John's pet service takes care of cats and dogs. Currently, there are 23 cats and 31 dogs at John's Pet Service.
What is the ratio of cats to dogs at the center? What is the ratio of cats to the total number of pets at the
center? Write the ratios in three different ways.

Answer:

Given:

To Find:

Solution:

★ Firstly, we have to find the amount:

According, to the question by using the formula, we get:

[tex] \longmapsto \: { \bold{ \boxed{\pink{ \rm{A \: = P \left( 1 + \frac{ \frac{r}{2} }{100} \right)^{2n} }}}}}[/tex]

Here,

So by putting their values, we get:

[tex] { \large{\longrightarrow{ \rm{A = 5000 \left( 1 + \frac{ \frac{10}{2} }{100} \right)^{2 \times 2} }}}}[/tex]

[tex] { \large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10}{2} \times \frac{1}{100} \right)^{4} }}}}[/tex]

[tex] {\large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10 \times 1}{2 \times 100} \right)^{4} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \left(1 + \frac{10}{200} \right)^{4} }}}}[/tex]

[tex]{ \large \longrightarrow {\rm{A =5000 \left( \frac{200 \times 1 + 10}{200} \right)^{4} }}}[/tex]

[tex]{ \large \longrightarrow{ \rm{A = 5000 \left( \frac{200 + 10}{200} \right)^{4} }}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \right)^{4} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \right)}}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210 \times 210 \times 210 \times 210}{200 \times 200 \times 200 \times 200} \right)}}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{1944810000}{1600000000} \right)}}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{1944810000}{1600000000} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{194481}{160000} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 5 \times \frac{194481}{160} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = \frac{972405}{160} }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{A = 6077.53 \: (approx.)}}}}[/tex]

Hence, the amount is Rs 6078.

★ Now, we have to find the compound Interest:

According, to the question by using the formula, we get:

[tex]{ \large{ \dashrightarrow{ \boxed{\green{ \rm{Compound \: Interest = A \: - \: P}}}}}}[/tex]

Here,

So, by putting their values we get:-

[tex] { \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 6078 \: - \: Rs \: 5000}}}}[/tex]

[tex]{ \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 1078}}}}[/tex]

Hence, Compound Interest is Rs 1078.

Answer:

x=65

Step-by-step explanation:

find the angles of the small square by completing the outer ones so the one on the left the missing one is 68 and the other side is 47, so 180= 68+47 + x

180= 115 + x

x= 65

Step-by-step explanation:

1. prove congruency

[tex]75 = (8x - 5) \: ( the \: angles \: are \: equal \: proven \: from \: congruency)\\ 75 + 5 = 8x \\ 80 = 8x \\ x = 10[/tex]

Remember that for this to work prove congruency first

To get the area of the shaded region, we must subtract the area of the bigger triangle on the outside and the area of the smaller triangle inside the bigger triangle.

Set up the equation:

  Area of big triangle - Area of small triangle = [tex]\frac{1}{2} *19*19 - \frac{1}{2} *13*13[/tex][tex]= \frac{1}{2} (19^{2} -13^{2} ) = \frac{1}{2}*192 = 96[/tex]

So the area of the shaded region is 96.

Hope that helps!

Answer:

7280

Step-by-step explanation:

you just have to multiply 56 and 130

Step-by-step explanation:

a. 9 + 4x = 6x + 17

4x - 6x = 17 - 9

-2x = 8

x = -4

b. 4x - 9 = 6x + 17

4x - 6x = 17 + 9

-2x = 26

x = -13

c. 9 - 4x = 6x + 17

9 - 17 = 6x + 4x

-8 = 10x

x = -8/10

d. 4x + 9 = 6x - 17

4x - 6x = -17 - 9

-2x = -26

x = 13

The slope of a line parallel to the line x + 5y = 9 is; Choice B: -1/5

The slope of parallel lines from line geometry are equal.

The given parallel line equation is; x + 5y = 9:

Hence, it follows that the two lines have equal slopes.

By rewriting the equation to take the slope-intercept form of straight lines, it follows that;

On this note, the slope of the parallel lines is; -1/5

Read more on slope of a line;

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Answer:

x is about 60.1

Step-by-step explanation:

1. We have the adjacent side and hypotenuse, therefore the cosine ratio must be used

2. Equation: cos37=48/x

3. Simplify on calculator by finding 48/cos37

4. about 60.1

Answer: x is approximately 60.1

Step-by-step explanation:

cos (37) = 48/x

x = 48/cos (37)

x = 60.1

A vertical line has points with all the same x-values. So if the line intersects (a,b) and (c,d), then a must equal c.

Answer: Number 5

Step-by-step explanation:

If Jachin needs $400 dollars to get the tablet and she already has $85 she now needs $315. (400 - 85) Since she gets paid $25 a week we have to find how many weeks it will take to reach the $315. So that would be 12.6 weeks. (12.6 x $25 = $315) And she should have no more than 13 weeks to get the money because 12.6 rounded up is 13.

And that should be Answer: Number 5 (w > 12.6 means that it will take Jachin no more than 13 weeks to save enough money to buy the tablet)

Hope that this is not too confusing

Answer:

  F.  w > 12.6, minimum of 13 weeks

Step-by-step explanation:

The amount Jachin will have in his savings account will be the sum of the initial amount and the product of the weekly deposit and the number of weeks. Jachin wants that amount to be more than $400. The inequality that represents Jachin's desired bank balance is ...

  85 +25w > 400 . . . . . initial balance plus deposits total more than $400

  25w > 315 . . . . . . . subtract 85

  w > 12.6 . . . . . . . divide by 25; solution to the inequality

__

Jachin makes a deposit once a week, so the value of w will be an integer. The requirement that the value of w be greater than 12.6 means it will take at least 13 weeks for Jachin to save more than $400.

_____

Additional comment

We don't know how much more than $400 Jachin needs to save. We only know it is some amount more than $400. Hence, we cannot say that after week 13 when Jachin has a balance of $410 that he can buy the tablet. This means the "no more than ..." answer choices have no basis in the problem statement and must be ignored.

This only leaves the first and last answer choices as being worthy of consideration. The first choice presumes that w may take on a non-integer value. If Jachin makes a deposit once a week, he will not be making a deposit when w = 12.6 weeks. He will be making his deposit when w = 13 weeks.

Answer:

D. 50

Step-by-step explanation:

plug 7 into the equation to get this

f(7) = 7^2 + 1

then solve

f(7) = 49 + 1

f(7) = 50

=====================================================

Explanation:

The line of best fit here is y = 6x+62

We started at (0,62) and go up 6 units and to the right 1 unit each time we move along this line.

If we tried something like x = 1, then,

y = 6x+62

y = 6*1+62

y = 6+62

y = 68

Meaning that someone spending 1 hour per week doing homework would lead to an estimated score of 68. This matches what the graph shows, and it helps confirm we have the correct regression line equation.

Let's now plug in x = 5

y = 6x+62

y = 6*5+62

y = 30+62

y = 92

Someone doing 5 hours of homework per week is estimated to get a score of about 92.

axis of symmetry would be where it becomes symmetrical

Answer:20%  i know because i had a question like this

Answer:

-1

Step-by-step explanation:

1(+-)2=

step 1: a positive and a negative is a negative

1-2=-1

Answer:

-1

Step-by-step explanation:

negative and positive is negative

1+(-2)

1-2

-1

Answer:

x=12

Step-by-step explanation:

Since it is on a right angle we can equate the sum of these 2 angles to 90:

3x+x+42=90

Simplify:

4x+42=90

Subtract 42 from both sides:

4x+42-42=90-42

Simplify:

4x=48

Divide both sides by 4

4x÷4=48÷4

Simplify

x=12

Answer:

Step-by-step explanation:

The overall angle in total is 90 degrees. The angles 'x+42' and '3x' equal ninety degrees, so we get the equation:

x + 42 + 3x = 90

4x + 42 = 90

4x = 48

x = 12

Hope that helps!

Answer:

B and E

Step-by-step explanation:

An isosceles has two congruent (equal) angles and all of the angles add up to 180.

In option B, there are 2 congruent angles (70 and 70), and all the angles add up to 180 (70+70+40=180).

In option E there are 2 congruent angles (40 and 40), and all of the angles also add up to 180 (40+40+100=180).

The rest of the options do not fit the criteria for an isosceles triangle.

Answer: linear???

Step-by-step explanation: not 100 percent sure

Answer:

4x^2 + 12y

Step-by-step explanation:

x + 7y + 4x^2 - x + 5y

4x^2 + 12y

Answer:

120 yaaaaaaaaaaaapppp

The value of x in the heptagon is 64

The measure of one central angle of a regular octagon is 135°

Regular polygon are polygon that are equiangular. This simply means all the angles are equal.

The regular polygon has 8 angles. Therefore, it is an heptagon.

The sum of internal angle of a regular heptagon is 900 degrees.

Therefore,

120 + 3x + 5 + x + 45 + 135 + x - 45 + 5x = 900

10x = 900 - 120 - 50 - 135 + 45

10x = 640

divide both sides by 10

x = 640 / 10

x = 64

The degree measure of one central angle of a nonagon can be calculated as follows;

sum of angle in a octagon = 1080

central angle = (n - 2)180 / n = 6 × 180 / 8 = 1080 / 8 = 135°

learn more on polygon here: https://brainly.com/question/10706262

Answer:

32 feet

Step-by-step explanation:

The area of a rectangle is [tex]a = lw[/tex], where the area equals the length times the width. Since we are given the area and the width, we can divide them to find the width, since it's the inverse operation.

⇒ 1152 ÷ 36 ≈ 32 feet

Answer:

81,000,000

Step-by-step explanation:

[tex]( {3}^{2} )^{2} \times ({10}^{3} )^{2} \\ \\ = ( 9)^{2} \times (1000 )^{2} \\ \\ = 81 \times 1000000 \\ \\ = 81,000,000[/tex]

The factor of the provided polynomial with the after the factorization process are similar to option A, which is

[tex]3xy(x^3y^2 - 5xy+ 2)[/tex]

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

[tex]3x^4y^3 - 15x^2y^2+ 6xy[/tex]

The above equation has the unknown variable x and y and the highest power of this unknown variable is 3.

Take out the highest common factor 3, which can divide each term of the above equation (3, 15, 6). Thus,

[tex]3(x^4y^3 - 5x^2y^2+ 2xy)[/tex]

Take out the highest common factor in terms of variable, which can divide each term of the above equation. Thus,

[tex]3xy(x^3y^2 - 5xy+ 2)[/tex]

Thus, the factor of the provided polynomial with the after the factorization process are similar to option A, which is

[tex]3xy(x^3y^2 - 5xy+ 2)[/tex]

Learn more about factor of polynomial here;

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Answer:

england

Step-by-step explanation:

Answer:

RQS= 54°

Step-by-step explanation:

Angles in a segment are equal.

90-36=54

The measure of <RQS is 54 degree.

The exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles.

Given:

Connect point S and C for SC= RC.

So, <CSR = <PRS= 36 {Equal sides to equal Angle}

Then, <SCP = <CSR + <PSR

                    = 36+ 36

                    = 72

Now, <SCP = <SPC = 1/2 (180- <SCP)

                                = 54

Now, the inscribes angle of the same Arc are same.

<RQS = <SPC = 54 degree.

Learn more about exterior angle Theorem here:

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#SPJ2

Answer:

$2.90

Step-by-step explanation:

Spinach    $5.75

Tuna         $7.20

2 lemonades    $2.60

tax =  $1.55

Sum = $17.10

Change = $20.00 - $17.10 = $2.90