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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?
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?
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 + 20Using 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.
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What is 18a and 12ab's GCF
Answer:
6a
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.
Find a nonzero vector normal to the plane
What is the reciprocal of 2 2/3
Find The Perimeter Of The Shaded Region
90 ft
58 ft
24 ft
38 ft
Answer:
38 ft
Step-by-step explanation:
Perimeter of the rectangle = 2* length + 2* width
Length of shaded part = Length of the larger rectangle - 4 = 11ft
width of the shaded part = width of the larger rectangle - 6 = 8 ft
Perimeter of the rectangle = 2* length + 2* width
Plug in the values of length and width
Perimeter of the shaded rectangle= 2(11) + 2(8)= 22+ 16= 38 feet
How do you convert 6 feet into meters?
Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20
The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.
Explanation:The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.
We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:
y = 4.302(20) - 3.293 = 82.041
So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.
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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.
Answer:
The solution is shown in attached figure.
Step-by-step explanation:
In table 1,
US currency (Dollars) Foreign currency
50.00 31.50
The foreign currency per US dollar is
[tex]\frac{31.50}{50}=0.63[/tex]
Therefore 0.63 is not equal to the exchange rate of Mexican peso and euro.
In table 2,
US currency (Dollars) Foreign currency
20.00 14.60
The foreign currency per US dollar is
[tex]\frac{14.60}{20}=0.73[/tex]
Therefore 0.73 is equal to the exchange rate of euro.
In table 3,
US currency (Dollars) Foreign currency
25.00 18.25
The foreign currency per US dollar is
[tex]\frac{18.25}{25}=0.73[/tex]
Therefore 0.73 is equal to the exchange rate of euro.
In table 4,
US currency (Dollars) Foreign currency
40.00 724.80
The foreign currency per US dollar is
[tex]\frac{724.80}{40}=18.12[/tex]
Therefore 18.12 is equal to the exchange rate of Mexican peso.
In table 5,
US currency (Dollars) Foreign currency
15.00 271.80
The foreign currency per US dollar is
[tex]\frac{271.80}{15}=18.12[/tex]
Therefore 18.12 is equal to the exchange rate of Mexican peso.
How do you interpret algebraic expressions in terms of their context
From the 11
male and 6
female sales representatives for an insurance company, a team of 3
men and 2
women will be selected to attend a national conference on insurance fraud.
In how many ways can the team of 5
be selected?
One card is selected at random from an ordinary deck of 52 playing cards. let a = event a face card is selected
(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)
Anoav uses which statistical distribution to determine the significance of the results
3 1/6 divided by 5/8
The result of 3 1/6 divided by 5/8 is equal to 76/15.
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction.
In this case, 3 1/6 can be written as an improper fraction as (3 × 6 + 1) / 6 = 19/6.
Next, we can multiply the numerator of the fraction by the reciprocal of the divisor.
The reciprocal of 5/8 is 8/5.
So, (19/6) ÷ (5/8) = (19/6) × (8/5) = (19 × 8) / (6 × 5) = 152/30.
The fraction 152/30 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2. So, (152/30) ÷ 2 = 76/15.
Therefore, 3 1/6 divided by 5/8 is equal to 76/15.
Final answer:
To find the result of 3 1/6 divided by 5/8, convert the mixed number to an improper fraction, multiply by the reciprocal of the divisor, and simplify the resulting fraction. The answer is 5 1/15.
Explanation:
The student's question 3 1/6 divided by 5/8 is a mathematics problem that involves division of mixed numbers and fractions. To solve this problem, the student first needs to convert the mixed number into an improper fraction. To do this, the student multiplies the whole number by the denominator of the fractional part and then adds the numerator:
Multiply 3 (the whole number) by 6 (the denominator of the fractional part): 3 x 6 = 18.
Add the numerator (the fractional part's numerator, which is 1): 18 + 1 = 19. So, 3 1/6 becomes 19/6.
The next step is to divide 19/6 by 5/8. In division of fractions, you multiply by the reciprocal of the divisor. The reciprocal of 5/8 is 8/5.
Therefore, you multiply 19/6 by 8/5: 19/6 x 8/5.
Perform the multiplication of numerators and denominators: 19 x 8 = 152 and 6 x 5 = 30.
The result is 152/30. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
The simplified answer is 76/15, or as a mixed number, 5 1/15.
This shows that 3 1/6 divided by 5/8 is 5 1/15.
The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?
Answer: the density approaches infinity
Step-by-step explanation:
Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.
a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?
Answer:a. first (-12,6) second (20,35)
b. y = -1/2x, 2y + 1x = 0 (neither horizontal or vertical)
c. y= -1/2x + 2.
Step-by-step explanation:
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
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.
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Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles
Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000
Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)
a garden table and a bench cost 817 dollars combined. The garden table costs 83 less than the bench. what is the cost of the bench
The casino la bella fortuna is for sale and you think you might want to buy it, but you wantto know how much money you are going to make. all the present owner can tell you is thatthe roulette game red or black is played about 1000 times a night, 365 days a year. eachtime it is played you have probability 19/37 of winning the player’s bet of $10 and probability18/37 of having to pay the player $10.
The expected value of the roulette game red or black is -$0.62 per game, indicating an expected average loss.
Explanation:The expected value of the roulette game red or black can be calculated by multiplying the probabilities of winning and losing by their corresponding outcomes. In this case, the probability of winning ($10) is 19/37, and the probability of losing ($-10) is 18/37. Multiply these probabilities by their corresponding outcomes and subtract to get the expected value:
Expected value = (19/37 * $10) + (18/37 * -$10) = -$0.54 + (-$0.54) = -$0.62
This means that if you play this game repeatedly, over a long string of games, you would expect to lose an average of 62 cents per game.
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A new basketball costs $25.00 at the sporting goods store. If the store is having a going-out-of-business sale and everything is 60% off, what is the actual cost of the basketball?
Final answer:
To calculate the discounted price of the basketball, multiply the original price ($25.00) by 60% to find the discount ($15.00), and subtract this from the original price to get the final price ($10.00).
Explanation:
To find out the actual cost of the basketball after a 60% discount, we start by calculating the amount of the discount. A 60% discount on a $25.00 basketball means the discount is 60/100 times $25.00. To do the calculation:
First, we convert the percentage to a decimal: 60% = 0.60.Then, we multiply the original price by the decimal: $25.00 × 0.60 = $15.00.This $15.00 is the amount of the discount.To find the discounted price, we subtract the discount from the original price: $25.00 - $15.00 = $10.00. Therefore, the discounted price of the basketball is $10.00.
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
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]
Consider the following.
Point
(-5, 4)
Line
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.
(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
Between 2005 and 2008, the average rate of inflation was about3.4 per year. If a cart of groceries cost $140 in 2005, what did it cost in 2008
If $3500 is invested at the rate of 8%, compounded quarterly, what will be the value of the investment 17 years from now, assuming no withdrawals?
i need to know the solution using a fraction or integer to 3 more than the product of 7 and a number x is less than 26
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)