There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
How to find how many ways can these students sit in their twelve seats if they must be grouped by majorThere are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.
We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.
For the chemistry group, there are 3 students who can be seated in any order.
For the business group, there are 2 students who can be seated in any order.
For the political science group, there are 3 students who can be seated in any order.
Finally, for the journalism group, there are 4 students who can be seated in any order.
Therefore, the total number of arrangements for the 12 students is:
3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728
Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
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Suppose you are an engineer tasked to design a multi-storey car park. The height restriction for vehicles entering the car park is calculated to be 2.51 m. A sign indicating the maximum height, correct to the nearest metre, is to be placed at the entrance. What should the maximum height be shown as? Explain your answer.
The nearest whole number when rounding to the nearest metre forces us to choose 3, which is the case here as 2.51 is closer to 3 than it is to 2.
How are significant figures employed in scientific measurements? What are they?The digits in a numerical value known as significant figures, sometimes known as significant digits, are those that show how precisely the measurement was made. The degree of precision of the measuring device used to perform the measurement determines the number of significant figures in the measurement.
We must round the height restriction to the closest metre in order to show it on the sign because it is specified as 2.51 metres.
We look at the digit in the tenths place, which is 5, to round to the closest metre. We round up the number to the next one since 5 is more than or equal to 5, which is 1. Thus, 3 m should be listed as the maximum height.
This is due to the fact that picking the nearest whole number when rounding to the nearest metre forces us to choose 3, which is the case here as 2.51 is closer to 3 than it is to 2.
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The question is in the image below
I am stuck on Part 2, and where it says 2 that's all I got
Grade 8
The equation has no solution as 10 + x ≠ 5 + x
When the value of x is 2, the equation also have no solution as 12 ≠ 7
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, factors and coefficients.
These algebraic expressions are expressions that are identified with arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have;
6 + x + 4 = 2 + x + 3
collect the like terms, we have
10 + x = 5 + x
But we know that 5 is not equal to x and thus, the equation has no solution
Now, let's substitute the value of x as 2, we have;
10 + 2 = 5 + 2
This gives;
12 = 7
This is not true and thus, the equation has no solution
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The cuboid below is made of silver and has a mass of 416 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p. Question attached
Answer:
3.5g/cm³ to 1d.p
Step-by-step explanation:
Density = mass/volume
Mass = 416g
Volume = 12 x 5 x 2 (length x width x height)
Volume 120cm³
Density = 416g/ 120cm³
Denaity = 3.47g/cm³
3. A wife thought that there seemed three reasons for the baby to cry; hungry, sleepy, or wet on the bottom (diaper!). The husband became curious about the probability of changing the diaper when his baby cries. The wife also told the husband that the probability is 0.3, but the husband felt that he had changed the baby's diaper half the times when the baby cries, i.e., 0.5. Thus, the husband decided to perform hypothesis testing to test his guess. Specifically, he record 1 if it is for a diaper change and 0 otherwise whenever the baby cries, assuming that these binary data X i 's are i.i.d. Bernoulli (θ) r.v.s., where θ represents the probability that his baby cries for a diaper. The husband records these data for 20 days (n=20). (a) (3 points) Set up the null and alternative hypotheses from the husband's perspective. (b) ( 3 points) Find the (approximate) likelihood ratio test rejection region. Please leave the decision boundary in an undetermined form, such as 'something >c j ' or 'something
the husband can reject the null hypothesis and conclude that his guess about the probability of changing the diaper when the baby cries is statistically significant at the 5% level if the LR exceeds 3.84.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 (indicating impossibility) to 1 (indicating certainty).
a) The null hypothesis (H0) from the husband's perspective is that the true probability of the baby crying for a diaper change is equal to the wife's claim, i.e., θ = 0.3. The alternative hypothesis (Ha) is that the true probability is different from the wife's claim, i.e., θ ≠ 0.3.
(b) To perform a likelihood ratio test, we first calculate the maximum likelihood estimates of the parameters under the null and alternative hypotheses.
Next, we calculate the likelihood ratio statistic:
LR = (L(0.5)/L(0.3))^20
where L(0.5) and L(0.3) are the likelihoods of the data under the alternative and null hypotheses, respectively.
