Vanita went to the library to read books. 1/6 of the books were about animals (zoology) and 5/12 of the books were about plants (botany). How do you write the fraction of the books that were based on biology?

Answer:

16. y=-5x-20; 17. y=6x+18, or factored y=6(x+3)

Step-by-step explanation:

Your slope is -5

y=-5x+b, solve for b by pluging the point (-3,-5) in for x and y

-5=-5(-3)+b, solve for b

-20=b, now rewrite the equation

y=-5x-20

Your slope is 6

y=-5x+b, solve for b by pluging the point (-3,-0) in for x and y

0=6(-3)+b, solve for b

18=b, now rewrite the equation

y=6x+18, or factored y=6(x+3)

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

q=13

Step-by-step explanation:

Given q - 12 = 1

we need to find q

to do so we need to isolate the variable using inverse operations

so to get rid of the 12 we add 12 but whatever we do to one side we do to the other

so we add 12 to each side

-12+12 cancels our

1+12=13

we're left with

q=13

Answer:

b. 12.2 months

A percentage is a way to describe a part of a whole. The correct option is B.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the colony of 100,000 ants has been declining in number at a rate of 11.4% per month. Therefore, the number of months it will take for the ant population to reach 25,000 ants is,

Population = 100,000(1-0.114)ⁿ

25,000 = 100,000(1-0.114)ⁿ

0.25 = 0.886ⁿ

log(0.25) / log(0.886) = n

n = 11.45335

Since the value is close to 12.2 months.

Hence, the correct option is B.

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Answer: D

How to: Find the asymptotes.

Vertical Asymptotes: x = − 1

Horizontal Asymptotes: y = 0

No Oblique Asymptotes

Have a great day and stay safe !

Answer:

-288

Step-by-step explanation: I took the following steps to find the answer:

(4 + 32)(15 – 23)

\             /

 (36)(15 – 23)

           \          /

 (36) (- 8)

   \        /

    -288

Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

so 7.892 u need to move the decimal to the right 9 times which is 7892000000

Answer:

Step-by-step explanation:

Exponential growth

Answer:

[6×(4−2)+(21×23+1)]÷3 exponent 2

Step-by-step explanation:

[6×(4−2)+(21×23+1)]÷3 exponent 2

The mean of the population can be calculated by finding the sum of all the heights and dividing it by the total number of observations.

This is also known as the arithmetic mean and can be represented by the formula:

Mean = (Sum of Observations) / (Number of Observations)

In this case, the sum of all the heights is 10,800 and the total number of observations is 100. Therefore, the mean of the population is:

Mean = 10,800 / 100 = 108 inches

To verify this result, we can also look at the histogram. Since the heights are grouped into intervals of 10 inches, the mean should be around the midpoint of the tallest bar, which is 108 inches. This confirms our calculation of the mean.

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Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

33m

Step-by-step explanation:

add up all of the sides

9+9=18

18+15=33

Answer:

9+9+15 = the perimeter.

Step-by-step explanation:

The perimeter is the length of the outside lines of the triangle.

9+9+15 = 33

The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.

First, remember that for a point (x, y):

For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:

(-4, -1)

Then we can see that this point is on the quadrant III.

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Answer:

0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1.  One way to do this is converting both into improper fractions.  To do this, multiply the whole number by the denominator and add that to the numerator.

2 3/5 --> 2*5 is 10 --> 10+3 is 13.  --> 13/5

2.  This leaves us with 13/5 - 8/5

3.  Subtract the numerators

13/5 - 8/5 = 5/5

4.  Simplify.  If the numerator is the same number as the denominator, it's a whole number.

5/5 = 1

Answer:

72% of the parking spaces are empty.

Step-by-step explanation:

There are 72 open spaces out of 100 total. 72/100=.72, .72*100= 72%.

Answer:

72% because 72+28 is 100 and 72/100 is 72%

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

The range is the difference between the biggest number and the smallest number

Let's put these numbers in order:

25,20,18,12,6

The biggest number is 25, the smallest number is 6

25-6=?

19

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

The absolute increase in population is 2200, and the relative increase is approximately 59.46%.

To find the absolute and relative increase in population, we can use the following formulas:

Absolute increase = Final value - Initial value

Relative increase = (Absolute increase / Initial value) * 100%

Given the population in 2005 is 3700 and the population in 2009 is 5900, we can calculate the absolute and relative increase as follows:

Absolute increase = 5900 - 3700 = 2200

To calculate the relative increase, we need to divide the absolute increase by the initial value and then multiply by 100:

Relative increase = (2200 / 3700) * 100% ≈ 59.46%

Therefore, the absolute increase in population is 2200, and the relative increase is approximately 59.46%.

The absolute increase represents the actual difference in population count between the two years, while the relative increase gives us the percentage change relative to the initial value. In this case, the population increased by 2200 individuals, and the relative increase indicates that the population grew by approximately 59.46% over the given period.

Note that the relative increase is expressed as a percentage, which makes it easier to compare changes across different populations or time periods.

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Answer:

5 seconds per foot

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.

Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.

As p is a prime number, and 2 is the smallest prime number, so, p\(\geq\)2

So, the positive divisors of the integer n are: 1,p,p².

As σ(n) represents the sum of all positive divisors of the integer n.

σ(n)=1+p+p²

In order to prove that σ(n) < 2n,for all n of the form n = p².

1+p+p²<2p²

p²-p-1>0

It is know that, p\(\geq\)2.

So, p²-p-1\(\geq\)1

Thus, σ(n) < 2n holds true for all n of the form n = p².

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Based on the total costs of buying at the two stores, it is not worth the extra drive going to the store across town.

The total costs for buying 5 pounds of chicken at each store are added to the total gas costs to and from each location to determine the total costs of each option.

Based on the cost difference of $1 ($18.34 - $17.34), it is not advisable to travel across town just for 5 pounds of chicken, especially when you factor in the wear and tear of the car along the distance and the time difference.

The cost of a pound of chicken at a neighborhood store = $2.99

The cost of a pound of chicken at the store across town = $3.29

The number of pounds of chicken required = 5 pounds

The distance to and from the neighborhood store = 4.6 miles (2.3 miles x 2)

The distance to and from the store across town = 17.6 miles (8.8 miles x 2)

The total time to and from the neighborhood store = 14 minutes (7 x 2)

The total time to and from the store across town = 42 minutes (21 x 2)

The time difference = 28 minutes.

Car's mileage per gallon = 19 mpg

The cost of gas per gallon = $3.66

The total cost of buying at the neighborhood store = $17.34 ($3.29 x 5 + $3.66 x 4.6/19)

The total cost of buying at the store across town = $18.34 ($2.99 x 5 + $3.66 x 17.6/19)

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The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer: C & D

Step-by-step explanation:

The residuals will have a pattern and form a parabola. Then the correct options are A and B.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The quadratic equation is also known as the equation of the parabola.

The residuals will have a pattern and form a parabola. Then the correct options are A and B.

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Hence, in option (A) the down payment is what percent of the purchase price is \(25\)% and in option (B) the purchase price would be \(90000\) $ down payment is \(45\) %.

What is the installation amount?

Installation Cost means the total cost payable by the Lessee to the Lessee’s direct contractor under the contract for the carpet installation works.

Payment of the Attendance Fees for the Designated Works may be made by the Lessee progressively in the course of the relevant Designated Works being carried out.

Here given that,

A family buys a studio apartment for $\(200,000\). They pay a down payment of $\(50,000\).

(A)

The down payment is the percentage of purchase price is

\(\frac{50000}{200000}\) × \(100\) \(=\) \(25\) %

(B)

The percent of the purchase price would be \(90000\) $ down payment is

\(\frac{90000}{200000}\) ×\(100\) \(=45\) %

Hence, in option (A) the down payment is what percent of the purchase price is \(25\)% and in option (B) the purchase price would be \(90000\) $ down payment is \(45\) %.

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Answer:

here is the answer please mark me as brainliest please