Given in the scenario:
a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.
Let's determine how many batches of cookies can she make in one hour.
Step 1: Let's convert the given into a ratio and proportion.
Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10
At x = number of batches of cookies in one hour, we get = x : 1
Step 2: Let's determine the value of x.
[tex]\frac{\frac{1}{5}}{\frac{1}{10}}\text{ = }\frac{x}{1}[/tex][tex](1)(\frac{1}{5})\text{ = (x)(}\frac{1}{10})[/tex][tex]\frac{1}{5}\text{ = }\frac{1}{10}x[/tex][tex](1)(10)\text{ = (1)(5)(x) }\rightarrow\text{ 10 = 5x}[/tex][tex]\frac{5}{5}x\text{ = }\frac{10}{5}[/tex][tex]\text{ x = 2}[/tex]Therefore, Mary can make 2 batches of cookies in one hour.
Points B and C lie on line segment AD, with AB < AC. If AD = 76, CD = 24 and AB = BC, what is the value of BC?
ANSWER
[tex]BC=26[/tex]EXPLANATION
First, let us make a sketch of the problem:
Since AB is equal in length to BC, they both have a value of x.
The total length of AD is 76. This implies that:
[tex]\begin{gathered} AB+BC+CD=AD \\ x+x+24=76 \end{gathered}[/tex]Solve for x by simplifying the equation above:
[tex]\begin{gathered} 2x+24=76 \\ 2x=76-24=52 \\ \\ x=\frac{52}{2} \\ \\ x=26 \end{gathered}[/tex]Therefore, the value of BC is:
[tex]BC=26[/tex]That is the answer.
Isabella painted a water colour design on gridpaper. Some of the points were at A (-4, 8),B (-2, 8), C(-1,6), D (-2, 4), E (-4, 4), andF (-5, 6). She folded the paper along y = 3 toreflect the design. The image points are A', B',C', D', E', and F.a) Draw the line y = 3. (Hint: The x-axisis the line y = 0. For which line is they-coordinate 3 for every point?)b) Determine the coordinates of A', B',C.D', E', and F'.c) Draw the image, and label A', B', C',D', E', and F'.y8-7-€6-4.32-5•1 C
EXPLANATION
Drawing the line y=3 give us the following graph:
Reflecting over the axis y=3 give us the following image points:
A' = (-4,2)
B' = (-2,-2)
C' = (-1,0)
D' = (-2,2)
E' = (-4,2)
F'= (-5,0)
Drawing the points in the graph calculator:
write each in scientific notation with the answer simplified:(8•10^13) ÷ (2•10^8)(5•10^8) (6•10^9) ÷ (15•10^14)
To write in scientific notation we must follow the formula below:
[tex]N=a\times10^b[/tex]where:
a is a number between 1 and 9;
b is a integer, i.e., can be a positive or negative number
We have also to do some power properties.
For the first question, we get:
[tex]\begin{gathered} \mleft(8•10^{13}\mright)\div2•10^8= \\ =\frac{8}{2}\times\frac{10^{13}}{10^8}= \\ =4\times10^{13-8}= \\ =4\times10^5 \end{gathered}[/tex]So the final answer is 4 x 10^5
For the second one:
[tex]\begin{gathered} \mleft(5•10^8\mright)6•10^9\div15•10^{14}= \\ =\frac{5\cdot6\cdot10^{8+9}}{15\cdot10^{14}}= \\ =\frac{30\cdot10^{17}}{15\cdot10^{}^{14}}= \\ =\frac{30}{15}\cdot10^{17-14}= \\ =2\cdot10^3 \end{gathered}[/tex]Our final answer here is 2 x 10^3.
Plan A minutes: Plan B minutes:monday-10 monday-30tuesday-20 tuesday-40wednesday-30 wednesday-50thursday-40 thursday-60friday-50 friday-70Prove that linear functions grow by equal differences over equal intervals.
the linear function,
of plan A,
initital term a = 10
second term = 20
common difference = 20 - 10 = 10
for plan B
initial term a = 30
second term =40
the common difference = 40 - 30 = 10
thus the both linear function grow by equal difference over equal interevals.
Aaaaaaaaaaaaaaaaaaaaaaa
To be Liam's puzzle true, then the numbers must be one positive and one negative, that way their products will always be less than the numbers.
