x+5y\(\leq\)-15

2 ( 3y + 10)

Use 2 to multiply both 3y and 10

Therefore, you have

2 x 3y + 2 x 10

6y + 20

Answer:

\( \boxed{y = 2x\: – \: 5} \)

the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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Remember that

The rule of a reflection over the line y=-x is equal to

(x,y) ------> (

Answer:

See below and attached graph.

Step-by-step explanation:

The slope-intercept form of a straight line equation is y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).

With a slope of -2, we can write:

y = -2x + b

To find b, enter the given point (-5,-3) and solve for b:

y = -2x + b

-3 = -2(-5) + b

-3 = 10 + b

b = -13

The equation becomes:  y = -2x -13

See the attached graph.

A percentage is a way to describe a part of a whole.  The most improbable simulation for this coin is heads are 9.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The most improbable simulation for this coin for heads is the frequency of heads coming up out of 20 which is far from the estimated frequency. Since out of these 20 times 75% of the times the head will come up. Therefore, the number of times the head will come up can be written as,

\(75\%\ of\ 20\\\\= \dfrac{75}{100} \times 20\\\\= 15\)

Now it is estimated that at least 15 times out of 20, the head will come up. Thus, the most improbable simulation for this coin is heads are 9.

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Answer:

A coin is biased to display heads 75% of the time. It is tossed 20 times, and the outcomes are recorded. The most improbable simulation for this coin is

9 heads.

Step-by-step explanation:

The standard deviation of the sample is 200.

As per the data given:

The distribution of prices for a certain car model is approximately normal with a mean of $21,800 and a standard deviation of $400.

The mean of the data will be $21,800.

The standard deviation of the data will be $400

A random sample of 4 cars of the model is to be selected.

That is n = 4

Here we have to determine the standard deviation of the sample.

By examining the square root of the variance, standard deviation measures how far apart a set of data is from the mean.

Therefore the standard deviation of the Sampling distribution of \($\bar{x}$\) is:-

\($ \sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}} \\\)

\($\Rightarrow & \sigma_{\bar{x}}=\frac{400}{\sqrt{4}} \\\)

\($\Rightarrow & \sigma_{\bar{x}}=\frac{400}{2} \\\)

\(\Rightarrow & \sigma_{\bar{x}}\) = 200

Therefore the standard deviation of the Sampling distribution \($\bar{x}$\) is 200

Hence option (a) is the correct answer

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Answer:

47/100 and 47%

Step-by-step explanation:

He missed 53 out of 100 so that means he made 47 out of a 100 and there you go... 47/100 and 47%

Answer:

y = 3x

Step-by-step explanation:

Choose a point that the perpendicular line will pass through.

(

0

,

0

)

Combine  

1

3

and  

x

.

y

=

x

3

+

6

Use the slope-intercept form to find the slope.

Tap for fewer steps...

The slope-intercept form is  

y

=

m

x

+

b

, where  

m

is the slope and  

b

is the y-intercept.

y

=

m

x

+

b

Using the slope-intercept form, the slope is  

1

3

.

m

=

1

3

The equation of a perpendicular line to  

y

=

x

3

+

6

must have a slope that is the negative reciprocal of the original slope.

m

perpendicular

=

−

1

1

3

Simplify  

−

1

1

3

to find the slope of the perpendicular line.

Tap for fewer steps...

Multiply the numerator by the reciprocal of the denominator.

m

perpendicular

=

−

(

1

⋅

3

)

Multiply  

3

by  

1

.

m

perpendicular

=

−

1

⋅

3

Multiply  

−

1

by  

3

.

m

perpendicular

=

−

3

Find the equation of the perpendicular line using the point-slope formula.

Tap for fewer steps...

Using the point-slope form  

y

−

y

1

=

m

(

x

−

x

1

)

, plug in  

m

=

−

3

,  

x

1

=

0

, and  

y

1

=

0

.

y

+

0

=

−

3

(

x

+

0

)

Solve for  

y

.

Tap for fewer steps...

Add  

y

and  

0

.

y

=

−

3

(

x

+

0

)

Add  

x

and  

0

.

y

=

−

3

x

Hello!

y=-1/3x+6

Perpendicular lines have slopes that are opposite reciprocals.

This means that if we have a slope of -1/3, its opposite reciprocal would be 3

Use Point-Slope form:

y-y1=m(x-x1)

y-4=3(x-2)

y-4=3x-6

y=3x-6+4

y=3x-2

Hope this helps you!

~Just a joyful teen

\(GraceRosalia\)

If a manufacturer have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 1.3 years, the probability that a randomly purchased item will last longer than 14 years is 0.966 or 96.6%.

We can use the standard normal distribution to calculate the probability that an item will last longer than 14 years. First, we need to calculate the z-score:

z = (14 - 11.6) / 1.3 = 1.846

Next, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1.846. Using a standard normal distribution table, we find that the probability is 0.9664.

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Answer:

y=3/4x+7

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-4,4) and has a slope of 3/4.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 3/4. So you can right away fill in the equation for a line somewhat to read:

y=3/4x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-4,4). When x of the line is -4, y of the line must be 4.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 3/4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-4,4).

So, why not plug in for x the number -4 and for y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-4,4). y=mx+b or 4=3/4 × -4+b, or solving for b: b=4-(3/4)(-4). b=7.

hope this answers your question sorry it's soo long i just like writing long stuff have a great day!!

Answer:

64 bats can eat 320 grams of insects in 1 night.

Step-by-step explanation:

Answer: 320

Step-by-step explanation:

Explanation with words: you take 64 and multiply it by 40 grams and you get 2,560

Which is what 64 bats could eat if one bat ate 40 grams a night. So you have to then devide it by 8 and the results are 320 which tells you that If 8 bats can eat 40 grams a night then 64 can eat 320

Explanation in expression form: 64 x 40 / 8

(/ means divide)

(I worked on hard this :) please consider giving me brainliest! Hope it helped :D)

The equation of the given circle in the standard form is given as x² + y² = 26.

In the question, we are given that the diameter of Circle \(Q\) terminates on the circumference of the circle at \((5,-1)\) and \((-5,1)\).

We are asked to write the equation of the circle in standard form.

The equation of the circle in standard form is given as (x - h)² + (y - k)² = r, where (h, k) is the center of the circle, and r is the radius of the circle.

The center of the circle can be found using the midpoint formula, as the center is the midpoint of the diameter.

Thus, the center is at ( (5 + (-5))/2, (-1 + 1)/2 ) = (0,0).

The length of the diameter can be calculated using the distance formula.

Thus, the length of the diameter of the circle is √((-5 - 5)² + (1 - (-1))²) = √( (-10)² + (2)² ) = √(100 + 4) = √104 = 2√26.

The radius is half the length of the diameter.

Thus, the radius, r = √26.

Now, we have the center (h, k) = (0,0), and the radius, r = √26.

Thus, the equation of the circle in the standard form, (x - h)² + (y - k)² = r ² can be shown as:

(x - 0)² + (y - 0)² = (√26)²,

or, x² + y² = 26.

Thus, the equation of the given circle in the standard form is given as x² + y² = 26.

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Answer 158Step-by-step explanation: you have to multiply the fraction by the numerator and divided by itsself and the subtract everything thren get myy642565780

The weight of each red marble is 120/5= 24 grams.

The bag contains 25 marbles and the mean weight is 16 grams.

In the bag, there are yellow, green, and red marbles.

Let us suppose the number of red marbles is x, and let the weight of each red marble be y grams.

Hence the total weight of the bag is: y × x + 10 × 12 + 20 × 8 = 25 × 16

y × x = 25 × 16 - 10 × 12 - 20 × 8

y × x = 400 - 120 - 160

y × x = 120 grams

Therefore, the weight of each red marble is 120/x grams.

x is 25-12-8= 5

The weight of each red marble is 120/5= 24 grams.

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Answer:

2 7/24 gallons

(sorry if its wrong)

Answer:

  -32

Step-by-step explanation:

change all the x and y's to the numbers

2(-4) + 3(-4)(2)

-8 + -24

Answer:

Step-by-step explanation:

Answer:

The situation of balloon B

Step-by-step explanation:

Balloon A is released 5 feet above the ground and our ground level be 0 feet. Let k be the rate at which it rises and t the time it takes to rise. Its height y, above the ground after time x is y = kt + 5

For Balloon B since it is released at ground level at which ground level is taken as 0 feet, let t be the time it takes to rise above the ground and k the rate at which it rises above the ground. Its height y above the ground after tie x is y = kt

Since the expression for Balloon B is y = kt and the expression for Balloon A is y = kt + 5, only the situation of Balloon B can be expressed in the form y = kx.

This is because the rate of rise of Balloon B follows a direct proportionality while the rate of rise of Balloon follow a joint proportionality since it starts from a point other than ground level.

Answer:

5:11 is the ratio is equivalent to 10:22

Step-by-step explanation:

10:22  if you simplify this ratio

5:11 ....so same as 10:22 just more simplified.

Answer:

17.6

Step-by-step explanation:

The analysis of the matrices and vectors components indicates;

a) coa(A) = 1

b) <A, B> = 37

c) ||u|| ≈ 91.79

A vector is an mathematical object has magnitude and direction. Vector quantities can be represented by an ordered list of numbers, representing the components of the vector.

a) The cosine of the angle between the vectors, can be obtained from the dot product formula as follows;

cos(A) = (5)·(0) + (0)·(0) + (82)·(1) = 82

The magnitudes of the vectors are; ||u|| = √(5² + 0² + 82²) = 82

||v|| = √(0² + 0² + 1²) = 1

cos(A) = (u·v)/(||u||·||v||) = 82/82 = 1

cos(A) = 1

b) The inner product of the matrices;  \(A=\begin{bmatrix} 4&7 \\ 8& 4 \\\end{bmatrix}\) and \(B = \begin{bmatrix}5 &-1 \\ 3&0 \\\end{bmatrix}\) can be found from the sum of the product of the corresponding entries of the matrices as follows;

<A, B> = 4 × 5 + 7 × (-1) + 8 × 3 + 4 × 0 = 37

The inner <A, B> = 37

c) The norm of a vector is defined as the square root of the sum of the squares of the components of the vector, therefore;

||u|| = √(|2 + 26i|² + |1 + 88i|² + |0|²)

|2 + 26i| = √(2² + 26²) = √(680)

|1 + 88i| = √(1² + 88²) = √(7745)

||u|| = √((√(680))² + (√(7745))² + (0)²) = √(8425) ≈ 91.79

The norm of the vector is ||u|| ≈ 91.79

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Answer:

sin(A) = 5/13 ≈ 0.38

cos(B) = 5/13 ≈ 0.38

tan(A) = 5/12 ≈ 0.42

Step-by-step explanation:

If you need more explanations just say it :)

Answer:

I hope your dreams come true! Beileve in your self! and do ur best <3

(a) The 95% confidence interval for proportion of residents in Muscat who consider television news as their major source of news is (0.485, 0.615).

(b) The sample-size of approximately 384 would be necessary to estimate the population proportion with a maximum error of 0.05 at a 95% confidence level.

To construct a confidence-interval for proportion of residents in Muscat who consider television news as their "major-source" of news, we use the  formula;

The Confidence-Interval = Sample Proportion ± Margin of Error

Part (a) : To calculate confidence-interval, we first find the sample proportion (p') and margin-of-error.

The Sample-Proportion (p') = Number of successes / Sample size

p' = 110 / 200 = 0.55,

The Margin-of-Error (ME) = Critical value × Standard Error

The "critical-value" depends on desired confidence-level. For 95% confidence-level, the "critical-value" corresponds to a z-score of 1.96.

The Standard-Error (SE) = √((p' × (1 - p')) / n)

Where n = sample size,

SE = √((0.55 × (1 - 0.55)) / 200) ≈ 0.033

Now we calculate the margin-of-error as :

ME = 1.96 × 0.033 ≈ 0.065,

Now, we construct the confidence interval:

Confidence Interval = 0.55 ± 0.065

Confidence Interval ≈ (0.485, 0.615)

So, the required confidence-interval is (0.485, 0.615).

Part (b) : To determine the sample size required to estimate the population proportion with "maximum-error" of 0.05 at a 95% confidence level, we use the formula:

Sample Size (n) = (Z² × p' × (1 - p'))/E²,

Where Z = critical value corresponding to desired confidence level,

p' = estimated proportion, and E = maximum error,

Using a Z-score of 1.96, and p' = 0.5 and E = 0.05, we calculate the sample size as :

n = (1.96 × 0.5 × (1 - 0.5)) / 0.05²

n ≈ 384.16

Therefore, the required sample-size is 384.

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The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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Answer:

0.1875

Step-by-step explanation:

Answer:

390 minutes I do believe.

Step-by-step explanation:

The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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To find the de Broglie wavelength of an electron, we can use the equation ke = 1/2 mv² and the relationship 1 electronvolt (eV) = 1.602×10⁻¹⁹ J.

The de Broglie wavelength can be expressed in meters to three significant figures.

The de Broglie wavelength (λ) of a particle is given by the equation

λ = h / p, where h is Planck's constant and p is the momentum of the particle.

For an electron with kinetic energy (ke) given by 1/2 mv², we can relate the kinetic energy to the momentum using the equation ke = p² / (2m).

First, we solve the equation ke = p² / (2m) for momentum (p):

p = √(2mke)

Using the relation ke = 1/2 mv², we can rewrite the equation as:

p = √(2mev)

Since 1 electronvolt (eV) is equal to 1.602×10⁻¹⁹ J, we can convert the energy (ev) to joules (J):

p = √(2m × 1.602×10⁻¹⁹ J)

Finally, we can substitute the known values for the mass of an electron (m) and Planck's constant (h) to calculate the de Broglie wavelength (λ):

λ = h / p

Expressing the result to three significant figures, we find the de Broglie wavelength of the electron.

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