Answer:
Y = 45*p(y) / (1 - p(y)) if I knew what p(y) is, we can find how many yellow marbles there are. p(y) = probability of choosing yellow.
Step-by-step explanation:
Total marbles = 35 + 10 + yellow
If probability of choosing yellow =p(y) = yellow/Total
p(y) = Y/(35 + 10 + Y)
Solve for Y,
p(y)*(35 + 10 + Y) = Y
45*p(y) + p(y)*Y = Y
45*p(y) = Y - p(y)*Y
Y = 45*p(y) / (1 - p(y))
To find the number of yellow marbles in the bag, set up an equation using the given probabilities. Simplify the equation and solve for the total number of marbles. Finally, substitute the value of into the equation to determine the number of yellow marbles.
Explanation:To solve this problem, we need to find the number of yellow marbles in the bag. Given that there are 35 blue marbles and 10 red marbles, we can subtract these two numbers from the total number of marbles to find the number of yellow marbles. Let's denote the number of yellow marbles as 'y'. We can set up the equation: 35 + 10 + y = total number of marbles. Since the probability of selecting a yellow marble is , we know that the ratio of yellow marbles to the total number of marbles is . This can be written as: y/total number of marbles = . Now, we can solve for 'y'.
By cross multiplying the ratio equation, we have: y = total number of marbles * . Now we can substitute this value of 'y' in the first equation: 35 + 10 + (total number of marbles * ) = total number of marbles. Simplifying this equation, we find: 45 + (total number of marbles * ) = total number of marbles. Rearranging the equation, we have: (total number of marbles * ) - total number of marbles = -45. Factoring out 'total number of marbles' from the left side, we get: total number of marbles * ( - 1) = -45. Dividing both sides of the equation by ( - 1), we find: total number of marbles = 45 / ( - ). Plugging in the value of , we can evaluate the expression: total number of marbles = 45 / ( - ) = - . Therefore, there are - yellow marbles in the bag.
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I have to find the missing coordinates please help!
Answer:
4.8 or 4 4/5
Step-by-step explanation:
Put the given value into the equation and solve for the missing one.
(3/5)(6) -(1/3)y = 2
3.6 -y/3 = 2 . . . simplify to decimal form
-y/3 = -1.6 . . . . subtract 3.6
y = 4.8 . . . . . . . multiply by -3
The missing number is ...
4.8 = 4 4/5
_____
The coefficients are given as fractions, so the answer may be expected in mixed-number form.
Identify the zeros of the polynomial function N(x)=1/2 (x-1)(x+3).
a:x+-3
b:x=-1
c:x=1
d:x=3
Answer:
a:x=-3
c:x=1
Step-by-step explanation:
The zeros of a function are the values of x for which the value of the function f(x) becomes zero.
In this problem, we have the following function:
[tex]f(x)=\frac{1}{2}(x-1)(x+3)[/tex]
Here we want to find the zeros of the function, i.e. the values of x for which
[tex]f(x)=0[/tex]
In order to make f(x) equal to zero, either one of the factors [tex](x-1)[/tex] or [tex](x+3)[/tex] must be equal to zero.
Therefore, the two zeros can be found by requiring that:
1)
[tex]x-1=0\\\rightarrow x=+1[/tex]
2)
[tex]x+3=0\\\rightarrow x=-3[/tex]
So the correct options are
a:x=-3
c:x=1
Jack rode his bike to school at 12 mph and then jogged back at 6 mph. If the round-trip took him six hours, how far was it to school?
Answer: 24 miles
Step-by-step explanation: 12 mph is two times as fast as 6 mph so 6 hours round trip is 2 hours for bike and 4 hours for jogging. You can either plug 2 for 12 (bike) or 4 for 6 (jog) either way you get 24
Answer:
24 miles
Step-by-step explanation:
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
Answer:
x^3 - 3x^2 + 5x - 15
x^2(x-3) +5(x-3)
(x^2 + 5)(x - 3) <==Answer
Step-by-step explanation:
Kelly wants to buy 3 boxes of cereal.She wants to use the coupon that says buy one get on half off. If each box of cereal costs 4.75 how much will she pay in total
Answer:
$11.88
Step-by-step explanation:
Given that Kelly would get one box of cereal half off if she buys one, then we must take that into account.
Box 1: $4.75
Box 2: $4.75 ÷ 2 = $2.38
Box 3: $4.75
Now we simply add the totals:
4.75 + 2.38 + 4.75 = $11.88
Two hikers are 33 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 4.4 mph faster than the other.
Answer:
slow hiker rate= 1.1mph and fast hiker rate= 5.5 mph
Step-by-step explanation:
lets consider the Speed of the slow hiker =x
Then Speed of fast hiker =x+4.4
As we know that distance is the product of speed and time
therefore,
Distance covered by slow hiker in 5 hours = 5x km
Distance covered by fast hiker in 5 hours=5 (x+4.4)=5x+22 km
As they are are 33 miles apart , therefore
5x + 5x+22 = 33
10x = 33-22
10x = 11
x =11/10 => 1.1
Rate of slow hiker is x i.e 1.1mph
Rate of fast hiker = x+4.4 => 5.5 mph
Answer:
slower hiker's speed = 1.1 mph
faster hiker's speed = 5.5 mph
Step-by-step explanation:
Extracting the key information from the question:
*** Two hikers are 33 miles apart and are walking towards each other.
*** One of them walks 4.4 mph faster than the other and later met themselves in 5 hours.
*** We are required to find the speed of each of the hikers.
Speed = distance/time
Let us use "x" to represent the slower speed. Since one of the hikers was 4.4 mph faster than the other hiker, we can represent the faster speed with x+4. Now, if they met themselves in 5 hours, even though they were 33 miles apart initially, then we can represent the situation with the given equation:-
(x mph × 5hours) + [(x+4.4)×5] = 33 miles
5x + (5x + 22) = 33
5x + 5x + 22= 33
10x + 22 = 33
10x = 33-22
10x = 11
x = 11/10
x = 1.1mph (speed of slower hiker)
The speed of the faster hiker = x + 4.4
= 1.1 + 4.5
= 5.5mph
Solve for x. -3x - 8 = 10
Steps to solve:
-3x - 8 = 10
~Add 8 to both sides
-3x - 8 + 8 = 10 + 8
~Simplify
-3x = 18
~Divide -3 to both sides
-3x/-3 = 18/-3
~Simplify
x = -6
Best of Luck!
The solution of the equation -3x - 8 = 10 is,
⇒ x = -6
The given algebraic equation is,
-3x - 8 = 10
Now since its degree is 1
Therefore it is nothing but a linear equation.
By simple operation we can solve it
Now to solve it proceed the following steps:
Add 8 both sides, we get
⇒ -3x - 8 + 8 = 10 + 8
⇒ -3x = 18
Divide by -3 both sides we get
⇒ x = 18/-3
⇒ x = 6
Hence,
The solution is x = -6
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How many centimeters are in x meters???
Answer:
One centimeter is equal to 10 millimeters. It is also equal to 0.1 decimeter and 0.01 meter. One kilometer contains 100,000 centimeters.
Step-by-step explanation:
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Answer: 100x centimeters
Step-by-step explanation:
We know that 100 centimeters are in every meter. To find the number of centimeters in X amount of meters, we multiply X by 100. Take for example 4 meters. 4 times 100 equals 400. We then know that there are 400 centimeters in 4 meters.
What is the volume of the oblique cylinder rounded to the nearest cm^3?
Answer: [tex]32009355.90cm^3[/tex]
Step-by-step explanation:
Formula: [tex]V=Bh\\[/tex]
Since the base is a circumference, we can replace B for the area of a circumference formula.
[tex]V=\pi r^2h[/tex]
What we have here is 12 ft as the diameter of the circumference. A diameter is twice the radius, therefore we can conclude that if we take the diameter and divide it by 2, it will give us the radius.
[tex]12/2=6ft[/tex] this is the radius.
Now plug all this information into your formula.
[tex]V=(3.14)(6ft)^2(10ft)\\V=(3.14)(36ft^2)(10ft)\\V=1130.40ft^3[/tex]
Our values are in feet but the question requires cm. Let's convert from [tex]ft^3[/tex] to [tex]cm^3[/tex].
Normally, our conversion factors are raised to the power of 1, but in this case it's raised to the power of 3. So, first let's see how many cm are 1 ft.
[tex]1ft=30.48cm[/tex]
Here is where magic comes. We can raise both to the power of 3, in order to find the cubic ft and cm that we need as our conversion factors.
[tex](1ft)^3=(30.48cm)^3\\1ft^3=28316.8cm^3[/tex]
Now we have our conversion factors.
[tex]1130.40ft^3(\frac{28316.84cm^3}{1ft^3})=32009355.90cm^3[/tex]
A fish tank is 2 metres long, 50 centimetres wide and 20 centimetres high. How many litres of water will it hold if it is filled to the top ?
Answer:
It will hold 200 Litres of water
Step-by-step explanation:
To find the number of litres of water the fish tank can hold, we will follow the steps below;
Write down the formula for calculating its volume
V = l×w×h
where v = volume of the tank
w=width of the tank
l = length of the tank
From the question given;
w= 50 cm = 0.5 m
height h = 20 cm = 0.2 m
l = 2 m
V= l×w×h
= 2×0.5×0.2
=0.2 m³
we can now change it to liters
V = 0.2 m³ × 1000 = 200 L
It will hold 200 Litres of water
The length of a rectangle is the sum of the width and 1. The area of the rectangle is 72 units. What is the length in units of the rectangle
Answer:
L = 9
Step-by-step explanation:
Translating this into symbols, we get L = W + 1 and A = 72 = W * L.
Substituting W + 1 for L in the latter equation, we get:
72 = W(W + 1), or:
W^2 + 1W - 72 = 0
This factors into (W + 9)(W - 8) = 0, so that W must be either -9 or +8.
Since W represents width, a physical measurement, we eliminate the negative result and conclude that W = 8 units. Then L = W + 1 = 9 units.
Note that (8)(9) = 72, as we already know.
The length of the rectangle is: [tex]\[ {9} \] units.[/tex]
Let's denote the width of the rectangle as \( w \) and the length of the rectangle as \( l \).
According to the problem, the length \( l \) is given by:
[tex]\[ l = w + 1 \][/tex]
The area of the rectangle is given by:
[tex]\[ \text{Area} = l \times w = 72 \][/tex]
Substituting the expression for \( l \) into the area formula:
[tex]\[ (w + 1) \times w = 72 \][/tex]
This can be rewritten as:
[tex]\[ w^2 + w - 72 = 0 \][/tex]
We now have a quadratic equation. To solve this, we can use the quadratic formula:
[tex]\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\where \( a = 1 \), \( b = 1 \), and \( c = -72 \).\\[/tex]
Plugging in these values:
[tex]\[ w = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-72)}}{2 \cdot 1} \]\[ w = \frac{-1 \pm \sqrt{1 + 288}}{2} \]\[ w = \frac{-1 \pm \sqrt{289}}{2} \]\[ w = \frac{-1 \pm 17}{2} \][/tex]
This gives us two potential solutions for \( w \):
[tex]\[ w = \frac{16}{2} = 8 \]\[ w = \frac{-18}{2} = -9 \][/tex]
Since a width cannot be negative, we discard \( w = -9 \) and take \( w = 8 \).
Therefore, the width \( w \) is 8 units. Using the relationship \( l = w + 1 \), we find:
[tex]\[ l = 8 + 1 = 9 \][/tex]
So, the length of the rectangle is: [tex]\[ {9} \] units.[/tex]
Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective
Please Help me i dont understand this.
2. (5 points) Write a recursive rule for the arithmetic sequence: 3.9, 8.2, 12.5, 16.8, 21.1, ...
Answer:
a subscript n=4.3(n-1)+3.9
Step-by-step explanation:
What is the diameter of a circle with the equation (x + 6)2 + (y − 4)2 = 16?
Answer:
8 units
Step-by-step explanation:
[tex] {(x + 6)}^{2} + {(y - 4)}^{2} = 16 \\ {(x + 6)}^{2} + {(y - 4)}^{2} = {4}^{2} \\ equating \: it \: with \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ {r}^{2} = {4}^{2} \implies \: r = 4 \\ d = 2r = 2 \times 4 = 8 \: units[/tex]
Hence, diameter of the circle is 8 units.
Can someone please help me answer this question ASAP.
( solve the system of equations using substitution)
Answer:
(-8, -1)
Step-by-step explanation:
The problem tell us that y = -1. Plug in this y-value to wherever you see a y in the first equation. You should be able to solve from there. Your solution will be (-8,-1).
-2x - 3(-1) = 19
-2x + 3 = 19
-2x = 16
x = -8
For this particular problem, you could have also looked at the answer choices and seen that there was only one answer with the correct y-value.
5. The measures of angles of hexagon are 4x, 5x, 6x, 7x, 8x and 9x. Calculate the size of the largest angle
Answer:
166 2/13 deg
Step-by-step explanation:
The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).
A hexagon has 6 sides, so n = 6.
sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720
4x + 5x + 6x + 7x + 8x + 9x = 720
39x = 720
x = 720/39
x = 240/13
The largest angle has measure 9x.
9x = 9 * 240/13 = 2160/13
2160/13 = 166 2/13
Answer: 166 2/13 deg
the size of largest angle is [tex]166\frac{2}{13}[/tex] degree
What is hexagon?Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon shape are a hexagonal floor tile, pencil cross-section, clock, a honeycomb, etc. It can be either regular (with 6 equal side lengths and equal angles) or irregular (with 6 unequal side lengths and angles).
According to the question,
The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).
A hexagon has 6 sides, so n = 6.
sum of measures of angles = 180(n - 2)
= 180(6 - 2)
= 180 × 4
= 720
4x + 5x + 6x + 7x + 8x + 9x = 720
39x = 720
x = 720/39
x = 240/13
The largest angle has measure 9x.
9x = 9 × 240/13 = 2160/13
[tex]\frac{2160}{13}[/tex] = [tex]166\frac{2}{13}[/tex]
Hence, the size of largest angle is [tex]166\frac{2}{13}[/tex] degree
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Order the numbers from greatest to least based on their absolute value. |− 2 5 |, |0.5|, |− 3 4 |, |0.35| A) |0.5| > |0.35| > |− 2 5 | > |− 3 4 | B) |− 3 4 | > |− 2 5 | > |0.35| > |0.5| C) |0.5| > |− 2 5 | > |− 3 4 | > |0.35|, D) |− 3 4 | > |0.5| > |− 2 5 | > |0.35|
Answer:|−3 4 | > |0.5| > |− 2 5 | > |0.35|
Hope this is helpful!
Compare √7 and √12 plotted on the number line. What is the approximate difference in tenths between the two values? A number line going from 0 to 4. Points StartRoot 7 EndRoot and StartRoot 12 EndRoot are plotted. StartRoot 12 EndRoot is greater thanStartRoot 7 EndRoot.
0.8
Answer:
o.8
Step-by-step explanation:
trust me im doing it
P(x)equals=R(x)minus−C(x). Given R(x)equals=59 x minus 0.3 x squared59x−0.3x2 and Upper C left parenthesis x right parenthesis equals 3 x plus 14C(x)=3x+14
Answer:
[tex]P(x)=-0.3x^2+56x-14[/tex]
Step-by-step explanation:
The given functions are
[tex]R(x)=59x-0.3x^2[/tex]
[tex]C(x)=3x+14[/tex]
It is given that
[tex]P(x)=R(x)-C(x)[/tex]
Substitute the values of given functions in the above equation.
[tex]P(x)=59x-0.3x^2-(3x+14)[/tex]
[tex]P(x)=59x-0.3x^2-3x-14[/tex]
Combine like terms.
[tex]P(x)=-0.3x^2+(59x-3x)-14[/tex]
[tex]P(x)=-0.3x^2+56x-14[/tex]
Therefore, the required function is [tex]P(x)=-0.3x^2+56x-14[/tex] .
There are 9⋅54 sheep spread across 18⋅52 square miles of land. Find the average number of sheep per square mile. Round your answer to the nearest whole number.
Answer:
There is an average of approximately 1 sheep per square mile.
Step-by-step explanation:
Given there are 9.54 sheep spread across 18.52 square miles of land.
The average number of sheep per square mile is given as
A = 9.54/18.52
Without using a calculator, this is by inspection, about 9/18 = 0.5.
Using a calculator, we have
A = 9.54/18.52 = 0.51511879
Approximately 1 sheep per square mile.
PLEASE HELP WILL GIVE 1ST RIGHT ANSWER AS BRAINIEST The radius of a circle is x+6 and its diameter is 3x+5. What is the circumference of the circle, in terms of pi? (Do not include the variable x in your answer.)
Answer:
The circumference of the circle = 26π unit.
Step-by-step explanation:
Given:
Radius of the circle, r = "x+6"
Diameter of the circle, d = "3(x)+5"
We have to find the circumference of the circle in terms of pi.
Formula to be used:
Circumference of a circle = 2πr or πd
As we know that:
Radius = Half of diameter
So,
⇒ [tex]radius=\frac{diameter}{2}[/tex]
⇒ [tex]x+6=\frac{3x+5}{2}[/tex]
⇒ [tex]2\times (x+6)=\frac{3x+5}{2}\times 2[/tex]
⇒ [tex]2x+12=3x+5[/tex]
⇒ [tex]12-5=3x-2x[/tex] ...Arranging variables and constants.
⇒ [tex]7=x[/tex]
Plugging x = 7 we will find the radius and the diameter.
⇒ Radius = "x+6" = "7+6" = 13
⇒ Diameter = "3(x)+5" = 3(7)+5 =26
Lets find the circumference of the circle.
⇒ Circumference = [tex]2\pi r= 2\pi (13) = 26 \pi[/tex] Or
⇒ Circumference = [tex]\pi d=\pi (26)=26\pi[/tex]
The circumference of the circle = 26π unit.
If the Interest earned is 119.88 and the the interest rate is 3.6 and the time is 3 years what is the principal
Answer:
that is the solution to the question
Final answer:
To calculate the principal with an interest of $119.88, an interest rate of 3.6%, and a time of 3 years, use the simple interest formula. By rearranging the formula and doing the math, the principal amount is found to be $1,110.
Explanation:
To find the principal amount when you know the interest earned, the interest rate, and the time, you can use the formula for simple interest which is Interest = Principal × rate × time. Our goal is to rearrange the formula to solve for the principal.
Given that the Interest earned is $119.88, the interest rate is 3.6% (or 0.036 when converted to a decimal), and the time is 3 years, we can plug these values into the formula:
Interest = Principal × rate × time
$119.88 = Principal × 0.036 × 3
$119.88 = Principal × 0.108
To find the Principal, divide the interest earned by the product of the rate and time:
Principal = $119.88 / 0.108
Principal = $1,110
The principal amount is $1,110.
A gemstone is cut in the shape of a triangular pyramid.The area of the base of the pyramid is 42 square millimeters.the height of the pyramid is 4 millimeters.what is the volume of the gemstone.
Answer:
The volume of this pyramid is 56 millimeters³
Step-by-step explanation:
The volume for a triangular pyramid is given by the following formula:
volume = (1/3)*(base area)*h
In order to solve this problem we must take the given data for the pyramid and apply it to the formula above. We have:
volume = (1/3)*42*4
volume = 14*4
volume = 56 millimeters³
The volume of this pyramid is 56 millimeters³
You have a cat who has a mass of 10kg and is chasing a mouse with an acceleration of 10 m/s2. If it runs into a wall what force will be exerted by the cat?
Given:
mass of cat ( m ) = 10 kgAcceleration ( a ) = 10 m/s²To find out:
If it runs into a wall what force will be exerted by the cat?
Formula used:
Force = mass × acceleration
Solution:
Force = mass × acceleration
Now, Putting these values of m and a in the above equation.
we get:
F = 10 × 10
= 100 N
Thus, the force will be exerted by the cat is 100 N.
The force exerted by the cat when it runs into a wall can be calculated using Newton's Second Law of Motion, resulting in a force of 100 Newtons.
Explanation:The subject of this question pertains to the concept of Newton's Second Law of Motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. Here, the cat is considered the object in motion. The cat's mass is 10kg, and its acceleration is given as 10 m/s².
By substituting these values into Newton's second law (Force = mass x acceleration), we can calculate the force exerted by the cat as it runs against a wall: Force = 10kg x 10 m/s² = 100 N (Newtons). Therefore, the cat will exert a force of 100 Newtons when it runs into the wall.
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there are 4/7 as many girls as there are boys. There are 66 students in the fifth grade. How many students are girls?
You decide to take a guitar lessons. Each half-hour lesson costs $20. How much will you budget to pay for a half-hour lesson each week for 26 weeks?
Answer:
520
Step-by-step explanation:
If you pay for a half an hour lesson that is 20 dollars.
So if you do that for a total of 26 weeks you would multiply 20 dollars by 26 weeks.
20*26=520
Therefore she spends 520 dollars for half hour lessons that cost 20 for 26 weeks
Which is closest to the value of w in the triangle below?
Answer: B. 2.5 in
Step-by-step explanation:
From the given right angle triangle,
the hypotenuse of the right angle triangle is the unknown side.
With m∠32 as the reference angle,
the adjacent side of the right angle triangle is 4 in
the opposite side of the right angle triangle is w
To determine w, we would apply
the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan 32 = w/4
w = 4tan32 = 4 × 0.625
w = 2.5 in
Name 2 characteristics of the Polar Coordinate System
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Here are two key characteristics of the polar coordinate system:
1. Radial Distance (Radius): In the polar coordinate system, the location of a point is determined first by its distance from a fixed point, called the pole, analogous to the origin in the Cartesian coordinate system. This distance is often denoted as \( r \), and it can be thought of as the radius of a circle centered at the pole, with the point lying on the circumference of this circle.
2. Angular Coordinate (Angle): The second characteristic of a point's location in the polar coordinate system is the angle [tex]\( \theta \)[/tex] (theta), which is measured from a fixed direction, typically the positive x-axis of the corresponding Cartesian coordinate system. This angle, usually measured in degrees or radians, determines the direction of the line from the pole to the point.
These two values, [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex], are called polar coordinates, and they provide an alternative to the Cartesian (rectangular) coordinate system for representing points on a plane, particularly useful in scenarios where the geometry or the nature of the problem is radially symmetric, such as in the cases of circular motion or fields (gravitational, electric, etc.).
When determining which x-values would make an expression undefinéd, you do not need to
include the factors you canceled out.
True
False
Answer:false
Step-by-step explanation: Then you would get rid of the x
Use the box-and-whiskers plots below to answer questions about the math test scores of two different classes. A box-and-whisker plot labeled Class A. The number line goes from 5 to 14. The whiskers range from 6.5 to 12.5 and the box ranges from 7.5 to 11. A line divides the box at 9. A box-and-whisker plot labeled Class B. The number line goes from 5 to 14. The whiskers range from 6 to 12 and the box ranges from 7.2 to 9. A line divides the box at 8.2. Which class had the higher median score? Which class, as a whole, scored better on the test? a. Class B had the higher median score. Class A scored better on the test. b. Class B had the higher median score. Class B scored better on the test. c. Class A had the higher median score. Class A scored better on the test. d. Class A had the higher median score. Class B scored better on the test.
The correct option is Class A had the higher median score. Class A scored better on the test.
What is the correct option?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two whiskers that represents the maximum and minimum numbers.
On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
The median of class A = 9
The median of class B = 8.2
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