The average rate of flow of gasoline into the gas tank is 2.2 gallons per minute.
What is the average?The average is the mean value of the data set values.
The mean is computed by dividing the total value by the number of items.
For the average rate of flow, divide the total gallons of gasoline filled by the driver, 8.8 gallons, by the number of minutes used in filling the tank.
In this case, the average rate of flow shows the speed that the driver used to fill the car with gasoline.
Starting time = 3:40 P.M.
Ending time = 3:44 P.M.
The difference in filling time = 4 minutes (3:44 - 3:40)
Total number of gallons of gasoline filled = 8.8 gallons
Average rate of flow of the gasoline = 2.2 gallons per minute (8.8/4)
Thus, at an average rate of 2.2 gallons per minute, the driver was able to fill his gas tank in 4 minutes.
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3. Harry also paid $14.50 for three T-shirts at the sale. The sale price saved Harry 30% of the
original price of the three T-shirts.
What is the original total price of his three T-shirts?
Show your calculations.
The cost price of three T-shirts is $11.2. Since, the cost price is less than the perchage price hence it is profit.
What is profit and loss?
When perchaging price is less than the original price then it is known as profit. But if it is more than the original price than it is known as loss.
Consider the original price of the three T-shirts is [tex]x[/tex]. Now, the percent saving is given by the following expression:
[tex]\textnormal{Percent saving}=\frac{\textnormal{Total amount without saving-Total amount after saving}}{\textnormal{Total amount without saving}} \times 100\\30=\frac{\$14.50-x}{x}\times 100\\\frac{30x}{100}=14.5-x\\0.3x=14.5-x\\0.3x+x=14.5\\1.3x=14.5\\x=\frac{14.5}{1.3}\\x=11.2[/tex]
Hence, the price of three T-shirts is $11.2.
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A new jewelery store opened recently. There are several sales associate positions that pay an hourly rate of
$11.00 plus a three percent commission of the total weekly sales. Based on an expected weekly average of
$2600 of sales, write an equation that gives the gross weekly pay (p) if you work a hours per week.
The equation that gives the gross weekly pay (p) if you work a hours per week is 11h+78.
what is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.
Here,
2600*3/100=26*3
=78
p=11h+78
The algorithm for calculating gross weekly pay (p) if you work a number of hours per week is 11h+78.
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Alexis biked a distance of 6 miles each day for 3 days. Then, she biked 7 miles each day for the next
5 days. What was the total distance in miles that Alexis biked during these 8 days?
O 35 miles
o 40 miles
o 19 miles
O 54 miles
The Anwser to this question
On the first of January, Jed had £48 in his bank account and Esther had £180 in her bank account. From then on, at the end of each month Jed put £40 into his account and Esther put £34 into her account. After how many months did they have the same amount of money in their accounts?
After 22 months, Jed and Esther have the same amount of money in their accounts.
How to balance the equations?Simplify both sides of the equation as much as possible using the order of operations (distribute, combine like terms, etc.)
Given: Jed has £48 in his bank account and from then on, at the end of each month he put £40 into his account and
Esther had £180 in her bank account and from then on, at the end of each month she put £34 into her account.
Now, let us consider after 't' months they have same amount of money in their accounts
⇒ £48 + £40t = £180 + £34t
⇒ £40t - £34t = £180 - £48
⇒ 6t = 132
⇒ t = 22.
Therefore, after 22 months, Jed and Esther have the same amount of money in their accounts.
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The zeros of the expression j2 - 4j-21 are the solutions of the equation
j²-4j-21.
j² - 4j-21 = 0
(+3_) (+5) = 0
j+ 3 = or j+ = -3
Set the expression equal to 0.
Write the equation in factored form
Use Zero Product Property.
j=7 or j = N
Solve.
The zeros of the expression j2 - 4j - 21 are 2 and .
The solutions of the quadratic equation is j = -3 and j = 7 .
