Answer:
8 grape and 16 cranberry
Step-by-step explanation:
To find this, we need to know what one-third of 24 boxes are; we'd then do 24 divided by 3, which is equal to 8. One-third of them were grape so we know 8 are grape. Cranberry makes up the other two-thirds; two-thirds is equal to one-third times 2. 8 (one-third) times 2 is 16, giving our answer of 16 cranberry.
Answer:
mr peterson bought 8 boxes of grape juice and he bought 16 boxes of cranberry juice
Step-by-step explanation:
Which of the following are equivalent to the function y=3 cos x+2 ? Check all that apply
A. y= 3sin(x-pi/2) +2
B. y= 3sin(x+ pi/2) +2
C. y= 3cos(-x) +2
D. y= -3cos x-2
Options B and C are the correct answer.
The given trigonometric function is y=3cosx+2.
We need to check which of the given options are equivalent to the function y=3 cos x+2.
How to solve a given trigonometric function?The given trigonometric function can be solved using complementary angles and even/odd identities.
Complementary angles are sin x=cos(π/2 -x) and cos x=sin(π/2 -x).
Even/odd identities are sin(-x) =-sin x and cos(-x)= cos x.
Now,
From option A:
y=3 sin(x-π/2) +2
using trigonometry identity, we get
y=3 sin(-(x-π/2)) +2
⇒y=-3 sin(π/2 - x)+2
⇒y=-3 cos x+2
From option B:
y= 3sin(x+ π/2) +2
Using Sin(A+B)= sin A cos B+ cos A sin B, we get
y= 3cosx +2
From option C:
y= 3cos(-x) +2 can be written as y=3cosx+2 (cos(-x)=cosx)
From option D:
y= -3cos x-2
Therefore, options B and C are the correct answer.
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Final answer:
The equivalent functions to y=3 cos x+2 are B: y= 3sin(x+ π/2) +2 and C: y= 3cos(-x) +2, as they use the co-function identity and the even property of the cosine function respectively.
Explanation:
The given function is y=3 cos x+2. We need to find functions that are equivalent to this function. The trigonometric identities necessary for this problem are:
cos(-x) = cos(x), which is the even function property of cosine. sin(x + π/2) = cos(x), which is a co-function identity.sin(-x) = -sin(x), showing that sine is an odd function.Now, considering the given options:
A. y= 3sin(x-π/2) +2: Using the co-function identity sin(x - π/2) = -cos(x), this option is not equivalent because it would yield y = -3cos(x) + 2, which is not the same as the given function.B. y= 3sin(x+ π/2) +2: By the co-function identity sin(x + π/2) = cos(x), this option is equivalent to the given function.C. y= 3cos(-x) +2: Using the even function property of cosine, this option is equivalent to the given function because cos(-x) = cos(x).D. y= -3cos x-2: This is not equivalent because it represents the reflection of the given function over the x-axis and a vertical translation down by 2 units.
Therefore, the equivalent functions are B and C.
You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. What is your expected final fortune
Answer:
$45
Step-by-step explanation:
In order to find this we need to understand that every time we bet we are selecting white ball. Because of this we have the chance of getting two times right and two times wrong irrespective of the order. For example we can any of the following orders:
White - White - Black - Black
White - Black - White - Black
Black - White - Black - White
Black - Black - White - White
Irrespective of any of the orders above every time our bet is right (we get white urn) the amount of dollars that we have get increased by half of the current amount. For example on the first turn we are betting $40 (half of initial amount = $80) and if we are right we now have $120 with us. This can be written as
1.5*$80 = $120
Similarly if on first turn we get wrong (black ball) then our amount is half of initial which can be written as
0.5*$80 = $40
So now we know that exactly two times we will be right and exactly two times we will be wrong irrespective of the order because the balls are not replaced hence final solution is:
E(X) = 80*1.5*1.5*0.5*0.5
= $45
The frequency table represents data gathered about how much time some farmers spend tending to their land each week. Complete the conditional relative frequency table by row by identifying the values for each letter. a = b = c = d =
Answer:
a= 0.6
b= 0.4
c= 0.2
d= 0.8
Step-by-step explanation:
Ons
The value of each letter in the conditional relative frequency table is
a = 0.6b = 0.4c = 0.2d = 0.8What is the value of each letter?Division is an arithmetic operation that is used to determine the quotient of two or more numbers. Division entails grouping a number into equal groups using another number.
