Step-by-step explanation:
The mean of a set of numbers is the average of those numbers. You can find the mean by adding the set of numbers and dividing by how many numbers are given. If you are given the mean and asked to find a missing number from the set, use a simple equation.
Add up the numbers you know. The problem states a mean of 58 with this set of numbers: 43, 57, 63, 52 and x. Assign the missing number a value of “x.” So add 43, 57, 63 and 52 to get 215.
Set up your equation by adding 215 plus “x” (the missing number), divided by 5, the number of values given. Set that side of the equation equal to the mean, 58. So, your equation would look like this: [tex] \frac{215+x}{5} = 58 [/tex]
Multiply each side by 5 since our goal is to get “x” by itself. This process cancels the 5 on the left side of the equation and gives you 290 on the right side (58 × 5). Now, your equation should look like this: [tex] 215+x=290 [/tex]
Subtract 215 from each side as you continue to work to get “x” alone. This cancels out the 215 on the left side of the equation and gives you 75 on the right side. Now, your equation should show that x = 75. Therefore, the missing number is 75.
Check the missing number by adding all the numbers together and dividing by 5.
[tex] \frac{43+57+63+52+75}{5} = \frac{290}{5} = 58 [/tex]
if sin 22.6°=5/13, what is cos 67.4° ?
The value of cos 67.4° is 5/13.
According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-
sin(90 - x) = cos x
Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos 67.4° only. Thus we can write the given equation as follows-
sin22.6° = sin(90 - 67.4°)
= cos 67.4°
Thus, sin 22.6° = cos 67.4°
Hence, cos 67.4° = 5/13
Thus, the value of cos 67.4° comes out to be 5/13.
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Brenda and Jenna saved up $81.75 and $45.25 respectively to buy a gift for Mother's Day. How
much money in all have the sisters set aside for the gift?
Answer: $127
Step-by-step explanation: $81.75+$45.25=$127
Two steamers leave a port on river at the same time traveling in opposite directions each is traveling 20mph how long will it take for them to be 140 miles apart
The correct answer is 3.5.
Let t be the amount of time each steamer takes.
Two steamers that are headed in opposite directions depart a port on a river at the same time, according to the information provided.
Given that both steamers move at the same speed, they would cover the same distance in t hours.
Given that both steamers covered 140 miles, we can write the following equation to reflect this data:
rate time distance
First stream 20 t 20t
Second stream 20 t 20t
140
setting the equation ,
20t + 20t = 140
40t = 140
t = 140/40
t = 3.5
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A grocery store sells a bag of 8 oranges for $4.48. What is the cost of oranges, in
dollars per orange?
The grocery store sells each orange at $0.56.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A grocery store sells a bag of 8 oranges for $4.48.
∴ The cost per orange is $(4.48/8) = $0.56.
The cost of each orange is $0.56.
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A model of the total cost C, in dollars, to produce n cell phones is given by
C = 240n + 800.
Find the C-intercept and the n intercept
Answer:
C intercept is 800, n intercept is -3.3333...
Step-by-step explanation:
C = 240n + 800 is a linear equation (the graph is a line)
C-intercept is the point with the coordinates ( 0, C-intercept ) where the line C = 240n + 800 is intersecting the vertical C-axis and
n-intercept is the point with the coordinates (n-intercept, 0) where the line C = 240n + 800 is intersecting the horizontal n-axis.
Find the C-intercept:
n has to be 0 for our line to intercept the C-axis, so substitute n = 0 in our given equation
C = 240n + 800
C = 240·0 + 800
C = 800
Find the n-intercept:
C has to be 0 for our line to intercept the n-axis, so substitute C = 0 in our given equation
C = 240·n + 800
0 = 240·n + 800, subtract 800 from both sides
-800 = 240 ·n, divide both sides by 240
-800/240 = n
-3.(3) = n
to lose 1 lb of body fat you need to burn 3.500 calories. If you burn 450 more calories than you take in each day, how long will it take to lose 1 lb? What about 10 lb?
Step-by-step explanation:
1 pound is equivalent to 3500 calories.
if you burn 450 more calories per day, it will take as many days as the times 450 fits into 3500 :
3500 / 450 = 7.77777777... days
for 10 pounds we need to burn 10×3500 = 35000 calories.
35000 / 450 = 77.77777777... days (10 times more logically than for 1 pound).
PLEASE HELP ASAP! I am struggling piece wise function
Answer:
[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]
Step-by-step explanation:
Looking at the graph we can see that it is a linear graph of the form
y = mx + b where m is the slope and b is the y intercept.
