The probability that Amie will select a large shirt is 0.25 or 25%.
Given information:
USA Spirit T-shirts are available for purchase in a shop.
The shirts are available in red, blue, and white, with sizes ranging from small to medium to large to extra-large.
Amie will choose one shirt at random from the shelf if the shelf includes an equal number of shirts in each color and size combination.
There are three colors and four sizes, so there are a total of 3 x 4 = 12 shirts on the shelf.
Since there are an equal number of shirts of each size and color, there are 12/4 = 3 large shirts.
The probability of selecting a large shirt is the number of large shirts divided by the total number of shirts, which is:
3/12 = 1/4 = 0.25.
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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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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?
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.
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.
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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What is the difference between the median math test score in the morning and the afternoon?
The difference between the median math test score in the morning and the afternoon is 9.5
What is median?The median can simply be described as the middle number in a given set of data when the values are arranged in an order from least to the greatest values.
From the information given, we have that;
The math scores for the afternoon test were;
55, 70, 76, 85, 95
The math scores for the morning test were;
70, 80.5, 85.5, 90.5 and 95.5
Hence,
The median for the afternoon test = 76
The median for the morning test =85.5
The difference between the values would be = 85.5 - 76 = 9. 5
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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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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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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.
From November to December of 2015, the price per share of BP Oil dropped from $90.75 to $82.75. Exxon shares also dropped from $87.25 to $61.25. In November, your rich cousin invested $97,918.25 into a combination of BP and Exxon shares. By December they sold their shares for $74,090.25 losing $23,828 from their investment. How many of each stock did they purchase?
By solving equations we get to know that your cousin bought 356 shares of BP and 1448 shares of Exxon.
Initial investment:
x shares of BP at $90.75 per share + y shares of Exxon at $87.25 per share = $97,918.25
Sale of shares:
x shares of BP at $82.75 per share + y shares of Exxon at $61.25 per share = $74,090.25
We now have two equations with two variables, which we can solve using either substitution or elimination
0.875x($90.75) + 0.875y($87.25) = $85,648.23
x($82.75) + y($61.25) = $74,090.25
0.875x($90.75) - x($82.75) = $11,558.98 - 0.875y($87.25) + y($61.25)
0.875x($8) = $11,558.98 - 0.875y($26)
7x = $11,558.98 - $22.75y
We can then substitute this expression for "x" into either of the original equations to solve for "y".
(7($11,558.98 - $22.75y))/$8 + y($87.25) = $97,918.25
$81,763.03 - $19.9375y + $87.25y = $97,918.25
$7.0125y = $10,155.22
y = 1448
and x = 356
Hence, your cousin bought 356 shares of BP and 1448 shares of Exxon.
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With workings, please help
Answer:
Step-by-step explanation:
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 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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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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I’m confused. Can somebody help me?
Answer:
The Correct answer is D and F
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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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.)
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.
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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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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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.
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.
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]
Rewrite this non-statistical
question as a statistical
question.
How many brothers do you
have?
Answer:
0
Step-by-step explanation:
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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A city garden club is creating a green space as a community project on 5.5 acres of land for their citizens’ enjoyment. A local landscaping company is expected to donate somewhere between 2500 and 3000 seedlings for the project. What will the density be in trees per acre upon completion? Round your answers to the nearest whole number
The density in trees per acre upon completion will be 500 trees per acre.
How to calculate the densityIn this scenario, let's say the landscaping provider donates 2750 seedlings.
Density of trees per acre = Total number of trees / Total area of land
Hence, applying the formula leads us to:
Density of trees per acre = 2750 trees / 5.5 acres
The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.
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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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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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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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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: