An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?

Answers

Answer 1

4 cats and 14 dogs.

Explanation:

Data :

Amount of cats : c = ?

Cost per cats : $1.50

Amount of dogs : d = ?

Cost per dogs : $6.50

Total spent for dogs and cats : $97.00

Total number of dogs and cats : 18

Formulas:

1.50c + 6.50d = 97.00

c + d = 18

Solution:

c + d = 18 => c = 18 - d

1.50(18 -d) + 6.50d = 97.00

27 - 1.50d + 6.50d = 97.00

27 - 1.50d + 6.50d - 27 = 97 -


Related Questions

find the values of x and y that maximize the objective function c = 3x + 4y for the graph

Answers

Answer:  The correct answer is x=0 and y=4 or (0,4) per the graph

Step-by-step explanation:

To find the maximum value, we must test each point using the equation:

Check for (0,4):

C=3x+4y

C=3(0)+4(4)

C=16

Check for (2,2):

C=3(2)+4(2)

C=6+8

C=14

Check for (4,0):

C=3(4)+4(0)

C=12

Answer:

Step-by-step explanation:

All of the following ratios are equivalent except 8 to 12 15/102/36:9

Answers

False

1) Let's examine those ratios, and simplify them whenever possible:

[tex]\begin{gathered} \frac{15}{10}=\frac{3}{2} \\ \frac{2}{3} \\ \frac{6}{9}=\frac{2}{3} \\ \frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]

2) Simplifying those ratios, all the following but 15/10 are equivalent to 8/12

3) So this is a false statement to say that all of those are equivalent except 8 to 12.

is this equation no solution, one solution, or infinitely may solutions

Answers

Given:

[tex]\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-\frac{1}{4}x+2\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]

To solve for x and y:

Substitute the equation (2) in (1) we get,

[tex]\begin{gathered} x+4(-\frac{1}{4}x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}[/tex]

Therefore, the given system has infinitely many solutions.

Plot the complex number, then write the complex number in polar form. You may express the argument in degrees.

Answers

DEFINITIONS

To represent a complex number we need to address the two components of the number.

Consider the complex number:

[tex]a+bi[/tex]

Complex numbers are the points on the plane, expressed as ordered pairs (a, b), where a represents the coordinate for the horizontal axis and b represents the coordinate for the vertical axis.

Note that the imaginary part is plotted out on the vertical axis while the real part is on the horizontal axis.

QUESTION

The complex number is given to be:

[tex]4\sqrt[]{3}-4i[/tex]

This means that the ordered pair representing the complex number is given to be:

[tex](a,b)=(4\sqrt[]{3},-4)[/tex]

This means that the point will be positive on the real axis and negative on the imaginary axis. Therefore, the point will be in the 4th quadrant.

The correct option is OPTION B.

the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions

Answers

You can read a pie chart as follows

Looking at the given pie chart.

The budget for Research is arounf 1/6

The budget for Engineering is around 2/6

The budget for Support is around 1/8

The budget for media and marketing are 1/16 each

The budget for sales is around 3/16

a) The department that has one eight of the budget is Support.

b) The budgets for sales and marketing together add up to

[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]

Multiply it by 100 to express it as a percentage

[tex]\frac{1}{4}\cdot100=25[/tex]

25% of the budget correpsonds to sales and marketing

c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3

[tex]\frac{18}{3}=6[/tex]

The budget for media is 6%

Figure A is a scale image of Figure B.27Figure AFigure B4535What is the value of x?

Answers

Answer:

x = 21

Explanation:

Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.

It follows then

[tex]\frac{27}{45}=\frac{x}{35}[/tex]

which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.

Now to find the value of x, we simply need to solve for x.

We do this by multipying both sides by 35:

[tex]undefined[/tex]

Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?

Answers

Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.

81 km=9 liters

9 km= 1 liter

She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.

By unitary method,

22 liters = 22 × 9 km

              = 198 km

Also, given that  if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.

We need to find the amount of fuel she would need.

Let 139.4 km = x liters

By unitary method,

x = 139.4 / 9

x = 15.5 liters

Therefore, Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

Learn more about Unitary method here:

https://brainly.com/question/22056199

#SPJ1

can you please solve this practice problem for me I need assistance

Answers

The missing angle in the triangle of the left is:

51 + 74 + x = 180

x = 180 - 51 - 74

x = 55°

The missing angle in the triangle of the right is:

55 + 74 + x = 180

x = 180 - 55 - 74

x = 51°

Then, both triangles are similar. This means that their corresponding sides are in proportion. These sides are:

35 in

hello I need help answering this homework question please thank you

Answers

Solution:

Case: Area

Given: A house to be painted

Method/ Final answers

a) Find the area of the garage to be painted.

