Area of a circle = PI x R^2
r = 1/2 diameter
r = 21.5/2
r = 10.75
Area of circle = 3.14 x 10.75^2 = 3.14 x 115.5625 = 362.86625 square units.
A semicircle is half a circle:
Area of semicircle = 362.86625 / 2 = 181.433125 square units (round the answer as needed).
If 4 more than two times a certain number is 3 less than the number, what is the number
Answer:
3
Step-by-step explanation:
If 4 less than 3 times a certain number is 2 more than the number
Let the number be x
First, three times of number is 3x
Then 4 less will be (3x - 4)
Two more than number is (x + 2)
Hence the algebraic equation will be
3x - 4 = x + 2
Now solving this equation
3x - 4 = x + 2
3x - x = 2 + 4
2x = 6
x = 6 / 2
x = 3
Thus the number is 3
Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), xxx seconds after Ming threw it, is modeled by:
h(x)=-5(x-1)^2+45h(x)=−5(x−1)
What is the maximum height that the stone will reach?
what is the meters
We have been given that Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), x seconds after Ming threw it, is modeled by [tex]h(x)=-5(x-1)^2+45[/tex].
We are asked to find the maximum that the stone will reach.
We can see that our given equation is in vertex form of parabola [tex]y=a(x-h)^2+k[/tex] with vertex at point (h,k).
We can also see that leading coefficient is negative, so our given parabola is a downward opening parabola and its maximum value be at vertex.
The maximum height will be equal to y-coordinate of vertex.
We can see that vertex of our given parabola is at point (1,45). Therefore, the maximum height will be 45 meters.
The stone that Ming throws off the bridge reaches a maximum height of 45 meters. This is determined by the model equation for the stone's height as a function of time, which is a quadratic or parabolic function, with 45 as the maximum value.
Explanation:The question specifically concerns a parabolic formula representing the height of the stone thrown off the bridge over time: h(x) = -5(x-1)^2 + 45. This is a standard form of a parabolic or quadratic function, which is used to model the trajectory of an object under the force of gravity. In this form, the 45 at the end of the equation represents the maximum height, in meters, that the stone will reach. Hence, the maximum height that the stone will reach is 45 meters.
The reason is that the graph of the equation is an upside-down parabola, which means it opens downward. Thus, its maximum point, or vertex, is the top point of the graph, which corresponds to the height of the stone when it is at its peak. The equation is shifted such that this maximum point is (x, h(x)) = (1, 45).
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Both circles have the same center. What is the area of the shaded region?
17.2 mm
r=12.6 mm
Answer:
2291.1
Step-by-step explanation:
Answer:
2290 mm² or 2289.94 mm²
Step-by-step explanation:
The radius of the outer circle is the sum of the inner radius and the width of the shaded area: 12.6 mm +17.2 mm = 29.8 mm.
The shaded area is the difference between the area of the outer circle and the area of the inner circle. The area of either circle is given by the formula ...
A = πr²
so, the area of the ring is ...
A = π(29.8 mm)² -π(12.6 mm)² = π(888.04 mm² -158.76 mm²)
A = 3.14(729.28 mm²) = 2289.9392 mm²
The area is about 2289.94 mm², which rounds to 2290 mm².
_____
Comment on pi
In the calculation here, we have used the required value of pi. If we use one that is more accurate, we find the area to be about 2291.10 mm².
Find the sum. Write your answer in standard form.
( 4x3 + 2x + 6) + (2x3 – x? + 2)
The sum is
Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Ivanna spins the spinner once. She wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. She loses $8 if the spinner stops on 5 or 6.
Answer:
The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.
I guess that we want to find the expected value in one spin:
number 1: wins $1
number 2: wins $3
number 3: wins $5
number 4: wins $7
number 5: losses $8
number 6: loses $8
The expected value can be calculated as:
Ev = ∑xₙpₙ
where xₙ is the event and pₙ is the probability.
We know that the probability for all the events is 1/6, so we have:
Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0
So the expected value of this game is $0, wich implies that is a fair game.
The question is a probability problem in Mathematics. It requires calculating the expected value of a game based on the potential winnings and losses and their respective probabilities. On average, Ivanna will lose a dollar each time she plays.
