Which is greater, the number of bacteria, or the number of all the other animals in the table put together?

The solution of the system of equations is (-4, 3).

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Given are two linear equations.

y = -3/2 x - 3

y = 3/4 x + 6

The two equations are in slope intercept form.

The solution of the two equations is the intersection of the two lines.

Equate both the equations.

-3/2 x - 3 = 3/4 x + 6

-3/2 x - 3/4 x = 6 + 3

-9/4 x = 9

-x/4 = 1

x = -4

Substitute x = -4 in y = 3/4 x + 6.

y = -3 + 6 = 3

Hence the solution of the equations are x = -4 and y = 3.

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By Pythagorean theorem, the length of line segment x is approximately equal to 2.609 feet.

In this problem we find a geometric system where line segment x is perpendicular to the hypotenuse of a right triangle. This system can be represented well by Pythagorean theorem:

4.6² = (5.8 - y)² + x²

3.5² = x² + y²

First, eliminate variable x and solve for y:

4.6² = (5.8 - y)² + (3.5² - y²)

4.6² = 5.8² - 10.6 · y + y² + 3.5² - y²

4.6² = 5.8² - 10.6 · y + 3.5²

10.6 · y = 5.8² + 3.5² - 4.6²

y = 2.333

Second, determine variable x:

x = √(3.5² - 2.333²)

x = 2.609

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Dividing the fraction (x - 2) / (3x - 21) by (5x - 10) / (9x - 63) will result to 3/5.

To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is simply the fraction flipped upside down. So, the reciprocal of the second equation (5x - 10) / (9x - 63) is (9x - 63) / (5x - 10). Now we can multiply the two fractions together to get the answer.

(x - 2) / (3x - 21) × (9x - 63) / (5x - 10)

= [(x - 2)(9x - 63)] / [(3x - 21)(5x - 10)]

Now we can simplify the numerator and denominator by factoring out the common factors:

= (9x - 63)(x - 2) / (3x - 21)(5x - 10)

= (3)(3x - 21)(x - 2) / (3x - 21)(5)(x - 2)

= 3/5

So, the final answer is 3/5.

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Answer:

a) [tex]\frac{2\pi }{3}[/tex]

b) 330

Work:

a) To convert degrees to radians you multiply by [tex]\frac{\pi }{180}[/tex]

[tex]\frac{120}{1}[/tex] x [tex]\frac{\pi }{180}[/tex]

= [tex]\frac{6}{1}[/tex] x [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{2\pi }{3}[/tex]

b) To convert radians to degrees you multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{11\pi }{6}[/tex] x [tex]\frac{180}{\pi }[/tex]

= [tex]\frac{11}{1}[/tex] x [tex]\frac{30}{1}[/tex]

= 330

a)1.746

b)0.119

To compare the null hypothesis that the population mean of the increase in sales is at least 50 units against the observed mean of 41.3 units, we will use both the critical value approach and the p-value approach.

For the critical value approach, we need to use the standard deviation of 12.2 units as well as the sample size of 20 supermarkets. This gives us a critical value of 1.746. As the observed mean (41.3 units) is less than 1.746 standard deviations away from the mean of 50 units, we can conclude that the null hypothesis cannot be rejected at the 5% level of significance.

For the p-value approach, we will use the same sample size and standard deviation. This gives us a p-value of 0.119, which is greater than the 5% level of significance. Thus, we can also conclude that the null hypothesis cannot be rejected at the 5% level of significance.

It is important to note that we are assuming that the data is normally distributed, and that there is no bias in the sample.

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Maria has $22,000 invested in account A and $8,000 invested in account B.

Let's begin by setting up a system of equations to solve for the amount Maria has invested in each account. Let x be the amount invested in account A and y be the amount invested in account B. Since Maria has a total of $30,000 invested in both accounts, we can write the first equation as:

x + y = 30,000

Next, we can write an equation to represent the total annual interest earned from both accounts:

0.045x + 0.038y = 1,294

Now, we can use the substitution method to solve for x and y. We'll rearrange the first equation to solve for x:

x = 30,000 - y

Then, we'll substitute this value of x into the second equation:

0.045(30,000 - y) + 0.038y = 1,294

Simplifying the equation gives:

1,350 - 0.045y + 0.038y = 1,294

Combining like terms and isolating y gives:

0.007y = 56

y = 8,000

Now, we can substitute this value of y back into the first equation to solve for x:

x = 30,000 - 8,000

x = 22,000

So, Maria has $22,000 invested in account A and $8,000 invested in account B.

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Answer:

Step-by-step explanation:23.80*34=809.20

If the length of the tile is x and the breadth of the tile is y then the area of each tile is equal to xy units.

Given that we can assume the length of tile be x and breadth of tile be y. We are required to find the area of the each tile and draw a figure showing the tile whose length is x and the breadth is y.

