Answer:
We can use the formula distance = speed x time to find the distance traveled by the bullet.
distance = speed x time
distance = 3 mi/s x 3290 s
distance = 9870 miles
Therefore, the target is 9870 miles away.
Step-by-step explanation:
What is the area of the polygon in square units?
Ay
6
T
68 square units
4
4-20 2
70 square units
72 square units
O80 square units
2
2
4
6
8
X
4
80 unit² is the area of the polygon in square units .
What do you mean by polygon?
A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves. The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). In order to create a closed figure, at least three line segments must be connected end to end.
The area of the polygon is required.
The area of the polygon is D. 80 square units
For triangle BCD
b = Base = 4-2 = 2 units
h = Height = 4 units
Area
1/2bh
= 1/2 * 2 * 4
= 4 unit²
For triangle DEF
b = Base = 2-(-1) = 3 units
h = Height = 4 units
Area
1/2bh
= 1/2 * 3 * 4
= 6 unit²
For trapezoid ABFG
a = 4-(-1) = 5.5 units
b = 4-(-8) = 12 units
h = 8 units
Area
1/2(a + b)h
= 1/2(5.5 + 12) * 8
= 70 unit²
Total area is
4 + 6 + 70 = 80 unit²
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PLEASE HELP ME OUT for both questions AND SHOW WORK PLEASEEE
Answer:
8) x = 5, y = -5
10) x = -2.8, y = 3.4
Step-by-step explanation:
To solve a system of linear equations we can use either the substitution method or the elimination method.
Question 8Given system of linear equations:
[tex]\begin{cases}-6x-3y=-15\\6y+6x=0\end{cases}[/tex]
Solve the given system of linear equations using the elimination method.
Add the two equations to eliminate the term in x:
[tex]\begin{array}{crcccl}&-6x & - & 3y & = & -15\\+&(6x & + &6y & = & \;\;\;\;0)\\\cline{2-6}&0&+&3y&=&-15\end{array}[/tex]
Solve the resulting equation for y by dividing both sides by 3:
[tex]\implies 3y \div 3 &=-15 \div 3[/tex]
[tex]\implies y=-5[/tex]
Substitute the found value of y into the second equation and solve for x:
[tex]\implies 6(-5)+6x=0[/tex]
[tex]\implies -30+6x=0[/tex]
[tex]\implies 6x=30[/tex]
[tex]\implies 6x \div 6=30 \div 6[/tex]
[tex]\implies x=5[/tex]
Therefore, the solution to the given system of equations is:
x = 5y = -5Question 10[tex]\begin{cases}-x+3y=13\\-3x-y=5\end{cases}[/tex]
Solve the given system of linear equations using the substitution method.
Rearrange the first equation to isolate x:
[tex]\implies -x+3y=13[/tex]
[tex]\implies 3y=x+13[/tex]
[tex]\implies x=3y-13[/tex]
Substitute the expression for x into the second equation and solve for y:
[tex]\implies -3(3y-13)-y=5[/tex]
[tex]\implies -9y+39-y=5[/tex]
[tex]\implies -10y+39=5[/tex]
[tex]\implies -10y=-34[/tex]
[tex]\implies -10y\div -10=-34 \div -10[/tex]
[tex]\implies y=3.4[/tex]
Substitute the found value of y into the expression for x and solve for x:
[tex]\implies x=3(3.4)-13[/tex]
[tex]\implies x=10.2-13[/tex]
[tex]\implies x=-2.8[/tex]
Therefore, the solution to the given system of equations is:
x = -2.8y = 3.4Gemme makes a conjecture that the sum of an odd integer and itself is always an even interger
Answer:
It's true - all whole numbers that are odd are going to add up to an even integer. An odd integer can be looked at as an even number plus one. For example, 21 would be 20 (the even number) plus one. So the addition of two odd integers is like saying two even numbers were added to each other (in that example, 20 + 20), and then adding the 1+1 that made them odd (which adds up to 2, an even number). So it would be [20 + 20 + (1 + 1)]
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(2,1)
Step-by-step explanation:
I need some help on both of the questions!
