1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
How many ounces are in 4 gallons?

Solution

for this case we can do the following multiplicating the two terms

If we multiply we got:

And if we simplify we got:

x 5x^2 9x 6

7x 35x^2 63x^2 42x

4 20x^2 36x 24

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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hi

budget is  170

we have  20 players and all of them need a package at  7.5 each.

So for 20 players  total amount spend is  :   20*7.5 = 150

there is  3.99 shipping cost

total spendings :   150 + 3.99 = 153.99

AS budget is  170 , so remais  :  170 - 153.99 = 16.01  

For fX(x;μ,σ2) as the probability density function of a normally distributed variable X with mean μ and variance σ2.

a. The value of x maximizes this function is μ

b. The maximum value of fX(x;μ,σ2) is   1/√2πσ.

For the first problem, the value of x that maximizes the probability density function of a normally distributed variable x with mean μ and variance is σ2 is μ, it is because the probability density function of a normal distribution is symmetric around its mean. Therefore, the maximum value of the probability density function of a normal distribution occurs when x is equal to the mean, μ.

For the second case, the solution is   1/√2πσ,because the probability density function of a normal distribution is expressed as 1/(σ√2π) e-((x-μ)^2/(2σ^2)). the maximum value of this function occurs when the exponent is equal to zero. Setting the exponent to zero and solving for x yields μ, which is the mean of the normal distribution. Plugging μ into the expression for the probability density functions yields  1/(σ√2π),

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The volume of the rectangular prism is 4.84 cm cube.

A rectangular prism is filled exactly with 605 cubes. Each cube has edge

length 1 / 5 cm. Therefore, the volume of the rectangular prism can be

calculated as follows:

volume of each cube = l³

volume of each cube = (1 / 5)³

volume of each cube = 1 / 125 cm³

Therefore,

volume of the rectangular prism = 605 × 1 / 125

volume of the rectangular prism = 605 / 125

volume of the rectangular prism = 4.84 cm³

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Answer:

second one

Step-by-step explanation:

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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Answer:

The x intercept is 3

(3,0)

Step-by-step explanation:

3x+y -9 =0

To find the x intercept, set y=9 and solve for x.

3x+0-9=0

3x -9=0

Add 9 to each side

3x-9+9=9

3x =9

Divide by 3

3x/3 = 9/3

x =3

The x intercept is 3

(3,0)

Answer:2(2x2+x−4)

Step-by-step explanation:

Factor 4x2+2x−8

4x2+2x−8

=2(2x2+x−4)

The drafting machine is a tool used for technical drawing and the instrument used is a T-square

Given data ,

A drafting machine is a tool used for technical drawing and drafting. It typically consists of a drafting arm or a mechanical linkage that allows for precise movements and measurements. While a drafting machine itself is useful for drawing straight lines and angles, it typically needs to be used in conjunction with other instruments to complete the drawing process.

A T-square is a crucial instrument in drafting that provides a straightedge for drawing horizontal lines and ensuring vertical alignment. It is commonly used in combination with a drafting machine to create accurate drawings.

Hence , Nathan will need a T-square in addition to his drafting machine to effectively complete his drafting tasks

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Answer:

Because If we tried to define scalar multiplication we would run into problems.  No there are not any special accommodations.

Step-by-step explanation:

Answer:

2 4/12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

\(P(B|A)\)

Step-by-step explanation:

Probability notation:

Suppose that we have two events, event A and event B. The probability of event B occuring, considering that event A has occurred, is given by:

\(P(B|A)\), which is the answer to this question.

The polynomial value equations are solved and the solutions are :

a) ( x - 2 )² = x² - 4x + 4

b) ( x - 4 ) ( x + 4 ) = x² - 16

c) ( x² + 2x ) ( -2x + 8 ) = -2x³ + 4x² + 16x

Given data ,

Let the equation be represented as A = (x - 2)²

Using the square of a binomial formula, (x - y)² = x² - 2xy + y², we can apply it to (x - 2)²:

(x - 2)² = x² - 2(x)(2) + 2²

A = x² - 4x + 4

Hence the polynomial (x - 2)² simplifies to x² - 4x + 4

b)

Let the equation be represented as A = (x - 4)(x + 4)

Using the distributive property, we can multiply (x - 4)(x + 4):

(x - 4)(x + 4) = x(x) + x(4) - 4(x) - 4(4)

A = x² + 4x - 4x - 16

A = x² - 16

Hence the polynomial (x - 4)(x + 4) simplifies to x² - 16

c)

Let the equation be represented as A = (x² + 2x)(-2x + 8)

Using the distributive property, we can multiply (x² + 2x)(-2x + 8):

(x² + 2x)(-2x + 8) = x²(-2x) + x²(8) + 2x(-2x) + 2x(8)

A = -2x³ + 8x² - 4x² + 16x

A = -2x³ + 4x² + 16x

Hence the polynomial (x² + 2x)(-2x + 8) simplifies to -2x³ + 4x² + 16x

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Financial Maths

A sequence of equal payments (or deposits) at equal periods of time is called an annuity.

The future value of an annuity can be calculated with the formula:

Where:

FV is the future value of the annuity

A is the periodic deposits

n is the number of compounding periods per year

i is the interest rate adjusted to the compounding periods. i = r/n where r is the APR.

t is the duration of the investment in years

The financial variables for this investment are:

A = $1100

r = 3.7% = 0.037

n = 360. Daily compounding

i = 0.037/360 = 0.000102777

It's crucial to keep as many decimals as possible in the calculations.

Applying the formula:

Calculating:

FV = $14,361,798.98

Calculation steps (in strict order)

* Add 1 + 0.00010277 = 1.00010277

* Multiply 360*23 = 8280

* Raise 1.00010277^8280 = 2.341885

* Subtract 1 = 1.341885

* Divide by 0.00010277 = 1.341885/0.00010277=13056.18

* Multiply by 1100: $14,361,798.98

Rounded to the nearest cent

we need to find the total area to fabric the sails

have a 2 triangles

we have to find th area of each one and then add it

the area of the triangle is given by the following formula

for first triangle

base=8

height=10

for second triangle

base=4

height=8

now the Total area is given by

AT=A1+A2

AT=45+12

AT=57 units^2

then Zulma needs 57units^2 to fabric the sails

Answer:

see below

Step-by-step explanation:

center of circle = (2,-1)

r = 6 -2 = 4

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

so the equation will be:

( x - 2 )^2 + ( y +1 )^2 =16

Answer:

A or C, but A is my guess.

Step-by-step explanation:

Answer:

A.) The sum will be an even integer.

Step-by-step explanation:

The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an even integer. This is because even integers are numbers that are divisible by 2, and odd integers are numbers that are not divisible by 2.

For example, consider the sum of the even integer 6 and the odd integer 7. The sum of these two numbers is \(6 + 7 = 13\), which is an odd integer. However, if we add another even integer to the sum, such as 4, the resulting sum is \(13 + 4 = 17\), which is an even integer. This shows that the sum of two even integers and one odd integer is always an even integer.

This conjecture can be proven using mathematical induction. We can start by showing that the sum of any two even integers and one odd integer is always an even integer. Then, we can assume that the sum of any n even integers and one odd integer is also an even integer. Finally, we can show that the sum of n+1 even integers and one odd integer is also an even integer, using the assumption that the sum of n even integers and one odd integer is even. This will prove that the conjecture is always true.

Answer:

50 degrees

Step-by-step explanation:

A triangle's angles added up together is 180 degrees. We already know that the right angle is 90 degrees, and the other angle is 40 degrees. To find the missing angle, we need to add 90+40 to get 130 degrees, and subtract the sum from 180 degrees to get our missing angle of 50 degrees.

Applying the exterior angle theorem, the value of x = 8.

According to the exterior angle theorem, the measure of an exterior angle of a triangle is always equal to the sum of the two remote interior angles of the triangle.

The image of triangle LMN is shown in the attachment.

We are given that:

m∠MNO = (5x + 2)° [exterior angle of the triangle]

m∠NLM = (x + 10)°

m∠LMN = (x + 16)°

Therefore, based on the exterior angle theorem, we have the equation below:

m∠MNO = m∠NLM + m∠LMN

Plug in the values:

5x + 2 = x + 10 + x + 16

Combine like terms

3x + 2 = 26

Subtract both sides by 2

3x + 2 - 2 = 26 - 2  [subtraction property of equality]

3x = 24

Divide both sides by 3

x = 8

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A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.

In the given question,

We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

..............< p <...............

We have to construct the 90% confidence interval.

From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.

So the total number of cell phone owners aged 18 - 24 is 240.

So n=240

From them 108 have an android phone.

So x=108

Estimation of sample proportion(\(\hat p\)) = x/n

Now putting the value

Estimation of sample proportion(\(\hat p\)) = 108/240

Estimation of sample proportion(\(\hat p\)) = 0.45

Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone

C.I. = \((\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})\)

As we know that

\(\hat p=0.45\)

Now finding the value of \(z_{\alpha /2}\)

We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90

So \(\alpha\) = 1-0.90

So \(z_{\alpha /2}=z_{0.10 /2}\)

\(z_{\alpha /2}=z_{0.05}\)

From the standard z table

\(z_{0.05}\) = 1.645

Now putting the value in the

C.I. =  \((\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})\)

C.I. = \((0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})\)

Simplifying

C.I. = \((0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})\)

C.I. = \((0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})\)

C.I. = \((0.45 \pm 1.645\sqrt{0.001031})\)

C.I. = \((0.45 \pm 1.645\times0.0321)\)

C.I. = \((0.45 \pm 0.053)\)

We can write it as

C.I. = {(0.45+0.053),(0.45-0.053)}

C.I. = (0.503,0.397)

Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

0.503 < p < 0.397.

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Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:

If something weighs more than 2000 pounds, then it weighs more than Jill’s car.

Sally weighs more than 2000 pounds.

Therefore, Sally weighs more than Jill's car.

2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Sally weighs more than Jill's car.

Therefore, Sally is too heavy for the bridge.

The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.

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Answer:

.....................

Answer:

\(f(x) =2 {(x - 1)}^{2} + 3x - 7 \\ f(0) = 2{(0 - 1)}^{2} + 3(0) - 7 \\ f(0) = 2 {( - 1)}^{2} + 0 - 7 \\ f(0) = 2(1)- 7 \\ f(0) = 2 - 7 \\ f(0) = - 5 \)

__o_o__

\(f(x) = 2 {(x - 1)}^{2} + 3x - 7 \\ f( - 3) = 2 {( - 3 - 1)}^{2} + 3( - 3) - 7 \\ f( - 3) = 2 {( - 4)}^{2} - 9 - 7 \\ f( - 3) = 2(16) - 16 \\ f( - 3) = 32 - 16 \\ f( - 3) = 16\)

I hope I helped you^_^

Answer:

(a)

\(S = \{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}\)

(b)

\(P(A) = \frac{1}{6}\)

Step-by-step explanation:

Given

The above sample space

A = Event of an occurrence of 3 or 4 then a head

(a): List out the sample space:

The rolls of the dice come first, followed by the toss of the coin.

So, the sample space are:

\(S = \{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}\)

The number of the sample space is:

\(n(S) = 12\)

(b): Find P(A)

First, we list out the outcomes of event A

\(A = \{(3,H),(4,H)\}\)

The number of outcome is:

\(n(A) = 2\)

The probability of A is then calculated as:

\(P(A) = \frac{n(A)}{n(S)}\)

\(P(A) = \frac{2}{12}\)

Simplify fraction

\(P(A) = \frac{1}{6}\)

Answer:

Step-by-step explanation:

f(x) = |2x−1|+3, reflected over the y-axis becomes

g(x) = |-2x−1|+3

We needed the point (0.5, 3) to go to the other side of the y-axis to get the point (-0.5, 3).

Answer:

its D

Step-by-step explanation:

calculator

Answer:

i think

Desktop: $2900.00,  Laptop: $3200.00

Step-by-step explanation:

Answer:

ABCDE is similar to the ZWYXV