Simplifying, we get:
LR = (0.5/0.3)^20 = 4.19
To find the rejection region, we compare the LR with the critical value of the chi-squared distribution with 1 degree of freedom at the desired significance level (α). Let's assume a significance level of α = 0.05.
The critical value for this test is approximately 3.84. Thus, the rejection region is:
LR > 3.84
Therefore, the husband can reject the null hypothesis and conclude that his guess about the probability of changing the diaper when the baby cries is statistically significant at the 5% level if the LR exceeds 3.84.
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a plane flying horizontally at an altitude of 1 mile and a speed of 580 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (round your answer to the nearest whole number.)
The rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station is 656 mi/h (rounded to the nearest whole number).
To solve this problem, we can use the equation
rate = distance/time.
We know the distance and the time, so we can calculate the rate:
rate = 5 mi/ 1 hour
= 5 mi/3600 sec
= 5/3600 mi/sec
= 0.00138889 mi/sec.
Multiplying this by 3600 to convert it to mi/h gives us 656 mi/h.
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In circle K with
m
∠
J
K
L
=
60
m∠JKL=60 and
J
K
=
17
JK=17 units find area of sector JKL. Round to the nearest hundredth.
Answer:
KL=43
Step-by-step explanation:
JKL=60, jk=17, KL=43
How do I get full marks on this question?
Therefore , the solution of the given problem of triangle comes out to be y + y√2 and y - y√2. are the two possible numbers for x.
A triangle is exactly what?If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Due to the similarity of the two triangles in the diagram, we can create an equation and solve for x using the ratios of respective sides.
Assuming that the line segment's length is x, we can construct the following equation:
=> (2x + y) / x = x / y
=> (2x + y) y = x²
=> 2xy + y² = x²
=> x² - 2xy - y² = 0
This quadratic equation in x has the coefficients a = 1, b = -2y, and c = -y2 in it. The quadratic algorithm yields:
=> x = [2y ± √((2y)² - 4(1)(-y²))] / 2(1)
=> x = [2y ± √(4y² + 4y²)] / 2
=> x = [y ± y√2]
Therefore, y + y√2 and y - y√2. are the two possible numbers for x.
The two triangles in the illustration are thought to be comparable.
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Measure the height of the tin in mm and write the real height in mm
Measurement is the act of comparing an object's properties to a standard quantity. It is crucial in determining an object's quantity.
How to measure the height of a tinFor instance, to measure the height of a tin, one must measure the vertical distance from the base to the top.
The measurement must be in millimeters, and a ruler is the most suitable tool.
To do this, place the ruler vertically with point 0 at the baseline of the tin, mark the point where the ruler coincides with the top, and read the height to the nearest millimeter.
To measure the height of a tin in millimeters, follow these steps:
Obtain a ruler that has millimeter markings.
Place the tin upright on a flat surface.
Position the ruler vertically with its zero point aligned with the base of the tin.
Carefully move the ruler up or down until it reaches the top edge of the tin.
Read the measurement value at the point where the ruler aligns with the top edge of the tin.
Record the height measurement in millimeters to the nearest whole number.
For example, if the measurement value is 65.5 millimeters, then the real height of the tin in millimeters is 66 millimeters (rounded to the nearest whole number).
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List the procedure to measure the height of a tin in mm and write the real height in mm
Which of the following rational functions has a horizontal asymptote at y = 2 and vertical asymptotes at x = 3 and x = –4?
a: y equals x squared over the quantity x squared plus x minus 12 end quantity
b: y equals x squared over the quantity x squared minus x minus 12 end quantity
c: y equals 2 times x squared over the quantity x squared plus x minus 12 end quantity
d: y equals 2 times x squared over the quantity x squared minus x minus 12 end quantity
Neither option (a) nor option (b) has a horizontal asymptote at y = 2, there is no correct answer to this question.
What is rational function?A rational function is a mathematical function that can be expressed as a ratio of two polynomial functions, where the denominator is not equal to zero.
To have vertical asymptotes at x = 3 and x = –4, the denominator of the rational function must have factors of (x – 3) and (x + 4), respectively.
Option (a) has a denominator of (x² + x – 12), which can be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Option (b) has a denominator of (x² – x – 12), which can also be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Therefore, the answer is either option (a) or option (b).
To determine which of these options has a horizontal asymptote at y = 2, we can perform long division or use the fact that the leading term of the rational function will determine the horizontal asymptote.
