Any angle that shares a common vertex with <4 and whose measure adds up to 180 degrees is supplementary to <4.
To determine which angles are supplementary to <4, we first need to understand the concept of supplementary angles. Supplementary angles are pairs of angles whose sum is 180 degrees. In other words, if we have two angles, and their measures add up to 180 degrees, then they are supplementary to each other.
To find angles that are supplementary to <4, we need to look for other angles that add up to 180 degrees with <4. We can do this by examining the angles that intersect <4 or that share a common vertex with <4.
One way to identify such angles is to draw a diagram of the situation. Suppose we have a line with <4 marked on it. We can then draw another line that intersects the first line at <4, creating two angles on either side of <4. Let's call these angles A and B, where A is adjacent to <4 and B is adjacent to the other side of <4.
If we can find angle A or angle B, we can determine the other angle that is supplementary to <4. We know that A and B add up to 180 degrees, so if we find one of these angles, we can subtract it from 180 degrees to find the other angle.
To summarize, to find angles that are supplementary to <4, we can:
Draw a diagram of the situation, with <4 marked on a line and another line intersecting it at <4.
Identify the adjacent angles on either side of <4.
Label these angles A and B.
Determine the measure of either A or B.
Subtract the measure of the known angle from 180 degrees to find the measure of the other angle.
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a bowl contains 7 7 red balls and 8 8 blue balls. a woman selects 4 balls at random from the bowl. how many different selections are possible if at least 3 balls must be blue?
If at least 3 of 4 balls must be blue then the number of possible selections = 462
Let us assume that m represents the number of red balls in a bowl.
So, m = 7
And n represents the number of blue balls in a bowl.
So, n = 8
A woman selects 4 balls at random from the bowl.
We need to find the number of possible selections if at least 3 balls must be blue.
The first combination would be 4 blue balls + 0 red balls
And the second combination would be 3 blue balls + 1 red ball
so, using combination formula the number of possible selecctions:
(⁸C₄ × ⁷C₀) + (⁸C₃ × ⁷C₁)
= (70 × 1) +(56 × 7)
= 462
Therefore, the number of possible selections: 462
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Consider the inequality −2.45x+9.3>2.44
What is the answer?
Answer: the answer is x < 2.80
Step-by-step explanation: can i get brainliest pls
What is the y-coordinate of the solution of the system?
3x−y=22
y= x−14
The y-coordinate of the solution of the system is -10.
What is the linear equation?
A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:
y = mx + b
To find the y-coordinate of the solution of the system:
3x - y = 22 ...(1)
y = x - 14 ...(2)
We can substitute the expression for y from equation (2) into equation (1) to eliminate y:
3x - (x - 14) = 22
Simplifying this equation:
3x - x + 14 = 22
2x + 14 = 22
Subtracting 14 from both sides:
2x = 8
Dividing both sides by 2:
x = 4
Now we can substitute x = 4 into equation (2) to find the corresponding value of y:
y = x - 14
y = 4 - 14
y = -10
Therefore, the y-coordinate of the solution of the system is -10.
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I need to find the answer
The missing length a of the shaded region is calculated to be 12.8 miles using the area and the height of the triangle.
How to evaluate for the the length "a" with the area the triangleFor any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;
Area of triangle = 1/2 × base × height
Given the area as 117.76 mi², we have the base of the triangle to be "a" and the height as 18.4 miles, so we solve for the length "a" as follows:
117.76 mi² = 1/2 × a × 18.4 miles
by cross multiplication;
a = (117.76 mi² × 2)/18.4 mi
a = 235.52 mi²/18.4 mi
a = 12.8 miles
Therefore, the missing length "a" of the shaded region is calculated to be 12.8 miles using the area and the height of the triangle.
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Will give you brainliest answer
Enlarge shape A by scale factor 2 with centre of enlargement (-3, -5).
What are the coordinates of the vertices of the image?
The coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).
What do you mean by scale factor?In mathematics and geometry, a scale factor is a numerical factor that describes how much a figure or object has been enlarged or reduced in size. It is the ratio of any two corresponding lengths in the original figure and the scaled figure.
What is vertices?In geometry, a vertex (plural vertices) is a point where two or more line segments, lines, or rays meet to form an angle. In other words, a vertex is a point where two or more edges of a polygon, polyhedron, or any other geometrical shape meet.
