probability of drawing a blue marble is 1/3
Find the maximum and minimum values of the function.
y=7cosx
Answer:
B
Step-by-step explanation:
If a sinusoidal function is given in the form y = B Sin x or y = B Cos x, then,
B is called the amplitude of the function. It will define minimum and maximum.
The minimum & maximum of this form of a cos function is B and -B.
The function given is y = 7 Cos x, so the Maximum is 7 and Minimum is -7
Correct answer is B.
IXL question
I don't understand this one and I need more than 0 points :/
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 6.
a)x squared divided by 81 plus y squared divided by 9 = 1
b)x squared divided by 9 plus y squared divided by 3 = 1
c)x squared divided by 9 plus y squared divided by 81 = 1
d)x squared divided by 3 plus y squared divided by 9 = 1
C seem reasonable to me
the volume of a storage tub shaped like a rectangular prism is 24 ft cubed. The height of the top is 3 ft the width is W feet in the length is W + to use the formula V equals l w h to find the value of w
[tex]\boxed{W=2ft}[/tex]
Step-by-step explanation:A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. On the other hand, a rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:
[tex]V=L\times W\times H[/tex]
From the statement of the problem we know:
[tex]V=24ft^3 \\ \\ H=3ft \\ \\ W=W \\ \\ L=W+2[/tex]
So:
[tex]24=(W+2)(W)(3) \\ \\ 3W(W+2)=24 \\ \\ 3W^2+6W-24=0 \\ \\ From \ the \ Quadratic \ Formula: \\ \\ W_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{12}=\frac{-6 \pm \sqrt{6^2-4(3)(-24)}}{2(3)} \\ \\ W_{1}=2 \\ \\ W_{2}=-4[/tex]
Since we can't have negative distance, the only valid option is [tex]\boxed{W=2ft}[/tex]
Which of the following is true?
A. Sine is negative in Quadrant I.
B. Tangent is positive in Quadrant III.
C. Cosine is positive in Quadrant III.
D. Sine is negative in Quadrant II.
Please help!
Answer:
Tangent is positive in Quadrant III.
Step-by-step explanation:
All trigonometric functions are positive in QUADRANT I
The Sine function is positive in QUADRANT II
The Tangent function is positive in QUADRANT III
The Cosine function is positive IN QUADRANT IV
*ASTC JUST REMEMBER THAT :)*
There are four quadrants in a plane, and the true statement is (b) Tangent is positive in Quadrant III.
How to determine the true statement?There are four quadrants in a coordinate plane, and they have the following properties
Quadrant I
All positiveQuadrant II
Sine positiveOther negativeQuadrant III
Tangent positiveOther negativeQuadrant IV
Cosine positiveOther negativeThe above means that the true statement is (b) Tangent is positive in Quadrant III.
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Chose a prize and explain your reasoning:
1st prize: $250000 in cash
2nd prize: free gas for life
Answer:
1st prize
Step-by-step explanation:
Not all people use a car. Some people walk, take a bike, etc. So, if you won free gas for life, you might not be able to use it.
1st prize. To decide between $250,000 in cash or free gas for life, one must analyze projected gas consumption, inflation, and investment opportunities. The cash offers immediate value and investment potential, whereas the value of free gas depends on driving habits and future fuel prices.
When presented with the options of receiving a 1st prize of $250,000 in cash or a 2nd prize of free gas for life, a comparative analysis based on present value, inflation, personal consumption, and lifestyle must be conducted. The choice primarily depends on one's driving habits, projected longevity of vehicle use, and the current and forecasted price of gas.Concretely, one could estimate the amount of gas consumed annually and project this over an expected driving lifetime, accounting for inflation and potential changes in fuel costs. Then one would compare the total estimated value of free gas to the lump sum of $250,000, determining if it could be invested to yield a greater return than the estimated value of the free gas.Using a net present value calculation, if the $250,000 is invested at an assumed interest rate, you could assess which option has a higher present value, factoring in that the value of the money may also depreciate due to inflation over time. If an individual expects to drive significantly and fuel prices are expected to rise, the free gas for life could potentially be of greater value.However, the flexibility of cash and potential returns on investment typically make the cash prize more appealing for most people. So, 1st prize.Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units left and 3 units up
B. shifted 4 units left and 4 units up
C. shifted 4 units left and 3 units up
D. shifted 3 units left and 4 units up
C. shifted 4 units left and 3 units up
If you compare the graphs (ABCD=Blue; A’B’C’D’=Red), you see that ABCD was moved left 4 and up 3 to become A’B’C’D’.