Dividing x² by (x² + x – 12), we get:
x² + x - 12 | x² + 0x + 0
- x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² + x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
Dividing x² by (x² – x – 12), we get:
x² - x - 12 | x² + 0x + 0
+ x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² - x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
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pls help with my Algebra 2
Answer: second graph,and upper curve is right answer .
Step-by-step explanation: just put X= 0,1,2,..
and you get Y. and those are the dots which you have to see that are on that graph.
Find m2).
K
2
J
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m2] =
Submit
The measure of angle J is 51.3 degrees (rounded to the nearest tenth).
We can use the Pythagorean theorem to find the length of the hypotenuse KJ of the right triangle KIJ. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
KJ² = KI² + IJ²
Substituting the given values, we get:
KJ² = 4² + 2²
KJ²= 20
Taking the square root of both sides, we get:
KJ = √20 = 2√5
Now, we can use the definition of cosine to find the measure of angle J
cos(J) = 2 / (2√5)
Simplifying the expression, we get:
cos(J) = √5 / 5
Taking the inverse cosine of both sides, we get:
J = cos⁽⁻¹⁾(√5 / 5)
We find that the inverse cosine of √5 / 5 is approximately 51.3 degrees. Therefore, the measure of angle J is 51.3 degrees (rounded to the nearest tenth).
What is Cosine of a right angled triangle?The cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse.
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Write an equation of the Line that passes thru (5,-2);and is perpendicular to y=5/3x -3
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{3}}x-3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{5}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{5} }}[/tex]
so we're really looking for the equation of a line whose slope is -3/5 and it passes through (5 , -2)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{5} \\\\\\ \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}{(-2)}=\stackrel{m}{- \cfrac{3}{5}}(x-\stackrel{x_1}{5}) \implies y +2= -\cfrac{3}{5} (x -5) \\\\\\ y+2=-\cfrac{3}{5}x+3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{5}x+1 \end{array}}[/tex]
Jamie is on her first day's work at a new furniture delivery job. Driving to her first delivery, she
encounters a parabolic tunnel. She is not sure that her van will fit through the tunnel.
This tunnel is 8 m wide at its base and 8 m tall at its highest point.
Unfortunately Jamie is late for the
delivery so hopes for the best and drives through the tunnel.
There are two lanes, but heavy oncoming traffic forces her to stay in her own lane (so that she cannot cross
the middle line.)
If Jamie’s van is 2.5 m wide and 5 m tall, will she make it?
(Or is her first day's work also going to be her last)?
From the problem, the minimum height of the tunnel that Jamie's van must be able to pass through is 12.5 m.
How to get the Height?We can approach this problem by determining the minimum width and height of the tunnel that Jamie's van must be able to pass through. If her van is able to fit through these minimum dimensions, then it should be able to pass through the entire tunnel.
Let's start with the width of the tunnel. Since Jamie cannot cross the middle line due to heavy oncoming traffic, her van must fit entirely within her own lane. Therefore, the width of the tunnel must be at least equal to the width of her van, which is 2.5 m.
Next, let's consider the height of the tunnel. At its highest point, the tunnel is 8 m tall. However, Jamie's van is 5 m tall. To pass through the tunnel, the van must fit under the lowest point of the tunnel that is at least 5 m above the ground. We can use the shape of the parabolic tunnel to determine the minimum height that Jamie's van can pass through.
The shape of a parabolic curve is given by the equation y = ax^2, where y is the height, x is the distance from the center of the curve, and a is a constant that determines the steepness of the curve. In this case, we can use the fact that the tunnel is 8 m wide at its base to determine the value of a.
At the center of the tunnel (x = 0), the height is 8 m. Therefore, we have:
8 = a(0)^2
a = 8
Substituting this value of a into the equation for the parabolic curve, we have:
y = 8x^2
To determine the minimum height that Jamie's van can pass through, we need to find the value of x that corresponds to the edge of her van. Since her van is 2.5 m wide, this corresponds to a distance of 1.25 m from the center of the lane.
Substituting x = 1.25 into the equation for the parabolic curve, we have:
y = 8(1.25)^2
y = 12.5
Therefore, the minimum height of the tunnel that Jamie's van must be able to pass through is 12.5 m.
Since the height of the tunnel is greater than the height of Jamie's van, she should be able to pass through without any problems. However, she should still exercise caution and be mindful of the height and width of her vehicle when driving through narrow spaces.
