Average rate of change formula:
[tex]\dfrac{\Delta y}{\Delta x}[/tex]
[tex]\Delta y=6-1=5\\\\\Delta x=4.95-0.40=4.55[/tex]
[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{5}{4.55}=\dfrac{500}{455}=\dfrac{100}{91}\approx1.1[/tex]
URGENT HOMEWORK!!! MULTIPLE CHOICE! Four bags of flour and three bags of sugar weigh 44 pounds. Six bags of flour weigh 48 pounds. All bags of flour weigh the same, and all bags of sugar weigh the same. What is the ratio of the weight of a bag of flour to a bag of sugar?
a) 2:1 b) 1:2 c) 3:2 d) 2:3
Answer: 4 flour + 3 sugar = 44lbs
6 flour = 48lbs
We can divide 48lbs by 6 bags of flour to get 8lbs per bag of flour.
4 bags of flour multiplied by 8lbs is 32lbs. 44lbs - 32lbs = 12lbs
12lbs divided by 3 bags of sugar = 4lbs per bag of sugar.
The ratio is flour to sugar: 8:4 or 2:1
We create two equations based on the information given: 4F+3S=44 and 6F=48. By solving these equations, we find the weight of a bag of flour is 8 pounds and the weight of a bag of sugar is 4 pounds. Thus, the ratio of weight is 2:1.
Explanation:
We can solve this problem by setting up two equations based on the information given and then solve the equations to find the weights of the bags of flour and sugar. Let's denote the weight of a bag of flour as F and the weight of a bag of sugar as S.
According to the problem, 4 bags of flour plus 3 bags of sugar weigh 44 pounds. So we can write the equation 4F + 3S = 44.The problem also tells us that 6 bags of flour weigh 48 pounds. So we have another equation 6F = 48.From the second equation, we can find that F = 48 / 6 = 8 pounds. Substitute F = 8 into the first equation, we find S = 4 pounds.
Therefore, the ratio of the weight of a bag of flour to a bag of sugar is 8:4 or simplified to 2:1 (option a).
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The function f(x) is shown in the graph. What is the equation for f(x)?
f(x)=____
express the equation in slope-intercept form: f(x) = mx + b.
Here's a general outline of the process we'll follow once I have the graph:
Identify key features:
Slope: Determine the slope of the line, which signifies the rate of change of the function. You can calculate it using the formula slope = (change in y) / (change in x) between any two points on the line.
Y-intercept: Locate the point where the line intersects the y-axis. This point is crucial for determining the function's vertical shift.
Apply slope-intercept form:
Once you have the slope (m) and y-intercept (b), express the equation in slope-intercept form: f(x) = mx + b.
Verify with points:
Choose a few points on the graph and substitute their coordinates into the equation to ensure it accurately represents the line.
Plz Help I don't understand.
And could you Plz explain how to do it As well.
At the end of 2007-2008 football seasons, 38 super bowl games had been played with the current two football leagues, The American football conference (AFC) and the national football conference (NFC). The NFC won two more games than the AFC. How many games did each conference win?
Answer: AFC won 18 times, NFC won 20 times
============================
N = number of times an NFC team won the superbowl
A = number of times an AFC team won the superbowl
The two unknown numbers (N and A) must add to 38 as there are no other options (either there is an NFC or AFC champion) so N+A = 38
The other equation is N = A+2 because "the NCF won two more games than the AFC"
We can replace the "N" in N+A = 38 with A+2 because N = A+2, meaning that N and A+2 are the same
So,
N+A = 38
A+2+A = 38 ... replace N with A+2; solve for A
2A+2 = 38
2A+2-2 = 38-2
2A = 36
2A/2 = 36/2
A = 18
The AFC won 18 times. Use this value of A to find N
N = A+2
N = 18+2
N = 20
The NFC won 20 times.
As a check, adding up the two counts should get us 38
N+A = 38
20+18 = 38
38 = 38
Answer is confirmed
8. Workpad Note: Remember to show all of the steps you use to solve a problem. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure yiu recieve proper credit for your answer.
At the half-time show, a marching band marched in formation. The lead drummer started at a point with coordinates (2,-5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
Answer: a) (x, y) → (x + 1, y + 3)
b) (2, -5) → (3, -2)
Step-by-step explanation:
the x-axis goes left and right, so 1 step to the right means you need to add 1 unit to the x-coordinate.
the y-axis goes up and down, so 3 steps up means you need to add 3 units to the y-coordinate.
