The probability that out of 5 pencils taken, 2 are blue and 3 are black is 0.4381.
What is probability?Probability simply means the likelihood that something will occur or happen.
In this case, the the box contains 8 blue and 4 black pencils. The probability of drawing 2 blue balls will be:
= 8/12 × 7/11
= 0.4242
The probability of drawing 3 blacks will be:
= 4/12 × 3/12 × 2/12
= 1/3 × 1/4 × 1/6
= 0.0139
The probability will be the addition of the values. This will be:
= 0.4242 + 0.0139
= 0.4381
The probability is 0.4381.
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shelly wants to tile a rectangular floor that measures 132 feet by 150 feet using square tiles that are all of the same size, with no overlap and no squares hanging over the edge. what is the measurement of the largest square tiles she can use?
The measurement of the largest square tiles she can use is 6 feet.
Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF). For instance, the numbers 8 and 12 share the elements 1, 2, and 4. Four is the greatest common factor.
Steps for calculating HCF:
Step 1: Write each integer as the sum of its prime factors in step one.
Step 2: List the shared factors between the two numbers.
Step 3: The HCF is the sum of all the common prime factors ( use the lower power of each common factor)
Given,
Measurement of the rectangular floor:
length = 150 feet
breadth = 132 feet
The measurement of the largest square can be calculated by finding the HCF of 132 and 150.
132 = 2*2*3*11
150 = 2*3*5*5
So, HCF (132, 150) = 2*3 = 6.
Hence, the measurement of the largest square tiles she can use is 6 feet.
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At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile.
Do Han and Tyler meet on the path within 1 hour?
If Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han and Tyler will not meet on the path within 1 hour
Calculations to show if Han and Tyler meet on the path within 1 hourThe following information is gotten from the question
Han and Tyler both started running toward each other from opposite ends of a 10-mile path
Han runs at a pace of 12 minutes per mile
Tyler runs at a pace of 15 minutes per mile
Distance covered by Han in 1 hour
12 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 12
? = 5 miles
Distance covered by Tyler in 1 hour
15 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 15
? = 4 miles
This means that Han covers 5 miles in and Tyler covers 4 miles, in a 10 mile distance.
In one hour the distance covered
= 5 miles + 4 miles
= 9 miles
9 miles is less than 10 miles hence they will not meet in the path within one hour
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Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A ands who did Plan
B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B
Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
The number of hour (time) for which workout plan A would last is 0.75 hour. Also, the number of hour (time) for which workout plan B would last is 0.5 hour.
How to calculate the number of hours (time)?In order to solve this word problem, we would assign variables to the number of hours (time) each plan and then translate the word problem into algebraic equation as follows:
Let x be the number of hours (time) for workout plan A.Let y be the number of hours (time) for workout plan B.Translating the word problem into an algebraic equation, we have;
On Friday ⇒ 6x + 5y = 7 ....equation 1.
On Saturday ⇒ 2x + 3y = 3 ....equation 2.
Next, we would solve the simultaneous equation by using elimination method:
3 × (2x + 3y = 3) = 6x + 9y = 9 ........equation 3.
Subtracting equation 1 from equation 3, we have:
6x + 9y = 9
6x + 5y = 7
4y = 2
y = 2/4
y = 1/2
y = 0.5 hour.
For the value of x, we have:
6x + 5y = 7
6x + 5(0.5) = 7
6x + 2.5 = 7
6x = 7 - 2.5
6x = 4.5
x = 4.5/6
x = 0.75 hour.
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Complete Question:
Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A and 5 clients who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
a lake is stuck with 1,550 young carp. the number of the original fish alive after t years is given by the function P (t)= 1550e^-0.4t, when will there be 440 of the original fish left from to the nearest tenth
so the time needed is 3.1 years
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,1) Midpoint: (-4,-6)
Answer:
(-13, - 6)
Step-by-step explanation:
Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2
(-4,-6) = (9+x)/2, (1+y)/2
9+x= - 4
X= - 13
1+y= - 6
Y= - 7
Ans=
(-13, - 6)
Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope −1.
Answer: y = -1x + 3
Step-by-step explanation:
Point-Slope form: y - y1 = m(x-x1)
Replace the form with the values provided:
y - 15 = -1(x+12)
Once you get this, you need to get y by itself in order to get it in slope intercept form.
Distribute:
y -15 = -1x - 12
Add -15 to the right side:
y = -1x + 3
Bella's mother is 5 less than 4 times her
daughter's age. If her mom is 39 years old, how
old Is Bella?
6) Bill found a pair of jeans that cost $35.00. If he had a 20%-off coupon, how much would the
jeans cost?
solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
[tex]\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}[/tex]The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
Graph the equation after rewriting it in slope-intercept form. 9x+3y=18
The equation of a line in the slope intercept form is expressed as
y = mx + c
The given equation is
9x + 3y = 18
We would rearrange it so that it takes the form of the slope intercept equation shown above.
We would divide both sides of the equation by 3, we have
9x/3 + 3y/3 = 18/3
3x + y = 6
Subtracting 3x from both sides of the equation, we have
3x - 3x + y = 6 - 3x
y = 6 - 3x
The slope intercept form is
y = - 3x + 6
To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have
For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12
For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9
For x = 0, y = 6 - 3(0) = 6 - 0 = 6
For x = 1, y = 6 - 3(1) = 6 - 3 = 3
For x = 2, y = 6 - 3(2) = 6 -6 = 0
The graph is shown below
Describe the end behavior of the graph of the following polynomial function:
We will have the following:
From the polynomial we will have that:
*It falls to the left and rises to the right.
This can be seeing as follows:
Explain how the points A(9,-) and 8(9,3) are related. Use vocabulary words
in your explanation.
Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.
Step-by-step explanation:
You and a friend have each randomly draw a card.
There are 52 cards in a deck.
There are 12 face cards in the deck, that is 3 face cards per suit.
The probability of getting at least from two draws is given to be:
[tex]P=P(X=1)+P(X=2)[/tex]Therefore, the probability is calculated using the formula:
[tex]P=\frac{^{12}C_1\times^{40}C_1}{^{52}C_2}+\frac{^{12}C_2}{^{52}C_2}[/tex]Using the combination formula, we have the solution to be:
[tex]\begin{gathered} \Rightarrow\frac{12\times40}{1326}+\frac{66}{1326}=\frac{480}{1326}+\frac{66}{1326} \\ P=\frac{546}{1326} \\ P=\frac{7}{17} \end{gathered}[/tex]The LAST OPTION is correct.
Solve the equation. (Enter your answers as a comma-separated list.)x210x − 6x10x = 27(10x)x =
Answer:
x = -3, 9
Explanation:
First, let us divide both sides of the equation by 10^x; this gives,
[tex]\frac{x^210^x-6x\times10^x}{10^x}=\frac{27\times10^x}{10^x}[/tex][tex]\Rightarrow x^2-6x=27[/tex]subtracting 27 from both sides gives
[tex]x^2-6x-27=0[/tex]The left-hand side can be factored as
[tex](x-9)(x+3)=0[/tex]which gives us two further equations
[tex]\begin{gathered} x-9=0 \\ \boxed{x=9.} \end{gathered}[/tex][tex]\begin{gathered} x+3=0 \\ \Rightarrow\boxed{x=-3.} \end{gathered}[/tex]Hence, the two solutions we get are x = 9 and x = -3.
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3). What is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2?
The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;
(5, 3+2) +2 = (5, 5) + 2
Given,
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).
To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2
Now,
What is the equation of the parabola?
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).
Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.
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What is the midpoint of line segment (-6,-10) ,(-2,-8)
The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9).
What is a line segment?A line section that can connect two places is referred to as a segment.
A line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
The midpoint associated with two points (x₁, y₁) and (x₂, y₂) is given by
x = (x₁ + x₂)/2 , y = (y₁ + y₂)/2
x = (-6 - 2)/2 = -4 , y = (-10 - 8)/2 = -9
So, the coordinate will be (-4,-9).
Hence "The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9)".
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RS = 8y +4, ST = 5y + 7, and RT = 115.What is the value of y?
EXPLANATION:
1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line
2. The correct and most appropriate method is the matching method.
The exercise is as follows:
[tex]\begin{gathered} RS\text{ }=8y+4\text{ } \\ ST=5y\text{ }+7 \\ RS=ST\text{ } \\ 8y+4=5y+7 \\ 8y-5y=7-4 \\ 3y=3 \\ y=\frac{3}{3} \\ \textcolor{#FF7968}{y=1} \\ \text{\textcolor{#FF7968}{the answer is y}}\textcolor{#FF7968}{=1}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{as}\text{\textcolor{#FF7968}{ a whole number or y}}\textcolor{#FF7968}{=\frac{3}{3\text{ }}}\text{\textcolor{#FF7968}{ as a }}\textcolor{#FF7968}{fractional}\text{\textcolor{#FF7968}{ number}} \end{gathered}[/tex]I dont know pls help me
In Close Encounters of a Bear Kind, the statement that represents the author's primary attitude towards John's work is that C. John's work is dangerous.
How to illustrate the information?According to the author, he stated that people don't usually realize that bears
can be very dangerous.
He further stated that they will reap people apart of they e the chance. The narrator gave an example about how he walked out at night and had to run back home for his dear life. This was why he stated that the job of John whom was a photographer was a dangerous one.
In conclusion, the correct option is C.
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hemoglobin determinations were made on sixteen animals exposed to ionizing radiation. the following observations were recorded: 15.6, 14.4, 14.8, 13.8, 16.6, 14.0, 17.4, 17.3, 18.6, 16.2, 15.7, 14.7, 16.4, 13.9, 14.8, 17.5. construct a 95 percent confidence interval for population standard deviation?
