The equation of the circle described in the problem is x² + (y - 8)² = 64.
What is the equation of a circle?
The general equation of any type of circle is represented by: x2 + y2 + 2gx + 2fy + c = 0, for all values of g, f, and c.
The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The standard form equation of a circle with center at (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
Substituting the given values into this equation, we get:
(x - 0)² + (y - 8)² = (8)²
Simplifying this equation gives:
x² + (y - 8)² = 64
Hence, This is the equation of the circle described in the problem.
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A plane flying horizontally at an altitude of 2 km and a speed of 600 km/h passes directly over a radar station. Find the rate (in km/h) at which the distance from the plane to the station is increasing when it is 3 km away from the station. (Round your answer to the nearest whole number.)
Answer:
When the plane is 2mi away from the radar station, its distance's increase rate is approximately 433mi/h.
Step-by-step explanation:
Sketch a right triangle with one leg going vertically a length of 3 miles above the station, and the other leg x going horizontally from the top of the first leg. Distance r from plane to station is related by r2 = x2 + 32. Differentiate: 2r dr/dt = 2x dx/dt, which rearranges to the desired dr/dt = x/r dx/dt. When r = 4, x2 = 42 - 9 and x = √7. So dr/dt = (√7 / 4) * 520 mph = 344 mph.
What is the sampling method that involves taking a random selection of people from a defined population?.
A sampling method is simple random sampling.
What is sampling method?In statistical analysis, sampling is the procedure by which researchers choose a specific number of observations from a larger population. The sample strategy will depend on the sort of study being done, although it may involve systematic sampling or just plain random sampling.
A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same probability of getting chosen. Then, data are gathered from as much of this randomly selected subgroup as feasible.
Since it only uses one random pick and is very simple, this method is the easiest of all the probability sampling techniques.
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write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
According to the task content, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
Consequently, the required expression is an arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
Ultimately, The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term of the arithmetic sequence is given by the expression; T (n) = 1 + 7 (n -1).
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Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars. What fraction of a cup of nuts does Brielle use for 1 cup of oatmeal?
Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
What is unitary method?
The unitary method is a process of finding the value of a single unit, and based on this value finding the required solution.
According to the given question:
Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars.
To find the fraction cup of nuts required for 1 cup of oatmeal, using unitary method
2 cups ----- 2/3 cup of nuts
1 cup ------- [tex]\frac{2/3}{2}[/tex] cup of nuts = 1/3 cup of nuts
Therefore Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.
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every answer i have put is wrong can someone help
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour is 87.03 feet.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
The stopping distance d is directly proportional to the square of the speed v.
This can be written as,
d ∝ v²
Now,
Converting 40 miles into feet.
1 mile = 5280 feet
40 miles = 40 x 5280 feet
40 miles = 211200 feet
Now,
40 feet ∝ 211200 feet per
Now,
The stopping distance is 40 feet when the speed is 40 miles per hour
d = 40 and v = (40 x 5280) feet per hour
d = k v²
k = d/v²
k = 40/(40 x 5280)²
k = 1/(40 x 5280²)
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour
v = (59 x 5280) feet per hour
d = 1/(40 x 5280²) x (59 x 5280)²
d = (59 x 59) / 40
d = 87.03 feet
Thus,
The mathematical model that gives the stopping distance d in terms of speed v is
d = 1/(40 x 5280²) v²
The stopping distance when v is 59 miles per hour is 87.03 feet.
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B. Hannah approximates the areas of circles using the equation A=3 r², and records areas of circles with different radius lengths in a table.
a. Graph the ordered pairs from the table.
b. Is the relation a function? Explain.
Answer Questions 9 to 11 using the lines shown in the coordinate grid below.
1. Is it true that m parallel to n?Include any relevant measurements and calculations.
2. Is it true that m is congruent to p?include relevant measurements and calculations.
3.Is it true that n is congruent to p? Include any relevant measurements and calculations.
