Doug can read 33 pages in one hour.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total pages in a book= 231 pages
Time to read books= 7 hours
so, in 1 hour he can read = 231/7
= 33 pages.
Hence, he can read 33 pages in one hour.
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What is the arc length when 0=3pi over 5 and the radius is 7?
Describe how the graphs of functions f and g are related: f (x) = 2cos(pi x) g(x) = 2cos(2pi x)
Design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
The two pairs of polar coordinates are : [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
Polar coordinates are coordinates labeled as ( r, θ ) , where r = radial coordinate while θ is known as the angular coordinate. Polar coordinates are also plotted on a polar grid.
Using the given data
Point ( 3 , - 3 )
[tex]r = \sqrt{3^2 + (-3)^2} = 3\sqrt{2}[/tex]
θ =
[tex]tan^{-1} (\frac{-3}{3}) = \pi - \frac{\pi }{4} , 2\pi - \frac{\pi }{4} \\\\= 3\pi , \frac{7\pi }{4} , -\frac{\pi }{4}[/tex]
In degrees = 135° , 315° , -45° ( neglecting -45° )
Hence the two pairs of polar coordinates for the point ( 3 , -3 ) can be taken as ; [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
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Answer:
c on edge
Step-by-step explanation:
Henry is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Henry has been adding money. Suppose that x and y are related by the equation y=20x+650 . Answer the questions below. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What was the starting amount of money in the account? $
What is the change per week in the amount of money in the account? $
Update: solved
$14,146,727 is what percent of $117,190,375
The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y
****PLEASE HELP********
(05.03)
Karma baked 48 cookies yesterday. Every hour, she bakes another batch of 12 cookies.
What is the rate of change for the scenario described?
4
12
60
48
Divide 40x/ 64y by 5x/ 8y
A. 1
B. 3/4
C. 25x^2/ 64y^2
D. 25/64
The division to the expression Divide 40x/ 64y by 5x/ 8y is (a) 1
How to evaluate the quotient expression
From the question, we have the following parameters that can be used in our computation:
Divide 40x/ 64y by 5x/ 8y
As an expression we have
40x/ 64y ÷ 5x/ 8y
So, we have
40x/ 64y ÷ 5x/ 8y = 40x/ 64y * 8y/5x
Divide the variables
This gives
40x/ 64y ÷ 5x/ 8y = 40/64 * 8/5
Lastly, we have
40x/ 64y ÷ 5x/ 8y = 1
Hence, the solution to the expression is (a) 1
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What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors?
Factoring Polynomials with Four Terms, and Factoring Trinomials by Grouping can be used to rewrite square trinomials and difference of squares binomials as separate factors
Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Step-by-step explanation:
Please find the attachment of graph representing the axis of symmetry.
We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:
[tex]f(x)=(x-2)^2+1[/tex]
We can see that our function represents a parabola.
Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.
Let us find the vertex of our given parabola using formula: [tex]x=\frac{-b}{2a}[/tex], where,
a = Coefficient of [tex]x^{2}.[/tex]
b = Coefficient of x.
To apply this formula we will represent our parabola as a quadratic equation [tex](ax^2+bx+c)[/tex] as:
[tex]f(x)=x^2-4x+4+1[/tex]
[tex]f(x)=x^2-4x+5[/tex]
Upon substituting a= 1 and b= -4 in the formula we will get,
[tex]x=\frac{-(-4)}{2*1}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.
I was wondering if anybody had the questions to the module 8 DBA for FLVS. I usually dont do well unless I see the question, I dont need the answers just the question.
Which logarithmic equation is equivalent to the exponential equation below 4c=256
To convert the exponential equation 4c = 256 into a logarithmic form, one can apply the logarithm to both sides, simplifying using the property that the logarithm of a power is the exponent times the logarithm of the base, yielding the equivalent equation c = 4.
The question requires us to convert the exponential equation 4c = 256 into a logarithmic form. To achieve this, we need to recognize that a logarithm function is the inverse of an exponential function. Therefore, applying a logarithm to both sides of the equation will allow us to solve for the variable c.
It's important to note that any logarithmic base can be used, but common practice is to use either base 10 (common logarithm) or the natural base e (natural logarithm).
Since 256 is 4 raised to the 4th power (4⁴), we can write the equation as 4c = 4⁴. By applying the logarithm, we then get the equivalent logarithmic equation log(4c) = log(4⁴).
Using the property of logarithms that states the logarithm of a number raised to an exponent will be the product of the exponent and the logarithm of the number, we can simplify this to c*log(4) = 4*log(4). Since log(4) is a common factor on both sides, dividing by log(4) gives us c = 4.
select the TWO binomials that are factors of this
since the last number -s -20 you need the 2 that when multiplied together would equal -20
so x-5 and x +4 are the correct answers
Simplify the expression 32 • 5 − 6 ÷ 2.
18 19.5 36 42
Which of the following is a polynomial with roots 5, 7, and −8?
What is the difference between an image and a pre-image in a transformation? How do you tell them apart?
The image is the product of a transformation while a pre-image is the original image on which a transformation operation is performed.
What is the image in a transformation?The image is the product of a transformation or it is the figure obtained after a transforms operation is performed.
What is the preimage in transformation?A pre-image is the original image on which a trabsosfiemarion operation is performed.
The pre-image is differentiated from the image by the labelling convention used as well as by studying the transformation performed.
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A bag contains 10 tiles with the letters A, B, C, D, E, F, G, H, I, and J. Five tiles are chosen, one at a time, and placed in a row. Meghan says that the probability of the five tiles spelling FACED is 1/252 . Her work is shown below.
The cost of a daily newspaper varies from city to city. however, the variation among prices remains steady with a standard deviation of 20?. a study was done to test the claim that the mean cost of a daily newspaper is $1.00. ten costs yield a mean cost of 96? with a standard deviation of 18?. do the data support the claim at the 1% level?
First, we establish our hypothesis:
Null hypothesis H0: μ = $1.00
Alternative hypothesis Ha: μ ≠ $1.00
Let’s say X = the sample average cost of a daily newspaper = 0.96
u = population mean cost = 1.00
S = sample standard deviation = 0.18
Calculating for z value:
z = (X – u) / S
z = (0.96 – 1) / 0.18
z = – 0.222
From the standard distribution table at this z value, p-value = 0.4129
Since alpha = 0.01, the decision therefore is:
Do not reject the null hypothesis because the p-value is greater than 0.01. There is enough evidence to support the claim that the mean cost of newspapers is $1.
Elisa needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and Elisa scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch? (in inches)
The gross weight of a package in its contents is 11 lbs. 5 oz. if the packaging weighs 1 lb. 15 oz. what the net weight of the content
The vertex of the functions graph is given. Find c. y=2x^2-6x+c;(3/2, 0.5)
Multiply 8 times the square root of 3 by 9 times the square root of 27.
8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
To multiply 8 times the square root of 3 by 9 times the square root of 27, we can simplify the expression using the properties of square roots and perform the multiplication.
First, let's simplify the square roots:
Square root of 3 can be written as √3.
Square root of 27 can be written as √(9 * 3), which further simplifies to √9 * √3 = 3 * √3.
Now, we have:
8 * √3 * 9 * √27 = 8 * √3 * 9 * (3 * √3) = 8 * 9 * 3 * √3 * √3 = 216 * 3 * √3 * √3.
Since the square root of 3 multiplied by itself (√3 * √3) simplifies to 3, we have:
216 * 3 * 3 = 1944.
Therefore, 8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
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Which table describes the behavior of the graph of f(x) = 2x³ - 26x - 24?
Answer:
The answer is the table B
Step-by-step explanation:
we have
[tex]f(x)=2x^{3}-26x-24[/tex]
Using a graphing tool
see the attached figure to better understand the problem
Relation of graph to the x-axis
Interval (-∞,-3) -----> below (the function is negative)
Interval (-3,-1) -----> above (the function is positive)
Interval (-1,4) -----> below (the function is negative)
Interval (4,∞) ----->above (the function is positive)
How many degrees are in the compliment of 54 degree angle? Why?
Find the area ratio of a cube with volume 125 m to a cube with volume 64 m.
The required ratio of area of cubes is 25 : 16.
Volume of cube 1 = 125
Volume of cube 2 = 64
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Volume of cube 1 = 125
a³ = 125
a = 5
Volume of cube 2 = 64
A³ = 64
A = 4
Area of cube 1 = a² x 6
= 5² x 6
= 150
Area of cube 2 = A² x 6
= 4² x 6
= 96
Now ,
The ratio of areas of cube 1 to cube 2 = 150:96.
= 25:16
Thus, the required ratio of area of cubes is 25 : 16.
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Kristin opens a savings account with $3500. She deposits $2400 every year into the account that has a 0.65% interest rate, compounded quarterly. If she doesn't withdraw any money, what will the account balance be in 10 years?
1. $28551.51
2. $24776.39
3. $28511.25
4. $24816.65
I don't know what formula to use or how to solve.
The height of a triangle is 6 m more than its base. The area of the triangle is 56 m2. Find the length of the base. 7 m 8 m 14 m 15 m
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute, can be approximated by the formulas
for women
for men,
where a represents the person’s age. If the desirable heart rate for a man is 135 beats per minute, how old is he?
a.
22.5 years old
b.
40 years old
c.
45 years old
d.
42.5 years old
Please select the best answer from the choices provided
The area of a circular trampoline is 112.07 square feet. What is the radius of the trampoline? Round to the nearest hundredth.
A. 3.37 feet
B. 10.59 feet
C. 35.67 feet
D. 5.97 feet