A snowstorm dumped 22 inches of snow in 8 hours. What was the average snowfall per hour?
2.615
Step-by-step explanation:
22 divided by 8
the average snowfall per hour is 2.75 inch.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, given that,
A snowstorm dumped 22 inches of snow in 8 hours.
i.e. per hour = 22/8
=2.76
hence, the average snowfall per hour is 2.75 inch.
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x = 15.
PQ = SQ.
Find y, explain good for brainliest
Answer:
y = 25.
Step-by-step explanation:
PQ and RQ and SQ are congruent so
x + 10 = 2x - 5
15 = x.
So PQ = 15 + 10 = 25.
But PQ = RQ = y, so
y = 25.
How do you integrate [tex]\int\limits ln({x+1}) \, dx[/tex] using integration by parts?
Thank you!
Answer:
[tex]\int \ln (x+1) \, dx=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
Step-by-step explanation:
Use integration by parts formula:
[tex]\int u \, dv=uv-\int v \, du[/tex]
For the integral
[tex]\int \ln(x+1) \, dx,[/tex]
[tex]u=\ln (x+1)\\ \\dv=dx,[/tex]
then
[tex]du=d(\ln (x+1))=\dfrac{1}{x+1}\ dx\\ \\v=x[/tex]
and
[tex]\int \ln(x+1) \, dx\\ \\=x\cdot \ln (x+1)-\int x\cdot \dfrac{1}{x+1} \, dx\\ \\= x\cdot \ln (x+1)-\int \dfrac{x+1-1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-\int \left(1-\dfrac{1}{x+1}\right) \, dx\\ \\=x\cdot \ln (x+1)-\int \, dx +\int \dfrac{1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
Marissa has 10 grapes. Roger has 3 times as many grapes as Marissa. How many grapes do Marissa and Roger have in all?
Answer:
The answer is 40
Step-by-step explanation:
First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40
A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second is a peach.
Answer:
Step-by-step explanation:
Total fruits T= 5+7 = 12
No. Of apple n(A) = 5
No. Of peaches n(P) = 7
P(A) 1st = n(A)/T = 5/12
P(P) 2nd = n(p)/(T-1) = 7/11
: P(A and P) = 5/12 × 7/11
= 35/132
Can yall help me with the second part Pls
Answer:
Step-by-step explanation:
Total money raised = 658 + 95.60 = $ 753.60
donated to each charity = 753.60/12 = $62.80
70 percent of 330 is the same as 60 percent of what number?
Answer:
yassar
Step-by-step explanation:
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ?
o left 4, down 9
O left 4, up 23
Oright 4, down 9
O right 4, up 23
Answer:
Move right by 4 units and down by 9 units
Step-by-step explanation:
The vertex of the parabolic function f(x) = x² is at (0,0)
Now, the parabolic function g(x) = - 8x + x² + 7 can be rearranged to vertex form.
g(x) = x² - 8x + 16 + 7 - 16
⇒ g(x) = (x - 4)² - 9
⇒ (x - 4)² = (y + 9) {If y = g(x)}
Therefore, the vertex of the parabolic function g(x) is at (4,-9).
Therefore, we have to move right by 4 units and down by 9 units to reach from vertex of f(x) to vertex of g(x). (Answer)
Using translation concepts, it is found that the translation that maps f(x) into g(x) is described by: right 4, down 9
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, function f(x) is defined by:
f(x) = x².
Function g(x) is defined by:
g(x) = x² - 8x + 7
Completing the squares, we have that g(x) can be written as:
g(x) = (x - 4)² - 9
Hence, the correct translation is:
right 4, down 9
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Find the roots of this polynomial x^2 -9x+8
Final answer:
x = 1 and x = 8.
Explanation:
This can be completed through factoring the quadratic equation. To factor x^2 - 9x + 8, we look for two numbers that multiply to +8 and add to -9. These numbers are -1 and -8 since (-1) * (-8) = +8 and (-1) + (-8) = -9. Therefore, we can write the polynomial as (x - 1)(x - 8). The roots are the values of x which make each factor zero, hence we get the roots as x = 1 and x = 8.
