0
2) x = 23.0; y = 12.0
3) x = 12.0; y = 19.6
4) x = 12.0; y = 23.0
x=12.0; y=19.6
Option 4 is the right answer.
What are the properties of tangent of the circle?
A tangent is correctly formed only if touches the circle at only one point. A tangent never passes through a circle, that is, it never crosses the circle while entering its interior. A tangent is also not known for intersecting the circle at the two different points.
Since, in a circle the radii are equal.
So, OA=OB=x=12
Tangent to a circle is the line that touches the circle at only one point.
The length of tangents from an external point to a circle are equal.
By the theorem,
If two tangents are drawn from an external point of the circle, then they are of equal lengths.
So, AC =BC (by the theorem)
AC and BC look to be tangents- tangents to a circle from a point are congruent.
So, AC is congruent to BC.
Thus, AC=BC=y=19.6
Hence, x=12.0 and y=19.6
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which of the following describes the derivative function f'(x) of a quadratic function f(x)
The first derivative of quadratic function is obtained as a linear function.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = lim h --> 0 (f(x + h) - f(x)) /(x + h - x).
It can also be described as the slope of the tangent of function at a given point.
The general form of a quadratic function is as below,
f(x) = ax² + bx + c
Its first derivative can be written as below,
f'(x) = 2ax + b
The degree of the function f'(x) is 1.
Thus, it is a linear function.
Hence, the function to describe the derivative of quadratic function is linear.
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2
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
1
2
3
4
5
In step 2, the
In step 4, the
3x
©2022 Edmentum. All rights reserved.
3x
-
Statement
- 10 -16
=
10+ 10 = -16 10
3x = -6
-6
33
x= -2
Use the table to complete each statement.
=
property of equality was a
s appled.
property of equality was applied.
In step 2: the additive property of equality was applied.
In step 4: the division property of equality was applied.
What are the properties to solve equation?
The properties of the relationship of equality, reflexivity, symmetry, transitivity, and the properties of operations are employed to solve an equation.
These characteristics hold true in both propositional language and arithmetic.
The following can be used to sum up this: An equality is still valid if the exact same operation is carried out on both sides of the equality.
Given that:
Step 1: 3x - 10 = -16
The additive inverse of -10 is +10
Step 2: 3x - 10 + 10 = -16 + 10 [Additive inverse]
Step 3: 3x = -6
Step 4: 3x/3 = -6/3 [Division property]
Step 5: x = -2
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Identify the angle shown
A. Alternate interior angles
B. Alternate exterior angles
C. Corresponding angles
D. Same side interior angles
Help!!!
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are angles opposite outside of each other and have the same degree. So the answer is B
Two pieces of metal measure one and one third yards and five sixths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed?
Answer: 6 1/2. yards
Step-by-step explanation: you have to add 1 1/3 + 5/6, which is 2 1/6. 2 1/6x3=6 1/2. then thats your answer