Explanation:The subject matter of this question is a probability problem within Mathematics. One way to approach the problem would be to calculate the expected value of Ivanna's winnings from a single spin of the spinner. Each outcome (1, 2, 3, 4, 5, 6) has an equal chance of being chosen, which is 1/6, because there are 6 equally likely outcomes.
The formula for the expected value is the sum of all potential outcomes multiplied by their respective probabilities. Numerically, this would be (1*$1 + 1*$3 + 1*$5 + 1*$7 - 2*$8) / 6, which equals -$1.
Therefore, on average, Ivanna will lose a dollar each time she plays this game.
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What two numbers does the square root of 2 lie between
Answer:
1 and 2
Step-by-step explanation:
Kay earns $78,400 per year. She takes a standard deduction of $5,700 and pays tax at a 21% rate. What is the amount of Kay's income tax? Hint: Income Tax = Taxable Income * Tax Rate
Answer:
$15,267
Step-by-step explanation:
Kay earns $78,400 per year and gets a standard deduction of $5,700.
Her taxable income is amount of money that she can pay tax on and that is:
Income - Standard Deduction
= $78,400 - $5,700 = $72,700
She pays tax at a 21% rate, hence, her income tax is:
[tex]\frac{21}{100} * 72,700[/tex]
= $15,267
Her income tax is $15,267.
part of the population of 4,500 elk at a wildlife preserve is infected with a parasite a random sample of 50 elk shows that 8 of them are infected how many elk are likely to be infected
Answer:
A total of 720 elk are likely to be infected
Step-by-step explanation:
we shall be using the proportion by survey to estimate the number of infections
From the survey 8 out of 50 are infected. Thus the likelihood of infection is 8/50
We have 4,500 elk to consider. The number of elk likely to be infected will be 8/50 * 4500 = 720
Based on the sample proportion, it is estimated that approximately 880 elk out of the 5,500 elk in the wildlife preserve are infected with the parasite.
Step 1
To estimate the number of elk likely to be infected with a parasite at a wildlife preserve, we use the sample proportion to project the infection rate to the entire population.
Given:
- Total population of elk [tex]\( N = 5500 \)[/tex]
- Sample size [tex]\( n = 50 \)[/tex]
- Number of infected elk in the sample [tex]\( x = 8 \)[/tex]
First, we calculate the sample proportion [tex]\( \hat{p} \)[/tex]:
[tex]\[ \hat{p} = \frac{x}{n} = \frac{8}{50} = 0.16 \][/tex]
This sample proportion represents the estimated infection rate. To estimate the number of infected elk in the entire population, we multiply this proportion by the total population:
[tex]\[ \text{Estimated number of infected elk} = \hat{p} \times N \][/tex]
Step 2
Substituting the values:
[tex]\[ \text{Estimated number of infected elk} = 0.16 \times 5500 \][/tex]
Performing the calculation:
[tex]\[ \text{Estimated number of infected elk} = 0.16 \times 5500 = 880 \][/tex]
So, approximately 880 elk in the wildlife preserve are likely to be infected with the parasite.
Complete question : Part of the population of 5,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected.
How many elk are likely to be infected?
A piggy bank containing nickels and
dimes contains 60 coins. The total value in
the piggy bank is $4.25. How many of each
coin is there in the piggy bank?
There are 35 nickels and 25 dimes in the piggy bank.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let N be the number of nickels in the piggy bank, and let D be the number of dimes. We can set up the following system of equations to represent the given information:
N + D = 60
0.05N + 0.1D = 4.25
The first equation represents the total number of coins in the piggy bank, and the second equation represents the total value of the coins.
To solve this system of equations, we can use the substitution method. First, we solve the first equation for N:
N = 35
Substituting this equation for N into the second equation, we get:
D = 25
Thus, 35 nickels and 25 dimes are in the piggy bank.
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7 to the second power + 24 to the second power
Answer:
625
Step-by-step explanation:
Simplify the following:
7^2 + 24^2
7^2 = 49:
49 + 24^2
| 2 | 4
× | 2 | 4
| 9 | 6
4 | 8 | 0
5 | 7 | 6:
49 + 576
| 1 | 1 |
| 5 | 7 | 6
+ | | 4 | 9
| 6 | 2 | 5:
Answer: 625
Answer:
it would be 625
Step-by-step explanation:
7 squared is 49 and 24 squared is 576. so if you do 49+576=625
what is 2042.8.8 rounded to the nearest tenth
Answer:
the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.