In one region the slope is positive and the other region it is negative
Interval 1 is -6 ≤ x < -3
How do I know that one uses a ≤ and the other uses a <?
A filled circle means that the point is included in the domain(range of x values) and therefore (≤, ≥) and an unfilled circle means it is not(<, >)
Find the slope of line in this interval
Take two points, say (-5, 0) and (-3, 4)
Slope = rise/run = (4 - 0)/(-3 - (-5) = 4/2 = 2
So slope of line is 2 and its equation in slope-intercept form is
y = 2x + b
Choose any point, plug in values, solve for b
Point (5, 0) is chosen
0 = 2(-5) + b
0 = -1 + b
or
b = 10
So equation of line in the interval (-6 ≤ x < -3) is
y = f(x) = 2x + 10
Interval 2: -3 < x < 2
We see this line intersects the y axis at y = 1
So b = 1
Equation is y = mx + 1
Choose point x = 0, y = 1 to find slope m
At x = 0, y = m(1) + 1 = m + 1
So m + 1 = 0
m = -1
So equation of this line is
y = f(x) = -1x + 1 in the interval -3 < x < 2
Putting all these together we get the piecewise function as:
[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]
The admission fee to a carnival is $5.00, and each game costs an additional $1.50 to play. The carnival also has a
special admission price of $14 that includes unlimited games. What is the minimum number of games a customer
must play to make the special admission price less than paying for each game separately?
Answer:
9.3333333
Step-by-step explanation:
14÷1.50=9.333333
Can someone help with this question?✨
Answer:
the answer is y=3x - 9
Step-by-step explanation:
From y=mx+c
;m=3 (slope)
Therefore y=3x+c
SOLVING FOR C
y=3x+c
From (2,-3)
x=2
y=-3
-3=3(2)+c
-3=6+c
SUBTRACTING (6) FROM BOTH SIDES
-3-(6)=6-(6)+c
-3-(6)=0+c
c= -3-(6)
c=-9
THEREFORE THE EQUATION OF THE LINE IS
y=3x-9
Drag and drop the range of each data set into the boxes.
PLEASEE
The range of data set 1 is 4
The range of data set 2 is 4.
What is the range?A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.
The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.
Range = highest number - lowest number
The range of data set 1 = 7 - 3 = 4
The range of data set 2 : 7 - 3 = 4
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Two cars, initially at rest and 5 km apart at t=0 , simultaneously move toward each other. Car A travels at a constant speed of 55 km/hour, while car B travels at a constant speed of 12 km/hour. How far will car A travel before meeting car B in the middle?
Car A travel before meeting car B in the middle is 268 second.
Constant Speed Motion
An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
v= d/t
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for d:
d = v . t
And we can also solve it for t:
t = d/v
Two cars are initially separated by 5 km are approaching each other at relative speeds of 55 km/h and 12 km/h respectively. The total speed at which they are approaching is 55+12 = 67 km/h.
The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.The time it will take for them to meet is:
t = 5/67
t = 0.0746 hours
Converting to seconds: 0.0746*3600 = 268.56
Therefore the closest answer is d. 268 s.
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Triangle ABC has been translated to create triangle A′B′C′. Which of the following statements is true? Group of answer choices m∠B′ = 63° m∠C = 63° m∠A′ = 63° m∠B = 63°
We have to know about translation inorder to understand the question.The correct answer for the question is m∠A'=63°.
A translation is a rigid transformation where a figure is moved from one location to another without changing it's size,shape or orientation.This means that the triangle that we get after translation is same as it's pre-image. So here we can say that traingles ABC and A'B'C' are congruent.When two triangles are congruent their respective sides and angles are congruent too,se we can say that
AB=A'B' and m∠A=m∠A'
BC=B'C' m∠B=m∠B'
AC=A'C' m∠C=m∠C'
It is given that in triangle ABC, m∠A=63° thus we can say that m∠A'=63°
Thus we see that using the concept of traingle translation and congruency we found that m∠A'=63° is the correct answer.
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A small business office uses 307 pieces of paper every 3 days. Which is a reasonable estimate for the pieces of paper the business office uses in 7 days?
A.
600
B.
2,100
C.
900
D.
700
700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
How to calculate the estimate ?The office uses 307 pieces of paper every 3 days
The first is to calculate the number of paper used per day
= 307/3
= 102.3
The number of paper used in 7 days can be calculated as follows
= 7 × 102.3
= 716
Hence 700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
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Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines. Which list shows all the possibilities for the number of toy soldiers Jamal could place in each line
The list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
How to illustrate the information?From the information, Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines.