a = 180 / 300 = 0.6
b = 120 / 300 = 0.4
c = 40 / 200 = 0.2
d = 160 / 200 = 0.80
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Abigail is climbing up and rappelling down a series of cliffs and drop-offs. She starts at her base camp, which is on the middle of a mountain. She begins by rappelling down an 82.5-foot drop-off and then climbs a cliff of 30.4 feet. Next she rappels down a 45.5-foot drop-off and then climbs a 25.2-foot cliff. Finally she makes two 45.4-foot climbs.
Answer:
Alibagi is [tex]18.4[/tex] feet above the base camp
Step-by-step explanation:
Complete question -
An explorer is climbing up and rappelling down a series of cliffs
and drop-offs. She starts at her base camp, which is on the middle
of a mountain. She begins by rappelling down an 82.5-foot
drop-off and then climbs a cliff of 30.4 feet. Next she rappels
down a 45.5-foot drop-off and then climbs a 25.2-foot cliff.
Finally she makes two 45.4-foot climbs.
Part A: How far above or below her base camp is the
explorer now?
Solution
Given -
First movement is in the downward direction which is equal to [tex]- 82.5[/tex] feet
Second movement is in in the upward direction which is equal to [tex]+ 30.4[/tex] feet
Third Movement is in the downward direction which is equal to [tex]- 45.5[/tex] feet
Fourth movement is in in the upward direction which is equal to [tex]+ 25.2[/tex] feet
Fifth movement is in in the upward direction which is equal to [tex]45.4[/tex] feet
Sixth movement is in in the upward direction which is equal to [tex]45.4[/tex] feet
Net movement of Abigail is
[tex]- 82.5 + 30.4 -45.5 + 25.2 + 45. 4 + 45.4 \\18.4[/tex]
Alibagi is [tex]18.4[/tex] feet above the base camp
Leo wants to paint a mural that covers a wall with an area of 600 square feet. The height of the wall is 2/3 of its length. What is the length and the height of the wall? answer: the dimensions (length by height) of the wall are __feet by __ feet.
Answer: attached
Step-by-step explanation:
help pleases with this question !!!!
Answer: 2.13
Step-by-step explanation:
1.42/2=0.71
1.42+0.71=2.13
Answer:
The answer to your question is £ 2.13
Step-by-step explanation:
Data
Cost of 1 kg or oranges = £1.42
Cost of the oranges in the scales = ?
Process
1.- Determine the weight of the oranges in the scales.
As we can see the weight of the three oranges is 1.5 kg
2.- Use proportions and cross multiplication to find the cost.
1 kg of oranges --------------------- £ 1.42
1.5 kg of oranges ------------------ x
x = (1.5 x 1.42) / 1
x = 2.13 / 1
x = £ 2.13
round 1395 to the nearest hundred
Answer:
1400
Step-by-step explanation:
It is closer to 1400 than 1300
Answer:
1,395.00
Step-by-step explanation:
There were 200,000 animals of a certain species in 1980. Since then,this number has decreased by 4.5% each year. Approximately how many animals of this species will be left in 2025?
Answer: Approximately 25187 animals of this species will be left in 2025
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
y = b(1 - r)^x
Where
y represents the population of animals after x years.
x represents the number of years.
b represents the initial population of animals.
r represents rate of decay.
From the information given,
b = 200000
r = 4.5% = 4.5/100 = 0.045
x = 2025 - 1980 = 45 years
Therefore,
y = 200000(1 - 0.045)^45
y = 200000(0.955)^45
y = 25187
Answer:
There'll be approximately 25187.3059 animals of this species in 2025.