A television is identified by the diagonal measurement of the of screen. A television has a 36 inch screen whose height is 22 inches.what is the length of the television screen
Answer:
28.5 inches.
Step-by-step explanation:
Given: Measurement of diagonal= 36 inch.
Height= 22 inches
Picture attached to show the measurement.
As the screen of televison is measured by diagonal of screen.
∴ Hypotenous= diagonal of screen, which is 36 inches.
Now, using pythagorean theoram to find length of television screen.
[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]
∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]
Here adjacent is the length of television.
⇒[tex]1296= 484+ length^{2}[/tex]
Subtracting both side by 484.
⇒[tex]length^{2} = 812[/tex]
Taking square root on both side
remember: [tex]\sqrt{a^{2} } = a[/tex]
∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]
Hence, length of televison screen is 28.5 inches.
The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.
Explanation:To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.
Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.
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m = 3, through (1,-1)
Point-Slope
Slope intercept
Answer:
[tex]\large\boxed{y+1=3(x-1)}\\\\\boxed{y=3x-4}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - a point on a line
We have
[tex]m=3,\ (1,\ -1)\to x_1=1,\ y_1=-1[/tex]
Substitute:
[tex]y-(-1)=3(x-1)\\\\\boxed{y+1=3(x-1)}[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]y+1=3(x-1)[/tex] use the distributive property
[tex]y+1=3x-3[/tex] subtract 1 from both sides
[tex]\boxed{y=3x-4}[/tex]
The double number line show that 4 bottles of water cost 10 dollars at a music festival.
Based in the ratio shown in the double number line, how much does 3 bottles of water cost?
Answer:
$7.50
Step-by-step explanation:
10 divided by 4 = $2.50
so, $2.50 x 3 = $7.50
Answer:
$7.5 Dollars
Step-by-step explanation:
The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50 (division)
Now, to find the cost of 3 water-bottles, we have to multiply.
$2.50 * 3 = $7.50.
So, the answer to this question is 3 bottles = $7.50
(Hope this helps!)
Which of the following is an odd function?
f(x) = x3 + 5x2 + x
O F(x)= √x
Of(x) = x2 + x
O f(x) = -x
Option 4
f(x) = -x is an odd function
Solution:
A function is odd if and only if f(–x) = –f(x)
Option 1
[tex]f(x) = x^3 + 5x^2 + x[/tex]
Substitute x = -x in above equation
[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]
Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative
Ans squaring results in positive
[tex]f(-x) = -x^3 + 5x -x[/tex] --- eqn 1
[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex] ---- eqn 2
Comparing eqn 1 and eqn 2,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 2
[tex]f(x) = \sqrt{x}[/tex]
[tex]f(-x) = \sqrt{-x}[/tex]
[tex]-f(x) = - \sqrt{x}[/tex]
Therefore,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 3
[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]
[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 4
[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]
[tex]-f(x) = -(-x) = x[/tex]
[tex]f(-x) = -f(x)[/tex]
Thus option 4 is correct and it is an odd function
Answer:
D
Step-by-step explanation:
just took test on edge
PLZ HELP !!!
SCREENSHOT
PLEASE HELPPPPPPP
Espress 15 x^1/2 y^1/5 using a radical
Answer:
The correct answer is C. 15 ¹⁵√x⁵y³
Correct question and statement:
Express 15x^1/3 y^1/5 using a radical, as it is written in the graph attached.
Step-by-step explanation:
15x^1/3 y^1/5
15 * (x^1/3 y^1/5)
For multiplying two fractional exponents with different bases, we need to equal the denominator of the fractional exponents.
Therefore, we have:
1/3 * 5/5 = 5/15 ⇒ 1/5 * 3/3 = 3/15
15 * (x^5/15 y^3/15)
Now we can express the fractional exponents as an only radical, this way:
x^a/b = ᵇ√xᵃ
15 * ¹⁵√x⁵y³
The correct answer is C. 15 ¹⁵√x⁵y³
Bill wants to post three parcels.
Parcel 1
Parcal 2
Parcel 3
Each parcel costs £1.10 to post.
How much change should he get from a £10 note?
