Answer:
Step-by-step explanation:
answer D would also be true
Answer:
Step-by-step explanation:
answer D would also be true
Suppose that after I wrote this problem, Richard Rusczyk thought he could be more clever than I could, so he wrote his own problem. Suppose that both of our problems are in the set of 12 problems you are currently working on. If you sat down at your computer this morning and randomly loaded 4 of the 12 problems, what is the probability that both this problem and Richard Rusczyk's problem were among the four you loaded?
Answer:
P = 0.0909
Step-by-step explanation:
To know the number of ways or combinations in which we can select x elements from a group of n elements, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, if you sat down at your computer and randomly loaded 4 of the 12 problems, there are 495 different possibilities and it is calculated as:
[tex]12C4=\frac{12!}{4!(12-4)!}=495[/tex]
Then, from 495 different possibilities, there are 45 possibilities that both this problem and Richard Rusczyk's problem were among the four you loaded. This 45 possibilities are calculated as:
[tex](1C1)*(1C1)*(10C2)=(\frac{1!}{1!(1-1)!})*(\frac{1!}{1!(1-1)!})*(\frac{10!}{2!(10-2)!})=45[/tex]
Because you need to select: this problem and there is only one, the problem that Richard Rusczyk wrote and there is only one, and 2 problems from the other 10.
Finally, the probability that both this problem and Richard Rusczyk's problem were among the four you loaded is equal to:
[tex]P=\frac{45}{495}=0.0909[/tex]
Find the sum of
(3a+7)+(a−1)
The sum is ___
Answer:
4a+6
Step-by-step explanation:
To find the answer to this problem, you need to combine the like terms. (3a+7)+(a-1)=(3a+a)+(7-1)=4a+6. Hope this helps!
The of the given expression is 4a+6.
What is an expression?An algebraic expression is formed by using integers, constants, variables, and arithmetic operations. Variables and constants can be combined in an algebraic expression through mathematical operations.
Given that, an expression (3a+7)+(a−1), we need to find sum,
So,
(3a+7)+(a−1)
Opening the brackets,
3a+7+a-1
Combining the like terms,
3a+a+7-1
= 4a+6
Hence, the of the given expression is 4a+6.
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Find the area of the shaded polygons:
Answer:
For the green one the answer is 8 square units
For the red one the answer is 9 square units
Hope this helps
The area of the shaded green polygon is equal to 8 square units.
The area of the shaded red polygon is equal to 9 square units.
In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):
Area of triangle = 1/2 × b × h
Where:
b represent the base area.h represent the height.Note: When the green polygon is dissected, three triangles would be formed.
By substituting the given side lengths into the formula for the area of a triangle, we have the following;
Area of triangle = (1/2 × 1 × 1) + (1/2 × 3 × 1) + (1/2 × 3 × 4)
Area of triangle = 0.5 + 1.5 + 6
Area of triangle = 8 square units.
In order to determine the area of the shaded red polygon, we would have to apply Pick's theorem;
Area of polygon = (b/2 + i) - 1
where:
i is the number of lattice points inside a polygon.b is the number of lattice points on the perimeter of a polygon.By substituting the number of lattice points, we have the following;
Area of polygon = (b/2 + i) - 1
Area of red polygon = (4/2 + 8) - 1
Area of red polygon = 10 - 1
Area of red polygon = 9 square units.
PLEASE HELP NEED ANSWER ASAP!! 30POINTS!!!!!!
who can help me with The Sum of The Angles in a Triangle
Answer:
Suppose that you had a right angle triangle. Note that if you take it and another copy of it (moved around a bit) the two triangles together can be placed to make a rectangle.
This rectangle has four 90 degree angles adding up to 360 degrees. Since the triangles are congruent each triangle has half as many degrees, namely 180. So this is true for any right triangle.
