Please help me with these two questions.

a. Calculate the expected arrival time:

Given: Time range for arrival of elevator during the next 4.7 minutes is equally likely. The expected value of a discrete random variable is calculated by multiplying each possible value by its probability and adding up the products. So, we can calculate the expected value of the elevator arrival time by integrating the value of the probability density function (which is a straight line in this case) over the given interval. The area under the curve of the probability density function over the entire interval of possible values is 1. The expected arrival time (E) of the elevator is given by: E = (1/4.7) ∫(0 to 4.7) tdt= (1/4.7) [t²/2] [from 0 to 4.7]= 2.3596 minutes or 2.36 minutes (rounded to 2 decimal places)Therefore, the expected arrival time is 2.36 minutes.

b. Probability that an elevator arrives in less than 1.8 minutes:

To calculate the probability of an event happening, we need to find the area under the probability density function (pdf) over the given interval (in this case, less than 1.8 minutes). The pdf is a straight line with a slope of 1/4.7, so the equation of the line is: f(t) = (1/4.7) t. The probability of the elevator arriving in less than 1.8 minutes is: P(T < 1.8) = ∫(0 to 1.8) f(t) dt= ∫(0 to 1.8) (1/4.7) t dt= (1/4.7) [t²/2] [from 0 to 1.8]= 0.56765 (rounded to 4 decimal places)Therefore, the probability that an elevator arrives in less than 1.8 minutes is 0.568 (rounded to 3 decimal places).

c. Probability that the wait for an elevator is more than 1.8 minutes: The probability that the wait for an elevator is more than 1.8 minutes is the complement of the probability that it arrives in less than 1.8 minutes. P(T > 1.8) = 1 - P(T < 1.8) = 1 - 0.56765= 0.43235 (rounded to 3 decimal places)Therefore, the probability that the wait for an elevator is more than 1.8 minutes is 0.432 (rounded to 3 decimal places).

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Answer:

4 units

Step-by-step explanation:

Considering the triangle KLJ, using the trigonometric ratios defined by the notation SOH CAH TOA

Line LJ is the opposite side while LK is the hypotenuse side. Hence,

Sin 30 = LJ/8√2

LJ = 8√2 × 1/2

= 4√2

Considering triangle LJM, line LJ is now the hypotenuse while line LM which is equal to x is the opposite side.

Sin 45 = x/4√2

x = 4√2 × 1/√2

x = 4

Answer:

4

Step-by-step explanation:

Just took the test in k12

Answer:

h(3) = 1

Step-by-step explanation:

\(h\left(3\right)=\left(3\right)\cdot \:2-3\\h\left(3\right)=3\cdot \:2-3\\h\left(3\right)=6-3\\h\left(3\right)=3\)

Divide

\(\frac{h\cdot \:3}{3}=\frac{3}{3}\\h=1\)

Hello!

\(\large\boxed{x = 4.5}\)

To solve, we can use proportions:

Since the triangles are similar, their side lengths will be proportional to each other. We can set up a proportion to solve for the missing side length. Remember to use corresponding sides:

CA ~ FD and AB ~ DE

Therefore:

\(\frac{6}{16} = \frac{x}{12}\)

Cross multiply to solve for x:

6 · 12 = 16 · x

72 = 16x

Divide both sides by 16:

72/ 16 = 16x / 16

x = 4.5

The confidence interval is (0.451, 0.549).

To find the confidence interval, we need to use the formula:

Confidence interval = sample proportion +/- margin of error

where the margin of error is calculated as:

Margin of error = z* (standard error)

The standard error is the standard deviation of the sampling distribution of the proportion, which is calculated as:

Standard error = \(\sqrt{p*(1-p)/n}\)

where p is the sample proportion and n is the sample size.

The z-value corresponding to a 95% confidence level is 1.96.

