Number of chicken = 26
And, Number of dogs = 17
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has a collection of chickens and dogs.
And, all together there are 120 legs and 43 heads.
Hence, Number of chicken = x
And, Number of dogs = y
Thus, We get;
⇒ x + y = 43
⇒ x = 43 - y .. (i)
⇒ 2x + 4y = 120
⇒ x + 2y = 60 .. (ii)
Substitute value of x from (i) to (ii);
⇒ x + 2y = 60
⇒ 43 - y + 2y = 60
⇒ y = 60 - 43
⇒ y = 17
And, From (i);
⇒ x = 43 - y
⇒ x = 43 - 17
⇒ x = 26
Thus, Number of chicken = 26
And, Number of dogs = 17
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natalie guessed on the last four true or false questions on her math quiz. what is the probability that she got all four quiz questions correct?
The probability that Natalie got all four quiz questions correct after guessing would be 6. 25 %.
How to find the probability ?If Natalie guessed on the last four true or false questions, there are two possible outcomes for each question (correct or incorrect), and she has a 50% chance of guessing correctly for each question since there are only two options.
To find the probability that she got all four quiz questions correct, you can multiply the probabilities for each question:
Probability of guessing a question correctly = 0.5 (since there are 2 options, and she has a 50% chance of guessing correctly)
Probability of getting all four questions correct = (0.5) * (0.5) * (0.5) * (0.5)
= 0.0625
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y = x – 6
x = –4
What is the solution to the system of equations?
(–8, –4)
(–4, –8)
(–4, 4)
(4, –4)
the answer is (-4 -8)
Please find the domain and range of this equation: y=3 (x-2)^2+5
Two wheels rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel is 2r feet If both wheels did a total of 4 rotations, how much farther did the larger wheel travel?
The feel better spa has two specials for new members. They can receive 3 facials and 5 manicures for $114 or 3 facials and 2 manicures for $78
Choose the correct product of (6x − 2)(6x + 2). (1 point)
Choose the correct product of (6x − 2)(6x + 2). (1 point)
If you can't see the images here
36x2 − 4
The area of a square is greater than the area of the circle by 12 cm². find the length of the side of a square if the area of the circle is 36 cm².
Final answer:
To find the length of a side of the square, calculate the square root of the sum of the areas of the circle (36 cm²) and the additional 12 cm². This results in a square side length of approximately 6.93 cm.
Explanation:
We are given that the area of the circle is 36 cm², and we know that the area of a square is greater than the area of the circle by 12 cm², which means the area of the square is 36 cm² + 12 cm² = 48 cm².
The area of a square is given by A = a², where a is the length of the side of the square. So, we need to find the value of a that satisfies the equation a² = 48 cm².
By taking the square root of both sides of the equation, we get a = √(48 cm²). Simplifying the square root of 48 gives us a ≈ 6.93 cm. Therefore, the length of a side of the square is approximately 6.93 cm.
The average speed of a car is three times as fast as the average speed of a cyclist. to travel 225 km, the cyclist requires 5 h more than the car. determine the average speeds of the cyclist and the car.
To determine the speeds, we set up relative speed equations and solve for 'x'. The cyclist's average speed is 15 km/h and the car's average speed is 45 km/h.
Explanation:Let's denote the cyclist's speed as 'x' km/h and the car's speed as '3x' km/h (since it's three times the cyclist's speed).
Given that speed is distance over time, we can set up the following equations:
For the cyclist: 225km / x = time, and for the car: 225km / 3x = time - 5.
By equating these two expressions, we get: 225/x = 225/3x + 5.
Solving this equation for 'x', we get x = 15. Thus, the average speed of the cyclist is 15 km/h and the car (3x) is 45 km/h.
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WILL GIVE BRAINLIEST FOR CORRECT ANSWER!
How is energy transferred during the water cycle
A. water gains energy during evaporation and condensation
B. water gains energy in condensation and releases it in evaporation
C. water releases energy during evaporation and condensation
D. water gains energy during evaporation and releases it during condensation
A building that is 115 feet tall casts a shadow that is 190 feet long. determine the angle at which the rays of the sun hit the ground to the nearest degree.
The angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.
What is the meaning of the angle of depression?Its an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given is that a building that is 115 feet tall casts a shadow that is 190 feet long
Assume that the angle of elevation or the angle at which the rays of the sun hit the ground is equivalent to {β}. Then, with respect to the question, we can write -
tan{β} = (height of building)/(length of shadow)
tan{β} = (115/190)
tan{β} = 0.606
{β} = tan⁻¹(0.606)
{β} = 31.22°
Therefore, the angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A ?
Enter your answer in the box.
°
Answer:
The measure of the ∠A is 59°.
Step-by-step explanation:
It is given that a quadrilateral ABCD is inscribed in a circle, and from the properties of circle, we know that the sum of the opposite angles of the quadrilateral inscribed in the circle is equal to 180°.
Therefore, ∠A+∠C=180°
⇒[tex]A+121^{\circ}=180^{\circ}[/tex]
⇒[tex]A=180-121[/tex]
⇒[tex]A=59^{\circ}[/tex]
Therefore, the measure of the ∠A is 59°.
Apologies on this being 4 years late, but to anyone else who stumbles across this; answer is 59°
I had taken the test and got it correct
Good luck, and i hope this helps!! :]
What is the value of n? Enter your answer in the box.
Answer:
n=6
Step-by-step explanation:
Since, we know that when two chords intersect each other inside a circle, the products of their segments are equal. Thus, using this property, we have
[tex](n+8)5=(n+4)7[/tex]
⇒[tex]5n+40=7n+28[/tex]
⇒[tex]40-28=7n-5n[/tex]
⇒[tex]12=2n[/tex]
⇒[tex]n=6[/tex]
Thus, the value of n is 6.
Answer:
[tex]n=6[/tex]
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the value of n.
We can see that two chords of our given circle are intersecting inside it, so we will use intersecting chords theorem to solve for n.
Intersecting chords theorem states that when two chords of a circle intersect inside the circle, then product of the segments of both chords is equal.
Using intersecting chords theorem we can set an equation as:
[tex]5(n+8)=7(n+4)[/tex]
Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,
[tex]5*n+5*8=7*n+7*4[/tex]
[tex]5n+40=7n+28[/tex]
Subtracting 40 and 7n from both sides we will get,
[tex]5n-7n+40-40=7n-7n+28-40[/tex]
[tex]-2n=-12[/tex]
Dividing both sides by -2 we will get,
[tex]\frac{-2n}{-2}=\frac{-12}{-2}[/tex]
[tex]n=6[/tex]
Therefore, the value of n is 6.
PLEASE HELP!!!!!!
A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x =[tex] \frac{1}{12} [/tex] y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.
Final answer:
To find the height of the digital monitoring system, we rearrange the given parabolic equation to solve for y, substitute the known distance of 3 inches, and determine that the monitoring system is attached 6 inches above the focal point.
Explanation:
The equation given for the reflecting telescope by the library for their astronomy program is x = \frac{1}{12} y^2. To solve for the height of the digital monitoring system as a function of the distance x, we need to rewrite the equation in terms of y. First, we multiply both sides by 12 to get 12x = y^2. Then, take the square root of both sides to solve for y, which gives us y = \sqrt{12x}. Given that the distance between the base and the focal point is 3 inches, we substitute x with 3 to find the height of the monitoring system. Thus, we have y = \sqrt{12 \cdot 3} which simplifies to y = \sqrt{36} or y = 6 inches. This means the digital monitoring system is attached 6 inches above the focal point of the telescope.
Clark left for school at 7:43 am he git to school 36 minutes later.what time. Did clark get to school???
if x-15=7-5(x-4) then x=?
0
5
4
2
7
In a "torture test" a light switch is turned on and off until it fails. if the probability that the switch will fail any time it is turned on or off is 0.001, what is the probability that the switch will fail after it has been turned on or off 1,200 times?
