A fair six sided number cube has the following faces 1,1,2,2,5,6 this number cube is rolled 50 times what is the probability that fewer than 30% of the rolls result in a two
The probability that fewer than 30% of the rolls result in a two is given as follows:
0.3085 = 30.85%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:
n = 50, p = 2/6 = 1/3 = 0.3333.
The mean and the standard error are given as follows:
[tex]\mu = p = 0.3333[/tex][tex]s = \sqrt{\frac{0.3333 \times 0.6667}{50}} = 0.0667[/tex]The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:
Z = (0.3 - 0.3333)/0.0667
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
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Ten upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 9. The smallest domino, #0, is 3.00 inches tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 15% taller than the one before. What is the height of domino #9?
Answer:
8.604 in.
Step-by-step explanation:
We can use the formula for compound interest to find the height of domino #9:
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).
Substituting the given values:
A = 3.00 in * (1 + 0.15)^9
Simplifying:
A = 3.00 in * 2.86797199
A ≈ 8.604 in
Therefore, the height of domino #9 is approximately 8.604 inches.
PLEASE HELP ME SOLVE THIS!! I AM LOST! HELP ME PLEASE!!!! THANKS
The Cost of the blue paint that would cover the shaded area = $0.495
The Cost of the white paint that would cover the triangular shapes = $0.6678
How to Find the Area of a Circle and Triangle?Recall the following formulas:
Area of a circle = πr²
Area of a triangle = 1/2 * base * height.
Area the blue paint will cover = 2(1/2 * base * height) = 2(1/2 * 1.5 * 1)
= 1.5 ft²
Cost of the blue paint = 1.5 * 0.33 = $0.495
Area the blue paint will cover = πr² - area of the two triangles
= 3.14 * 1.5² - 1.5 = 5.565 ft²
Cost of the white paint = 5.565 * 0.12 = $0.6678
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Use the substitution u = 1/x and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then substitute to determine the solution set to the original system in terms of x and y.
1/x + 2/y = 1
-1/x + 8/y = -6
Step-by-step explanation:
We have the system of equations:
1/x + 2/y = 1 -----(1)
-1/x + 8/y = -6 -----(2)
We can use the substitutions u = 1/x and v = 1/y to rewrite the equations in terms of u and v. Substituting, we get:
u + 2v = 1 -----(3)
-u + 8v = -6 -----(4)
Now we can solve the system in terms of u and v. Adding equations (3) and (4) gives:
2v = -5
Dividing both sides by 2, we get:
v = -5/2
Substituting this value of v into equation (3) gives:
u + 2(-5/2) = 1
Simplifying:
u - 5 = 1
u = 6
Therefore, we have u = 6 and v = -5/2.
To find the solution set in terms of x and y, we substitute back:
u = 1/x, so 6 = 1/x, and x = 1/6
v = 1/y, so -5/2 = 1/y, and y = -2/5
Therefore, the solution set to the original system is x = 1/6 and y = -2/5.
The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected giraffe adult. Round all answers to 4 decimal places.
D. What is the probability that a randomly selected giraffe will be shorter than 18.5 feet tall?
E. probability that a randomly selected giraffe will be between 19 and 19.9 ft tall?
F. 75th percentile for the height of giraffes.
D. The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is given as follows: 0.7340 = 73.40%.
E. The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is given as follows: 0.0968 = 9.68%.
F. The 75th percentile for the height of giraffes is given as follows: 18.54 ft.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 18, \sigma = 0.8[/tex]
The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is the p-value of Z when X = 18.5, hence:
Z = (18.5 - 18)/0.8
Z = 0.625
Z = 0.625 has a p-value of 0.7340.
The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is the p-value of Z when X = 19.9 subtracted by the p-value of Z when X = 19, hence:
Z = (19.9 - 18)/0.8
Z = 2.375
Z = 2.375 has a p-value of 0.9912.
Z = (19 - 18)/0.8
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
Hence:
0.9912 - 0.8944 = 0.0968 = 9.68%.
The 75th percentile is X when Z = 0.675, hence:
0.675 = (X - 18)/0.8
X - 18 = 0.8 x 0.675
X = 18.54 ft.
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Find an equation of the line passing through the given points. Use function notation to write the equation.