Using the given information, we have:

Sample proportion (p) = 0.50

Sample size (n) = 400

Margin of error = 0.052 * 0.5 = 0.026

Standard error = \(\sqrt{0.5(1-0.5)/400}\) = 0.025

Z-value for 95% confidence level = 1.96

So the confidence interval is:

0.50 +/- 1.96 * 0.025

= 0.50 +/- 0.049

Therefore, the confidence interval is (0.451, 0.549) or 45.1% to 54.9%. We can say with 95% confidence that the true proportion of respondents who agree with the statement lies between 45.1% and 54.9%.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Americans spent a total of about $9,000 each on health care in 2013.

Health care is one of the most common expenses that people have to do. This derives from the comon saying that heath is wealth.

The graph shows the degree of expenses by the American people on the issue of health care in the year 2013. From the graph, we can see that Americans spent a total of about $9,000 each on health care in 2013.

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Answer:

C.) About $9,000

Step-by-step explanation:

Edge, 2022.

Answer:

9

Step-by-step explanation:

We have to solve in order to find out if Sam is correct

Remember PEDMAS:

For Multiplication, division and addition, subtraction, do what appears first left to right

Parenthesis

Exponent

Division

Multiplication

Addition

Subtraction

16 - 18 + (2+1)+2^3

Parenthesis first: 2+1 = 3

16 - 18 + 3 + 2^3

Exponent next: 2^3 = 8

Subtraction (it's on the left) : 16-18 = -2

Addition: -2 + 3 = 1

Addition : 1 + 8 = 9

Sam is not correct, the answer is 9, not 16.

Hope this helps :)

Have a great day!

Answer:

18

Step-by-step explanation:

\(16-18:(2+1)+2^3\)

We must use the BEDMAS rules (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

We must first calculate what's in the brackets:

\(2 + 1 = 3\)

So the new expression is:

\(16-18:3+2^3\)

Next, we calculate the exponent:

\(2^3 = 8\)

So our expression is now:

\(16-18:3+8\)

Next we divide:

\(18:3 = \frac{18}{3} = 6\)

Our expression is now:

\(16 - 6 + 8\)

Then we subtract:

\(16 - 6 = 10\)

The new expression:

\(10 + 8\)

And finally we add:

\(10 + 8 = 18\)

Lines KL and MN  are related is by the lines being perpendicular. Therefore, the correct option is C.

Perpendicular lines are lines that are formed when two lines meet each other at the right angle or 90 degrees. This property of lines is said to be perpendicularity.

If a line passes through two points, then the slope of the line is

\(\text{m}=\dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).

The slope of line KL is

\(\text{m}_1=\dfrac{2-2}{6-(-8)} =0\)

The slope of line KL is 0, it means it is a horizontal line.

From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).

The slope of line MN is

\(\text{m}_2=\dfrac{-6-8}{-4-(-4)} =\dfrac{1}{0}\)

The slope of line MN is 1/0 or undefined, it means it is a vertical line.

We know that vertical and horizontal lines are perpendicular to each other. Therefore, the lines KL and MN are perpendicular to each other.

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Answer:

answer is 55° ..........

Answer:

1. 6v+8

2.5x+6y

These triangles are d. not similar

The given angles in the triangles are not sufficient to establish similarity. In order for two triangles to be similar, their corresponding angles must be equal, and their corresponding sides must be in proportion.

In this case, while the two triangles have two equal angles (88° and 88°), there is no information provided about the lengths of their sides. Therefore, we cannot determine if the triangles are similar based on the given information.

The triangles are not similar.

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Answer:

\(1.35*10^{-5}\)

You can simply convert them to their decimal form, then add and then make it scientific notation after you're done.

Hope this helps!

In step 1 mistake has been made because negative multiplication gives a positive result but is written negative.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given that,

−4(6−y) + 4 = −4

By using distribution property

-24 + 4y + 4 = -4

But in the question +4y is written as -4y which is wrong.

Hence In step 1 negative multiplication gives a positive result but is written negative so in step 1 mistake has been made".

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The given question is not complete.

Consider this solution to a problem.

Problem: −4(6−y)+4=−4

Step 1: −24−4y+4=−4

Step 2: −20−4y=−4

Step 3: −4y=16

Step 4: y=−4

In the first response box, enter the number of the step where the mistake is made.

a. The function is not strictly convex.Now, let's check the homotheticity of the function. A function is homothetic if it is continuous, quasiconcave and there exists a positive function, v(x1), such that u(x)=v(x1)f(x2).  b. We can say that the function is homothetic.

We are also given the values of L, X and the utility function. The values are\(L=2,X=(−[infinity],[infinity])×R +​,\)≿ is represented by the utility function\(u(x)=x 1​+ln(1+x 2​).\)

Let's solve this.

Suppose the utility function u(x) is represented as:

\(u(x)=x 1​+ln(1+x 2​)\)

We can see that the utility function is quasilinear. It has a linear component in x1 and a quasi-linear component in x2.

Therefore, we can say that the utility function is quasilinear.Now, let's check the convexity of the utility function. We will find the Hessian matrix and check its properties. The Hessian matrix is given by: H = [0 0; 0 1/(1+x2)^2]The determinant of \(H is 0(1/(1+x2)^2)-0(0) = 0\), which is neither positive nor negative.

Hence, the Hessian matrix is neither positive definite nor negative definite.

Therefore, we cannot determine whether the function is convex or concave.

However, we can check the strict convexity of the function by checking if the Hessian matrix is positive definite or not. The eigenvalues of the Hessian matrix are 0 and \(1/(1+x2)^2\), which are non-negative.

Hence, the Hessian matrix is positive semi-definite.

Therefore, the function is not strictly convex.Now, let's check the homotheticity of the function. A function is homothetic if it is continuous, quasiconcave and there exists a positive function, v(x1), such that \(u(x)=v(x1)f(x2)\)

If we take \(v(x1) = x1, then u(x)=x1(1+ln(1+x2)) = x1ln(e^(1+x2)) = ln(e^(1+x2)^x1)\)

Therefore, we can say that the function is homothetic.

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Answer:

-3

Step-by-step explanation:

when you have a power to the - it creates a fraction instead of a whole number.

2^3 = 8

2^-3=1/8

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

We have,

3.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees.

= 25

We add up all the dots above the numbers between 98.5 and 98.7.

We will not include the dots above 98.5 and 98.7.

4.

The dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population with a mean temperature of 98.6 degrees shows that the majority of the sample means are close to 98.6, and there are very few samples means that exceed 98.6, then it would be surprising to obtain a sample mean of 98.8 or greater from a different random sample.

Thus,

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

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Answer:

x= 42

Step-by-step explanation:

2 over 7 = 12 over x

12 divided by 2 = 6

6 x 7 = 42

x=42

Answer

:

42

Step-by-step explanation:

i got it correct. i hope this helps

Answer:

51

Step-by-step explanation:

a squared+2 squred=c

7×7- 10×10= 49-100= 51

c= 51

find square root of it 51= 7.14

Answer: x = 6 UNITS

Step-by-step explanation:

Answer:

D. Cl₂

Step-by-step explanation:

The measurement of angle DEF in the triangle since it's a scaled copy is 46°.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. Angle Sum Property of Triangle is the name of this property.

The six different kinds of triangles are right, obtuse, acute, equilateral, scalene, and isosceles. A triangle having two congruent sides and one distinct side and angle is called an isosceles triangle.

In this case, the measurement of angle DEF in the triangle since it's a scaled copy is 46°. This can be seen based on the value given in the second triangle.

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Answer:

-5/2, -2, 1.7

Step-by-step explanation:

Answer:

i think b

Step-by-step explanation:

Answer:

B. y = 2x + 8

Step-by-step explanation:

14x - 7y = 1

7y = 14x - 1

y = 2x - 1/7

If two lines are parallel, their slopes are equal.