Hence, the answer is D.There are 100 jelly beans in a jar, 15 are black. 20 are red, 25 are yellow and 30 are green and the are orange. Write a fraction in the simplest form of the number of jelly beans that are orange Explain your reasoning for your answer.
Answer:
The fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]Explanation:
Given that;
There is a total of 100 jelly beans in the jar.
Of the total;
15 are black
20 are red
25 are yellow
30 are green
And the rest are orange.
The number of orange jelly beans can be calculated by deducting the number of black,red,yellow,and green jelly beans from the total.
[tex]\begin{gathered} n=100-(15+20+25+30) \\ n=100-90 \\ n=10 \end{gathered}[/tex]So, there are 10 orange jelly beans in the jar.
We now need to write a fraction of the number of jelly beans that are orange;
[tex]\begin{gathered} f_o=\frac{\text{ number of orange jelly beans }}{\text{Total number of jelly beans}} \\ f_o=\frac{10}{100} \\ f_o=\frac{1}{10} \end{gathered}[/tex]Therefore, the fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]
Can you please help me out with a question
Tangents to a circle that intersects at a point are equal in length.
Therefore,
|AB| = |AC|
Where
|AC| is the length of line AC
and
|AB| is the length of line AB
Hence,
[tex]\begin{gathered} 4x+2=2x+8 \\ \text{this implies that} \\ 4x-2x=8-2 \\ 2x=6 \\ \text{Dividing both sides by 2, we have} \\ \frac{2x}{2}=\frac{6}{2} \\ \text{thus} \\ x=3 \end{gathered}[/tex]x = 3 units
A) lena entered a raffle to win a movie ticket. The probability that she wins a movie ticket is 8/17. Find the odds in favor of her winning a movie ticket.B) keth is watching his favorite soccer team playing a match. The odds against his favorite team winning are 9/4. What is the probability of his favorite team winning?
A) The given information is:
The probability that Lena wins a movie ticket is 8/17.
This probability is given by:
[tex]P(winning)=\frac{favorable\text{ number of outcomes}}{total\text{ number of outcomes}}[/tex]The odds is favor are given by:
[tex]\text{ Odds in favor}=\frac{favorable\text{ outcomes}}{unfavorable\text{ outcomes}}[/tex]We can find the unfavorable outcomes by subtracting the number of favorable outcomes from the total number of outcomes, so:
Unfavorable outcomes=17-8=9.
So, the odds in favor are:
[tex]Odds\text{ }in\text{ }favor=\frac{8}{9}[/tex]B) The given information is:
The odds against Keith's favorite team winning are: 9/4
The odds against are given by:
[tex]Odds\text{ }against=\frac{\text{ unfavorable outcomes}}{\text{ favorable outcomes}}[/tex]The total number of outcomes is: unfavorable+favorable = 9+4=13
So, the probability of his favorite team winning is:
[tex]\begin{gathered} P(winning)=\frac{favorable\text{ outcomes}}{total\text{ number of outcomes}} \\ P(winning)=\frac{4}{13} \end{gathered}[/tex]Distributive Property: -3 1/2 divided by 1/2
ANSWER
-7
EXPLANATION
We want to solve the given fractional division by using the distributive property.
Basically, we are going to split the numerator into smaller pieces to make the division simpler.
That is:
[tex]\begin{gathered} \frac{-3\frac{1}{2}}{\frac{1}{2}} \\ =\text{ }\frac{\frac{-7}{2}}{\frac{1}{2}} \\ =\text{ }\frac{(\frac{-6}{2}\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{(-3\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{-3}{\frac{1}{2}}\text{ - }\frac{\frac{1}{2}}{\frac{1}{2}} \\ =\text{ -6 - 1} \\ =\text{ -7} \end{gathered}[/tex]The width of a picture frame is 16 3/5 centimeters. It’s length is 4 4/5 centimeters longer than the width . Find the length and the perimeter of the picture frame. Write the answer in simplest form.