It should be noted that the factors of 34 are 1, 2, 17, and 34.
Therefore, the list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
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Assuming a linear relationship, find the missing value in the table below.
The missing value in the table below assuming a linear relationship is 18
How to find the missing value in the table below assuming a linear relationship?The table of values represents the given parameters
From the question, we understand that the relationship is a linear relationship.
This means that the x and y values change at constant rate
From the table, we have
As x increases by 1, y increases by 2
So, the missing value is
Missing value = 16 + 2
Evaluate
Missing value = 18
Hence, the missing value in the table below assuming a linear relationship is 18
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if u arent beinggreat simply dont answer :)
Answer:
Step-by-step explanation:
The exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times:
9.2 -> 0.0092
The answer is D.
Answer:
0.0092.
Step-by-step explanation:
I have an explanation on this same question. Apparently, you have a duplicate of this.
Suppose the height of Rodrigo's triangle in the Example is doubled. Will the area of the triangle also double? Explain how you know.
Yes, area of the triangle also get doubled when the height of the triangle is doubled.
As given in the question,
Let 'b' be the base of the triangle
'h' be the height of the triangle
Area of the triangle = (1/2) × b × h
Base of the new triangle = b
Height of the new triangle doubled =2h
Area of new triangle = (1/ 2) × b × 2h
= 2 {(1/2) × b × h}
= 2 Area of original triangle
Therefore, area of the triangle also get doubled when the height of the triangle is doubled.
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Given f\left(x\right)=8-3xf(x)=8−3x, find the following
The value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
How to determine the value of the function?The function value is given as
f(x) = 8 - 3x
The above is a linear function
As a general rule
Linear functions are function that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
From the question, we have the value to be
f(2)
The above means that we determine the value of the function when x = 2
i.e., f(x) = ? when x = 2 or we substitute 2 for x in f(x)
Next, we test the above function with the x value
So, we have
f(x) = 8 - 3x
Substitute 2 for x in f(x)
f(2) = 8 - 3 x 2
Evaluate the product in the above equation
So, we have
f(2) = 8 - 6
Evaluate the difference in the above equation
So, we have
f(2) = 2
Hence, the value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
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Possible question
Given f(x)=8−3x, find the following: f(2)
Determine the value of the variable that makes the equation true.
b + (-8.3) = 0
The value of the variable that makes the equation true is: b = 8.3.
How to Determine the value of a Variable in an Equation?By isolating the given variable in an equation to one side of the equation, we can find out its value which will make the equation true.
Given the equation, b + (-8.3) = 0
b - 8.3 = 0 [plus times minus = minus]
Add 8.3 to both sides of the equation, to isolate variable b
b - 8.3 + 8.3 = 0 + 8.3
b = 8.3
Let's check if the value of b would make the equation true by plugging in the value of b:
b + (-8.3) = 0
8.3 + (-8.3) = 0
8.3 - 8.3 = 0
0 = 0 [true]
Therefore, the value of the variable that makes the equation true is: b = 8.3.
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On April 11, Maria's checking account balance was $922. She wrote a check on April 29 for $280, withdrew
$40 on May 1, and deposited $150 into her account on May 14. What is her account balance on May 15?
Write your answer as a whole dollar amount, such as: $148.
Odessa and Daxton are making a table that is 3 1/3m high and has an area of 32m2. What is the width?
Answer: 9.6 meters
Step-by-step explanation:
See attached image
10n + 2 =43 what is the value of n
Answer:
n = 41/10 OR 4.1
Step-by-step explanation:
10n + 2 =43
10 + 2 - 2 = 43 - 2
10n = 43 - 2
10n = 41
10n/10 = 41/10
n = 41/10
Answer:
n = 41/10Step-by-step explanation:
10n + 2 = 43 what is the value of n
10n + 2 = 43
10n = 43 - 2
10n = 41
n = 41/10
-------------------
check
10 * 41/10 + 2 = 43
41 + 2 = 43
43 = 43
the answer is good
Translate the English phrase into an algebraic expression: the sum of 11 times 4x2 and 5x.
Answer:
I believe it is 44x^2+5x
Step-by-step explanation:
According to a cookie recipe, I need 3 large eggs if I need to make 38 cookies.
Now, you want to make 300 cookies for a bake sale. How many eggs do I need?
O 25
O24
O22
O 23
Answer:
24
Step-by-step explanation:
Because 300 cookies / 38 cookies = 7.89,..