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I NEED ASAP
what’s the slope of the line
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The simpliest way to find a slope of a graph such like this is to find what we call the "rise" and "run"
Find two points on the graph that match with the grid in the background. Two points on this graph that can represent this example is (-3, 1) and (0, 2)
Start at the left-most point [-3, 1 in this case] and go up until you match the same y-axis as your second point. Then, go right until you meet said point. From (-3, 1) to (0, 2) you go up once, and then right four times. This results in the fraction 1/4
Can someone help me with this mixture problem
Answer:
25 pounds of cashews and 15 pounds of pistachios.
Step-by-step explanation:
Helping in the name of Jesus.
Answer:
15 pounds of pistachio and 25 pounds of cashews
Step-by-step explanation:
By the given information, we can make a system of equations: Pistachio + Cashew = 40
If we multiply the price of each to the weight, we get 10 cashews + 6 pistachio = 340 pounds. We can use this system of equations to find the amount of each nut.
he tree diagram below shows all of the possible outcomes for flipping three coins.
A tree diagram has outcomes (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).
What is the probability of one of the coins landing on tails and two of them landing on heads?
1/4
3/8
1/2
3/4
The correct answer is option (B) 3/8 for the probability based on given tree diagram.
The tree diagram shows all possible outcomes when flipping three coins. To find the probability of one coin landing on tails and two coins landing on heads, we need to find all the outcomes where this occurs.
From the tree diagram, we can see that there are three outcomes where one coin lands on tails and two coins land on heads: (H, H, T), (H, T, H), and (T, H, H).
Therefore, the probability of one coin landing on tails and two coins landing on heads is the sum of the probabilities of these three outcomes:
P(one tail, two heads) = P(H, H, T) + P(H, T, H) + P(T, H, H)
Using the multiplication rule of probability, we can see that each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.
Therefore, the probability of one coin landing on tails and two coins landing on heads is:
P(one tail, two heads) = 1/8 + 1/8 + 1/8 = 3/8
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Suruchi has $1.64 worth of change in the bottom of her purse If she reaches into her purse and randomly picks one of the coins, what is the probability Suruchi will pick a quarter?
Answer:
You need to know the total number of coins that was in her purse to answer this question.
A system of two linear equations has no solution. The first equation is -7x + y = 3. select the second equation that will make this system have no solution.
A. 3x+y=3
B. -7x+y=-10
C. 3x+y=-7
D. 4x+y=3
Answer:
It's B.
Step-by-step explanation:
To make the given system of linear equations have no solution, we need the second equation to be inconsistent with the first equation. This means that the two equations must be parallel lines, and they cannot intersect at any point.
We can see that the first equation -7x + y = 3 has a slope of 7, since it can be written in slope-intercept form as y = 7x + 3. Therefore, to create a parallel line with the same slope of 7, we can choose the second equation to be:
B. -7x + y = -10
This equation has the same slope of 7 as the first equation, but it intersects the y-axis at a different point (-10 instead of 3). Therefore, the two lines are parallel and do not intersect, so the system of equations has no solution
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what is the answer I am stumped
Answer: Repost this with the question (not just the graph) attached.
Step-by-step explanation: Please attach the question, otherwise I cannot help you:)
Malik measured the middle school and made a scale drawing. He used the scale 8 inches = 6 feet. What is the scale factor of the drawing?
Therefore, the scale factor of the drawing is 4/3.
What is scale factor?In mathematics, the scale factor is the ratio between two corresponding measurements in different scales. It is a measure of how much a figure or object has been scaled up or down, compared to its original size. The scale factor is often used in geometry and is particularly useful when creating scale drawings or models. A scale drawing is a drawing that is proportional to the actual size of the object it represents, but is scaled down or up by a certain factor to fit on a piece of paper or to make it easier to work with. The scale factor is used to determine the relationship between the measurements of the original object and the measurements of the scaled-down or scaled-up version.
Here,
To find the scale factor of the drawing, we need to determine the ratio of the length in the drawing to the actual length.
Here, the scale is given as 8 inches = 6 feet. This means that every 8 inches in the drawing represents 6 feet in real life.
To find the ratio of the length in the drawing to the actual length, we can set up a proportion:
8 inches / 6 feet = x inches / y feet
where x is the length in the drawing that corresponds to a length of y feet in real life.