From the diagram, the value of x to the nearest tenth is given as 8cm
What is trigonometry ratio?We should be aware that Trigonometry ratio is the relationship between the measurement of lengths and angles of a right triangle
The given triangle is a right angle triangle having the following:
Opposite = x
Adjacent = 12 cm and
Angle proportional to x = 35⁰
Using the trigonometrical ratio of Tangent
Tan∅ = opposite/adjacent
Tan35⁰ = x/12
Cross and multiply to have
x= 12*tan35⁰
x= 12*0.7002
The value of x is given by 8.402490459
Therefore the value to the nearest tenth is 8 cm
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major axis 12 units long and parallel to the y-axis, minor axis 8 units long, center at (-2,5)
center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1
The dimensions of the given ellipse are major axis 12 units long and parallel to the y-axis, minor axis 8 units long, and the center is located at (-2,5).Let us find the standard form equation of the ellipse. The standard form equation of an ellipse is given by:(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1Where (h, k) is the center of the ellipse, a is the distance from the center to either the x-axis or the y-axis, and b is the distance from the center to the other axis. Therefore, for the given ellipse, the equation of the ellipse in standard form is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1Thus, the standard form equation of the ellipse whose major axis is 12 units long and parallel to the y-axis, minor axis 8 units long, and center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1.
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Find the arc length of the shape
Answer:
The arc length of this quarter-circle is 7π/4.
the system2x-5y=1 -3x+7y=-3 is to be solved by elimination of x
the first equation is multiplied by 3
by which number should the second equation be multiplied
9 Is the value of x in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.
2x-5y=1 ..............1
-3x+7y=-3 ..................2
Multiply by 3 in (1) and by 2 in (2)
6x - 15y = 3
-6x + 14y = -6
after substtuting
y = 3
put value of y in 1
2*x - 5*3 = 1
2x = 1 + 15
2x = 16
x = 8
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Which of the following is an irrational number?
Answer:
52/68
Step-by-step explanation:
idr why
Answer: π
Step-by-step explanation:
An irrational number is a number that cannot be shown as a fraction. Based on this, π is an irrational number, since it goes on forever, and can never be written as a perfect fraction.
Suppose that you deposit $19,000 in an investment account that averages 4.1% growth annually. If the account managers charge a fee of 1% annually, how much money will you have at the end of 5 years? Round your answer to the nearest dollar.
The final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.
We need to find the amount of money you will have in the investment account at the end of 5 years if you deposit $19,000 in an investment account that averages 4.1% growth annually and if the account managers charge a fee of 1% annually.The formula to find the final amount of investment with annual compounding is given by:P (1 + r/n)^(n*t)P = $19,000r = 4.1% - 1% = 3.1% (as the account managers charge a fee of 1% annually)r = 0.031n = 1t = 5 Therefore, the final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.
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63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}]
PLS answer with proper explanation
BODMAS rule, helps us to determine the value of expression. The expanded value of expression,
63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}], is equals to the 61.14.
Mathematical operations such as addition, subtraction, multiplication, and division are included in arithmetic operations. For solving expression according to specific priority, we use the BODMAS rule, which follows as
First, the expressions within the brackets (), {}, are to be solved irrespective of the operators inside the brackets.Next, the square roots and numbers with powers are to be solved. The O in BODMAS stands for Of or Order.Then, we must solve the division operation, followed by multiplication, addition, and lastly, subtraction.Now, we have an expression, 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}] say x
=> x = 63 - [(- 3){- 2 - 8 - 3}] ÷ [3{5 + (- 2)(- 1)}]
we have to calculate value of x,
Using BODMAS rule,
=> x = 63 - [(- 3){- 13 }] ÷ [3{5 + 2}] (expands inner bracket)
=> x = 63 - [ 39 ] ÷ [3×7]
=> x = 63 - [ 39 ÷ 21]
=> x = 63/1 - 13/7
Taking least common multiple, (1,7) = 7
=> x = ( 63×7 - 13)/7
=> x = (441 - 13)/7 = 428/7
=> x = 61.14
Hence, value of expression is 61.14.
