An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many cats are at the shelter?

Answers

Answer 1

This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter

Answer 2

Final answer:

To find the number of cats at the animal shelter, we can set up and solve a system of equations using the given information. In this case, the number of dogs is 126 and the number of cats is 146.

Explanation:

To solve this problem, let's assign variables to represent the number of cats, dogs, and rabbits at the shelter. Let's say the number of cats is 'c', the number of dogs is 'd', and the number of rabbits is 'r'.

From the given information, we can form three equations:

The total number of animals is 350: c + d + r = 350The number of rabbits is 5 less than one-half the number of cats: r = (1/2)c - 5There are 20 more cats than dogs: c = d + 20

Using these equations, we can solve for the value of 'c' (the number of cats).

By substituting the value of 'c' from equation 3 into equation 2, we get:

r = (1/2)(d + 20) - 5

Now, we substitute the values of 'c' and 'r' from equations 3 and 1 into equation 1:

(d + 20) + d + ((1/2)(d + 20) - 5) = 350

Simplifying this equation, we get:

2d + (1/2)d + 35 = 350

Combining like terms, we have:

4d + d + 70 = 700

Simplifying further, we find:

5d + 70 = 700

Subtracting 70 from both sides of the equation, we get:

5d = 630

Dividing both sides by 5, we find that d = 126. Therefore, there are 126 dogs at the shelter.

Finally, by substituting the value of d back into equation 3, we find:

c = 126 + 20 = 146. Thus, there are 146 cats at the shelter.

Learn more about Solving Systems of Equations here:

https://brainly.com/question/29050831

#SPJ11

Related Questions

If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles

Answers

Because ∠A=40°, therefore ∠B + ∠C = 180.

To create two triangles, we could make a = 10 in.

From the Law of Sines,
a/sinA = b/sinB.

Therefore
10/sin(40) = 15/sin(B)
sin(B) = (15/10)*sin(40) = 0.9642
∠B = arcsin(0.9642) = 74.6°

Because the sine function is positive in quadrants 1 and 2, we could also have ∠B = 180 - 74.6 = 105.4°.
This means that
a/sin(105.4) = 15/sin(40°)
a = [sin(105.4)/sin(40)]*15 = 22.5 in

Answer:
We could have a = 10 in, or a = 22.5 in

8.76× 10 6 is times than 8.76× 10 2 .

Answers

10^6 = 10 *10*10*10*10*10 = 1,000,000

10^2 = 10*10 = 100

1000000/100 = 10,000 times larger

$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.

Answers

hmm is very straight forward, how much is whatever% of anything? is just (whatever/100) * anything.

[tex]\bf \textit{4\% of 2,500}\implies \cfrac{4}{100}\cdot 2,500\implies 100 \\\\\\ \textit{the rest is 7,500 at 5\%, what's 5\% of that?}\implies \cfrac{5}{100}\cdot 7,500\implies 375[/tex]

Text me the answer please

Answers

p(4)= 1/8

This is because there are 8 equal parts and 4 is just one of those 8 parts.

probablility=desired outcomes/total possible outcomes

so

we want to hit the 4

there are 1 of those numbers on the spinner
and 8 numbers total

1 desired outcome
8 total possible outcomes

1/8 is the probablitiy
?=8

a rectangle has a width of 17 ft and a lenghth of 8ft....PLEASE HELP ME SOS!!! ASAP!!!

Answers

perimeter is 17 +17 +8 + 8 = 50 feet

area = 17 x 8 = 136 square feet

cost = 136 x $3.50 = $476.00

G study find the exact value of each of the remaining trigonometric functions cos theta=4/5 270< theta

Answers

This will be a 4th quadrant 3,4,5 triangle.
Sin = -3/5
Tan = -3/4

Final answer:

Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.

Explanation:

The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.

This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.

Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.

Plugging in the given cosine value, we have:

sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5

However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:

sin(theta) = -3/5

For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:

tan(theta) = (-3/5) / (4/5) = -3/4

The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:

sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3

A journal entry for the sale of $10 par common stock for $18 per share would include
a. a credit to Cash
b. a debit to common stock
c. a credit to Paid in Capital in Excess of Par-Common Stock
d. a debit to Paid in Capital n Excess of Par-Common Stock

Answers

credit to paid in capital in excess of par-common stock. the word stock in the question instantly removes a and b there is no debit so c or d but i would go with c. just cause d is missing an i in one of its 'in'

(03.03 HC)

The table shows the outputs, y, for different inputs, x:

Input (x) 6 12 15 25
Output (y) 14 15 15 16

Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)

Answers

part A the table does not show function because 15 is repeated which is a relationship.