(−2,−3) and (−4,−4)
Answer:
Step-by-step explanation:
Let A(-2,-3), B(-4,-4).
Line f(x) = y = ax + b (C)
The line passes through these points so when substituting their coordinates into (C), we get:
-3 = -2a + b
-4 = -4a + b
Solving this set of equations gives us a = 1/2; b = -2.
So the equation of this line is [tex]f(x)=\frac{1}{2}x-2[/tex]
Solve for c ;;; upside down triangle 156.5° / 117.5°
Check the picture below.
I need help with this please
Answer: C
Step-by-step explanation:
Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.
The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy. A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 3, above 11 to 15 that stops at 4, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3. Which statement best describes the spread and distribution of the data? The data is almost symmetric, with a maximum range of 24. This means that the tide frequently measured around 11 to 20 feet. The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 16 to 25 feet range. The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 21 to 25 feet. The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.
The histogram is solved and the data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
Given data ,
Let the number of observations of each interval is:
1 to 5: 2 observations.
6 to 10: 5 observations.
11 to 15: 2 observations.
16 to 20: 6 observations.
21 to 25: 1 observations.
Let the maximum range be represented as M
And , there are two similarly high bins for the histogram , hence the distribution can be said to be bimodal, with maximum range given as follows
M = 25 - 5
M = 21 - 1
M = 20
Hence , the histogram is solved
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Jamal and his dad went scuba diving. They went on a 54-foot dive, descending from a motor boat located on the Gulf of Mexico. The boat was located
at sea level.
Where on a number line would you plot a point to represent the boat's location?
select all the equations that are equivalent to 81x^2+180x-200=100
The factorized form of the equation is 3((3x + 10)(9x - 10) ) = 0.
What is the simplification of the equation?
The given quadratic equation is simplified as follows;
81x² + 180x - 200 = 100
Collect similar terms together;
81x² + 180x = 100 + 200
81x² + 180x = 300
81x² + 180x - 300 = 0
Factorize the equation by using a common factor;
3(27x² + 60x - 100) = 0
Factorize further as follows;
3(27x² + 90x - 30x - 100) = 0
3( 9x (3x + 10) - 10(3x + 10) )= 0
3((3x + 10)(9x - 10) ) = 0
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james baked 5 1/4 dozen peanut butter cookies and 4 5/6 dozen oatmeal cookies for a bake sale what it is the estimate the number of dozen of cookies he baked
A 105 kg halfback runs north and is tackled by a 156 kg opponent running south at 6 m/s. The collision is perfectly inelastic. Just after the tackle, both players move at a velocity of 3 m/s north. Calculate the velocity (m/s) of the 105 kg player just before the tackle. Answer to one decimal place.
We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:
Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:
Total momentum before = Total momentum after
(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)
Simplifying and solving for v, we get:
v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg
v = 2.85 m/s
Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.
Use the graph to answer the question.
B
3
D
Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 5
Reflection across y = 6
8
C
D'
9
10
E'
11
12
B'
A'
13
The line of reflection of the graph is y = -3
Determining the line of reflection.The given graph is added as an attachment
From the graph, we can see that the shapes are symmetrical about the line y = -3
When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection
This means that the line of reflection is y = -3
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Answer:
The calculated line of reflection of the graph is y = -3
Step-by-step explanation:
The last customer of the day is a loyal customer who brings in a $15.00 off coupon. She purchases two paint brushes, one dozen colored pencils, and one sketch book.
What percent did she save by using her coupon?
~info of the art supplies~
*Paint brush- $10.50
*Colored pencils- $7.88
*Sketch Book- $16.12
The total cost of the art supplies without the coupon is:
2 paint brushes x $10.50 per brush = $21.00
1 dozen colored pencils x $7.88 per dozen = $7.88
1 sketch book x $16.12 per book = $16.12
Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00
With the $15.00 off coupon, the total cost becomes:
$45.00 - $15.00 = $30.00
The amount saved by using the coupon is:
$45.00 - $30.00 = $15.00
The percentage saved can be calculated as:
Percentage saved = (Amount saved / Total cost without coupon) x 100%
Percentage saved = ($15.00 / $45.00) x 100%
Percentage saved = 33.33%
Therefore, the customer saved 33.33% by using her coupon.
