Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?

The correct answer is option B which is the volume of the prism is 216 km³.

A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.

The volume of the prism will be calculated by using the formula below:-

V  =  Area of the base   x   Height

Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.

V  =  Area of the triangle  x  Height

V  =  ( 1/2 ) x 8 x 6 x ( 9 )

V  =  216 km²

Therefore the correct answer is option B which is the volume of the prism is 216 km³.

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A number where the digit 3 has a value ten times greater than the 3 in 145,317 can be 143,417.

In any number, the place value refers to the "place" that a digit has on a number. The first one is the units place, the second is the tens place, and so on.

As more in the left is the place value, the largest value it represents.

Particularly, in 145,317

The 3 is on the third place, so it represents the value 300.

For example, in 143,417

The 3 is more in the left than before, this time on the fourth place, this time the value of the 3 is 3,000.

Then, a number where the digit 3 has a value ten times greater than the 3 in 145,317 can be 143,417.

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Answer:

2.6 and 2.7

Step-by-step explanation:

The actual square root of 7 is 2.64 and that is between 2.6 and 2.7.

The number of each tortilla type that Mathew would need to feed everyone is = 6 packages of Soft tortillas and 5 packages of Crispy taco shells.

The number of people Matthew is expecting including himself = 60

The Soft tortillas coke appear = 10/pack

The Crispy taco shells appear = 12/pack

Since each person is to get 1 soft and 1 crispy taco, the number of tortilla type that Mathew would need to feed everyone is

= 60/10 = 6 packages of Soft tortillas

= 60/12 = 5 packages of Crispy taco shells

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Answer:

[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]

Step-by-step explanation:

I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:

[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]

Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.

Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.

The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is four times of cos2x plus logx plus x.

f(x)= 4cos2x + logx + x

We need to find the derivative of it f'(x)

d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

We know that

d/dx(cosx)=-sinx

d/dx(logx)=1/x

d/dx(x)=1

Apply in above equation

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4.2(-sin2x)+1/x+1

f'(x)=-8sin2x+1/x+1

Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

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Answer:

2

Step-by-step explanation:

we know the line goes through the origin, so we have point (0,0). next, find another point the line goes through. for example, point (2,4)

the slope formula for points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). plug in the 2 points to get (4-0)/(2-0) = 4/2 = 2

Answer:

Yes

Step-by-step explanation:

There is only one output value for each input value, which is the definition of a function.

Answer:

B) h=63

Step-by-step explanation:

Multiply both sides by 9.

h/*9=9*7

Simplify

h=63

[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]

Multiply both sides by 9.

Multiply 7 and 9 to get 63.

Therefore, the correct option is "B".

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Answer:

5,125

Step-by-step explanation:

Applying the Pythagorean theorem, the missing side of the right triangle is: √788.

To find the hypotenuse (c) of a right triangle, having two other legs a and b, the Pythagorean theorem states that, c = √(a² + b²).

Given the following:

Plug in the values

x = √(2² + 28²)

x = √788

Missing side is: √788.

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Answer:

z=4

Step-by-step explanation:

subtract 47-35

3z=12

divide both sides by 3

z=4

The distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Distance = average velocity × time

Let the time and distance of the run, respectively, be t₁ and.d₁

Let those of the bicycle race be t₂ and d₂

From the question,

t₁ + t₂ = 5

d₁ = 8t₁

d₂ = 27t₂

Total distance = 97

8t₁ + 27t₂ = 97

8 ( 5 - t₂ ) + 27t₂ = 97

40 - 8t₂ + 27t₂ = 97

40 + 19 t₂ = 97

19t₂ = 57

t₂ = 3 hours

t₁ + t ₂ = 5

t₁ = 5 - t₂

t₁ = 5 - 3 = 2 hours

Now the distances are calculated as:-

d₁ = 8t₁ = 8 x 2 = 16 miles

d₂ = 27t₂ = 27 x 3 = 81 miles

Therefore the distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

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Answer:

To pull our the first chocolate, it would be a probability of 1/2.

To pull the second chocolate out, it would be a probability of 2/5.

Hope that helps, you just use ratios, the first cupcake needs to be chocolate, and there are 3 chocolate cupcakes out of the 6. Make that into a fraction 3/6, and simplify into 1/2.

