At least 95% of the observations lie between 19 and 31.
To see why, we can use Chebyshev's theorem, which states that for any data set, regardless of the shape of the distribution, at least 1 - (1/k²) of the observations lie within k standard deviations of the mean. In this case,
we want to know the percentage of observations that lie within two standard deviations of the mean, since 19 and 31 are both two standard deviations away from the mean of 25.
So, we can use k = 2 in Chebyshev's theorem, which gives us:
1 - (1/2²) = 1 - (1/4) = 0.75
Therefore, at least 75% of the observations lie within two standard deviations of the mean. However, since we know the data set is normally distributed (since we know the mean and standard deviation), we can use the empirical rule,
which states that for normally distributed data, approximately 68% of the observations lie within one standard deviation of the mean, and approximately 95% of the observations lie within two standard deviations of the mean.
Therefore, we can conclude that at least 95% of the observations lie between 19 and 31.
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If a couch measures 10ft across in real life, what would it's measurement be in the scale drawing (in)
Explain
the measurement of the couch in the scale drawing would be 15 inches.
what is scale drawing?We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.
When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.
When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.
When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.
One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.
You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.
To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:
1/4 inch = 2 feet
This means that every 1/4 inch in the drawing represents 2 feet in real life.
To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.
First, we can convert the actual size of the couch to feet:
10 ft = 10 ft x 12 inches/ft = 120 inches
Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:
1/4 inch = 2 feet
1 inch = 8 feet (multiplying both sides by 4)
So, 120 inches in real life is equal to:
120 inches / 8 feet per inch = 15 inches in the drawing
Therefore, the measurement of the couch in the scale drawing would be 15 inches.
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Find the area of the composite figure to the nearest hundredth. Find the area total area = ________ mm²
The total area of the composite figure is 1650 mm
To find the area of a composite figure, you need to break it down into simpler shapes whose areas you can calculate and then add up the individual areas. In this case, the composite figure consists of two shapes: a rectangle and a trapezoid.
To find the area of the rectangle, you multiply its length by its width. From the given dimensions, the length of the rectangle is 40 mm and the width is 30 mm. So the area of the rectangle is 40 x 30 = 1200 mm².
To find the area of the trapezoid, you use the formula for the area of a trapezoid: (base1 + base2) x height / 2. From the given dimensions, the two bases of the trapezoid are 25 mm and 35 mm, and the height is 15 mm. So the area of the trapezoid is (25 + 35) x 15 / 2 = 450 mm².
Now you add the areas of the two shapes together to get the total area of the composite figure: 1200 + 450 = 1650 mm².
Therefore, the total area of the composite figure is 1650 mm², rounded to the nearest hundredth.
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9(x) = ln (3x+11) calculate gl (x) A) 2-3x + 11)-3 B) 3(-3x + 11)-1 C) -54(-3x +11)-3 D) -9(-3x +11)-?
Using given function 9(x) = ln(3x+11), gl (x) B) 3(-3x + 11)^-1.
We are given 9(x) = ln(3x+11) and we need to find gl(x).
First, we can use the chain rule to differentiate ln(3x+11):
d/dx [ln(3x+11)] = 1/(3x+11) * d/dx [3x+11] = 3/(3x+11)
Now, we can use the given equation 9(x) = ln(3x+11) to find d/dx [9(x)]:
d/dx [9(x)] = d/dx [ln(3x+11)] = 3/(3x+11)
Therefore, gl(x) = d/dx [9(x)] / 3(x) = 3/(3x+11) * 1/3 = (3(-3x+11))^-1.
Therefore, the correct answer is B) 3(-3x+11)^-1.
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Jose reads his book at an average rate of
2. 5
2. 5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read
20
20 pages?
It would take Jose approximately 3232 minutes (or about 53.87 hours) to read 2020 pages at the same rate of 2.5 pages every four minutes.
To determine how long it would take Jose to read 2020 runners at the same rate of2.5 runners every four twinkles, we can use a proportion. Let x be the number of twinkles it would take Jose to read 2020 runners. also, we can set up the following proportion:
2.5 pages / 4 minutes = 2020 pages / x minutes
To solve for x, we can cross-multiply and simplify:
2.5 pages * x minutes = 4 minutes * 2020 pages
2.5x = 8080
x = 8080 / 2.5
x = 3232
Therefore, it would take Jose approximately 3232 minutes to read 2020 pages at the same rate of 2.5 pages every four minutes.
