Answer:
We can do this using trial and error
which can also be illustrated as
1x+2y=14
where 1x represents the total length eaten by the cat and 2y represents the total amount eaten by the dog
(bear in mind they both should eat a certain length such that exactly 14cm is eaten COMPLETELY)
by trial and error we find that 1(8)+2(3)=14 which means that
the cat ate 8cm=8*2/1=16seconds
and the dog ate
6cm=6*3/2=9 seconds
so the total seconds is the sum 16+9=25seconds
The total time taken by them to eat the entire sausage is 11.996 seconds.
What is Ratio and Proportion ?When a number can be divided by another number , it can be written as p :q and when two ratios are equal they are said to be in proportion.
It is given that the sausage is 14cm
The kitten eats at the rate of 1 cm every 2 seconds
The puppy eats at the rate of 2 cm every 3 seconds
In 1 second kitten eats 0.5 cm
In 1 second puppy eats 0.667 cm
Total eaten in 1 second is 0.5 +0.667 = 1.167 cm
14 cm will be eaten in 14 /1.167 = 11.996 seconds
Therefore the total time taken by them to eat the entire sausage is 11.996 seconds.
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What is the formula forfinding the area of a circle using its radius or diameter.
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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Write the following statement as a mathematical expression.
Let x be a number.
The quotient of two and a number, subtracted from seventeen
Answer:
17 - (2 / x)
Step-by-step explanation:
because it is being subtracted from 17. that goes first, and then x is being divided by 2.
Hope this helps!
Answer:
17 - (2 / x)
Step-by-step explanation:
i just did it and got a 100%
What fraction with a numerator of 2 is equivalent to 48?
Answer:
\(\frac{2}{\frac{1}{24} }\)
Step-by-step explanation:
2/x = 48
48x = 2
x = (2)/ (1/24)
\(\frac{2}{\frac{1}{24} }\) = 48
Could someone please help here in so lost
Answer:
x=3
(26x+50degreese) = 134 degreese
Step-by-step explanation:
f(x) = –2x2 + 8x – 10
Find f(-4)
Answer: x = -74
Step-by-step explanation:
Find the LCM of A= 3^2 x 5^4 x 7 and B= 3^4 x 5^3 x 7 x11
The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.
Given are two numbers which are showed in the prime factorized form.
A = 3² × 5⁴ × 7
B = 3⁴ × 5³ × 7 × 11
Prime factorization is the factorization of a number in terms of prime numbers.
In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.
A = 3² × 5³ × 5 × 7
B = 3² × 3² × 5³ × 7 × 11
Bring down the primes in each column.
LCM = 3² × 3² × 5³ × 5 × 7 × 11
= 3898125
Hence the LCM is 3898125.
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linda Put $610 in a savings account that pays 1.2% interest each year. Enrique puts $590 in a high-yield account that pays 3.9% interest each year.
PART A: After one year who has more money? How much more?
PART B: After a second year who has more money? How much more?
PART A: Linda has $4.41 more than Enrique after one year.
PART B: Enrique has $12.10 more than Linda after the second year.
PART A: After one year, we can calculate the amount of money each person has in their respective accounts.
For Linda's account:
Principal amount = $610
Interest rate = 1.2%
\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)
\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)
For Enrique's account:
Principal amount = $590
Interest rate = 3.9%
\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)
Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91
Comparing the two amounts, after one year Linda has more money.
The difference in the amount is:
$617.32 - $612.91 = $4.41
Therefore, Linda has $4.41 more than Enrique after one year.
PART B: After a second year, we need to calculate the amounts again.
For Linda's account:
Principal amount = $617.32
Interest rate = 1.2%
\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)
Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73
For Enrique's account:
Principal amount = $612.91
Interest rate = 3.9%
\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)
Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83
Comparing the two amounts, after the second year Enrique has more money.
The difference in the amount is:
$636.83 - $624.73 = $12.10
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Find the 6terms of the series 247
The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.
To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.
Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.
The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.
Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.
