What is the area of a circle with a diameter of 8 meters? Use 3.14 for pi, nothing else. Express in pi term and number term.

Answer:

A and B are not independent.

Step-by-step explanation:

Two events are said to be independent if :\(P(A \cap B)=P(A)P(B)\)

A: {Sum of the numbers showing is odd}

B: {Sum of the numbers showing is 9,11, or 12}

Given two dice, the sample space is given as:

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

The outcomes of event A:{Sum of the numbers showing is odd}  are:

(2,1),  (4,1), (6,1) ,  (1,2), (3,2),(5,2), (2,3), (4,3), (6,3)

(1,4), (3,4),  (5,4),  (2,5),  (4,5),  (6,5) , (1,6), (3,6),  (5,6)

P(A)=18/36

The outcomes of event B:{Sum of the numbers showing is 9,11, or 12} are:

(6,3) , (5,4),(4,5) (6,5) , (3,6), (5,6), (6,6)

P(B)=7/36

The intersection of A and B are:

(6,3) , (5,4),(4,5) (6,5) , (3,6), (5,6)

\(P(A\cap B)=6/36\)

We can see from the above that:

\(P(A)P(B)=\dfrac{7}{36}\times \dfrac{18}{36}=\dfrac{7}{72}\neq P(A\cap B)\)

Therefore, events A and B are not independent.

Answer:

zero times

Step-by-step explanation:

9-9=0

Answer:

4<x<10

Step-by-step explanation:

-2x<-4

Divide by 2

-x<-4

Divide by -1 (remember if you divide by -1, flip the direction of the sign)

x>4

x-4<6

Add 4 to both sides

x<10

Combine these

4<x<10

Answer:

-8

Step-by-step explanation:

Answer:

40 Apples

Step-by-step explanation:

3/5 of the apples are good so divide 24 by 3 which is 8, then multiply 8 by 2 which is 16, add 24 and 16 together to get 40. Let me know if I'm wrong.

The expression that represents "5 more than the difference of t and 8" is t - 3.

An expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can include constants, variables, and coefficients, and they can be simple or complex, depending on the number and types of operations involved.

In the given question,

To write an expression that represents "5 more than the difference of t and 8", we can start by finding the difference of t and 8, which is t - 8.

Next, we need to add 5 to this difference. So, the expression becomes:

(t - 8) + 5

Simplifying this expression by adding the terms in the parentheses and combining like terms, we get:

t - 3

Therefore, the expression that represents "5 more than the difference of t and 8" is t - 3.

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Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

1) 4x + 5y

→ 4*6 + 5*1

→ 24 +5 = 29

2) 2x (20-y)

→ 2*6 (20-1)

→ 12 *19 = 228

3) x ÷ 3 + y

→ 6 ÷ 3 + 1

→ 2 +1 = 3

4) 4y ÷ 2 + (8x + 10)

→ 4*1 ÷ 2 +(8*6+10)

→ 2 + (48+10)

→ 2 + 58

→ 60

5 ) 5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?

Money made each weekend = $34

Money made in 3 weekend = $34*3 =$102

Money spent = $50

Therefore ,

→Money left = Money made in 3 weekends - Money spent

→ Money left = $102 - $50 = $52

6.Carlos solved 20-(2x6) + 8 divide 4 = 29. Is this the correct answer? ( In attachment it's written 29 and not 28 .)

Given equation is ,

→ 20 - (2 × 6) + 8 ÷ 4 = 29

Solve inside the brackets ,

→ 20 - 12 + 8 ÷ 4

Perform division ,

→ 20 -12 + 2

Perform addition ,

→ 22 - 12

Perform subtraction,

→ 10

No , he is wrong the answer should have been 10 but he got 29 .

I hope this helps .

Answer:  $1.40

Work Shown:

x = cost before markup

1.45x = cost after the 45% markup

1.45x = 2.03

x = (2.03)/(1.45)

x = 1.40

The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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Answer:

x = 21.8

Step-by-step explanation:

x = 42.3 - 22.5

Answer:

Hence, n 3 −n=n(n+1)(n−1) is divisible by 6.

Step-by-step explanation:

The condition for any number to be divisible by 6 is that the number must be individually divisible by 3 and 2.

Check whether n 3−n is divisible by 3.

n3−n=n(n+1)(n−1)

When a number is divided by 3 then by the remainder theorem, the remainder obtained is either 0 or 1 or 2.

n=3p or n=3p+1 or n=3p+2, where p is some integer.

If n=3p, then the number is divisible by 3.

If n=3p+1, then n−1=3p+1−1=3p. The number is divisible by 3.

If n=3p+2, then n+1=3p+2+1=3(p+1). The number is divisible by 3.

So, any number in the form of n

3

−n=n(n+1)(n−1) is divisible by 3.

Check whether n

3

−n is divisible by 2.

When a number is divided by 2, the remainder obtained is either 0 or 1 by the remainder theorem.

n=2p or n=2p+1, where p  is some integer.

If n=2p, then the number is divisible by 2.

If n=2p+1 then n−1=2p+1−1=2p. The number is divisible by 2.

So, any number in the form of n

3

−n=n(n+1)(n−1) is divisible by 2.

Since, the given number n

3

−n=n(n+1)(n−1) is divisible by both 3 and 2. Therefore, according to the divisibility rule of 6, the given number is divisible by 6.

Answer:

Step-by-step explanation:

Let's simplify the equation first:

(n-3)(n+2)-(n-3)(n+8)

= n² - n - 6 - (n² + 5n - 24)

= n² - n - 6 - n² - 5n +24

= -6n - 18

Divisible means that the equation can be divided by 6 with no remainder.

If I divide the equation by 6, I get (-n-3)

It goes in evenly, therefore it is divisible by 6

9514 1404 393

Answer:

  245 cm²

Step-by-step explanation:

The surface area of a cone is given by ...

  SA = πr(r +s) . . . . where r is the radius, and s is the slant height

Filling in the given values, we have ...

  SA = (3.14)(3 cm)(3 cm +23 cm) = (3.14)(3)(26) cm² ≈ 245 cm²

The surface area of the cone is about 245 cm².

Answer:

uh l.m.a.o this is why im failing math

Step-by-step explanation:

lol

A two proportion significance test must be performed and pass all parameters. Ans is true since all three requirements have been met (I, II and III). Option (e).

Given,

For the two proportion significance test, the following assumptions were met: The populations are independent. (Populations exist in distinct groups.) The sample size multiplied by the success probability for each population is more than or equal to ten, as is the sample size multiplied by the failure probabilities. (We look at this normality criterion; if it holds true, we say that the data is roughly normally distributed.)

Every sample is chosen randomly. (The sample must be selected at random; else, bias may occur.) A two-proportion Z-test is a statistical hypothesis test that determines whether two proportions are different from one another. Two independent samples are used in the test, and Z-statistics are calculated with the null hypothesis that the two proportions are equal.

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Answer:

C(min)   =  8763.4 $

Step-by-step explanation:

Area =  24000 ft²

In a rectangle,    A =  x * y            x  is the base side and  y the height side

Cost of low and upper side   (x)  is 20 $ per foot

Cost of east and west sides  ( y)  is  10 $per ft

total cost is:

C(r)  =  2 * 20* x  +  2*  10* y

from  A =  x * y      y  =  A / x        y  =  24000 / x

And by substitution in C(r) we get:

C(x)  =   2 * 20* x  +  2*  10* 24000 / x

C(x)  =  40 * x  + 480000 / x

Tacking derivatives on both sides of the equation:

C´(x)  =  40  -  480000 / x²

C´(x)  =  0                40   -   480000/x²   = 0

40* x²  -  480000  = 0

x²  =  480000 / 40

x²  =  12000

x  =  √ 12000   =  109,54 ft

and  y  =  24000 / 109,54

y  =  219,09  ft

Chequing for second derivative

C´´(x)  =   480000 / x⁴     is always positive so we have a minimum of C at the value  x  =  109,54

Minimum cost C (min)  =  40* 109,54 +  20 * 219,09

C(min)   =  4381.6  +  4381.8

C(min)   =  8763.4 $

Answer:

  (b)  32x^3 - y^3 + 42x^2y + 11xy^2 + 17

Step-by-step explanation:

To find the difference of the polynomials, write the equation expressing the difference, then simplify.

  (19x^3 +44x^2y + 17) - (y^3 -11xy^2 +2x^2y -13x^3)

  = (19 -(-13))x^3 -y^3 +(44 -2)x^2y +(-11)xy^2 +17

  = 32x^3 -y^3 +42x^2y -11xy^2 +17

Therefore , the solution of the given problem of area comes out to be  Area of circle  85π cm2.

Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.

Here,

Given:

Points :P(-7; -2), Q(-1; 9) and R(5; -3).

The area of the circumscribed circle of the triangle.

is:

=> PQ = √(-7 - (-1))² + (-2 - (-9))²

=> PQ = √85

The radius is √85

=> Area of circle = π(√85)²

=>  Area of circle = 85π cm2

Therefore , the solution of the given problem of area comes out to be  Area of circle : 85π cm2.

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Step-by-step explanation:

Consider the Cartesian equation,

2

x+3

=

4

y−5

=

2

z+6

Now,

a

=−3

i

+5

j

−6

k

b

=2

i

+4

j

+2

k

Vector equation,

r

=

a

+λ.

b

=−3

i

+5

j

−6

k

+λ(2

i

+4

j

+2

k

)

This is the required equation

Answer:

Step-by-step explanation:

If the quadrilateral ABCD was translated, or moved upwards by 5, that would mean that the Y axis of the quadrilateral ABCD would change by 5. the X axis of the quadrilateral ABCD would not change, as the Quadrilateral was not translated on the X axis, but on the Y axis.

the Y axis, as you probably know, goes up, and down, and the X axis goes Left and Right, and when these two lines cross each other, that's the ordered pair, (0, 0).

and an Ordered pair is organized like (X, Y).

so, if you placed the ordered pairs (-5, 5) (-1, 5) (-1, 2) and (-5, 1) on a grid, and connect it, it would make a quadrilateral, and if I told you to move, or translate the shape by 5 along the Y axis, you would move it upwards by 5, and it would be (-5, 10) (-1, 10) (-1, 7) and (-5, 6).

9/16 must be added to this expression \(x^{2} -3x/2\) to make it a perfect square.

According to the question,

We have the following expression:

\(x^{2}\) -3x/2

Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.

Now, 9/16 is the square of 3/4.

So, we will first solve it using 9/16:

\(x^{2}\)-3x/2+9/16

Now, this formula is of identity \((a-b)^{2}\) where we have a = x and b = 3/4.

The formula of the identity \((a-b)^{2} = a^{2} + b^{2} -2ab\).

Now, adding 9/16 make it a perfect whole square.

(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)

Hence, the correct option is C.

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The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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The way that the mean will change when a value of 98 is added is C. The mean increases by 1.4°

The mean can be found by summing up all the temperatures given and then dividing by the number of cities listed.

The mean is therefore :

= ( 58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 ) / 12

= 965 / 12

= 80. 42 degrees

The new mean when 98 degrees is added is:

= ( 58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 98 ) / 13

= 81. 77 degrees

The change is :

= 81. 77 - 80. 42

= 1. 35

= 1. 4 degrees

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Answer:

\( \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} \)

V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters

The closest answer is 1,001.73 square meters.

The patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.

Given that, a doctor administers a drug to a ​34-kg ​patient, using a dosage formula of ​55mg/kg/day.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of tablets should a 34​-kg patient takes every four​ hours to be x.

Now, 55 × 34 = 1870 mg/day

For every four hours:

1870 × 1 /24 × 4 = 311.666

≈312 mg per 4 hours

So, x=312/4 × 1/300 = 78 × 0.0033

=0.26 tablet

Liquid suspension is for every 12 hours:

So, 312/12 × 1/200 = 26 × 0.005 = 0.13 mL

Hence, the patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.

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