Step-by-step explanation:
Answer: 2042.9
Step-by-step explanation: Round to the nearest tenths place or the (1 decimal place)
If the number is higher than 5, 6, 7, 8, or 9, round the number up. If not, then do not round it up.
I hope this helps!
How much does it cost to buy 3 orange buttons if each orange button costs $0.09?
Answer:
$0.27
Step-by-step explanation:
Multiply the cost of one button times the number of button desired
3 * .09 = .27
Answer:
.27
Step-by-step explanation:
djjdndysjsbzkshsmszjddndbekbeskakqkshdnxkdfxnkduejehejekskshemeje
6.
Find the area of the figure.
9 in.
11 in.
11 in.
6 in.
9 in.
Answer:
58806
Step-by-step explanation:
multiply them together
75 POINTS!!! WILL MARK BRAINLIEST!!!
Find the measure of angle LNM
m∠LNM = 54°
Here is why:
In this photo there are two important angles with very important features, a central angle and an inscribed angle.
A central angle is an angle that is in the center of the circle, so angle P is a central angle. The arc that is associated with this angle is going to be the same measure as the central angle. I have labeled this in the photo below as blue.
An inscribed angle is an angle that lies on the circle, so angle N is an inscribed angle. The arc that is associated with this angle will be double the amount of the inscribed angle, or the angle is half of the measure of the arc. I have labeled this in the photo below as red.
Since we know that the central angle is 108°, with what we know about central angles we know that arc LM is going to be 108° as well.
We also know that an inscribed angle is half the amount of the arc so...
108 ÷ 2 = 54
m∠LNM = 54°
The measure of the angle ∠LNM will be 54°.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The central angle is double the angle at the periphery that was subtended by the same chords. Then the equation is given as,
∠LNM = 1/2 ∠LPM
∠LNM = 1/2 x 108°
∠LNM = 54°
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A rule of thumb refers to _____
(A) a set process people follow
(B) rules everyone follows
(C) a general rule most people follow
(D) a way to measure growth
#pickle rick yu ight
Answer:
q= 6
Step-by-step explanation
Answer:
6
Step-by-step explanation:
6+7q =48
7q= 48-6
7q= 42
q=42/7
q= 6
If an English teacher marks 220 essays in 28 hours 36 minutes, how long on average does it take to mark one essay?
First, let us break down 28 hours 36 minutes into minutes.
Number of minutes taken to grade 220 essays = (28 x 60) + 36 = 1680 + 36 = 1716 minutes
Now, we can find the average time taken to grade an essay by dividing the time taken to grade 220 essays by 220.
Average amount of time taken to grade an essay = [tex]\frac{1716}{220}[/tex] = 7.8 minutes, or 7 minutes and 48 seconds
Suppose $1750 is put into an account that pays an annual rate of 4.5%
compounded quarterly. How much will be in the account after 6 years?(round to the
hundredth place)
Answer:
There will be $2288.98 in the account after 6 years
Step-by-step explanation:
We are given that $1750 is put into an account that pays an annual rate of 4.5% compounded quarterly.
So, Principal = $1750
Rate of interest = 4.5%
No. of compounds per year = 4
Time = 6 years
Formula :[tex]A =P(1+\frac{r}{n})^{nt}[/tex]
Where A = Amount
P = Principal
r = rate of interest
n = no. of compounds per year
t = time
Substitute the values in the formula :
[tex]A =1750(1+\frac{4.5}{400})^{4 \times 6}[/tex]
A=2288.98
Hence There will be $2288.98 in the account after 6 years
Is the following function exponential?
Answer:
Yes
Step-by-step explanation:
the given function is exponential, because x is the exponent of 3
Will give brainliest! please answer correctly!
Answer:
A and C
Step-by-step explanation:
w+c must be up to (<=) 41. corn must be less than (<) 28.
The base of a cylinder has a radius of 9 cm. The cylinder is 12 cm tall. What is the approximate LATERAL area of the cylinder? Use 3.14 and round your answer to the nearest whole number.
