Sowen rolled two number cubes with sides numbered 1 through 6, 20 times. Her sums are recorded in the table below.49899462.1012879111087935What is the experimental probability of rolling a sum of 9?4/20Сь5/20Od4/365/36
Answers
The total number of experiment, N=20.
From the given data, 9 is obtained 5 times.
The number of times of getting 9, n=5.
Hence, the probability of getting a sum of 9 is,
[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{5}{20} \end{gathered}[/tex]Hence, option b is correct.
Related Questions
at 37 ft string of lights will be attached to the top of a 35 ft pole for Holiday display how far from the base of a pool should the end of the string of lights be anchored
Answers
Answer:
12 feet
Explanation:
The diagram representing the problem is attached below:
The distance of the pole to the base of the string is the value x.
Using Pythagoras Theorem:
[tex]\begin{gathered} 37^2=35^2+x^2 \\ x^2=37^2-35^2 \\ x^2=144 \\ x^2=12^2 \\ x=12ft \end{gathered}[/tex]The end of the string should be anchored 12 ft from the base of the pole.
MINI Statistics in 2021 900Carissa Brooks & 10Homework: 2.52016 (18 completeNW Score:Score: DaX 25.49Aceasta es am 38,000 miles and advisor 2, 250 mes. Assume the lens of the res have a belspetsin)the tears are my cheese 3700 ms 31.000 ms. meore that corresponds to amanten
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In order to find the z-score for the value 34000, we can use the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where μ is the mean and σ is the standard deviation.
So using x = 34000, μ = 38000 and σ = 2250, we have:
[tex]Z=\frac{34000-38000}{2250}=-\frac{4000}{2250}=1.78[/tex]So the z-score for the value 34000 is 1.78.
which of the following is the correct way to simplify
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We need to apply the law of exponents. In this case we need to
Keep the base and add the exponents,
that is the third option.
which is rational?3 2/3 + 3
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Which best explains the transformation of TUV to form T'U'V
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the figure T'U'V' is reflected on the x-axis, therefore is transformed by (x, - y)
answer: the first one
Simplify (sqrt)98m^12 using factor tree or splitting up using perfect squares. Quick answer showing work = amazing review :)
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The expression is:
[tex]\sqrt[]{98m^{12}}[/tex]We need to use a factor tree to solve the problem. We will draw it as shown below:
According to the factor tree we can represent the 98 as:
[tex]\sqrt[]{2\cdot7^2m^{12}}[/tex]We can now remove the terms that have a power of 2 and a power of 12. For that we need to divide the exponents by 2.
[tex]7^{}\sqrt[]{2}m^6[/tex]The simplified expression is 7*sqrt(2)*m^6.
15 lb of beans are distributed equally into 10 bags that give out of at the food bank how many pounds of beans are in each bag until your answer in simplest form
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Determine the pounds of beans in each bag.
[tex]\begin{gathered} \frac{15}{10}=\frac{3\cdot5}{2\cdot5} \\ =\frac{3}{2} \\ =1\frac{1}{2} \end{gathered}[/tex]So answer is 1 1/2.
Use the distance formula to determine if angle ABC is congruent to angle DEF.Select Yes or No for each statement.
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Dorsain, this is the solution for option A:
Option A:
Step 1: Let's calculate the distance from A to B, as follows:
d = √0² - -5² + 0² - -7²
d = √5² + 7²
d = √25 + 49
d = √74
d = 8.6 units
Step 2: Let's calculate the distance from B to C, this way:
d = √4² - 0² + -7² - 0²
d = √4² - 7²
d = √16 + 49
d = √65
d = 8.06 units
Step 3: Let's calculate the distance from A to C, as follows:
d = √(4 - -5)² + (-7 - -7)²
d = √9² + 0²
d = √81
d = 9 units
Step 4: Let's calculate the distance from D to E, this way:
d = √(-1 - -6)² + (1 - -6)²
d = √5² + 7²
d = √25 + 49
d = √ 74
d = 8.6 units
Step 5: Let's calculate the distance from E to F, as follows:
d = √(5 - -1)² + (-8 -1) ²
d = √6² + -9²
d = √36 + 81
d = √117
d = 10.81 units
Step 6: Let's calculate the distance from D to F, this way:
d = √(5 - -6)² + (-8 - -6)²
d = √11² + -2²
d = √121 + 4
d = √125
d = 11.18 units
Step 7: We can conclude that only sides AB and DE are congruent, (8.6 units) but the other two sides of triangles ABC and DEF aren't congruent. Therefore, these two triangles are not congruent.