Rule:
If original x-coordinate is x, then the new coordinate is x + 1 (x → x+1)
If original y-coordinate is y, then the new coordinate is y + 3 (y → y+3)
Final position:
If original x-coordinate is 2, then the new coordinate is 2 + 1 (2 → 3)
If original y-coordinate is -5, then the new coordinate is -5 + 3 (-5 → -2)
Solve the following equation below ax=15+b
Solve for x.
Answer:
x=15/a+b/a
Step-by-step explanation:
a*x=15+b
you need to move all the variables (a) to one side and to do that you can re-organize it to say
x*a=15+b
to get the answer you need to divide (a) and that gets you your answer,
x=15/a+b/a
Here is your equation:
[tex]ax=15+b[/tex]
You're trying to find x alone. To find a specific variable, you have to do the opposite of what's happening to the variable, which is x in this equation.
In this equation, x is being multiplied by a. That means you have to do the opposite of multiplying, which is dividing by a. To leave x alone, divide both sides by a.
[tex]ax \div a = \frac{15+b}{a}[/tex]
Now that you have divided both sides by a, which leaves x alone, you have:
[tex]x = \frac{15+b}{a}[/tex]
Your answer is [tex]x = \frac{15+b}{a}[/tex]
If you have any questions, feel free to ask in the comments! :)
The price of a mango at a fruit stand goes up 5 cents each month. The first month the stand was open, a mango cost $1.25. What will the cost of a mango be in the 25th month?
Answer:
$2.45
Step-by-step explanation:
Let x be the number of months.
We have been given that price of a mango at a fruit stand goes up 5 cents each month. This means that price of mango in dollars after x months will be 0.05x (1 dollar=100 cents).
The first month the stand was open, a mango cost $1.25. This means that cost of mango in the x months after 1st month will be: [tex]1.25+0.05x[/tex]
Now let find the cost of mango in the 25 month by substituting x=24 in our expression because price will increase 24 times after 1st month.
[tex]\text{The cost of a mango be in the 25th month}=1.25+0.05*24[/tex]
[tex]\text{The cost of a mango be in the 25th month}=1.25+1.2[/tex]
[tex]\text{The cost of a mango be in the 25th month}=2.45[/tex]
Therefore, the cost of a mango in the 25th month will be $2.45.
Final answer:
To calculate the cost of a mango in the 25th month, you multiply the 24 intervening months by the $0.05 monthly price increase, which equals $1.20, and add it to the initial cost of $1.25, resulting in a total cost of $2.45.
Explanation:
You want to calculate the cost of a mango in the 25th month if the price increases by 5 cents each month from the initial price of $1.25. To find the cost on the 25th month, we will first find out the total increase in cost after 24 months (since the first month is already at $1.25, we only calculate the increase for the following 24 months). The calculation is 24 months × $0.05 increase per month.
The total increase is:
24 × $0.05 = $1.20.
Add this increase to the initial cost to find the cost on the 25th month:
$1.25 + $1.20 = $2.45.
Therefore, the cost of a mango in the 25th month will be $2.45.
can someone please help me i am failing my math and am very behind my math grade level can someone explain this to me please
Answer:
The answer to number 7 is -1.25
The answer to number 8 is 1.25
Circle A has a radius of 6. Which circles are congruent to circle A? Check all that apply. circle D circle E circle F circle G circle H
Answer:
circle E & circle F
Step-by-step explanation:
We want to see which circles are congruent to circle A, a circle of radius of 6 units.
The correct options are E and F.
Let's see how to solve this:
First, we need to understand what congruent figures are.
We say that two figures are congruent if they have the exact same shape and size.
Then we need to see which other circles also have a radius (distance from the center to the line) is also of 6 units. (or a diameter of 12 units)
The image of the options can be seen at the end of the answer, there, we can see that circle E has a radius of 6 units, so we know that circle E is congruent to circle A.
We also can see that circle F has a diameter (twice the radius) of 12 units, then the radius is:
R = D/2 = 12/2 = 6 units.
Then circle F is also congruent to circle A.
Then the correct options are E and F.
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Kara is sorting buttons by length for a craft project. The line plot shows the length of each button. If Kara lines up all the 3/4-inch buttons, what would be the total length?
Answer:
2 and 1/4 or 2.25. Both numbers are the same.
Step-by-step explanation:
Hi,
Please see the picture I had to upload in order for this question to be complete. Please also note that Kara has 3 buttons in the 3/4 length. You have to sum up only those in that length and ignore the ones in different lengths.