What is the inverse of the function below? F(x) = x - 6

Answers

To compute the inverse function of F(x) you simply have to get how argument x depends of value F(x).
F(x)=x-6
Inverse function:
x = F(x)+6
To show that there are different mathematical objects just use e.g F(y)
F(y)=y+6

Answer:

f(x)=x+6

Step-by-step explanation:

its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6

A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rate of the boat in still water.

Answers

recall your d = rt, distance = rate * time.

now, if the boat has a speed of say "b", and the current has a speed of say "c", when the boat is going upstream, is not really going "b" fast, is going " b - c " fast, because the current is eroding speed from it, going upwards.

And when the boat is going downstream, is not going "b" fast either, because the current is now adding to speed to it, so is really going " b + c " fast.

The time it took one way, is the same time it took back, 4 hours each way.

thus

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ Upstream&20&b-c&4\\ Downstream&32&b+c&4 \end{array} \\\\\\ \begin{cases} 20=4(b-c)\implies \frac{20}{4}=b-c\implies 5+c=\boxed{b}\\ 32=4(b+c)\implies \frac{32}{4}=b+c\implies 8=b+c\\ --------------------\\ 8=\left(\boxed{5+c} \right)+c \end{cases} \\\\\\ 8=5+2c\implies 3=2c\implies \cfrac{3}{2}=c\implies 1\frac{1}{2}=c[/tex]

what's the speed of the boat? well, 5 + c = b.

How do you interpret algebraic expressions in terms of their context

Answers

Algebraic expressions are composed of numbers and variables. To interpret them, you must have the word problem to provide you with some context. The variables signify parameters that are maybe unknown in the problem. Although unknown, they can have relationships with each other. The relationships are expressed in algebraic equations.

The scatter plot below shows the relationship between the length (x) in meters and mass f(x) in kg of a marine animal
(1,0)(2,10)(3,20)(4,30)(5,40)(6,50)(7,65)(8,70)(9,80)(10,90)

Which of the following fuction is best represented by the scatter plot?
F(x)=9-10.3x
F(x)=-10.3+9x
F(x)=-9+10.3x
F(x)=10.3-9x

Answers

F(x) = -9 + 10.3x probably.
It's definitely not the first or last option as they have negative gradients (i.e. negative x-coefficient) and so represent a negative correlation. The data given tells us there is a positive gradient and so a positive correlation.
It could be the second option as the second and third are not so vastly different but I would go for the third because it appears to most closely fit the data pattern.

Answer:

F(x)=-9+10.3x

Step-by-step explanation:

Given:

(1,0)

(2,10)

(3,20)

(4,30)

(5,40)

(6,50)

(7,65)

(8,70)

(9,80)

(10,90)

F(x)=9-10.3x and F(x)=10.3-9x cannot be the function of given scatter plot since the slope in these functions are negative

So, The equation of line can be F(x)=-10.3+9x or F(x)=-9+10.3x

Refer the attached figure.

Using desmos calculator

We conclude that the function is best represented by the scatter plot is [tex]F(x)=-9+10.3x[/tex]

What is 18a and 12ab's GCF

Answers

Answer:

Step-by-step explanation:

18a = 2 · 3² · a

12ab = 2² · 3 · a · b

Factors common to both lists are 2, 3, a, so the GCF is 2·3·a = 6a.

a culture started with 6,000 bacteria. After 4 hours, it grew to 6,600 bacteria. Predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number.

Answers

P = 6,600

A = 6,000

t = 4

k = ?

6600 = 6000e^(4k)

6600/6000 = e^(4k)

1.1 = e^(4k)

Take the natural log of both sides.

ln 1.1 = 4k ln e (remember that ln e = 1)

ln 1.1 = 4k

(ln 1.1) / 4 = k

k = 0.0238

Bacteria after 10 hours.

P = 6000e^(0.0238*10)

= 6000e^0.238

= 7612

Therefore, the bacteria will grow to 7612 after 10 hours.

Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles

Answers

18 hours.

Proportions and stuff.

[tex] \frac{204}{4} [/tex] = [tex] \frac{918}{x} [/tex]

Cross multiply,

204x = 918 * 4

204x = 3672
/204 /204
x = 18

18 hours.

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)

Answers

PART A:

Total of students who like football = 77 students
Students who like football and baseball = 48 students
Students who like football and not baseball = 77 - 48 = 29 students

Students who do not like football = 100 - 77 = 23 students

Students who like baseball = 65 students
Students who like baseball but not football = 65 - 48 = 17 students

Students who do not like baseball = 100 - 65 = 35 students

These data can be represented in a two ways table as shown below

PART B:

The number of students who do not like either football or baseball is 29+17+6=52

The probability is 52/100 = 52%

PART C:

The number of students who don't like football is 17+6=23 students
The number of students who don't like baseball is 35 students

The survey result reveals a greater dislike for baseball

Two pairs of shoes and four pairs of socks cost $131, and three pairs of shoes and five pairs of socks cost $190. Find the cost of a pair of socks.