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
To know the steps that were applied to ABCD to obtain A'B'C'D, we need to observe the coordinates of any one point of the polygon given.
Now, if we look at the coordinates of the points D and D', then it can be observed that point D is shifted 3 units left and 3 units up to form A'B'C'D.
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A medium sized apple has 70 calories. This is 10 calories less than 1\4 of the calories in an old westie chocolate bar.How many calories are in the chocolate bar?
Answer:
[tex]\boxed{320}[/tex]
Step-by-step explanation:
Let x = calories in chocolate bar
¼x = ¼ of the calories
¼x – 10 = 10 calories less than half the calories
¼x – 10 = 70
¼x = 80
x = 320
There are [tex]\boxed{320}[/tex] calories in the chocolate bar.
Given: circle k(O), m RK =70° Find: m∠ERK
Check the picture below.
Answer:
Step-by-step explanation:
55
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Suppose the ages of cars driven by employees at a company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
What is the z-score of a car that is 6 years old?
Answer: b) -0.625
Step-by-step explanation:
The formula for the z-score is:
[tex]z=\dfrac{x-\mu}{\sigma}\\\\\bullet z \text{ is the z-score}\\\bullet x \text{ is the value}\\\bullet \mu \text{ is the mean}\\\bullet \sigma \text{ is the standard deviation}\\\\z=\dfrac{6-8}{3.2}\\\\\\.\ =\dfrac{-2}{3.2}\\\\\\.\ =\large\boxed{-.0625}[/tex]
Identify the surface area of the composite figure in terms of π. HELP PLEASE!!
Answer:
S = 264π m²
Step-by-step explanation:
Left cone
= π(6)(8)
= 48π m²
Central cylinder
= 2π(6)(14)
= 168π m²
Right cone
π(6)(8)
= 48π m²
Surface area = 48π + 168π + 48π = 264π m²
The surface area of the composite figure is 264π [tex]m^{2}[/tex]
How to find the surface area of a composite figure?r = 6m
h = 14m
l = 8m
The curved surface area of the cylinder = 2πrh
= 2*[tex]\pi[/tex]*6*14
=168π [tex]m^{2}[/tex]
The curved surface area of the cone = πrl
=π*6*8
=48π [tex]m^{2}[/tex]
The total surface area of the composite figure
= CSA of cylinder + 2( CSA of cone )
= 168π + 2*48π
=168π + 96π
= 264π [tex]m^{2}[/tex]
Therefore, option S = 264π [tex]m^{2}[/tex] is the correct answer
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-2 is a solution of 5x + 3 = 13
True OR False
False.
Replace x with -2 and simplify. 5(-2) + 3 = 13
Multiply. -10 + 3 = 13
Add. -7 = 13
This is not true, so -2 is not a solution, therefore the answer to the question is false.
Kesha rode her bike 12 miles from home to the store. She rode her bike back towards home from the store for 8 miles then walked another 4 miles. How many more miles does Kesha needs to go before she is home?
Answer:
0 Kesha is already home 8+4 is 12 and it's 12 miles from the store to her house .-.
Step-by-step explanation:
Answer:
0 more miles.
Step-by-step explanation:
If 12 miles is the total distance from her house to the store the answer should be 0. She should be at home because 8 miles on the bike + the 4 walked = 12 miles, which is how many she rode to the store in the first place.
Write the standard form of the equation of the circle with center (-5,-7) that passes through the point (7,5).
Answer:
(x + 5)² + (y + 7)² = 288
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)
r = [tex]\sqrt{(7+5)^2+(5+7)^2}[/tex] = [tex]\sqrt{12^2+12^2}[/tex] = [tex]\sqrt{288}[/tex]
Hence
(x - (- 5))² + (y - (- 7))² = ([tex]\sqrt{288}[/tex])², that is
(x + 5)² + (y + 7)² = 288
A catch and release fisherman catches a fish and then releases the fish back into the river so as to not to harm the fish.