(i) Front.

A = l X w - Garage door area

l= 15 ft, b= 10-4 gives 6ft

A= 15 X 6 - (10 X 7)

A= 90 - 70

A= 20 square feet

ii) Side

A= l X w

A= 6 X 5

A= 30 square feet

iii) The sum of areas

A= 20 + 30

A= 50 square feet

b) Area of the painted region around windows 5 and 6.

Since 12 in = 1 ft

Area of front door converted to feet is (20/3) ft by 3 ft

Areas of windows 5 and 6 converted to feet is 3 ft by (5/3) ft each

A= Area of space - (Area of front door + window 5 + window 6)

A= (30 X 10) - [(20/3) X 3 + 3 X (5/3) + 3 X (5/3)]

A= 300 - [20 + 5 + 5]

A= 300 - 30

A= 270 square feet.

c) Area of the painted region around windows 3

A= Total face - Area of window 3

A= (Rectangle + Parallelogram + Triangle) - Area of window 3

A= [(10 X 4) + (5 X 4) + (0.5 X 4 X 3)] - [1 X (5/3)]

A= [40+20+6] - [5/3]

A= 66 - (5/3)

A= 193/3 square feet

A= 63.33 square feet

d) Area of the region on the second floor with 2 rectangles and the region around window 4

i) region with rectangle 1 from left to right

A= 10 X (15- 6)

A= 10 X 9

A = 90

ii) region with rectangle 2 from left to right

A= 10 X (15- 6)

A= 10 X 9

A = 90

iii) Area of region around window 4

Area of space - area of window

A= 10 X (30-9-12) - [3 X (5/2)]

A= 10 X 9 - (15/2)

A= 82.5.

Total area= 90 + 90 + 82.5

= 262.5 square feet

e) Total area of the painted region (white)

262.5 + 63.33+ 270 + 50

= 645.83 square feet.

f) Additional question

The total cost if it cost $8 per sq ft

645.83 square feet X $8 per sq ft

=$5166.64

A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure.What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.

Answers

Solution

For this case we can do the following:

We can find the value of s on this way:

[tex]s=\sqrt[]{6^2+4^2}=\sqrt[]{52}=7.21[/tex]

And solving for r we got:

[tex]r=\sqrt[]{6^2+3^2}=\sqrt[]{45}=6.71[/tex]

Then the answer for this case would be:

[tex]\sqrt[]{52}=7.21[/tex]

which describes the solution of the inequality y>-15? a) solid vertical line through (0,-15) with shading to the left of the line. b) dashed vertical line through (0,-15) with shading to the left of line. c) solid horizontal line through (0,-15) with shaing below line. d) dashed horizontal line through (0,-15) with shaing above line.

Answers

The solution to the inequality y > - 15 is all values of y greater than -15. This means the number -15 itself is not included; therefore, the line is a dashed line that passes through (0, -15). Furthermore, the > sign implies that the shaded region is found above the dashed line. Hence, the solution to our inequality is a dashed horizontal line through (0, -15), with shading above the line.

Find the value of x to make this equation true. 6x + 1 = 6 + 2x.

Answers

6x + 1 = 6 + 2x.​

collect the like term

6x - 2x = 6-1

4x = 5

divide both-side of the equation by 4

4x/4 = 5/4

x=1.25

1.25

I need to double check 15 I got answer B

Answers

We will have that the area of one sector of the circle will be:

[tex]A=(\frac{45}{360})\pi(20in)^2\Rightarrow A=\frac{25\pi}{2}in^2[/tex]

So, the solution is option B.

The angle of depression from the top of a sheer cliff to point A on the ground is 35º. If point A is280 feet from the base of the cliff, how tall is the cliff? Round the answer to the nearest tenth of afoot.

Answers

In this case, to calculate the tall of the cliff, consider the distance from the base of the cliff to the point A, as a hypotenuse of a right triangle.

The tall of the clift is given by:

h = 280 sin(35)

h = 280(0.573)

h = 160.60

Hence, the tal of the clift is 160.60 feet

in 3 years Donald wants to buy a bicycle that costs 600.00 if he opens a savings account that earns 4% interest compounded quarterly how much will he have to despoit as principal to have enough money in 3 years to buy the bike

Answers

We want the future value to be $600. With an interest of 4% quarterly in 3 years, we have the following information:

[tex]\begin{gathered} FV=600 \\ i=0.04 \\ t=3 \\ n=4 \end{gathered}[/tex]

Then we apply the following formula:

[tex]PV=\frac{FV}{(1+\frac{i}{n})^{n\cdot t}}[/tex]

therefore, we have that:

[tex]PV=\frac{600}{(1+\frac{0.04}{4})^{4\cdot3}}=\frac{600}{(1.01)^{12}}=532.46[/tex]

therefore, Donald would have to deposit $532.46 as principal.

Construct a probability distribution for a discrete random variable uses the probability experiment of tossing a coin three times. Consider the random variable for the number of heads

Answers

Answer:

Explanation:

By building a tree diagram we can find the theoretical probability of each number of heads when tossing three coins.

What is the slope of a line perpendicular to the line whose equation is 3x-5y=45. Fully simplify your answer

Answers

The slope of a line perpendicular to the line whose equation is 3x-5y=45 is -5/3.

So first of all, we have to find the slope of the given line. Convert it into Slope-Intercept Form.

The Slope - Intercept Form is : y = mx + c

Converting the given equation, we get :

3x - 5y = 45

5y = 3x + 45

y = (3/5)x + 15

Perpendicular Lines

The lines having opposite reciprocal slopes are perpendicular. That means you flip the sign (+/-) and flip the numerator and denominator. The slope of the line perpendicular to this one is -5/3.

To learn more about slope of a line , check :

https://brainly.com/question/24810955

I inserted a picture of the question Check all that apply

Answers

Recall that the line equation is of the form

[tex]y=mx+c\ldots\ldots\text{.}(1)[/tex]

The points lie in the line are (2,5) and (-2,-5).

Setting x=2 and y=5 in the equa

The following are the annual salaries of 15 chief executive offers of major companies. The salaries are written in thousands of dollars.

Answers

The original data is:

405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633

To find the required percentiles, we need to sort the dataset from lowest to highest.

84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108

The total number of data is 15.

a) The 25th percentile is the element located at the position:

25/100 * 15 = 3.75

Rounding down, the position is 3, so the 25th perc

Earth's Moon is 384,400 km from Earth. What is the correct way to write this distance in scientific notation? O A. 3.844 x 105 km OB. 38.44 x 10-4 km O C. 38.44 x 104 km O D. 3.844 x 10-5 km SUBMIT

Answers

To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive.

So, in this case, you have

Therefore, the correct way to write this distance in scientific notation is

[tex]3.844\times10^5[/tex]

And the correct answer is

[tex]undefined[/tex]

I need help on this calculus practice problem, I’m having trouble on it.

Answers

From the question

We are given

[tex]\lim _{x\to-7}g(x)[/tex]

We are to determine if the table below is appropriate for approximating the limit

From the table

The value of the limit as x tends to -7

Can be found using

[tex]x=-7.001\text{ and x = 7.001}[/tex]

Hence, from the values given in the table

The table is appropriate

mrs Middleton makes a solution to Clean her windows she uses 2:1 ratio for every two cups of water she uses one cup of vinagar if ms middleton uses a gallon of water how mant cups of vinagara. 12 cups b. 2 quartz c. 2 pints d. 1 gallon

Answers

To answer this question we have to find (among the options) the amount that represents half the amount of water used.

Since the ratio of water to vinegar is 2:1, half of the amount of water will be used of vinegar.

In this case we have to find the answer that represents half a gallon.

That answer is 2 quarts. 2 guarts are 0.5 gallons, it means they are half the amount of water used.

It means that the answer is b. 2 quarts.

PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..