In the question ,
it is given that the quadratic equation is j² - 4j - 21 = 0,
we need to find the solution of the given equation .
to find the solution , we use splitting the middle term method .
j² - 4j - 21 = 0
j² - 7j + 3j - 21 = 0 .... splitting the middle term -4j = - 7j + 3j
taking j common form first wo terms and 3 common from last two terms ,
we get
j(j - 7) +3(j - 7) = 0
(j + 3)(j - 7) = 0
j + 3 = 0 and j - 7 = 0
j = -3 and j = 7
Therefore , The solutions of the quadratic equation is j = -3 and j = 7 .
The given question is incomplete , the complete question is
Find the solutions of the quadratic equation j² - 4j - 21 = 0 ?
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¿De cuántas formas puede un juez otorgar el
primero, segundo y tercer premio en un
concurso que tiene ocho concursantes?
Hay 336 formas diferentes en las que se pueden entregar los 3 premios.
¿De cuantas formas se pueden otorgar los premios?
Sabemos que hay 8 participantes y de estos se elegiran a 3 para darles 3 premios diferentes.
Para el primer premio, hay 8 posibles concursantes que lo pueden recibir.Para el segundo premio, hay 7 concursantes que lo pueden recibir (hay uno menos por que uno ya recibio el primer premio)Para el tercer premio, hay 6 concursantes que lo pueden recibir.El numero total de combinaciones es lo que obtenemos cuando tomamos el producto entre los números de opciones:
C = 8*7*6 = 336
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a jet flies 600 kilometers in 3/4 pf an hour. How far can this jet fly in 1/2
Answer:
If you divide 600/ 45 mins you get the kilometers per minute which is 13.33. Then you multiply 13.33 times 30 mins and you get 399.9 or 400 kilometers
Step-by-step explanation:
No links help please how are triangles similar
Both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
As given in the question,
For the given diagram of the two triangles,
To prove : Both the triangles are similar to each other.
Side length of the corresponding sides of both the triangles :
Altitude of :
Small triangle : 6 - 3 = 3 units
Big triangle : 3 - (-3) = 6 units
Base :
Small triangle : -2 + 4 = 2 units
Big triangle : 2 - (-2) = 4 units
Corresponding sides are in proportion:
( 3/6) = 1/2 = ( 2 / 4)
And the included between the two sides is equal to 90° ( right angle ).
By SAS ( Side angle Side ) theorem,
Both the triangles are similar to each other.
Now slope of :
Small triangle is equal to,
Consider two end points ( -4, 6) and ( -2 , 3)
Slope = ( 3 -6)/ (-2 + 4)
= -3/2
Big triangle is equal to,
Consider two end points ( -2, 3) and ( 2 , -3)
Slope = ( -3 -3)/ ( 2 + 2)
= -6 /4
= -3/2
Therefore, both the triangles of the given figure are similar to each other by SAS
( Side angle Side ) the property of corresponding sides are in proportion and included angle of both the triangles is right angle.
Slope of the both the triangles is (-3/2) .
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Consider the equation and the following ordered pairs: (1,y) and (x,3).
6x+1.2y=−2.4
Step 1 of 2: Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Pair (1,y)
[tex]6(1)+1.2y=-2.4 \\ \\ 1.2y=-8.4 \\ \\ y=-7[/tex]
Pair (x,3)
[tex]6x+1.2(3)=-2.4 \\ \\ 6x=-6 \\ \\ x=-1[/tex]
How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times (in minutes): 6.1, 6.9, 6.9, 6.7, 6.8, and 6.4?
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
What are Sample Mean?
The average value of the provided sample data is determined using the sample mean formula. Instead of expressing them using actual terms, it is occasionally essential to calculate the sample term average. The ratio of the sum of terms to the total number of terms can be used to describe the sample mean formula. The center of the data is measured by the sample mean. The sample mean is used to estimate the mean of any population. Many times, without surveying the entire population, we must make educated guesses about how the population as a whole is behaving or what variables are affecting the population as a whole. In these situations, the sample mean is helpful. The sample mean is the average value obtained from the sample. The variance and subsequently the standard deviation are determined using the sample mean that was so obtained.
