Explanation
In the bag of tokens, we are told 55 red, 44 green, and 55 blue tokens. Therefore, the total number of tokens in the bag is
[tex]55+44+55=154[/tex]Hence to find the probability that a randomly selected token is not red becomes;
[tex]Pr(not\text{ red black})=\frac{n(green)+n(blue)}{n(tokens)}=\frac{44+55}{154}=\frac{99}{154}=\frac{9}{14}[/tex]Answer: 9/14
Ryan bought 3 1/2 boxes of paper clips. Allan bought 1 3/4 more boxes than Ryan.
Colin bought 1 1/2 times as many boxes as Allan How many boxes did Colin buy?
Answer:
Colin bought 7 7/8 boxes
Step-by-step explanation:
Let R represent the number of boxes bought by Ryan and A represent the number of boxes bought by Allan
R = 3 1/2
Convert to improper fraction:
3 1/2 = (3 x 2 + 1)/2 = 7/2
Allan bought 1 3/4 more boxes than Ryan
A = R + 1 3/4
Convert 1 3/4 to improper fraction:
1 3/4 7/4
So A = 7/2 + 7/4 = 14/4 + 7/4 = 21/4
Colin bought 1 1/2 times as many boxes as Allan
C = 1 1/2 x A
Convert 1 1/2 to improper fraction:
1 1/2 = 3/2
So C = 3/2 x 21/4
= 63/8 = 7 7/8 boxes
60 went into a machine and 72 came out.What percent increase did this machine use?
From this question, we can deduce he following:
Original value = 60
New value = 72
Let's find the percentage increase.
To find the percentage increase, apply the formula below:
[tex]\text{ Percent increase = }\frac{New\text{ value - old value}}{old\text{ value}}\ast100[/tex]Thus, we have:
[tex]\begin{gathered} \text{Percent increase = }\frac{72-60}{60}\ast100 \\ \\ \text{Percent increase = }\frac{12}{60}\ast100 \\ \\ \text{Percent increase = }0.2\ast100 \\ \\ \text{Percent increase = 20 \%} \end{gathered}[/tex]Therefore, the percent increase is 20%.
ANSWER:
20%
Solve the equation below by completing the square and then solving for x.2 + 14x + 24 = 0A. X=-12 or x= -2B. x=2 or x=-2C. X=-2 or x=-5D. X= 8 or x= 3
2x^2 + 14x + 24 = 0
x^2 + 7x + 12 = 0
Then
x^ + (14/2) x + 12 + [7x + 49 ] = 7x + 49
Now form square
[ x + 7x + 7x + 49 ] = 7x + 49 - 12
[ x + 7]^2 = 7x + 37
Then now find x
x^2 + 7x = -6
x^2 + 7x + 7^2/4 = 7^2/4 - 6
then
( x + 7/2)^2 = 49/4 - 24/4
(x + 7/2) = ±√ (25/4)
. x = 5/2 - 7/2
and. x = 5/2 + 7/2
Then solutions are
x = -2
x= -12
ANSWER IS
OPTION A
True or False? A circle could be circumscribed about the quadrilateral below.B82"O A. TrueA 105°98° cO B. False75%
Solution
For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:
Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary
And we cna verify:
105+ 98= 203
82 +75= 157
Then we can conclude that the answer is:
False
Find the average rate of change of f(x)=3x^2-8x from x=1 to x=6
Answer:
The answer is 13
10 of 25Jackie and Ruth both studied very hard for their history test. Ruth studied 2 hours less than twice as many hours as Jackie.Together,"heir study time was 10 hours. How many hours did Ruth study for her history test?
Answer: 6 hours
Explanation:
We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:
[tex]R=2J-2[/tex]The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.
Now, we are told that "Together, their study time was 10 hours" so we have the following equation:
[tex]R+J=10[/tex]This will be our equation 2.
The next step is to substitute equation 1 into equation 2:
[tex]2J-2+J=10[/tex]And we solve for J.
