Answer:7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
420÷60 is the same as 42÷6.
42 goes into 6, 7 times:
6, 12, 18, 24, 30, 36, 42.
Therefore, 420÷6 is 7.
Please use a calculator next time.
The carpenter cuts 1-
1
inches off a piece of wood every 2 minutes. How many inches
2
will be cut in 25 min?
What is the average rate of change?
Answer:
1/12
Step-by-step explanation:
See attached worksheet.
Kathy and Peter both drive older cars that dont always work in the wintertime. Suppose that Kathy's car works 80% of the time and Peter's works 65% of the time. What is the probability they will both be working on any given morning?
a spherical snowball is melting in such a way that its volume is decreasing at a rate numerically equal to twice the surface area. how quickly is the radius of the snowball decreasing?
The radius of the snowball decreasing by -2.
What is rate?
A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.
Let r(t) be a function of the radius of the sphere over time.
The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]
The rate of change of the volume is then [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]
Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex], it seems perfectly possible for the volume to decrease at a rate equal to 2s(t).
That just means that
[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]
Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.
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help please thank you !
a*c=c*a
what property is this?
associative communitive identity distributive
Answer: its associative property Hope I helped
Step-by-step explanation:
The angles of a triangle are in the ratio 2:8:5 find the size of each side
Answer:
24° , 60° , 96°
Step-by-step explanation:
sum the parts of the ratio, 2 + 8 + 5 = 15 parts
divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.
180° ÷ 15 = 12° , then
2 parts = 2 × 12° = 24°
5 parts = 5 × 12° = 60°
8 parts = 8 × 12° = 96°
the 3 angles in the triangle are 24° , 60° , 96°
Please Help :))
Given:
Prove: AABC = ACDA.
Step
-
2
try
Statement
ZB ZD
BC AD
AC
AC
Type of Statement
B
Reason
Given
Reflexive Property
D
3) [tex]\angle BCA \cong \angle CAD[/tex] (alternate interior angles theorem)
4) [tex]\triangle ABC \cong \triangle CDA[/tex] (AAS)
How to rewrite the equation. Need the answers fast
Answer:
In this photo.
Put a heart and 5 mark for the answer.
Thanks ヽ(>∀<☆)ノ: o(≧▽≦)o
ヽ(・∀・)ﾉ: (´｡• ω •｡)
(o･ω･o): (＠＾◡＾)
(´• ω •: (＾▽＾)
Rewrite the expression using the Distributive Property. Then simplify.
7(h−10)7h-10
Write the simplified expression.
By the Distributive Property, the expression is 7h - 70
How to rewrite the expression?From the question, the expression is given as
7(h − 10)
As a general rule, the Distributive Property of algebra states that
a(b - c) =a * b - a * c
Using the above as a guide, we have
a = 7, b = h and c = 10
Substitute a = 7, b = h and c = 10 in the equation a(b - c) =a * b - a * c
So, we have
7(h − 10) =7 * h - 7 * 10
Evaluate
7(h − 10) =7h - 70
Hence, the simplified expression is 7h - 70
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Algebra homework pls help
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.
Detailed explanation:Assume that a team has N players.
Each squad may have anywhere from 3 to 5 players, so
3 ≤ 5 ...(i)
Let P represent a player's total points in a single game round.
Each round of the game allows for a maximum of 10 points for each player, so
0 ≤ p ≤ 10 ....( i)
(1) Elena assembled a team of five people.
As a result, 5 players' points in 1 round equal 5P.
Equation (ii) yields the range of
0 ≤ 5p ≤ 50.
As a result, Elena's team's points total ranges from 0 to 50.
(2) If each shot is off by one point, then
One player's points in one round are equal to 10-1=9.
So, 9 x 5 = 45 points were collected by 5 players in 1 round.
(3) Assume that R represents the number of teams as an integer.
the game involves at least three teams, therefore
R ≥ 3 ...( iii)
Given that N players make up one team,
R team has NR players, where R is 3, 4, or more.