For the given data,
Standard Deviation = 0.3204
Mean =(6.1+6.9+6.9+6.7+6.8+6.4)/6=6.633
The margin of error = 2% of mean
Z score for 95.5 confidence interval = 1.96
Number of cycles, sqrt(n)
= (1.96× 0.3204) / (6.633×0.02)
= 4.7337
n = 22.408
Rounding to the next integer, then work cycles = 23
Hence,
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
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How do you graph it?
Answer:
See picture below
Step-by-step explanation:
Desmos is a free graphing calculator.
x-y = 1 Subtract x from both sides
-y = -x + 1 Divide all the way through by -1
y = x - 1
These line are parallel because they have the same slope.
On the green line I highlightes tow points (0,4) and (3,7) . (0,4) tells us where the line crosses the y anxis. Thiis will be in the form (0,b) b stands for the y intercept. This graph is crossing the green line at 4. The slope is 1. The patern form the first point (0,4) is to move up one and move right one. This pattern continues throuhg point (3,7) and beyond.
The blue line in the slope intercept from is
y = x +1 . Its slope is the same as the first line. It is up one and one to the right and that pattern continues. This line cross the y axis at -1.
The headlights on a car are set so the light beam drops 2 in. for each 21 ft measured horizontally. If the headlights are mounted 36 in. above the ground, how far ahead of the car will they hit the ground?
The headlights of the car will hit the ground 378ft
Unitary Method:The unitary method is a numerical process that is used to calculate any value i.e., cost or speed, or any desired quantity. In this method, we will find the desired value for 1 unit so that we can find the value for multiple units.
Here we have
The headlights on a car are set to the light beam drops 2 in. for each 21 ft measured horizontally.
The headlights are mounted 36 in. above the ground
For 2-in - 21 ft measured horizontally
Then for 1 - in = 21/2 = 10.5 ft
then for 36 in = 36 × 10.5 = 378 ft
Therefore,
The headlights of the car will hit the ground 378ft
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Newton earns $195 for
working 15 hours as a radio host. How
much money does Newton earn in
3 hours?
Newton earns $39 for working 3 hours as a radio host.
What is meant by time and work?In terms of time and work, it refers to how long it takes a person or group of individuals to perform a task and how well each of them does it. A crucial concept that time and labour have in common with other arithmetic topics is the concept of proportionality. Efficiency is inversely proportional to time required while the amount of work is constant.
Efficiency serves as the proportionality constant, and work and time are directly proportional.
Given,
As a radio host, Newton puts in 15 hours and makes $195..
For a one hour the employee earns $13
So with this information we can put:
13×3=39
In 3 hours Newton earns $39 for working as a radio host.
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Linda is making curtains . She has 2 1/3 yards of material . She wants to make 3 curtains . She needs 8/9 yard for each curtain . Does she have enough material for 3 curtains?
======================================================
Use this formula
a & b/c = (a*c + b)/c
to convert from a mixed number to an improper fraction.
Let's use that formula to find the following
a & b/c = (a*c + b)/c
2 & 1/3 = (2*3+1)/3
2 & 1/3 = 7/3
She has 7/3 yards of material.
Linda wants to make 3 curtains. Each curtain needs 8/9 of a yard.
3*(8/9) = 24/9 = (8*3)/(3*3) = 8/3
Therefore, she needs 8/3 yards of material.
But this is a problem because she needs more material than what she has on hand. In other words, 8/3 > 7/3 since 8 > 7.
-----------
Another way to look at it:
7/3 = 2.333 yards is the approximate amount of fabric she has
8/3 = 2.667 approximately is the total amount of fabric she needs, which is clearly larger than the 2.333 yards she has.
Unfortunately Linda does not have enough fabric to make 3 curtains.
Question 7:
Several health insurance companies are bidding for an insurance contract. Of these companies, 3
are local, 3 have state-wide operations, and 6 have national operations. Only one company will
be awarded the contract. If each company is equally likely to win the contract, what is the probability
that the contract will be awarded to one of the companies with state-wide operations?
Note: For any final answer that has up to four decimal places, enter your answer without rounding the
number. For any answers with more than four decimal values, round your final answer to four decimal
places.
I
The probability of contract bring given to a state wide operation is 0.2500
What is probability?
The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that a press release is true. associate degree event's likelihood may be a range between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Main body:
Number of local insurance contract operations = 3
Number of state-wide operations = 3
Number of national wide operations = 6
Therefore total companies = 3+3+6
= 12
Probability of contract being given to state wide company = 3/12
P(state wide) = 0.2500
Hence the probability of the given case is 0.2500.
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Which fraction is greater of 8/400 or 8/10
Simply 9/24 fraction
Answer: [tex]\frac{3}{8}[/tex]
Step-by-step explanation: dividing the top and bottom of the fraction [tex]\frac{9}{24}[/tex]by 3 will give you the simplest form. Your welcome
Answer:
3/8
Step-by-step explanation:
The fraction 9/24 simplifies to 38. The way to arrive at this solution is to find the greatest common multiple for both the numerator and the denominator. In this case, the greatest common multiple is 3.
Hope that helps! Have amazing rest of your day! Brainliest welcome! :)
Can you solve the system of equation using substitution 5x + 2y = 7 4X +y =8
The solution of the given system of equations using substitution is x = 9/5 and y = -1.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equations,
5x + 2y = 7 and 4x +y =8
4x +y =8 → 4x = 8 - y
⇒ x = 2 - y/4
Substitute this x into the above,
5(2 - y/4) + 2y = 7
10 - 5/4 y + 2y = 7
10 + y(2 - 5/4) = 7
3y/4 = -3
y = -1
And, 5x + 2(-1) = 7
5x = 9
x = 9/5
Hence "The solution of the given system of equations using substitution is x = 9/5 and y = -1".
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Write y = 4x in function form
Can you please show the equation or rewrite the equation?
Which ordered pairs in the form (x, y) are solutions to the equation
4x−5y=24
Select each correct answer.
Responses
(1, −4)
Begin ordered pair 1 comma negative 4 end ordered pair
(−9, −12)
Begin ordered pair negative 9 comma negative 12 end ordered pair
(4, 8)
Begin ordered pair 4 comma 8 end ordered pair
(6, 0)
The solutions to the given linear equation are (1, -4), (-9, -12), and (6, 0)
Determining the solutions to a linear equationFrom the question, we are to determine the ordered pairs that are solutions to the given equation
The given equation is
4x - 5y = 24
To do this, we will check for the ordered pairs that satisfy the equation.
(1, -4)
Substitute x = 1 and y = -4
4x - 5y = 24
4(1) - 5(-4) = 24
4 + 20 = 24
24 = 24
Therefore, (1, -4) is a possible solution to the equation
(-9, -12)
Substitute x = -9 and y = -12
4x - 5y = 24
4(-9) -5(-12) = 24
-36 + 60 = 24
24 = 24
Therefore, (-9, -12) is a possible solution to the equation
(4, 8)
Substitute x = 4 and y = 8
4x - 5y = 24
4(4) - 5(8) = 24
16 - 40 = 24
-24 ≠ 24
Therefore, (4, 8) is not a solution to the equation
(6, 0)
Substitute x = 6 and y = 0
4x - 5y = 24
4(6) -5(0) = 24
24 + 0 = 24
24 = 24
Therefore, (6, 0) is a possible solution to the equation.
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On November 2, Sheffield Company discounted at Sunshine Bank a $5,760 (maturity value), 129-day note dated August 15. Sunshine's
discount rate was 7%. (Use Days in a year table.)
What proceeds did Sheffield Company receive?
Note: Use 360 days a year. Do not round intermediate calculations.
Proceeds received
Sheffield would get $5,704 in revenues to signify that there are 50 days left before the note matures and that the maturity amount must thus be deducted from the proceeds.