The same goes for the second cupcake.

Answer:

= .75 gallons or 3 quarts

Step-by-step explanation:

Known

Problem:

4 gallons 2 quarts - 3 gallons 3 quarts

⇒ 2 quarts: 0.5 gallons

⇒ 3 quarts: 0.75 gallons

Add on both sides

4 + 0.5 = 4.5 gallons

3 + 0.75 = 3.75 gallons

This leaves the equation at:

This equals 3 quarts or 0.75 gallons.

The volume of water that was displaced is 0. 000019 cubic meters.

Volume is known to be the amount of space or capacity occupied by a three-dimensional solid shape.

It is denoted in cubic units.

The formula for calculating volume is;

Volume = mass ÷ density

Given that mass = 3. 3 Ibs and density = 32. 5Ibs/ ft∧3

Volume = 3. 3 ÷ 32. 5 = 0. 10 Ibs

How to covert Ibs to cubic meters

Ibs = 0. 00019 m∧3 (cubic meters)

Then, 0. 10 Ibs = 0. 00019 × 0.10 ÷ 1 = 0. 000019 cubic meters.

Therefore, the volume of the water displaced is 0.000019 cubic meters.

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Answer:

16cm and 48 degrees

Step-by-step explanation:

Answer:

The answer is C: (2x +3, 2y)

Step-by-step explanation:

When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.

Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.

(x, y) -----> (2x, 2y)

Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.

Translation 2 units right:

(2x, 2y) -----> (2x +3, 2y)

Answer:

a) -3

b) 9

c) -3

Step-by-step explanation:

a)

[tex]2^5 * 2^{-8} = 2^a[/tex]

In cases where we have a multiplication with exponents we keep the integer as it is and we add the exponents. 5 + -8 = -3. Therefore a is 3.

b)

[tex]\frac{4^7}{4^-{2}} = 4^b[/tex]

In cases when we have a division with exponents we keep the integers as it is and we subtract the exponents. 7 - (-2) = 7 + 2 = 9. Therefore, b is 9

c)

[tex]\frac{7^9}{7^c} = 7^{12}[/tex]

We are dividing again however we are finding the denominator.

9 - (c) = 12

Subtract from both sides: -c = 3, To make c positive we just make the value negative, c = -3. Therefore c is -3

Answer:

9 inches

Step-by-step explanation:

I assume you mean the volume of the box is 450.

In that case, to figure out for the volume we multiply 10 by 5. This gives us 50.

450/50=9

The height of the box is 9 inches

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The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.

The slope and y-intercept of an equation can be easily found using slope intercept equation.

y = mx + b

where

Therefore,

3x + 2y = 14

2y = -3x + 14

y = -3 / 2 x + 7

Therefore,

slope = - 3 / 2

y-intercept = 7

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The true statement is the correlation is most likely due to a lurking variable.

Correlation is a statistical measure used to measure the relationship that exists between two variables. Negative correlation is when there is an inverse relationship between the two variables. If one variable increases, the other variable decreases.

Assume that the store is located near a school where the students live on an allowance. So, students do not have time to buy both computers and microwaves. When students buy computers they do not have enough money to buy microwaves. This explains the negative correlation.

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Answer:

  (d)  32

Step-by-step explanation:

An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.

__

An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.

We are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.

Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.

The desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.

Ryder's estimate was 32.

_____

Additional comment

The actual product is ...

  (25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).

As a first approximation of the error in the product 32.5, we can sum the middle two terms:

  -0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.

Then the first refinement of the estimate will give us ...

  32.500 -0.276 = 32.224

The actual value is obtained by adding the final error term:

  32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.

Answer:

yo

Step-by-step explanation:

its C, or 20

edge

ur welcome

Answer:

coz it is

Step-by-step explanation:

the angle is 57° , so y is 63 as 63-6 = 57

Answer:

19 is suitable no in which 1 is square of itself and 9 is of 3

Answer:

C

Step-by-step explanation:

the explicit formula for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

from the recursive formula in the form

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

given

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 7

with d = - 7 and a₁ = 4 , then explicit formula is

[tex]a_{n}[/tex] = 4 + (n - 1)(- 7)

Answer:

68 inches

Step-by-step explanation:

y = x + 2

x = 66

y = 66 + 2

y = 68