The number of chickens she had was 352
Applications of equationsFrom the question, we are to determine the number of chicken she has
Let c represent chicken
and d represent ducks
From the given information,
Mrs. Anderson had twice as many chickens as ducks
c = 2d ---------- (1)
She sold 272 chickens and 16 ducks and then had half as many chickens as ducks
(c-272) = 1/2(d -16) ---------- (2)
Put equation (1) into (2)
2d - 272 = 1/2(d - 16)
2(2d - 272) = d- 16
4d - 544 = d - 16
4d - d = 544 - 16
3d = 528
d = 528/3
d = 176
Substitute the value of d into equation (1)
c = 2d
c = 2(176)
c = 352
Hence, the number of chickens she had was 352
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The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:
The missing lengths are 8, 6, 9 and 16.
Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
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make x the subject. show work!
Answer:
[tex]x = \frac{b}{6a} - c[/tex]
Step-by-step explanation:
Steps are as below:
(I will refer A as 'a' and B as 'b')
[tex]a = \frac{b}{c + x} - 5a \\ a + 5a = \frac{b}{c + x} \\ 6a = \frac{b}{c + x} \\ 6a(c + x) = b \\ 6ac + 6ax = b \\ 6ac = b - 6ax \\ b - 6ax = 6ac \\ - 6ax = 6ac - b \\ 6ax = - (6ac - b) \\ 6ax = b - 6ac \\ x = \frac{b - 6ac}{6a} \\ x = \frac{b}{6a} - \frac{6ac}{6a} \\ x = \frac{b}{6a} - c[/tex]
I don’t get this either please save me from this ahhhhhh
Answer:
y=
[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]
Step-by-step explanation:
calculate the product, use (a+b)^2=a^2+2ab+b^2
WILL GIVE BRAINLEST!!!
I. The diagonals in a trapezoid are always equal in length.
II. The diagonals in a trapezoid always bisect each other.
III. The diagonals in a trapezoid always intersect at the median.
Which of the above statements are NOT true for all trapezoids?
I only
I, II, and III
I and III
I and II only
Answer:
I and II only
According to the weather report, there is a 25% chance of snow in the mountains tomorrow. how likely is it to snow tomorrow in the mountains?
It is likely is it to snow tomorrow in the mountains is 1/4
A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment
We need to find that what is the chance that it will snow tomorrow in the mountains
According to the weather report, there is a 25% chance of snow in the mountains tomorrow.
Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4
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You’ve gone to visit your friend in Germany. As you’re getting dressed for a day out, your friend tells you it’s 16 degrees (Celsius) outside. The formula for degrees Celsius in relation to degrees Fahrenheit is
C=(5f-160)/(9)
a. Invert this equation to solve for Fahrenheit.
b. Tell what the temperature is in degrees Fahrenheit.
c. What kind of clothing should you wear for the day to be comfortable at that temperature?
d. Is there a temperature at which Celsius and Fahrenheit are described by the same number? Explain how you would find that number.
Please help
The area of a circle is 354 cm². Find in degrees and minutes, the angle subtended at the centre of the circle by a 2.9cm arc.
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
What is the measure of the central angle of a circular section?
In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:
r = √ (A / π) (1)
r = √ (354 / π)
r ≈ 10.615 cm
Then, the measure of the central angle in radians is found by the equation of circular arc:
θ = s/r
θ = 2.9 cm / 10.615 cm
θ = 0.273 radians
Finally, we convert the angle into DMS system:
θ = 0.273 rad × 180°/π
θ = 15.641°
Degrees: 15°
Minutes and seconds: 0.641° (38.46')
Minutes: 38'
Seconds: (0.46' = 27.6'')
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
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The organizers of a community fair set up a small Ferris wheel for young children. The table shows the heights of one of the cars above the ground for different rotations of the wheel. The function below, where a
and b are constants, models the height of the Ferris wheel car at a rotation of x radians. What are the values of a and b?