To solve for x, we can cross-multiply and simplify:
8 inches * y feet = 6 feet * x inches
8y = 6x
x = (8/6) y
x = (4/3) y
This means that the length in the drawing is (4/3) times the length in real life.
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Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average proportion of defective widgets (choose your confidence level)?
At a confidence level of 95%, the interval estimate for the average proportion of defective widgets is approximately 0.020 to 0.082.
To find the confidence interval for the proportion of defective widgets, we can use the formula:
CI = p ± z*(sqrt(p*(1-p)/n))
where:
p = proportion of defective widgets in the sample
z* = the z-value for the desired confidence level
n = sample size
The z-value depends on the desired confidence level. For example, if we want a 95% confidence level, we would use a z-value of 1.96 (from the standard normal distribution table).
Plugging in the values given in the problem, we get:
p = 23/450 = 0.0511
n = 450
z* = 1.96 (for a 95% confidence level)
sqrt(p*(1-p)/n) = sqrt(0.0511*(1-0.0511)/450) ≈ 0.016
Therefore, the 95% confidence interval for the proportion of defective widgets is:
CI = 0.0511 ± 1.96*0.016
= (0.020, 0.082)
This means we are 95% confident that the true proportion of defective widgets in the population is between 0.020 and 0.082.
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Find the missing angle measure to the nearest degree SIN X = 0. 7547 *
O 47 degrees
48 degrees
49 degrees
50 degree
The angle x is approximately equal to option (c) 49 degrees
Sine is a trigonometric function that relates the ratios of the sides of a right triangle. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin(X) = opposite / hypotenuse.
Since the sine function is periodic, there can be multiple angles that have the same sine value. In general, for any angle X, sin(X) = sin(180° - X), which means that the sine of an angle and its supplement have the same value.=
Therefore, it's important to specify the range of the angle we're interested in when finding the inverse sine function, which gives us the unique angle in the range of -90° to 90° that has the specified sine value.
sin⁻¹(0.7547) ≈ 49°
Therefore, the correct option is (c) 49 degrees
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Classify the quadrilateral. Justify
your reasoning
Answer:
The quadrilateral is a square. A quadrilateral is a polygon with four sides. There are many types of quadrilaterals such as parallelogram and rhombuses. A rhombus is a parallelogram with four congruent sides. The plural of a rhombus is rhombi. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A square is a rhombus becasue it has 4 congruent sides and angles
Step-by-step explanation:
Hope this helps!!
A triangle has angles (w² +84)°, w°, 3w°
Find the value of w
Answer:
Below
Step-by-step explanation:
The three internal angles f ANY triangle add up to 180 °
w^2 + 84 + w + 3w = 180
w^2 + 4w + 84 = 180
w^2 + 4w - 96 = 0 Use Quadratic Formula a = 1 b = 4 c = -96
to find the positive value of w = 8
4. A physical model suggests that the mean temperature increase in the water used as coolant in a compressor chamber should not be more than 5 Celsius. Temperature increases in the coolant measured on 8 independent runs of the compressing unit revealed the following data: 6. 4, 4. 3, 5. 7, 4. 9, 6. 5, 5. 9, 6. 4, 5. 1. Do the data contradict the assertion of the physical model
The question asks if the data contradict the assertion of the physical model, which suggests that the mean temperature increase should not be more than 5 Celsius.
To answer the question, we need to calculate the mean temperature increase from the data given: 6.4, 4.3, 5.7, 4.9, 6.5, 5.9, 6.4, 5.1. We can do this by adding all the values and dividing them by the number of runs (8): (6.4 + 4.3 + 5.7 + 4.9 + 6.5 + 5.9 + 6.4 + 5.1)/8 = 5.4. The mean temperature increase of 5.4 does not exceed the maximum of 5 Celsius, which means that the data does not contradict the physical model.
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Describe in practical terms the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2)
In practical terms, the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2) are as follows:f^(-1)(0.7): This means the value of x for which f(x) = 0.7. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.7. In other words, if y = f(x), then f^(-1)(y) = x. Hence, f^(-1)(0.7) means the input value of x for which the function returns 0.7 as the output.f^(-1)(0.5): This means the value of x for which f(x) = 0.5. Similarly, the inverse of the function f, f^-1, returns the value of the input x for which the output of the function is 0.5.f^(-1)(0.2): This means the value of x for which f(x) = 0.2. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.2. Hence, f^(-1)(0.2) means the input value of x for which the function returns 0.2 as the output.