Given,
Maturity value = $5,760
129 day note dated August 15
Sunshine's discount rate = 7%
We have to find the proceeds received by Sheffield Company;
Here,
Number of days that have passed since Note was issued is;
16 days in August
30 days in September
31 days in October
2 days in November
= 16 + 30 + 31 + 2
= 79 days
79 days have already elapsed out of the 129 so days left is;
= 129 - 79
= 50 days
Assuming a 360 day Calendar, Sheffield Company will receive;
= Maturity level - Discount Amount
= 5760 - (5760 × 7% × 50/360)
= 5760 - 56
= $5704
Sheffield would get $5,704 in revenues to signify that there are 50 days left before the note matures and that the maturity amount must thus be deducted from the proceeds.
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A vehicle is running at a constant speed on a highway. Ignore the initial acceleration at the start and final acceleration when the vehicle runs out of gasoline and comes to halt. Its gas consumption per mile is also constant. The amount of gasoline, in gallons, in the vehicle can be modeled as a linear function G ( t ) = 10 -- 2t, where t is time, in hours. Select all the true statements.le
The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:
Initially, the tank has 10 gallons of gasoline.The rate of consumption is of 2 gallons per hour.The slope of G(t) represents the fuel consumption of the vehicle.The t-intercept represents the time it takes for the vehicle to run out of gas.What are the parameters of the linear function?The linear function is defined as follows:
G(t) = 10 - 2t.
In which the variables are:
G(t) is the amount of gasoline that the car has after t hours.t is the time in hours.The slope and the intercept are presented as follows:
Slope of -2: 2 gallons are consumed each hour.Intercept of 10: The initial fuel in the car is of 10 gallons.The t-intercept is:
10 - 2t = 0
2t = 10
t = 5.
Which is the time it takes for the car to run out of fuel.
Missing InformationThe options are given by the image shown at the end of the answer.
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The legend on a map states that
1 inch is 500 miles. If you measure
8 inches on the map, how many
miles would the actual distance be?
The actual distance will be 4000 miles.
According to the question,
We have the following information:
The legend on a map states that 1 inch is 500 miles.
So, this statement can be rewritten in the form of following expression:
1 inch = 500 miles
Now, in order to find the actual distance for 8 inches, we will multiply the distance in 1 inch with 8.
(More to know: measurements like this are used in daily life to find the actual distance between two places.)
So, we have the following expression:
8 inches = 500*8 miles
8 inches = 4000 miles
Hence, the actual distance will be 4000 miles if it measures 8 inches on the map.
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Graph the function. f(x)=-3(x+1)^2+5f(x)=−3(x+1) 2 +5
Answer:
See attachment.
Step-by-step explanation:
1. Use the slope-intercept form to find the slope and y-intercept.
y = mx + b ; m= slope b= y-intercept
2. Find the values.
m = 0
b = 7
slope: 0
y-intercept: ( 0, 7)
3. Find two points on the line, then graph them.
x = 0, 1
y = 7, 7
Solve the system of equations by graphing.
x-y=-4
x+y=8
18) In the Pie Chart Example below, the city of Miami is trying to determine how many new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 how many visitors come in June? A. 30,000 B. 60,000 C. 135,000 D. 72,000
The number of visitors to the beach in June is B. 60000.
How to calculate the value?Since the pie chart isn't given, let the assumed percentage for the visit to the beach in June be 20%.
In this case, the new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 will be:
= Percentage for visits × Total people
= 20% × 300000
= 60000
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can somebody please help me
Answer: D
Step-by-step explanation: I believe this the correct answer. If you start by looking at the "right 3 units", going right on a coordinate plane is - and left is +, so right 3 units is -3. Then, down 4 units is -4 (on coordinate plane, up is + and down is -).
So then, plug it into the equation: h(x)= {x-3}-4
I hope this helps and you get it right :)
The light in a lighthouse flashes every 20 seconds.
How many times will it flash in one hour?
Answer:
180 flashes
Step-by-step explanation:
The lighthouse flashes 3 times in a minute then multiplied by 60 which is 180 flashes.
another way to write 6axbcx2d without using multiplication sign
????
Answer:
Step-by-step explanation:
(6a)(b)(c)(2d)
If 56 apples were placed in each bag instead how many bags would be left over
Its 112 bags how much?
Answer:
56
Step-by-step explanation:
one apple = one bag
the 56 apples = 56 bags
112 -56 =56