In the given question,
To enlarge the shape A by a scale factor of 2 with a centre of enlargement of (-3, -5), we need to:
Translate the centre of enlargement to the origin (0, 0) by adding 3 to the x-coordinates and 5 to the y-coordinates of all points.
Apply the enlargement by multiplying the coordinates of each point by 2.
Translate the centre of enlargement back to its original position by subtracting 3 from the x-coordinates and 5 from the y-coordinates of all points.
So, the coordinates of the vertices of the enlarged shape A are:
Vertex 1:
Original coordinates: (0, -4)
Translate to origin: (3, 1)
Enlarge: (6, 2)
Translate back: (3, -3)
Final coordinates: (3, -3)
Vertex 2:
Original coordinates: (2, -4)
Translate to origin: (5, 1)
Enlarge: (10, 2)
Translate back: (7, -3)
Final coordinates: (7, -3)
Vertex 3:
Original coordinates: (1, -6)
Translate to origin: (4, -1)
Enlarge: (8, -2)
Translate back: (1, -6)
Final coordinates: (1, -6)
Vertex 4:
Original coordinates: (0, -6)
Translate to origin: (3, -1)
Enlarge: (6, -2)
Translate back: (0, -6)
Final coordinates: (0, -6)
Therefore, the coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).
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Solve each system of inequalities[tex]\left \{ {3x-10\ \textgreater \ 0} \atop {2x\ \textgreater \ 0}} \right.[/tex]
The solution to the system of inequalities is:
x > 10/3 and x > 0
What is inequality?
In mathematics, an inequality is a statement that shows the relationship between two values, expressions or quantities using inequality symbols such as <, >, ≤, or ≥. Inequalities convey that one value is not the same as the other, but rather is either greater than or less than the other value.
The system of inequalities is:
3x-10 > 0
2x > 0
To solve this system, we need to find the values of x that satisfy both inequalities at the same time.
From the first inequality, we can isolate x by adding 10 to both sides:
3x - 10 + 10 > 0 + 10
3x > 10
Then, we can divide both sides by 3:
x > 10/3
So we know that x is greater than 10/3.
From the second inequality, we know that x must be greater than 0.
Therefore, the solution to the system of inequalities is:
x > 10/3 and x > 0
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SOMEONE HELP ME WITH QUESTION 29 PLEASE
Answer:
Step-by-step explanation:
im sorry im not sure
17 a 15 c to b
For geometry: sinx=12/15
The value of the angle x using trigonometric ratio is: x = 53.13°
How to Solve Trigonometric ratios?Some of the trigonometric ratios in mathematics based on a right angle triangle are:
Sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Similarly:
cot x = 1/tan x
sec x = 1/cos x
cosec x = 1/sin x
We are given that:
sin x = 12/15
Thus:
x = sin⁻¹(12/15)
x = 53.13°
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we want to obtain a sample to estimate a population mean. based on previous evidence, researchers believe the population standard deviation is approximately . we would like to be 98% confident that the estimate is within 0.1 of the true population mean. how large of a sample size is required?
A sample size of 541 is required to be 98% confident that the estimate is within 0.1 of the true population mean.
To calculate the required sample size for a given population mean, standard deviation, and confidence level, you can use the following equation:
n = (z * σ / E)^2
where:
n = sample size
z = z-score for the desired level of confidence (98% = 2.33)
σ = population standard deviation (we assume σ = 1)
E = desired margin of error (0.1)
Therefore,
Sample size = (23.3 * 1)^2
Sample size = 540.89
Rounding up to the nearest whole number, we get a sample size of n = 541
Therefore, a sample size of 541 is required to be 98% confident that the estimate is within 0.1 of the true population mean.
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please show with working out
According to the information, each of the cases of equations has a different solution depending on the value that is given to the unknown or x.
How to explain each equation case?Let p = √(x - 3), then the equation becomes p^2 - 2p - 3 = 0. This is a quadratic equation that can be factored as (p - 3)(p + 1) = 0. Therefore, p = 3 or p = -1. Since p = √(x - 3) and we want real solutions, we have two cases:
Case 1: p = √(x - 3) = 3. Squaring both sides, we get x - 3 = 9, so x = 12.
Case 2: p = √(x - 3) = -1. This case gives no real solution, since the square root of a real number cannot be negative. Therefore, the only real solution is x = 12.