Now you can continue, following steps 1 to 7 to evaluate options B and C.
Find the greatest possible percent error in calculating the volume of the prism.
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Answer:
23%
Step-by-step explanation:
Volume of a rectangular prism:
A rectangular prism has three dimensions, which are the base b, the height h and the width w.
The volume is:
V = b*w*h
In this question:
The base is 12 inches, so b = 12.
The width is 5 inches, so w = 5.
The height is 7 inches, so h = 7.
The volume is:
V = 12*5*7 = 420 cubic inches.
With error:
They are rounded to the nearest inch, so:
The base can go from 12 - 0.5 = 11.5 to 12 + 0.5 = 12.5 inches.
The width can go from 5 - 0.5 = 4.5 to 5 + 0.5 = 5.5 inches
The height can go from 7 - 0.5 = 6.5 to 7 + 0.5 = 7.5 inches.
Volume with the smallest values:
We have that b = 11.5, w = 4.5, h = 6.5. So
V = 11.5*4.5*6.5 = 336.375
Error of 420 - 336.375 = 83.625
As a percent, the error is of (83.625/420)*100 = 19.9%
Volume with the higher values:
We have that b = 12.5, w = 5.5, h = 7.5. So
V = 12.5*5.5*7.5 = 515.625
515.625 - 420 = 95.625
As a percent, the error is of (95.625/420)*100 = 22.7% = 23%
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for < or ">" for >(4,2)(-4,0)
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EXPLANATION
We can write an inequality in slope-intercept form by using the two given points, (x_1,y_1)= (-4,0) and (x_2,y_2)=(4,2), as shown as follows:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing terms:
[tex]\text{Slope}=\frac{(2-0)}{(4-(-4))}[/tex]Subtracting terms:
[tex]\text{Slope}=\frac{2}{8}=\frac{1}{4}[/tex]Now, we need to find the y-intercept.
As we can see in the dashed line, the y-intercept is at point (x,y)=(0,1).
Hence, the equation of the dashed line is as follows:
y = (1/4)x + 1
But as the solution represents all the points that are below this line, the inequality should be as following:
y < (1/4)x + 1
In the following exercise a formula is given, along with the values of all but one of the variables in the formula. Find the value of the variable that is not given S = 2LW+2WH + 2LH; S = 108, L= 3, W= 4
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Answer:
H = 6
Explanation:
We are given the values of S, L, and W, and so we put them into the formula to get
[tex]108=2(3)(4)+2(4)H+2(3)H[/tex]We simplify the above to get
[tex]108=24+8H+6H[/tex]Subtracting 24 from both sides gives
[tex]108-24=24-24+8H+6H[/tex][tex]84=8H+6H[/tex]Adding the like terms on the right-hand sides gives
[tex]84=14H[/tex]Finally, dividing both sides by 14 gives
[tex]\frac{84}{14}=\frac{14H}{14}[/tex]which gives
[tex]H=6[/tex]which is our answer!
5) Each table represents a proportional relationship. (From Unit 2 Lesson 2) a) Fill in the missing parts of the table. b) Draw a circle around the constant of proportionality. a х у a b т n 2 10 12 3 15 20 10 3 735 5 10 18 1 1 1
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Given:
The table represents a proportional relationship.