Answers

s = shoes
x = socks

3( 2s + 4x = 131) ------> 6s + 12x = 393
-2( 3s + 5x = 190) ------>-6s - 10x = -380

(2x = 13)/ 2

x = 6.5

A pair of socks is equal to $6. 50

Hope this helps :)
Please give brainliest

The cost of a pair of socks would be $6.50

A bag contains 40 marbles, 4 of which are blue, 10 are red, 25 are green, and 1 is purple. Shawna takes a marble out of the bag, records the color, and returns it to the bag. How many green marbles should she expect after 400 trials? (5 points)

Answers

250.

Since she returns the marble every time, the probability of drawing a green marble remains constant, which is 25/40.

A $28,000 car loan is used to purchase a new car. The loan is for 6 years and has a 5.75% APR. Use the amortization formula to determine the amount of the monthly payments.

Answers

[tex]\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]

[tex]\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount}\\ \end{array}\to & \begin{array}{llll} 28,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5.75\%\to \frac{5.75}{100}\to &0.0575\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &6 \end{cases} \\\\\\ pymt=28000\left[ \cfrac{\frac{0.0575}{12}}{1-\left( 1+ \frac{0.0575}{12}\right)^{-12\cdot 6}} \right][/tex]

Kurt wants to have $25,000 in an investment account four years from now. the account will pay 0.2 percent interest per month. if he saves money every month, starting one month from now, how much will he have to save each month to reach his goal

Answers

Given:
F = 25000, future value
i=0.02 per month, compounded monthly
n=4*12=48 periods (months)
Need A=monthly deposit

The amount A is given by the formula
A=Fi/((1+i)^n-1) [can be derived from the annuity formula]
=25000*0.02/((1.02^48-1)
= 315.05

Answer: Kurt will need to save $315.05 each month to reach the goal of saving $25000 after 4 years.

Kurt will have to save an amount of $496.75 each month.

What is Compound Interest?

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Final amount of the account, A = $25,000

Interest rate, r = 0.2% = 0.002

Number of years, t = 4 years

Interest compounded monthly, so n = 12

Annuity can be found using the formula,

Annuity = 25,000 ÷ {[(1 + 0.002)^(12×4) - 1] / 0.002}

= 25,000 ÷ {[(1.002)⁴⁸ - 1] / 0.002}

= 496.75

Hence the amount Kurt needs to save each month is $496.75.

To learn more about Annuities, click on the link :

https://brainly.com/question/29759069

#SPJ6

An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground? (s= 16t^2)

Answers

Given
s=16t^2
where
s=distance in feet travelled (downwards) since airborne with zero vertical velocity and zero air-resistance
t=time in seconds after release

Here we're given
s=144 feet
=>
s=144=16t^2
=>
t^2=144/16=9
so
t=3
Ans. after 3 seconds, the object hits the ground 144 ft. below.

Answer:

After 3 seconds the object hit the ground.

Step-by-step explanation:

An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.

Given that displacement, s = 16t²

To reach ground displacement should be 144 feet.

That is

s = 16t² = 144

t² = 9

t = 3 seconds.

After 3 seconds the object hit the ground.

A = h/2 * (a + b ); for h

Answers

[tex]A=\dfrac{h}{2}(a+b)\\ 2A=h(a+b)\\ h=\dfrac{2A}{a+b} [/tex]

h/2 * (a + b )=A
h/2=A/(a+b)
h=2A/(a+b)

WILL GIVE BRAINLIEST...
You have 45 ft of the fence you enclose your yard, you are going to use the side of your house as one of the sides and put a fence down the width of the yard so your dog as a place to play, the length is three less than the width. What is the area of your yard?

Answers

We have 45 ft of the fence and we are going to use the side of the house as one of the sides ( on length ).
L = W - 3
2 W + L = 45
2 W + W - 3 = 45
3 W = 45 + 3
3 W = 48
W = 48 : 3
W = 16 ft
L = 16 - 3 = 13 ft
A = 16 * 13 = 208 ft²
Answer: The area of the yard is 208 ft².

A certain species of tree grows an average of 4.2 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.

Answers

Average growth rate = 4.2 cm/week.

So, common difference d = 4.2

The height of the tree a0 = 200 centimeters.

The height of the tree after end of the first week a₁ = 200 + 4.2 = 200 + 4.2(1)

The height of the tree after end of the second week a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).

The height of the tree after end of the third week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).

The height of the tree after the end of the nth week an = 200 + 4.2(n).

The equation is a_n = 200 + 4.2(n).

Two people are traveling and need to exchange the currency of their native country for the currency of the country they are visiting. drag each exchange to match the ratio of currency to currency in each category.

Answers

Answer:

The solution is shown in attached figure.

Step-by-step explanation:

In table 1,