Answers

[tex]b,c\text{ and d}[/tex]

Explanation

remember some properties of the exponents

[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]

then, to solve this solve each option and compare

Step 1

[tex]6^{-5}\cdot6^2[/tex]

solve

[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]

so, this is not an answer

Step 2

[tex](\frac{1}{6^2})^5[/tex]

solve

[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]

so, this is an answer

Step 3

[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]

so, this is an answer

Step 4

[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]

so, this is an answer

Step 5

[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]

so, this is not an answer

I hope this helps you

Use Pythagorean theorem to find right triangle side lengthsFind the value of c in the triangle shown below.682Choose 1 answer:A = 28B= 64=9= 10

Answers

EXPLANATION

Given the Right Triangle, we can apply the Pythagorean Theorem in order to get the value of x as shown as follows:

[tex]\text{Hypotenuse}^2=Short_-leg^2+Long_-leg^2[/tex]

Replacing terms:

[tex]x^2=6^2+8^2[/tex][tex]x^2=36+64=100[/tex]

Applying the square root to both sides:

[tex]x=\sqrt[]{100}=10[/tex]

Hence, the solution is x=10

On the graph below, what is the length of side AB? B ...

Answers

The distance between two points in the plane is:

[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2[/tex]

The points A and B have coordinates A(5,3) and B(5,6). Then the distance between them is:

[tex]\begin{gathered} d(A,B)=\sqrt[]{(5-5)^2+(6-3)^2} \\ =\sqrt[]{(3)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]

Therefore, the length of the side AB is 3 units.

what is the slope intercept form of the line passing through the point (2,1) and having a slope of 4?

Answers

The equation of a line has the form:

[tex]y=mx+b[/tex]

if the slope is equal to 4 then we know that: m = 4 and now we can replace the slope and the coordinate ( 2,1 ) to find b so:

[tex]\begin{gathered} 1=4(2)+b \\ 1-8=b \\ -7=b \end{gathered}[/tex]

So the final equation will be:

[tex]y=4x-7[/tex]

8+7t=22 in verbal sentence

Answers

Eight plus Seven times t equals twenty-two

Explanation

Step 1

Let

a number= t

seven times a number= 7t

the sum of eigth and seven times a number=8+7t

the sum of eigth and seven times a number equals twenty-two=8+7t=22

or,in other words

Eight plus Seven times t equals twenty-two

I hope this helps you

The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term

Answers

SOLUTION

The following is a geometric series

We will use the formula

[tex]T_n=ar^{n-1}[/tex]

Where Tn is the nth term of the series,

n is the number of terms = 8,

a is the first term = 15

And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15

Now let's solve

[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]

So the 8th term = 53.748

Answer the questions below about the quadratic function.g(×)=2×^2-12×+19Does the function have a minimum or maximum? minimum or maximum what is the functions minimum or maximum value?Where does the minimum or maximum value occur?x=?

Answers

Given the function:

[tex]g(x)=2x^2-12x+19[/tex]

Let's determine if the function has a minimum or maximum.

The minimum and maximum of a function are the smallest and largest value of a function in a given range or domain

The given function has a minimum.

Apply the general equation of a quadratic function:

[tex]y=ax^2+bx+c[/tex]

To find the minimum value, apply the formula:

[tex]x=-\frac{b}{2a}[/tex]

Where:

b = -12

a = 2

Thus, we have:

[tex]\begin{gathered} x=-\frac{-12}{2(2)} \\ \\ x=-\frac{-12}{4} \\ \\ x=3 \end{gathered}[/tex]

To find the function's minimum value, find f(3).

Substitute 3 for x in the function and evaluate:

[tex]\begin{gathered} f(x)=2x^2-12x+19 \\ \\ f(3)=2(3)^2-12(3)+19 \\ \\ f(3)=2(9)-36+19 \\ \\ f(3)=18-36+19 \\ \\ f(3)=1 \end{gathered}[/tex]

Therefore, the function's minimum value is 1

Therefore, the functions minimum value occurs at:

x = 3

ANSWER:

• The function has a minimum

• Minimum value: 1

• The minimum occurs at: x = 3

Find the volume of the figure. Round to the nearest hundredths place if necessary.

Answers

The volume of a Pyramid

Given a pyramid of base area A and height H, the volume is calculated as:

[tex]V=\frac{A\cdot H}{3}[/tex]

The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:

[tex]c^2=a^2+b^2[/tex]

Solving for b:

[tex]b^{}=\sqrt[]{c^2-a^2}=\sqrt[]{19.3^2-16.8^2}=9.5\operatorname{mm}[/tex]

The area of the base is the semi-product of the legs:

[tex]A=\frac{16.8\cdot9.5}{2}=79.8\operatorname{mm}^2[/tex]

Now the volume of the pyramid:

[tex]V=\frac{79.8\operatorname{mm}\cdot12\operatorname{mm}}{3}=319.2\operatorname{mm}^3[/tex]

The volume of the figure is 319.2 cubic millimeters

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