if the product of 11 positive integers is odd, how many of these integers must be odd

0.8926 is the probability that the shipment will be rejected.

What does the math term "probability" mean?

Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                              Statistics describes the examination of events subject to probability.

The probability that a digital​ watch is defective p = 10/50 = 0.2

                                                                       n = 10

Using the binomial probability formula

             P(x) = ⁿCₓ pˣ ( 1 - p)ⁿ⁻ˣ

Let x be the random variable that represents the number of defective watches.

The probability that the shipment will be​ rejected

  P(x ≥ 1 ) = 1 - P(0)

               = 1 - ¹⁰C₀ ( 0.2)⁰ ( 0.8)¹⁰

               = 1 - ( 0.8)¹⁰

                = 0.8926258176  ≈ 0.8926

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Answer:

No solution

Step-by-step explanation:

You will get zero

Answer:

54678 years

Step-by-step explanation:

Answer:

The third option

Step-by-step explanation:

Since both perimeters are equal, they are equal to each other. You would have to work out the perimeter for each shape and make them equal to each other.

Using the Central Limit Theorem, it is found that the measures are given by:

a) 2,500,000.

b) 88,388.35.

c) 2,500,000.

By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean \(\mu\) and standard deviation \(\sigma\) has the same mean as the population, but with standard deviation \(s = \frac{\sigma}{\sqrt{n}}\)

Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:

\(s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.\)

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The two variables to have a negative correlation are x and y.

Negative correlation is the relationship where x grows as y decreases.

Given,

Here, negative correlation is used to describe the relationship between two variables that results in independent variables moving in one direction while dependent variables move in another.

Positive correlation

Positive correlation is when the value of the variable x rises as the value of the variable y rises.

Negative Correlation

Negative correlation is the relationship where x grows as y decreases.

No correlation

No correlation exists between the two variables.

That example, the term "no-correlation" refers to the absence of a connection between two variables.

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The question is improper. Proper question is given below;

What two variables are likely to have a negative correlation

Step-by-step explanation:

This is of the form

(x-h)^2 + ( y-k)^2 = r^2        so r^2 = 16  means r = 4   units

The simplified ratio of 800 pounds to one ton is 2 : 5.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

There are 2000 pounds in one ton. Therefore, the ratio of 800 pounds to one ton can be written as:

800 pounds : 2000 pounds

To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which is 200. This gives:

800 pounds : 2000 pounds = 4 : 10 = 2 : 5

Therefore, the simplified ratio of 800 pounds to one ton is 2 : 5.

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Apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2 where c is the hypotenuse.

a^2 + b^2 = c^2
8^2 + 5^2 = c^2
64 + 25 = c^2
89 = c^2
√89 = √c^2
c = √89

For the given exponential function f(x) = abˣ, the value of a and b is given as 7 and 5 respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
f(x) = abˣ

Put x = 2 and f(x) = 175,
175 = ab² - - - - (1)

Put x = 0 and f(x) = 7,
7 = ab⁰
Since b° = 1
a = 7

Put a = 7 in equation 1,
175 = 7b²
b² = 175 / 7
b² = 35
b = 5

Thus, the required simplified value of the a and b is 7 and 5 respectively.

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

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

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Set B_V spans V and is linearly independent, satisfying the requirements for a basis.

The statement is true.

If W is a subspace of a vector space V and B_W is a basis for W, then it is true that there exists a unique subspace U such that V = W ⊕ U, where ⊕ represents the direct sum of subspaces.

This means that every vector in V can be uniquely expressed as the sum of a vector in W and a vector in U.

Additionally, there exists a basis B_U for U such that the union of B_W and B_U, denoted as B_V = B_W ∪ B_U, forms a basis for the entire vector space V.

This means that the set B_V spans V and is linearly independent, satisfying the requirements for a basis.

Hence, the statement is true.

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Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

r=S/2πr+πh

STEP BY STEP EXPLANATION

By solving this question we will make r the subject of the formula

2πr²+πrh=S

factorise(between the two values find the common factors which is πr)

πr(2r+h)=S

divide both sides by the factorised expression which is (2r+h)

πr=S/(2r+h)

to get our r we need to divide both sides by π which is the coefficient of r

r=S/(2r+h)π

r=S/(2πr+πh)

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In order to calculate the balance in compound interest, we can use the formula below:

Where A is the balance after t years, P is the principal (initial amount), r is the interest rate and n is how many times the interest is compounded in a year.

For continuous compounding, we use this formula instead:

So we have:

If Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. Approximately the distance from the cliff is Catarina’s boat is : 63.6ft.

Distance can be defined as how far an object is from another object.

Now let find the distance:

AE/CD = BC/DE

Hence,

5.5/3.5 = 10/DE

Cross multiply

AE = 350/5.5

AE = 63.6ft

Therefore we can conclude that the distance is 63.6ft.

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the standard deviation of 2nd student data is least so the measurement of 2nd student is more precise.

In this problem we have four sample of four students which measure by same meter stick. Average of all student's data is 12.4 which is same. we have to check whose measurement is precision. according to least standard deviation is least which data is more precision.

the standard deviation=\(\sqrt{\frac{\sum(xn-x')^2}{n-1} }\) ,where x' is average of data .

by the above formula.

We have standard deviation for first student is 0.40.

2nd student is 0.23, 3rd student is 0.52 and 4th student is 0.36.

after examining the standard deviation of all data 2nd student measurement is more precision.

The complete question is,

Four students used the same meter stick to measure an edge of the same wooden cube four times. They obtained the following results:

Student I II III IV

11.90 cm 11.95 cm 11.90 cm 11.95 cm

12.25 cm 12.35 cm 12.15 cm 12.30 cm

12.70 cm 12.60 cm 12.45 cm 12.55 cm

12.75 cm 12.70 cm 13.10 cm 12.80 cm

Average 12.40 cm 12.40 cm 12.40 cm 12.40 cm

Which student’s measurements represent the

greatest precision?

A. Student I

B. Student II

C. Student III

D. Student IV

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The equation is given to be:

We can write the equation in the standard form of the equation of a hyperbola to be:

Therefore, we have the following parameters:

Recall the hyperbola foci definition:

Therefore, the value of c will be:

Therefore, the foci will be:

The correct option is the FIRST OPTION.

Answer:

The answer is C

Step-by-step explanation:

There are other examples but C

Answer:

Step-by-step explanation:

A: not correct. You're changing phase. That's a physical change.

B: not correct. You are just changing the shape of something. That is physical as well. No electrons moving around is involved.

C: Here's your answer. Anytime you get a gas given off you can suspect that a chemical reaction has taken place.

D: Not true. A mixture formation is not a chemical reaction

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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The inverse statement is false.

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Answer:

$25

Explanation:

The compound interest formula gives

where

A = final balance

P = principle amount

r = interest rate /100

n = # of compounds applied per interval

t = # of intervals

The interest earned, therefore, is the difference of the final balance and principle.

Now in our case.

P = $2500

r = 1 / 100

n = 1 ( 1 year = 12 months )

t = 1 ( 12 months = 1 year )

Therefore, our formula gives

which simplifies to give

This tells us that the interest earned is $25.

Using the parentheses to rewrite the equation 8×9-2-3​ gives 67.

In mathematics, the order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.

A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation. There is also another version called BODMAS but the principles are the same

Parenthesis            (  )

Exponent                a⁷

Multiplication          ×

Division                   ÷

Addition                  +

Subtraction             -

Given: 8×9-2-3​

We can rewrite the equation using parenthesis using PEMDAS:

Multiplication first, then followed by addition/subtraction:

8×9-2-3​ = (8 × 9) - 2 - 3

             = 72 - 2 - 3​

             = 67

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The coordinates to which the portable irrigation system should be sent to water the area are:

(495.75, 672).

The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.

Hence the coordinates are given as follows:

Hence the x-coordinate of the point to which the system should be sent is:

x = (56 + 144 + 888 + 895)/4 = 495.75.

(the mean is given by the sum of the observations divided by the number of observations).

The y-coordinate of the point to which the system should be sent is:

y = (289 + 332 + 1012 + 1055)/4 = 672.

The area is given by the image at the end of the answer.

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The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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