The change Bill should receive from a £10 note after paying to post three parcels, each costing £1.10, is £6.70.
Explanation:Bill wants to post three parcels and each parcel costs £1.10 to post. The total cost for posting all three parcels would be £1.10 * 3 = £3.30. If he pays this fee with a £10 note, we can calculate the change by subtracting the total cost of posting parcels from the value of the note: £10 - £3.30 = £6.70. So, the change Bill should get back from a £10 note after posting 3 parcels each costing £1.10 is £6.70.
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the diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 8.5 cm. what is the approximate area of the shaded region.
PLZZZ HELP
Answer:
[tex]A=65.97\ cm^2[/tex]
Step-by-step explanation:
The complete question is
The shaded region is the area outside the smaller circle and inside the larger circle
we know that
The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
so
The area of the shaded region is
[tex]A=\pi [r_1^2-r_2^2][/tex]
where
[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)
[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)
assume
[tex]\pi =3.1416[/tex]
substitute
[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]
[tex]A=65.97\ cm^2[/tex]
This month 9,675 people visited Hank’s web site.This is 3 times the number that visited last month.How many people visited Hank’s web site last month?
Answer:
29,025 is the answer
Step-by-step explanation:
9,675 × 3
The number of people who visited Hank's website last month is found by dividing the total visitors this month (9,675 people) by 3, resulting in 3,225 visitors last month.
Explanation:The student is faced with a mathematics problem involving division with whole numbers. The problem states that the number of people who visited Hank's website this month is three times the number of visitors from the previous month. Given that we know the number of visitors this month is 9,675, we can find out the number of visitors from the previous month by dividing this number by three.
So, the calculation is:
9675 people (this month) ÷ 3
From this calculation, we can determine that 3,225 people visited Hank's website last month.
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John sells tickets to a school concert. Adult tickets cost $6.50 and children’s tickets cost $4.50. John collects a total of 157.50 from the ticket sales and he sells twice as many adult tickets as children’s tickets. How many tickets does he sell all together?
John sold 18 adults tickets and 9 children tickets.
Step-by-step explanation:
Given,
Cost of adult ticket = $6.50
Cost of children ticket = $4.50
Total collected = $157.50
Let,
Number of adult tickets sold = x
Number of children tickets sold = y
According to given statement;
6.50x+4.50y=157.50 Eqn 1
he sells twice as many adult tickets as children’s tickets.
x=2y Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]6.50(2y)+4.50y=157.50\\13y+4.50y=157.50\\17.50y=157.50[/tex]
Dividing both sides by 17.50
[tex]\frac{17.50y}{17.50}=\frac{157.50}{17.50}\\y=9[/tex]
Putting y=9 in Eqn 2
[tex]x=2(9)\\x=18[/tex]
John sold 18 adults tickets and 9 children tickets.
Keywords: linear equation, substitution method
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How do I graph 7x+2y=-10
Can someone Please Help Me
Answer:
a= 63 ⁰; z= 80⁰; x= 30⁰; N= 102⁰;M = 66⁰
Step-by-step explanation:
Example 1 : the angle opposite to angle 2a is 54 degrees because it is the opposite exterior angle of 54 degrees angle so
2a+54⁰= 180⁰
2a= 180⁰-54⁰
2a= 126⁰
a= 126/2= 63⁰
EXAMPLE 2: Opposite exterior angles are equal so
z+25⁰= 105⁰-------A
z= 105⁰-25⁰
z=80⁰
It is making a straight angle so
105⁰+ 3x-15= 180⁰
3x-15=180-105
3x-15=75⁰
3(x-5)=75⁰
x-5⁰=75/3
x-5⁰=25⁰
x= 25⁰+5⁰
x=30⁰
EXAMPLE 3:
114⁰= N+12⁰ (exterior opposite angles are equal)
N= 114⁰-12⁰
N= 102⁰
114⁰+M= 180⁰ (straight angles)
M= 180⁰- 114⁰
M= 66⁰
Choose the graph below that represents the solution to the system of equations
y= 3x + 2
10x + 2y = 20
Answer:
Graph 3 represents the solution to the system of equations.