It is a very simple multiplication, and there are 2 ways to do so. You can use either fractions or integer numbers. See the 2 options below:
3/4 (fractions) = .75 (integer numbers)
Option one - 3 * 3/4 = 9/4 which is represented by 2 and 1/4.
Option two - 3 * .75 = 2.25
Have a good one!
1/8 of pizza cost 2 dollars. In an hour, 6 1/4 pizzas were sold. How much money was made at the food booth in that hour
If the area of a square is 625 cm^2 then what is the length of one side of the square
Question
If the area of a square is 625 cm^2 then what is the length of one side of the square
Answer:
Step-by-step explanation:
The sides can be found by taking the square root of the area
√625 =
25 cm
---------------
check
Area = s²
25² = 625
the answer is good
How many solutions does the system of equations have?
y= -2x +9
6x + 3y =27
A) one
B) two
C) infinitely many
D) none
The given equations have infinitely many solutions.
What is an equation?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression. If there are two equations ax + by + c = 0 , dx + ey + f = 0 and if [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] , then the equations are said to have infinite solutions.How to know how many solutions does the system of equations have ?The given equations are y= -2x +9 and 6x + 3y =27
Comparing with the standard equations we can see that,
a = 2b = 1c = -9d = 6e = 3f = -27∴ [tex]\frac{a}{d} =\frac{2}{6} = \frac{1}{3}[/tex]
∴ [tex]\frac{b}{e} = \frac{1}{3}[/tex]
∴ [tex]\frac{c}{f} = \frac{-9}{-27}= \frac{1}{3}[/tex]
∴ The conditions of [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] is satisfied and hence the equations have infinitely many solutions.
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HELP PLEASE! WILL GIVE 100 POINTS AND BRAINLY IF CORRECT
Answer:
f(3) = - 1
Step-by-step explanation:
to evaluate f(3) substitute x = 3 into f(x)
f(3) = - [tex]\frac{2}{3}[/tex] × 3 + 1 = - 2 + 1 = - 1
Answer:
f3 = -1
Step-by-step explanation:
to evaluate f(3) substitute x = 3 into f(x)
f(3) = - \frac{2}{3} × 3 + 1 = - 2 + 1 = - 1
What’s the answer show your WORK Plz
Answer:
732.7 I think
Step-by-step explanation:
You just multiply 28 by 26.17
Answer:
26.17*28=723.76 inches
Why?
There is 28 desks and they are 26.17 inches long. If you line them all up you have 28 desks each 26.17 inches in a line. Which is 26.17*28. Multiple and you get 723.76
Ladder You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. What angle does the ladder make with the ground?
The ladder with a length of 20 feet makes 1.37° with the ground.
Length of the ladder = 20 feet
Distance of base of the ladder from the wall = 4 feet
What is the Cosine of an angle?The cosine of an angle is the ratio of the adjacent side(to that angle) to the hypotenuse of the right triangle.
Suppose the ladder makes [tex]\theta[/tex] from the ground.
So, [tex]Cos\theta = \frac{4}{20}[/tex]
[tex]Cos\theta = \frac{1}{5}[/tex]
[tex]\theta =Cos^{-1} (\frac{1}{5} )[/tex]
[tex]\theta =Cos^{-1} 0.2[/tex]
[tex]\theta=1.37[/tex]°
Thus, the ladder makes 1.37° with the ground.
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The ladder makes an angle of approximately 76.31 degrees with the ground.
Given:
- The length of the ladder (hypotenuse) is 20 feet.
- The distance from the wall (adjacent side) is 4 feet.
Using the tangent function, we have:
[tex]\[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \][/tex]
Let h be the height the ladder reaches on the wall. Then:
[tex]\[ h^2 + 4^2 = 20^2 \] \[ h^2 = 20^2 - 4^2 \] \[ h^2 = 400 - 16 \] \[ h^2 = 384 \] \[ h = \sqrt{384} \] \[ h = 19.6 \text{ feet (approximately)} \][/tex]
Now we can find the angle [tex]\(\theta\)[/tex]:
[tex]\[ \tan(\theta) = \frac{h}{4} \] \[ \tan(\theta) = \frac{19.6}{4} \] \[ \tan(\theta) = 4.9 \][/tex]
To find the angle [tex]\(\theta\)[/tex], we take the arctangent (inverse tangent) of 4.9:
[tex]\[ \theta = \arctan(4.9) \] \[ \theta \approx 76.31^\circ \][/tex]
Therefore, the ladder makes an angle of approximately 76.31 degrees with the ground.