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I need help with number 3 ASAP please! cos^2u- cos u sec u= cot^2 u
PLEASE I NEED HELP
Answer:
cosx
Step-by-step explanation:
using the identity
• sin² = 1 - cos²x
cos²x + cosx - 1 + sin²x
= cos²x + cosx - 1 + 1 - cos²x ← collect like terms
= cos x
Solve the equation. If you get stuck consider using a diagram to help you. −4(y−2)=12
y=?
Answer:
[tex] \sf \: y = - 1[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of y.
The equation is,
→ -4(y - 2) = 12
Then the value of y will be,
→ -4(y - 2) = 12
→ -4(y) - 4(-2) = 12
→ -4y - (-8) = 12
→ -4y + 8 = 12
→ -4y = 12 - 8
→ -4y = 4
→ y = 4 ÷ (-4)
→ [ y = -1 ]
Hence, the value of y is -1.
A health expert evaluates the sleeping patterns of adults. Each week, she randomly selects 50 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 9 hours and 5% of average sleep time is more than 9.4 hours.
What are the mean and standard deviation (in hours) of sleep time for the population?
The mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
What does "normal distribution" mean?In statistics and probability theory, the normal distribution is a continuous probability distribution that is often utilised. Due to its distinctive form, it is sometimes referred to as the bell curve or the Gaussian distribution. Many statistical and data analysis techniques, such as confidence intervals, regression analysis, and hypothesis testing, all make use of the normal distribution. It is well recognised that many real-world occurrences, like heights, weights, and IQ scores, follow a normal distribution, making it a useful tool for data analysis and interpretation.
Given that, 5% of average sleep time is less than 9 hours.
The z-score for the lower 5% percentile is z = -1.645.
Similarly, for upper 5th percentile we have z = 1.645.
The z-score is given as:
z = (x - μ) / σ
For the lower 5th percentile:
-1.645 = (9 - μ) / σ
For the upper 5th percentile:
1.645 = (9.4 - μ) / σ
Adding the two equations we have:
-1.645σ = (9 - μ)
1.645σ = (9.4 - μ)
0 = 18.4 - 2μ
μ = 9.2 hours.
Substitute the value of μ:
1.645σ = (9.4 - 9.2)
1.645σ = 0.2
σ = 8.225
Hence, the mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
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Let X be a normal random variable with mean 209 units and standard deviation 7 units. Answer the following questions, rounding your answers to two decimal places.(a) What is the probability that X will be less than 201 units, P(X<201)?(b) What is the probability that X will be within 8units of the mean?(c) The probability is 0.04 that X will be more than how many units?
196.75 units
Answer:(a) P(X < 201) = 0.0099(b) P(201 < X < 217) = 0.9544(c) P(X > 227.12) = 0.04Explanation:Given that, X be a normal random variable with mean 209 units and standard deviation 7 units.We need to find the following.(a) P(X < 201)(b) P(201 < X < 217)(c) P(X > x) = 0.04.(a) We know that,When X is a normally distributed variable with mean μ and standard deviation σ,thenZ = (X - μ) / σ is a standard normal variable.Then,P(X < 201) = P(Z < (201 - 209) / 7)= P(Z < -1.14)Using the z-tables, the probability is 0.0099.(b) We need to find the probability that X will be within 8 units of the mean. Therefore,X will be within 8 units of the mean, if 201 < X < 217.Therefore,P(201 < X < 217) = P((X - μ)/σ) < (217 - 209)/7) - P((X - μ)/σ) < (201 - 209)/7)= P(0.57 < Z < -0.57)Using z-tables, P(0.57 < Z < -0.57) = 0.9544(c) We need to find the value of X such that P(X > x) = 0.04.Then,P(Z > (X - μ)/σ) = 0.04P(Z < -1.75) = 0.04Using z-tables, P(Z < -1.75) = 0.04By using the standard normal distribution tables, the value of -1.75 corresponds to 0.0401.Therefore,-1.75 = (X - 209)/7-12.25 = X - 209X = 209 - 12.25X = 196.75Therefore, the probability is 0.04 that X will be more than 196.75 units.
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