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In a random sample of 1500 Arts majors who are graduating from the University of Western Cape this summer (2021), we observe that 1380 have already found a job.
What is the proportion of students that have already NOT found a job (rounded off to two decimals)? [3]
The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.
To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.
The total number of students who have not found a job would be 1500 - 1380 = 120.
To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:
The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.
Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.
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A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
\(\pi = 0.5\)
Then the sample size for M = 0.04 is obtained as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 2.575 \times 0.5\)
\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)
n = 1037.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
to
76⁰
41
The measures of the angles of a triangle are 76⁰, 41⁰, and 63⁰.
What is Angle Sum Property?
The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angle.
We have,
The measures of the angles of a triangle are:
x,
76⁰,
41⁰.
so, we have to calculate the value of the x⁰:
The sum of all the angles in the triangle is 180⁰
so,
to calculate the measure of x put the all values in equation such that using the above rule:
x + 76⁰ + 41⁰ = 180⁰
x = 180⁰ - 76⁰ - 41⁰
x = 63⁰
Hence, the measures of the angles of a triangle are 76⁰, 41⁰, and 63⁰.
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Pls help thank you :)
Answer:
points= (0,4) (1,-4) (-1,4) and make the line
Step-by-step explanation:
i just know
a) Alex, an eighth grader, and Eric, a seventh grader, need to determine who came
closer to their grade’s state record for the triple jump. Alex jumped 38 feet 11 2/3
inches and Eric jumped 36.89 feet. Who was closer to the state record if the eighthgrade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches? (2
points)
The person that was closest to the state record after the jump is; Alex
How to solve Algebra word problems?We are told that Alex jumped 38 feet 11²/₃ inches or 38.9725 ft and that the eighth-grade record is 40.17 feet.
Let see how closer Alex jumped was;
40.17 feet - 38.9725 ft = 1.2425 ft
We are told that Eric jumped 36.89 feet and the state record of the eighthgrade record is 40.17 feet. Thus;
Let see how closer Eric jumped was;
40.17 feet - 36.89 ft = 3.28 ft
We conclude that 1.2425 ft is less than 3.28 ft and as such Alex was closer.
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solve for x.
2x + 15
5x - 12
Answer:
x = 9
Step-by-step explanation:
2x + 15 = 5x - 12 (since it is parallel)
15 + 12 = 5x - 2x
27 = 3x
x = 9
please help graph this equation
Arrange the steps in order to simplify the expression
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
please help meeeeeeeeeeee
using the space below, in complete sentences, reflect on how writing a rate is related to what you know about writing equivalent ratios. Don't forget that you need 1 topic sentence and 1 conclusion sentence in your paragraph
Answer:
Identifying and Writing Equivalent Rates
Ratios compare two quantities. A rate is a type of ratio that compares two quantities that have different units of measurement. The word “per” is often used to describe rates.
Rates can be written as fractions. The first quantity is the numerator and the second quantity is the denominator. Different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios—divide or multiply the numerator and the denominator by the same number.
Step-by-step explanation:
Select the correct answer.
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to
finish the season with a 90% winning percentage?
A.12
B.14
C.15
D.27
Answer:
C
Step-by-step explanation:
First find how many games they need to have 90% by multiplying .9(30)=27
then, 15(.8)=12
Then 27-12=15
Answer:
c
Step-by-step explanation:
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Hello!
The distance, d, is less than 200 miles.
B. d > 200
Question 5 of 8
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-); for example, enter to as x^3. Do
not include "G(x) =" in your answer.
Answer: g(x) = (x - 1)^3
Step-by-step explanation:
There is a transformation called "horizontal translation"
For an initial function f(x), a horizontal translation of N is written as:
g(x) = f(x - N)
where if N is positive, we have a translation of N units to the right.
If N is negative, we have a translation of N units to the left.
Here, we can see that:
f(x) = x^3, such that when x = 0, f(0) = 0.
And g(x) seems to be a horizontal translation of f(x) (because the graph of g(x) is equidistant to the graph of f(x)), then:
g(x) = (x - N)^3
And we can see that when x = 0, g(0) = 1
Then:
g(0) = (0 - N)^3 = 1
N^3 = 1
N = ∛1 = 1
Then the equation for g(x) is:
g(x) = (x - 1)^3
write a rule to describe the function shown
Which of the following numbers
is a solution to this inequality?
14x > 36
3
2.
Answer:
\(x=\frac{18}{7}\)
Step-by-step explanation:
How much miles will the car use with 17 gallons of gas?
Answer:
from the graph we can see that
for 2 gallones - it can travell 70 miles
4 gallones - 140 miles
we will take the first case
2 gallones - 70 miles
17 gallones - ? miles
cross multiply
\( \frac{17 \times 70}{2} \)
= 595 miles
Find the midpoint M of the line segment joining the points P = (4, 2) and Q = (-6, -8)
Answer:
(- 1, - 3 )
Step-by-step explanation:
the coordinates of the midpoint are the average of the coordinates of the endpoints, then
midpoint = (\(\frac{4-6}{2}\), \(\frac{2-8}{2}\) ) = ( \(\frac{-2}{2}\), \(\frac{-6}{2}\) ) = (- 1, - 3 )
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?
Chay can use 3 bags of mulch per flower bed.
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.
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we have 2 fractions 5/8 and 5/4
Plz help i need helpful plz
The local government is concerned with the population of a new predatory fish, the tiger gar, which was first observed in Lake Richmond about 5 years ago. The following table shows the approximate number of tiger gars living in the lake since 2016:
2016 2017 2018 2019 2020 2021
322 399 507 618 785 975
Using the TI-nspire calculator, write an exponential function that models the population of tiger gar in the lake. (Round all numbers to the nearest hundredth.)
y=blank(blank)x
The exponential function that models the population of tiger gar in the lake is given as follows:
\(y = 322.63(1.25)^x\)
How to define an exponential function?An exponential function has the definition presented as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.Considering x as the number of years since 2016, the points are given as follows:
(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).
Inserting these points into an exponential regression calculator, the equation is given as follows:
\(y = 322.63(1.25)^x\)
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An army camp had a food provision of 35 days for 800 soldiers on the first day of the month. On
the same day, some of the soldiers were transferred to another camp. The food provision lasted for
50 days for the remaining soldiers. How many soldiers were transferred to the other camp?
(Assume that each soldier consumes equal quantity of food per day.)
240 soldiers were transferred to the other camp. Let's assume the number of soldiers transferred to the other camp is "x." we can solve for the unknown variable representing the number of soldiers transferred.
Initially, the food provision was planned for 800 soldiers for 35 days. This means that the total food supply is equal to 800 soldiers multiplied by 35 days, which gives us a total of 28,000 soldier-days of food.
After some soldiers were transferred, the remaining soldiers had enough food to last for 50 days. So the food supply for the remaining soldiers can be calculated as the product of the number of remaining soldiers and the number of days, which gives us (800 - x) * 50 soldier-days of food.
Since the amount of food remains the same, we can set up the following equation:
\(28,000 = (800 - x) * 50\)
Now, let's solve this equation to find the value of x, representing the number of soldiers transferred to the other camp:
\(28,000 = 50 * 800 - 50x28,000 = 40,000 - 50x50x = 40,000 - 28,00050x = 12,000x = 12,000 / 50x = 240\)
By setting up the equation based on the total food supply for the initial and remaining soldiers, we can solve for the unknown variable representing the number of soldiers transferred. In this case, 240 soldiers were transferred to the other camp.
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What should be done to solve the following equation? d - 5 = 3
Answer:
d=8
Step-by-step explanation:
Firstly you need to get d by itself. To get d by itself you need to get 5 onto the other side. To do that you need to add 5 to 3 (because adding is the opposite of addition). Therefore you will get 8! So d = 8
Answer:
add 5 both sides making it
d=5+3
solve 5+3
=8
d=8!!!