Final answer:
The probability of a light switch failing after 1,200 operations can be calculated by first finding the likelihood of it not failing across those operations with the formula [tex]0.999^{1200}[/tex], and then subtracting that result from 1.
Explanation:
The question asks about the probability that a light switch will fail after being turned on or off 1,200 times, given that the probability it will fail on any given operation is 0.001. This can be approached by calculating the probability that the switch does not fail in all 1,200 operations and then subtracting that probability from 1.
To calculate the probability of the switch not failing in a single operation, we subtract the failure probability from 1: 1 - 0.001 = 0.999. The probability of the switch not failing in all 1,200 operations is [tex]0.999^{1200}[/tex].
Finally, the probability of the switch failing at least once in 1,200 operations is [tex]1 - 0.999^{1200}[/tex]. When you calculate this, it gives the probability of failure after 1,200 operations.
PLS PLS PLS HELP I rly need help in geometry
-22+0.3z=3-0.5z-0.8z
What are the estimated annual wages for a person who earns 10.25 an hour
Which of the following is true regarding the solution to the logarithmic equation below?
Answer:
Option C. is the correct option.
Step-by-step explanation:
The given expression is [tex]log_{2}(x+11)=4[/tex]
We further solve this
[tex](x+11)=2^{4}=16[/tex]
[tex]x = 16-11=5[/tex]
Now we evaluate the options
A). [tex]log_{5}16\neq 2[/tex]
But the expression is given as [tex]log_{2}(x+11)=4[/tex]
Wrong expression so not correct.
B). [tex]log_{5}16\neq 4[/tex]
Wrong expression again so not correct
C). By putting x = 5 in the expression
[tex]log_{2}(x+11)=4[/tex]
[tex]log_{2}(5+11)=log_{2}(16)=log_{2}(2^{4})=4[/tex]
Therefore this option is the correct option.
D). By putting x = 5 in the expression
[tex]log_{4}(5+11)=log_{4}(16)=log_{4}(4^{2})=2[/tex]
But the expression is [tex]log_{2}(x+11)=4[/tex]
So this option is also not correct.
Answer:
c
Step-by-step explanation:
Jason can paint a room in 6 hours. Lorissa can paint a room in only 3 hours. Which of the following can be used to determine the amount of time it would take for Jason and Lorissa to paint a room together?
a-1 over 6 plus 1 over 3 equals 1 over x
b-1 over x plus 1 over 3 equals 1 over 6
c-1 over 6 plus 1 over x equals 1 over 3
d-1 over 3 plus 1 over 6 equals x over 9
What is the common difference in the arithmetic sequence -4x,-x,2x,5x,8x,... ?
a school district requires all graduating seniors to take a mathematics test. This year, the rest scores were approximately normally distributed for the 1208 graduating seniors. This mean score on the test was a 74 and the standard deviation was 11. what percent of the graduating seniors had a test above 85? Express your answers to the nearest percent.
Based on the mean score of the test, the percentage of students who scored above 85% in the test was 16%.
Which students scored above 85 in the test?Based on the fact that this distribution is normally distributed, the percentage of students that scored higher or lower than 85% within 1 standard deviation is:
= 100% - 68%
= 32%
The number of students who scored above 85% would therefore be:
= 32% / 2
= 16%
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Heidi's hair was 2/3 of a meter long. her grandfather cut off 1/6 of a meter of her hair. how long is heidi's hair now?
Expand the logarithmic expression. I will award brainliest.
Natalie picked 135 berries in 15 minutes if she continues picking at that rate how long will it take her to pick 486 berries? @skullpatrol,
Math help!!!!!!!!!!!!!!
Answer:
The answer is E
Step-by-step explanation:
$1200.00 is deposited into an account that earns 6.5% interest, which is compounded four times per year. How much money will be in the account after 6 years?
Using the definition of even and odd functions explain why y= sin x+ 1 is neither even or odd ?
Can you show how you worked it out cause I'm not sure on how to plug it in exactly
what is the volume of a spear with the radius of 6in.