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1. A bucket is filled from a hose that has a constant flow rate. Is the amount of water in the bucket best described by a linear or exponential function of time during the filling process? Explain.
A. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is an exponential function.
B. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an linear function.
C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.
D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function.
2. A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount earned described by a linear or exponential function?
A. A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount earned described by a linear or exponential function?
B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.
C. The interest paid each year is constant, so the amount earned is multiplied by a constant factor for equal time intervals. This is an exponential function.
D. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is an exponential function.
3. A savings account has an initial balance of $1,000 and earns 3 percent interest compounded monthly. Is the balance of the account described by a linear or exponential function?
A. The interest paid each month is a factor of the current balance, so the balance increases by a constant value for equal time intervals. This is an exponential function.
B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.
C. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is a linear function.
D. The interest paid each month is a factor of the current balance, so the balance increases by a constant value for equal time intervals. This is a linear function.
Answer:
C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.
B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.
B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.
Step-by-step explanation:
Answer: Your welcome!
Step-by-step explanation:
1. Answer: D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function. As time increases, the amount of water in the bucket will increase exponentially (each successive unit of time will add a multiple of the original amount).
2. A. The amount earned is described by a linear function. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.
3. Answer: B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.
An exponential function is one in which the value of a variable increases or decreases by a constant factor for each equal time interval. In this case, the balance of the savings account increases by a fixed amount of interest each month, which is calculated from the current balance. This amount is multiplied by the current balance, resulting in an exponential function.
Offering brainliest to whoever gives explanation
Answer:
To find the volume of a rectangular prism, we need to know the length, width, and height of the prism. However, the height is not given in the problem, so we cannot calculate the volume.
We can use the surface area and given dimensions to set up an equation to solve for the height. The surface area of a rectangular prism is given by:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area is 62 square feet, and the width and length are 2 and 5 feet, respectively. Substituting these values into the surface area equation, we get:
62 = 2(2)(5) + 2(5)h + 2(2)h
62 = 20 + 14h
42 = 14h
h = 3
Now that we have found the height of the rectangular prism, we can calculate its volume. The volume of a rectangular prism is given by:
V = lwh
Substituting the given dimensions and calculated height, we get:
V = (5)(2)(3)
V = 30
Therefore, the volume of the rectangular prism is 30 cubic feet.
Step-by-step explanation:
Answer:
[tex]30ft^3[/tex]
Step-by-step explanation:
Surface area of a rectangular prism is A = 2(wl +hl +hw)
Volume, height, and Width is given now we can solve for l, v
[tex]A = 2(wl + hl + hw)\\62ft^2 = 2(2ft * l + 5ft * l + 5ft * 2ft)\\62ft^2 = 2(2lft + 5lft + 10ft^2)\\62ft^2 = 2(7lft + 10ft^2)\\62ft^2 = 14lft + 20ft^2\\14lft = 42ft^2\\l = 3ft[/tex]
Now that we have the length, we can solve for the volume
Volume of a rectangular prism = Length x Width x Height
[tex]V = 3ft * 2ft * 5ft\\ = 30ft^3[/tex]
Hope this helps!
Brainliest is much appreciated!
Write your answer in simplest form. 4-:(5)/(6)
Answer:
[tex]\frac{24}{5}[/tex]
A scientist is studying the drinking habits of rabbits. She collected the daily volumes of water consumed by the rabbits in the sample. The data had a mode of 19, a median of 17, and u = 14. Which of the following is likely true? a. The data are negatively skewed. b. The data are positively skewed. c. The data are symmetrical d. The data are bimodal
The data collected on the daily volumes of water consumed by rabbits in the sample is most likely positively skewed, given the mode of 19, the median of 17, and u = 14.
Positive skewness occurs when there are more data points on the right side of the mean than on the left side, resulting in a “tail” that is skewed to the right side.