ANSWER:
[tex]\begin{gathered} \text{Length = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Perimeter = 76 centimeters} \end{gathered}[/tex]EXPLANATION:
Since the length is 4⅘ longer than the width, the length will be:
Length = 4⅘ + 16⅗
[tex]\begin{gathered} W\text{ = 16}\frac{3}{5}\text{ centimeters} \\ Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5} \end{gathered}[/tex]Let's solve for length:
[tex]\begin{gathered} Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5}\text{ = }\frac{24}{5}\text{ + }\frac{83}{5}\text{ = }\frac{107}{5}\text{ = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Length = 21}\frac{2}{5}\text{ centimeters} \end{gathered}[/tex]From the given dimensions, it shows the picture frame is a rectangle.
To find the perimeter, use the perimeter of a rectangle formula:
Perimeter of a rectangle = 2(Length + Width)
[tex]\begin{gathered} \text{Perimeter = 2(}\frac{107}{5}+\frac{83}{5}) \\ \\ \text{ = 2(}\frac{190}{5}) \\ \\ \text{ = }2(38) \\ \\ \text{ = 76 centimeters} \end{gathered}[/tex]#9 - A card is drawn from a standard deck of playing cards. Find the probability that youdraw an ace.O 7.7%O 6.8%O 5.5%O 6.2%
Answer:
7.7%.
Explanation:
The number of cards in a standard deck, n(S)= 52
The number of aces in a standard deck, n(A) = 4 i.e 1 per suit.
Therefore, the probability that you draw an ace:
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ =\frac{4}{52} \\ \approx0.0769 \\ \approx7.7\% \end{gathered}[/tex]The probability that you draw an ace is 7.7%.
scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be between 70 and 93.
Answer:
0.8486
Explanation:
To find the probability that a score will be between 70 and 93, we first need to standardize these values, so we will use the following
[tex]z=\frac{value-mean}{standard\text{ deviation}}[/tex]Therefore, for 70 and 93, we get
[tex]\begin{gathered} z=\frac{70-81}{8}=-1.375 \\ \\ z=\frac{93-81}{8}=1.5 \end{gathered}[/tex]Then, we need to find the following probability
P(-1.375 < z < 1.5)
This probability can be calculate using a standard normal table, so
P(-1.375 < z < 1.5) = P(z < 1.5) - P(z < -1.375)
P(-1.375 < z < 1.5) = 0.9332 - 0.0846
P(-1.375 < z < 1.5) = 0.8486
Therefore, the probability is 0.8486
A tract of land, indicated by Quadrilateral MNPQ, is shown on this grid where one square unit represents 50 square feet.What is the area, in square feet, of the tract of land?
We have to find the area of the quadrilateral MNPQ.
We can divide it in two right triangles and then calculate the area as the sum of the area of the two triangles. To do that we would have to calculate the distances between N and P and M and N, as this are the legs of the upper triangle.
We can simplify it by making three right triangles by adding one vertex R(1,0):
Now, the length of the legs of the triangles are easier to find.
We then can calculate the area of the quadrilateral (A) as:
[tex]\begin{gathered} A=A_{\text{MRN}}+A_{\text{PRN}}+A_{\text{MPQ}} \\ A=\frac{(MR)\cdot(RN)}{2}+\frac{(PR)\cdot(RN)}{2}+\frac{(MP)(PQ)}{2} \\ A=\frac{1}{2}(9\cdot6+4\cdot6+13\cdot8) \\ A=\frac{1}{2}(54+24+104) \\ A=\frac{1}{2}\cdot182 \\ A=91 \end{gathered}[/tex]The area covers 91 square units.
As each unit represents 50 square feet, we can calculate the area in feet as:
[tex]A=91\text{ sq. units}\cdot\frac{50\text{ sq. ft.}}{1\text{ sq. unit}}=4550\text{ sq. ft.}[/tex]Answer: the land's area is 4550 square feet.
car is coasting backwards downhill at a speed of 2.9 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.8 m/s. Assuming that the uphill is the positive direction, what is the car's average acceleration? m/s2
The average acceleration of the car is 3.08 m/s² .
The speed of the car down hill = - 2.9m/s
The speed of the car uphill = 4.8 m/s
An object's average acceleration over time is determined by dividing the change in velocity, Δv, by the duration of the period, Δt.
Average acceleration = Δv ÷ Δt
Now the change in velocity ΔV = 4.8 - (-2.9) = 7.7 m/s
Change is time Δt = 2.5 seconds
Average acceleration of the car = 7.7 / 2.5 m/s² = 3.08 m/s²
In mechanics, the acceleration is the change is speed that refers to the exact rate at which the object's velocity varies with respect to time varies. Acceleration is a vector quantity since it has both a magnitude and a direction. The direction of an object's acceleration is determined by the direction of the net force acting on it.
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Justin has $200 in a bank account that earns 3% in annual interest. Does this describe a linear or exponential function? Select the equation.
Justin has $200 in a bank account that earns 3% in annual interest.
This can be modeled using an exponential function given by
[tex]f(x)=P(1+r)^x[/tex]Where P is the invested amount, r is the interest rate in decimal, and x is the number of years.
For the given case,
P = $200
r = 3% = 0.03
So, the exponential function becomes
[tex]\begin{gathered} f(x)=200(1+0.03)^x \\ f(x)=200(1.03)^x \end{gathered}[/tex]Therefore, the given situation describes an exponential function.
[tex]Exponential\colon f(x)=200(1.03)^x[/tex]Refer to the line for Exercises 17-22.17. If RS 19 and RV = 71, find SV.
Solution:
(17) Given;
[tex]RS=19,RV=71,SV=RV-RS[/tex]Thus;
[tex]\begin{gathered} SV=71-19 \\ \\ SV=52 \end{gathered}[/tex]ANSWER: SV = 52
uve a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know3-36. Write and solve an equation for the following problem.In the last election, candidate C received 15,000 fewer votes than candidate B. If a total of 109,000votes were cast, how many votes did candidate B receive?
If candidate C received 15,000 FEWER votes than candidate B, and the total was 109,000 votes, then :
C + B = 109000
and
C = B - 15000
Then we replace C by (B - 15000) in the first equation:
(B - 15000) + B = 109000
combine like terms on the left
2 B - 15000 = 109000
add 15000 to both sides
2 B = 109000 + 15000
2 B = 124000
divide bothe sides by 2:
B = 124000 / 2
B = 62000
Then, candidate B received 62000 votes.
the linear function f(x)=mx+b is one to one for all slopes, expect when m=____ then find f exponent negative 1(x).
Find the area of the rhombus9 in12 inA = [ ? ] in2?=Enter
The formula for calculating the area of a rhombus is expressed as
Area = d1d2/2
where
d1 is the length of one diagonal
d2 is the length of the other diagonal
From the information given,
length of one diagonal = 12 + 12 = 24
length of other diagonal = 9 + 9 = 18
By substituting these values into the formula,
Area = 1/2 x 24 x 18
Area = 216 in^2
the statue of liberty is approximately 305 feet tall. if the angle of elevation of a ship to the top of the statue is 20.5°, how far, to the nearest foot, is the ship from the statue's base?
The situation forms a right triangle:
Since it's a right triangle, we can apply the trigonometric function:
Tan α = opposite side / adjacent side
Replacing:
Tan 20.5= 305/x
Solve for x:
x = 305/tan 20.5
x= 816 ft
need help asappppppp
To find a, we will use the Pythagoras theorem,
adjacent² + opposite² = hypotenuse²
From the diagram, opposite = 5 adjacent = a hypotenuse =13
substitute the values into the formula and evaluate
a² + 5² = 13²
a² + 25 =169
subtract 25 from both-side of the equation
a² = 169 - 25
a² =144
Take the square root of both-side
a = 12
3. The results of the primary election are shown. Smith 15% Goron 35% Other 10% Fishman 40% (a) Order the popularity of the choices from greatest to least. (b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (c) 40 people voted for "Other." Was the estimate of total voters from Part (b) accurate? Explain. Answer: I C Focus 33
a) The order is;
Fishman
Goron
Smith
Other
b) 98 people would have voted for Goron if the estimation was true
c) The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
a) We want to order the popularity of choices from greatest to least
What we have to know and understand here is that the higher the percentage, the greater the popularity
Thus, we have it that;
Fishman
Goron
Smith
Other
b) As we can see from the data presented, Goron had 35% of the votes
So, the number of people that voted for Goron will be;
[tex]\begin{gathered} 35\text{ \% of 280} \\ =\text{ }\frac{35}{100}\times280\text{ = 98} \end{gathered}[/tex]98 people would have voted for Goron if the estimation was true
c) Here, we want to evaluate if the total we had from part B was correct
What we have to do here is get the number that would have been correct if at all 280 people voted
We have this as;
[tex]\begin{gathered} 10\text{ \% of 280} \\ =\text{ }\frac{10}{100}\times280\text{ = 28} \end{gathered}[/tex]The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
4 Surfboards atMorgun's Surf Shopcost $792. If they areall priced the sameamount, how muchdoes 1 surfboardcost?$198
Given that:
- The cost of 4 surfboards is $792.
- All the surfboards cost the same.
Therefore, in order to find the cost of 1 surfboard at Morgun's Surf Shop, you only need to divide the total cost of the four surfboards, by 4.
Let be "x" the cost (in dollars) of 1 surfboard.
You get that:
[tex]\begin{gathered} x=\frac{792}{4} \\ \\ x=198 \end{gathered}[/tex]Hence, the answer is: 1 surfboard costs $198.
5. The sum of two numbers is 24. The second number is 4 less than the first. Write a system of equations andsolve it to find the numbers.A. (16,8)B. (14, 10)C (18, 14)D (6,4)
Take x and y as the two numbers, the sum of these is 24:
[tex]x+y=24[/tex]It is also stated that the second number, y, is 4 less than the first, x, it means:
[tex]y=x-4[/tex]The system of equations is:
[tex]\begin{gathered} x+y=24 \\ y=x-4 \end{gathered}[/tex]Use the second equation, which is solved for y and replace this expression for y in the first equation, then solve for x:
[tex]\begin{gathered} x+y=24 \\ x+(x-4)=24 \\ x+x-4=24 \\ 2x=24+4 \\ 2x=28 \\ x=\frac{28}{2} \\ x=14 \end{gathered}[/tex]x has a value of 14. Use this value and the second equation to find the value of y:
[tex]\begin{gathered} y=x-4 \\ y=14-4 \\ y=10 \end{gathered}[/tex]The solution for the system is (14,10). The correct answer is B.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than or equal to 2". Find P(not A). Outcome Probability 1 0.26 2 0.45 3 0.06 4 0.04 5 0.15 6 0.04
A Probability
1 0.26
2 0.45
3 0.06
4 0.04
5 0.15
6 0.04
Probability to be less or equal than 2 = 0.45 + 0.26
= 0.71
Which graph represents y as a function of x? please help!! im sorry if not all photos show up
The graph does not represent a function between y and x.
How to check if the graph is a function?A function is a relation that maps inputs x into outputs y, such that each input is mapped into at most one output.
To check if a graph belongs to a function, we need to do the vertical line test, this means that if we draw a vertical line on the coordinate axis where we have the graph, and that vertical line touches the graph at more than one point, then the graph does not represent a function.
In this case, if we draw a line at x = 1 we will intersect the graph twice, then it is not a function.
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Yolanda bought 14 books. Yolanda bought 2 times as many books as Hans. Let n be the number of books that Hans bought.(a) Write an equation that relates the number of books that they bought.Use 2, 14, and n.
number of books Yolanda bought = 14 books
Yoland bought 2 times as many books as Hans. Therefore, Yolanda number of books can be represented as 2n. Where n is the number of books Han bought.
n = number of books Hans bought
2n = 14
divide btoh
f (x) = x² + x - 1 F (X + 2)
I will show you the question
The given system is
[tex]\begin{cases}3x+6y=12 \\ x+2y=4\end{cases}[/tex]First, we multiply the second equation by -3.
[tex]\begin{cases}3x+6y=12 \\ -3x-6y=-12\end{cases}[/tex]Then, we combine the equations
[tex]\begin{gathered} 3x-3x+6y-6y=12-12 \\ 0=0 \end{gathered}[/tex]This means the system has infinitely many solutions.
Hence, the answer is D.Point M is the point of reflection for point A. Find the coordinates of the image A' A(-3, 2) M(-1,5)
You know that the distance between each point on the preimage and the point of reflection M(-1,5) are equal to the distance between M(-1,5) and each point on the image.
So, you can observe this graph
Therefore, the coordinates of the image A' will be (1,8).