One quart or one liter? Which is greater?
1 liter = 1.06 quarts.
This makes the liter greater than a quart.
please help i really need help
The price of a shampoo, cut, and style at the hairstyling salon where you work is $18.00. You generally get a 20% tip from each customer, and the salon owner pays you ¼ of each job's cost. On a typical day, you give shampoos, cuts, and styles to 8 customers. About how much can you expect to earn for yourself on such a day?
Answer:
The amount you would earn is $64.80
Step-by-step explanation:
We know to start that you get 45% of the cost per customer. That's because the customer gives you 20% and you boss gives you 25% (1/4). To find how much that is, multiply it by the cost.
$18 * 45% = $8.10
Now knowing this, we can multiply that amount by the 8 customers per day.
$8.10*8 = $64.80
On a typical day, I can expect to earn $64.80 for myself.
To calculate my earnings for the day, we'll break it down step by step:
Shampoo, cut, and style cost: Each job's cost is $18.00.
Tips: I generally receive a 20% tip from each customer. To calculate the total tip earnings for the day, we multiply the job cost by 0.20 (20%):
Total tips = 8 customers * ($18.00 * 0.20) = 8 * $3.60 = $28.80
Salon owner's payment: The salon owner pays me ¼ of each job's cost. To calculate the total payment from the salon owner for the day, we multiply the job cost by 0.25 (1/4):
Total owner's payment = 8 customers * ($18.00 * 0.25) = 8 * $4.50 = $36.00
My earnings: Finally, to calculate my total earnings for the day, we sum up the tips and the salon owner's payment:
Total earnings = Total tips + Total owner's payment = $28.80 + $36.00 = $64.80
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Find all the whole values of a for which the solution of the equation ax = 6 is a whole number.
Answer:
1, 2, 3, 6
Step-by-step explanation:
The given equation is,
[tex]\Rightarrow ax = 6[/tex]
[tex]\Rightarrow x = \dfrac{6}{a}[/tex]
We need to to find all the whole values of a for which the solution of the equation i.e x will be a whole number.
We know that when a number is divided by one of its factor it leaves a remainder of 0 or the result we get is a whole number.
That is why, we need a as one of the factors of 6, i.e 1, 2, 3, 6 in order to get x as a whole number.
Roger earns $24 a week mowing lawns. he spends 1/6 of his earnings on lunch and 2/3 of his earnings on music. He saves the rest. how many dollars does Roger save? tell how you found the answer
[tex]\mathsf{Given : Roger\;earns\;24\;Dollars\;a\;Week}\\\\\mathsf{Given : Roger\;spends\;\frac{1}{6}\;of\;his\;Earnings\;on\;Lunch}\\\\\mathsf{\implies Dollars\;he\;spends\;for\;Lunch = (\frac{1}{6} \times 24) = 4}[/tex]
[tex]\mathsf{Given : Roger\;Spends\;\frac{2}{3}\;of\;his\;Earnings\;on\;Music}\\\\\mathsf{\implies Dollars\;he\;spent\;on\;Music = (\frac{2}{3} \times 24) = (2 \times 8) = 16}[/tex]
[tex]\mathsf{Dollars\;remaining\;in\;Roger's\;Pocket\;after\;all\;his\;Spendings = [24 - (16 + 4)]}[/tex]
[tex]\mathsf{Dollars\;remaining\;in\;Roger's\;Pocket\;after\;all\;his\;Spendings = [24 - 20] = 4}[/tex]
Roger saves 4 Dollars!
Roger earns $24 weekly and spends 1/6 on lunch and 2/3 on music. Calculating these expenses, he spends $4 on lunch and $16 on music, totaling $20. Roger saves the remaining $4.
To find out how much Roger saves, we need to calculate these expenses and subtract them from his total earnings.
Amount spent on lunch: 1/6 of $24 = $24 / 6 = $4.Amount spent on music: 2/3 of $24 = $24 * (2/3) = $16.Adding the amounts spent on lunch and music: $4 + $16 = $20.
subtract the total expenses from his total earnings: $24 - $20 = $4.
Therefore, Roger saves $4 after his expenses on lunch and music.
Vardan thought of a prime three-digit number, all the digits of which are different. What is the last digit, if it is known that the last digit is equal to the sum of the first two digits?
Answer:
Prime number states that a whole number greater than 1 whose only factors are 1 and itself.
For example; 2, 3, 5, 7 ,......