a) To find the missing values of table,
For first table,
[tex]\begin{gathered} \frac{10}{2}=\frac{15}{x} \\ 10x=15\times2 \\ 10x=30 \\ x=\frac{30}{10}=3 \\ \frac{15}{3}=\frac{y}{7} \\ 15\times7=3y \\ 3y=105 \\ y=\frac{105}{3}=35 \\ \frac{35}{7}=\frac{y}{1} \\ 35=7y \\ y=\frac{35}{7}=5 \end{gathered}[/tex]For second table,
[tex]\frac{3}{12}=\frac{b}{20}=\frac{10}{a}=\frac{b}{1}[/tex][tex]\begin{gathered} \frac{3}{12}=\frac{b}{20} \\ 3\times20=12y \\ b=\frac{60}{12}=5 \\ \frac{5}{20}=\frac{10}{a} \\ 5a=10\times20 \\ a=\frac{200}{5}=40 \\ \frac{10}{40}=\frac{b}{1} \\ 40b=10 \\ b=\frac{10}{40}=\frac{1}{4} \end{gathered}[/tex]For third table,
[tex]\begin{gathered} \frac{3}{5}=\frac{n}{10}=\frac{18}{m}=\frac{n}{1} \\ \frac{3}{5}=\frac{n}{10} \\ 30=5n \\ n=\frac{30}{5}=6 \\ \frac{3}{5}=\frac{18}{m} \\ 3m=90 \\ m=30 \\ \frac{3}{5}=\frac{n}{1} \\ 5n=3 \\ n=\frac{3}{5} \end{gathered}[/tex]b) To draw the circle around the constant of proportionality.
For first table the constant of proportionality is 5.
For second table the constant of proportionality is 1/4.
For third table the constant of proportionality is 3/5 .
which of the following represents a line that is parallel to the line with equation y = – 3x + 4 ?A. 6x +2y = 15B. 3x - y = 7 C. 2x - 3y = 6D. x + 3y = 1
Answers
In order to have parallel lines, the slopes of the lines need to be the same.
In order to check the slope for each option, let's put the equations in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
So we have that:
A.
[tex]\begin{gathered} 6x+2y=15 \\ 2y=-6x+15 \\ y=-3x+7.5 \end{gathered}[/tex]B.
[tex]\begin{gathered} 3x-y=7 \\ y=3x-7 \end{gathered}[/tex]C.
[tex]\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}[/tex]D.
[tex]\begin{gathered} x+3y=1 \\ 3y=-x+1 \\ y=-\frac{1}{3}x+\frac{1}{3} \end{gathered}[/tex]So the only option with a line with a slope of -3 is Option A.
Find the exact value of cos -1050.OA.-3OB.-12/2OC. 1OD. 1/3Reset Selection
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Solution:
Given;
[tex]\cos(-1050)[/tex]Rewrite the expression using;
[tex]\cos(-x)=\cos x[/tex]Thus;
[tex]\begin{gathered} \cos(-1050)=\cos(1050) \\ \\ \cos(1050)=\cos(330) \end{gathered}[/tex]Then;
[tex]\cos(330)=\frac{\sqrt{3}}{2}[/tex]CORRECT OPTION: D
Isabelle is making a scrapbook. Each page of the scrapbook is a square with a length of 11in. If each page holds three pictures that each have an area of 15in2, what is the remaining area on each page in square inches that can be used for decoration?
Answers
Given:
A page of the scrapbook is a square with a length of 11 in
Each page holds three pictures that each have an area of 15in²
To find the remaining area, we will find the area of the page and the total area of the pictures, then subtract the area of the pictures from the area of the page
The area of the page = 11 x 11 = 121 in²
Total area of the pictures = 3 x 15 = 45 in²
So, the remaining area = 121 - 45 = 76 in²
01 Question 11 What is the area of the shaded region? 12cm 6 cm 10cm 8cm 128cm? 96cm2 X 144cm? a 112cm?
Answers
We can calculate the area of the shaded region as the difference between the area of the rectangle (sides 12 cm and 10 cm) and the area of the triangle in the corner.
The triangle has base of b=12-8=4 cm and height h=10-6=4 cm.
Then, we can calculate the area of the shaded area as:
[tex]\begin{gathered} A=A_r-A_t \\ A=b_r\cdot h_r-\frac{b_t\cdot h_t}{2} \\ A=12\cdot10-\frac{4\cdot4}{2} \\ A=120-\frac{16}{2} \\ A=120-8 \\ A=112\operatorname{cm}^2 \end{gathered}[/tex]Answer: 112 cm^2
which rational number is the opposite of 1.7? Select all that apply. -1 7/10-1.71 7/10
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Answer:
The opposite of 1.7 are;
[tex]\begin{gathered} -1.7 \\ \text{and} \\ -1\frac{7}{10} \end{gathered}[/tex]Explanation:
We want to find the rational number that is opposite of 1.7.