Step-by-step explanation:
In this case we have a compounded interest problem, but the interest rate is negative, since the number will be decreasing. To solve it we can use the compound interest formula shown bellow:
M = C*(1 + r)^(t)
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed.
In this case the time elapsed was from 1980 to 2025, so 45 years. Applying the data to the formula gives us:
M = 200000*(1 + (-0.045))^(45)
M = 200000*(1 - 0.045)^(45)
M = 200000*(0.955)^(45)
M = 25187.3059
There'll be approximately 25187.3059 animals of this species in 2025.
What is the value of n when (9)^2n-1 = (27)^n+2
[tex]9^{2n-1} = 27^{n+2} \\ ( {3}^{2} ) ^{2n - 1} = ( {3}^{3} )^{ n + 2} \\ {3}^{4n - 2} = {3}^{3n + 6} \\ 4n - 2 = 3n + 6 \\ 4n - 3n = 6 + 2 \\ n = 8[/tex]
Answer: n=8
Dennis has three identical cylinders filled with water. How many cones should he be able to fill with the water if the cones have the same radius and the same height as the cylinders?
Answer:
3 cylinder will fill 9 cones with water
Step-by-step explanation:
This problem bothers on mensuration of slides, cone and cylinder
We know that the
Volume of a cylinder = πr²h
Volume of a cone = 1/3(πr²h)
Given that both cylinder and cone has same height and radius
From the given expression we can deduce that the cone is 3 times smaller than the cylinder in volume
So if 1 cylinder will fill 3 cones
Then 3 cylinders will fill x cones
By cross multiplication we have
x= 3*3cones
x= 9 cones
Hence 3 cylinder will fill 9 cones with water
Answer:
9 cones
Step-by-step explanation:
The formula to find a volume of a cylinder is:
V1 = pi*r^2*h
Where r is the base radius and h is the height
The formula to find a volume of a cone is:
V2 = (1/3)*pi*r^2*h
So, if they have the same base radius and same height, we have that:
V1/V2 = 1/(1/3) = 3
The volume of the cylinder is 3 times bigger than the volume of the cone, so each cylinder of water can fill 3 cones.
Is Dennis has 3 cylinders, he is able to fill 3*3 = 9 cones with water.
does finding the volume of a solid means the inside or outside of a solid?
Answer: Inside (depending on your definition).
Step-by-step explanation: Finding the volume of a solid means measuring what space that solid takes up. Volume is a measure of how much matter an object is made up of. Technically, finding the volume of a solid does not mean finding the "inside" or "outside" of a solid. If you are referring to the surface area of a solid as the outside, then the answer to your question would be the inside of the solid.
Arie has $46 in his account and is saving $8.50 each week. Olga has $14 in her savings account and is saving $12.50 each week. After how many weeks will Arie and Olga have the same in their accounts?
Answer:
5 weeks until they have the same
Arie and Olga have the same amount in their accounts in 8 weeks.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Amount in Arie's account = $46
Arie's each week savings = $8.50
Amount in Olga 's account = $14
Olga 's each week savings = $12.50
Let x be the number of weeks when Arie and Olga will have the same amount in their accounts
Total savings of Arie = 8.5x
Total savings of Olga = 12.5x
Amount in Arie's account = 8.5x + 46
Amount in Olga's account = 12.5x + 14
For, Arie and Olga have the same amount in their accounts
8.5x + 46 = 12.5x + 14
Taking alike terms together,
12.5x - 8.5x = 46 - 14
⇒ 4x = 32
Dividing both side by 4 we get,
x =8 weeks
which is the required number of weeks.
Thus, Arie and Olga will have the same amount in their accounts in 8 weeks.
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PLEASE HELP
A radius of 4 millimeters. What is the area?
Answer:
50.24 mm²
Step-by-step explanation:
Area = pi × r²
3.14 × 4²
50.24 mm²
Answer:
The area equals 50.2654 rounded up 50.27
Step-by-step explanation:
A= pi times radius squared equals pi times 4 squared equals 50.2654 (50.27)
The legs of a right triangle measure 15 and 20. what is the length of the hypotenuse?