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If I wanted to draw Circles X and and wanted to make sure they were congruent to Circle A, what
would be required?
To ensure that Circles X are congruent to Circle A, you need to ensure that they have the same size and shape. In other words, the radii of Circle X should be equal to the radius of Circle A.
Here are the steps you can follow to draw congruent Circles X:
Use a compass to measure the radius of Circle A.
Without changing the radius setting on your compass, place the tip of the compass at the center of where you want to draw Circle X.
Draw Circle X using the compass, making sure that the radius is the same as the radius of Circle A.
Check that Circle X and Circle A have the same size and shape. You can do this by measuring their radii with a ruler or by comparing their circumference.
By following these steps, you can ensure that Circle X is congruent to Circle A.
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En un viaje en mula hacia el pico duarte el jinete observa en un poste 1, 290 m sobre el nivel del mar , luego de 5 horas de camino presta atencion a otro poste que indica , 2, 480 m sobre el nivel de mar. ¿ cual ha sido su desplazamiento en direccion vertical?
The vertical displacement of the mule comes out to be the difference between the final and the initial position which is 1190 m.
The displacement refers to the distance between the final and the initial position of an object. It is the shortest distance between these points is the displacement of the object. It is a vector quantity.
Vector quantity refers to the measurement in which both magnitude and direction are considered.
Starting point = 1290 m
Final point = 2480 m
Displacement = 2480 - 1920
= 1190 m
1190 m is the vertical displacement of the mule when traveling from one post to another.
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The question is in Spanish and when translated to English, it is:
On a mule trip to Duarte Peak, the rider observes a post 1,290 m above sea level, after 5 hours of walking he pays attention to another post that indicates 2,480 m above sea level. What has been its displacement in the vertical direction?
Can someone please answer numbers 12, 13, 14, and 15?
There are 4 mathematics books, 5 science books and 3 english books in the library. In how many ways can you arrange these so that the books are arranged in this order: Mathematics, Science, and English, and books of the same subjects are together?
To arrange the books in the specified order (Mathematics, Science, and English), you need to determine the number of arrangements for each subject's books and then multiply them together.
For the 4 mathematics books, there are 4! (4 factorial) ways to arrange them, which is 4 × 3 × 2 × 1 = 24 ways.
For the 5 science books, there are 5! (5 factorial) ways to arrange them, which is 5 × 4 × 3 × 2 × 1 = 120 ways.
For the 3 English books, there are 3! (3 factorial) ways to arrange them, which is 3 × 2 × 1 = 6 ways.
To find the total number of ways to arrange all the books in the required order, multiply the arrangements for each subject together: 24 (Mathematics) × 120 (Science) × 6 (English) = 17,280 ways.
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Jacob is building a square pyramid for a class project. He needs to cover the entire pyramid in aluminum foil. The base of the pyramid has a perimeter of 76 centimeters. The slant height of each triangular side is 28 centimeters. What is the surface area, in square centimeters, of Jacob’s pyramid?
The surface area of the pyramid is 390.8 cm².
What is the surface area of the triangular pyramid?The surface area of the triangular pyramid is calculated as follows;
S.A = base area + ¹/₂ (perimeter + slant height)
The height of the pyramid is calculated by applying Pythagoras theorem;
h = √ (28² - 14²)
h = 24.2 cm
Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²
The surface area of the pyramid is calculated as follows;
S.A = 338.8 cm² + ¹/₂ (76 cm + 28 cm)
S.A = 390.8 cm²
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Answer:
1,425
Step-by-step explanation:
I got this one correct
A line has a slope of – 7 and passes through the point (2,7). Write its equation in slope-intercept form.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ - 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- 7}(x-\stackrel{x_1}{2}) \\\\\\ y-7=-7x+14\implies {\Large \begin{array}{llll} y=-7x+21 \end{array}}[/tex]
(Linear Systems: Applications). Find a polynomial p(2) of degree three such that
7(-2)=3,P(-1)=3,7(1)=-9,8(2)=-33.
Therefore, the polynomial p(x) that satisfies the given conditions is:
p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23
So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.
To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:
-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33
We can solve this system using any method of linear algebra. One way is to use row reduction:
[ -7 2 -4 1 | 3 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R2 + R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ -1 -1 1 -1 | 3 ]
[ 7 1 1 1 | -9 ]
[ 8 4 2 1 | -33 ]
R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8 1 -3 0 | 6 ]
[ 0 -7 8 -1 | 51 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R4 + R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 -4 4 1 |-51 ]
[ 0 4 26 1 |-81 ]
R3 + (4/3)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 50 4 |-11 ]
[ 0 4 26 1 |-81 ]
R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 8 1 |-103 ]
R4 - R3 -> R3:
[ -8 1 -3 0 | 6 ]
[ 0 -3 34 0 | 30 ]
[ 0 0 8 4 |-34 ]
[ 0 0 0 -3 |-69 ]
Now we can back-substitute to find the coefficients of the polynomial:
d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1
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Suppose that a cylinder has a radius of r units, and that the height of the cylinder is also r units.The lateral area of the cylinder is 98 v square units.
Find the value of r. type your answer.....
units
Find the surface area of the cylinder to the nearest tenth. type your answer....
units
r = 4.0 units
Given that,
A cylinder has a radius of r units, and that the height of the cylinder is also r units.
The lateral area of the cylinder is 98 square units.
We need to find the value of r.
The formula for the lateral area of the cylinder is given by:
[tex]\text{A}=2\pi \text{rh}[/tex]
Put all the values,
[tex]2\pi \text{rh}=98[/tex]
[tex]\text{r}=\sqrt{\dfrac{98}{2\pi} }[/tex]
[tex]\text{r}=4.0 \ \text{units}[/tex]
So, the value of r is equal to 4.0 units.
A 5-minute international call costs $2.15 and a 12-minute call costs $3.06. The work shows how to write an equation where x represents the number of minutes, and y represents the total cost of an international call. Analyze the steps of the work to determine if the equation is correct.
1. Point 1: (5, 2.15). Point 2: (12, 3.06). 2. m = StartFraction 12 minus 5 Over 3.06 minus 2.15 EndFraction = StartFraction 7 Over 0.91 EndFraction = 7.69. 3. 5 = 2.15 (7.69) + b. b = negative 11.54. 4. y = 7.69 x minus 11.54.
In which step did Emilia make an error?
In step 2, she substituted the x values for y and the y values for x.
In step 3, she didn’t use an x and y from the same coordinate pair.
In step 4, Emilia solved for the wrong variable.
Emilia did not make an error.
Emilia make an error in step 3 she didn't use an x and y from the same coordinate pair.
In step 1 : point 1 : (5, 2.15) point 2 : (12, 3.06)
In step 2 : m = [tex]\frac{12-5}{3.06-2.15}[/tex]
m = 7/0.91
m = 7.69
In Step 3 : y = mx + b
m = slope
Point used by Emilia (2.15 , 5)
But the point should be used be Emilia is (5, 2.15)
2.15 = 5(7.69) + b
b = y intercept
b = -36.3
step 3 is wrong she didn't use right coordinates of x and y
In step 4 : y = mx +b
y = 7.69x -36.3
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Drake was trying to write an equation to help him predict the cost of his monthly phone bill.
He is charged $35 just for having a phone, and his only additional expense comes from the number of text that he sends,
He is charged $0. 05 for each text. Name the function C(t), where C(t) is the cost of bill according to number of text.
The function for Drake's monthly phone bill, C(t), is C(t) = 35 + 0.05t, where t represents the number of texts sent.
Drake has two components to his monthly phone bill: the base cost of $35 and the additional cost for texts sent. The base cost is fixed, meaning it does not change, so we can represent it as a constant value in the function (35).
The cost per text is $0.05, which means it varies depending on the number of texts sent (t). To find the total cost (C(t)), we need to add the fixed cost ($35) and the variable cost ($0.05 times the number of texts). Therefore, the function representing Drake's monthly phone bill cost is C(t) = 35 + 0.05t.
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A quantity with an initial value of 8200 grows continuously at a rate of 0. 55% per decade. What is the value of the quantity after 97 years, to the nearest hundredth?
Answer: 4000. 4
As per the growth function, the value of the quantity after 97 years would be $67,458.85.
In your problem, you have a quantity with an initial value of 8200 that grows continuously at a rate of 0.55% per decade. To find the value of the quantity after 97 years, we can use the following growth function:
A(t) = A₀[tex]e^{kt}[/tex]
In this formula, A(t) represents the value of the quantity after time t, A₀ represents the initial value of the quantity (in this case, 8200), e represents Euler's number (a mathematical constant equal to approximately 2.718), k represents the growth rate (in this case, 0.0055 per decade), and t represents the time elapsed (in this case, 97 years).
To solve for the value of the quantity after 97 years, we simply plug in the values we know and solve for A(t):
A(t) = 8200[tex]e^{(0.0055/10\times97)}[/tex]
= 8200[tex]e^{0.5285}[/tex]
≈ 67,458.85
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Among american adults, 42. 5 percent are considered: multiple choice question. Obese. Athletic. Anorexic. Underweight
Answer:
Obese
Step by Step Explanation:
looked it up :)
The roof of a building is in the shape of a hyperbola, y^2-x^2=38, where x and y are in meters. Determine the height of the outside. The distance between the center of the hyperbola and the walls is 3m.
a) -29. 1
b) 47. 3
c) 35. 2
d) 6. 9
The height of the outside is given as 17.44 meters
How to solveThe equation of hyperbola is :
[tex]y^2 - x^2 = 38[/tex]
=>[tex]y^2/38 - x^2/38 = 1[/tex]
(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)
Here, [tex]a^2 = b^2 = 38[/tex]
[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]
( a is the distance of vertices from the center and c is the distance of foci from the center.)
Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center
and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining
end points of the wall on one side is through the foci point.
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Mortgage payments Principal : $ 180,000.00 Interest Rate Monthly Payment How much money will be spent in interest alone over the course of the 3.5 % 30 - year mortgage described in the table ? 3.5% 5% $808 $966 $ 1079 6% A. $110,880 B. $6,300 C. $180,000 D. $ 290,880
Answer:
To calculate the amount of money spent in interest alone over the course of a 30-year mortgage, we can use the formula:
Total Interest = (Monthly Payment x Number of Payments) - Principal
For a 3.5% 30-year mortgage with a principal of $180,000, the monthly payment can be calculated using the formula:
Monthly Payment = (Principal x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
where Monthly Interest Rate = Annual Interest Rate / 12, and Number of Payments = 30 years x 12 months per year = 360.
Plugging in the values, we get:
Monthly Payment = (180,000 x 0.0035) / (1 - (1 + 0.0035)^(-360)) = $808.28
Using this monthly payment, we can calculate the total interest over the 30-year period:
Total Interest = ($808.28 x 360) - $180,000 = $101,020.80
Therefore, the correct answer is A. $110,880 (which is not one of the options given).
A boat travels a straight route from the marina to the beach. The marina is located at point (0,0) on a coordinate plane, where each unit represents 1 mile. The beach is 3. 5 miles east and 4 miles south from the marina. Use the positive y-axis as north. What is the distance the boat travels to get to the beach? Round your answer to the nearest tenth. *
The distance the boat travels to get to the beach is approximately 5.0 miles.
To see why, we can draw a right triangle on the coordinate plane, with one leg along the x-axis (going 3.5 miles east) and the other leg along the y-axis (going 4 miles south). The hypotenuse of this triangle is the straight distance from the marina to the beach, which is the distance the boat travels.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = (3.5)^2 + (4)^2
c^2 = 12.25 + 16
c^2 = 28.25
c ≈ 5.0
Therefore, the distance the boat travels to get to the beach is approximately 5.0 miles.
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On a standard dice, the sum of the numbers of dots on opposite faces is always 7. Four standard dice are glued together, as shown. What is the minimum number of dots that could lie on the whole surface?
The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.
This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.
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Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of
12
1212 draws, Romain didn't get picked even once.
Let's test the hypothesis that each brother has an equal chance of
1
3
3
1
start fraction, 1, divided by, 3, end fraction of getting picked in each draw versus the alternative that Romain's probability is lower.
Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of
12
1212 times? Round your answer, if necessary, to the nearest tenth of a percent.
Based on the observed outcome, it is therefore very or highly unlikely that Romain's probability is equal to that of the other brothers, and thus it is possible that Romain is cheating.
What is the probability?Beneath the assumption that each brother has an break even with chance of getting picked in each draw, the likelihood of Romain not getting picked indeed once out of 12 times is:
P(Romain not picked) = (2/3)¹²
= 0.0077
This is one that is less than 1%, which suggests that the observed result is made up of a likelihood less than 1% beneath the given speculation. Therefore, we need to reject the hypothesis that each brother has an equal chance of getting picked in all of the draw.
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See text below
Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of 12 draws, Romain didn't get picked even once. 1 Let's test the hypothesis that each brother has an equal chance of of getting picked in each draw versus 3 the alternative that Romain's probability is lower. Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of 12 times? Round your answer, if necessary, to the nearest tenth of a percent. Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis? Choose 1 answer: We cannot reject the hypothesis. B We should reject the hypothesis.
please help find uv 10 points like ill actually do anything for someone to respond fast please!! im bad at math
Answer:
0.8660
Step-by-step explanation:
sin24=opposite ÷hypotenus
sin24=opposite ÷5
cross multiply
sin24x5=opposite
sin24=0.4067x5
opposite =0.8660
b) In a certain group of 200 persons, 110 can speak Nepali, 85 can speak Maithili and 60 can speak both the languages. Find, (i) how many of them can talk in either of these languages? (ii) how many of them can talk in neither of these languages?
Answer:
(i) 135, (ii) 65-----------------------
Given:
Total number in the group - 200 persons,Nepali speakers - 110,Maithili speakers - 85,Both - 60.(i) We know 60 out of 110 can speak both languages, so as 60 out of 85. The number 60 is counted twice if we add them together.
Find the number of those speak either language:
Either = sum of each - bothEither = 110 + 85 - 60 = 135(ii) Find the number of thise who can talk neither of these languages:
Neither = total - eitherNeither = 200 - 135 = 65Last year, the revenue for medical equipment companies had a mean of 70 million dollars with a standard deviation of 13 million. Find the percentage of companies with revenue between 50 million and 90 million dollars. Assume that the distribution is normal. Round your answer to the nearest hundredth
The percentage of companies with revenue between 50 million and 90 million dollar is: 87.6%
How to find the percentage from z-scores?The formula for the z-score in this type of distribution is:
z = (x' - μ)/σ
where:
x' is sample mean
μ is population mean
σ is standard deviation
We are given:
μ = 70 million dollars
σ = 13 million dollars
Thus:
When x' = 50 million dollars, we have:
z = (50 - 70)/13
z = -1.54
When x' = 90 million dollars, we have:
z = (90 - 70)/13
z = 1.54
Using probability between two z-scores calculator, we have:
z = 0.87644 = 87.6%
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Select the correct answer from each drop-down menu. car model brake failure in new car a 0.0065% b 0.0037% c 0.0108% d 0.0029% e 0.0145% total 0.0048% the table gives the probabilities that new cars of different models will have brake failure. the car model that is least likely to have a brake failure is model , and the probability of brake failure for this model is %.
The car model that is least likely to have a brake failure is model d, and the probability of brake failure for this model is 0.0029%.
The given table provides the probabilities of brake failure for different car models. We need to identify the car model that has the lowest probability of brake failure and the corresponding probability.
From the table, we can see that the probability of brake failure is the lowest for model d, which is 0.0029%. To find this, we simply need to compare the probabilities given in the table and identify the smallest one.
It's worth noting that the total probability of brake failure across all car models is 0.0048%, which means that the probability of brake failure for any individual car model is quite low.
To express this in a more tangible way, we could say that out of 1000 new cars of model d, we can expect only about 2 or 3 to have brake failure. The low probabilities of brake failure suggest that new cars in general are quite safe and reliable when it comes to braking performance.
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i cant do math no more
Answer:
(1, 4)
Don't worry, I feel the same way sometimes, :)
Please give me Brainliest :)Step-by-step explanation:
Substitute the bottom equation into the top.
If y=3x+1, than the first y will equal 3x+1.
3x+1 = x+3
Subtract 1 from 3
3x = x+2
Subtract x from 3x.
2x=2
Divide everything by 2.
x=1
Now substitute it in the equation.
1. y=1 + 3
y=4
2. y= 3(1) + 1
y=3+1
y=4
(1, 4)
Evaluate the definite integral:
∫(e^z) + 8/ (e^z+8z)^2
The definite integral
[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
To evaluate this definite integral, we need to find the antiderivative of the integrand and evaluate it at the limits of
integration.
Let's start by using u-substitution:
Let [tex]u = e^z+8z[/tex]
Then [tex]du/dz = e^z+8[/tex]
And [tex]dz = 1/e^z+8 du[/tex]
Substituting this into the integral, we get:
[tex]∫(e^z) + 8/ (e^z+8z)^2 dz[/tex]
= [tex]∫(1/u^2)(e^z+8)^2 du[/tex]
= [tex]∫(1/u^2)(e^(2z)+16e^z+64) du[/tex]
= [tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
Now we need to evaluate this antiderivative at the limits of integration.
Let's assume the limits are a and b:
= [tex][-e^(2b)/(e^b+8b) + 16e^b/(e^b+8b) - 64ln(e^b+8b)/(e^b+8b)] - [-e^(2a)/(e^a+8a) + 16e^a/(e^a+8a) - 64ln(e^a+8a)/(e^a+8a)][/tex]
Simplifying this expression is not easy, but it can be done with some algebraic manipulation.
Therefore, The definite integral
[tex]-e^(2z)/u + 16e^z/u - 64ln(u)/u + C[/tex]
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Annette drives her car 115 miles and has an average of a certain speed. If the average speed had been 8mph more, she could have traveled 138 miles in the same length of time. What was her average speed?
Annette's average speed was 40 mph if Annette drives her car 115 miles and has an average of a certain speed.
What is Average speed ?
Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of the overall speed of an object or person over a certain period of time.
Let's call Annette's original average speed "x". We can use the formula:
distance = speed x time
to set up two equations based on the given information.
For the first part of the trip:
115 = x * t1 (where t1 is the time it took Annette to travel 115 miles at speed x)
For the second part of the trip:
138 = (x + 8) * t2 (where t2 is the time it would have taken Annette to travel 138 miles at a speed of x + 8)
Since Annette traveled the same amount of time for both parts of the trip, we can set t1 equal to t2:
t1 = t2
We can solve for t1 in the first equation:
t1 = 115 : x
And we can solve for t2 in the second equation:
t2 = 138 : (x + 8)
Since t1 = t2, we can set the two expressions for t equal to each other:
115 : x = 138 : (x + 8)
Now we can solve for x:
115(x + 8) = 138x
115x + 920 = 138x
920 = 23x
x = 40
Therefore, Annette's average speed was 40 mph.
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Unit test unit test review active 11 12 13 a computer company wants to determine the proportion of defective computer chips from a day's production. a quality control specialist takes a random sample of 100 chips from the day's production and determines that there are 12 defective chips. assuming all conditions are met he constructs a 95% confidence interva for the true proportion of defective chips from a day's production. what are the calculations for this interval? o 12 +1.65 12(1 - 12) 100 o 12 +1.96 12(1 – 12) 100 o 0.12 +1.65, 0.12(1 – 0.12) 100 0.12 +1.96 0.12(1– 0.12) 100
The 95% confidence interval for the true proportion of defective chips is between 0.043 and 0.197.
To calculate the 95% confidence interval for the true proportion of defective computer chips, the quality control specialist would use the formula:
proportion +/- z ×√(proportion x (1-proportion)/sample size)
In this case, the proportion of defective chips is 12/100 or 0.12. The sample size is 100. To find the value of z for a 95% confidence level, we look at a standard normal distribution table or use a calculator and find that it is 1.96.
So the calculation for the confidence interval would be:
0.12 +/- 1.96 × √(0.12 × (1-0.12)/100)
Simplifying this gives us:
0.12 +/- 0.077
This means that if we repeated this sampling process many times, we would expect the true proportion of defective chips to fall within this interval 95% of the time.
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Create a story context for the following expressions ( 5 1/4 - 2 1/8) divided by 4 and 4 x ( 4. 8/0. 8)
To create a story context for the given expressions, which are (5 1/4 - 2 1/8) divided by 4 and 4 x (4.8/0.8).
Imagine there is a fruit store where you have to prepare fruit baskets for a local charity event. The first expression (5 1/4 - 2 1/8) divided by 4 can be a story about the number of apples to be distributed equally among four baskets.
You initially have 5 1/4 dozen apples, but you realize that 2 1/8 dozen of them are not suitable for the baskets.
To find out how many dozens of apples should be put into each basket, you need to subtract the unsuitable apples and divide the result by 4:
(5 1/4 - 2 1/8) / 4
Now, let's move on to the second expression, 4 x (4.8/0.8). This can be a story about the number of oranges you need to purchase for the fruit baskets. You already have 4.8 dozen oranges, but you need to add more to reach the desired ratio of oranges to apples.
Your friend suggests that for every 0.8 dozen oranges you currently have, you should add 4 more dozen oranges. To find out how many dozens of oranges you need to buy, you can use this formula:
4 x (4.8/0.8)
By creating these story contexts, you can use the given expressions to solve real-life problems, such as distributing fruits among charity baskets.
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