The opposite of 1.7 is;
[tex]-(1.7)=-1.7[/tex]The opposite of 1.7 can be written as;
[tex]-1.7=-1\frac{7}{10}[/tex]The opposite of 1.7 are;
[tex]\begin{gathered} -1.7 \\ \text{and} \\ -1\frac{7}{10} \end{gathered}[/tex]Which one of the following graphs represents the solution of the inequality 2x + 1 ≥ 3?A.-3-2-1 0 123B.++-3-2-1 0123-3-2-1 0 123-3-2-1 0 1 2 3OC.OD.
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The inequality given is:
[tex]2x+1\ge3[/tex]Let's solve for x:
[tex]\begin{gathered} 2x\ge3-1 \\ . \\ x\ge\frac{2}{2} \\ . \\ x\ge1 \end{gathered}[/tex]The solution set of this inequality is the set of all numbers bigger or equal than 1.
Thus, the correct answer is option A, where we can see that the values start at 1 and goes to positive infinity.
3x-22x + 1A8If x=8, then the length of AB is
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Ok the length of AB is given by the equation:
[tex]3x-2[/tex]If x=8 then we simply have to replace this value in the equation:
[tex]\bar{AB}=3\cdot8-2=22[/tex]And that's the length of segment AB.
A ball is shot out of a cannon at ground level. it's height H in feet after t seconds is given by the function H(t) = 96t - 16t^2. Find H(1), H(5), H(2), and H(4). Why are some of the outputs equal? H(1) = ______ feetH(2)= ______ feetH(4)= ______ feet H(5)= ______ feet
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Follow the function we have that
[tex]\begin{gathered} H(1)=96(1)-16(1)^2 \\ =96-16=80 \end{gathered}[/tex]So H(1) = 80 feet. Now
[tex]\begin{gathered} H(2)=96(2)-16(2)^2 \\ =192-64=128 \end{gathered}[/tex]So H(2) = 128 feet. Now
[tex]\begin{gathered} H(4)=96(4)-16(4)^2 \\ =384-256=128 \end{gathered}[/tex]So H(4) = 128 feet. Now
[tex]\begin{gathered} H(5)=96(5)-16(5)^2 \\ =480-400=80 \end{gathered}[/tex]So H(5) = 80 feet.
where does the x-intercept in to the y-intercept
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x-intercept -3
y-intercept 6
2. g(x) = (x-3)^3 identity the parent function, shape (you can draw it), and domain and range of parent function
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Step 1
Domain: The domain is the set of values for x, in the function x can take any values, so the set is all the real numbers
Range:The range is the set of values for y, y can take any values, so the set is all the real numbers
[tex]\begin{gathered} \text{Domain(-}\infty,\infty) \\ \text{Range(-}\infty,\infty) \end{gathered}[/tex]five to the third power
Answers
We need to find the value of 5 to the third power, to do this let's remember that the third power of a number means multiplying this number three times by itself, that is:
[tex]5^3=5\times5\times5=125[/tex]The answer is 125
given the following trig equation, find the Exact value of the remaining 5 trig functionstan (theta) = 5/6 and cos theta < 0Start by drawing the triangle in standard position and use the Pythagorean theorem to find the remaining side. A. label the exact value of all 3 sides of the triangle drawn in the correct quadrantB. DETERMINE the EXACT value of the remaining 5 trig functions! (sin) (cos) (tan) (sec) (csc) (cot)
Answers
tan (theta) = 5/6 and cos theta < 0
tan (theta) = 5/6 ==> theta = tan^-1(5/6) = 39.80557109
theta = 39.80557109
cos(theta) = cos(39.80557109) = 0.7682212796
It says that cos(theta) < 0, so the 39.80557109 degrees is in rality an angle of 90 + 39.80557109 = 120.80557109
sin (theta) = sin (120.80557109) = 0.858910105
cos(theta) = cos(120.80557109) = −0.5121263824
tan(theta) = tan(120.80557109) = −1.677144811
sec(theta) = sec(120.80557109) = −1.952643008
csc(theta) = csc(120.80557109) = 1.164266195
cot(theta) = cot(120.80557109) = −0.5962514348
Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. A line was fit to the data to model the relationship.Which of these linear equations best describes the given model?A) ŷ = 5x + 1.5B) ŷ = 1.5x + 5Or C) ŷ = -1.5x + 5Based on this equation, estimate the mood rating for a student that spent 2.5 hours playing sports.Round your answer to the nearest hundredth.__________.
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We have to relate a linear function (the regression model) with its equation.
We can see in the graph that the y-intercept, the value of y(0), is b=5.
Then, we can estimate the slope with the known points (0,5) and (2,8):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-5}{2-0}=\frac{3}{2}=1.5[/tex]Then, with slope m=1.5 and b=5, the regression model equation should be:
[tex]y=1.5x+5[/tex]We can estimate the mood for students that spent 2.5 hours playing sports by replacing x with 2.5 in the model and calculate y:
[tex]y(2.5)=1.5\cdot2.5+5=3.75+5=8.75[/tex]NOTE: we could also have look on the graph instead of doing the calculation.
Answer: B) y=1.5x+5
The estimation of the mood for a student that spent 2.5 hours playing sports is 8.75.
Fnd the volume of each cylinder below.9.18 in15 in
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9) We can calculate the volume as the product of the base area and the height.
The base is a circle with radius r=18 in. Then, its area is:
[tex]A_b=\pi r^2=\pi\cdot18^2=324\pi[/tex]Then, we can calculate the volume V as:
[tex]V=A_b\cdot h=324\pi\cdot15=4860\pi[/tex]10) In this case the circular base is on the side, but we can still use the same principle to calculate the volume.
The area of the base with diameter D = 11 in is:
[tex]A_b=\frac{\pi D^2}{4}=\frac{\pi\cdot11^2}{4}=\frac{\pi\cdot121}{4}=\frac{121}{4}\pi[/tex]Then, we can calculate the volume V as:
[tex]V=A_b\cdot h=\frac{121}{4}\pi\cdot21=\frac{2541}{4}\pi=635.25\pi[/tex]Answer:
9) V = 4860π
10) V = 635.25π
Jefferson works part time and earns 1,520in four weeks how much does he earn each weet
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To determine how much he earns each week we need to divide the amount given by 4, that is we need to kae the division:
[tex]1520\div4[/tex]The long division is shown below:
To make the long division we notice that we can't divide the first number (one) by four, then we need to put down the five to get a 15, this number can be divided by four. Fifteen can be divided by four, the number four fits 3 times in fifteen, then we have a three as the first nonzero number. three by 4 is 12. We subtract 12 from 15 to get 3 and the we downed the following two. This procedure is repeated until we have a number that gives zero as a remainder. This is shown in the picture above.
From it we conclude that Jefferson earns $380 each week
The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 6.2% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Round your answer to the nearest hundredth.
Answers
Solution
for this case we have the following equation:
[tex]A=A_oe^{kt}_{}[/tex]the constant would be:
k= -0.062
Then we can do this:
[tex]\frac{1}{2}A_o=A_oe^{-0.062t}[/tex]solving for t we have:
[tex]\ln (\frac{1}{2})=-0.062t[/tex][tex]t=-\frac{\ln (0.5)}{-0.062}=11.179\text{days}[/tex]Rounded to the nearest hundredth would be:
11.18 days
Select the correct choice and fill in the answer box
Answers
To begin with, let us look at a few definitions that will help
A relation is a function if each x-value is paired with exactly one y-value. A vertical line test on a graph can be used to determine whether a relation is a function.
If we use a graph to check, we will have
We can see that there is no overlapping of coordinates. The table satisfies the vertical line test.
Hence, it is a function
The domain and range of function is the set of all possible inputs and outputs of a function respectively. The domain and range of a function y = f(x) is given as domain= {x ,x∈R }, range= {f(x), x∈Domain}.
The domain of the function, D is given by
[tex]D=\mleft\lbrace-1,0,1,2,3\mright\rbrace[/tex]The range, R is given by
[tex]R=\mleft\lbrace-6,-1,2,5,8\mright\rbrace[/tex]1) Find the angle in degrees without using a calculator: a) arcsin( √3/2)
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Then, since arcsin is a function:
[tex]\begin{gathered} R\rightarrow\mleft\lbrace-1;\text{ 1}\mright\rbrace \\ We\text{ take only value }\theta=\frac{\pi}{3},\text{ without the periodic values.} \\ \text{That means,} \\ \arcsin (\frac{\sqrt[]{3}}{2})=60\text{ degrees= }\frac{\pi}{3} \end{gathered}[/tex]