A.25
B.35
C.13
D.10
it depends on how big the triangle is if it is close to the same length of 20 go with 25 if theres a bigger difference go with 35. I think it would be 25 tho.
Answer:
I got this answer on my quiz correct it is in fact A. 25,
Have a wonderful day
Step-by-step explanation:
Mark the brainiest please
If f(x)=7(x−1)+8 , what is the value of f(1) ?
Answer:
8
Step-by-step explanation:
f(1)=7(1-1)+8
f(1)=0+8
f(1)=8
The question is asking us to find the value of the function f(x) = 7(x−1) + 8 when x equals 1. To find this, we substitute 1 in place of x in the equation. So, f(1) = 7(1-1) + 8. Calculating this, 7 multiplied by 0 equals 0, so the equation simplifies to 0 + 8. Therefore, f(1) = 8.
To solve the problem, we must first substitute the value of x in the function `f(x)` which is `7(x−1)+8`.
Here, substitute x = 1:
So we have f(1) = 7*(1-1) + 8.
Simplify the expression inside the parenthesis first (as according to BIDMAS or PEMDAS - operations in parenthetical expressions should be done before multiplication and addition):
7 * (1 - 1) + 8 simplifies to 7 * 0 + 8.
The multiplication operation takes precedence over addition (again per the rules of BIDMAS/PEMDAS), so multiply 7 and 0:
We get 0 + 8.
Finally, perform the addition operation:
0 + 8 equals 8.
So, f(1) = 8.
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Write a Linear Equation in Slope Intercept Form given the listed slopw and y-intercept.
m = –5, b = –3
Answer:
The equation is y = -5x - 3.
Step-by-step explanation:
The slope form equation is y = mx+b. So you just have to substitute the m and b value into the equation :
y = mx + b
m = -5
b = -3
y = -5x + (-3)
= -5x - 3
An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline and is losing 3.1 gallons per day. If the value of the gasoline is $2.55 per gallon, how quickly is the value of the stored gasoline changing?
Answer:
-$7.905 per day
Step-by-step explanation:
In this question, given that a tank is losing its fuel content at a certain rate, we are to calculate the rate at which the value in dollars of the content of the fuel tank
is changing
Please check attachment for complete solution and step by step explanation
An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline and is losing 3.1 gallons per day. The rate at which the value of the stored gasoline is changing is -$7.905 per day.
Suppose we make an assumption that the tank initial contains h(x) gallons of gasoline which leak in x days. Then, the rate of change of gasoline per gallon is;
[tex]\mathbf{\dfrac{dh}{dx} =- 3.1 \ \ \ \ \ \ \text{since the gas is leaking (-)}}[/tex]
Also, the rate of change of the gasoline in time(t) per unit change in the quantity can be computed as:
[tex]\mathbf{\dfrac{dt}{dh}=2.55 }[/tex]
Therefore, the value of the stored gasoline changing per unit change of days can be deduced by using the chain rule:
[tex]\mathbf{\dfrac{dt}{dx} = \dfrac{dt}{dh} \times \dfrac{dh}{dx}}[/tex]
[tex]\mathbf{\dfrac{dt}{dx} = -3.1 \times2.55}[/tex]
[tex]\mathbf{\dfrac{dt}{dx} =\$-7.905 \ per \ day}[/tex]
Therefore, we can conclude that the rate at which the value of the stored gasoline is changing is -$7.905 per day.
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The population of a town was 25,000 at the first year of a census.
(a) If the population of the town increased to 30,000 at the second year, by what percent did the population increase?
(b) If the population decreased from 30,000 to 27,000 at the third year, by what percent did the population decrease?
Step-by-step explanation:
a) 30,000-25,000= 5000
(5000/25,000) x 100= 20%
b) 30,000-27,000= 3000
(3000/30,000) x 100= 10%
I need help asap my friends
Answer:
The first one 24/4
Step-by-step explanation:
Into usually means divide when it's used as a math term,
therefore 24 into fourths means 24 divide by 4.