1/9 times 3 to the 3rd power minus 2(1/6+2/3)
The value of the expression is 28 2/3
How to determine the valueTo determine the value of addition, we need to know that fractions are described as part of a whole number or variables.
From the information given, we have that;
1/9 times 3 to the 3rd power
This is represented as;
(1/9 × 3)³
Divide the values, we get
(3)³
Find the cube
27
Then, we have;
27 + 2(1/6+2/3)
Solve the bracket
27 + 2( 1+ 4 /6)
27 + 2(5/6)
Divide the values
27 + 5/3
81 + 5/3
86/3
Divide the values
28 2/3
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A triangle has two 90° angles and a side 12 centimeters in length.
Select True or False for each statement about this type of triangle.
The triangle with 2 angles as 90° is not possible and the statement is false.
Given data ,
Let the triangle be represented as ∠ABC
Now , the measures of the angles of the triangle are
A triangle has two 90° angles and a side 12 centimeters in length
So , ∠ABC = ∠BAC = 90°
And , For a Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Therefore, a triangle cannot be formed with 2 angles as 90°
Hence, the statement, the third angle is 90° is False
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I’m confused. Can somebody help me?
Answer:
The Correct answer is D and F
HELPPPPPPPPPPP
Nathaniel has 132 DVDs in his collection.
Each DVD case has the dimensions shown.
He plans to buy shelves for the collection
that are 31.5 inches wide and cost $15.75
each. How much will it cost Nathaniel to
shelve his DVD collection? Explain how you
found your answer.
The dimensions are 7.5in, 5.3in, 0.6in
The cost of shelving Nathaniel’s DVD collection is 15.75×27=$425.25.
We are given that;
Dimensions =7.5in, 5.3in, 0.6in
To find the cost of shelving Nathaniel’s DVD collection, we need to find how many shelves he needs and multiply that by the price of each shelf. To find how many shelves he needs, we need to find how many DVDs can fit on one shelf and divide that by the total number of DVDs.
Since the shelves are 31.5 inches wide and the DVDs are 5.3 inches wide, we can fit 5.331.5≈5.94 DVDs on one shelf. We round this down to 5 DVDs per shelf because we cannot fit a partial DVD on a shelf.
Since Nathaniel has 132 DVDs in his collection, he needs 5132=26.4 shelves. We round this up to 27 shelves because we cannot use a partial shelf.
Therefore, by algebra the answer will be 15.75×27=$425.25.
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Rewrite this non-statistical
question as a statistical
question.
How many brothers do you
have?
Answer:
0
Step-by-step explanation:
The table shows the distribution, by age and gender, of the million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 2534 age range.
The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487
The total digit of individuals living independently in the area = 31.6
The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7
The probability formula will be applied ed as
P = required outcome / Total possible outcomes
From the information that is provided above the given data is:
P(range 25 - 34) = 4.7 / 31.6
= 0.1487
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The question is incomplete, Complete question probably will be is:
The table shows the distribution, by age and gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.
The probability is ___.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
X-2 = x-1 +2
____________
x-1 =. x+1 + x-1
Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1
Evaluating the expressionFrom the question, we have the following parameters that can be used in our computation:
(x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1)
Evaluating the like terms, we have
(x - 2)/(x - 1) = (x + 1)/(x + 1)(x - 1)
Cancel out the common factors
So, we have
(x - 2) = 1
Add 2 to both sides
x = 3
Hence, the solution is 3
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Two square carpets are used in the reception area of a hotel. The sum of the areas of the carpets is 720 square feet. The difference of the areas of the carpets is 432 square feet. Find the dimensions of each carpet.
Answer:
Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.
Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.
From the problem, we know that the sum of the areas of the two carpets is 720 square feet:
x^2 + y^2 = 720
We also know that the difference of the areas of the two carpets is 432 square feet:
x^2 - y^2 = 432
We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:
x^2 = y^2 + 432
Substituting this expression for x^2 into the first equation, we get:
y^2 + 432 + y^2 = 720
Simplifying and solving for y, we get:
2y^2 = 288
y^2 = 144
y = 12
Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:
x^2 + 144 = 720
x^2 = 576
x = 24
Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.