Answer:
The lateral area of the cylinder is 678 cm^2 to the nearest whole number
Step-by-step explanation:
Mathematically , the lateral area of a cylinder can be calculated using the formula
A = 2 π r h
where r is the radius = 9cm and h is the height = 12 cm
we are told to use a value of 3.14 for π
Thus the lateral area A is thus = 2 * 3.14 * 9 * 12 = 678.24 which is 678 cm^2 to the nearest whole number
100 pts
Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error? 4 (x minus one-fifth) = 2 and two-thirds. Step 1, 4 x minus four-fifths = 2 and two-thirds. Step 2, 4 x = StartFraction 8 over 3 EndFraction + four-fifths. Step 3, 4 x StartFraction 40 over 15 EndFraction + StartFraction 16 over 15 EndFraction. Step 4, 4 x = StartFraction 56 over 15 EndFraction times one-fourth. X = StartFraction 14 over 15 EndFraction. step 1 step 2 step 3 step 4
Answer:
Step 3
Reason:
I toke the test/review.
Answer:
the and should be step 3
Step-by-step explanation:
ANSWER ALL FIRST CORRECT ANSWER GETS BRAINLIEST, THANKS AND FIVE STAR!!
Answer:
1. A TUNNEL WITH LEAKS
2. A BIG ELECTRIC BILL
Step-by-step explanation:
H = 60
A = 20
W = 7
S = 26
E = 62
U = 22
B = 100
G = 8
R = 5
T = 0
K = 24
N = 81
C = 90
I = 32
L = 1
There you have it.....
The initial question lacks the specificity needed for a detailed and accurate response. More information on the subject and grade level is required to provide relevant help.
Explanation:Unfortunately, your question isn't clear enough for me to provide a concise and accurate answer. To ensure you get the help you need, please restate your question with more details, specifying the subject and grade level you're referring to. Once I have this information, I can offer you a more structured and detailed response that caters to your academic needs. Also remember, it's vital to review your questions for grammatical errors and make sure they're clear before posting, to ensure you receive the best possible responses.
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Do y’all like Tyler the created
Answer:
nah bro thats demarcus
Step-by-step explanation:
Which expression is equivalent to 6(a—3)
Answer:
6a - 18
Step-by-step explanation:
[tex]6(a - 3) \\ = 6 \times a - 6 \times 3 \\ = 6a - 18[/tex]
Answer:
The answer is B. 6(a)-6(3)
Step-by-step explanation:
I took quiz and got 100%
Mary needs a 90% on her final exam to get an a for the quarter.The exam has 75 questions how many questions does Mary need to answer correctly in order for her to get an A
Answer: 68 questions
Step-by-step explanation:
Given Data:
Exam questions = 75
Percentage needed by Mary for the quarter = 90%
therefore:
Total number of questions she needs to answer to get an A
= exam questions x percentage needed /100
= 75 * 90 / 100
= 6570 / 100
= 67.5
Approximately Mary needs to answer 68 questions correctly to score an A for the quarter
Find the volume of the cone
Answer:
Step-by-step explanation:
slant height l = 14cm
r = 6 cm
Use Pythagorean theorem.
h² + 6² = 14²
h² + 36 = 196
h² = 196 - 36
h² = 160
h = √160
h = 12.65 cm
[tex]Volume=\frac{1}{3}\pi r^{2}h\\\\=\frac{1}{3}*3.14*6*6*12.64\\\\[/tex]
= 476.61 cubic cm
Answer:
The volume of cone is 476.61 cm³.