Tile is in the shape of the rectangle because the length and breadth are different and we know that the area of the rectangle is equal to product of the length and breadth of that rectangle.

If the length of tile is x and the breadth of tile is y then the area of the tile is equal to x*y which is xy units. Figure is attached with the solution.

Hence if the length of the tile is x and the breadth of the tile is y then the area of each tile is equal to xy units.

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The measure of the vertex angle of triangle ACE is 50°. The solution has been obtained by using properties of angles.

What is an angle?

An angle is a figure in plane geometry that is created when two rays or lines share an endpoint.

We are given an isosceles triangle ACE which means that AC = CE.

We are given ∠BDE = 115°

Since, angles on a straight line form a linear pair, therefore

⇒∠BDE + ∠BDC = 180°

⇒115° + ∠BDC = 180°

⇒∠BDC = 65°

Since, BD║AE so,

∠BDC = ∠AEC

So, ∠AEC = 65°

Since, AC = CE so,

∠AEC = ∠CAE

So, ∠CAE = 65°

Now, using angle sum property, we get

⇒∠AEC + ∠CAE + ∠ACE = 180°

⇒65° + 65° + ∠ACE = 180°

⇒130° + ∠ACE = 180°

⇒∠ACE = 50°

Hence, the measure of the vertex angle of triangle ACE is 50°.

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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The surface area of the rectangular prism is 174 cm^2

Rectangular Prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangle such that all the pairs of the opposite faces are congruent.

To determine the surface area of Rectangular prism

SA = 2(LH + LW + WH)

Where W = Width = 2 cm

L = Length = 5 cm

H = Height = 11 cm

SA = 2[(5*11) + (5*2) + (11*2)]

SA = 2(55 + 10 + 22)

SA = 2(87)

SA = 2 * 87

SA = 174

Therefore, the surface area of rectangular prism is 174 cm^2

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Answer:

y=2-2x

so y=2x+2--£8;£++£

Answer: y=−2x + 2

Step-by-step explanation:

Subtract 2x from both sides of the equation.

y= 2 − 2x

Reorder 2 and −2x.

y= −2x + 2

Answer:

The discounted price of the shoes is:

$70 x 0.65 = $45.50

The amount of sales tax is:

$45.50 x 0.05 = $2.275

Therefore, the total amount you will pay for the shoes is:

$45.50 + $2.275 = $47.775

Rounded to two decimal places, the amount you will pay is $47.78.

Answer:

Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.

To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:

14 ÷ (7/4) = 8

Therefore, Keith can paint 8 classrooms in total.

Step-by-step explanation:

Answer:

12:44

12:16

12:08

12:32

12:28

Correct answer:

12:16

Step-by-step explanation:

Explanation:

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius r=6. The circumference of that circle is

C=2πr=2π⋅6=12π.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is 1012π,

and the number of minutes that have expired since noon is 1012π⋅60≈16.

Therefore, to the nearest minute, the time is 12:16.

Step-by-step explanation:

How many Oz make 1 Pound

Answer is 16

Divide 87 by 16

Answer is 5Lb 7oz

Answer: The answer is 21.1304347826 or 21.13 rounded

Step-by-step explanation:

hope this helps

Answer:

Well question is not clear rewrite

The measure of the central angle in the "Punk" section is 72 degrees.

The measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.

To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.

For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:

200/1000 * 100 = 20%

To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).

20% * 360 = 72 degrees

Therefore, the measure of the central angle in the "Punk" section is 72 degrees.

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a.) The value of this vector expression w(u + v) is  

b) The angle between the vectors u and v is  54.73 degrees.

c) the proy uv is -147/25 i + 98/25 j - 196/25 k

a) First we will have to find the sum of the vectors u+v= (3i - 2j + 4k) + (-7i + 4j - 5k) = (-4i + 2j - 1k)

now the dot product of w and (u+v) is

=  (i + j + k). (-4i + 2j - 1k)

= -4+2-1 = -3

b.)

The angle between u and w can be calculated using the dot product: u.w = |u|.|w| cos ∅

u • w = (3i - 2j + 4k) • (i + j + k) = 3 + (-2) + 4 = 5

|u| = √(3² + (-2²) + 4²) = √(25) = 5

|w| = √(1²+ 1² + 1²) = √(3) =3

The angle between u and w can be calculated using the formula: angle ∅ = cos⁻¹(u • w / (|u| • |w|))

angle = cos⁻¹(5 / (5 • √(3))) = cos⁻¹(1/ √3) = 0.6435 radians, or 54.73 degrees.

c.)

To calculate the projection of u onto v, use the formula: proy uv = (u•v/|u|^2) * u

here u.v = (3i - 2j + 4k).(-7i + 4j - 5k)= -49

|u|= 5

proy uv = (-49*(3i - 2j + 4k))/5² = -147/25 i + 98/25 j - 196/25 k

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Answer:

x = 50

Step-by-step explanation:

sin 40º = 32 / x

0.64 = 32 / x

x = 32 / 0.64

x =~ 50

Answer:

  39°

Step-by-step explanation:

You want to know the measure of the third angle in a triangle with two angles given as 39° and 102°.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  39° +102° +x = 180°

  x = 39° . . . . . . . . . . . . subtract 141° from both sides

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The final answer is 8*2=16 ways

Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?

There are a couple of steps to solving this problem.

Step 1: Consider the two people who insist on sitting next to one another as one unit. This means that there are now 7 units to be seated in the 8 chairs.

Step 2: Calculate the number of ways that the 7 units can be seated in the 8 chairs. This is done using the formula n!/(n-r)!, where n is the number of chairs and r is the number of units. In this case, n=8 and r=7, so the formula is 8!/(8-7)!, or 8!/1!, which simplifies to 8.

Step 3: Calculate the number of ways that the two people who insist on sitting next to one another can be seated within their unit. There are 2! or 2 ways that they can be seated.

Step 4: Multiply the number of ways that the 7 units can be seated in the 8 chairs by the number of ways that the two people can be seated within their unit. This gives us the total number of ways that the 8 people can be seated if two of them insist on sitting next to one another.

So the final answer is 8*2=16 ways.

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Answer:

Step-by-step explanation:

You want the objective function, its maximum value, and the variable values that give that maximum based on the model shown in the graph.

The problem statement tells you the profit function is ...

  1.00x +1.50y . . . . . . objective function

Since the objective is to maximize profit, this is the objective function.

The integer values nearest the vertex of the feasible region farthest from the origin are (x, y) = (69, 70). These are the numbers of 'economy' and 'best' brushes that maximize the profit.

The maximum profit for these numbers of brushes will be ...

  p = x +1.5y = 69 +1.5(70) = 69 +105

  p = 174 . . . . maximum profit

The maximum profit of the situation is $174

From the question, we have the following parameters that can be used in our computation:

Profit function = $1 for x and $1.50 for y

This means that the objective function is

P(x, y) = x +1.5y

Also, the graph is given where we have:

Optimal point, (x, y) = (69, 70)

Substitute these points in the profit function

So, we have

P(x, y) = 69 +1.5 * 70

Evaluate

P(x, y) = 174

Hence, the maximum profit is $174

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Answer: To check if (3x + 2) is a factor of a trinomial, we can use long division or synthetic division. However, we can also use the factor theorem, which states that if f(c) = 0 for a polynomial f(x) and a constant c, then (x - c) is a factor of f(x).

In this case, we can use the factor theorem with c = -2/3 to check if (3x + 2) is a factor:

f(-2/3) = 0 if and only if 3(-2/3) + 2 = 0, which is true. Therefore, (3x + 2) is a factor of f(x) if and only if f(-2/3) = 0.

Using this method, we can check each trinomial:

6x² +19x+10: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x² +19x+10.

6x²-x-2: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x²-x-2.

6x² +7x-3: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6x² +7x-3.

6х2 - 5x - 6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6х2 - 5x - 6.

12x²-x-6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 12x²-x-6.

Therefore, the trinomials that have (3x + 2) as a factor are:

6x² +19x+10

6x²-x-2

Note: We could also use long division or synthetic division to confirm our results.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ok so we're just going to be doing a lot of supplementary work:

The angle adjacent to 85 degrees is equal to 180 - 85 = 95

We want to find the angle measures in the triangle where 95 degrees is. We can do this by using 40, finding the opposite angle, which is also 40 due to vertical angles theorem, finding the missing angle in the right-most triangle which is 180 - 105 - 40 = 35

Using vertical angles theorem again, we know the angle opposite 35 degrees is also 35. We found another angle for the middle triangle.

The missing angle for the middle triangle is 180 - 35 - 95 = 50

The angle opposite 50 is 50 because of the vertical- you already know.

Now the left triangle has angles Z, 60 and 50.

m<Z = 180 - 60 - 50

m<Z = 70

Hope this helps!

Answer:

y=3x+8

2y=6x+16

2(3x+8)=6x+16

6x+16=6x+16

Infinite Many Solutions

Answer:

55

Step-by-step explanation:

First, we need to divide 44 by 8 to find what to times 10 by.

44/8= 5.5.

After, we need to times 10 by 5.5 to get the answer

5.5x10=55

Answer: She can plant 55 plants within 44 feet.

Step-by-step explanation:

First; We must divide 8 by 44 receiving the result 5.5

( 8 ÷ 44 = 5.5 )

Second; We must multiply 5.5 with 10, giving the final result of 55.

( 5.5 x 10 = 55 )

Answer:

-2

Step-by-step explanation:

Whenever you see f(x), for any number x, you plug x into the function. In your function, f(x) = -x - 1, you want to find f(1).

So, f(1) = -(1) - 1, which equals -2