Answer: The required ratio in simplest form is 7 : 5 : 8.
Step-by-step explanation: Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. [tex]\frac{1}{4}[/tex] of the drink is apple juice and [tex]\frac{2}{5}[/tex] is orange juice.
We are to find the ratio of cranberry juice to apple juice to orange juice in its simplest form.
Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.
Then, according to the given information, we have
[tex]y=\dfrac{1}{4},~~z=\dfrac{2}{5}.[/tex]
Now,
[tex]x+y+z=1\\\\\\\Rightarrow x+\dfrac{1}{4}+\dfrac{2}{5}=1\\\\\\\Rightarrow x=1-\dfrac{1}{4}-\dfrac{2}{5}\\\\\\\Rightarrow x=\dfrac{20-5-8}{20}\\\\\\\Rightarrow x=\dfrac{7}{20}.[/tex]
Therefore, the ratio of cranberry juice to apple juice to orange juice is given by
[tex]x:y:z\\\\\\=\dfrac{7}{20}:\dfrac{1}{4}:\dfrac{2}{5}\\\\\\=\dfrac{7}{20}:\dfrac{5}{20}:\dfrac{8}{20}\\\\=7:5:8.[/tex]
Thus, the required ratio in simplest form is 7 : 5 : 8.
Help please Algebra Two!!
Answer:
a) -1 mult. 2 & 2 mult. 2
b) [tex]-a(x+1)^2(x-2)^2[/tex]
c) 4 at least (even degree could be 4, 6, 8, etc)
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity.Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial.The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -1,2
We can write them in intercept or factored form as (x+1) and (x-2).
Because the graph never crosses the x-axis each has an even multiplicity of at least 2.
The graph is facing down and is an upside down W so is negative. [tex]-a(x+1)^2(x-2)^2[/tex]
This means the function has a degree of 4 or higher with the degree being even.
At the newest animated movie, for every 99 9 children, there are 44 4 adults. There are a total of 3939 39 children and adults at the movie. How many children are at the movie?
Answer:
27 children.
Step-by-step explanation:
We are told that at the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults at the movie.
We can see that number of children is proportional to number of adults. So we will use proportions to solve for number of children at the movie.
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{4+9}[/tex]
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{13}[/tex]
Let us substitute number of children and adults in our proportion.
[tex]\frac{\text{Number of children}}{39}=\frac{9}{13}[/tex]
Multiply both side of equation by 39.
[tex]39*\frac{\text{Number of children}}{39}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=3*9[/tex]
[tex]\text{Number of children}=27[/tex]
Therefore, 27 children are at the movie.
The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon with two sides of length 3.
The first hexagon: 2, 2, 3, 4, 6, 7
The second hexagon: 3, 3, a, b, c, d
The hexagons are similar. Therefore the sides are in proportion.
[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex] multiply both sides by 3
[tex]a=\dfrac{3}{2}=4.5[/tex]
[tex]\dfrac{b}{4}=\dfrac{3}{2} [/tex] multiply both sides by 4
[tex]b=\dfrac{3}{2}\cdot4=6[/tex]
[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex] multiply both sides by 6
[tex]c=\dfrac{3}{2}\cdot6=9[/tex]
[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex] multiply both sides by 7
[tex]d=\dfrac{21}{2}=10.5[/tex]
The perimeter:
[tex]P=4.5+6+9+10.5=30[/tex]
A scanner can scan 40 pages in 4 minutes. At this rate, how many pages can its can in 2 minutes?
Answer:
20 pages
Step-by-step explanation:
2 minutes is 1/2 of 4 minutes.
By proportion number of pages he scans in 2 minutes = 1/2 * 40
= 20 pages
Final answer:
To calculate the number of pages a scanner can scan in 2 minutes, you divide the total pages scanned in 4 minutes by 4 to find the rate per minute, and then multiply by 2. The scanner can scan 20 pages in 2 minutes.
Explanation:
To find out how many pages a scanner can scan in 2 minutes if it can scan 40 pages in 4 minutes, we use proportion or unit rate since the scanning speed is constant. We start by determining how many pages are scanned in one minute. Since 40 pages are scanned in 4 minutes, we divide 40 by 4 to find the scanning speed per minute:
40 pages ÷ 4 minutes = 10 pages per minute.
Now we find out how many pages can be scanned in 2 minutes by multiplying the rate by the number of minutes:
10 pages per minute × 2 minutes = 20 pages.
Therefore, the scanner can scan 20 pages in 2 minutes at the given rate.