Step-by-step explanation:
A cyclist is riding on a mountain trail. Her current elevation is 1.9 km, and she is riding at a constant speed of 25 km/hr. She is riding downhill, and her angle of
descent is 2° from the horizontal. See the figure below. (The figure is not drawn to scale.) Find her new elevation, h, after 0.50 hours. Carry your Intermediate
computations to at least four decimal places, and round your answer to the nearest tenth of a kilometer.
1.9 km
2°
- Cyclist after 0.50 hours
Ih km
Sea Level
After 0.50 hours, the cyclist's new elevation is h = 1.8 km.
Since the cyclist is riding downhill, we can use the formula h = h0 - Vt sin θ to calculate her new elevation. In this formula, h0 represents her initial elevation, V her speed, t her time, and θ her angle of descent. We are given h0 = 1.9 km, V = 25 km/hr, t = 0.50 hours, and θ = 2°.
h = 1.9 km - (25 km/hr)(0.50 hours)(sin 2°)
h = 1.9 km - (25 km/hr)(0.50 hours)(0.03492)
h = 1.8282 km
h ≈ 1.8 km
Therefore, after 0.50 hours, the cyclist's new elevation is h = 1.8 km.
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Tarea de rendimiento
12
La señora Ericson preparó sándwiches para sus 4 hijos. Todos los sándwiches tenían
el mismo tamaño. Después del almuerzo, a cada niño le quedaba una fracción
diferente de su sándwich. Matt tenía, Elisa tenía
7
3, Carl tenía 2, y Riley tenía 8
8
4
A Usa esta información para escribir un problema en que se comparen dos fracciones
con el mismo numerador.
The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
How to solveFour sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.
The children consumed varying portions of their respective sandwiches during the shared midday meal.
Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.
Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.
Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
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The question in English is:
Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had
The same size. After lunch, each child had a fraction left.
different from your sandwich. Matt had, Elisa had
7
3, Carl was 2, and Riley was 8
8
4
Use this information to write a problem comparing two fractions
with the same numerator.
What is the fraction and mixed number for this decimal 0.5
Answer: 1/2
Step-by-step explanation:
The fraction equivalent of 0.5 is 1/2.
To convert it into a mixed number, we can divide the numerator by the denominator:
1 ÷ 2 = 0 with a remainder of 1
So, the mixed number is 0 1/2.
Translate A’B’C by the directed line segment from (0,0) to (-3,-2)
By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.
How to find the image of the figure by rigid transformations
In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointT(x, y) - Translation vector.P'(x, y) - Resulting pointIf we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:
A''(x, y) = (4, - 1) + (- 3, - 2)
A''(x, y) = (1, - 3)
B''(x, y) = (1, 1) + (- 3, - 2)
B''(x, y) = (- 2, - 1)
C''(x, y) = (0, - 3) + (- 3, - 2)
C''(x, y) = (- 3, - 5)
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Please answer these I’m so confused
The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.
The graph of the solution set of -48 < -8t is shown below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Next, we would determine the solution to the given inequality as follows;
2.5x ≥ 20
x ≥ 20/2.5
x ≥ 8 (Sebastian was wrong)
-48 < -8t
-48/-8 < -8t/-8
6 < t
t > 8
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With workings, please help
Answer:
Step-by-step explanation:
A rectangular brochure is designed so that it has an area of 30 square inches and a perimeter of 23 inches. Find the width and height of the brochure. Assume the height is greater than the width.
The width of the brochure is 3/2 inches and the height is 10 inches.
Let's assume that the width of the brochure is x and the height is y.
The area of the brochure is given as 30 square inches:
xy = 30
The perimeter of the brochure is given as 23 inches:
2x + 2y = 23
We can use the second equation to solve for one variable in terms of the other.
2x + 2y = 23
2x = 23 - 2y
x = (23 - 2y)/2
Now we can substitute this expression for x into the equation for the area:
xy = 30
[(23 - 2y)/2]y = 30
23y/2 - y^2 = 60/2
y^2 - 23y/2 + 30 = 0
We can solve for y using the quadratic formula:
y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)
y = [23/2 ± sqrt(529/4 - 120)]/2
y = [23/2 ± sqrt(289/4)]/2
y = [23/2 ± 17/2]/2
y = 10 or y = 3/2
Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.
So, y = 10 and
x = (23 - 2y)/2 = (23 - 20)/2 = 3/2
Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.
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