Suppose you triangle is not a right triangle. Draw a perpendicular from the vertex opposite the longest side, to the longest side. What you have now is two right triangles which, by the above contain 360 degrees in total. But if you look at the two right angles that add up to 180 degrees so the other angles, the angles of the original triangle, add up to 360 - 180 = 180 degrees.
Step-by-step explanation:
Answer:
The sum must be 180° for the angles to be a triangle.
The Triangle Sum Theorem states that every angle in a triangle must equal 180° in total.
m∠A +m∠B +m ∠C = 180°
The equation above can help you solve for an angle in a triangle if two measurements of the angle are given.
A circle has an area of 81 7 square inches. What is the circumference of the circle?
A. 4.5 inches
B. 2.25 inches
C. 18 inches
D. 9 inches
For his hiking club, Trinity is making a container of trail mix with 3.5 kg of nuts. He has 1.78 kg of Peanuts and 0.625 kg of almonds. The rest of the nuts will be cashews. How many kilograms of cashews does he need?Use estimation to check your answer for reasonableness
There will be 1.095kg of cashews.
Step-by-step explanation:
Peanut = 1.78kg
Almonds = 0.625kg
If the total mass of the nuts should be 3.5kg then the cashew will be,
Cashew = 3.5 - 1.78 - 0.625
= 1.095 kg
There will be 1.095kg of cashews.
Answer:
There will be 1.095kg of cashews.
Step-by-step explanation:
Peanut = 1.78kg
Almonds = 0.625kg
If the total mass of the nuts should be 3.5kg then the cashew will be,
Cashew = 3.5 - 1.78 - 0.625
= 1.095 kg
There will be 1.095kg of cashews.
The cricket ball has a diameter of 20 cm. Calculate the volume of the cricket ball
Answer: I believe the volume is 4188.79 cm^3.
Step-by-step explanation: The equation for the volume of a sphere is (4/3)(pi)(r^3) = (4/3)(pi)(1000) = 4188.79 cm^3.
[tex] \frac{w}{7} = . 3[/tex]
Please help me answer this before 5pm. I need to know what w is.
Answer:
2.1
Step-by-step explanation:
w/7 = .3
Multiply each side by 7
w/7 *7 = .3*7
w = 2.1
PLEASE HELP!!! WILL GIVE BRAINLIST!!
Answer: 10
This is the asnwer
What is the value of x?
Please help
Answer:
x = 4
Step-by-step explanation:
Assuming these are similar triangles,we can use ratios to solve
3x+8 25
---------- = ------
4 5
Using cross products
5(3x+8) = 4*25
Distribute
15x +40 = 100
Subtract 40 from each side
15x+40-40 = 100-40
15x= 60
Divide each side by 15
15x/15 = 60/15
x =4
First, find the scale factor between both triangles.
25 / 5 = 5
15 / 3 = 5
Second, multiply to find the missing side length.
4 * 5 = 20
Third, solve for x.
3x + 8 = 20
3x + 8 - 8 = 20 - 8
3x = 12
3x/3 = 12/3
x = 4
Best of Luck!
If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 5)^2 + (y − 8)^2 = 100
B) (x + 5)^2 + (y − 8)^2 = 10
C) (x − 5)^2 − (y + 8)^2 = 10
D) (x − 5)^2 + (y + 10)^2 = 8
Answer:
A. [tex](x+5)^2+(y-8)^2=100[/tex]
Step-by-step explanation:
1. The standard form of the equation of a circle is [tex](x-h)^{2} + (y-k)^2=r^2[/tex]
2. To find the center we require the midpoint of the 2 given points
center =[tex][\frac{1}{2}(-4-6),\frac{1}{2}(11+5)][/tex]
=(-5,8)
3. The radius is the distance from the centre to either of the 2 given points calculate the radius using the distance formula
d= [tex]\sqrt{(x_{2}+x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]
let [tex](x_{1},y_{1})= (-5,8) \\[/tex] and [tex](x_2,y_2)=(-4,11)[/tex]
r=[tex]\sqrt{(-4+5)^2+(11-8)^2} =\sqrt{81+9}=10[/tex]
--> [tex](x-(-5)^2+(y-8)^2=10^2[/tex]
--> [tex](x+5)^2+(y-8)^2=100[/tex]
Answer:
The anser is B 100% willing to put $100 on it.