Which of the following equations has a slope of -3 and a y-intercept of -4?
Answer:
An equation with a slope of -3 and an intercept of -4 is y = -3x - 4
Step-by-step explanation:
To find this we start with the base form of slope-intercept.
y = mx + b
Now we know that the slope goes in for m and the intercept goes in for b. Simply input those values.
y = -3x - 4
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Jeremy bought a new truck for $32,000. The value of the truck after t years can be represented by the formula V = 32,000(.8)^t. How much will the truck be worth in 2 years?
Answer: A
Step-by-step explanation:
[tex]V = 32,000(.8)^{t}[/tex]
[tex]= 32,000(.8)^{2}[/tex]
[tex]= 32,000(.64)[/tex]
= 20,480
Joey's eyes are 5.5 feet above the ground. He sets a mirror on the ground so he can see the top of a nearby building. The mirror is 8 feet away from Joey and 130 feet away from the base of the building. Estimate the height of the building using similar triangles. Round the height to the nearest foot.
A. 89 ft
B. 189 ft
C. 715 ft
D. 1040 ft
Answer:
89 feet
Step-by-step explanation:
First of all, we will make a diagram to demonstrate the given scenario as shown in the attached picture.
Now we will use similar triangles to set the ratios as shown below to figure out the height of the building.
[tex]\frac{x}{130} =\frac{5.5}{8}[/tex]
Now we will solve for x from this equation by cross multiplying.
[tex]8x=130\cdot5.5[/tex]
[tex]8x=715[/tex]
[tex]x=89.375[/tex]
Therefore, height of the building is approximately 89 feet.
The area of the triangle is 1560 m2
True
False
Answer:
FALSE
Step-by-step explanation:
Area of triangle is given by formula :
[tex]Area\ =\ \frac{1}{2}\left(base\right)\left(Altitude\right)[/tex]
From picture we see that Altitude = 60 m
Base = 52 + 71 = 123 m
Now plug these values into above formula:
[tex]Area\ =\ \frac{1}{2}\left(123\right)\left(60\right)[/tex]
[tex]Area\ =\ \frac{1}{2}\left(15129\right)[/tex]
[tex]Area\ =\ \frac{15129}{2}[/tex]
[tex]Area\ =\ 7564.5[/tex]
Which is different than given area 1560 m^2.
Hence answer is FALSE.
What is the difference in height between a bird flying at 100m above surface of the ocean and a shark swimming 30 m below surface?
Answer:
130m
Step-by-step explanation:
Let the ocean be the origin (0,0)between the the bird flying and the shark swimming. If the distance between a bird flying and the ocean is 100m and the distance between the ocean above and a shark swimming below the sea is 30 m, the distance between the flying bird and the shark will be calculated by adding the two distances to give;
=(100-0)+(30-0)
= 100+30
= 130m
Note that the ocean serves ad the origin(0,0) therefore the distance between each animal and the sea will be known first and the two values will be added as shown above to get the distance between the two animals.
Find the 100th term in the arithmetic sequence
-19,-14,-9,-4,1...
a.
100
c.
476
b.
471
d.
481
Please select the best answer from the choices provided
A
B
C
D
[tex]a_n=a_1+(n-1)d\\\\d=a_{n+1}-a_n[/tex]
[tex]a_1=-19;\ a_2=-14;\ a_3=-9;\ a_4=-4;\ a_5=1;\ ...\\\\d=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\d=-14-(-19)=-14+19=5\\\\a_n=-19+(n-1)(5)=-19+5n-5=5n-24\\\\a_{100}=5(100)-24=500-24=476\to\boxed{c.}[/tex]
What is the end behavior of the graph of the exponential function f(x)=b^x when 0
Answer:
(1) B. f(x)->0 as x->∞, f(x)->∞ as x->-∞
(2) D. [tex]f(x)= 2^{-x}+5[/tex]
Step-by-step explanation:
[tex]f(x) = b^x[/tex]. Given 0<b<1
'b' is between 0 and 1 so b should be a fraction
'b' is a fraction, so for positive value of x , the value of f(x) cannot be negative.
the graph of f(x) will goes close to 0 but it never cross x axis
So end behavior is f(x)->0 as x->∞
for negative values of x , the y value increases
So end behavior is f(x)->∞ as x->-∞
(2) f(x) = 2^x
When graph reflects across y axis, x becomes -x
so [tex]f(x)= 2^{-x}[/tex]
For translating up by 5 units we add 5 at the end
so [tex]f(x)= 2^{-x}+5[/tex]
When 0 < b < 1, the graph of the function f(x) = [tex]b^x[/tex] is decreasing. This means that the values of f(x) will get smaller and smaller as x gets larger and larger.