As per the statement: Vardan thought of a prime three-digit number, all the digits of which are different.
Let any three digit prime number Vardan thought is, 437 (all digits 4, 3, and 7 are different).
It is given that: if it is known that the last digit is equal to the sum of the first two digits.
⇒ Sum of first two digit = 4+ 3 = 7 which is equal to the last digit of a 3-digit number 437 i.,e 7.
Therefore, the last digit of a prime three-digit number (i.e 437) is, 7
Which graph represents the function
A
B
C
D
Answer:
a , b , c , or d, I t h I n k I t ccon fun sed8nh
URGENT!!!!
LM is the mid segment of ABCD. AB=69 and DC=182. What is LM
Answer: 125.5 is the answer in decimal form. If you need it in fraction form it would be 251/2
To get this answer, you add up the parallel sides AB+DC = 69+182 =251
Then you divide by 2 leading us to get 251/2 = 125.5
The midsegment is basically the average of the two parallel sides
CAN SOMEONE PLS HELP!???
Answer: 10%, 0.5, 3/4
Step-by-step explanation:
What you want to do is convert them all to one unit. The eaisest would be a decimal.
Starting off with .5, it's already in decimal form.
Next go to 10%. 10% as a decimal will be 0.1, because its 1/10.
Lastly, go to 3/4. 3/5 as a decimal would be 0.75.
Putting them in order from least to greatest would be 10%, 0.5, 3/4.
(Hope that helps)
Answer:
10%, 0.5, 3/4
Step-by-step explanation:
This is actually quite simple, all you need is a quick calculation.
I'm going to convert all of the numbers to decimals for the easiest comparison.
put 3/4 into a calculator, and you get 0.75
0.5 is already a decimal
and with percents, you just move the decimal point back two, making it 0.1
Now you have an easy way to compare: 0.1 is the least, 0.5 is next, the 0.75 is the largest.
Hope this helps =D
Evaluate 2(10 - d) + f, when d = 7 and f = -3.
A. -2
B. 3
C. 9
D. 20
Answer:
B. 3
Step-by-step explanation:
2(10 - d) + f
d = 7 and f = -3
Substitute these value in
2(10 - 7) + -3
2 * (3) -3
6 -3
3
Put the values of d = 7 and f = -3 to the expression 2(10 - d) + f
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
------------------------------------------------------------------------------
2(10 - 7) + (-3) = 2(3) - 3 = 6 - 3 = 3
Answer: B. 3Simplify
0.1 (3x - 4y) + 0.7x - 3y.
Answer:
0.1(3x-4y)+0.7x-3y
0.1(3x-4y)+0.7x-3y Distribute 0.1 through the parenthesis
0.3x-0.4y+0.7x-3y Collect the like terms ex.(x,x) (y,y)
(0.3+0.7)x+(-0.4-3)y
↓ ↓
x - 3.4 y
The answer is
X-3.4y
Step-by-step explanation:
Express 16/2^1/2 as a power of 2
Question
Express 16/2^1/2 as a power of 2
Answer:
2²Step-by-step explanation:
16/2^1/2 =
8/2 =
4
4 = 2²
An organization will give a prize to a local artist. The artist will be randomly chosen from among 7 painters, 4 sculptors, and 5 photographers. What is the probability that the artist choosen will be a painter or a photographer?
Noah wants to put a varitey of fish in his new tank his tank is large enough to hold 70 fish find how many fish of each breed he can have 20% are raibbow 40% are swordtail molly are 30%
The amounts of each type of fish that Noah is going to have in his tank are given as follows:
14 raibbow.28 swordtail molly.21 of the remaining.How to obtain the amounts?The quantity of each type of the fish listed in this problem that Noah will have in his tank is obtained applying the proportions in the context of the problem.
The total capacity of the tank is of 70 fish, hence for the amounts of each fish we multiply 70 by the decimal equivalent to each percentage.
Applying the proportions, the amounts are given as follows:
14 raibbow, as 0.2 x 70 = 14.28 swordtail molly, as 0.4 x 70 = 28.21 of the remaining, as 0.3 x 70 = 21.More can be learned about proportions at https://brainly.com/question/24372153
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Maria deposited some money in to an account, and had an annual simple interest rate of 5%. If she left the money in the account for 9 months and earned $18.75 in interest, how much money did she originally deposit into the account?
Answer:
$18.71
Step-by-step explanation:
18.75 = P x .05 x .75
18.75 = P x .0375
18.75 - .0375 = P
$18.71 = P