Step-by-step explanation:
Solution :
As per given question we have provided :
[tex]\green\star[/tex] Slant height = 14 cm[tex]\green\star[/tex] Radius = 6 cm[tex]\begin{gathered}\end{gathered}[/tex]
Firstly, finding the height of cone by substituting the values in the formula :
[tex]{\longrightarrow{\pmb{\sf{l = \sqrt{(r)^{2} + {(h)}^{2} }}}}}[/tex]
[tex]\orange\star[/tex] Slant height (l) = 14 cm[tex]\orange\star[/tex] Radius (r) = 6 cm[tex]\orange\star[/tex] Height (h) = ?Substituting all the given values in the formula to find the height of cone :
[tex]\begin{gathered}\begin{array}{l}\quad{\longrightarrow{\sf{l = \sqrt{(r)^{2} + {(h)}^{2}}}}}\\\\\quad{\longrightarrow{\sf{{(l)}^{2} =(r)^{2} + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(14)}^{2} =(6)^{2} + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(14 \times 14)} =(6 \times 6) + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(196)} =(36) + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^{2} = 196 - 36}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^{2} = 160}}}\\\\\quad{\longrightarrow{\sf{h = \sqrt{160}}}}\\\\\quad{\longrightarrow{\sf{h = 12.65}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{h = 12.65}}}}}} \end{array}\end{gathered}[/tex]
Hence, the height of cone is 12.65 cm.
[tex]\begin{gathered}\end{gathered}[/tex]
Now, finding the volume of cone by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}[/tex]
[tex]\orange\star[/tex] V = Volume [tex]\orange\star[/tex] π = 3.14 [tex]\orange\star[/tex] r = radius [tex]\orange\star[/tex] h = heightSubstituting all the given values in the formula to find the volume of cone :
[tex]\begin{gathered}\begin{array}{l}\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(6)}^{2} 12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(6 \times 6)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(36)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{\cancel{3}}\times 3.14 \times \cancel{36}\times 12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = 3.14 \times 12 \times 12.65}}\\ \\\quad\longrightarrow{\sf{Volume_{(Cone)} = 476.61 \: {cm}^{3}}}\\\\\quad\star{\underline{\boxed{\sf{\pink{Volume_{(Cone)} = 476.61 \: {cm}^{3}}}}}}\end{array}\end{gathered}[/tex]
Hence, the volume of cone is 476.61 cm³.
[tex]\rule{300}{2.5}[/tex]
The weight of oranges growing in an orchard is normally distributed with a mean
weight of 5 oz. and a standard deviation of 1 oz. Using the empirical rule, what
percentage of the oranges from the orchard weigh between 3 oz. and 7 oz.?
Given that the weight of oranges falls in a normal distribution, the empirical rule states that about 68% of oranges should weigh between 3 oz. and 7 oz., which are one standard deviation away from the mean of 5 oz.
Explanation:The question involves the concept of the empirical rule in statistics. The empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this scenario, the mean weight of the oranges is 5 oz. and the standard deviation is 1 oz. So, oranges that weigh between 3 oz. and 7 oz. fall within 1 standard deviation on either side of the mean. According to the empirical rule, this represents approximately 68% of the data. So, we can conclude that about 68% of the oranges in the orchard weigh between 3 oz. and 7 oz.
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Which situation can be modeled by a linear function?
(1) The population of bacteria triples every day.
(2) The value of a cell phone depreciates at a rate of 3.5% each year.
(3) An amusement park allows 50 people to enter every 30 minutes.
(4) A baseball tournament eliminates half of the teams after each
round.
The population of bacteria triples every day is the situation can be modeled by a linear function. Option 1 is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
A linear function may be used to describe the circumstance in which the number of bacteria triples every day.
Hence,option 1 is correct.
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Final answer:
The situation that can be modeled by a linear function is (3) An amusement park allowing 50 people to enter every 30 minutes.
It represents a scenario with a constant rate of change, suitable for a linear model such as y = 50x.
Explanation:
The situation that can be modeled by a linear function is (3) An amusement park allows 50 people to enter every 30 minutes. This scenario represents a situation where there is a constant rate of change, which aligns with the characteristic of a linear function. In this context, the independent variable represents the time in 30-minute intervals, and the dependent variable represents the number of people allowed to enter. The equation to model this situation could be y = 50x, where y is the total number of people and x is the number of 30-minute intervals that have passed.
Scenarios (1), (2), and (4) represent non-linear relationships. Specifically, (1) involves exponential growth as the bacteria population triples each day, which is a multiplicative rate of change rather than a constant additive rate. (2) Involves exponential decay as the value of a cell phone decreases at a percentage rate annually, and (4) involves exponential decay in the number of teams as the number is halved after each round.
Please help me solve this
The answer would be that by excluding the outlier, a better description can be given for the data set. This would be because that the plant might grow very very slowly since it depends on the type of plant it is or other factors that might attribute to it.