Then 7.89,... x 3 = 23.68,...
round to the nearest tenths= 24
In order to meet the demand for the bake sale, a total of 300 cookies will be prepared, requiring the use of precisely 24 fresh eggs.
To calculate how many eggs you need to make 300 cookies, set up a proportion based on the information given in the cookie recipe:
Number of eggs / Number of cookies = Constant ratio
Let the number of eggs needed for 300 cookies as "x."
So, x eggs / 300 cookies = 3 eggs / 38 cookies
Now, cross-multiply and solve for "x":
x * 38 = 3 * 300
38x = 900
x = 900 / 38
x = 23.6842
x ≈ 24
Therefore, you need 24 eggs to make 300 cookies for the bake sale.
Thus, option (b) is correct.
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A food truck vendor sells small drinks for $1.15, medium drinks for $1.75, and large
drinks fro $2.25. The vendor sold a total of 1,385 drinks for a full week of business.
During the same week, his total sales were $2,238.75. During the week, he also sold
twice as many small drinks as medium drinks. Write a 3X3 system of equations that
models the vendors situation. Use s for small drinks, m for medium drinks, and g for
large drinks.
The system of equations is given by :
s + m + g = 1385
1.15 s + 1.75 m + 2.25 g = 2238.75
s = 2m
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
We shall employ the linear combination method to resolve a system of three equations in three variables. This time, we will solve for the third variable while eliminating the second variable using the equations that follow from the elimination of the first.
Given the number of small drinks by the vendor is s , number of medium drinks is m and the number of large drinks is g.
The vendor sold all three drinks total of 1385, hence the equation:
∴ s + m + g = 1385.
Each small drink costs 1.15 , medium drinks cost 1.75 and large drinks cost 2.25, hence the equation:
∴ 1.15 s + 1.75 m + 2.25 g = 2238.75
He sold twice as many small drinks as medium drinks, hence the equation:
∴ s = 2m
The system of equations is given by:
s + m + g = 1385
1.15 s + 1.75 m + 2.25 g = 2238.75
s = 2m
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HELP ME IF U HELP ME ILL GIVE U A SURPRISE!!!!!!
Abbie, Chloe, and Xander are playing a dice game. The game consists of ten rounds. In each round, each person takes a turn rolling two dice and earns or loses points based on what they role. Points are awarded according to the following table:
Roll Points
Same number on both dice +3
Different numbers, with an even sum +1
An odd sum -2
At the end of ten rounds, the person with the highest number of points wins.
In the first five rounds, Abbie got four odd sums and one pair of threes. How many points does she need to have an exact score of zero? What is the least number of rounds it will take her to have an exact score of zero? Explain your reasoning using complete sentences.
Answer:
okay so she got and odd sum 5 times which will mean she has -10 points and then she got a pair of threes which gives her 3 points so now she has -7 which means she needs 7 more points so the least amount would be 3
Step-by-step explanation:
Circle the problem in which you need to regroup use the strategy that is easier to find the sum. a 496 + 284. B 482 + 506
Correct answer is B. In A, there is no number from which to regroup (all the numbers may be added together), so you must regroup. In B, the number 6 cannot be added to the number 2, therefore you must regroup.
What is regrouping in mathematics?Making groups of ten while doing math operations like addition or subtraction is known as regrouping. This frequently occurs while dealing with double digits. Technically speaking, it also happens whenever you get a response that is more than 10.
Additionally, if the numbers you are adding result in a two-digit number and they are not in the farthest left column, you must regroup. When the numbers you are subtracting from are more than the ones you are subtracting from, you regroup.
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You started this year with $447 saved and you continue to save an additional $27 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Answer:
s = 13m + 384
hope this helped <3
A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
Answer:
above below
9
9
16
15
17
less than 4 hours
4-8 hours
8-12 hours
more than 12 hours 14
%
11
What percent of the students who spend less than 4 hours a week on screens reported
a grade average below 80? Round your answer to the nearest whole number percent.
20
Submit Answer
p
attempt 2 out of 2
The percentage of students who spend less than 4 hours a week on screens which reported a grade average below 80 is 50%
Given, we have the report representing children spending time online, on social media or watching T.V, which has there effect on there grades as above or below 80.
By the question we know that the number of students who spends less than 4 hours a week on screen is:
9 + 9
= 18
And among the 18 students there are 9 students whose grade average is below 80.
So the percentage of the students who spends 4 hours a week on screen is:
= 9 ÷ 18 × 100%
= 100/2
= 50%
hence 50% students spend less than 4 hours a week on screens.
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Add. Write your answer in scientific notation.
(9.2×102)+(5.3×103)