Answer:
the answer is 24 divided by 4
Step-by-step explanation:
Help please? 15 points here
Answer:
64°
Step-by-step explanation:
In circle with center P, AD is diameter.
[tex] \therefore m\angle DPE + m\angle APE = 180\degree \\
\therefore (33k-9)\degree + 90\degree = 180\degree \\
\therefore (33k-9)\degree = 180\degree -90\degree \\
\therefore (33k-9)\degree = 90\degree \\
\therefore 33k-9 = 90\\
\therefore 33k= 90+9\\
\therefore 33k= 99\\
\therefore k= \frac{99}{33}\\
\therefore k=3\\
m\angle CPD = (20k +4)\degree \\
\therefore m\angle CPD = (20\times 3 +4)\degree \\
\therefore m\angle CPD =(60+4)\degree \\
\therefore m\angle CPD =64\degree \\
m\overset {\frown}{CD} = m\angle CPD\\
\therefore m\overset {\frown}{CD} = 64\degree
[/tex]
Help with this math question and i will give you 40 points and mark you the brainliest
Answer:
a) CD = 6a + 4.5b
b) k = 4
Step-by-step explanation:
CD = CA + AB
CA = -AC
CD = -3b + 6a + 7.5b
CD = 6a + 4.5b
BC is parallel to CD
BC = BA + AC
BC = ka + 3b
BC is a scalar multiple of CD
Scale factor:
3/4.5 = 2/3
k = ⅔(6)
k = 4
What is the radius of a circle with an area of 28.26 square feet
Answer:
The radius is 3 square feet.
(Working is shown in the picture)
The radius of a circle with an area of 28.26 square feet is 3 feet
What is Radius?A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.
Given,
Area of the circle = 28.26 square feet
Area of the circle = [tex]\pi r^{2}[/tex]
Then
[tex]28.26 =\pi r^{2}\\ r^{2}=9\\ r=\sqrt{9}\\[/tex]
r = 3 feet
Hence, the radius of a circle with an area of 28.26 square feet is 3 feet
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charles needs to fill a large fish tank gallons per min, and what is the rate? a total of 110 gallons of water can flow through hose b in 10 minutes. which hose has a faster water flow rate, in gallon per minute, and what is that rate?
The question is incomplete, the correct question is:
Charles needs to fill a large fish tank with water using a hose. he has two hoses from which to choose. Water flows through each hose at a constant rate. The graph below shows the amount of water, in gallons , that flows through holes A based on the number of minutes used. A total of 110 gallo s of water can flow through Hose B in 10 minutes. Which hose has a faster water rate, in gallons per minute, and what is that rate?
Answer:
Hose B has a faster water flow rate in comparison to Hose A
Step-by-step explanation:
For Hose B,
From the information above, it is said that a total of 110 gallons of water can flow through hose b in 10 minutes. Therefore, divide 110 by 10 to get the amount of water that flows through hose b in gallons in one minute.
So,
110/10=11
y=11 x
This implies that 11 gallons of water flows through hose b in 1 minute.
For Hose A,
Select two points to get the rate of change,and then subtraction of y2 from y1 and x2 from x1 is done
Points selected: (2,12) , (4,24)
(x1,y1)=(2,12)
(x2,y2)=(4,24)
So, Subtract 24 from 12 and 2 from 4
M=y2-y1/x2-x1= 24-12 / 2-4= 12/2=6
This implies that in hose a a total of 6 gallons of water flows in one minute.
Therefore, the equation for hose a is y=6 x
In conclusion, hose b has a faster water flow rate since y=6 x < y=11 x.
Answer:
is b the correct
Step-by-step explanation:
At a conference, there are 121 math teachers and 11 science teachers. Write the
ratio of math teachers to science teachers in simplest form.
Answer:11:1
Step-by-step explanation: the are 121 math teachers and there are 11 science teachers so that is 121:11 divide both numbers by 11 which is their highest common multiple and the result is 11:1
What is the diameter of a circle with a circumference of 132ft Use 22/7 for pi.
