Answer:
7 Cows and 8 Chickens
Step-by-step explanation:
Note that cows have four legs each and chickens have two legs each.
if there were only cows, then 15 cows times 4 legs for each cow would give 15 x 4 = 60 legs. 60 is greater than 44, so some (maybe all) of the animals are chickens.
If there were only chickens, then 15 chickens times 2 legs for each chicken would give 15 x 2 = 30 legs. 30 is less than 44, so we have confirmed that there is a mixture of both cows and chickens on the farm.
One approach would be to build a table of possibilities:
Total legs will equal number of cows times 4 plus number or chickens times 2 and we know the total number of animals is 15, so we keep cows plus chickens equal to 15 and just keep adding a cow and subtracting a chicken and do the math until.we get 44 legs. We know that it will take less than 13 tries, since we already ruled out 15 cows or 15 chickens. We'll start with 1 cow and 14 chickens and go from there
1 Cow + 14 Chickens = (1 x 4) + (14 x 2) = 4 + 28 = 32 legs
2 Cows + 13 Chickens = (2 x 4) + (13 x 2) = 8 + 26 = 34 legs
3 Cows + 12 Chickens = (3 x 4) + (12 x 2) = 12 + 24 = 36 legs
4 Cows + 11 Chickens = (4 x 4) + (11 x 2) = 16 + 22 = 38 legs
5 Cows + 10 Chickens = (5 x 4) + (10 x 2) = 20 + 20 = 40 legs
6 Cows + 9 Chickens = (6 x 4) + (9 x 2) = 24 + 18 = 42 legs
7 Cows + 8 Chickens = (7 x 4) + (8 x 2) = 28 + 16 = 44 legs
We can stop here because we can see that 7 Cows and 8 Chickens have a total of 44 legs.
Another way to approach this is to use algebra and to make is shorter to write we can assign a variable to each item and relate them in some way.
Let's use the letter x to stand for cows and the letter y to stand for chickens so we don't have to keep writing chickens and cows. x and y are just common letters to use, by the way, could use w and k perhaps since cow has a w and chicken has a k...sadly they both start with c, so we can't use that for both.
We know a couple different, but related, things.
One thing we know is that the total number of animals is 15. We can write that as:
x + y = 15
That means cows (x) plus chickens (y) equals 15.
A second thing we know is that the total number of legs is 44. We can write that as
4x + 2y = 44
That means 4 times x (cow) plus 2 times y (chicken) is equal to 44 since each cow has 4 legs and each chicken has 2 legs.
Since we now have two related equations and two variables we can solve for the variables.
If we take the first equation and rearrange it, by subtracting x from both sides, we can see that one way to do it is the following
y = 15 - x
That means the number of chickens (y) is equal to 15 minus the number of cows (x). As long as we do the same thing on both sides of the equals sign the equation is still.equal...you will see this again below.
Now we can then substitute 15 - x for y in the second equation and then all we have is x in that equation. (We can do this because y is equal to 15 minus x...they both have the same value and mean the same thing...they are equal to each other)
4x + 2(15 - x) = 44
As you can see, we now have 2 times 15 minus x where we had 2 times y before. If we multiply the 2 through we get because 2 times 15 is 30 and 2 times x is 2x
4x + 30 - 2x = 44
We can subtract the 2x from 4x and we get
2x + 30 = 44
Now we can subtract 30 from both sides of the equation because as long as we do the same thing on both sides of the equals sign the equality holds true
2x + 30 - 30 = 44 - 30
30 minus 30 is zero and 44 minus 30 is 14 so now we have
2x = 14
If we divide both sides by two, we still maintain the equality and we get x on one side as 2x divided by 2 is 1x or just x and we get 7 on the other side as 14 divided by 2 is 7
x = 7
That means we have 7 Cows as x represents cows, so half the problem solved
If we now go back to our first equation,
x + y = 15
We can replace x with 7 and get
7 + y = 15
We can subtract 7 from both sides and maintain the equality and isolate y
7 - 7 + y = 15 - 7
Again, 7 minus 7 is zero so we have isolated y and 15 minus 7 is 8
y = 8
This means we have 8 Chickens since y represents chickens
Once again we have shown that Old MacDonald has 7 Cows and 8 Chickens
Express sin A, cos A, and tan A as ratios.
Answer:
sin(A) = 2rad19/20 = rad20/10
cos(A) = 18/20 = 9/10
tan(A) = 2rad19/18 = rad19/9
Which graph represents a function
Answer and Step-by-step explanation:
The graph to the top right is a function.
This is a function because it a straight, connected line.
The First graph isn't a function because the lines are connected, and doesn't pass the horizontal test.
The Bottom left graph isn't a function because there are two lines and they intersect.