Step-by-step explanation:
The given two linear equations of x and y are
y = 3x + 2 ........ (1) and
10x + 2y = 20 .......... (2)
Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).
Hence, 10x + 2(3x + 2) = 20
⇒ 16x = 16
⇒ x = 1
And from equation (1), y = 3x + 2 = 5
Therefore, the solution of the system of equations (1) and (2) are (1,5).
Therefore, graph 3 represents the solution to the system of equations. (Answer)
1/8x___=7/8
0 1 2 3 4 5 6 7 8 9
Answer:
1/8x___________=7/8 the answer is 6
Here is a list of numbers.
32 29
20
30
37
34
33
31
Tanya thinks that to work out the median, she simply needs to find
the middle number. So she says that "37" is the median for this list of numbers.
Tanya's answer is not correct.
a) Describe what is wrong with her method.
b) Work out the median of the numbers in the list.
The median is found by ordering the numbers and choosing the middle one (or the average of the two middle ones in the case of an even set). Tanya's mistake was not ordering the numbers before choosing the median. Thus, the correct median for the provided list is 31.5.
Explanation:In mathematics, the median is the middle number in a sorted, ascending or descending, list of numbers. It can be found by arranging all the numbers from smallest to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.
So, here is the mistake in Tanya's method: She didn't arrange the numbers in order from smallest to largest before choosing the middle number. This is why 37 is not the correct median.
Now, let's find the correct median for the provided list of numbers: 20, 29, 30, 31, 32, 33, 34, 37. Since it's an even number of observations, we take the average of the two middle numbers, which are 31 and 32. Hence, the median of the numbers in the list is (31+32)/2 = 31.5.
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(a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order.
(b) The median of the numbers in the list is 31.5.
a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order. The median is the middle number in a sorted list of numbers. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle numbers. Tanya needs to sort the numbers before finding the median.
b) Sort the numbers in ascending order, so the list will become.
[tex]\[ 20, 29, 30, 31, 32, 33, 34, 37 \][/tex]
Determine the median:
Since there are 8 numbers (an even number of elements), the median will be the average of the 4th and 5th numbers in the sorted list.
- The 4th number is 31.
- The 5th number is 32.
[tex]\[ \text{Median} = \frac{31 + 32}{2} = \frac{63}{2} = 31.5 \][/tex]
Therefore, the median of the numbers in the list is 31.5.
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2 kg, the acceleration of the object is 35 /ms2. When the same force acts upon another object, its acceleration is 10 /ms2. What is the mass of this object?
Answer:
7 kg
Step-by-step explanation:
F=35*2=m*10
70=10m
7=m
The mass of the second object is 7 kg
First, we make the following representations
[tex]F \to[/tex] Force
[tex]a \to[/tex] acceleration
[tex]m \to[/tex] mass
The formula of force is:
[tex]F = m * a[/tex]
Since force is constant, then:
[tex]m_1 =2kg[/tex] [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object
[tex]m_2 = ??[/tex] [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object
We are to calculate the mass of the second object
A constant force means:
[tex]m_1 * a_1 = m_2 * a_2[/tex]
Make m2 the subject
[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]
Substitute known values
[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]
[tex]m_2 = \frac{2kg * 35}{10}[/tex]
[tex]m_2 = \frac{70kg}{10}[/tex]
[tex]m_2 =7kg[/tex]
Hence, the mass of the second object is 7kg
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if sin(x)=m, with m>0, find the value of sin(pie-x)
Answer:
Step-by-step explanation:
Sin (π - x ) = Sin x = m
(x/(x+1) + 1)*((1+x)/(2x-1))
The question is a college-level mathematics problem involving taking the third derivative of the function f(x) = 2x/(x^2 - 1). The process requires the application of quotient rule and chain rule of differentiation.
Explanation:The student question involves calculating the third derivative of the function f(x) = 2x/(x2 - 1). This function is a rational function and can be differentiated using the quotient rule and chain rule of differentiation. Let's proceed with the derivative calculations.
First, we should recall that the function can be rewritten as:
f(x) = 2x/(x2 - 1) = 2x/[(x - 1)(x + 1)]
Now we can calculate the derivatives. For the first derivative f'(x), we use the quotient rule:
f'(x) = [(x2 - 1)(2) - (2x)(2x)]/(x2 - 1)2
For the second derivative f''(x), we differentiate f'(x) again:
f''(x) = Derivative of f'(x) with respect to x
The third derivative f'''(x) is then the derivative of f''(x). Calculations for the second and third derivatives can be a bit complex and lengthy, and it is necessary to apply the quotient rule and product rule carefully.
Through this process, we will arrive at the third derivative, f'''(x), which is what the question asks for.
The area of a rectangle is 4y + 10.
A. Represent the area of the rectangle in factored form.
B. Use the factored form to give one possible set of dimensions for this rectangle.
A) The factored form of area of rectangle is 2(2y + 5)
B) length of rectangle is 2 and width is 2y + 5 and one possible set of dimensions of rectangle is length 2 and width 7
Solution:
Given that area of rectangle is 4y + 10
A. Represent the area of the rectangle in factored form
The factored form is a parenthesized algebraic expression.
Factored form is a product of sums of products or a sum of products of sums
Given area of rectangle is 4y + 10
Taking 2 as common,
4y + 10 = 2(2y + 5)
Therefore, the factored form of given area of rectangle is 2(2y + 5)
B. Use the factored form to give one possible set of dimensions for this rectangle
The area of a rectangle is given by the formula:
area of rectangle = length x width
Therefore, area of rectangle = 2(2y + 5)
So the length of rectangle is 2 and width is 2y + 5
Or the length of rectangle is 2y + 5 and width is 2
If y = 1, then one possible set of dimensions of rectangle is:
length = 2 and width = 2(1) + 5 = 7
So one possible set of dimensions of rectangle is length 2 and width 7
Final answer:
The factored form of the area of the rectangle is 2(2y + 5).
One possible set of dimensions, based on the factored form, is a length of 2y units and a width of 5 units.
Explanation:
To represent the area of a rectangle in factored form, we look for factors of the expression 4y + 10. Both terms have a common factor of 2, so the factored form is:
2(2y + 5).
Now, to give one possible set of dimensions for the rectangle using the factored form, we can consider each factor as a dimension:
Length: 2yWidth: 5Thus, one possible set of dimensions for the rectangle could be 2y units (length) and 5 units (width).
A hotel has 150 rooms. Those with kitchen facilities rent for $100 per night in those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $13,000. How many of each type of room does the hotel have?
Answer:
50 rooms with kitchen facilities and 100 rooms without kitchen facilities
Step-by-step explanation:
Let the rooms without kitchen facilities be x and those with kitchen facilities be y
Form set of equations
Since the total rooms are 15, then the first equation is
x+y=150
Therefore, x=150-y
Considering the cost of rooms and what was collected, then
80x+100y=13000
Substituting x with 150-y then
80(150-y)+100y=13000
12000-80y+100y=13000
20y=1000
[tex]y=\frac {1000}{20}=50 rooms[/tex]
Therefore, x=150-y=150-50=100 rooms
Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities
Kurt says factors and multiples are
related. Use the equation 8 X 5 = 40
to label each number as a/
factor or a multiple..
Step-by-step Explanation:
Before heading towards the solution, you need to make sure how multiple and factors are related to each other.
The multiple of a number could be obtained by multiply it with another number.
For example, the first five multiples of 12 are 12, 24, 36, 48 and 60
1 X 12 = 122 X 12 = 243 X 12 = 364 X 12 = 485 X 12 = 60Factors are the numbers that are multiplied to get a given number.
For example,
1 X 12 = 122 X 12 = 243 X 12 = 36The factors of 12 are 1, 2, 3, 4, 6 and 12.
As division and multiplication can be used to find factors and multiples.
For example a whole number is a multiple of its factors.
Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.
As 2 is a factor of 20 because 20 ÷ 2 = 4
20 is a multiple of 2 because 2 X 10 = 20
So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.
Let the equation be
8 X 5 = 40
8 is a factor of 40 because 8 X 5 = 40
40 is a multiple of 8 because 40 ÷ 5 = 8
So, this is how factors and multiples are related to each other.
Keywords: factors, multiples, division, multiplication
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