In this case, the mode of 19 is greater than the median of 17, which is greater than u of 14, indicating that there are more data points on the right side of the mean than on the left side. This means that the data is likely positively skewed.
It is important to note that the data cannot be negatively skewed, symmetrical, or bimodal based on the information given. Negative skewness occurs when there are more data points on the left side of the mean than on the right side, which is not the case here.
Symmetrical data is when the mean, median, and mode are all the same, which is not the case here.
Bimodal data is when there are two distinct modes, which is not the case here either.
Given the information, the data collected of the daily volumes of water consumed by the rabbits in the sample is most likely positively skewed.
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someone please help me thank u
Answer:
C, E
Step-by-step explanation:
You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.
End behaviorThe function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.
RangeThe range of any odd-degree polynomial function is (-∞, +∞).
Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].
DomainThe domain of any polynomial function is "all real numbers." Both f and g have the same domain.
SymmetryAn even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.
Points of intersectionTwo polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.
Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet Service. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.
A) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they would be interested.
B) Hold a meeting in each of the fifteen towns, and tally the opinions expressed by those who attend the meetings
C) Randomly select one street in each town and contact each of the households on that street.
D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.
The least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.
Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet Service. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.A) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they would be interested. This type of sampling strategy is known as convenience sampling.
This technique is biased since only those who watch the local TV news and are interested in high-speed internet services can participate in the survey. The majority of the consumers who are in need of high-speed internet may not watch the local TV news. Hence the survey is biased and does not represent the entire population.B) Hold a meeting in each of the fifteen towns and tally the opinions expressed by those who attend the meetings. This type of sampling strategy is called a Quota sampling. It is biased since there is no guarantee that everyone will attend the meeting or that they will represent the opinions of the entire population.
This sampling strategy also has a higher risk of selection bias since the people who are likely to attend the meeting are the ones who are interested in the product.C) Randomly select one street in each town and contact each of the households on that street. This type of sampling strategy is called Cluster Sampling. This method is less biased compared to the other two strategies mentioned earlier. Since each street is chosen at random, there is a higher chance of getting opinions from a wider range of customers. However, this strategy can still be biased as the opinions may differ from one street to another.D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen. This type of sampling strategy is called Systematic Sampling.
This strategy is the least biased among the four strategies. Since customers are selected randomly, there is a higher chance of obtaining a representative sample. The opinions of customers who have discontinued the services are not included, and the survey can only be conducted with current customers.
Hence, the least biased sampling strategy is D) Go through the company’s customer records, selecting every 40th subscriber. Send employees to those homes to interview the people chosen.
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Part a) (6 marks) Calculate the value of the test statistic, set up the rejection region, undertaking hypothesis test and interpret the result. H0: μ=20 H1: μ≠20 Given that σ=5, n=25, =21, α=0.05. X Part b) (8 marks) A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X=175 and s=22. i) Calculate the value of the test statistic of the test required to determine whether. ii) there is enough evidence to infer at the 5% significance level that the population means is different from 180. ii) Repeat the part i) with the population standard deviation to be 22.
When answering questions on Brainly, you should always be factually accurate, professional, and friendly, be concise and do not provide extraneous amounts of detail, provide a step-by-step explanation in your answer, and use the following terms in your answer, "statistic", "X=175 and s=22", "standard deviation".Part a)Hypothesis: H0: μ=20, H1: μ≠20The sample size n=25Given that α=0.05σ=5The X (sample mean) is 21.The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{21 - 20}}{{\frac{5}{{\sqrt {25} }}}} = 2\]The rejection region is obtained by finding the Z value that will cut off 2.5% of the area in each tail of the standard normal distribution curve at 0.025.The rejection region is Z< -1.96 and Z > +1.96.Interpretation: Since the calculated Z value 2 lies outside the rejection region, reject the null hypothesis H0 and conclude that there is sufficient evidence to support the alternative hypothesis H1.Part b)Given,Sample size n=200, X=175 and s=22Null hypothesis H0: µ=180Alternative hypothesis H1: µ ≠ 180.Level of significance α=0.05i) The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 5.68\]ii) Since the calculated Z value (-5.68) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.When the population standard deviation is 22, the test statistic is,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 3.37\]Since the calculated Z value (-3.37) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.