The Bottom right graph isn't a function because there are points but aren't connected.
#teamtrees #PAW (Plant And Water)
if i drive 118.3 miles and my cars miles to gallon is 26.8 how many times would i have to fill up my tank?
Answer:
4.4.
Step-by-step explanation:
I rounded my answer to 4.4. You can divide 118.3 by 26.8 to get your answer. Hope this was helpful.
A line goes through the point (-8,9), and has a slope of 3/4
Write in form of a Ax + B and C for this line
Answer:
[tex]y=\dfrac{3}{4}x+15[/tex]
Step-by-step explanation:
Given that,
A line goes through the point (-8,9), and has a slope of 3/4.
We need to express in the form of Ax+B for this line.
We have, m = 3/4
So,
[tex]y=\dfrac{3}{4}x+B[/tex]
Put y = 9 and x = -8 in the above equation.
[tex]9=\dfrac{3}{4}(-8)+B\\\\9=-6+B\\\\9+6=B\\\\B=15[/tex]
So,
[tex]y=\dfrac{3}{4}x+15[/tex]
It is the required equation of the line.
(x + 5)(x – 5)
Multiply
Answer:
[tex] {x}^{2} - 25[/tex]
Step-by-step explanation:
[tex](x + 5)(x – 5) \\ \\ = {(x)}^{2} - {(5)}^{2} \\ \\ = {x}^{2} - 25[/tex]
Answer:
x²-25
Step-by-step explanation:
To do a sum like this, break up the first bracket and multiply by the second (terms from the first bracket is in bold in first few steps for clarity):
(x + 5)(x – 5)
x(x-5)+5(x-5)
x²-5x+5x-25
x²-25
How do you solve 2.5x + 10 = 50?
Answer:
I think the answered is x = 16 hope I right
Answer:
X = 16
Step-by-step explanation:
2.5x+10 = 50
distribute the ten to the other side by substracting
2.5x = 50-10
2.5x = 40
Now divide 2.5 on both sides
2.5x/2.5 = 40/2.5
x = 16
What is the median of 30,33,38,40,51,57,81,91?
Answer:[tex]{ \left[\begin{array}{ccc}45.5\\\\\end{array}\right] }{}\\\\\end{array}\right] } ----[/tex]
Step-by-step explanation: Hey, Basically we are going to arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
Hope this helps!
Help Please 15 points!!!
A school reserved a banquet hall for the spring dance. In addition to a $100 deposit, each couple must pay $20. If the total cost of the banquet hall is $1, 140, write and solve an equation to find the number of couples attending the spring dance.
Please help me!! I have been stuck on this question for too long.
Answer: A school reserved a banquet hall for the spring dance. In addition to a $100 deposit, each couple must pay $20. If the total cost of the banquet hall is $1,140, write and solve an equation to find the number of couples attending the spring dance. b. Solve the problem arithmetically. Show the steps you used. c. Compare and contrast the steps you used to solve the problem algebraically and arithmetically.
Step-by-step explanation:
there ya go this was hard
The table shows the relationship between the number of brownies, fill in the missing value in the table.
Answer:
The answer is 25
Step-by-step explanation:
The diagram shows a door lock.
А
B
1
2
3
4
The code is a letter followed by a number.
Write down all the possible codes,
write your answers like this: (A, 1) You must write all of your answers on one line.
Answer:
(A, 1); (A, 2); (A, 3); (A, 4); (B, 1); (B, 2); (B, 3); (B, 4)
Step-by-step explanation:
What a tedious question...
A researcher for a polling organization used a random sample of 1,540 residents in a city to construct a 95 percent confidence interval for the proportion of voters who would vote for candidate Jones. The resulting confidence interval was 0.480 ± 0.025. What is the correct interpretation of the confidence interval?
A proportion of 0.455 and 0.505 of respondents think that Jones has a 95% chance to win.
If 95% of all the voters voted, then Jones would receive between 45.5% and 50.5% of the votes.
The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.
If we repeatedly sampled voters from this city, taking samples of size 1,540, approximately 95% of those samples would have between 45.5% and 50.5% voting for Jones.
Answer:
The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.
Step-by-step explanation:
took the quiz
The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.
What is confidence interval?A confidence interval is a set of values used to estimate an unknown population parameter with a high degree of certainty. It is calculated from a sample of data and takes into account the sample's variability.
The polling organisation is 95% confident that the range of 0.455 to 0.505 accurately represents the proportion of all city voters who would vote for Jones.
This means that if the researcher repeated the sampling process a number of times and created a confidence interval for each sample, 95% of those intervals would contain the true proportion of all city voters who would vote for Jones.