With m = 2, x = -2, y = 4

y = mx + b

4 = 2(-2) + b

4 = -4 + b

b = 8

so y = 2x + 8

The equation of the tangent plane to the surface \(z = \frac{2xy+4y}{xy-2x}\) at the point \((1, 1, -6)\) is \(z = -5x - 8y - 6\).


To find the equation of the tangent plane to a surface at a given point, we need to compute the partial derivatives of the surface equation with respect to \(x\) and \(y\) and evaluate them at the given point.

Taking the partial derivatives of \(z\) with respect to \(x\) and \(y\) gives:
\(\frac{\partial z}{\partial x} = -\frac{6y^2 - 8y - 4}{(xy - 2x)^2}\) and
\(\frac{\partial z}{\partial y} = \frac{2x^2 - 2x - 4}{(xy - 2x)^2}\).

Evaluating these derivatives at \((1, 1)\) gives:
\(\frac{\partial z}{\partial x} = -10\) and
\(\frac{\partial z}{\partial y} = -18\).

Using the point-normal form of a plane equation, we substitute the values into the equation:
\(z = -10(x - 1) - 18(y - 1) - 6\).

Simplifying, we obtain the equation of the tangent plane to be \(z = -5x - 8y - 6\).

Therefore, the equation of the tangent plane to the surface at the point \((1, 1, -6)\) is \(z = -5x - 8y - 6\).

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Answer:

x = 4

Step-by-step explanation:

5x-4=16

Add 4 to both sides of the equation.

5x = 20

Divide both sides by 5.

x = 4

Answer:

x=4

Step-by-step explanation:

You first add 4 to both sides and get 5x=20. Then you divide both sides by 5 to isolate the x and get x=4.

Hope this helped :)

We use the BODMAS method to solve the given questions.

Solve the Bracket then Divide Multiply Add and Subtract

1. 32÷4×(16×1/2) - 2

= 32÷4 × ( 8 ) - 2

= 8 × 8 - 2 = 64 - 2 = 62

2. 20 ÷ (5×2/5) + 3

= 20 ÷ (2) + 3 = 20 ÷ 2 + 3

= 10 + 3 = 13

3. 1/2 ×(6×4) ÷ 3 + 2

= 1/2 × 24 ÷ 3 + 2

= 1/2 × 8 + 2

= 4 + 2 = 6

4. 2 (6÷2+8) - 4

= 2 (3+8) - 4

= 2 × 11 - 4

= 22 - 4

= 18

Answer:

8 1/2

Step-by-step explanation:

She read 8 1/2 pages each day because if you divide 85 by 10 you will get 8 1/2.

answer:

N(t)=2×\(1.7^{t}\)

17

15

step by step explain:

before lesson (t=0), she knows 2 words.

after a week (t=1), she knows

2×(1+70%)=3.4 words

after one more week (t=2), she knows

3.4×(1+70%)=5.78 words

one more week later (t=3), she knows

5.78×(1+70%)=9.826 words

and so on ...

from pattern shown above, we know that she knows

2×\(1.7^{t}\) words after t weeks

so N(t)=2×\(1.7^{t}\)

after 4 weeks (t=4), she knows 2×\(1.7^{4}\)=16.7042≈17 words

for learning 5000 words, she need:

2×\(1.7^{t}\)=5000

   \(1.7^{t}\)=2500

t log(1.7)=log(2500)

         t=\(\frac{log(2500)}{log(1.7)}\)

          =14.7448727

          ≈15 (round up)

Answer:

(a) N(t) = 2(1.7)^t

(b) 17

(c) 15

Step-by-step explanation:

(a) N(t) = 2(1.7)^t

There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)

(b) Just plug in the equation

N(4) = 2(1.7)^4

N(4) = 2(8.3521)

N(4) = 16.7042

Round, so it is 17

(c) Once again, plug in the equation

5000 = 2(1.7)^t

2500 = (1.7)^t

use a calculator for the part below

log1.7(2500) = log1.7(1.7)*t

t = log1.7(2500)

t = 14.7448

Round, so it is 15

Answer:

y=65x      and      8455 there yall go

Step-by-step explanation: