What is the slope of the line shown?

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is,\(\lambda=\frac{1}{\mu}=\frac{1}{7}\).

The probability density function of X is:

\(f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0\)

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

\(P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx\)

                      \(=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148\)

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Using the exponential distribution, it is found that there is a 0.1479 = 14.79% probability that the child must wait between 6 and 9 minutes on the bus on a given morning.

The exponential probability distribution, with mean m, is described by the following equation:  

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

In this problem, we have that mean of 7 minutes, hence:

\(m = 7, \mu = \frac{1}{7}\)

The probability that the child must wait between 6 and 9 minutes on the bus on a given morning is:

\(P(6 \leq X \leq 9) = P(X \leq 9) - P(X \leq 6)\)

In which:

\(P(X \leq 9) = 1 - e^{-\frac{9}{7}} = 0.7235\)

\(P(X \leq 6) = 1 - e^{-\frac{6}{7}} = 0.5756\)

Hence:

\(P(6 \leq X \leq 9) = P(X \leq 9) - P(X \leq 6) = 0.7235 - 0.5756 = 0.1479\)

0.1479 = 14.79% probability that the child must wait between 6 and 9 minutes on the bus on a given morning.

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Answer: Neither

Step-by-step explanation:

Answer:

nnnnnnnnnnnnnnnnnx ce 3rd d

Answer:

Step-by-step explanation:

r = √3 v/πh

Putting values

= 6.77

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

The probability that 2 of the apples have blemishes will be 0.0746.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as,

\(\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}\)

The probability is calculated as,

P(X = 2) = ¹⁰C₂ * (0.05)² * (0.95)⁸

P(X = 2) = 0.0746

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Answer:

B (1, 1),(3, 9), (7, 49)

Step-by-step explanation:

Given function:

Let's verify which set of pairs are same with the given function:

A....................

B....................

C....................

D....................

Answer:

A= 184.4 yards

Step-by-step explanation:

couldnt figure out b

The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:50.18

Step-by-step explanation:

8x+17+9x+11=102

17x+28=102

-28. -28

17x=74

<CAD=9x+11=50.18

x=74/17

Answer:

Adult-. $4

Student-. $2.50

Step-by-step explanation:

equation

1a + 3s = $11.50

3a + 2s = $17.00

$4+$2.50(3)=$11.50

$12+$2.50(2)=$17.00

or

1($4)+3($2.50)=$11.50

3($4)+2($2.50)=$17.00

sorry if this is a little confusing, this is a simpler equation-

$4.00+($2.50x3)=$11.50

($4.00x3)+($2.50x2)=$17.00

Answer:

25.37%

Step-by-step explanation:

fillerfillerfillerfiller

Answer:

its be 9th of square centimeter

Answer:

(0,2)

(3,0)

Step-by-step explanation:

Answer: 11,923

Step-by-step explanation:

Answer:

option- a

Step-by-step explanation:

the length of AB = A'B'

Answer:

1/200????????????????

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Given

\(M \to\) randomly selecting a male

\(B \to\) randomly selecting someone with blue eyes

Solving (a): Interpret P(M|B)

The above implies conditional probability

The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected

Solving (b): is (a) the same as P(B|M)

No, they are not the same.

The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected

Therefore, option (C) Micah is the correct answer. The graph displays how they fared throughout the race. Distance (meters).

The pace at which an object moves from one location to another is the fundamental definition of speed. The magnitude of an object's velocity is considered to be its speed. It is unquestionably a scalar amount. Distance is the separation of any two locations by any amount of space.

In most cases, distance is employed to express how far apart two things are. This concept gets slightly more precise when viewed from a mathematical standpoint. To understand distance geometrically, line segments must first be discussed.