The value of a is 6 and the value of b is 7
How to determine the values of a and b?The function is given as:
h(x) = a . sin(x - π/2) + b
From the table of values, we have:
x = π/2 when y = 7
So, we have:
a . sin(π/2 - π/2) + b = 7
Evaluate the difference
a . sin(0) + b = 7
Evaluate the value of sin(0)
a . 0 + b = 7
Evaluate the product of a and 0
b = 7
Substitute b = 7 in h(x) = a . sin(x - π/2) + b
h(x) = a . sin(x - π/2) + 7
From the table of values, we have:
x = π when y = 13
So, we have:
a . sin(π - π/2) + 7 = 13
Evaluate the difference
a . sin(π/2) + 7 = 13
Subtract 7 from both sides
a . sin(π/2) = 6
Evaluate sin(π/2)
a . 1 = 6
Divide both sides by 1
a = 6
Hence, the value of a is 6 and the value of b is 7
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A certificate of deposit offers a nominal interest rate of 5.5 percent annually.If inflation is 2.5 percent, what is the real rate of return?
The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The real rate of return exists at 2.926%.
How to estimate the real rate of return?The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The formula for the real rate of return:
R = (1+N)/(1+i) - 1
Where, N exists the nominal rate and i exists the inflation rate, as decimals.
A certificate of deposit offers a nominal interest rate of 5.5 percent annually.
This means that N = 0.055
Inflation exists 2.5 percent
i = 0.025
Substitute the values in the above equation, we get
[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]
= [1.055/1.025] - 1
= 1.02926 - 1
= 0.02926
0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%
The real rate of return exists at 2.926%.
Therefore, the correct answer is option D. 3%.
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A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
The number of degrees that the direction of the boat change when it made its first turn is 39°.
How to calculate the value?From the information given, we would use the cosine function to solve the information.
This will be:
18² = 28² + 25² - 2(28)(25)(cos x)
324 = 784 + 625 - 1400cosx
x = 39.19
Therefore, the value is 39°.
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Triangle M N O maps to triangle M prime N prime O prime.
In the diagram, triangle MNO maps to triangle M'N'O'.
Complete the statements.
Angle M corresponds to angle
Side
is the image of side NO.
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.
Here it is given that Triangle MNO maps to triangle M'N'O'
We need to find that Angle M corresponds to which angle and the image of side NO
By one to one correspondence we get that
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
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Ellen has a bag with 3 red marbles and 2 blue marbles in it. she is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw. how many times do you predict that the marble picked will be blue using the theoretical probability?
The blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.
The theoretical probability of any event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
If we have an event A, the number of favorable outcomes to event A as n, and the total number of possible outcomes in the experiment as S, then the theoretical probability of event A is given as:
P(A) = n/S.
In the question, we are given that Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw.
We are asked the predict the number of times that the marble picked will be blue using the theoretical probability.
Let the event of picking a blue marble be A.
The number of favorable outcomes to event A (n) = 2 {The total number of blue marbles in the bag}.
The total number of possible outcomes in the experiment of picking a ball (S) = 5 {The total number of marbles in the bag}.
Thus, the theoretical probability of event A is,
P(A) = n/S = 2/5 = 0.4.
To predict the number of times marble picked was blue, we multiply the time's the experiment was performed by the theoretical probability of picking a blue ball.
Thus, the predicted number of times = 300 * 0.4 = 120.
Thus, the blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.
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Which search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
The wide-area search method employs the use of markers such as knots at regular intervals along the search line.
Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.
In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.
Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
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An account pays 8% per year simple interest. in year 1, the amount in the account is $850. how much is in the account in year 6?
Answer:
Step-by-step explanation:
$1,248.92
4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(
What is the approximate number of minutes that avery spends in extra circular activities
The approximate number of minutes that Avery spends on the extra curricular activities are 122 minutes.
Given that Avery spent 10 minutes outside, 64 minutes in riding her bike, 48 minutes on the trampoline.
We have to calculate the approximate time that Avery spends on extra curricular activities.
Time spent by Avery outside=10 minutes
Time spent by Avery in riding her bike=64 minutes
Time spent by Avery on trampoline=48 minutes
Total time spent by Avery on extra curricular activities is equal to 10+64+48
=122 minutes
Hence the total time spent by Avery on extra curricular activities is 122 minutes.