At a local river, 50% of the fish are white sturgeon, 35% brook trout, and 15% Chinook salmon.
If a fisherman catches then releases a fish and then catches and releases a second fish, then what is the probability that both fish he caught were white sturgeon?
Answer:
25%
Step-by-step explanation:
Assuming the catching of a fish is a random process and that the probability of catching any of the listed kinds of fish is proportional to their population, then the probability of catching a sturgeon is 50%. The probability of catching another one is also 50% (assuming the events are independent). So, the joint probability is the product of these:
0.50 × 0.50 = 0.25 = 25% . . . . . probability of catching 2 sturgeon in a row.
The probability of both fish being white sturgeon is 0.25.
To calculate the probability, we need to multiply the probabilities of catching a white sturgeon each time. Since 50% of the fish are white sturgeon, the probability of catching one is 0.5. Therefore, 0.5 multiplied by 0.5 equals 0.25.
Rearrange the formula a2 + b2 = c2 for a. A) a = (c2 − b2)2 B) a = (c2 + b2)2 C) a = c2 − b2 D) a = c2 + b2
Answer:
C2 + a2 +2 = b
Would be the new formula
Answer:
the correct answer is:
a = √ c^2 − b^2
Step-by-step explanation:
a^2 + b^2 = c^2
Explanation:
a^2 + b^2 = c^2
a^2 = c^2 − b^2
a = √ c^2 − b^2
A cooler at a picnic contains 100 cans of soda covered by ice. There are 34 cans of cola, 50 cans of orange soda, 12 cans of ginger ale, and 4 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected is root beer, cola comma or ginger ale.
The probability that the can selected is a root beer, cola comma or ginger ale is nothing .
(Type an integer or a simplified fraction.)
Answer:
P = 1/2 = 0.5
Step-by-step explanation:
Total amount of cans = 100
Cans of cola = 34
Cans of orange soda = 50
Cans of ginger ale = 12
Cans of root beer = 4
Probability of selecting
- a can of cola = 34/100 = 0.34
- a can of orange soda = 50/100 = 0.5
- a can of ginger ale = 12/100 = 0.12
- a can of root beer = 4/100 = 0.04
Since we are asked the probability that the can selected is a root beer, cola, or ginger ale, we need to add together the probabilities of each.
P = 0.04 + 0.34 + 0.12 = 0.5 = 1/2
hot tub depot has a new promotional payment plan. all purchases can be made on the installment plan with no interest as long as the total is paid in full within 12 months there is a $25 minimum monthly payment required.
A) if the haugh family buys a hot tub for $4,355 and make only the minimum payment for 11 months how much will they need to pay in the 12th month?
B) what should they pay every month?
PLEASE SHOW ALL WORK!
Answer: $4080
Step-by-step explanation: 25 x 11 = 275, 4355-275 = 4080
The Haugh family will need to pay $4,080 in the 12th month if they make only the minimum payment for 11 months. The monthly payment they should pay is $362.92 (rounded to the nearest cent).
Explanation:A) To find out how much the Haugh family will need to pay in the 12th month if they make only the minimum payment for 11 months, we need to calculate the remaining balance after 11 months. The total cost of the hot tub is $4,355. The minimum monthly payment is $25, so the remaining balance after 11 months is $4,355 - 11 * $25 = $4,080. Therefore, the Haugh family will need to pay $4,080 in the 12th month.
B) To calculate the monthly payment, we divide the total cost of the hot tub by the number of months (12). So, the monthly payment is $4,355 / 12 = $362.92. However, since there is a minimum payment requirement of $25, the Haugh family should pay $362.92 each month (rounded to the nearest cent).
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In the system shown below, what are the coordinates of the solution that lies in quadrant IV?
Write your answer in the form (a,b) without using spaces
[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]
Answer:
The coordinates of the solution that lies in quadrant IV are (2, -5)
Step-by-step explanation:
We have 2 equations, the first of an ellipse and the second of a circumference.
[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]
To solve the system solve the second equation for x and then substitute in the first equation
[tex]x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y[/tex]
So Substituting in the first equation we have
[tex]x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0[/tex]
Now we must factor the quadratic expression.
We look for two numbers that multiply as a result -5 and add them as result 4.
These numbers are -1 and 5.
Then the factors are
[tex]y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0[/tex]
Therefore the system solutions are:
[tex]y = 1[/tex]; [tex]y = -5[/tex]
In the 4th quadrant the values of x are positive and the values of y are negative.
So we take the negative value of y and substitute it into the system equation to find x
[tex]y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4[/tex]
[tex]x = 2[/tex], and [tex]x= -2[/tex]
In the 4th quadrant the values of x are positive
So we take the positive value of x
the coordinates of the solution that lies in quadrant IV are (2, -5)
2) If events A and B are DEPENDENT, then A) A and B must occur together. B) A and B cannot occur together. C) A's occurrence can affect the probability of B's occurrence. D) A's occurrence cannot affect the probability of B's occurrence.
Answer:
by 5
Step-by-step explanation: because tgey wou;d nred help
Answer:
C.) If events A and B are DEPENDENT, then A's occurrence can affect the probability of B's occurrence. For example, when two cards are chosen from a deck without replacement, the possibilities change for the second card.
Identify the volume of a cube with edge length 13 ft. HELP PLEASE!!
Answer:
V=2197
Step-by-step explanation:
Equation for volume of a cube:
V= side length cubed
V=(13)(13)(13)
V=2197
Answer:
V = 2,197 ft3
Step-by-step explanation:
Your welcome ;)
Please help me out with this!!
BRAINLIEST AVAILABLE!!
Answer:
xy = 1
k = 79
Step-by-step explanation:
Question One
The first and third frames look to me to be the same. I'll treat them that way.
y = x^2 Equate y = x^2 to the result of 2y + 6 = 2x + 6
2y + 6 = 2(x + 3) Remove the brackets
2y + 6 = 2x + 6 Subtract 6 from both sides
2y = 2x Divide by 2
y = x
Now solve these two equations.
so x^2 = x
x > 0
1 solution is x = 0 from which y = 0. This won't work. x must be greater than 0. So the other is
x(x) = x Divide both sides by x
x = 1
y = x^2 Put x = 1 into x^2
y = 1^2 Solve
y = 1
The second solution is
(1,1)
xy = 1*1
xy = 1
Answer: A
Question Two
square root(k + 2) - x = 0
Subtract x from both sides
sqrt(k + 2) = x Square both sides
k + 2 = x^2 Let x = 9
k + 2 = 9^2 Square 9
k + 2 = 81
k = 81 - 2
k = 79
Choices:
14.63
26.96
36.95
61.51
Correct answers show work!
Tan(angle) = opposite leg / adjacent leg.
Tan(64) = x /30
x = 30 * tan(64)
x = 61.51
Answer:
the answer is d 61.51
Step-by-step explanation:
the equation of a line is given below.
4x + 3y = -24
find the x-intercept and the y-intercept.
then use them to graph the line.
x-intercept: ?
y-intercept: ?
Answer:
See below.
Step-by-step explanation:
4x + 3y = -24
We convert to slope/intercept form ( y = mx + b):
3y = - 4x - 24
Divide through by 3:
y = (-4/3)x - 8
Comparing this with y = mx + b:
we see that b ( the y-intercept) is -8.
To find the x -intercept solve (-4/3)x - 8 = 0
(-4/3)x = 8
Multiplying through by -3/4:
x = 8 * -3/4 = -6 = x-intercept.
To draw the graph draw a line through the points (-6,0) and (0, -8).
Answer:
-3/4 y-6
Step-by-step explanation:
what is the solution for the system of equations?
y= 2x - 3
4x - 3y = 31
Answer:
It is easy it is a 2 step equation if you know the 2 four boxes
Step-by-step explanation:
is the variable alone?
No
what is it attached to?
you always do adding or subtracting first so it is attached to 3
How is it attached?
by subtraction
what is the inverse operation?
it is addition
then all you do is the same thing but with multiplication or division
Answer:
Use Substitution.
Plug in 2x-3 in place of y in the second equation.
4x - 3(2x-3) = 31
4x - 6x + 9 =31
-9 -9
-----------------------
-2x=22 so x=-11
Then, y=2(-11)-3, so y=-25
So the solution would be (-11,-25).
URGENT PLEASE HELP 98 POINTS Find the direction angle of vector v to the nearest tenth of a degree.