The late fee at the library is based on the number of days a book is late. Carter paid $1.08 for a book that was 9 days late. If his sister Sydney had a fee of $1.92 for a late book, how many days late was the book?
Answer:
16 days late
Step-by-step explanation:
[tex]1.08 \div 9 = .12[/tex]
So the overdue book charge is 12¢ per day. Letting d be the number of days, we have:
.12d = 1.92
d = 16
Make a the subject of relation in a(n-m)=t.
Answer:
the answer is t/(n-m)
Step-by-step explanation:
a(n-m)=t
divide both sides by (n-m) to make a the subject of formula
a(n-m)/(n-m)=t/n-m)
a=t/(n-m)
How do I evaluate these?
Solution is in da attachment!! :D
Which set of measurements would prove that Δ
ABC and Δ
DEF are similar?
Triangle A B C has side A B of length 9, side A C of length 12, and the angle between them 35 degrees. Triangle D E F has no measures given.
A. DE = 15, EF = 20 and m∠D = 35
B. DE = 16, DF = 21 and m∠D = 35
C. DE = 12, DF = 16 and m∠D = 35
D. DE = 18, EF = 24 and m∠D = 70
Therefore , the solution of the given problem of triangle comes out to be DE = 15, EF = 20, and m∠D = 35, so the solution is A.
What exactly is a triangle?A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.
Here,
We must demonstrate that the respective sides and angles of two triangles are proportional in order to establish their similarity.
We are aware of the lengths of two of the sides and one of the angles in the triangular ABC. The third side's length can be determined using the Law of Cosines:
=> BC² = AB² + AC² - 2ABACcos(35°)
=> 9² + 12² - 2912*cos(35°) = BC²
=> BC ≈ 8.455
The edges of triangle ABC are therefore AB = 9, AC = 12, and BC 8.455.
=> A. DE=15, EF=20, and m=35
The angle measurement is 35 degrees, which corresponds to the angle in the triangular ABC. If the ends are proportionate, we can verify this:
=> DE/AB = 15/9 = 1.67
=> EF/AC = 20/12 ≈ 1.67
This collection of measurements meets the requirements for the triangles to be similar because the ratios are equal.
=> DE = 15, EF = 20, and m∠D = 35, so the solution is A.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
The true statements are:
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Step-by-step explanation:
The general equation of a circle is:
[tex]\boxed{(x - h)^2 + (y - k)^2 = r^2}[/tex]
where:
(h, k) is the center of the circle.r is the radius of the circle.To rewrite the given equation x² + y² - 2x - 8 = 0 in standard form, begin by moving the constant to the right side of the equation and collect like terms on the left side of the equation:
[tex]\implies x^2-2x+y^2=8[/tex]
Add the square of half the coefficient of the term in x to both sides of the equation. (As there is no term in y, we do not need to add the square of half the coefficient of the term in y):
[tex]\implies x^2-2x+\left(\dfrac{-2}{2}\right)^2+y^2=8+\left(\dfrac{-2}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2-2x+1+y^2=9[/tex]
Factor the perfect square trinomial in x:
[tex]\implies (x-1)^2+y^2=9[/tex]
We have now written the equation in standard form.
Comparing this with the standard form equation, we can say that:
[tex]h = 1[/tex][tex]k = 0[/tex][tex]r^2 = 9 \implies r = \sqrt{9} = 3[/tex]Therefore, the center of the circle (h, k) is (1, 0) and its radius is 3 units.
As the y-coordinate of the center is zero, the center lies on the x-axis.