Step-by-step explanation:
What’s the answer???
Answer:
81
Step-by-step explanation:
9*7 = 63
6*3 = 18
63 + 18 = 81
A drawer contains 10 blue pens, 10 black pens, and 10 red pens. Without looking. Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer:
1/9
Step-by-step explanation:
There are 30 pens in total, 1/3 of the pens are each the following colours: blue; black; red.
This will result in a one in three chance of picking up a red pen. As Mr.Lopez puts the pen back, the fractions stay the same as it's the same possibility both times.
As it's again a one in three chance, we just have to multiply it for the possibility of him picking a blue pen, which is 1/3.
1/3 * 1/3 = 1/9
A rectangle has a height of 7 and a width of 2x^2 – 3.
Express the area of the entire rectangle.
Expression should be expanded.
2x^2 -3 7
Area -
Answer:
14x² - 21
Step-by-step explanation:
given for a rectangle,
height = 7
width = 2x² - 3
Area = height x width
= 7 (2x² - 3)
= (2x²) (7) - 3 (7)
= 14x² - 21
The graph of the function f is shown. If f(x) = 4 then x could equal
A:0
B:4
C:5
D: 7
Answer: 7
Step-by-step explanation:
The question pertains to finding the x value for a given output on a graph of a function. The x value corresponds to the point where the y value is 4 on the graph.
Explanation:The subject matter in this question pertains to the interpretation of a graphical representation of a function, specifically determining the input, or x value, for a given output, y value (f(x) = 4) in this case. Without the actual graph, it's impossible to definitively identify the correct x value. However, the process involves locating the point on the graph where the y-value is 4 and then identifying the corresponding x value.
For example, if the graph is a line that passes through the point (0,4), then x would equal 0. If the graph passes through the point (4,4), then x could equal 4. Similarly, if the line goes through (5,4) or (7,4), then x could equal 5 or 7 respectively.
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what is the slope intercept form of 9x - y = 9
a) y= 9x
b) y= 9x-9
c) y= -9x + 9
d) y=9
Final answer:
The slope-intercept form of the equation 9x - y = 9 is y = 9x - 9, which shows a slope of 9 and a y-intercept of -9, corresponding to option b).
Explanation:
The slope-intercept form of the equation 9x - y = 9 can be found by solving for y. We want to rearrange the equation to get y by itself on one side, which allows us to see the slope and y-intercept more clearly. The standard slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To solve for y, we perform the following steps:
Add y to both sides of the equation: 9x - y + y = 9 + y, resulting in 9x = 9 + y.
Next, we subtract 9 from both sides to get y by itself: 9x - 9 = y.
The resulting equation is y = 9x - 9, which matches option b).
This shows the slope of the line is 9 and the y-intercept is -9. The values correspond to the terms in the slope-intercept form where the coefficient of x is the slope, and the constant term is the y-intercept.
Design your own fruit punch recipe for brunch! Your recipe must create
exactly 5 liters of punch and include at least three of the juices. Also be sure
to include how many containers of each juice you need. Show your work by
writing equations that show how you determined the capacity.
Answer:
Step-by-step explanation:
So, we know that 5000 milliliters = 5 liters right? So we have to add up the right juices in order to get 5000 milliliters.
Lemonade
4 containers.
Pineapple.
4 containers.
Grape juice.
6 containers.
Now we're gonna multiply them by their containers.
Lemonade.
250*4 = 1,000
Pineapple.
500*4 = 2,000
Grape juice.
250* 6 = 2,000
Now we add them up :)
1,000 milliliters + 2,000 milliliters + 2,000 milliliters = 5 liters.
Ps. I had this question on my test and got a good grade so ik what i'm doing.
The correct answer is: 800 milliliters + 800 milliliters + 2400 milliliters = 5000 milliliters.
By taking;
the volume of each juice container is 400 milliliters.
Since we know that 5000 milliliters = 5 liter
So we have to add up the right juices in order to get 5000 milliliters.
let the volume of each juice container is 400 milliliters.
Mango 2 containers=2×400=800 milliliters.
Pineapple 2 containers= 2×400=800 milliliters.
Orange juice 6 containers=6×400=2400 milliliters.
Now on adding them;
800 milliliters + 800 milliliters + 2400 milliliters = 5000 milliliters.
In equation form;
Let the volume of all containers are equal i.e 'x'
∴ 2×x+2×x+6×x=5000
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I need help. I don’t understand how to do this. I need to turn this assignment in a few minutes
Answer:
40
Step-by-step explanation:
If the dimensions are proportional, then you just need to multiply 5 by 8 to get what ? is equal to.
Answer:The Answer is 40
Step-by-step explanation:the bottom is 7 x 8 to get 56 the side length is 8x8 to get 64 and the other is 5 x8 to get 40.
Hope this helped ;D
PLEASE HELP ME Every day, Navya's teacher randomly picks a number from 1 to 100 to be the number of the day. The
number of the day can be repeated. There are 180 days in the school year. Predict how many days the
number of the day will be greater than 25.
The number of days in which a number chosen is greater than 25 is
Answer:
135 days
Step-by-step explanation:
There are 100 numbers
There are 75 numbers greater than 25 (26-100)
P(number greater than 25) =
= number of numbers greater than 100/ total outcomes
= 75/100
=3/4
There are 180 days, so multiply the number of days by the probability
3/4*180 =135
Answer:
135 of the random selections would be numbers greater than 25.
Step-by-step explanation:
Since 25 is 25% of 100, that means that 75% of the random selections would be over 25.
75% = 0.75
180*0.75 = 135
135 of the random selections would be numbers greater than 25.
Need answer has soon as possible???????
Simplify the radical by breaking the radicand up into a product of known factors.
Therefore the answer would be 2! Hopefully this helps.
What is 4x + 2y = 20 in slope-intercept form?
Y = -4x + 20
Y =-2x + 10
Y = 2x + 20
Y = 2x + 10
32% of what number is 16?
Answer:
50
Step-by-step explanation:
Unknown number = x
32% = 0.32
Write an equation
0.32(x) = 16
Simplify
0.32x = 16
Divide both sides of the equation by 0.32
x = 50
50
Hope this helps :)
Find the price per pound to the nearest cent . Remember 16oz = 1 lb
12 oz cereal-$3.75
Answer:
$5.00 per pound
Step-by-step explanation:
12oz = $3.75
12(1.33333333) = 16
3.75(1.33333333) = 4.9 repeating
so the answer is $5.00
find cos -15 degrees
Answer:
-0.75968791285
Step-by-step explanation:
To find cos(-15°), we recognize that cosine is an even function, so cos(-15°) = cos(15°). Utilizing the cosine angle subtraction formula and known cosine and sine values, we find that cos(15°) = (√6 + √2) / 4, thus cos(-15°) = (√6 + √2) / 4.
Finding Cosine of -15 Degrees:
To find cos(-15°), we can use the cosine angle addition formula. This is particularly useful as we can break down -15° into simpler angles:
cos(-15°) = cos(15°) because cosine is an even function: cos(-θ) = cos(θ).
Next, we utilize the angle subtraction formula for cosine:
cos(15°) = cos(45° - 30°) = cos(45°)cos(30°) + sin(45°)sin(30°)
We know that:
cos(45°) = √2 / 2
cos(30°) = √3 / 2
sin(45°) = √2 / 2
sin(30°) = 1 / 2
Substituting these values into the formula, we get:
cos(15°) = (√2 / 2) × (√3 / 2) + (√2 / 2) × (1 / 2)
Simplify the expression:
cos(15°) = (√6 / 4) + (√2 / 4)
Thus:
cos(15°) = (√6 + √2) / 4
Therefore, cos(-15°) = (√6 + √2) / 4.
What is the answer?
Answer:
B (it's kinda cut off)
Step-by-step explanation:
Use the acronym SOHCAHTOA to determine which trigonometric function to use. We'll use cosine since we have the hypotenuse and the adjacent length.
Set up an equation:
cos(41)=x/18
cos(41)*18=x
13.585=x
So your best choice would be B
4. Point A has coordinates (8, -1) and Point
Bhas coordinates (-7,-4).
est
What is the slope of the line segment
with endpoints A and 8?
imes
c. - 1/3
A.
B.
5
1
D. - 3
Combine like terms to simplify the expression below. 14x - (2x + y)
NEED THIS ASAP & STEP BY STEP!!!!
Answer:
12x - y
Step-by-step explanation:
The numbers in the brackets are being multiplied by -1. For this you can just use the opposite signs for the things in brackets and remove the brackets. (AKA 14x - 2x - y)
Then you can ignore the y for now, and just deal with the x's first.
14x - 2x = 12x
Since there's only 1 y, you don't need to do anything with it other than put it back in the equation.
The finished equation is 12x - y
a cone has a height of 30in. and a diameter of 20in. What is the approximate volume of the cone?
Answer:
The volume of the cone is equal to 1000π in³ in terms of π or is approximately equal to 3140 in³
Step-by-step explanation:
To find the volume of a cone with a height of 30 in. and diameter of 20 in., we will follow the steps below;
First write down the formula for finding the volume of a cone
V = πr²[tex]\frac{h}{3}[/tex]
where v is the volume of the cone, r is the radius of the cone and h is the height of the cone.
From the question given, the height h of the cone is 30 in and the diameter is given to be 20 in. but radius is half of diameter, this implies that r=d/2=20/2=10 in., that is radius r = 10 in
We can proceed to inert the values into the formula
V = πr²[tex]\frac{h}{3}[/tex]
=π×10²×[tex]\frac{30}{3}[/tex]
=π×100×10
=1000π
v =1000π in³ in terms of π
substituting π = 3.14
v ≈1000(3.14)
v≈3140 in³
Therefore the volume of the cone is equal to 1000π in³ in terms of π or is approximately equal to 3140 in³
The approximate volume of the cone is [tex]\(\frac{10000\pi}{3}\)[/tex] cubic inches.
To find the volume of a cone, the formula used is:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Given that the diameter of the cone is 20 inches, we can find the radius by dividing the diameter by 2:
[tex]\[ r = \frac{diameter}{2} = \frac{20 \text{ in}}{2} = 10 \text{ in} \][/tex]
Now we can substitute the values of r and h into the volume formula:
[tex]\[ V = \frac{1}{3} \pi (10 \text{ in})^2 (30 \text{ in}) \][/tex]
[tex]\[ V = \frac{1}{3} \pi (100 \text{ in}^2) (30 \text{ in}) \][/tex]
[tex]\[ V = \frac{3000\pi}{3} \text{ in}^3 \][/tex]
The approximate volume of the cone is [tex]\(\frac{10000\pi}{3}\)[/tex] cubic inches.
In the figure, angle ABC = 2x-65° and reflex angle AOC = 3x. Find x.
Answer:
x = 70
Step-by-step explanation:
The measure arc AC is twice as angle B
The center angle that sees arc is equal to the arc it sees
<B = 2x - 65 so the measure of arc AC is 4x - 130 since this is gonna complete 3x to 360°
4x - 130 + 3x = 360°
7x = 490
x = 70