In the limit as x approaches positive infinity, f(x) will approach zero. On the other hand, in the limit as x approaches negative infinity, f(x) will approach positive infinity.
The correct answer is g(x) = 2*+5.
The function g(x) = 2*+5 reflects the graph of f(x) = 2x across the y-axis and translates it up 5 units.
The reflection across the y-axis is achieved by multiplying the function by -1.
The translation up 5 units is achieved by adding 5 to the function.
The graph of g(x) is also shifted up 5 units.
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Martha wants to rent a car for a week and to pay no more than 130 how far can she drive if the car rental 94 a week plus 12 cent a mile
Answer:
Let x be the number of mile.
Total cost is no more than 130.
As per the given statement: if the car rental 94 a week plus 12 cent a mile.
12 cent a mile means 12x
then the equation become:
[tex]94 + 12x \leq 130[/tex]
Subtract 94 to both sides we get;
[tex]94 + 12x-94 \leq 130-94[/tex]
Simplify:
[tex]12x \leq 36[/tex]
Divide both sides by 12 we get;
[tex]x \leq 3[/tex]
Therefore, 3 miles she drive if the car rental 94 a week plus 12 cent a mile.
What is the product?
(9t-4)(-9t-4)
a) -81t^2-16
b)-81t^2+16
c)-81t^2 - 72t+16
d)-81t^2 +72t+16
List the 6 congruency statements given ABC ~ DEF
Answer:
First choice is correct ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF
Step-by-step explanation:
Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.
We know that corresponding angles of congruent triangles are equal so we can write:
∠A ≅ ∠D
∠B ≅ ∠E
∠c ≅ ∠F
We know that corresponding sides of congruent triangles are equal so we can write:
AB = DE
BC = EF
AC = DF
comparing these with given choices we see that, First choice { ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF} is correct.
The table show the total distance d, in miles, a car traveled after t hours. Time in hours (h) Distance in miles (d) 0 0 1 50 2 100 3 150 Which equation shows the relationship between d and t? d=t+50 d=50t d=t+150 d=150t
answer is d=50t
am i right
Answer:
yes you are right
Step-by-step explanation:
d=50t
Answer:
Yes. It is :
D=50t
Step-by-step explanation:
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answer:
The population at the end of 2017 is 65,550
Step-by-step explanation:
step 1; find the population at the end of 2016
if 60,000 increases by 15% therefore final % = 100 +15 =115%
Therefore 60,000 = 100%
? = 115%
by cross multiplication
={ (115 % x 60,000) /100} =69,000
Step 2: find the population at the end of 2017
if 69,000 decrease by 5% therefore the final% = 100 -5 =95%
Therefore 69000 = 100%
? = 95%
by cross multiplication
= 69000 x 95/100 = 65,550
Ryan made 65 ounces of apple jelly. He put the same amout of jelly into 6 jars. About how much jelly is in each jar
Answer:
10 5/6 ounces
Step-by-step explanation:
That is 65 / 6
= 10 5/6 ounces
The area of a rectangle is length x width.Sasha is looking for rent the floor plan is rectangular.The length of the store is 21 and 2/3feet amd the area is 325 square feet.What is the width of the store?
Answer:
Width of the store = 15 feet.
Step-by-step explanation:
Area = length * width
Plugging in the given dimensions:-
325 = 21 2/3 * x
x = 325 / 21 2/3
= 325 / 65/3
= (325 * 3) / 65
= 15 feet (answer)
In the 1918 baseball season Ty cobb had 421 at bats and 161 base hits. What was his batting average? Write your answer as a decimal rounded to the nearest thousandth
Answer:
Batting average = 0.382
Step-by-step explanation:
In the 1918 baseball season Ty cobb had 421 at bats and 161 base hits.
number of bat hits= 161
Number at bats = 421
Batting average = [tex]\frac{base \ hits}{at \ bats}[/tex]
Plug in the values in the formula
Batting average = [tex]\frac{161}{421}=0.382422802[/tex]
Now round the answer to three decimal places
Batting average = 0.382
The rabbit population in a certain area is 200% of last years population.There are 1,100 rabbits this year.How many were there last year?
Answer:
550
Step-by-step explanation:
We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. Since we know the population increased to 200% of last year and is 1,100.