Next, using equation (i)
3R ≤ 5R
Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.
The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.
Answer:
(I) Between 0 and 50.
(ii) Between 3 and 5.
(iii) Between 3R and 5R, where R = 3,4,5,...
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A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75% Calculate the state income tax owed on an $90,000 per year salary. tax = $[?] Round your answer to the nearest whole dollar amount.. Enter
The state income tax owed on a $90,000 per year salary is $5,175.
What is the income tax owed?
Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.
Tax paid = income x tax rate
$90,000 x 5.75%
$90,000 x 0.0575 = $5,175
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The state income tax owed on an $90,000 per year salary is $5,175.
What is Tax?Taxes are mandatory contributions levied on individuals or corporations by a government entity
Given,
A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%
We need to find the state income tax owed on an $90,000 per year salary.
Tax paid = income x tax rate
$90,000 x 5.75%
5.75% should be converted to decimal by dividing with 100.
5.75/100=0.0575
So $90,000 x 0.0575 = $5,175
Hence the state income tax owed on an $90,000 per year salary is $5,175.
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The triangle shown is dilated with scale factor =2 which is the image of vertex m after the dilation
ANSWER
(-4, 2)
(Option D)
EXPLANATION
The triangle in the picture is dilated with scale factor 2.
This simply means that the size of the triangle was increased by 2.
To do this, first, let us write out the cordinates of the vertices of the original triangle:
M(-2, 1)
P(2, -2)
A(3, 5)
To dilate this, we will multiply the cordinates by 2, they become:
M' (-4, 2)
P' (4, -4)
A' (6, 10)
Therefore, the vertex M on the image after the dilation is (-4, 2).
(Option D)
y=-3x^2+6x-9
vertex?
Axis of symmetry?
Y-intercept?
show work thx
Step-by-step explanation:
I wrote it on paper. I hope this is helpful
The graph below represents the number of miles, y, that Jacob can drive his car for
every gallons of gas. Find the rate of change.
The average rate of change of the given graph is 31.3
How to determine the average rate of changeThe graph of the function is represented as the given parameter
From the graph, we have the following points
(x, y) = (10, 313) and (20, 626)
The average rate of change is the slope of the function and the average rate of change is calculated as
Average rate = [f(b) - f(a)]/[b - a]
Where
(a, f(a)) = (10, 313) and (b, f(b)) = (20, 626)
Substitute the known values in the above equation
So, we have
Average rate = [626 - 313]/[20 - 10]
Evaluate
Average rate = 31.3
Hence, the average rate is 31.3
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A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps
The standard form of a hyperbola with center (h,k) is
We know the vertices are at (5,0) and (-5,0)
The vertices are at (h+a,k) and ( h-a,k)
The center must be at (0,0) and the a value is 5
The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)
c is equal to 6
We know that c^2 = a^2+b^2
6^2 = 5^2 + b^2
36 = 25+b^2
11 = b^2
We can write the equation
What is the midpoint of A B if A = (−2, 2) and B = (3, −1)? Enter your answer in the boxes below. Midpoint of A B = ( , )
The coordinate of the midpoint AB is (1/2, 1/2)
How to determine the midpoint?From the question, the coordinates of the points are given as
A = (-2, 2)
B = (3, -1)
The midpoint of a line or points is then calculated using the following midpoint formula
Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)
Where x and y are the coordinates of A and B
Substitute the known values in the above equation
So, we have the following equation
AB = 1/2 * (-2 + 3, 2 - 1)
Evaluate the sum
AB = 1/2 * (1, 1)
Evaluate the products
AB = (1/2, 1/2)
Hence, the midpoint is (1/2, 1/2)
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the radius of a closed right circular cylinder is increasing at a rate of 5 inches per minute and the height is decreasing at a rate of 3 inches per minute. (a) what is the rate of change of the volume of the cylinder when the radius is 10 inches and the height is 20 inches? round your final answer to the nearest thousandth. (b) what is the rate of change of the surface area of the cylinder when the radius is 10 inches and the height is 20 inches? round your final answer to the nearest thousandth.
