A manufacturer knows that their items have a normally distributed length, with a mean of 10.6 inches, and standard deviation of 2.8 inches.
If 13 items are chosen at random, what is the probability that their mean length is less than 10 inches? (Give answer to 4 decimal places.)'

Answer:

\(P(B) = \frac{4}{18} = \frac{2}{9} = 0.2\)

Step-by-step explanation:

Sample space 2+5+7+4=18

Answer:

4/18 or 2/9

Step-by-step explanation:

The total number of balls = 2 + 5 + 7 + 4 = 18

4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9

Hope this helps!

Answer:

5/2

Step-by-step explanation:

→ 5/x = 2

→ 5 = 2x

→ 5/2 = x ★

Answer:

x= 10

Step-by-step explanation:

×=5 × 2= 10

Answer. x=10

The probability that Julie got exactly seven questions correct is approximately 0.117 or 11.7%.

The probability of guessing the correct answer on any single true-false question is 1/2, and the probability of guessing the wrong answer is also 1/2.

The probability of guessing exactly seven questions correctly can be calculated using the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where:

n is the total number of questions, which is 10 in this case.

k is the number of questions guessed correctly, which is 7 in this case.

p is the probability of guessing any individual question correctly, which is 1/2 in this case.

Using the formula, we get:

P(X = 7) = (10 choose 7) * (1/2)^7 * (1/2)^(10-7)

= 120 * (1/2)^10

= 0.1171875

Therefore, the probability that Julie got exactly seven questions correct is approximately 0.117 or 11.7%.

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To determine the upstream throat area, stagnation temperature, and mass flow in the system of a converging-diverging nozzle, we need to apply the equations of fluid dynamics. Given the downstream test section parameters of area (A) = 53 cm^2, pressure (p) = 12 kPa, density (rho) = 0.182 kg/m^3, and velocity (V) = 760 m/s, we can calculate the required values.

(a) The upstream throat area (A*) can be determined using the mass flow rate equation, which states that mass flow rate (m_dot) is equal to the product of density, velocity, and area: m_dot = rho * V * A. Rearranging the equation, we have A* = m_dot / (rho * V). Substituting the given values, we find A* = 0.733 kg/s / (0.182 kg/m^3 * 760 m/s) = 0.002 m^2.

(b) The stagnation temperature (T0) can be calculated using the isentropic relations. We need to use the specific heat ratio (gamma) of the gas, which is typically given for a specific fluid. Assuming a value of gamma = 1.4 for air, the relation is T0 = T / (1 + (gamma - 1) / 2 * M^2), where T is the static temperature and M is the Mach number. Given the information provided, we don't have the static temperature or Mach number, so we cannot calculate the stagnation temperature.

(c) The mass flow rate (m_dot) is already given as 0.733 kg/s.

In summary, we have determined the upstream throat area (A*) to be 0.002 m^2 and the mass flow rate (m_dot) to be 0.733 kg/s. However, we couldn't calculate the stagnation temperature (T0) without additional information about the static temperature and Mach number.

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Answer:

n=-5

Step-by-step explanation:

Isolate the variable

The height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches. The z-score associated with the 96th percentile is 1.75.

To find the z-score associated with the 96th percentile, we can use the following steps:

1. Locate the percentile in a standard normal distribution table or use a calculator that can compute percentiles (e.g., a graphing calculator or an online calculator).

2. For the 96th percentile, we find the corresponding z-score. Using a standard normal distribution table or an online calculator, the z-score is approximately 1.75.

So, the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the following formula:

Height = mean + (z-score × standard deviation)

Here, the mean height is 68.3 inches, the z-score is 1.75, and the standard deviation is 2.9 inches. Plugging these values into the formula:

Height = 68.3 + (1.75 × 2.9) ≈ 68.3 + 5.075 ≈ 73.375 inches

So, the height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches.

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Answer:

17

Step-by-step explanation:

Plug in 3 for x and you'll get

\(4(3) + 5\)

Which is 17.

Answer:

I think it is 19

Step-by-step explanation:

In this case,when r = 20cm and ℎ = 5cm, the rate of increase of the volume of the cone is 800π/3 cm³/s.

When the radius and height ℎ of a circular cone are increasing at a rate of 2cm/s, the rate of increase of the volume of the cone is 20π cm³/s.

0/This is known as the volume of the cone when r = 20 cm and ℎ = 5 cm.

As a result, the formula for the volume of the cone is V(r, ℎ) = 1/3 πr²ℎ.

Differentiating both sides of the formula with respect to t, we get:

dV/dt = 1/3 π [2r dr/dt ℎ + r² dh/dt]

By substituting the given values, we obtain:

dV/dt = 1/3 π [2(20)(2)(5) + 20²(2)] = 800π/3 cm³/s

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Answer:

I believe its b and c

Step-by-step explanation:

Answer:

B. and D.

Step-by-step explanation:

To get the distance you must subtract Han's house from Lin's house since her house is closer. D. works as well because it is the inverse operation of B.

Answer:

Step-by-step explanation:

1. 4x-4\(\leq\)x+6/2

2. 4x\(\leq\)x+6/2+4

3. 4x\(\leq\)x+7

4. 3x/3\(\leq\)7/3

5. x\(\leq\)2 1/3 or x\(\leq\) 2.33333333333

Answer:

-2j - (5j + 2) = -1 (3j -1)

Step-by-step explanation:

-2j -1 (5j + 2) = -1 (3j -1)

-2j-5j-2=-3j+1

-7j+1= -3j+1

0=4j

Answer:

x = 1.6 , y = 13.8

Step-by-step explanation:

y - 3x = 9 ( add 3x to both sides )

y = 9 + 3x → (1)

7x + y = 25 → (2)

Substitute y = 9 + 3x into (2)

7x + 9 + 3x = 25

10x + 9 = 25 ( subtract 9 from both sides )

10x = 16 ( divide both sides by 10 )

x = 1.6

Substitute x = 1.6 into (1)

y = 9 + 3(1.6) = 9 + 4.8 = 13.8

The slope of the tangent line to the parabola y = 3x^2 + 5x + 3 at the point (3, 45) is 23 that can be found by calculating the first derivative of the function with respect to x and then evaluating it at the given point.

First, let's find the first derivative of y with respect to x:
y = 3x^2 + 5x + 3
dy/dx = (d/dx)(3x^2) + (d/dx)(5x) + (d/dx)(3)
dy/dx = 6x + 5
Now that we have the first derivative, we can find the slope of the tangent line at the point (3, 45) by plugging in x = 3:
dy/dx = 6(3) + 5
dy/dx = 18 + 5
dy/dx = 23

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The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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Answer:

Step-by-step explanation:

f(x) = 3x - 1

g(x) = 2x + 1

To find (f +g)(3) , first find (f + g)(x)

To find (f + g)(x) add g(x) to f(x)

That's

(f + g)(x) = 3x - 1 + 2x + 1

= 3x + 2x + 1 - 1

(f + g)(x) = 5x

Now to find (f + g)(3) substitute 3 into

(f + g)(x)

That's

(f +g)(3) = 5(3)

Hope this helps you

Answer:

$210

Step-by-step explanation:

Given data

time = 6 weeks

initial amount= $90

saving per week = $25

Hence the expression for the total savings after the 6 weeks is given as

y= mx+c

where

m= $25

x= 6 weeks

c= $90

substitute

y=25*6+90

y= 150+60

y= $210

Hence the total amount after 6 weeks is $210

Answer:

A = (5, 3), so the x-value is 5

Step-by-step explanation:

Answer:

(5, 3), so the x-value is 5

Step-by-step explanation:

Person above me right thank you person above me

The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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\( \sf2x + 3y = - 6 \\ \sf2x + 3 \times 0 = - 6 \\ \sf2x = - 6 \\ \boxed{ \tt x = - 3}\)

Answer:

the answer is a=6π ~~~~~~~~~~~~~~~~

Answer:

Options (1), (2), (4) and (5) are correct.

Step-by-step explanation:

Characteristics of the given hyperbola,

1). Vertex of the given hyperbola are at (-3, 6) and (-3, 4).

2). Since center of a hyperbola is the center of a line joining vertices of the hyperbola,

Center of the given parabola will be,

\((\frac{-3-3}{2},\frac{6+4}{2})\) ⇒ (-3, 5)

3). Vertical line joining the foci of the hyperbola is the transverse axis.

4). A line perpendicular to the transverse axis and passing through the center will be the conjugate axis.

5). Directrices of a horizontal hyperbola are the horizontal lines.

Therefore, Options (1), (2), (4) and (5) are correct.

Answer:

check photo. <3

Step-by-step explanation:

Answer:

-6 2/3

Step-by-step explanation:

Answer

 - 6   2 / 3

Step-by-step explanation:

answer is - 6  2/ 3

Answer:

x > 16

Step-by-step explanation:

The ratio of A₂/A₁ is 10.89:1 and the ratio of V₂/V₁ is 35.937:1.

Given, Sphere 1 has surface area A₁ and volume V₁ and Sphere 2 has surface area A₂ and volume V₂.

If the radius of sphere 2 is 3.3 times the radius of sphere 1, then the ratio of the following will be:

                          Ratio of Areas: A₂/A₁= (4πr₂²)/(4πr₁²)= r₂²/r₁²

                         Ratio of Volumes: V₂/V₁= (4/3)πr₂³/ (4/3)πr₁³ = r₂³/r₁³

Given that radius of sphere 2 is 3.3 times the radius of sphere 1,

                                    then r₂/r₁ = 3.3

Substituting this value in the above ratios, we get:

                                        Ratio of Areas: A₂/A₁= r₂²/r₁² = (3.3)² = 10.89:1 (approx)

                                        Ratio of Volumes: V₂/V₁= r₂³/r₁³ = (3.3)³ = 35.937:1 (approx)

Hence, the ratio of A₂/A₁ is 10.89:1 and the ratio of V₂/V₁ is 35.937:1.

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The correct slope and y-intercept for the linear equation y=2x+7 are 2 and 7, respectively.

The y-intercept of a graph is the point where the graph crosses the y-axis. It is written as (0, b), where b is the y-intercept. The y-intercept is the value of y when x is equal to zero. It can be used to determine the equation of a line when two points on the line are known.

The slope of a linear equation is the coefficient of the x variable, which is 2 in this case. The y-intercept is the constant term, which is 7 in this case.

So, the slope is 2 and the y-intercept is 7.

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A good method for evaluating the integral ∫2 to -√27 involves using the fundamental theorem of calculus and applying techniques of integral calculus.

Here's an explanation of the steps involved:

1. Start by determining the antiderivative of the integrand. In this case, the integrand is not specified, so let's assume it as f(x).

2. Apply the fundamental theorem of calculus, which states that if F(x) is the antiderivative of f(x), then ∫[a, b] f(x) dx = F(b) - F(a).

3. Find the antiderivative F(x) of f(x). This step can be challenging depending on the specific integrand. If the integrand has a known antiderivative, such as a polynomial or trigonometric function, then you can use the appropriate integration techniques.

4. Evaluate F(x) at the upper and lower limits of integration, which are 2 and -√27, respectively. Plug in these values into F(x) and subtract F(2) from F(-√27).

5. Simplify the expression obtained in step 4 to obtain the final result.

It's important to note that without the specific form of the integrand, it's not possible to provide an exact solution or determine the integral's numerical value. The above steps outline a general approach to evaluating integrals using the fundamental theorem of calculus and integration techniques. However, the specific method for evaluating the integral will depend on the nature of the integrand.

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The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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