[tex]\frac{200}{100}=\frac{1100}{y}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
200y=100(1100)
200y=110,000
y=550
There was 550 rabbits last year.
By applying percentages and division, we find that there were 550 rabbits last year, as this year's population of 1,100 rabbits is 200% or twice the amount of last year's.
Explanation:The rabbit population in a certain area is 200% of last year's population. This year, there are 1,100 rabbits. It means that 1,100 is double the population from last year because 200% is equal to 2 times the original number. To find the population of rabbits last year, we need to take this year's total and divide it by 2. So, 1,100 rabbits divided by 2 equals 550 rabbits. Therefore, last year, the population of rabbits was 550.
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Two towns are 6 inches apart on a map. If the scale for this map is 1 inch equals 100 miles, how many miles apart are the two towns?
Answer:600 miles apart
Step-by-step explanation: one inch is 100 miles multiply that by 6 you get 600 miles
PUT IN POINT SLOPE FORM (-2,-3)m=8
Answer:
y+3= 8(x+2)
Step-by-step explanation:
original eq
y-y1=m(x-x1)
then you plug in given numbers
Answer:
[tex]y+3=8(x+2)[/tex]
Step-by-step explanation:
The point slope form:
[tex]y-y_1 = m(x-x_1)[/tex]
[tex]m=8\\(-2, -3)\\x_1=-2\\y_1=-3[/tex]
[tex]y-(-3)=8(x-(-2))[/tex]
[tex]y+3=8(x+2)[/tex]
pleaseeeeeee someone help me
Answer: D
Step-by-step explanation:
The orange color is represented by the bottom line, which is y > x - 2
The purple color is represented by the top line, which is y < x + 1
How do we know the equations of those lines?
The equations can be written in the form y = mx + b where;m = slopeb = y-interceptThe orange line:
crosses the y-axis at -2 --> b = -2 has a rise over run of 1 -> m = 1 --> y = x - 2the line is dashed and is shaded above so y > x - 2The purple line:
crosses the y-axis at +1 --> b = 1 has a rise over run of 1 -> m = 1 --> y = x + 1the line is dashed and is shaded below so y < x + 1Th kc royals won 11 of 14 of their playoff games in 2014 what percent of their games did they win (round to the nearest ones)
(02.03)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
Question 1 (5 points)
Correlation implies causation.
Question 1 options:
True
False
Question 2 (5 points)
A correlation between two variables means...
Question 2 options:
that both variables are always equal
that there is no relationship between the variables
that a change in one variable is matched by a change in the other variable
there is something wrong with the data
Question 3 (5 points)
A negative correlation between two variables means...
Question 3 options:
both variables are decreasing
both variables are increasing
there is no correlation
when one variable goes up, the other goes down
Question 4 (5 points)
A strong linear correlation means...
Question 4 options:
both variables are increasing
the graph of data points stay close to a line
there is a wide spread in the data
Question 5 (5 points)
Standard deviation is a measure of...
Question 5 options:
how linear data is.
the spread of data.
the difference between the greatest and the lowest values.
Question 6 (5 points)
The formula for standard deviation uses which average?
Question 6 options:
mean
median
mode
zero
Question 7 (5 points)
According the the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible, then even A followed by event B has...
Question 7 options:
m + n outcomes
m - n outcomes
m x n outcomes
m / n outcomes
Question 8 (5 points)
What is the value of 4! ("four factorial")
Question 8 options:
4
16
10
24
Question 9 (5 points)
If the probability of passing an exam is 80%, what is the probability of not passing it?
Question 9 options:
80%
50%
100%
20%
Question 10 (5 points)
Given that when flipping a coin, there is 1/2 chance of getting a heads:
What is the probability of flipping a coin and getting heads twice in a row?
Question 10 options:
1
1/2
1/4
1/2
Answer:
Question 1 (5 points)
Correlation implies causation.
False
Question 2 (5 points)
A correlation between two variables means...
that a change in one variable is matched by a change in the other variable
Question 3 (5 points)
A negative correlation between two variables means...
when one variable goes up, the other goes down
Question 4 (5 points)
A strong linear correlation means...
the graph of data points stay close to a line
Question 5 (5 points)
Standard deviation is a measure of...
the spread of data.
Question 6 (5 points)
The formula for standard deviation uses which average?
mean
Question 7 (5 points)
According the the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible, then even A followed by event B has....
m x n outcomes
Question 8 (5 points)
What is the value of 4! ("four factorial")
24
Question 9 (5 points)
If the probability of passing an exam is 80%, what is the probability of not passing it?