When the radius is 10 inches and the height is 20 inches
(a) rate change of the volume of the cylinder is 5340.7 inch²/min.
(b) rate of change of the surface area of the cylinder is 1068.14 inch²/min.
Volume and surface area of the closed cylinder both increase with time.
Let r be the Radius and h be the height of the cylinder in inches at time t.
[tex]\frac{dr}{dt} =5[/tex] inch/min and [tex]\frac{dh}{dt} =-3[/tex] inch/min
Let V be the volume of the cylinder then
Differentiating with respect to t,
[tex]\frac{dV}{dt} =2\pi r(\frac{dr}{dt} )h+\pi r^{2} \frac{dh}{dt}[/tex]
At r=10 inch and h=20 inch,
[tex]\frac{dV}{dt} =1700\pi =[/tex] 5340.7 inch²/min ≈ 5000 inch²/min
Thus, it is increasing with time as it has a positive sign.
Let S be the surface area of a closed cylinder
[tex]\frac{dS}{dt} =2\pi r(\frac{dr}{dt} )h+2\pi r(\frac{dr}{dt} )+4\pi (\frac{dr}{dt} )r[/tex]
At r=20 inch and h=20 inch
[tex]\frac{dS}{dt} =340\pi =[/tex] 1068.14 inch²/min ≈ 1000 inch²/min
It is also increasing with time as it is also having a positive sign.
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PLEASE HELP!!!!!!!!!!!!!
A stem and leaf plot shows the number of kilometers walked for charity. The plot is titled 'Kilometers Walked for Charity.' The numbers 12, 13, 14, 15, 16, and 17 are in a vertical column to the left of a vertical line.
· On the same line as 12 but on the right of the vertical line are the numbers 3, 3, 6, 7, 9, and 9.
· On the same line as 13 but on the right of the vertical line are the numbers 1, 1, 4, 5, and 5.
· On the same line as 14 but on the right of the vertical line are the numbers 0, 0, 2, 3, 3, 8, 8, and 9.
· On the same line as 15 but on the right of the vertical line are the numbers 2, 2, 2, 2, 2, 3, 5, 5, and 7.
· On the same line as 16 but on the right of the vertical line are the numbers 4, 5, 5, 9, and 9.
· On the same line as 17 but on the right of the vertical line are the numbers 3 and 5.
The key to the stem and leaf plot identifies that 12 vertical line 3 means 12.3.
a. Describe how to find the range of the data set.
b. Find the range.
The range is the difference between the largest and the smallest and the range is 5.2
What is a stem and leaf plot?This is a graph that is divided into two vertical axes such that one axes represent the stem and the other axis represents the leaf
How to determine the range of the stem and leaf plot?From the question, we have the following parameters:
Stems = 12, 13, 14, 15, 16, and 17
Each of these stem elements have their own leaves
So, the complete stem and leaf plot is as follows
12 | 3, 3, 6, 7, 9, 9.
13 | 1, 1, 4, 5, 5.
14 | 0, 0, 2, 3, 3, 8, 8, 9.
15 | 2, 2, 2, 2, 2, 3, 5, 5, 7.
16 | 4, 5, 5, 9, 9.
17 | 3 5.
Key
12 | 3 means 12.3.
To determine the range, we simply take the smallest number and the largest number represented by the plot and calculate the difference
The actual rangeIn (a), we have
The range is calculated from the smallest number and the largest number represented by the plot
So, we have
Smallest = 12.3
Largest = 17.5
So, the range is
Range = 17.5 - 12.3
Evaluate
Range = 5.2
Hence, the range is 5.2
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Multiply: -6 x 1 II don't get it!!!
