It takes four (4) comedy routines to hear 360 jokes
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
1 minute = 3 jokes
X minutes = 360 jokes
Cross-multiplying, we have:
3X = 360
X = 360/3
X = 120 minutes
Now, we can determine the number of comedy routines required for 360 jokes as follows:
Number of comedy routines = 120/35
Number of comedy routines = 3.42 ≈ 4 comedy routines.
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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.
A statistics professor plans classes so carefully that lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes.The Probability that a given class period runs between 51.5 and 51.75 minutes is 0.025.
What is density?The density of a place refers to the quantity of things—which may include people, animals, plants, or objects—there are in it. Divide the number of objects by area's measurement to determine density. A country's population density is calculated by dividing its total population by its area, expressed in the square kilometers or miles.
A flat distribution with the same probability density for each number is called a uniform distribution. The area beneath the distribution's graph must be 1. This distribution has a range of 10.0 and runs from 46.0 to 56.0 minutes (56.0-46.0). Since the density must be 1/10, 10.0*0.1 Equals 1.0.
Multiply the range between the numbers by the probability density to get the likelihood of being between two numbers
range: 50.75-50.5 = 0.25
0.25*0.1 = 0.025
P(50.5 < x < 50.75) = 0.025
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Five of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a
randomly selected item is defective?
Answer:
1:20
Step-by-step explanation:
Because it's maths duhh
The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.
The value of x for the given arithmetic sequence is x = 4.
What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given,
First three terms of an arithmetic sequence are x, 2x + 4, 5x
The difference of 1 and 2 term equals the difference of 3 and 2 term.
⇒ 2x + 4 - x = 5x - 2x - 4
⇒ x + 4 = 3x - 4
⇒ 2x = 8
⇒ x = 4
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Think About the Process The length of cell A is 4 x 10^-5 length to cell B's length? Use pencil and paper. Is it easier to find notation or in standard form? Explain your reasoning. m. The length of cell B is 0.000002 the ratio when the numbers m. What is the are expressed ratio of cell A's in scientific
Ratio of length of cell A to the length of cell B will be 20 : 1.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
Length of cell A = 4 x 10⁻⁵
Length of cell B = 0.000002 = 2 x 10⁻⁶.
Now,
Length of cell B into scientific notation = 2 x 10⁻⁶
Hence, The ratio of the length of cell A to cell B = 4 x 10⁻⁵ / 2 x 10⁻⁶
= 2 x 10⁻⁵⁺⁶
= 2 x 10¹
= 20
Thus, Ratio of length of cell A to the length of cell B is 20 : 1.
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HELP I WILL GIVE YOU POINTS!
Describe in words the one transformation that maps
ΔABC to ΔA'B'C'
∆ABC to ∆A′B′C′
. Make sure that you include specific details (Reflection – over which axis, Rotation – direction, degrees, and center of rotation, Translation – direction(s) and number of units). 15 points
Answer:
ΔABC
∆ABC
is transformed by a:
Type of Transformation:
Details of transformation:
The description of the one transformation that maps ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin
What is a rotation transformation?A rotation transformation can be described as the angular motion of a rigid, geometric figure around a point
The vertices on the triangle ∆ABC are;
A(-5, -2), B(-7, -4), C(-5, -5)The vertices on the triangle ∆A'B'C' are;
A'(2, -5), B'(4, -7), C'(5, -5)The rotation of a point A(x, y), 90° counterclockwise about the origin gives the point A'(-y, x)
The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)
Therefore;
The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;
A(-5, -2) → A'(2, -5)
B(-7, -4) → B'(4, -7)
C(-5, -5) → C'(5, -5)
Therefore;
The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin
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Find the perimeter of the triangle
Answer:30 in.
Step-by-step explanation:13+5+12
m^2+7m-51/4=0 by completimg square
By completing squares, we will see that the two solutions of the quadratic equaiton are:
m = -7 + √(145)/2
m = -7 - √(145)/2
How to solve by completing squares?Here we have the quadratic equation:
m^2 + 7m - 51/4 = 0
If we multiply both sides by 4, we will get
4m^2 + 28m - 51 = 0
Now, remember the relation:
(a + b)^2 = a^2 + 2ab + b^2
Then to complete the squares we can write:
(2m)^2 + 2*14*m + (14)^2 - (14)^2 - 51 = 0
(2m + 14)^2 - 14^2 - 51 = 0
(2m + 14)^2 = 145
We already completed squares, now the solutions are:
2m = -14 ± √145
m = (-14 ± √145)/2
m = -7 + √(145)/2
m = -7 - √(145)/2
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Find the x-intercept and y-intercept of the line.
2x+5y = -10
The x-intercept is when y=0.
[tex]2x+5(0)=-10 \\ \\ 2x=-10 \\ \\ x=-5 \\ \\ \therefore (-5, 0)[/tex]
The y-intercept is when x=0.
[tex]2(0)+5y=-10 \\ \\ 5y=-10 \\ \\ y=-2 \\ \\ \therefore (0, -2)[/tex]
what is equivlent 10x-30
Answer:10(x-3)
Step-by-step explanation:
Just divide 10 on both sides and be done with it
10/10x-30/10
move ten to the left
10(x-30/10)
10(x-3)
Answer please please
Answer: 31,000
Step-by-step explanation: You need to find two numbers that if you add the two variables will equal 76,000 and i checked 40,000-14,000=A=40,000 which equaled 66,000 and then 50,000-14,000=A+50,000 which equaled 86,000 so i knew the number in between was the one which was 45,000 and 45,000-14,000=31,000
b) Draw the graph of y = 3x - 1
on the grid.
c) Use the graph to estimate the
value of y when x = 2.5
The graph is attached below.
We are given a linear function.The function "y" equals 3x-1.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.y = 3x - 1Now, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that has a positive slope of magnitude 3 and a y-intercept of -1.If x = 2.5, then:y = 3(2.5) - 1y = 7.5 - 1y = 6.5To learn more about functions, visit :
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find the ratio of 15k to 65k
Answer:
Step-by-step explanation:
If its 15000:65000
Then we divide both sides by 1000 first :
15 : 65
Then we divide both sides by 5 :
3 : 13
This is simplified
If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.
Hope this helped and have a good day
You have $50 in your bank account. Each week you plan to deposit $8 from your allowance and $20 from your paycheck. The equation b=50+(20+8)w gives the amount b in your account after w weeks. How many weeks from now will you have $210 in your bank account?
If you have $50 in your bank account and each week you plan to deposit $8 from your allowance and $20 from your paycheck. The number of weeks from now that you will have $210 in your bank account is: 5.71w.
Number of weeksThe given equation is:
b=50+(20+8)w
Where:
b is the amount in your account after w weeks.
w = Number of week
Hence,
b = 50+(20+8)w
b = 50+28w
b-50 = 28w
(b-$50)/28 = w
(210-$50)/28 = w
160/28 = w
5.71 = w
Therefore we can conclude that you will have the amount of $210 in your account in 5.71 weeks.
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The point P(6,4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, P'?
Check the picture below.
Suppose an online store has an item on sale for 10% off the original price. By what perceny does the store have to increase the price of the item in order to sell it for the original amount
The most appropriate choice of percentage will be given by-
The store have to increase the price of the item by [tex]11\frac{1}{9}[/tex] % in order to sell it for the original amount.
What is Percentage?
Percentage is a ratio expressed as a percentage of 100.
Let the original price be x
Percentage decrease in price due to sale = 10%
Decrease in price due to sale = [tex]\frac{10}{100} \times x[/tex]
= [tex]\frac{x}{10}[/tex]
New price = ([tex]x - \frac{x}{10}[/tex])
= [tex]\frac{10x-x} {10}[/tex]
= [tex]\frac{9x}{10}[/tex]
Now,
Increase in price from [tex]\frac{9x}{10}[/tex] to [tex]x[/tex] = [tex]\frac{x}{10}[/tex]
Percentage by which the store have to increase the price of the item in order to sell it for the original amount =
[tex]\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100[/tex]
=[tex]\frac{x}{10} \times \frac{10}{9x} \times 100[/tex]
= [tex]\frac{100}{9}[/tex]
= [tex]11\frac{1}{9}[/tex] %
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Can anyone Solve 2.5 ≤ 25
Answer:
true
Step-by-step explanation:
2.5≤25
Compare 2.5 and 25.
True
An astronaut on the moon throws a baseball upward. The height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
y = -2.7x² + 30x + 6.5
How high will the ball be after 3 seconds? Use your calculator to pull up a function
table to help you. (6 points total)
a.
b.
Height after 3 seconds =
feet. (2 points)
Give two approximate times (in seconds) that the ball will be at a height of
75 feet.
and
seconds (on its way up). (2 points)
seconds (on its way down). (2 points)
y = feet in the air
x = seconds it takes
well, what's "y" when x = 3?
[tex]y=-2.7(3)^2 + 30(3) + 6.5\implies y=-2.7(9)+96.5\implies \boxed{y=72.2~feet}[/tex]
now, what's "x" when y = 75?
[tex]75=-2.7x^2+30x+6.5\implies 0=-2.7x^2+30x-68.5 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-2.7}x^2\stackrel{\stackrel{b}{\downarrow }}{+30}x\stackrel{\stackrel{c}{\downarrow }}{-68.5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x=\cfrac{-30\pm\sqrt{(30)^2 - 4(-2.7)(-68.5)}}{2(-2.7)}\implies x=\cfrac{-30\pm\sqrt{900-739.8}}{-5.4} \\\\\\ x=\cfrac{30\mp\sqrt{160.2}}{5.4}\implies x\approx \begin{cases} 3.2&\textit{on the way up}\\\\ 7.9&\textit{on the way down} \end{cases}[/tex]
If a rotation takes triangle CAT to C’A’T where is AT
Answer:
The measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
Step-by-step explanation:
What is a rotation transformation?
A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.
For the given situation,
The graph shows the triangle CAT.
If a rotation takes triangle CAT to C'A'T',
then from the definition of rotation transformation the size and shape of the figure stays exactly the same.
Thus the measure of C'T' is same as CT.
Hence we can conclude that the measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
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find the x intercepts of f(x)=x^4+x^3-4x^2-4x
The x intercepts are 0, 1, -2, 2.
What is intercepts?
The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.
In the linear equation, we have the general form as y=mx+b
where m and b are constants.
We have to find the x intercept of the given function.
Given equation is [tex]x^{4} +x^{3} -4x^{2} -4x[/tex]
put this equation equals to 0
x^{4} +x^{3} -4x^{2} -4x = 0
[tex]x(x^{3} +x^{2} -4x-4)=0[/tex]
from this x = 0
x =1 is also the root of the equation
we get [tex]x^{2} -4=0[/tex]
from this
x = -2, 2
The intercept are 0,1,2,-2.
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Hi can someone please help me out?
Happy Halloween!
Answer:
A=14
B=pi 7^2
Step-by-step explanation:
All you need to do is put pi symbol on calculator and x by 7 squared to get answer
q=p(r+s)
Solve for p
-2x+4=y ( ,-2)
Help
Complete the missing value in the solution to the equation
Answer:
3
Step-by-step explanation:
let unknown point (x, -2)
-2(x)+4=-2
-2x=-6
x=3
is the relation in this graph a function ?
Answer:
No it's not a function
Step-by-step explanation:
You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.
All the fruit a farmers' market booth is on sale for 1.75 per pound. William bought 2 2/5 pounds of peaches and 2 1/3 pounds of apricots. To the nearest cent, what was the total cost of the fruit?
Algebra - The total cost of the fruit 8.26
What is Algebra ?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.
Given that,
The cost of all fruit is = 1.75/pound
William bought Peaches = 2(2/5)pounds = 12/5pounds
William bought Apricot = 2(1/3)pounds = 7/3pounds
The cost of Peaches = 12/5 x 1.75
= 12 x 0.35
= 4.2
The cost of Apricot = 7/3 x 1.75
= 7 x 0.58
= 4.06
Total cost of the fruit = 4.2 +4.06
= 8.26
Hence, the total cost of the fruit is 8.26
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Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is
measured in yards. The line of fit is given by ý = 3.98 +53.59s.
If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?
O 267.95 feet
O271.93 feet
O 283.87 feet
O287.85 feet
The predicted distance of the ball is 271.93 feet.
What is speed?The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time. Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
Given Data
The speed, s, is measured in miles per hour, and distance, y, is
measured in yards.
The line of fit is given by ý = 3.98 +53.59s.
When s = 5 sec
y = 3.98 + 53.59(5)
y = 3.98 + 267.95
y = 271.93
The predicted distance of the ball is 271.93 feet.
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A bakery makes fruit pies and cream pies.
Twelve out of every 20 pies baked are fruit
pies. What is the ratio of cream pies to fruit
pies?
Answer:
12:20 because for ever 12 fruite pies 20 cream pies are made so it would look like the following!
12:20
Step-by-step explanation:
Hope it helps! =D
write a part to part and a part to whole ratio for each problem situation of the 250 students surveyed, 142 prefer carrots and 97 prefer peas
∵ There are 142 who prefer carrots
∵ There are 250 all
∴ The fraction represents who prefer carrots is
[tex]\frac{142}{250}[/tex]We must simplify the fraction by divide up and down by the same number until getting the simplest form
∵ 142 and 250 can divide by 2
[tex]\therefore\frac{\frac{142}{2}}{\frac{250}{2}}=\frac{71}{125}[/tex]∵ 71 and 125 can not divide by any number
∴ The fraction is 71/125
∴
∵ There are 97 who prefer peas
∵ There 250 all
∴ The fraction represents who prefer peas is
[tex]\frac{97}{250}[/tex]∵ 97 and 250 can not divide by the same number
∴ The fraction is 97/250
∴ The ratio is 97: 250
hello can you help me with this trigonometry question please
Question:
On a circle of radius 6 feet, what angle would subtend an arc of lenght 5 feet?
nswer:
he frormula for the lenght of arc (s) given an angle theta (in radians) and a radius R is:
[tex]S=\theta R[/tex]We'll just have to clear theta from this equation, and convert it to degrees.
[tex]\begin{gathered} S=\theta R\rightarrow\frac{S}{R}=\theta \\ \theta=\frac{5}{6}\text{ radians} \\ To\text{ convert from radians to degrees, multiply by }\frac{180}{\pi} \\ \theta=\frac{5}{6}\times\frac{180}{\pi}\rightarrow\theta=47.74\text{ degrees} \end{gathered}[/tex]Therefore, the angle that would subtend an arc of lenght 5 feet on a circle of radius 6 feet is 47.74°
What is the slope of the line passing through (-2, 5) and (3, -4)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9}{3 +2}\implies {\Large \begin{array}{llll} -\cfrac{9}{5} \end{array}}[/tex]
Factor PLS PLS PLS:
b(a+1)^2 -5(a+1)
The value of the expression given as b(a+1)² -5(a+1) will be a²b + 2ab + 2b - 5a - 5.
How to illustrate the information?It should be noted that based on the information that given, we want to factor out the variables that are given.
This will be illustrated thus:
b(a+1)² -5(a+1)
= b(a + 1)(a + 1) - 5(a + 1)
= b(a² + 2a + 2) - 5a - 5
= a²b + 2ab + 2b - 5a - 5
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