Therefore, the true statements are:
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Please hurry. Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
A. Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
B. Sample space = lemon-lime, watermelon, grape
C, Sample space = 1, 2, 3, 4, 5, 6
D. Sample space = 1, 2, 3
The cοrrect sample space fοr the gumballs in her bag is, Sample space = watermelοn, lemοn-lime, lemοn-lime, grape, grape, grape
Hοw dοes Sample space wοrk?A sample space is a set οr cοllectiοn οf pοtential οutcοmes frοm a randοm experiment. The letter "S" stands fοr the sample space in a symbοl. The term "events" refers tο a subset οf pοssible experiment results. Depending οn the experiment, a sample space may cοntain variοus οutcοmes. It is referred tο as discrete οr finite sample spaces if there are a finite number οf pοssible οutcοmes.
The sample space is the set οf all pοssible οutcοmes οf an experiment. In this case, the experiment is selecting a gumball frοm Julia's bag, and the pοssible οutcοmes are watermelοn, lemοn-lime, and grape.
Sο the cοrrect sample space fοr the gumballs in her bag is:
Sample space = {watermelοn, lemοn-lime, grape, grape, lemοn-lime, grape}
Therefοre, the cοrrect οptiοn is A.
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The orange spinner is spun and then the aqua spinner is spun. what is the probability that the numbers will add to 4 or less?
the probability of the numbers will add to 4 or less will be 25%
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
The orange spinner is spun and then the aqua spinner is spun.
The probability that the numbers will add to 4 or less will be of 1 out of 4 that will be 1/4*100
= 25%
Hence the probability of the numbers will add to 4 or less will be 25%
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what relation is this graph
one-to-one, many-to-one, one-to-many, or many-to-many
For the graph given for function |x-1|, the relation is one - to - one.
What is a relation?
In mathematics, a relation describes the connection between two distinct collections of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their components.
The graph given is a graph of function |x-1|.
The graph of |x-1| is a V-shaped graph, with the vertex at (1, 0) and the arms extending upward and downward from the vertex.
Since the graph of |x-1| passes the horizontal line test, it is a one-to-one function.
This means that every input (x-value) has a unique output (y-value) and no two different inputs can have the same output.
Therefore, the relation represented by the graph of |x-1| is a one-to-one relation.
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You borrow $2000 from a friend and promise to pay back $3000 in two years. What simple interest rate will you
pay?
In September 1998 the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. At the same time the population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas x is the year, where x=0 corresponds to September 1998. Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.A. 2009B. 1987C. 2008D. 11
In September 1998, the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. The population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas, x is the year, where x=0 corresponds to September 1998.
To find the year when the population of West Goma will equal the population of East Goma, we will use the following method:
$$f(x)=g(x)$$
$$16.9e^{0.001x} = 13.8e^{0.019x}$$
Taking natural logarithms of both sides we have,
$$\ln(16.9) + 0.001x = \ln(13.8) + 0.019x$$
$$0.018x = \ln(16.9) - \ln(13.8)$$
$$x = \frac{1}{0.018}(\ln(16.9) - \ln(13.8))$$
$x \approx 41.06$, which corresponds to September 2039.
Therefore, the year when the population of West Goma will equal the population of East Goma is September 2039. Option E. 2039 is the correct answer.
Note: The growth rate of West Goma is smaller than that of East Goma, hence it will take a longer time to equalize.
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What does constant time mean? Please hurry! :)
Answer:
When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant rate of change.
Step-by-step explanation:
The constant would be 2.
Joanna bought three circular rugs to put in her bedroom. Each rug has a 4 ft radius. What is the area of her floor that will be covered by rugs?
Answer:
The area of a circle can be calculated using the formula:
Area = π x radius^2
where π (pi) is a mathematical constant approximately equal to 3.14159.
Since each rug has a radius of 4 feet, the area of one rug is:
Area = π x 4^2
Area = 16π square feet
To find the total area covered by the three rugs, we need to multiply the area of one rug by three:
Total area = 16π square feet x 3
Total area = 48π square feet
Using a calculator, we can approximate the value of π to two decimal places as 3.14, so the total area covered by the three rugs is:
Total area ≈ 48 x 3.14 square feet
Total area ≈ 150.72 square feet
Therefore, Joanna's bedroom floor will be covered by approximately 150.72 square feet of rugs.