Combining like terms:
[tex]3J-2=10[/tex]We add +2 on both sides of the equation to cancel the -2 on the left side:
[tex]\begin{gathered} 3J-2+2=10+2 \\ 3J=12 \end{gathered}[/tex]And we divide both sides by 3:
[tex]\begin{gathered} \frac{3J}{3}=\frac{12}{3} \\ \\ J=4 \end{gathered}[/tex]Jackie studied for 4 hours.
Since we are asked for Ruth, we substitute J=4 into the equation 1:
[tex]\begin{gathered} R=2J-2 \\ R=2(4)-2 \\ R=8-2 \\ R=6 \end{gathered}[/tex]Ruth studied for 6 hours.
Each of 6 students reported the number of movies they saw in the past year. This is what they reported:20, 16, 9, 9, 11, 20Find the mean and median number of movies that the students saw.If necessary, round your answers to the nearest tenth.
Solution:
The number of movies 6 students reported they saw in the past year is;
[tex]20,16,9,9,11,20[/tex]The mean number of movies that the students saw is;
[tex]\begin{gathered} \bar{x}=\frac{\Sigma x}{n} \\ n=6 \\ \bar{x}=\frac{20+16+9+9+11+20}{6} \\ \bar{x}=\frac{85}{6} \\ \bar{x}=14.2 \end{gathered}[/tex]The mean round to the nearest tenth is 14.2
Also, the median is the middle number of the data set after arranging either in ascending or descending order.
[tex]9,9,11,16,20,20[/tex]The median number of movies the students saw is the average or mean of the third and fourth.
[tex]\begin{gathered} \text{Median}=\frac{11+16}{2} \\ \text{Median}=\frac{27}{2} \\ \text{Median}=13.5 \end{gathered}[/tex]The median round to the nearest tenth is 13.5
50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
The expression that represents the area of the rectangle is 6x²+29x+35.
Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Part A:
Now, area = (2x+5)(3x+7)
= 2x(3x+7)+5(3x+7)
= 6x²+14x+15x+35
= 6x²+29x+35
So, the area of a rectangle is 6x²+29x+35
Part B:
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
Here, the degree of the expression 6x²+29x+35 is 2.
Part C:
Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.
Here, we obtained product of two binomials is trinomial
Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
#SPJ1
Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(
The correct option is D
8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares
Explanation:To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.
The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).
The area of a square is the square of its side length.
Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.
A.
[tex]2\sqrt[]{3},4,2\sqrt[]{5}[/tex]This is NOT a Pythagorean triple.
B.
[tex]\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}[/tex]This is NOT a Pythagorean triple.
C.
[tex]2,\sqrt[]{5},2\sqrt[]{3}[/tex]This is NOT a Pythagorean triple
D.
[tex]2\sqrt[]{2},4,2\sqrt[]{6}[/tex]This is a Pythagorean triple.
CHECK[tex]\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}[/tex]Yea I can see if it works if it’s okay
SOLUTION
We want to find the derivative of
[tex]y=sin(1.2t-3.7)[/tex](a) So, using chain rule, the inside function is u,
we have the inside:
[tex]u=1.2t-3.7[/tex]outside becomes
[tex]y=sin(u)[/tex](b) The derivative of
inside, we have
[tex]\frac{du}{dt}=1.2[/tex]derivative of the outside, we have
[tex]\frac{dy}{du}=cos(u)[/tex]chain rule we have
[tex]\begin{gathered} \frac{dy}{dt}=\frac{dy}{du}\times\frac{du}{dt} \\ =cos(u)\times1.2 \\ =cos(1.2t-3.7)\times1.2 \end{gathered}[/tex]Hence the answer is
[tex]\frac{dy}{dt}=1.2cos(1.2t-3.7)[/tex]please help I think I know how to do this it I am not sure it has a time limit and I'm sorry I need to andwer it quick I've been working on it for awhile so it took time off the time limit
we are given the following polynomial:
[tex]x^2+3-7x[/tex]The standard form of a polynomial is of the following form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+\cdots+d[/tex]Rewriting the given polynomial we get:
[tex]x^2-7x+3[/tex]This is a trinomial because it has 3 terms.
Since the maximum exponent of the polynomial is 2, this is a quadratic polynomial.
Solve this system of equations by substitution. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer.
We have the following:
[tex]\begin{gathered} y=-\frac{1}{2}x+4 \\ y=2x-1 \end{gathered}[/tex]Solving by substitution
[tex]\begin{gathered} -\frac{1}{2}x+4=2x-1 \\ 2x+\frac{1}{2}x=4+1 \\ \frac{5}{2}x=5 \\ x=\frac{2\cdot5}{5} \\ x=2 \end{gathered}[/tex]Now for y
[tex]\begin{gathered} y=2\cdot2-1=4-1=3 \\ \end{gathered}[/tex]Therefore, the answer is:
[tex](2,3)[/tex]Examine the graph and write a statement about the data. Use specific information from the graph.
This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.
U Last Saturday V. Tomo los restaurant sold 85 cheese pizzes and 54peperon p2205 Wechple was cut into elchihs, how many peces ofpedid hosilinona nlgh?2Adeleydiverlor the realanddeliverpiznes ot 5-13 ke arrivedback at therestaurant 6 45. How many manutes wesheoulding p2205 ?3 Tomola hoz 158 ounces domaSouce The uses 9 aunces of louce bonepi? how many plazos canhe moke with mesouce behet?41 Au months ago the restaurar had 2 258pizobe in their warehouse Today they have749 boxen led. How many pizza bazea haether
Answer : The amount of boxes of pizzas used is 2009 boxes
A few months ago, the company has 2, 758 boxes of pizzas in the warehouse
Today, they have 749 boxes of pizzas in the warehouse
To calculate the amount left
The amount used = 2758 - 749
The amount of boxes used = 2009 boxes
the value of y is directly proportional to the value of x. if y = 45 when x = 180 what is the value of y = 90
We have a direct proportionality between y and x.
If "k" is the constant of proportionality, the equation for this situation is:
[tex]y=kx[/tex]To find the constant of proportionality, we solve that equation for k:
[tex]k=\frac{y}{x}[/tex]And since when y=45, x=180, substituting these values to find k:
[tex]\begin{gathered} k=\frac{45}{180} \\ k=0.25 \end{gathered}[/tex]Now, we substitute the value of k into the equation of proportionality:
[tex]y=0.25x[/tex]And in this equation, we can substitute any value of the variables, and find the value of the other variable.
In this case, we have y=90, so we substitute that value and solve for x:
[tex]\begin{gathered} 90=0.25x \\ \frac{90}{0.25}=x \\ 360=x \end{gathered}[/tex]Answer: when y=90, x=360
I need help with review on functions
The answer is Option 2
Its not a function
The domain and range of the function is shown at the various endpoints of the graph.
At every point you can always identify a value for x (the input value) and also a corresponding value for y (the output value).
Please note the endpoints marked in blue.
These are the endpoints, and for every point, you will have (x, y).
However, note that at the endpoints, the values of y remains the same.
For every relation to be a function, there must be exactly one corresponding y value for every x value. As shown by the blue markings on the graph, the x values on the horizontal axis both have the same y value (which is zero).
Hence, the relationship shown by the graph is not a function
You want to purchase an automobile for 28,711. The dealer offers you 0% financing for 60 months or a 3,972 rebate. You obtain 5.7% financing for 60 months at the local bank. Which option should you choose
Answer:
option 1
Step-by-step explanation:
the dealer one ok.......
Drag the tiles to the boxes to form correct pairs.Match each set of vertices to the triangle they form.acute equilateralright isoscelesacute isoscelesA(3,5),B(3,4),C(5,4)A(2,4), B(4,5), C(3,6)A(3,5),B(5,6),C(3,0)A(2,4),B(3,5), C(2,6)obtuse scaleneright scalene
Step 1
Plot the triangles
let
A)
we can see that angle in B is 90 ° and length AB is different to BC, When one of the three angles measure 90 degrees and the angles or lengths of other two sides are not congruent, then the scalene triangle is called right scalene triangle
right scalene
Step 2
triangle 2
[tex]A(2,4)\text{ B\lparen4,5\rparen c\lparen3,6\rparen}[/tex]in this case, we have that length AC equlas AB,also we can see that angle A is smaller than 90 ° ,an acute angle measure less than 90 degrees,so
so
[tex]AC=AB[/tex]a triangle in which two sides have the same length is called acute isosceles
Step 3
A(3,5),B(5,6),C(3,0)
an obtuse scalene triangle can be defined as a triangle whose one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. All three sides and angles are different in measurement.so this is an
obtuse scalene
Step 4
finally, A(2,4),B(3,5), C(2,6)
An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.
we can see that
[tex]\begin{gathered} m\angle B=90 \\ AB=BC \end{gathered}[/tex]therefore, this is an
rigth isosceles
I hope this helps you
Answer:(3,5) (4,5) (3,6)
acute isosceles
Step-by-step explanation:
If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.
Supplementary angles add up to 180°
A+ B = 180
A is 9 times as large as B.
A = 9B
We have the system of equations:
A+ B = 180
A = 9B
Put the second equation into the first one, and solve for B
(9B)+ B = 180
10B = 180
B= 180/10
B = 18
Replace the value of B on any equation and solve for A:
A = 9B
A= 9(18)
A= 162
A= 162°
B=18°
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
15. Find m<1.
Observing the given figure n< 1 can be found using the Vertical angel theorem to be 132.75 degrees
What is vertical angle theorem?The vertical angle theorem is used when two straight lines intersect, at their point of intersection four angles are formed. The angles opposite to each other are equal
How to find m< 1 using vertical angle theoremThe figure shows
(x² - 6x)⁰
(x/2 + 42)°
From vertical angle theorem
(x² - 6x)⁰ = (x/2 + 42)°
solving for x by multiplying out by 2
2x² - 12x = x + 84
2x² - 12x - x - 84 = 0
2x² - 13x - 84 = 0
factorizing the parabolic equation gives
(x + 4)(2x-21)
using the positive value of x
x = 21/2
substituting x = 21/2 into (x/2 + 42) gives
= 47.25
sum of angles at a point = 360 degrees
2 * 47.25 + 2 * m< 1 = 360
2 * m< 1 = 360 - 94.5
m< 1 = 265.5/2
m< 1 = 132.75
Learn more on vertical angles here: https://brainly.com/question/68367
#SPJ1
Hello,
I have paid the $29.00 monthly subscription for my son (jalen); I have signed up only to pay the monthly payment. Sorry to say, he does not live with me. I earlier sent you an email explaining the same with no reply from you. So how does he proceed using his information to freely access your program?
Looking forward to hearing from you shortly.
THANKS,
climacus
Answer:
Step-by-step explanation:
A manager measured the number of goods, y, that his company produced in a hours. The
company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45
goods.
Which equation, in point-slope form, correctly represents the goods produced by the company
after x hours?
Oy-45 = 5(x-9)
Oy+9= 5(x +45)
Oy 45= 5(x + 9)
Oy-9=5(x - 45)
Answer:
[tex]y-45=5(x-9)[/tex]
Step-by-step explanation:
Definition of the variables:
y = total number of goods produced.x = time in hours.Given information:
The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.As the rate of change is constant and linear, the rate of change is the slope of the line. Therefore, the slope is 5.
At hour 9 (x-value) the company had produced 45 (y-value) goods. Therefore, this can be represented by the point (9, 45).
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-45=5(x-9)[/tex]
Therefore, the equation that correctly represents the goods produced by the company after x hours is:
[tex]\boxed{y-45=5(x-9)}[/tex]
Radicals and Exponents Identify the choices that best completes the questions 3.
3.- Notice that:
[tex]\sqrt[]{12}=\sqrt[]{4\cdot3}=2\sqrt[]{3}\text{.}[/tex]Therefore, we can rewrite the given equation as follows:
[tex]2\sqrt[]{3}x-3\sqrt[]{3}x+5=4.[/tex]Adding like terms we get:
[tex]-\sqrt[]{3}x+5=4.[/tex]Subtracting 5 from the above equation we get:
[tex]\begin{gathered} -\sqrt[]{3}x+5-5=4-5, \\ -\sqrt[]{3}x=-1. \end{gathered}[/tex]Dividing the above equation by -√3 we get:
[tex]\begin{gathered} \frac{-\sqrt[]{3}x}{-\sqrt[]{3}}=\frac{-1}{-\sqrt[]{3}}, \\ x=\frac{1}{\sqrt[]{3}}\text{.} \end{gathered}[/tex]Finally, recall that:
[tex]\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Therefore:
[tex]x=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Answer: Option C.
Sue wants to plant 545 acres of wheat. She has planted a 128 acre field near the river. Whatpercent of her wheat crop has she planted?
Percentage of the wheat crop planted = 128/ 545 x 100
= 12800/545
= 23.4 percent
The half-life of a radioactive isotope is the time it takes for quantity of the isotope to be reduced to half its initial mass. Starting with 175 grams of a radioactive isotope, how much will be left rafter 5 half-lives? Round your answer to the nearest gram
Exponential Decay
The model for the exponential decay of a quantity Mo is:
[tex]M=M_o\cdot e^{-\lambda t}[/tex]Where λ is a constant and t is the time.
The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:
[tex]\begin{gathered} \frac{M_o}{2}=M_o\cdot e^{-\lambda t} \\ \text{Simplifying:} \\ e^{-\lambda t}=\frac{1}{2} \\ \text{Taking natural log:} \\ -\lambda t=-\log 2 \\ t=\frac{\log 2}{\lambda} \end{gathered}[/tex]It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.
Substituting in the model:
[tex]M=175gr\cdot e^{-\lambda\cdot\frac{5\log 2}{\lambda}}[/tex]Simplifying (the value of λ cancels out):
[tex]\begin{gathered} M=175gr\cdot e^{-5\log 2} \\ \text{Calculating:} \\ M=175gr\cdot0.03125 \\ M=5.46875gr \end{gathered}[/tex]Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.
Find the difference.5 - 12 = don’t be specific be quick i leave. a good review
Given:
5 - 12
To find the difference , all we have to do is to perform the subtraction. The result of subtraction is called the difference.
Subtract 12 from 5.
Thus, we have:
5 - 12 = -7
Therefore, the difference between 5 and 12 is -7
find the value of x
For supplementary angles, we can do the following equality
[tex]3x+4=x+70[/tex]What we have to do, is to clear "x" to find its value.
[tex]\begin{gathered} 3x-x=70-4 \\ 2x=66 \\ x=\frac{66}{2} \\ x=33 \end{gathered}[/tex]In conclusion, the value of x is 33
A number cube is rolled once, {1,2,3,4,5,6)Determine the likelihood of each situation,Column AColumn B1.rolling an even numbera. unlikely2.rolling a 7b. impossible3.rolling a number greater than 0Ccertain4.rolling a number that is greater than 2d. likely5.rolling a 2 or 3e equally likely
The likelihood of the following situations:
1. rolling an even number is likely.
2. rolling a 7 is impossible.
3. rolling a number greater than 0 is certain.
4. rolling a number that is greater than 2 is likely.
5. rolling a 2 or 3 is equally likely
Graphed the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation
To dilated the figure by a scale factor 3 and center origin
Multiply the coordinates of each point by 3
The image of the point (x, y) is (3x, 3y)