20%
Question 10 (5 points)
Given that when flipping a coin, there is 1/2 chance of getting a heads:
What is the probability of flipping a coin and getting heads twice in a row?
1/4
Step-by-step explanation:
These are just facts you should know.
A correlation between two variables means that a change in one variable is matched by a change in the other variable. Standard deviation is a measure of the spread of data. The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.
Explanation:A correlation between two variables means that a change in one variable is matched by a change in the other variable. For example, if there is a positive correlation between studying time and test scores, it means that as the studying time increases, the test scores also increase.
A negative correlation between two variables means that when one variable goes up, the other variable goes down. For instance, if there is a negative correlation between temperature and ice cream sales, it means that as the temperature increases, the ice cream sales decrease.
A strong linear correlation means that the data points on a graph stay close to a line. This indicates a strong relationship between the variables being measured.
Standard deviation is a measure of the spread of data. It tells us how much the individual data points differ from the mean (average) of the data set.
The formula for standard deviation uses the mean as the average.
According to the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible outcomes, then event A followed by event B has m x n outcomes.
The value of 4! (four factorial) is 24. Factorial represents the product of all positive integers from 1 to the given number.
If the probability of passing an exam is 80%, the probability of not passing it would be 20%.
The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.
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A ticket cost $4.80 the new ticket price will be 1.25 times the old price what will the new ticket be
Answer:
$6.
Step-by-step explanation:
Let x be the new price of ticket.
We have been given that a ticket cost $4.80. The new ticket price will be 1.25 times the old price.
We can represent this information as:
[tex]x=1.25\times 4.80[/tex]
[tex]x=6[/tex]
Therefore, the cost of new ticket will be $6.
Final answer:
The new ticket price will be $6.00
Explanation:
Increased Price: The problem states that the new ticket price will be 1.25 times the old price. This means the new price will be 25% higher than the old price.
Calculating the Increase: To calculate the new price, we need to find 1.25 times the old price. Mathematically, this is done by multiplying the old price by 1.25.
Old ticket price: $4.80
Calculation: New ticket price = Old ticket price × 1.25
Calculation: New ticket price = $4.80 × 1.25 = $6.00
Therefore, the new ticket price will be $6.00
How far is Town Center from Maple Station? (please look at attachment) 15 POINTS
4
2
5.83
5.57
Answer:
5.83 units
Step-by-step explanation:
We write the coordinate points of Maple Station (-3,5) and Town Center (0,0). We label the points left to right as [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] and substitute the values.
[tex](x_{1}, y_{1}) = (-3, 5)\\(x_{2}, y_{2})=(0,0)[/tex]
[tex]d=\sqrt{(0-5)^{2} + (0-(-3) })^{2}}[/tex]
[tex]d=\sqrt{(0-5)^{2} + (0+3) })^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2} + (3) }^{2}}[/tex]
[tex]d=\sqrt{25 +9}}[/tex]
[tex]d=\sqrt{34}}[/tex]
5.83 units
Janice bought juice packets for the 15 players on the soccer team The juice packets come in boxes of 6 How many boxes did Janice buy?
Answer:
3 boxes.
Step-by-step explanation:
We are told that Janice bought juice packets for the 15 players on the soccer team. The juice packets come in boxes of 6.
To find the number of boxes that Janice need to buy for 25 players, we will divide 15 by 6.
[tex]\text{Number of boxes that Janice needs to buy}=\frac{15}{6}[/tex]
[tex]\text{Number of boxes that Janice needs to buy}=2.5[/tex]
Since the juice packets come in boxes of 6, so we will round our answer to nearest whole number.
[tex]\text{Number of boxes that Janice needs to buy}=2.5\approx 3[/tex]
Therefore, Janice will buy 3 boxes of juice packets for 15 players.
The question entails a simple division operation of 15 players divided by 6 juice packets per box which gives 2.5. However, since Janice can't buy half a box, she ends up buying 3 boxes of juice packets.
Explanation:To answer your question, we need to perform a simple division arithmetic operation. This involves taking the total number of players which is 15 and dividing that by the number of juice packets in one box, which is 6 . The calculation is as follows: 15 ÷ 6 = 2.5. However, Janice cannot purchase half of a box so she would need to round up to the nearest whole number. Hence, Janice bought 3 boxes of juice packets for the soccer team.
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Stacy is saving $5 each week to buy a new bike. She already has 15 dollars saved in her bank account. SHe needs to save at least 75 dollars in order to buy a new bike.
She nee to save $60 more so she can buy a new bike