Answer:
d = 42
Step-by-step explanation:
Formula = π × d
22/7 × d = 132
d = 132 : 22/7
d = 132 × 7/22
d = 6 × 7
d = 42
Final answer:
The diameter of a circle with a circumference of 132ft, using 22/7 for pi, is calculated by dividing the circumference by pi. The diameter is found to be 42 feet.
Explanation:
To find the diameter of a circle when given the circumference, you can use the formula:
C = πd
Where C is the circumference and d is the diameter. In this case, the circumference (C) is 132ft and we are using π (pi) as 22/7. To find the diameter (d), you rearrange the formula to solve for d:
d = C/π
Plugging in the given values we get:
d = 132ft / (22/7)
Calculation:
d = 132ft × (7/22)
d = 924ft/22
d = 42 feet
Therefore, the diameter of the circle is 42 feet.
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?
Answer:
P( That it will take over 10 years or more of a year with a rainfall above 50inches) = (0.9938)^10
Step-by-step explanation:
Since the annual rainfall is normally distributed,
Given: that
Mean (µ )= 40
and σ = 4.
Let X be normal random variables of the annual rainfall.
P(that there will be over 10 years or more before a year with a rainfall above 50 inches)
P(>50) = 1-P[X ≤50]
1 - P[X- μ/σ ≤ 50 - 40/4]
=1 - P [Z≤ 5/2]
=1 -Φ(5/2)
=1 - 0.9939
= 0.0062
P( the non occurrence of rainfall above 50 inches)
= 1-0.0062
=0.9938
ASSUMPTION:
P( That it will take over 10 years or more of a year with a rainfall above 50inches) =[tex](0.9938)^10[/tex]
The diameter of a circle is 2 inches. What is the circle's area?
Use 3.14 for .
Answer:
3.14
Step-by-step explanation:
Answer:3.14
Step-by-step explanation:
You are feeding a room that is 25‘ x 25‘ there is a window in the room there's 4‘ x 3‘ x 6‘ the paint cost $12 per gallon 1 gallon of paint covers 100 ft.² what is the area of the room
Answer:
With an assumption of room height = 8 ft we have;
The area of the room is 800 ft²
Area to be painted = 794.667 ft²
Paint required ≈ 7.95 gallons of paint
Cost of paint = $95.36
Step-by-step explanation:
Here we have if the height of the room is taken as 8 ft,
Therefore the total area in the room is 25 × 8 × 4 = 800 ft²
since the room has a window with three sides, therefore a triangular window of dimensions
4 ft by 3 ft by 6 ft
The area of the window is then
[tex]A = \sqrt{6.5(6.5-4)(6.5-3)(6.5-6)}[/tex]
Where the semi perimeter = (4 + 3 + 6)/2 = 6.5
Area of window, A = 5.333 ft²
Therefore, the total area to be painted = 800 ft² - 5.333 ft² = 794.667 ft².
Therefore the number of gallons of paint required ≈ 7.95 gallons
Cost of paint= $12 × 7.95 = $95.36.
The double number line shows that Toni can type 180180180 words in 222 minutes. Based on the ratio shown in the double number line, how many words can Toni type in 333 minutes?
Answer:
Toni can type words in 3 minutes is 270 wordsStep-by-step explanation:
Given that the double number line shows that Toni can type 180 words in 2 minutes.
To find how many words can Toni type in 3 minutes:From the given Toni can type 180 words in 2 minutes,
⇒ Toni can type [tex]\frac{180}{2}[/tex]
[tex] = 90[/tex]
∴ 90 words per minuteFor Toni would be able to type words in 3 minutes is
[tex]90\times 3[/tex]
[tex] = 270[/tex]
∴ 270 words per minute.∴ Toni can type words in 3 minutes is 270 words.Answer:
put 270 and the anwser shoud be correct
How else can I describe the data
Answer:
Data is distinct pieces of information, usually formatted in a special way.
Step-by-step explanation: