1) Gathering the data
3 pencils ----------- $0.45
Explain why the volume of these two stacks of quarters are equal? Use Cavaliens principle in your explanation (If you need to)
Given the word problem, we can deduce the following information:
1. Two stacks of 18 pennies each are shown.
To determine if the volumes of the given stacks of quarters are equal, we note that Cavelieri's Principle states:
The volumes of two solids are equal if the areas of the corresponding sections drawn parallel to some given plane are equal.
Since each penny in both stacks has the same base area and has the same number of pennies. Therefore, the volumes of the given stacks are equal.
In 1991 the average family income was about 39000, and in 2011 it was about 66820.
Let
x
=
0
represent 1991,
x
=
1
represent 1992, and so on. Find values for
a
and
b
(rounded to one decimal place if necessary) so that
f
(
x
)
=
a
x
+
b
models the data
a
=
b
=
What was the average family income in 2006?
The average family income in 2006 is $59865.
What is the income?Based on the information illustrated, the required model is given as:
y = ax + b
y = average family income
x = years since 1991
The slope based on the information given is b = 39000.
Therefore, the family income in 2006 will be:
= (1391 × 15) + 39000
= 59865
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Question 1 of 10
What is the slope of the line shown below?
A. 3
B. -1/3
C. -3
D. 1/3
which function is best represented by this graph?A) f(x) = -3x² + 2x + 1 B) f(x) = 3x² + 2x - 4C) f(x) = x² + x - 4D) f(x) = x² + 2x - 3
Answer:
From the graph, the roots of the equation are given below as
[tex]\begin{gathered} x=-3 \\ x=1 \end{gathered}[/tex]These are the points where the curve cuts the x-axis
The y-intercepts of the graph is given below as
[tex](0,-3)[/tex]Concept:
To find the equation of the graph, we will use the formula below
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ x=0,y=-3 \\ -3=a(0+3)(0-1) \\ \frac{-3}{-3}=\frac{-3a}{-3} \\ a=1 \end{gathered}[/tex]Hence,
By substituting the values, we will have
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ f(x)=1(x+3)(x-1) \\ f(x)=x^2-x+3x-3 \\ f(x)=x^2+2x-3 \end{gathered}[/tex]Hence,
The function of the graph is
[tex]f(x)=x^2+2x-3[/tex]OPTION D is the right answer
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $26 monthly fee and charges an additional0.09 for each minute of calls. The second plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls. For how many minutes of callswill the costs of the two plans be equal?
First Plan
Monthly fee = $26
charge per min = $0.09
Second Plan
Monthly fee = $19
charge per min = $0.13
Solution
Let the number of minutes spent on calls in a specific month be x
The total cost spent using the first plan:
[tex]0.09x\text{ + 26}[/tex]The total cost spent using the second plan:
[tex]0.13x\text{ + 19}[/tex]If the cost from the first plan would be equal to that of the second plan:
[tex]\begin{gathered} 0.09x\text{ + 26 = 0.13x + 19} \\ \text{collect like terms} \\ 0.04x\text{ = 7} \\ x\text{ = 175} \end{gathered}[/tex]Hence, the number of minutes of calls for which both plans would be equal is 175mins
Write an inequality that represents the situation.A certain swimming pool holds no more than 700,000 gallons. How many gallons might be in the pool?
Let x represent the number of gallons that might be in the pool. When we say 'no more than 700000 gallons', it means 'less than or equal to 700000'. The symbol for 'less than or equal' to is '≤ '
Thus, the inequality representing this situation is
x ≤ 700000
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
1.
the distance is 6 units
Explanation: you can just count the squares cince the line is straight and even if you use the Distance Formula... you'll get the same answer.
2.
A to B = 6 units
B to C = 4 units
C to D = 3 units
So...
6+4+3 = 13 units
3.
The distance between A to D is = 5 units
You can find the answer by using the Distance Formula.
Help me pretty please I need help
Answer:i have no idea good luck
Step-by-step explanation:
Answer:
4,3 DONT BE MAD IF IM WRONG
Enter an inequality that represents the graph in the box.
The inequality that represents the graph is (1/4)x - y + 3/2 ≤ 0.
What is inequality?An inequality compares two non-qual objects.
We know the general equation of a line is ax + by + c = 0.
From observation, we can conclude that the given line has points (0, -6) and (2, 2).
∴ The slope of the line is [tex]\frac{y_2 - y_1}{x_2- _ x_1}[/tex].
= (0 - 2)/(-6 - 2).
= -2/-8.
= 1/4.
∴ Equation of the line in slope intercept form y = mx + b.
2 = (1/4)(2) + b.
2 = 1/2 + b.
b = 3/2.
∴ Equation of the line is y = 1/4(x) + 3/2.
(1/4)x - y + 3/2 = 0 but the region will be (1/4)x - y + 3/2 ≤ 0.
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Solve 5 and 6
for 40 POINTS
Answer:
A= 184.4 yards
Step-by-step explanation:
couldnt figure out b
Last year Collin's salary was $45,000. Because of furlough days, this year his salary was $30,000. Find the percent decrease.Round to the the nearest tenth of a percent
ANSWER:
33.3%
STEP-BY-STEP EXPLANATION:
We can calculate the value of the percentage starting from the following equation:
[tex]45000-x\cdot45000=30000[/tex]We solve for x:
[tex]\begin{gathered} -x\cdot45000=30000-45000 \\ x=\frac{15000}{45000} \\ x=\frac{1}{3}=0.333 \\ \text{ in the percent form:} \\ 0.333=33.3\text{\%} \end{gathered}[/tex]The percentage that decreased was 33.3%
On the first day of summer break, Katie and her friends go to the theater to see the latest action movie, Dark Emperor: Fist of Vengeance. After Katie buys a ticket, she also buys a bucket of popcorn and a soda for $9.25. In all, Katie spends $23.25 at the movie theater. Which equation can you use to find the cost c of Katie's ticket?
We have the following information:
c is the cost of Katie's ticket; a bucket of popcorn and a soda cost $9.25, we determine c by using the following expression:
[tex]c=23.25-9.25\Rightarrow c=14[/tex](This assuming there is no additional information).
Answer:1234567890
Step-by-step explanation:
hguhouhujnkujnuhb uj kj bk
Mary’s credit card company charges 16% interest on her outstanding credit card balance each month. Her minimum payment is $20 each month. Mary’s credit card bill is $70 in January. Mary only pays the minimum amount each month, and she does not spend any additional money on her credit card. How long, in months, will it take her to pay off her bill from January?
Answer:
Step-by-step explanation:
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Answer:
Step-by-step explanation:
tipptrptprprprptprtprptpprtprtpprtprptprtprptprtprptr
Omar earns $7 each time he sweeps the house. He sweeps
the house 3 times. How much money does Omar earn?
Answer:
$21
Step-by-step explanation:
1,857.205 round each number to the place of the underlined digit.0 is the underlined digit
Answer:
1,857.21
Explanation:
In the number: 1,857.205
The digit after 0 is 5.
Since it is a number between 5 and 9, we round up to obtain:
[tex]1,857.205\approx1,857.21\text{ (to the nearest hundredth)}[/tex]
1118 11 + 600-1110
[tex]12 \times (5 + 4)[/tex]
Answer:
111811 + 600 - 1110
111871 - 1110
= 110761
12 × (5+4)
60+4
= 64
6ft , 5ft , c. What is the length of the hypotenuse
The length of the hypotenuse of the triangle is √61 ft
How to determine the length of the hypotenuse?From the question, we have the following parameters that can be used in our computation:
Smaller sides = 6ft and 5 ft
Hypotenuse = c
The hypotenuse of a triangle is calculated using the following Pythagoras theorem
Hypotenuse^2 = Opposite^2 + Adjacent^2
Where Opposite and Adjacent are 6 and 5
So, we have
c^2 = 5^2 + 6^2
Evaluate
c^2 = 61
Take the square roots
c = √61
Hence, the hypotenuse is √61 ft
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Suppose r varies directly as the square of m, and inversely as s. If r equals 16when m equals 9 and s equals 9, find r when m equals 27 and s equals 9.
Answer:
144
Step-by-step explanation:
r = k m^2 / s <====given ( k is proportionality constant)
16 = k ( 9^2) / 9 shows k = 1 7/9
then:
r = 1 7/9 * 27^2 / 9 = 144
How do I draw the fourth diagram in a square? How do I know how many sticks in the sixth diagram? How many thumb tacks are in the seventh diagram?
First, we have to analyze how each number grows (the number of thumbs and the number of sticks for each diagram)
So we can build two equations that give us the number of thumbs and the number of sticks for each diagram, let be n for the number of the diagram, so :
Now we can know the number of thumbs and sticks for any diagram, and we can solve the questions provided, first, let's draw the 4th diagram:
Now
How do I know how many sticks are in the sixth diagram?
sticks= 4(6) = 24
There are 24 sticks in the sixth diagram.
How many thumb tacks are in the seventh diagram?
thumbs= 3(7)+1 = 22
There are 22 thumbs in the seventh diagram.
Convert 3.5 ⋅ 104 to standard form. (5 points)
3,500
35,000
0.000035
six men can complete a certain work in 20 days .how many men are required to complete the same work in 12 days ?
6 men complete the work in 20 days.
In 1 day it takes:
6 x20 = 120 men
You need to do the same work done in 20 days, in one day. (more manpower)
So, to finish the work in 12 days:
120 men / 12 days = 10 men
What is the distributive property for 3×546 how do you rewrite that
Answer:
1638
Step-by-step explanation:
3(500)+3(40)+3(6)=1500+120+18=1638
FV - OVSolve for FV in the scientific formula A =Twhere FV and OV are variables.FV =Pls help
FV=OV +TA
1) To solve for a variable means let that variable isolated on one side of the equation.
[tex]A=\frac{FV-OV}{T}[/tex]2) Since we want to solve for FV, let's multiply it crossed like this
[tex]\begin{gathered} TA=FV-OV \\ -FV+TA-TA=-OV-TA \\ -FV=-OV-TA \\ FV=OV\text{ +TA} \end{gathered}[/tex]3) So now we can solve for FV, all that's left are the figures for OV and TA.
Use the data shown to answer the questions that follow.
Person Minutes Shopping in the Store Amount Spent on Groceries at Checkout
1 56.5 177.5
2 84.4 260.2
3 66.3 197.9
4 47.3 82.9
5 48.7 147.1
6 47.1 148.3
7 60.7 182.1
8 76 228
Which graph is most appropriate for these data?
Bar Chart
Scatter Plot
Pie Chart
Time Series Plot
Copy and paste the above data into Excel and make the most appropriate graph for these data. Make sure the x-axis represents the "Minutes Shopping in the Store" and that the y-axis represents the "Amount Spent on Groceries at Checkout."
I have successfully created this graph in Excel as requested.
I have not graphed the data.
One of the values in the plot of this data does not fit the pattern of the other values. It would be called an outlier.
What is the x-value and y-value of the outlier?
(
Number
,
Number
)
Hint: If you hover your mouse over the points in your Excel graph it will show you the exact x-value and y-value of the point.
The one data point that does not fit in scatter plot to the pattern is (60.7 , 182.1)
What is a scatter plot meaning?
A scatter plot is a collection of dots that are plotted on a horizontal and vertical axis. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).Determine the link or correlation between two variables using a scatter plot. You may find out whether your data points might be related by plotting a scattergram with them.The best chart is Scatter Plot
The one data point that does not fit to the pattern is
(60.7 , 182.1)
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Help pleaseeeeeeeeeeeee
First, notice that we have in total 15 items. Then, we have that the probabilities are:
[tex]\begin{gathered} \text{ \# of items with yellow: }3 \\ \Rightarrow P(Yellow)=\frac{3}{15}=\frac{1}{5} \\ \text{ \# of items with purple: 2} \\ \Rightarrow P(Purple)=\frac{2}{15} \\ \text{ \# of items striped: 4} \\ \Rightarrow P(not\text{ striped)}=1-P(striped)=1-\frac{4}{15}=\frac{11}{15} \\ \text{ \# of items solid: 5} \\ \Rightarrow P(solid)=\frac{5}{15}=\frac{1}{3} \\ \text{ \#items with polka dot: 3} \\ \Rightarrow P(not\text{ polka dot) = 1 - P(polka dot) = 1-}\frac{3}{15}=\frac{4}{5} \end{gathered}[/tex]HELP PLEASE ASAP!!!!!!!!!!
Answer:
a b
Step-by-step explanation:websites and etc helped.
Which of the following is equivalent to 1,000,000?
The statement that is equivalent to 1, 0 0 0, 0 0 0 is: C. 10 power of 6.
Determining the equivalent numberGiven digit:
1,0 0 0,0 0 0
Hence,
When something is equivalent to another things it implies or means that both of them are the same or correspond.
We know that 1,000,000 can be re- write as 1 Million and 1000 Thousands.
Now let determine or find the equivalent of 1,000,000 using scientific notation
Scientific notation = 1,000,000
Scientific notation = 10^6
Based on the above 10^6 is equivalent to 1,000,000. We can justified it by pressing 10^6 on our calculator which will in turn gives us 1,000,000.
So,
1,000,000 = 10^6
Therefore we can conclude that the correct option is C based on the fact that 10 raise to power of 6 is the same as 1,0 0 0,0 0 0.
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The complete question is:
Which expression is equivalent to 1,000,000?
A .5 power of 10. B .6 power of 10. C. 10 power of 6. D. 10 power of 5
Solve the following inequality algebraically. [tex] |x - 1| \leqslant 13[/tex]
lx-1 l ≤ 13
There are 2 solutions:
x-1 ≤ 13
and
x-1 ≥ -13
Solve each one
x-1 ≤ 13
add 1 to both sides of the equation
x-1+1≤ 13+1
x ≤ 14
x-1 ≥ -13
Add 1 to both sides:
x-1+1 ≥-13+1
x ≥ -12
-12 ≤ x ≤ 14
A textbook store sold a combined total of 217 sociology and history textbooks in a week. The number of history textbooks sold was 77 less than the number of
sociology textbooks sold. How many textbooks of each type were sold?
Answer:
there were 246 chemistry textbooks and 169 psychology textbooks sold
Step-by-step explanation:
Let
c = the number of chemistry textbooks sold
p = the number of psychology textbooks sold
a textbook store sold a combined total 415 chemistry and psychology textbooks in a week
c + p = 415
the number of chemistry textbooks sold was 77 more than the number of psychology textbooks sold
c = 77 + p
by solving the system of equations
c + p = 415
c = 77 + p
we find
c = 246 chemistry textbooks
p = 169 psychology textbooks
the variable y varies directly as x. when x =20, y= 12 what is the value of y when x = 15a:7b:9c:18d:25
To direct variations use a rule of three, as follow:
[tex]\begin{gathered} \frac{?}{12}=\frac{15}{20} \\ \\ ?=12*\frac{15}{20} \\ \\ ?=\frac{180}{20} \\ \\ ?=9 \end{gathered}[/tex]Then, when x=15, y is 9Answer: B.9