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Question is incomplete as the question should include that Avery spent 10 minutes outside,64 minutes in riding her bike, 48 minutes on trampoline and rest of the time in swimming.
What is the perimeter of the contest area on the judo mat?
(please be quick)
The perimeter of the contest area on the judo mat will be 32 meters.
What is the perimeter of the square?For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The side length of square is 8 m.
Then the perimeter of the contest area on the judo mat will be
P = 4 x 8
P = 32 m
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Using the defects method, which of these relationships represents the law of cosines if the measure of the included angle between the sides a and b of ∆abc is more than 90°? a. area of square c2 = -area of square a2 − area of squareb2 area of defect1 area of defect2 b. area of square c2 = area of square a2 area of squareb2 area of defect1 − area of defect2 c. area of square c2 = area of square a2 area of squareb2 − area of defect1 − area of defect2 d. area of square c2 = area of square a2 area of squareb2 area of defect1 area of defect2 e. area of square c2 = area of square a2 − area of squareb2 area of defect1 − area of defect2
The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2
What is the law of cosine?It should be noted that the cosine law is simply used to solving triangles.
The law simply states that c² = a² + b² - 2abcosC.
The correct option that illustrates this is D.
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Answer:
c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2
Step-by-step explanation:
PLEASE HELP
If BC DA, then which segment is the shortest side?
The length of the shortest side is DC
How to determine the shortest side?As a general rule in triangle;
The smallest angle in a triangle is opposite the shortest side.
Similarly, the largest angle in a triangle is opposite the largest side.
From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.
The side opposite this angle is side length DC
Hence, the length of the shortest side is DC
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Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?
Answer:
Step-by-step explanation:
70 = x/4
x = 4 cos 70 = 1.37m
x = 4 cos 80 = 0.69m
The range is ( 0.69m, 1.37m)
The range of distances from the wall (x) that the foot of the ladder placed to fall within the safety guidelines is between 0.7052 meters and 1.456 meters.
To determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines, use trigonometry.
Let's assume the distance from the wall to the foot of the ladder is x meters the ladder is 4 meters long.
The angle between the ladder and the ground is given to be between 70° and 80°. Let's consider the extreme cases for each angle:
When the ladder makes an angle of 70° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 70° = 20°.
When the ladder makes an angle of 80° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 80° = 10°.
Now, use trigonometry to calculate the range of distances (x) from the wall:
For the first case (θ = 20°):
tan(20°) = Opposite / Adjacent
tan(20°) = x / 4
x = 4 × tan(20°)
For the second case (θ = 10°):
tan(10°) = Opposite / Adjacent
tan(10°) = x / 4
x = 4 × tan(10°)
Now, let's calculate the values:
x ≈ 4 × 0.3640 ≈ 1.456 meters (rounded to three decimal places) - for the first case.
x ≈ 4 × 0.1763 ≈ 0.7052 meters (rounded to four decimal places) - for the second case.
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2. Find the area of the circle. Round to the nearest tenth.
A.113.1
B.37.7
C.18.8
D.28.3
The answer is D.
The formula to find area of a circle is : πr²
Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.
Let's find the area.
A = π × r²A = 3.14 × (3)²A = 3.14 × 9A = 28.26A ≈ 28.3
Graph the rational function
by identifying its key features.
The graph of the rational function is shown below
Graph of rational functionsFrom the question, we are to graph the given rational function
To determine the graph that corresponds to the given rational function,
First, we will graph the given rational function.
The given rational function is
x²+3x-1/x+1
The graph of the rational function is shown below
Now, we will compare each of the rational graphs in the provided options with the attached graph
The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.
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A sample of workers exhibit the following production rates before and after a workshop. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 The point estimate for the difference between the means of the two populations is: Group of answer choices
The point estimate here is 0.
Calculating the Mean of Each Set
The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}
The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}
The mean of set S1 = (20+25+27+23+22+20+17)/7
= 154/7
= 22
The mean of set S2 = (22+23+37+20+25+19+18)/7
= 154/7
=22
Calculating the Point Estimate
The formula for point estimate is given as,
Point Estimate = The mean of set S1 - The mean of set S2
Point Estimate = 22-22
Point Estimate = 0
Therefore, the point estimate for the difference between the means of the two populations or sets is 0
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What is the rule of -3,18,-108,—,—,—
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The rule for this sequence is 'multiply by -6'.
Verification ↓
-3*(-6)[tex]\stackrel\checkmark{=}[/tex]18
18*(-6)[tex]\stackrel\checkmark{=}[/tex]-108
So the rule for the sequence is 'multiply by -6'
And the Common ratio is -6.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{calligraphy}\star[/tex]
[tex]\textbf{Heya !}[/tex]
✏✏[tex]\large\textsf{Given:-}[/tex]
The first 3 terms of a sequence :- [tex]\large\textsf{-3, 18, -108}[/tex]✏✏ [tex]\large\textsf{To Find:-}}[/tex]
The rule for the sequence = ?✏✏ [tex]\large\textsf{Solution Steps:-}[/tex]
What do we multiply each term of the sequence by to arrive at the next one ? we can find that by dividing the last term of the sequence, -108, by the middle term, 18:-
[tex]\large{\sf{\longmapsto{-108\div18=-6}[/tex]
Now divide 18 by the first term (-3) :-
[tex]\longmapsto\sf{18\div-3=-6}[/tex]
we arrived at -6 twice, So the rule for this sequence is:- "Multiply by -6, And you'll arrive at the next term"
`hope it helped ~ :D
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue
(C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.To find what fraction of the marbles now in the bag is blue:
Important information is that immediately before the last step blue marbles formed [tex]\frac{1}{5}[/tex] from the marble in the bag. That means that there were [tex]x[/tex] blue and [tex]4x[/tex] other marbles, for some [tex]x[/tex]. When we double the number of blue marbles, there will be [tex]2x[/tex] blue and [tex]4x[/tex] other marbles. Hence, blue marbles now form [tex]\frac{1}{3}[/tex] all marbles in the bag.Therefore, (C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.
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Complete question:
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 1/2
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
1.4 meters
2 meters
0.5 meters
1 meter
Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.
What is the seesaw's maximum length?This can be found as:
Sin 30° = 1 / Maximum length
Solving gives:
Sin 30° = 1 / Maximum length
Ml = 1 / Sin 30°
= 1 / 0.5
= 2 meters
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Enter the degree of the polynomial below.
5,5 + 8,2 + 2x - 319 - 8x1 -4,5
Based on the given polynomial, the degree of the polynomial can be calculated to be 1.
what is the degree of the polynomial?the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.
from the above, we see that the highest power is 1 from 8x¹.
the degree of the polynomial is therefore 1.
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Pls, I need help. Whoever gets it right gets the brainliest.
There can be 18, 12, 9, 6, 4 , 3 or 2 students on each team depending on the number of teams selected.
How to know the number of students on each team?Considering there are at least 2 teams but no more than 19 teams, let's calculate the number of students in each case:
2 teams: 18 students per team (36/2 = 18)3 teams: 12 students per team (36/3 =12)4 teams: 9 students per team (36/4 = 9)6 teams: 6 students per team (36/6 = 6)9 teams: 4 students per team (36/9 = 4)12 teams: 3 students per team (36/12= 3)18 teams: 2 students per team (36/18 = 2)Learn more about teams in: https://brainly.com/question/10750297
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The number of jobs for nurses is expected to increase by 711,900 between 2010 and 2020. during the same decade, the number of jobs for physicians is expected to increase by 168,300. find the ratio of the increase in jobs for physicians to the increase in jobs for nurses.
The Ratio would be 43:100.
Lets simplify the problem,
Expected increase of nurses = 711900
Expected increase of physicians = 168300
Ratio = Expected increase of nurses / Expected increase of physicians
Ratio = 711900 / 168300
= 43/100
Ratio = 43:100
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Help needed
65. Solve for in the logarithmic equation 3 log x = 2.
O * = 1,000,000
O * = 150
O * = 56.423
O * = 4.642