Thus, it does not imply that the true proportion is 95% likely to fall within the interval.
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NEED ASAP !! HELP PLEASE 10 PTS
This is really easy but I’m lazy
Answer:
D
Step-by-step explanation:
it does not matter which side you put the eight.
A fruit basket is filled with 8 bananas, 3 oranges, 5 apples, and 6 kiwis.
For every 3 kiwis, there are 4
Answer:
83
Step-by-step explanation:
666
Answer:
Bananas
Step-by-step explanation:
what is 612.0÷0.06
please help me
Answer:
10,200
Step-by-step explanation:
Answer:
10,200
Step-by-step explanation:
Use a calculator or a piece of paper.
I hope this helps, and have a great day!
A pair of noise-canceling headphones regularly sells for $116. They
are on sale for 35% off. What is the sale price of the headphones?
Answer:
The headphones are now $40.60.
They started on their trip with a full 20 gallon gas tank. They drove 700 miles and ran out of gas. How many miles per gallon did they average? miles per gallon.
Answer:
35 per miles
Step-by-step explanation:
im dum∵b
Subtract. Write your answer in simplest form.
6 3/4 - 2 3/20
Answer:
(6-2) (3/4-3/20)
4 ((3×20-3×4)/80)
4 48/80
4 3/5
Please help, marking brainliest for the best answer. Serious answers only please
52° 38° 128 xo degrees
Answer:
x = 142°
Step-by-step explanation:
Since angle x and the 38° angle are supplementary angles, we know that the following is true...
x + 38° = 180°
x = 180° - 38°
x = 142°
Sloving. Two step equation.
Answer:
w=18
Step-by-step explanation:
Answer:
W=18
Step-by-step explanation:
-6+2w=30
2w=30+6
2w=36
The comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents are provided. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. Two samples are contained in the Excel Online file below. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.
Student’s Parents
College
485
534
650
554
550
572
497
592
Grads
487
533
526
410
515
578
448
469
High School
442
580
479
486
528
524
Grads
492
478
425
485
390
535
a. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. population mean math score parents college grads. population mean math score parents high school grads. _____ _____
b. What is the point estimate of the difference between the means for the two populations?
c. Compute the p-value for the hypothesis test.
d. At αα= .05, what is your conclusion?
Answer:
H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.
Step-by-step explanation:
Part a:
The null and alternate hypothesis can be formulated as
H0 : u1 ≤ u2 the two means ( of students whose parents did or did not attain a higher level of education) are equal .
against the claim
Ha: u1 > u2 the students show a higher population mean math score on the SAT if their parents attained a higher level of education.
Part b:
The point estimate of the difference between the means for the two populations is the difference of sample means
x1`- x2`
525- 487= 38
Student’s Parents
College Grads
x x²
485 487 235,225 237,169
534 533 285,156 284,089
650 526 422,500 267,676
554 410 306,916 168,100
550 515 302,500 265,225
572 578 327,184 334,084
497 448 247,009 200,704
592 469 350,464 219,961
∑xi = 8400 ∑xi ²= 4,462,962
x1`= ∑ xi/n1= 8400/16= 525
Using statistic calculator Using formula : σ(n-1)
s1= 59.4205
High School Grads
x x²
442 492 195,364 242,064
580 478 336,400 228,484
479 425 229,441 180,625
486 485 236,196 235,225
528 390 278,784 152,100
524 535 274,576 286,225
∑xi = 5844 ∑xi ²= 2,875,484
x2`= ∑ xi/n2= 5844/12= 487
Using statistic calculator Using formula : σ(n-1)
s2= 51.7476
x1`- x2`= 525- 487= 38
The test statistic is
t= (x1`- x2`) / √ s1²/n1+ s2²/n2
t= 38/ √(59.4205)²/16 + (51.7476)²/12
t=38 / √3530.7958/16 + 2677.8141/12
t= 1.804
and the degrees of freedom is
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
= [3530.7958/16 + (2677.8141/12) ]²/ (3530.7958/16)²/15 +(2677.8141/12)²/11
≈ 25
The degrees of freedom is always rounded in this calculation
From the table t∝ = 1.708
Hence critical value is t ≥ t∝
Reject H0:
Part C.
The p-value is 0.041647.
The result is less than 0.05.
Result:
H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.
A lawn seed mixture contains three types of seed: bluegrass, rye, and Bermuda. The costs per pound of the three types of seed are 12 cents, 14 cents, and 3 cents, respectively. In each batch there must be at least 25% bluegrass seed, and the amount of Bermuda must be no more than 2/3 the amount of rye. To fill current orders, the company must make at least 6000 pounds of the mixture. How much of each kind of seed should be used to minimize cost
Answer:
612 dollars
Step-by-step explanation:
From the given information:
Amount of the total mixture = 6000 pounds
Also, for each batch, there needs to be at least 25% bluegrass seed.