Let p = √(x - 5), then the equation becomes p^2 - 4p - 12 = 0. This is a quadratic equation that can be factored as (p - 6)(p + 2) = 0. Therefore, p = 6 or p = -2. Since p = √(x - 5) and we want a real solution, we have only one case:
Case 1: p = √(x - 5) = 6. Squaring both sides, we get x - 5 = 36, so x = 41. However, we need to check that this solution is valid. Since p = √(x - 5) = 6 > 0, we have x - 5 > 0, so x > 5. Therefore, the only real solution is x = 41.
Let p = 3^x, then the equation becomes p^2 + 11p - 12 = 0. This is a quadratic equation that can be factored as (p + 12)(p - 1) = 0. Therefore, p = -12 or p = 1. Since p = 3^x and we want a real solution, we have only one case:
Case 1: p = 3^x = 1. This gives x = 0. However, we need to check that this solution is valid. Since 3^x > 0 for all x, we have x > -∞. Therefore, the only real solution is x = 0.
There is only one real solution because the function 9^x + (11x3^x) - 12 is continuous and strictly increasing for all x, which means that it can cross the x-axis at most once. Since we have found one real solution, there cannot be any others.
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a school gives an entry exam for admission. suppose the score of this exam follows a normal distribution n(400, 60). this year, the school decides to admit students who score in the top 30%. suppose a student scored 428 on the test. will the student be admitted? explain your reasoning.
The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:
z = (x - μ) / σ
where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).
Plugging in the values, we get:
z = (428 - 400) / 60 = 0.467
Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.
Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.
Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.
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Winter coats are on
clearance at 40% off. If
the regular price is
$79, what is the sale
price?
last year the enrollment for drama club was 103 students. this year the enrollment is 87 students. what is the percent of change? round to the nearest tenth if necessary
The percent of change is approximately -15.5% (rounded to the nearest tenth).
To find the percent change between last year's enrollment and this year's enrollment, we can use the following formula
percent change = [(new value - old value) / old value] x 100%
where "new value" is the enrollment for this year, and "old value" is the enrollment for last year
Plugging in the numbers, we get:
percent change = [(87 - 103) / 103] x 100%
percent change = (-16 / 103) x 100%
percent change = -15.53%
Therefore, the percent of change is approximately -15.5% . This means that there was a decrease of about 15.5% in the enrollment for the drama club from last year to this year.
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HI! Please answer!!
Teacher said K=144, but I'm not sure how to solve from here. Please explain!
Answer:
144
Step-by-step explanation:
The angles on the line next to the big c must add up to 180, and 180-58=122, so the space next to the 58 must be 122
The interior angles of a polygon can be calculated with 180(n-2) where n is the sides, so a pentagon has 540 degrees of interior angles
540 - 96 - 88 - 90 - 122 = 144
Answer:
Step-by-step explanation:
90+96+88+180-58=540-k
k=540-396
k = 144
The pentagons JKLMN and PQRST are similar.
Find the length x of RS.
The length of the segment SR for the given pentagons is 9 units.
What is a pentagon?A polygon having 5 sides and 5 angles is called a pentagon. The words "pentagon" (which implies five angles) are formed up of two other terms, namely Penta and Gonia. End to end, the sides of a pentagon come together to form a shape. Hence, there are 5 sides in a pentagon.
The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangles. There are several sorts of pentagon forms, including regular and irregular pentagons as well as convex and concave pentagons, depending on the sides, angles, and vertices.
We know that, for similar figures the length of the ratios of their corresponding segments are equal.
Thus,
NM/TS = ML/SR
4/7.2 = 5/x
Using cross multiplication we have:
4x = 5(7.2)
4x = 36
x = 9
Hence, the value of the segment SR for the given pentagons is 9 units.
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A student's course grades and their corresponding weights are given in the table below.
What is the minimum grade needed on the final exam to earn an overall grade of 85% in the class?
Answer:
84%
Step-by-step explanation:
This is a pretty normal grading weight system. Think of a perfect score being 100. The grade earned may be a percent but think of it as 100/100.
So we can set up an equation to represent the missing grade earned in the "Final Exam" row.
0.4(x) + 0.3(80) + 0.2(90) + 0.1(100) = 85
The x represents the percent grade earned for the final exam, in order to achieve an 85% total.
Evalulate and solve the above equation for x to find its value.
0.4x + 24 + 18 + 10 = 85
0.4x = 33
x = 33/0.4
x = 82.5
The question asks for the minimum grade to achieve 85% total. This means that whatever choice we choice must be the least choice that is also greater than 82.5%. That answer is B, 84%.
Create different examples of triangles. ∠c is represented by the purple section on line p. when manglec increases, what happens to the middle section on line p? when manglec decreases, what happens to the middle section on line p?
As the angle ∠c in a triangle increases, the length of the middle section on line p decreases.
Conversely, as the angle ∠c decreases, the length of the middle section on line p increases. This is because the middle section on line p is a portion of the altitude of the triangle, which is the perpendicular segment from the vertex of the angle to the opposite side. As the angle ∠c increases, the altitude of the triangle gets shorter, resulting in a shorter middle section on line p. Similarly, as the angle ∠c decreases, the altitude of the triangle gets longer, resulting in a longer middle section on line p. Examples of triangles can include equilateral, isosceles, scalene, acute, right, and obtuse triangles, among others.
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Please answer this question
Answer:
a = 12
Step-by-step explanation:
Pythagorean theorem states that the the square value of hypotenuse is equal to the sum of the squares of two legs.
Now, according to this statement:
15² = 9² + a²
Calculate the square values on both sides225 = 81 + a²
Subtract 81 from both sides144 = a²
Find the root of both sides12 = a
April has a sheet of paper that is 4 feet long. She cuts the length of paper into halves and then cuts the length of each of these 1 2 pieces into thirds. How many pieces does she have? How many inches long is each piece? April has pieces. Each piece is inches long
April has six pieces of paper, each measuring 8 inches in length which can be calculated using fractions.
April starts with a sheet of paper that is 4 feet long, which is equivalent to 48 inches since there are 12 inches in a foot. She then cuts the length of paper into halves, which gives her two pieces, each of them 24 inches long.
Next, she cuts the length of each of these 24-inch pieces into thirds, which gives her six pieces in total. Each of these pieces is 8 inches long, since 24 divided by 3 equals 8. Therefore, April has six pieces of paper, and each piece is 8 inches long.
It's worth noting that April's process of cutting the paper into halves and then into thirds is an example of how fractions can be used to divide a whole into equal parts. In this case, cutting the paper into halves means dividing it into two equal parts, and cutting each of these halves into thirds means dividing each half into three equal parts.
Overall, April has six pieces of paper, each measuring 8 inches in length. These pieces could be useful for various purposes, such as for creating small origami figures, for making decorations, or for use in a crafting project.
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A collector's edition
comic was originally
purchased for $15.
Its value increases by
10% each year.
Growth/decay factors
Value when t=8
The value of the collector's edition comic when t=8 is approximately $32.77.
Value calculationThe growth factor for the value of the collector's edition comic is 1.10 per year (10% increase). Therefore, after t years, the value V of the comic can be calculated using the formula:
V = 15 × 1.10^t
To find the value when t=8, we can substitute t=8 into the formula:
V = 15 × 1.10^8
V ≈ $32.77
Therefore, the value of the collector's edition comic when t=8 is approximately $32.77.
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Brown paint can be made by mixing green and red paint in a 3 : 4 ratio. What fraction of the brown paint is green paint? Give your answer in its simplest form.
Answer:
3/7
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
Let’s assume that we have 7 units of paint in total. Then, we have 3 units of green paint and 4 units of red paint. When we mix them together, we get 7 units of brown paint.
Because 3 out of the 7 units of paint are green, the fraction of the brown paint that is green paint is [tex]\frac{3}{7}[/tex].
Therefore, [tex]\frac{3}{7}[/tex] of the brown paint is green.
In analyzing hits by certain bombs in a war, an area was partitioned into 573 regions, each with an area of 0.55 km2. A total of 515 bombs hit the combined area of 573 regions. Assume that we want to find the probability that a randomly selected region had exactly three hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
[tex]P(X=x)[/tex] = (e^-μ * μ^x) / x!
Where, x is the number of successes
e = 2.71828 is the Euler number, μ is the mean in the given interval.
Given that, total of 515 bombs hit the combined area of 573 regions.
The mean hits per region is;
μ = 515/573 = 0.898
We want to find the probability that a randomly selected region had exactly three hits, that is P(X = 3)
[tex]P(X=x)[/tex] = (e^(-μ) * μ^x) / x!
[tex]P(X=3)[/tex] = (e^(-0.898) * (0.898)^3) / 3!
[tex]P(X=3)[/tex] = 0.04915
Therefore, 4.915% probability that randomly selected region had exactly three hits.
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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%
What is a probability?A subfield of statistics known as probability studies random events and their odds of happening. It is used to predict the future and determine the likelihood of events by dividing the number of favorable outcomes by the total number of possible outcomes.
The following formula gives the probability that X indicates the number of successes of a random variable in a Poisson distribution:
[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]
Where, x is the number of successes
e = 2.71828 is the Euler number, μ is the mean in the given interval.
As a result, 573 regions were struck by a total of 515 bombs.
The mean hits per region is;
[tex]\mu=\frac{515}{573}[/tex]
[tex]\mu= 0.898[/tex]
P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.
[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]
[tex]P(X=3)=\frac{e^{-0.898}\times\ \(0.898^3 }{3!}[/tex]
p(X=3)= 0.04915
P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.
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√[{1.794*0.038}÷124.3]
Answer:
0.0234189518
Step-by-step explanation:
algebra
pls help asap
The expression [tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex] when simplified to the simplest form is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]
How to simplify the expressionFrom the question, we have the following expression to be used in our computation:
[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]
Simplifying the numerator, we get
[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]
Simplifying the denominator, we get
[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y}/x^{y+x}}}[/tex]
Applying the following fraction rule:
(a/b)/(c/d) = (a * d)/(b * c)
So, we have
[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x} \cdot x^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y} \cdot y^{x+y}}}[/tex]
Cancel the common factors
So, we have
[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{x^{x+y}}{y^{x+y}}}[/tex]
Hence, the expression when simplified is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]
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A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,000 hours and a standard deviation of 1,000 hours. a) What is the probability that a randomly chosen light bulb lasts more than 10,500 hours? # (please round to four decina!places)
The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668 (rounded to four decimal places).
The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668(rounded to four decimal places).Here's how to calculate it:Given data mean μ = 9,000 and standard deviation σ = 1,000.To calculate the probability that a random light bulb lasts more than 10,500 hours, convert the problem to a standard normal distribution.
z = (10,500 - μ)/σ = (10,500 - 9,000)/1000 = 1.50
Here's the standard normal distribution curve with the shaded area representing the probability required: Standard normal distribution curve with the shaded area
Now, the area under the curve to the right of z = 1.5 is the probability that a randomly chosen light bulb will last more than 10,500 hours.
Using the Z table, we can look up the value corresponding to a z-score of 1.5. The table gives us a value of 0.9332.Now, the area to the left of z = 1.5 is 1 - 0.9332 = 0.0668, which is the probability that a randomly chosen light bulb lasts more than 10,500 hours, rounded to four decimal places.
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Can anyone help me with this, please?
Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1.
How to solve the problemIt should be noted that to determine which option is better in terms of decreasing total litres used, we need to calculate the total amount of fuel consumed in each case and compare them.
Option 1: For every 100 km traveled, the first vehicle consumes 23.5 litres of fuel.
For the same distance, the second vehicle consumes 11.7 litres of fuel.
Thus, the second vehicle would save 23.5 - 11.7 = 11.8 litres of fuel per 100 km traveled compared to the first vehicle.
So, the percentage reduction in fuel consumption would be:
(11.8 / 23.5) x 100 = 50.21%.
Option 2: For every 100 km traveled, the first vehicle consumes 11.7 litres of fuel.
For the same distance, the second vehicle consumes 4.7 litres of fuel.
Thus, the second vehicle would save 11.7 - 4.7 = 7 litres of fuel per 100 km traveled compared to the first vehicle.
So, the percentage reduction in fuel consumption would be:
(7 / 11.7) x 100 = 59.83%.
Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1. Therefore, replacing an 11.7 L/100 km vehicle with a 4.7 L/100 km vehicle is better in terms of decreasing the total litres used.
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what is the value of u?
Answer:26
Step-by-step explanation:
Solve for x. Type your answer as a number
The value of x is 8
What is triangle theorem?The theorems of triangle are the rules that governs solving mathematical problems. Part of this theorem is a theorem that states that: The line joining the midpoint of the two sides of a triangle is parallel to the base.
Therefore ;
If we represent a side by y, using similar triangle,
y/2y = x+8/(3x+8)
1/2 = x+8/(3x+8)
3x +8 = 2(x+8)
3x +8 = 2x +16
collect like terms
3x-2x = 16-8
x = 8
therefore the value of x is 8
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Chase throws a football in the air. The height of the football t seconds after it is thrown can be modeled by h(t)=-16t(t-2)^2+40. What is the maximum height of the ball? When does it reach this height?