How many numbers from 1 to 50 are multiples of 3?
3, 6, 9, 12, 15, 18 .......
Let's change the start and end value of the array and find the number of terms
Start at 3 and go all the way to 48 because those are the first and last multiples of 3 in this array.
There is a formula that allows us to quickly find the number of terms
We subtract the first term from the last term and divide by the amount of increase, then we add 1.
(48 - 3) / 3 + 1 = 16 numbers are exactly divisible by 3.
We have 50 numbers and 16 of them divisible by 3
16 / 50 = 8 / 25 probability
The probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have the number from 1 to 50.
Total numbers between 1 to 50 or total outcomes = 50
Total favorable outcomes = total number which is divisible by 3
[tex]=\frac{48-3}{3} +1[/tex]
= 15 + 1
= 16
Now probability will be:
= 16/50
= 8/25
Thus, the probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.
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Tyler has completed 60 pages in his
French workbook. This is 20% of the total
number of pages in the workbook.
How
many pages are in the workbook?
Answer:
300 pages
Step-by-step explanation:
this is the answer
Originally, a department store bought a set of dishes at a cost of $57.68 and marked it up 125%. After a month, the set of dishes had not sold, so the store marked it down 50%. What was the discounted price?
Answer:
$64.89
Step-by-step explanation:
57.68 + 1.25 × 57.68
= 57.68 + 72.1
= 129.78
The original price was $129.78.
129.78 – 0.50 × 129.78
= 129.78 – 64.89
= 64.89
The discount price was $64.89.
Find ℒ{f(t)} by first using a trigonometric identity. (write your answer as a function of s. ) f(t) = cos2(t)
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex].
How to determine the Laplace transform of a non-simple trigonometric expression
In this we need to rewrite the given function in terms of sines and cosines, whose Laplace transforms are well known. There is the following trigonometric formula:
[tex]\cos ^{2} t = \frac{1-\cos 2t}{2}[/tex] (1)
Now we proceed to apply the Laplace transforms:
[tex]\mathcal {L} \{f(t)\} = \frac{1}{2}\cdot \mathcal {L} \left\{1 \right\}-\frac{1}{2}\cdot \mathcal {L}\left\{\cos 2t\right\}[/tex]
[tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]. [tex]\blacksquare[/tex]
Remark
The statement is poorly formatted, the correct form is shown below:
Find [tex]\mathcal {L}\{f(t)\}[/tex] by first using a trigonometric expression. (Write your answer as a function of s). f(t) = cos² t
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Jim rented a truck for one day. there was a base fee for $19.95 and there was an additional charge of 91 cents for each mile driven. Jim had to pay $243.81 when he returned the truck. For how many miles did he drive the truck?
Answer:
Jim travelled 246 Miles.
Step-by-step explanation:
find the slope of the line that passes through the pints (2,7) and (2,6)
Answer:
Undefined Slope
Step-by-step explanation:
The points (2,6) and (2,7) are on the same vertical line of 2, which results in an undefined slope.
Answer:
m=undefined
Step-by-step explanation:
The formula to find the slope isn't very complicated. The formula is:
y₂-y₁
m= --------
x₂-x₁
You have the points (2,7) and (2,-6). In (2,7) 2 is your x and 7 is your y. Since (2,7) is your first coordinate set, we put 2 as our x₁ . We put 7 as our y₁ .
In (2,-6) 2 is your x and -6 is your y. Since (2,-6) is your second coordinate set, we put 2 as our x₂ . We put -6 as our y₂ .
Let's substitute all of these numbers in:
-6-7 -13
m= ------- = -------
2-2 0
So we have -13/0 .You would think that any number divided by 0 is 0, right?
No. Any number divided by 0 is undefined.
Therefore, you slope, m, would be:
m=undefined .
A square is cut in half and the diagonal creating two equal triangles of each triangle has an area of 4.5 in.² what is the length in inches of the original square
the inverse of the function f(x)=-x+3
Answer: [tex]f^{-1}(x)=-x+3[/tex]
Step-by-step explanation:
To find the inverse of a function replace f(x) with x and replace the original x with y
[tex]f(x)=-x+3\\x=-y+3[/tex]
Now solve for y
[tex]x=-y+3[/tex]
First subtract 3 from both sides
[tex]x-3=-y+3-3\\x-3=-y[/tex]
Now divide both sides by -1 (this will make y positive)
[tex]\frac{x-3}{-1} =\frac{-y}{-1} \\-x+3=y[/tex]
Now replace y with the inverse of f(x), [tex]f^{-1}(x)[/tex]
Two lines, A and B, are represented by equations given below: Line A: y = x − 2 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (1 point) a (−3, −5), because the point does not lie on any axis b (−3, −5), because the point satisfies both equations c (−4, −8), because the point satisfies one of the equations d (−4, −8), because the point lies between the two axes
The solution to the system of equations is (-3, -5) because the point satisfies both equations
What is a linear function?A linear function is in the form:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept
Line A:
y = x − 2 (1)
Line B:
y = 3x + 4 (2)
Solving both equations simultaneously gives:
x = -3, y = -5
The solution to the system of equations is (-3, -5) because the point satisfies both equations
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Keisha received a $90 gift card for a coffee store. She used it in buying some coffee that costs $8.47 per pound. After buying the coffee, she had $47.65 left on her card. How many pounds of coffee did she buy?
Answer: 4
Step-by-step explanation:
It sounds like you want to know how many pounds of coffee Latoya bought. First, let's figure out how much she spent. Subtract the amount she has left from the amount she started out with:
90 - 57.68 = 32.32
Latoya spent $32.32 on coffee. Since it cost $8.08 per pound, we can divide the total cost by 8.08 to figure out how many pounds she bought:
32.32/8.08 = 4
let f(x)=3x+4 and g(x)=2x-5 find (f-g)(x)
Step-by-step explanation:
find; (f-g)(x)
(f(x) - g(x))
f(x) = 3x + 4, g(x) = 2x - 5
3x + 4 - 2x + 5
x +9
Helpppppp!!!
(Show work)
Answer:
Step-by-step explanation:
Evaluate the expression 3^-2
Answer:
-9 is the answer for 3^-2
Question on picture(how the question short bozo)
Answer: The correct answer is C.
Step-by-step explanation: C Shows multiple animals and shows plants. It also shows water which is needed in an ecosystem.
Hope this helps!
The area of this figure.
square meters
10 m
2 m
12 m
7 m
4 m
4 m
Answer:
I believe it is 106 Square meters
Step-by-step explanation:
Easiest way to find area for these kind of shapes is to break them into smaller rectangles, this specific one can be broken 3 ways...
Right: 4m long, 7m tall
Top: 10 long, 5 tall *(12-7)*
Left: 4m long, 7m tall
*To find incomplete ones, you find clues in other sides, for instance the whole side was 12, the broken part was 7, therefor you just subtract 7 from 12, giving you 5 for the top.*
Then you just multiply...
4x7=28
4x7=28
10x5= 50
Now, you have the area for three individual smaller rectangles. So you simply add them together to get the whole shapes area...
28+28+50=106
Therefor, your answer should be 106 square meters- if I'm not mistaken.
Hope this helps, brainliest is appreciated if its right, trying to rank up :)
Have a great day! cx
~Mitsuna
Answer:
106
Step-by-step explanation:
Here's one way of finding the area:
Find the area of the entire outer rectangle. Then subtract the area of the samlle rectangle in the bottom middle.
A = LW - lw
A = (10 m)(12 m) - (2 m)(7 m)
A = 120 m² - 14 m²
A = 106 m²
Please help extremely confused
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. (picture of diagram included)
Answer:
basic geometry and trig ratios
Step-by-step explanation:
sin 10 = 500/x
x = 500/sin 10
x = 2 879,4 m
Write an equivalent expression to 16x + 20 using factoring.
Answer:
4(4x + 5)
Step-by-step explanation:
4 goes into both 16 and 20.
4×4 is 16 and
4×5 is 20.
When factoring you put the nunber you factored out typically, in front. Then the remaining factor goes in a set of parenthesis.
This is like undoing distributive property.
16x + 20
= 4(4x+5)
Take 2 common
2(8x+10)Again take two common
2(2(4x+5)Simplify
4(4x+5)Done
Use the graph of triangle JKL to answer a-b.
a.Reflect JKL over the x-axis. Record the coordinates of the original and new image below.
Pre Image: J:_____ K:_____
L: ______
Now Image: J:______ K:______
L:_______
b. Describe what happened to the x and y coordinates once they were reflected.
*ignore the erasing marks and the lines ^^
After reflection, the x-coordinates remains unchanged while the y-coordinates are negated.
Reflection of coordinates over the xy axisThe translation rule for reflecting the coordinate (x, y) over the x-axis is expressed as:
[tex](x, y) \rightarrow (x,-y)[/tex]
Given the following coordinates of the vertices from the figure J(-7, 7), K(-5, -2) and L(-2, 3)
If the coordinates ara reflected over the x-axis, the resulting coordinates will be J(-7, -7), K(-5, 2), and L(-2, -3).
After reflection, the x-coordinates remains unchanged while the y-coordinates are negated.
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Write the word sentence as an equation.
5 is one-fourth of a number c. PLEASE HELP
Help solve this circle
You're basically using the supplement angle to find the missing number.
Dont undersrand this at allll...
Answer:
2.3 2 1/3
Step-by-step explanation: you add up all the bikes then divide them by 3 because that's the number of people
Can someone solve this?
Step-by-step explanation:
First box =25
Second Box = 0.25
All right answers = 20 points
Pls help
4. Find the perimeter of the figure below. Use 3.14 for pi.
number answer.
Answer:
90.24 mm
Step-by-step explanation:
Circumference = 2πr
C = 2(3.14)(16)
C = 100.48 mm
Perimeter of the figure = 20 + 20 + 1/2 (circumference)
P = 40 + 1/2 (100.48)
P = 40 + 50.24
P = 90.24 mm
I hope this helps!
Tile the rectangle shown using square inches to find the area, and then use multiplication to confirm the area. Use paper to show your work.
Answer:
19 11/16
Step-by-step explanation:
5 1/4 x 3 3/4
Area = width x length
The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.
Answer:
Length of rectangle = 63 mWidth of rectangle = 21 mStep-by-step explanation:
Given:
Perimeter of rectangle = 168 mLength of rectangle is five times the widthTo Find:
Length and WidthSolution:
Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle
Perimeter of rectangle = 2(L + B)
Substituting the required values:
→ 168 = 2(3x + x)
→ 168 = 2(4x)
→ 168/2 = 4x
→ 84 = 4x
→ 84/4 = x
→ 21 = x
Hence,
Length of the Rectangle = 3x = 3(21) = 63 mWdith of the rectangle = x = 21 mAnswer:
Length = 70 metreWidth = 14 metre⠀
Step-by-step explanation :
⠀
As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle 14 metre .⠀
Now, we are to find the length of the rectangle :
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 70 metreWhat is the value of z?
Enter
your answer in the box.
Answer:
the value of z is 60 degree
Describe the correlation you would expect with these data sets.
(i) The height of a person and the speed at which they can run.
(ii) The age of a second car and its value.
(iii) Time spend watching TV and exam score
(iv) Height and income
(v) Sale of the apartment and high cost
Answer:
(i) no correlation as one variable is not dependent on the other.
(ii) The age of a car does affects its value. Therefore, the age will be the independent variable (x-axis) and the value will be the dependent variable (y-axis). Unless the car is a classic, sought-after car, as the age increases, its value decreases, so this will be a negative correlation.
(iii) The time spent watching TV may affect exam score (since the more time spent watching TV equals less available time to spend studying). Therefore, the time spent watching TV will be the independent variable (x-axis) and the exam score will be the dependent variable (y-axis). As time spent watching TV increases, the exam score could potentially decrease, so this will be a negative correlation.
(iv) no correlation, since one variable is not dependent on the other.
(v) The cost of an apartment may affect its sale, but there are many factors that can affect this such as location of the apartment and the buyers it appeals to. The cost will be the independent variable (x-axis) and the sale will be the dependent variable (y-axis). In usual circumstances, we would expect to see as the cost of an apartment increases, the sale may decrease, as less and less buyers can afford to buy it, so this will be a negative correlation.
The first three terms of a geometric sequence are as follows.
-3, 15, -75
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Here the common ratio is -5
next terms will be 375 and -1875
If 1/10 of a scarf is knit in 48 minutes.what fraction of a scarf is knit in 1 hour
Answer:
1/8
Step-by-step explanation:
i believe this is the answer
Given similar terms, solve for the missing variables (x)
Answer:
x=10
Step-by-step explanation:
the image above shows the work to solve the equation