The multiplication we need to make is:
[tex]-6\times1[/tex]To answer this question we need to use the following rules for multiplications with signs:
[tex]\begin{gathered} (+)\times(+)=+ \\ (-)\times(-)=+ \\ (+)\times(-)=- \\ (-)\times(+)=- \end{gathered}[/tex]We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.
So, we know from the rule that the result will be negative.
And finally, we multiply just the numbers: 6 by 1 is 6.
In summary, the result is:
[tex]-6\times1=-6[/tex]Answer: -6
Answer:
-6
Step-by-step explanation:
hope this helps
PLEASE ANSWER
A) A local shoe store buys shoes at a wholesale price and then marks them up 80% to calculate the retail price. The wholesale price varies, depending on the quantity of shoes purchased. (2 points)
Quantity 0-20 pairs 21-40 pairs 41-60 pairs 61-80 pairs 81 or more pairs
Wholesale Price
(per pair) $25.00 each $23.00 each $21.00 each $19.00 each $17.00 each
Write an equation that could be used to find the retail price for each range. How do you know the equation will work consistently for each range?
The equation will be used for solving the retail price is y = 1.8x
Given,
The equation will be used for solving the retail price is y = 1.8x
A local shoe store buys shoes at a wholesale price.
and mark up 80%
The table is:
Quantity Wholesale Price
0-20 pairs $25.00
21-40 pairs $23.00
41-60 pairs $21.00
61-80 pairs $19.00
81 or more pairs $17.00
To find the retail price for each range.
Now, According to the question:
An equation will be used :
the equation for all of them would be :
y = new price
x = wholesale price
y = 1.8x
Quantity of :0 - 20 pairs.
= 25 x 1.80
= $45.00
Quantity of: 21 - 40 pairs
= 23 x 1.80
= $41.40
Quantity of: 41 - 60 pairs
= 21 x 1.80
= $37.80
Quantity of: 61 - 80 pairs
= 19 x 1.80
= $34.20
Quantity of: 81 or more pairs
= 17 x 1.80
= $30.60
Hence, The equation will be used for solving the retail price is y = 1.8x
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one sheet of paper in a notebook is 8 1/2 inches by 11. a smaller notebook has a similar shape, and its pages are 5 1/2 inches long. what is the width of the paper in the smaller notebook?
The width of the paper in the smaller notebook is 4 1/4 inches.
When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.
For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.
If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is
11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook
width of smaller notebook = 4 1/4 inches
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Question is stated in picture. Don’t forget to round to nearest hundreth!!
The volume of a cylinder is given by the following formula:
[tex]V=\pi r^2h[/tex]Where r is the radius and h is the height of the cylinder.
By replacing 8 for r and 6 for h into the above formula, we get:
[tex]V=\pi\times8^2\times6=1205.76[/tex]Then, the volume of the cylinder equals 1205.76 units³
solve equationx^2-2x-7=0
After solving the equation x^2-2x-7=0, values of x are -1 + 2√2 and
-1 - 2√2.
A quadratic equation has a leading coefficient of the second degree.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
After applying the quadratic formula to it we get,
[tex]x = \frac{-b +\sqrt{b^{2} - 4ac } }{2a} \\ x = \frac{-b -\sqrt{b^{2} - 4ac } }{2a}[/tex]
where a = 1
b = 2
c = -7
After putting the values of a,b, and c, we get
x = -1 + 2√2 and,
x = -1 - 2√2 .
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Rhoni reads at a rate of 75 pages per hour. The number of pages Rie reads over time is shown in the table.
A table with two rows and five columns is shown. The first row is Time in hours. The second row is number of pages. Three hours, one hundred ninety-five pages. Five hours, three hundred twenty-five pages. Nine hours, five hundred eighty-five pages. Ten hours, six hundred fifty pages.
Question 1
Part A
Who has a greater rate of reading?
Select the answers from the drop-down lists to correctly complete the sentence.
The individual that has a greater rate of reading is Rhoni.
Who has a greater rate of reading?Rate measures how fast a person is reading a book. Rate is the total pages read per time. Rate is determined by dividing total pages read by the total time spent reading.
Division is the operation used in mathematics that is used to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
Rie's rate = pages read / time
195 / 3 = 65 pages per hour
325 / 5 = 65 pages per hour
Rie's rate is 65 pages per hour. While Rhoni's rate is 75 pages per hour. This means that Rhoni reads faster than Rie.
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Determine whether there is enough information to conclude that the triangles are congruent. If so, select the theorem
you used.
Given: TR intersects NP, TU RU, NU - PU
Is ATUN ARUP?
N
No. There is not enough information to conclude that the triangles are congruent.
SAS
Yes. There is enough information to conclude that the triangles are congruent.
ASA
SSS
Previous
Answer:
SAS
Step-by-step explanation:
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP HELP
Answer:
a) 1.6×10∧-6
b)2×10∧7
O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...
Answer:
[tex]\begin{gathered} length\text{ = 8 m} \\ width\text{ = 5.5 m} \end{gathered}[/tex]Explanation:
Here, we want to get the dimensions of the rectangle
Let us represent the length by l and the width by w
From the question:
The length of the rectangle is 3 m less than double the width
Mathematically:
[tex]l\text{ = 2w-3}[/tex]The product of the two represents the area
[tex]\begin{gathered} A\text{ = l }\times\text{ w} \\ lw\text{ = 44} \end{gathered}[/tex]Now, let us substitute the first equation with the second:
[tex]\begin{gathered} w(2w-3)\text{ = 44} \\ 2w^2-3w\text{ = 44} \\ 2w^2-3w-44\text{ = 0} \end{gathered}[/tex]Solving the quadratic equation, we have:
[tex]\begin{gathered} 2w^2-11w+8w-44\text{ = 0} \\ 2w^2+8w-11w-44\text{ = 0} \\ 2w(w\text{ + 4\rparen -11\lparen w+4\rparen = 0} \\ (2w-11)(w+4)\text{ = 0} \\ 2w=\text{ 11} \\ w\text{ = }\frac{11}{2} \\ \\ w\text{ = 5.5} \end{gathered}[/tex]Recall:
[tex]\begin{gathered} lw\text{ = 44} \\ 5.5l\text{ = 44} \\ l\text{ = }\frac{44}{5.5}\text{ = 8 } \end{gathered}[/tex]9. What is the value of x?
Answer:
A, 61.
Step-by-step explanation:
(2x+24). If we sub in 61 for x, we get (2(61)+24). Follow order of operations.
2 times 61= 122. Add 24 and you get 146. We can know this is correct because we are given the other angle and it's degrees, whch is also 146 degrees. Therefore, the answer is A, 61.
The school play sells children's
tickets for $3 each and adult
tickets for $5 each. They sold $340
worth of tickets The total number
of tickets sold was 80 How many
aduit tickets were sold?
Taking into account the definition of a system of linear equations, the number of adult tickets sold was 50.
System of linear equationsA system of linear equations is a set of linear equations in which two or more variables are related.
In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in the equations.
Amount of adults tickets soldIn this case, a system of linear equations must be proposed taking into account that:
"a" is the amount of adults tickets sold."c" is the amount of childrens tickets sold.You know:
The school play sells children's tickets for $3 each and adult tickets for $5 each. They sold $340 worth of tickets.The total number of tickets sold was 80.The system of equations to be solved is
3c + 5a= 340
c + a= 80
From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "c" from the second equation:
c= 80- a
Replacing this expression in the first equation:
3×(80- a) + 5a= 340
Solving:
3×80- 3a + 5a= 340
3×80- 3a + 5a= 340
240- 3a + 5a= 340
- 3a + 5a= 340- 240
2a= 100
a=100÷ 2
a= 50
Finally, 50 adult tickets were sold.
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