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Answer:

Step-by-step explan

decimal answer: 0.06

fraction: 1/15

(edited)

Answer: 1/15

1/5*1/3 = 1/15

Step-by-step explanation:

Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

V = 4 2/3 units ^3

Step-by-step explanation:

We are given the area of the back rectangle

V = BH where B is the area of the base

V = 3 1/3 * 1 2/5

Rewriting the mixed numbers as improper fractions

V = 10/3 * 7/5

V = 70/15

Simplifying

V = 14/3

Changing back to a mixed number

V = 4 2/3 units ^3

Answer:

its the one closest to 120. its correct on plato/edmentum

Step-by-step explanation:

Answer:

the point just to the right of 120

Step-by-step explanation:

I got it right on PLATO

Answer:

it is option A bro

follow me if it is helpful

43.131

/\

|

This is the tenths spot.

40.000 or 40

The  expressions that could represent how much Leila pays in total for the model

\dfrac{107}{100}x

100 107 Option A is correct.

This is further explained below.

The price of the model is  x

Now we are given that she also has to pay a 7  tax.

Amount of tax =7 % x

\(=\frac{7}{100} x\)

the Total cost\(=x+\frac{7}{100} x\)

\(=\frac{107}{100} x\)

In conclusion, the statement might signify Leila's overall cost for the model. \(\frac{107}{100} x\)

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The appropriate hypothesis test is a two-sample t-test for independent samples.

The appropriate hypothesis test in this scenario is a two-sample t-test for independent samples. Since the population standard deviations are known, we can use the Z-test instead.

The test statistic can be calculated using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

x1 and x2 are the sample means for Manufacturer A and Manufacturer B, respectively.

s1 and s2 are the population standard deviations for Manufacturer A and Manufacturer B, respectively.

n1 and n2 are the sample sizes for Manufacturer A and Manufacturer B, respectively.

Plugging in the given values:

x1 = 179, x2 = 178, s1 = 1, s2 = 5, n1 = n2 = 108

t = (179 - 178) / sqrt((1^2 / 108) + (5^2 / 108))

t = 1 / sqrt(0.00926 + 0.0463)

t ≈ 1 / sqrt(0.05556)

t ≈ 1 / 0.2357

t ≈ 4.241

To determine whether there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different, we compare the calculated t-value to the critical value from the t-distribution at the desired significance level (0.05).

The decision depends on the degrees of freedom for the test, which is calculated as (n1 + n2 - 2) = (108 + 108 - 2) = 214.

Using a t-table or statistical software, we find that the critical value for a two-tailed test with a significance level of 0.05 and 214 degrees of freedom is approximately ±1.972.

Since the calculated t-value of 4.241 exceeds the critical value of 1.972, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different at the 0.05 significance level.

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Answer: 10

Step-by-step explanation:

For simplicity, I will let the intersection of the diagonals be point E.

Since diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.

Thus, we can use the fact that the acute angles of a right triangle are complementary to conclude that:

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: x = 10°\)

____________________________________

\( \large \tt Solution \: : \)

Diagonals of a Rhombus bisect each other at right angle (90°)

\(\qquad \tt \rightarrow \: x + 58 + 90 = 180\)

[ Sum of interior angles of a triangle ]

\(\qquad \tt \rightarrow \: 3x - 13 + 8x - 7 + 90 = 180\)

\(\qquad \tt \rightarrow \: 11x + 70 = 180 \)

\(\qquad \tt \rightarrow \: 11x = 180 - 70 \degree\)

\(\qquad \tt \rightarrow \: 11x = 110\)

\(\qquad \tt \rightarrow \: x = \cfrac{110}{11} \)

\(\qquad \tt \rightarrow \: x = 10 \degree\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(f(x) = \frac{4}{3} (x - 2) ^{2} + 7\)

Step-by-step explanation:

the answer is :- .

\(f(x) = \frac{4}{3} (x - 2) ^{2} + 7\)

Answer:

y=-4(x+2)^2+7

Step-by-step explanation:

cost of 8 books = 520 AED

we can do this using direct proportion

8/520 , 10/x

(cross multiply

= 8x = 520 x 10

= 8 x 5200

x = 5200/8

x =  650 AED

therfore,

cost of 10 books is 650.