a veterinarians office has 2100 animals it sees in one month. of these animals, 1500 of them are dogs. what is the ratio of dogs to all animals, in simplest form?

Answer:6

Step-by-step explanation:

Answer:

6.............................

Step-by-step explanation:

Recall that a relation as a set of ordered pairs, is the set of points of the form:

such that x is related to y.

Now, from the given table we get that:

3 is related to 7,

5 is related to 11,

7 is related to 15,

9 is related to 19,

11 is related to 23.

Therefore, the relation is:

Now, recall that, for any relation as a set of ordered pairs, the set of all first components of the ordered pairs is called the domain and the set of all second components is called the range.

Therefore, the domain of the given relation is:

And its range is:

Answer:

Answer:

-7

Step-by-step explanation:

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

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Answer:

Step-by-step explanation:

The angle where chords cross is the average of the measures of the intercepted arcs. The angle that is the supplement of x° will be the average of interecepted arcs 60° and 80°.

  180° -x° = (60° +80°)/2

  180 -70 = x . . . . . . . . . . . divide by °, add x-70

  x = 110

__

The external angle where secants meet is half the difference of the intercepted arcs.

  59° = (180° -y°)/2

  118 = 180 -y . . . . . . . multiply by 2, divide by °

  y = 180 -118 . . . . . add y-118

  y = 62

Answer:

she would take 140 minutes to run 15 miles

Step-by-step explanation:

28 X 5 os equal to 140

Answer:

139.95

Step-by-step explanation:

28 divided by 3 is 9.33 so 9.33x 15=139.95

Answer:

The answer is 20 because 8 goes into 40 5 times as does 20 to 100.

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Answer:

x = 67.4°

y = 22.6°

Step-by-step explanation:

The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The side opposite angle x is 7.2, and the side adjacent angle x is 3.

Use the tangent trigonometric ratio to find the measure of angle x:

\(\begin{aligned}\tan(x)&=\dfrac{7.2}{3}\\x&=\tan^{-1}\left(\dfrac{7.2}{3}\right)\\x&=\vphantom{\dfrac12}67.380135...^{\circ}\\x&=67.4^{\circ}\;\sf (nearest\;tenth)\end{aligned}\)

Therefore, x = 67.4°.

The side opposite angle y is 3, and the side adjacent angle y is 7.2.

Use the tangent trigonometric ratio to find the measure of angle y:

\(\begin{aligned}\tan(y)&=\dfrac{3}{7.2}\\y&=\tan^{-1}\left(\dfrac{3}{7.2}\right)\\y&=\vphantom{\dfrac12}22.6198649...^{\circ}\\y&=22.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}\)

Therefore, y = 22.6°.

Answer:

-10p

Step-by-step explanation:

-4p + (-6p)

Because both have a variable p, you can combine them. Both are negative so you get the equation:

-4p -6p

This would give you:

-10p

I hope that this helps! :)

Step-by-step explanation:

please read carefully. it says the polynomial of degree 4. that means the polynomial has the degree 4. and that means the highest exponent of the variable is 4.

further it says here that there are 2 roots (so, 2 solutions, where the functional value is 0) at x = 3. this is a double 0 solution.

then there is another 0 solution at x = 0, and a fourth zero solution at x = -4.

remember, a polynomial of the degree n must have n roots (n zero solutions).

we can construct this easily by building the whole function definition via multiplication terms (factors).

each factor represents one expression that turns 0 at the specified x value.

what expression turns 0 when x = 3 ?

well, (x - 3). there is no magic involved.

and we need that twice.

what expression turns 0 when x = 0 ?

well, simply x.

and what expression turns 0 when x = -4 ?

well, (x + 4).

so, the corresponding functional definition is then

P(x) = x(x-3)(x-3)(x+4)

that gives us a polynomial of degree 4 (highest exponent of x is 4) with the desired roots (0 function results at the specified x values).

but it has to go through the point (5, 18).

let's see :

P(5) = 5×(5-3)(5-3)(5+4) = 5×2×2×9 = 180.

aha ! too much !

how do we get the result down to just 18 ?

by dividing the whole thing by 10 !

dividing 0 by 10 is still 0, so this does not change our 0 solutions.

so, the final solution and correct polynomial is

P(x) = x(x-3)(x-3)(x+4)/10 = x(x-3)²(x+4)/10

oh, and if you want this in pure x terms without any factors, then we need to do the multiplications :

x×(x² - 6x + 9)(x+4)/10 =

(x³ - 6x² + 9x)(x+4)/10 =

(x⁴ - 6x³ + 9x² + 4x³ - 24x² + 36x)/10 =

(x⁴ - 2x³ - 15x² + 36x)/10

The 10 minutes duration used for stretching and the fraction of 2/3 of the practice time used for scrimmaging, indicates;

The duration of the practice on Wednesday = 2.25 hours

A fraction is a part of a specified quantity, represented as quotient or a smaller number (the numerator), placed on another number (the denominator) separated by a line.

The time duration of the stretching during the daily practice = 10 minutes

The fraction of the entire practice time used for scrimmaging during the practice = 2/3 of the entire practice

Duration of working on drills of specific skills = The remaining time of the practice

The time the coach planned for stretching and scrimmaging on Wednesday = 100 minutes

Therefore;

The time for scrimmaging = 100 minutes - 10 minutes for stretching = 90 minutes
Therefore;

(2/3) of the time for the entire practice = 90 minutes

The time for the entire practice = (3/2) × 90 minutes = 135 munites

The duration of the entire practice = 135 minutes

135 minutes = 2.25 hours

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The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².

To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:

Area = ( Perimeter × Apothem ) / 2

Perimeter would be :

= 5 x sides

= 5 x 6

= 30 inch

The area is therefore :

= ( Perimeter × Apothem ) / 2

= ( 30 in x 3. 5 in ) / 2

= 105 / 2

= 52. 5 in²

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The increasing and decreasing function is discussed above.

Given is the function f(x).

Increasing and decreasing functions are functions in calculus for which the value of f(x) increases and decreases respectively with the increase in the value of x. We can write -

Therefore, the increasing and decreasing function is discussed above.

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Answer:

n = 1, this means the interest compounds ANNUALLY.

Step-by-step explanation:

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?

Compound Interest Formula

: A = P(1 + r/n)^nt

A = Amount after time t

P = Principal (Initial Amount Invested)

r = Interest rate

n = Number of times the interest is compounded

t = time in years

A = $30,541.83

r = 4.6% = 0.046

t = 30

P = $7,924

Hence,

$30,541.83 = $7924(1 + 0.046/n)^30n

Divide both sides by 7924

$30,541.93/$7924 = (1 + 0.046/n)^30n

$30,541.93/$7924 = (n + 0.046/n)^30n

3.8543576477 = (n + 0.046/n)^30n

We take the logarithm of both sides

log 3.8543576477 = log (n + 0.046/n)^30n

Solving for n,

n = 1

Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.

The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

Answer:

  z ∈ (-∞, -3]

Step-by-step explanation:

You want the solution to −2(2z−3)≥2z+24.

Simplify the inequality:

  -4z +6 ≥ 2z +24

  -18 ≥ 6z . . . . . . . . . add 4z -24

  -3 ≥ z . . . . . . . . divide by 6

The solution is z ∈ (-∞, -3].

Answer:

C

Step-by-step explanation:

By moving point B 1.5 units to the right, you create an icoselles triangle, which has just one line of symmetry

Hello!

a. 10

b. 1

c. -11

To evaluate f(x) at a certain x, you simply substitute that value of x into the equation for x.

For example:

a. f(x) = 2x, find f(5)

Plug in 5 for x into f(x):

f(5) = 2(5) = 10.

b. f(x) = 4x + 5, find f(-1)

f(-1) = 4(-1) + 5 = 1

c. f(x) = -3x - 5, find f(2)

f(2) = -3(2) - 5 = -11

The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Answer: z = 7 or z=-5

Step-by-step explanation:

First you need to factor the polynomial.

To factor \(z^{2}\)  - 2z -35       You will need to find two numbers that their product is -35 and their sum is -2  and the numbers -7 and 5  works out.

Rewrite the polynomial as,

\(z^{2}\) - 7z + 5z - 35  = 0   factor the left by grouping

(\(z^{2}\) -7z) (5z -35)  = 0

z(z -7)  5(z - 7) = 0      Factor out z-7

(z-7)(z+5) = 0        Now apply the zero product by setting each of them equal 0.

z-7= 0      or  z+5=0

 +7  +7             -5  -5

z = 7     or  z= -5  

Answer:

A is correct.  f(n) = -3n + 24

Step-by-step explanation:

We can see in the first two steps that two meals have been served, and six cups of pet food consumed.  In other words, six cups are consumed in two meals, therefore three cups are consumed in each meal.

If we look at the remaining numbers on the chart, we can see that this carries through.  This tells us that the correct answer must be either a or b, as "-3n" represents the consumption rate.  If it were (1/3)n, then only a third of a cup would be consumed per meal.

Finally, we can figure out which of those two equations is correct simply by plugging a value pair into them.  Starting with a:

f(1) = -3(1) + 24

= 24 - 3

= 21

correct.

To be certain, let's check with answer c:

f(1) = -3(1) + 64

= 64 - 3

= 61

incorrect.

So we can clearly say that the correct answer is "a".  You can plug the other values into it to test that too:

f(3) = -3(3) + 24

= 24 - 9

= 15

correct

So we definitely have the right answer.

Answer: There are 210 pages that ty read in 6 hours.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer: 79

Step-by-step explanation:

i just did it on acellus and its right

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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