The required values for a 95 percent confidence interval for population standard deviation are CI₈² = [1.1894, 5.221]
CI₈ = [1.0906, 2.2849]
n = 16, Standard Deviation = 1.4764, Var = 2.1796
X²₀.₀₂₅,₁₅ = 6.26, X²₀.₉₇₅,₁₅ = 27.49
CI₈² = [(15ₓ2.1796/27.48),(15ₓ2.1796/6.26)] = [1.1894, 5.221]
CI₈ = [[tex]\sqrt{15*2.1796/27.48} , \sqrt{15*2.1796/6.26}[/tex]] = [1.0906, 2.2849]
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The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.
The sphere has a surface area of 482.8064 square meters
How to determine the surface area of the sphere?From the question, the given parameters are:
Diameter, D = 12.4 meters
π = 3.14
The surface area of the sphere is calculated using the following formula
S = 4π(D/2)²
Substitute the given parameters in the above formula
So, we have
S = 4 * 3.14 * (12.4/2)²
Evaluate the exponent
This is represented as
S = 4 * 3.14 * 38.44
Evaluate the product
This is represented as
S = 482.8064
Hence, the surface area of the sphere is 482.8064 square meters
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for anyone that knows how to do this i only need help with these two questions
-4x-1=-y
solve for y
-4y+20+3x=0
solve for y
[tex]-4x-1=-y\\y[/tex]
Flip the equation:
[tex]-y=-4x-1[/tex]
Divide both sides by -1:
[tex]\frac{-y}{-1} =\frac{-4x-1}{-1}[/tex]
[tex]y=4x+1[/tex]
__________________________________________________________
[tex]-4y+20+3x=0\\y[/tex]
Add -3x to both sides of the equation:
[tex]3x-4y+20+-3x=0+-3x\\-4y+20=-3x[/tex]
Add -20 to both sides of the equation:
[tex]-4y+20+-20=-3x+-20\\-4y=-3x-20[/tex]
Divide both sides by -4:
[tex]\frac{-4y}{-4} =\frac{-3x-20}{-4}[/tex]
[tex]y=\frac{3}{4} x+5[/tex]
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answer:
The answer is D
Step-by-step explanation:
Check to see when the graph is increasing and decreasing from left to right.
It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.
Then, it increases from x = -3 to x = 0 or (-3,0)
Then, it stays constant from x = 0 to x = 2 or (0,2)
Lastly, it decreases from x - 2 to x = 5 or (2,5)
To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)
The only option that fits these conditions is D.
5) Naomi painted 16.5 square feet of a mural at a rate of 2 square feet per hour. Calire painted 7.5 square
feet of the mural at a rate of 4 square feet per hour. If they continue to paint at the same rates, how many
more hours will it take until Naomi and Claire have painted equal areas of the mural?
Answer: 4.5
Step-by-step explanation:
We need to find the amount of time until Calire paints a total of 9 more square feet.
Since the difference in their rates is 2 square feet per hour, it will take 9/2 = 4.5 more hours.
25 lbs of potatoes cost $100. How much
would 15 lbs cost?
Round the answer to two decimal digit
Which of the following statements are not true regarding functions?Check all that apply.A. A function is a relation in which each value of the input variable ispaired with at least one value of the output variable.I B. The vertical line test may be used to determine whether afunction is one-to-one.O C. A sequence is a function whose domain is the set of naturalnumbers.D D. The horizontal line test may be used to determine whether afunction is one-to-one.
Only B is not true, because the vertical line test is to know if a graph is from a function.
Which statement about the location of √ 7 on a number line is true?
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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39+(20.4) can u help me with this answer I don't know how to do it
You have the following expression:
39 + (-20.4)
In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:
39 + (-20.4)
= 39 - 20.4
= 18.6
Hence, the simplified expression is 18.6
solve the following system of equation graphically on the set of axes below y= x + 5y= -2x -1
To solve graphically this set of equations, we should first draw both lines and see the value of x at which the lines crosses
Both graphs can be drawn as follows
We can see that both graphs intersect at a negative value of x. With a more accurate graph, we can determine that both lines intersect at x=-2.
So the solution for this system of equation is x=-2.
Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answer:
Step-by-step explanation:
Can someone help me out (I will give branliest)
Answer: Emma > Amelia > Brandon > Celesle > Damian
Step-by-step explanation:
We convert all the fractions to decimals (2 decimals).
Amelia 4.35 lbs
Brandon [tex]4\frac{1}{3}= \frac{12}{3} +\frac{1}{3} =\frac{13}{3}[/tex] ≈ 4.33 lbs
Celesle 4.2 lbs
Damian √15 ≈ 3.87 lbs
Emma [tex]4\frac{2}{3} =\frac{12}{3} +\frac{2}{3} =\frac{14}{3}[/tex] ≈ 4.67 lbs
4.47 lbs > 4.35 lbs > 4.33 lbs > 4.2 lbs > 3.87 lbs
Emma > Amelia > Brandon > Celesle > Damian