Evaluate the following when a = 4 and b = 7 (a+b)^2 - (a^2 + b^2)

Answer:

The answer is C, as you'd need to multiply the chance of getting a convertible by the chance of getting a red car, or vice versa.

Step-by-step explanation:

Notice in A it says OR, meaning that it can't be both red and a convertible. B would be impossible, and D would be adding and not multiplying, so C would be the answer. 0.40*0.25=0.10

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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at first we should find the equation of this line so we should find a in the equation of y = a x + b and we do not care about b as it is parallel so a = ( (4 -(-2)) ÷ 1 -(-2)) = 2 so y = 2 x + b and we put x = 3 and y = 7 the result is 7 = 2×3 + b and b = 7 - 6 = 1 the equation is y = 2x + 1

Step-by-step explanation:

A

=

h

b

b

2

=

11

·

22

2

=

121

cm²

The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².

To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:

Area = (1/2) * base * height

In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.

Substituting these values into the formula, we have:

Area = (1/2) * 22 cm * 11 cm

Calculating this expression, we get:

Area = (1/2) * 242 cm²

Simplifying further, we have:

Area = 121 cm²

The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².

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Answer:

1/2.25 or 4/9

Step-by-step explanation:

Step-by-step explanation:

1. In the picture down below.

2. Because they are = 20

100 ÷ 5 = 20

10 ÷ 0.5 = 10 x 2 = 20

1 ÷ 0.05 = 1 x 20 = 20

The total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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The total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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Answer:

1/6

Step-by-step explanation:

They're independent which means to find their intersection you just multiply

(1/4)*(2/3)= 2/12= 1/6

Answer:

Yes

Step-by-step explanation: Not enough context.

Answer:

a = 17

c = 9

Step-by-step explanation:

2a + 3c = 61

3a + 5c = 96

3a = 96 - 5c   (solve for 'a'. Then you can substitute)  

a = 32 - \(\frac{5}{3}\) c

2(32 - \(\frac{5}{3}\)c) + 3c = 61     (Substitute)

64 - \(\frac{10}{3}\)c + 3c = 61        (\(\frac{10}{3}\) = 3 \(\frac{1}{3}\). So subtracting, adding a negative, leaves \(\frac{-1}{3}\))

-\(\frac{1}{3}\) c= -3  

c = 9

2a + 3(9) = 61

2a + 27 = 61

2a = 34

a = 17

The exact answer without rounding is 166.276877527

The area of a hexagon can be calculated by finding the area of one of the six triangles that make it up by 6.

I added a picture below on how I got it and how it looked like!

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer:

1.5 rounded to the nearest tenth

Step-by-step explanation:

To find how much greater WBC are from RBC we do,

3.92 ÷ 2.6

= 1.50769230769

Which is 1.5 rounded to the nearest tenth.

Thus,

there are approximately 1.5 times WBC than RBC.

Hope this helps :)

The 1.5 times greater is the number of red blood cells than white blood cells

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Adult humans have approximately 2.6 red blood cells and 3.92 white blood cells.

To find the number of times greater is the number of red blood cells than white blood cells:

Use division operation,

3.92 / 2.6

= 1.5076

≈ 1.5 rounded to the nearest tenth.

Therefore, the required number is 1.5 times.

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Answer:

Bottom Right Graph (Absolute Value)

General Formulas and Concepts:

Step-by-step explanation:

When we apply the VLT to the 4 different graphs, we see that the only graph that actually passes the VLT is the absolute value graph. Therefore, that is our answer (none of the other graphs pass the VLT).

a) The coordinates of the ellipse are centered at (3, 2).

b) The area of the ellipse is a = √5 and b = √20.

c) Perimeter ≈ π * (3(a + b) - √((3a + b)(a + 3b))).

d) The vertices of the ellipse are located at (3 ± √5, 2) and (3, 2 ± √20).

e) The foci of the ellipse cannot be determined in this case because the equation does not contain information about the foci.

f) The length of the major axis is 2a, The length of the minor axis is 2b.

Let's analyze each given equation of the ellipse and determine the requested information.

a) Equation: 4x² + 5y² - 24x - 20y + 36 = 0

To write the equation in standard form, we need to complete the squares for both x and y terms.

Rearranging the terms:

4x² - 24x + 5y² - 20y + 36 = 0

Completing the squares for x:

4(x² - 6x) + 5y² - 20y + 36 = 0

4(x² - 6x + 9) + 5y² - 20y + 36 = 4(9)

4(x - 3)² + 5y² - 20y + 36 = 36

4(x - 3)² + 5(y² - 4y) = 0

Completing the squares for y:

4(x - 3)² + 5(y² - 4y + 4) = 0 + 5(4)

4(x - 3)² + 5(y - 2)² = 20

Comparing this with the standard form of the ellipse equation:

[(x - h)²/a²] + [(y - k)²/b²] = 1

We can see that a² = 5, b² = 20, h = 3, and k = 2.

b) Area of the ellipse:

The area of the ellipse can be calculated using the formula: Area = π * a * b, where a and b are the semi-major and semi-minor axes, respectively.