Answer:
The direction angle of vector v is equal to [tex]9.5\°[/tex]
Step-by-step explanation:
Let
[tex]A(-5,0),B(7,2)[/tex]
The vector v is given by
[tex]v=B-A[/tex]
[tex]v=(7, 2) - (-5, 0)[/tex]
[tex]v=((7 - (- 5)), (2-0))[/tex]
[tex]v=(12, 2)[/tex]
Remember that
The direction angle of the vector is equal to
[tex]tan (\theta) =\frac{y}{x}[/tex]
substitute the values
[tex]tan (\theta) =\frac{2}{12}[/tex]
[tex]\theta=arctan(\frac{2}{12})=9.5\°[/tex]
Answer:
The direction angle of vector v is equal to 9.5\°
Step-by-step explanation:
Let
A(-5,0),B(7,2)
The vector v is given by
v=B-A
v=(7, 2) - (-5, 0)
v=((7 - (- 5)), (2-0))
v=(12, 2)
Remember that
The direction angle of the vector is equal to
tan (\theta) =\frac{y}{x}
substitute the values
tan (\theta) =\frac{2}{12}
\theta=arctan(\frac{2}{12})=9.5\°
Step-by-step explanation:
put that in a computer calc and it shoud give u the awnser
The longest side in a right triangle is 24 cm, and the second longest side is 20 cm. Find the length of the shortest side
Answer:
13.3 cm
Step-by-step explanation:
Apply the Pythagorean Theorem:
hyp² = (2nd longest side)² + (shortest side)². Here the numbers are:
(24 cm)² = (20 cm)² + (shortest side)², or
576 - 400 = 176 = hyp²
Taking the square root of both sides, we get (shortest side) = 13.3 cm
Answer: the answer is 13.3
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.15x2 − 6x + 400
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
50 75
60 60
70 55
80 60
90 75
Based on the given information, the minimum production cost for company _____ is greater.
[Put 1 or 2 in the blank space]
Answer:
The answer is confirmed 1. Just took it.
Step-by-step explanation:
Answer:
Company 1 is greater.
Step-by-step explanation:
Given,
The function that shows the production cost of company 1,
[tex]f(x)=0.15x^2-6x+400[/tex]
Differentiating with respect to x,
We get,
[tex]f'(x)=0.30x-6[/tex]
Again differentiating,
[tex]f''(x)=0.30[/tex]
For minimum or maximum,
f'(x) = 0,
[tex]\implies 0.3x-6=0[/tex]
[tex]\implies x = 20[/tex]
Since, at x = 20, f''(x) = Positive,
So, f(x) is minimum at x = 20,
⇒ Minimum cost in company 1 is,
[tex]f(20)=0.15(20)^2-6(20)+400[/tex]
[tex]=340[/tex]
Also, by the given table,
The minimum cost of company 2 is at x = 70,
g(70) = 55,
Since, 340 > 55,
Hence, Based on the given information, the minimum production cost for company 1 is greater.
The value of ∛x^10, when x = -2, can be written in simplest form as a∛b, where a = ___ and b = ___.
Answer:
a = -8
b = -2
Step-by-step explanation:
We have been given the following radical expression;
[tex]\sqrt[3]{x^{10} }[/tex]
The radical can be expressed using the law of exponents;
[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex]
The radical can thus be re-written as;
[tex]\sqrt[3]{x^{10} }=(x^{10})^{\frac{1}{3} }[/tex]
Using the law of exponents;
[tex](a^{b})^{c}=a^{bc}[/tex]
The last expression becomes;
[tex](x^{10})^{\frac{1}{3} }=x^{\frac{10}{3} }=x^{3}*x^{\frac{1}{3} }\\\\=x^{3}\sqrt[3]{x}[/tex]
substituting x with -2 yields;
[tex]-2^{3}\sqrt[3]{-2}=-8\sqrt[3]{-2}[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The number generator is fair. it picked the approximate percentage of red most of the time.
Answer:
The number generator is fair, It picked the approximate percentage of red s*ckers most of the time.
Step-by-step explanation:
7*3+9*3+8*4 = 80
80 divided by 10 gives you an average of 8 red s*ckers each time which is exactly 80% of the amount of s*ckers picked
(s*ckers is banned for some reason)