The solution to the parallel lines identification and congruency are;
1) They are not parallel.
2) They are not congruent.
3) They are not congruent.
How to Identify Parallel lines?
Parallel lines are defined as lines in a plane that are always the same distance apart. Parallel lines never intersect.
1) Looking at lines m and n , for them to be parallel, it means that they must be the same width all through. However, we see that along the x-axis they are 6 units while going further down, it is not always 6 units as some are 5.5 units. Thus, they are not parallel.
2) No, m is not congruent to p because it is not the same distance from the x and y-axis at similar points.
3) No, n cannot be congruent to p because we see that the distance between the marked points are not congruent.
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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 80.2% of their carbon-14. How old were the bones at the time they were discovered?
The age of the bones when they were discovered is 13439.66 years
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
The radioactive element carbon-14 has a half-life of 5750 years
So , the value of t½ = 5750 years
Now , the decay constant λ = 0.693 / t½
Substituting the values in the equation , we get
Decay constant λ = 0.693 / t½
Decay constant λ = 0.693 / 5750
Decay constant λ = 1.205 x 10⁻⁴
N=N₀e ^ −λt
where N₀ = Mass of radioactive element initially
N = Mass of radioactive element after time t
Apply natural logarithm on both the sides of the equation , we get
ln N = ln N₀ - λt
Let N0 be 100 then N will be 100 - 80.2 = 19.8
Substituting the values in the equation , we get
ln 19.8 = ln 100 - 1.205 x 10⁻⁴ ( t )
ln [ 19.8 / 100 ] = - 1.205 x 10⁻⁴ ( t )
-1.61948 = -1.205 x 10⁻⁴ ( t )
Therefore , the value of t is
t = -1.61948 / -1.205 x 10⁻⁴
t = 1.343966 x 10⁴
t = 13439.66 years
Therefore , the value of t is 13439.66 years
Hence ,
The age of the bones when they were discovered is 13439.66 years
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Triangle ABC is drawn with AB = 36 units, BC = 42 units, and ZBCA = 31°. The measure of ZABC is
The value of [tex]\angle[/tex]ABC=6° was found with the help of the law of cosines.
What is the law of cosines of a triangle?
The lengths of a triangle's sides are correlated with the cosine of one of its angles according to the law of cosines. We can now determine values for distances and angles that are impossible to measure without the aid of trigonometry. When calculating the third side of a triangle given two sides and their enclosed angle, as well as when calculating the angles of a triangle if we know all three sides, the law of cosines is used.
Given values are AB = c = 36 units, BC = a = 42 units, and [tex]\angle[/tex]BCA = 31°.
Now let AB = b, we find b using the law of cosines and quadratic equation:
[tex]c^2 = a^2 + b^2 - 2a b \cos C \\36^2 = 42^2 + b^2 - 2 \cdot \ 42 \cdot \ b \cdot \ \cos 31\degree \\ b > 0 \\ b = 7.22[/tex]
Now, we calculate [tex]\angle[/tex]ABC using the law of cosines:
[tex]\angle ABC=arc cos(\frac{a^{2}+c^{2}-b^{2} }{2ac}) \\\angle ABC=arc cos(\frac{42^{2}+36^{2}-7.22^{2} }{2.42.36}) \\\angle ABC=5.55[/tex]
[tex]\angle[/tex]ABC=6°
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Find the volume of the figures
1. The volume of the cylinder is 942 m³.
2. The volume of the cone is 33.16 mm.
3. The volume of the sphere is 33.50 in³.
4. The volume of the cuboid is 672 in³.
What is volume?Volume is defined as how much of a three-dimensional object occupies
a space.
We know the volume of a cylinder is πr²h.
∴ The volume of the given cylinder is = π(5)²×12 m³ = 942 m³.
We know the volume of a cone is = (1/3)πr²h.
∴ The volume of the given cone is = (1/3)π(2)²×8 mm³ = 33.16 mm.
We know the volume of a sphere is (4/3)π×r³.
∴ The volume of the given sphere is = (4/3)×π×(r³) in³ = 33.50 in³.
We know the volume of a cuboid is = (length×width×height).
∴ The volume of the given cuboid is = (7×8×12) in³ = 672 in³.
The volume of the object in figure 8 is the sum of the volume of a cuboid and a pyramid.
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Use the number line to represent the solution to x + 3 > 5. Select the ray. Move the point on the ray to the correct place on the number line.
Hence, the point on the ray is [tex]x > 2[/tex].
What is the number line?
A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides
Here given that,
Use the number line to represent the solution to [tex]x + 3 > 5.[/tex]
i.e.,
[tex]x+3 > 5\\\\x > 5-3\\\\x > 2[/tex]
Hence, the point on the ray is [tex]x > 2[/tex].
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Need help with this problem
The equation of inequality for the given graph will be;
⇒ y < - 4/3x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph is shown in figure.
Now,
Take two points on the graph as;
⇒ (0, 5) and (3, 1)
Hence, The equation of line will be;
⇒ y - 5 = (1 - 5) / (3 - 0) (x - 0)
⇒ y - 5 = - 4/3x
⇒ y = - 4/3x + 5
Since, The inequality is shown in figure.
Hence, We get;
⇒ y < - 4/3x + 5
Thus, The equation of inequality for the given graph will be;
⇒ y < - 4/3x + 5
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The relationship between the cone cylinder and sphere is sphere takes up two-thirds of the volume of the cylinder, the cone takes up one-third of the volume of the cylinder.
What is the properties of the cone cylinder and sphere?Similar to a prism, a cylinder has two bases, however they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a form in space with equal distances between each of its points and the centre.Any sphere has a volume that is 2/3 the size of any cylinder with an equivalent radius and height.While CYL, or cylinder, is the amount of lens power required to correct astigmatism, SPH, or sphere, is the amount of lens power required to correct nearsightedness or farsightedness. People frequently allude to their SPH value while discussing their eye degree or "power."Answers of blank :
Blank 1 = 1/3
Blank 2 = Three
Blank 3 = Two
Blank 4 = 2/3
Blank 5 = 1/3
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On a team, 3 girls and 2 boys scored a total of 41 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 13. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer:
each girl scored 9 points
each boy scored 7 points
Step-by-step explanation:
41-13=28
28/2=14
14 is the number scored by boys
14/2
one boy scored 7 points
14+13=27
27 is the number scored by girls
27/3=9
each girl scored 9 points
Please help anyone. I need help especially with #4
Answer:
#4 x=70
Step-by-step explanation:
Because this is an Isosceles triangle, we know that the 2 base angles have to be equivalent. So subtract 40 from 180 which leaves you with 140, then divide 140 by 2 because there are 2 base angles. Then arrive at the answer of x=70.
-Hope this helped & Happy Holidays!
Write and graph the inverse of y=-x²+5
Write the inverse of y=-x²+5
y=
Answer:
Below
Step-by-step explanation:
y = - x^2 + 5 solve for x
y-5 = - x^2
x^2 = 5-y
x = ± sqrt (5-y) now switch the x's and y's
y = ± sqrt(5-x)
Here is a picture:
At the city museum, child admission is 5.70 and adult admission is 9.80. On Friday, 114 tickets were sold for a total sales of 912.20. How many adult tickets were sold that day?
According to the given information The 50 child tickets and 64 adult tickets were sold that day.
What exactly is arithmetic?The area of mathematics concerned with the characteristics and use of numbers a field of study that concentrates on multiplying, dividing, adding, and subtracting numbers. Mathematical simplifications are made using fractions, decimals, percentages, fractions, square roots, exponents, and other arithmetic operations.
Briefing:child admission (c)= $5.70
adult admission (a)= $9.80
5.70c + 9.80a = 912.20 (i)
a + c = 114 (ii)
Set up the equation:
5.70(114 - a) + 9.80a = 912.20
649.8 - 5.7a + 9.80a = 912.20
4.1a = 262.4
a = 64
adult tickets = 64
Put the value of a in equation (ii) we get,
64 + c = 114
c = 114 - 64
c = 50
child tickets = 50
Therefore , the 50 child tickets and 64 adult tickets were sold that day.
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In triangle WXY, the measure of W is 10 less than the measure of X and the measure of Y is 14 less than the measure of X. Find the measure of each angle
X = 63°
W = 60°
Y = 57° are the measure of each angle in triangle.
In math, what is a triangle?
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
W = X - 10
Y = X - 14
X + W + Y = 180 substitute
X + (X - 10) + ( X - 14)
= 3 X - 24 = 180
3X = 180 + 24.
X = 204/3
X = 68
W = 58
Y = 54
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Max baked 5 pies for the bake sale. He cut each pie into 8 equal slices. In the first 30 mins of the bake sale, Max sold 19 slices of pie. How many pies did max sell in that time? Give your answer in 2 ways
Answer: He sold 19/40 of his pies or 0.475% of his pies
Step-by-step explanation: There are 40 total slices of pie and if he sold 19, then the fraction is 19/40. Additionally the fraction 19/40 as a decimal is 0.475 so it would be 0.475% of the pies.
SOLVE FOR R
-7 - 7r= -10r + 8
R =
Answer:
the answer is 5
Step-by-step explanation:
(Add 10r to both sides)
-7-7r+10r= 8
Then -7+3r = 8
(Add 7 to both sides)
3r = 8+7
3r = 15
Divide both sides by 3.
r = 5
In a study comparing 4 types of batteries, 60 batteries (15 of each type) were tested, and their lifetimes were compared. (Here, k = 4, and N-60) (a) The hypotheses are Part of the ANOVA summary table is given below. Sum of Squares df Mean SquaresF MSB/MSW MS SS/df Between (Factor) 25.7375 Within (Error) 75 (b) Complete the table. (Remember that the df for the numerator (Between Groups) is k-1, and the df for the denominator (Within Groups) is N-k. (c) Use the Fcdf on your calculator to find the p-value. (Go to 2nd is Fcdf( F, 10000, df Between, df Within).) DISTR VARS and choose FEeff. The syntax and choose Fcdf. The syntax (d) State your decision and conclusion.
a) The hypotheses for this study would be the Null hypothesis and Alternative hypothesis.
b) The completed ANOVA summary table would be the Sum of Squares.
c) The calculator would give a p-value of approximately 0.03.
d) The results of the ANOVA test may not be reliable.
(a) The hypotheses for this study would be:
Null hypothesis ([tex]H_0[/tex]): There is no difference in the average lifetime of the four types of batteries.
Alternative hypothesis ([tex]H_1[/tex]): There is a difference in the average lifetime of the four types of batteries.
(b) The completed ANOVA summary table would be:
Sum of Squares (SS) df Mean Squares (MS) F
Between (Factor) 25.7375 3 8.578 3.77
Within (Error) 75 56 1.34
Total 100 59
(c) To find the p-value, you would use the Fcdf function on your calculator. The syntax for this would be Fcdf(F, 10000, df Between, df Within). In this case, the F value is 3.77, the df Between is 3, and the df Within is 56. Plugging these values into the calculator would give a p-value of approximately 0.03.
(d) Based on the p-value, we can reject the null hypothesis and conclude that there is a significant difference in the average lifetime of the four types of batteries. This suggests that the type of battery has an effect on its lifetime. However, it is important to note that this conclusion is based on the assumptions of the ANOVA test, including the assumption of equal variances among the groups. If these assumptions are not met, the results of the ANOVA test may not be reliable.
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“24 hours per day” translate the algebraic expression
Answer:
24*X or 24X
Step-by-step explanation:
24X or 24*X or 24 multiplied by X days
The variable "X" represents the number of days.
Write out, in paragraph form, a plan for completing the following proof.
For example, will you prove triangles congruent? How? By what theorem?
Given:
AR = AQ
RT = QS
Prove:
∠ RAT = ∠ QAS
Can someone help me understand how to answer this
Because AR = AQ, you have an isosceles triangle with triangle RAQ. This also means ∠ARQ = ∠AQR.
You're also told that RT = QS, so this gives you SAS to show triangle ART = triangle AQS.
side: AR = AQ
angle: ∠ART = ∠AQS
side: TR = QS
Knowing that the two triangles are congruent gives you that the two top angles are also congruent.
Need help with this 2
Write the equation of the line that is parallel to z = 4 and passes through (-3, 7).
Answer:
x = -3
Step-by-step explanation:
If you look at the graph.
x = 4 is a vertical line.
Another vertical line that would be parallel to this can contain the point (-3, 7) would be the line x = -3
The monthly cost of water use is a linear function of the amount of water used (HCF). The cost for using 16 HCF of water is $39.04, and the cost for using 44 HCF is $79.64. What is the cost for using 22 HCF?
Answer:
The cost for using 22 HCF is $47.74------------------------------
Equation of line:
y = mx + b, where m- slope, b- y-intercept
Given values can be interpreted as pairs of coordinates of the two points:
(16, 39.04) and (44, 79.64)Find the slope of the line:
m = (79.64 - 39.04)/(44 - 16) = 40.6/28 = 1.45Find the y-intercept, by substituting coordinates of one point:
39.04 = 1.45*16 + b39.04 = 23.2 + bb = 39.04 - 23.2b = 15.84The equation becomes:
y = 1.45x + 15.84Find the value of y when x = 22:
y = 1.45*22 + 15.84 = 31.9 + 15.84 = 47.74{y:y is an integer AND Y>10
{y:y is an integer AND y>10} is a set of integers that are greater than 10. Some examples of elements that would be included in this set are 11, 12, 13, 14, and so on.
B + 6 divided by 4 when b = 1.5
Answer:
Step-by-step explanation:
Write it out
[tex](B+6)/4[/tex]
plug in the value
[tex](1.5+6)/4[/tex]
solve
[tex](1.5+6)/4\\7.5/4\\= 1.875[/tex]
ASAP!! Which graph could be used to find the distance between the points (−3, −13) and (11, 9)?
graph of a right triangle with hypotenuse beginning at negative 13 comma negative 3 and ending at 9 comma 11
graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9
graph of a right triangle with hypotenuse beginning at negative 11 comma negative 9 and ending at 3 comma 13
graph of a right triangle with hypotenuse beginning at negative 9 comma negative 11 and ending at 13 comma 3
The graph that could be used to find the distance between the points
(-3, -13) and (11, 9) is given as follows:
B. graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9.
What is distance between two points?
The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation
d=√((x2 - x1)^2 + (y2 - y1)^2) is used to calculate the distance between two points.
Suppose we have a pair of points, with the coordinates given as follows:
[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
The two points form a right triangle, in which the sides are given as follows:
[tex]y_2-y_1\\x_2-x_1[/tex]
The distance between these two points is given by the hypotenuse of the right triangle.
Hence, applying the Pythagorean Theorem, the distance is obtained as follows:
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
In this problem, the coordinates of the points are given as follows:
(−3, −13) and (11, 9).
Hence the correct option is given by option B.
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Ms. Bobadilla has a 24 ounce coffee. I drink 8 ounces. What percent of the coffee is left? 7th grade math
The required percent of the coffee left is given as 66.67%.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
24 ounces of coffee Ms. Bobadilla,
And 8 ounces of coffee has been drinking,
Applying the percentage evaluation, in order to calculate the remaining coffee to Ms. Bobadilla.
Percentage of coffee remaining = 24 - 8 / 24 × 100%
Percentage of coffee remaining = 0.6667 × 100%
Percentage of coffee remaining = 66.67%
Thus, the percentage is given as 66.67%.
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