It implies that:
In 6000 pounds, there are (25×6000)/100 = 1500 pounds of bluegrass seed.
The remaining amount of (6000 - 1500 = 4500)pounds will be for rye and Bermuda.
Suppose the amount of rye seeds = x pounds
while that of Bermuda is (4500 - x) pounds
Then, since the amount of Bermuda contains no more than 2/3 of that of rye.
The equation can be written as:
[tex]( 4500 - x) = \dfrac{2x}{3}[/tex]
13500 - 3x = 2x
13500 = 5x
[tex]x = \dfrac{13500}{5}[/tex]
x = 2700
Now, the amount of rye seed = 2700 pounds
while that of Bermuda seed = 4500 - 2700 = 1800 pounds
However, For Bluegrass, we are told that the cost of 1 pound is 12 cents.
So, the cost of 1500 bluegrass seeds = 12 × 1500 = 18000 cents
For rye seed; cost of 1 pound = 14 cents
the cost of 2700 rye seeds = 14 × 2700 = 37800 cents
For Bermuda seed; cost of 1 pound = 3 cents
the cost of 1800 rye seeds = 3 × 1800 = 5400 cents
The total amount = (18000 + 37800 + 5400) = 61200 cents
Recall that:
100 cents = 1 dollars
61200 cents = x dollars
x = 61200 cents/100 cents
x = 612 dollars
Thus, the minimum cost is 612 dollars.
A bicycle path starts 5 miles due east of an intersection, and continues in a straight line to finish 8 miles due north of the same intersection. Let the intersection be represented by the point (0, 0). Suppose a cyclist rides the path from start to finish in 2 hours. Which parametric equations model the path of the rider?
The parametric equations that models the path of the rider are:
x(t) = -5/2t + 5 and y (t)= 4tx(t) = -5/2t + 5 and y(t) = 4t + 8What is a Parametric Equation?This refers to the type of equation that makes use of a parameter to define dependent variables.
Hence, we can see that to model the path of the rider, the parametric equation that can be best used is to model the direction of the bicycle which is moving 5 miles east and then continues 8 miles north, and the fact that they started at rest 0 and the equations to make the model are:
x(t) = -5/2t + 5 and y (t)= 4tx(t) = -5/2t + 5 and y(t) = 4t + 8
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How many times do parallel lines intersect?
A. 0
B. 1
C. 2
D. 3
Please help. Will make brainiest !!
Answer:
A) 0
Step-by-step explanation:
The actual definition of parallel lines are lines that never intersect, so the answer is 0
The number of times parallel lines intersect is (a) 0
How many times do parallel lines intersect?From the question, we have the following parameters that can be used in our computation:
The list of options in relation to parallel lines
By definition of parallel lines, we have
Parallel lines are lines that extend indefinitely on both sides without intersecting
Using the above as a guide, we have the following:
Point of intersection = 0
Hence, parallel lines intersect (a) 0 times
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How do you create and solve equations in one variable given a real–world situation?
Step-by-step explanation:
1) first eliminate constant(number without variable) you eliminate constant by doing the inverse operation(if constant is being added, then subtract)(if constant is being subtracted, then add it)
ex: if x+9=32
subtract 9 from both sides to get rid of it
x=23
2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it
you could multiply by 3 on both sides:
x+9=69
x=60
Answer:
1) first eliminate constant(number without variable) you eliminate constant by doing the inverse operation(if constant is being added, then subtract)(if constant is being subtracted, then add it)
ex: if x+9=32
subtract 9 from both sides to get rid of it
x=23
2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it
you could multiply by 3 on both sides:
x+9=69
x=60
Hope this helps!
Step-by-step explanation:
please help me asap!!!
Answer:
6
Step-by-step explanation:
40/5 has a whole numbe
Answer:
Yes 40/5 is 8
Step-by-step explanation:
40/5=8
In your backpack there are three math books, two science books, and five notebooks. If you reach into your backpack and select a math book, and then reach in and select a notebook, are these independent events? Explain.
Answer:
No, because grabbing the math book changed the odds of grabbing the notebook.
These are not independent events as you didn't replace the first book so that changed the probability that you would draw a notebook second , Option C is the answer.
What is Probability ?Probability is the likeliness of an event to happen.
It is given that there are three math books, two science books, and five notebooks.
Total number of books = 3 + 2 + 5 = 10
The probability of drawing a mathbook is 3 / 10 = 0.3
and then if the mathbook is not replaced then the total outcomes for drawing a notebook changes.
Therefore they are not independent events and Option C is the answer.
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