In this case, a = √5 and b = √20.

So, the area of the ellipse is Area = π * √5 * √20 = π * 2 * √5.

c) Perimeter of the ellipse:

There is no simple formula to calculate the exact perimeter of an ellipse. However, an approximation formula can be used: Perimeter ≈ π * (3(a + b) - √((3a + b)(a + 3b))).

In this case, a = √5 and b = √20.

Plugging in the values, we can calculate the approximate perimeter of the ellipse.

d) Vertices:

The vertices of the ellipse can be determined using the formula:

Vertex on the x-axis: (h ± a, k)

Vertex on the y-axis: (h, k ± b)

In this case, the vertices will be (3 ± √5, 2) and (3, 2 ± √20).

e) Foci:

The foci of the ellipse can be determined using the formula:

Foci on the x-axis: (h ± c, k)

Foci on the y-axis: (h, k ± c)

where c = √(a² - b²) for a > b.

In this case, c = √(5 - 20) = √(-15) = imaginary value (since it is negative).

f) Length of major and minor axes:

The length of the major axis is 2a, where a = √5.

The length of the minor axis is 2b, where b = √20.

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The surface area of the given sphere is approximately 2124 units². The correct answer is option A.

The surface area of a sphere is given by the formula:

SA = 4πr²

Here r is the radius of the sphere and π is a constant approximately equal to 3.14.

As per the question, the radius of a sphere is 13 units.

Substituting the given value of r = 13 units, we get:

surface area of a sphere = 4π(13)²

surface area of a sphere = 4π(169)

surface area of a sphere = 676π  units²

Therefore, the given surface area of a sphere is 676π units².

Hence, the correct answer is option A.

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True. The r command "qt(0.95, 7)" calculates the critical value of the distribution with 7 degrees of freedom at a significance level of 0.05 and a two-tailed test. The "qt" function in R is used to find the critical value of a t-distribution for a given probability and degrees of freedom.

In this case, the command returns the critical value of the t-distribution with 7 degrees of freedom at a significance level of 0.05, which can be used to perform hypothesis testing or confidence interval calculations. It is important to note that the critical values of the t-distribution change as the degrees of freedom change, and different significance levels require different critical values. Answering in more than 100 words, it is necessary to understand the concept of degrees of freedom in statistics. Degrees of freedom represent the number of independent observations that are available for estimation in a statistical model. The number of degrees of freedom depends on the sample size, the number of parameters being estimated, and any constraints on the model. In general, more degrees of freedom lead to greater precision in estimates and narrower confidence intervals.

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We can find the bat's wholesale cost by working backwards -

Do $41 - 9 to get $32, then we can divide the 32 by the 4 to get $8.

Therefore, the wholesale cost of the bat is $8.

Happy to help!

Answer:

The bat's wholesale cost is $8

Step-by-step explanation:

You first have to subtract 9 from 41 as that will be 4 times the wholesale cost, which is $32. Then you have to divide 32 by 4, as we want to get the wholesale cost, not 4 times of the wholesale cost, and this would give us the wholesale cost, which is $8.

Answer:

I think it is complement. Not so sure so sorry If i get it wrong I haven't done this in 2 or 3 years

Step-by-step explanation:

Answer:

You can use the exponential rule where

\((n^x)^y=n^{xy}\)

Therefore,

\((a^3)^{-2}=a^{3*(-2)}=a^{-6}\)

\(\\ \rm\leadsto (a^3)^{-2}\)

\(\\ \rm\leadsto a^{-6}\)

\(\\ \rm\leadsto \dfrac{1}{a^6}\)

The size of the crowd is 21,120 standing along a 1 mile section of a parade route that is 10 feet deep on both sides of the street.

A mile is a unit of distance equal to 5,280 feet or exactly 1.609344 kilometers.

Given

The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street assume that each person occupies 2.5 square feet.

1 miles is equal to 5280 feet thus,

\(\rm= 5280 \times 10\\\\= 52800\)

Divide this by the amount of space a person takes up

\(= \dfrac{52800 }{ 2.5}\\\\ = 21120\)

Hence, the size of the crowd is 21,120 standing along a 1 mile section of a parade route that is 10 feet deep on both sides of the street.

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Answer:

20

Step-by-step explanation:

count the sides of the boxes for each side of the shape

Answer:

16 students are taking Physics and 12 are taking calculus

Step-by-step explanation:

40×40%=16 students taking Physics

40×30%=12 students taking calculus

16+12=28

40-28=12 students are taking both

Answer:

2, 3, 4, 6

Step-by-step explanation:

Answer:

2,3,4,6

Step-by-step explanation

12 divided by 2 is 6

12 divided by 3 is 4

12 divided by 4 is 3

12 divided by 6 is 2