The diameter of the circle is 30 feet.
What is diameter?
The center of the circle is the midpoint of a line segment that connects two points on the circle's perimeter, and this line segment is indicated by the diameter of a circle.
The diameter of a circle is precisely equal to twice the radius' length.
Let us suppose the diameter of a circle is D then, the area is computed according to the formula
[tex]A = \frac{\pi D^2}{4}[/tex]
where
A is the area and D is the diameter.
Plug A = 225 pi in the above equation,
[tex]225 \pi =\frac{\pi D^2}{4} \\225 = \frac{D^2}{4} \\D^2 = 900\\D = 30[/tex]
Hence, the diameter of the circle is 30 feet.
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Select the correct answer
3/4x + 4 = 7
1. 4
2. 44/3
3. -3
4. 8
Answer:
A) x=4
Step-by-step explanation:
Answer:
1. 4
Step-by-step explanation:
3/4 x + 4 = 7 Multiply all the way through by 4 to clear the fraction
3x + 16 = 28 Subtract 16 from both sides
3x = 12 Divide both sides by 3
x = 4
3. based on the results of this t-test, report the p value. explain what this means in context of a type 1 error.
based on the results of this t-test, report the p value. explain this means in context of a type 1 error is you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
What does p-value tell you about error?
The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis. If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
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question what is the hundreds digit of the integer z? (1) 10z > 25,670 (2) z rounded to the nearest hundred is 2,600.
Part a: 10z > 25,670; infinite integer.
Part b: Range = 2550 to 2649.
Explain the term integer?All whole numbers including negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results. An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 10, 21, 15, 18, 97, and 343.Part a: 10z > 25,670
Divide the inequality on both sides by 10.
z > 2,567
Thus, there are infinite number which are greater than 2567.
Part b: z rounded to the nearest hundred is 2,600.
Range = 2550 to 2649.
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what is the median of the following numbers? 8, 10, 10, 10, 6, 7, 88,10,10,10,6,7,88, comma, 10, comma, 10, comma, 10, comma, 6, comma, 7, comma, 8
The median is 10 as the value 10 is at 10th position.
What is Median?
The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data collection.
Solution:
Firstly we need to arrange the data in ascending order
6,6,6,7,7,7,8,8,10,10,10,10,10,10,10,10,10,88,88
the total number of digits are
n = 19
So, the middle value that divide the data in two halves will be at n = 10
The median is 10 as the value 10 is at 10th position.
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consider the process of throwing $m$ balls into $n$ bins, where each ball is thrown into a uniformly random bin, independent of other balls. what is the expected number of balls in a particular bin $b$?
The predicted quantity of balls in the first bin is (1/n)n.
Considering that,
There are the same number of balls and containers.
If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.
For instance -
Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.
According to the same logic, bins 2 and 3 should also have expected values of 1.
How probable is it that the first bin will receive all three balls?
In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.
Therefore, (1/n)n would be the expected number of balls in the first bin.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
In the quadratic function f(x) = -x² – 5x + 12 the true statement is
The graph of the function is a parabola.The graph of the function opens downThe graph contains the point (0, 0)How to know the true statementsA quadratic equation when plotted traces a parabolic path hence the graph of the quadratic equation is said to be a parabola hence this is a true statement
When x² opens up when positive but down when negative. since the function is negative hence the curve opens down
from the attached graph the points in the graph is shown and the origin (0, 0) is inclusive
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Write an expression to show how to find Milan's age when Raul is 14
The expression to show how to find Milan's age when Raul is 14 is x + 6 = 14.
What is an expression to calculate the age?An expression is simply used to show the relationship between the variables in the data.. Addition, subtraction, multiplication, and division are possible mathematical operations.
Let Milan's age be x
Rauls age = x + 6
Therefore, when Raul is 14, Milan will be:
x + 6 = 14
Collect like terms
x = 14 - 6
x = 8
Milan is 8 years.
The expression is x + 6 = 14
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Complete question
Milan is 6 years younger than Raul. Write an expression to show how to find Milan's age when Raul is 14
If $\frac{x}{2} + \frac{y}{3} = 1$ and $\frac{x}{4} + \frac{2y}{3} = -1$, what is the value of the sum of $x$ and $y$?
For the given set of equations x/2 + y/3 = 1 and x/4 + 2y/3 = -1 the sum of x and y is 1.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equations are,
x/2 + y/3 = 1,
x/4 + 2y/3 = -1.
Simplify both the equations,
3x + 2y = 6 (1)
3x + 8y = -12 (2)
Subtract equation (2) and (1),
6y = -18
y = -3
Substitute the value of y = -3, in equation (1)
3x + 2(-3) = 6
3x - 6 = 6
3x = 12
x = 4
The sum of x and y,
x+y = 4 - 3
= 1
The sum of x and y for the given equations, is 1.
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Enter the equation of the line in slope-intercept form that has a slope of -4 and passes through (0, 21).
Answer:
y = -4x + 0 or y = -4x
Step-by-step explanation:
y = mx + b
y = -4x + b
21 = -4(0) + b
21 = 0 + b
b = 0
y = -4x + 0 or y = -4x (the 0 is unnecessary to write but you could write it both ways)
Could you please give me brainliest? Thank you!
if the speed limt was 80 kilometers per hour, and elenas mom was driving 75 miles er hourm was sh speeding? by how much?
Answer: 40.7 kph is how much she was speeding
Step-by-step explanation:
if the slope of a line is k, and the line passes through the points (0, k 3) and (-3 , 0), what is the value of k
Answer:
1
Step-by-step explanation:
assuming your points are (0,3) and (-3,0) you would "rise" 3 and "run" 3 to get from one point to the next on a graph, making your rise over run (aka slope) 3/3 which is equal to 1.
6. A solution containing 80% chicken broth is to be mixed with water to
make 200L containing 60% chicken broth. How much of each should be
mixed?
x = amount of the 80% broth
y = amount of water with 0% broth
keeping in mind that water has no broth in it, so 0% of broth, let's plug in those percentages in decimal format to see how much each one has.
what's 80% of "x"? well (8/100) * x = 0.80x.
what's 0% of "y"? well hell is just 0.
what's 60% of 200? well anyhow is just 120.
[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{broth only}}&\stackrel{\textit{liters of}}{\textit{broth only}}\\ \cline{2-4}&\\ \textit{80\% Sol'n}&x&0.80&0.80x\\ water&y&0.00&0\\ \cline{2-4}&\\ mixture&200&0.60&120 \end{array}~\hfill \begin{cases} x + y = 200\\\\ 0.80x+0=120 \end{cases} \\\\[-0.35em] ~\dotfill\\\\[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{0.8x=120}\implies x=\cfrac{120}{0.8}\implies \boxed{x=150~liters} \\\\\\ \stackrel{\textit{using the 1st equation}}{150 + y = 200}\implies y=200-150\implies \boxed{y=50~liters}[/tex]
Hypatia has read 13 chapters of a 22-chapter book.
What percent of the chapters has she read?
Answer:
Step-by-step explanation:
13+22=35%
suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. what would be the formula of an expected count in this situation?
The expected counts for each possible outcome are given by Ei = npi
What is mutually exclusive outcomes?
When two events cannot happen simultaneously or at the same time, they are said to be mutually exclusive in probability theory. In other words, discontinuous occurrences are described as being mutually exclusive. The likelihood of two events occurring simultaneously is 0 if they are regarded as disjoint events. Events that do not occur simultaneously are said to be mutually exclusive. When a coin is tossed, for instance, the outcome will either be head or tail, but we cannot get both outcomes.
The expected counts for each possible outcome are given by Ei = npi
Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes,
where pi represents the probability of observing the ith outcome.
The expected counts for each possible outcome are given by Ei = npi
Where, pi is the probability of observing the ith outcome
Ei is the expected count of the ith outcome.
Hence, The expected counts for each possible outcome are given by Ei = npi.
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-2(y - 3) = y + 24
please help
Answer:
y=-6
Step-by-step explanation:
1. -2y+6=y+24
2. -2y-y=24-6
3.-3y=18
4. y=-6
Which set of measurements can represent the lengths of a triangle's sides? classify each set of lengths as a triangle or not a triangle.
The measurements are represented by lengths of a triangle's sides by -
Option C: 3 in, 7 in, and 8 inOption D: 3 in, 5 in, and 7 inExplain the term triangle?A triangle is a polygon with three vertices and three sides. The angles of a triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.The triangle's three sides must satisfy the following condition:
"The total of any two triangle sides must be larger than or equal here to third side of the triangle."
We have four options in this question, so we'll go through them one at a time.
Option A: 1 in, 3 in, and 7 inSince (1+3)<7 in this case, a triangle cannot be formed.
Option B: 3 in, 3 in, and 7 inSince (3+3)<7 in this case, a triangle cannot be formed.
Option C: 3 in, 7 in, and 8 inIn this instance, (3+7)>8, (3+8)>7, and ((7+8)>3
Thus, a triangle will be formed by these.
Option D: 3 in, 5 in, and 7 inIn this instance, (3+5)>7, (3+7)>5, and (5+7)>3
Thus, a triangle will be formed by these.
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The options for the question are attached.
several people form groups with eight people in each group. write an expression for the number of groups formed by p people. how many groups are formed if there are 96 people?
If 96 people divide into groups of eight, the following expression indicates that 12 groups are created.
Eight persons form groups made up of multiple people. a expression for how many groups made up of p people there are.
P = the number of groups.
12 groups out of 96
If there are 96 individuals, 12 groups are created.
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Given parallelogram DEFG, if DF = 5x + 1, what is XF?
Applying the property of the diagonals of a parallelogram, XF = 13 units.
What are Some Properties of a Parallelogram?A parallelogram is a quadrilateral with the following properties:
The opposite sides are equal and parallelThe two diagonals of a parallelogram bisects each other into equal halves each.DF and EG are diagonals of parallelogram DEFG, where:
DF = 5x + 1
EX = 2x
XG = 3x - 5
Based on the property of the diagonals of a parallelogram, we have:
EX = XG
Substitute
2x = 3x - 5
2x - 3x = -5
-x = -5
x = 5
Length of XF = 1/2(DF)
Substitute
Length of XF = 1/2(5x + 1)
Plug in the value of x
Length of XF = 1/2(5(5) + 1)
Length of XF = 13 units
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M inverly proportional to g^3
M=24 when g=2. 5
a) find a formula for M in term of g
b) work out the value of g when M=1/9
The answers to both the subparts using the inversely proportional property are shown:
(A) The formula will be: M = 375/g³
(B) The value of g is 15 when M = 1/9.
What do we mean by inversely proportional?When one variable decline, the others also decline in the same ratio.
When two variables move in opposite directions, one variable reduces as another increase, and the other increases as another variable lower, the variables are said to be inversely proportional.
Since M and g3 have an inverse relationship, we can say:
M = k/g^3
Assuming that g = 2.5 and that M = 24 then:
24 = k/(2.5)^3
24*(2.5)^3 = k = 375
(A) Formula for M in terms of G:
The formula will be M = 375/g³.
(B) Value of G when M = 1/9:
If M = 1/9, we get:
1/9 = 375/g^3
g^3 = 9*375
g = ∛(9*375) = 15
Therefore, the value of g is 15 when M = 1/9.
Therefore, the answers to both the subparts using the inverse proportional property are shown:
(A) The formula will be: M = 375/g³
(B) The value of g is 15 when M = 1/9.
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let s be a set of n segments in the plane. a line ? that intersects all segments of s is called a transversal or stabber for s.
Suppose 's' be a collection of 'n' plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of 's'.
Explain the term transversal?A transversal in geometry is a line, ray, as well as line segment that, on a plane, overlaps other lines, rays, including line segments at various locations.
A transversal is a line that, at two different locations in the geometry, cuts through two lines within the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection between two lines.Thus, if 's' be a collection of n plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of s.
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At 11:00 am, a body was found within a closed room of a mansion where the air temperature is a constant 70 degrees F. At the time of discovery, the core temperature was determined to be 85 degree F. One hour later, a second measurement showed the core temperature of the body was 80 degrees F. Assume the core temperature of the body at the time of death was 98.6 degrees F. Use Newton’s Law of Cooling to determine the time of death. Hint: Let t=0 represent 11:00 am and work backwards to 98.6 degrees F.
The time that has elapsed before the body was found is 1.5 hour
What is Newton's method of cooling ?Newton's law of cooling states that the rate of heat loss from a body is inversely related to the temperature difference between the body and its surroundings.
Given:
when time, t = 0, temperature = 98.6 ⁰F
when time, t = 1, temperature = 75⁰
when time, t = t, temperature = 80⁰
By Newton's method of cooling equation;
T(t) = [tex]T_s (T_0 - T_s)e^{kt[/tex]
T(t) = 70+ 28.6[tex]e^{kt[/tex]
Now, At the time of discovery
80 = 70+ 28.6[tex]e^{kt[/tex]
10= 28.6[tex]e^{kt[/tex]
Then, 1 hour later( t + 1) we have the second equation;
75= 70 + 28.6[tex]e^{kt[/tex]
28.6[tex]e^{kt[/tex] = 5
Now, divide equation 1 by equation 2;
2= [tex]e^{-k[/tex]
k = -0.693
The time when he dead body was discovered
10= 28.6[tex]e^{kt[/tex]
10= 28.6[tex]e^{-0.693[/tex]
-0.693t = ln (10 /28.6)
-0.693t = -1.05
t= 1.5 hour
Hence, the time that has elapsed before the body was found is 1.5 hour
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Which one blue, light blue , yellow or red
Step-by-step explanation:
light blue.
our function needs to calculate r out of h.
P does not recognize h (hours after midnight) as parameter. P needs c as input.
T needs h as input and delivers c as output.
therefore (P ○ T)(h) = r is correct.
first the "inner" T function is calculated with h as parameter and then P is calculated using the result from T (c) as input and delivers r.
can anyone please write this in word form.
Answer:
four x plus three divided by two
Step-by-step explanation:
in the problem to the left if Tim mows 9 lawns this week, by how much will he have exceeded his goal
( Tim earns 120 plus 30 for each lawn he mows. )
PLEASE HELP
Answer:
Step-by-step explanation: 69
PLS HELP WILL GIVE BRAINLIEST The table shows a hot air balloon's height h, in feet, during a descent at various times t, in seconds.
Step-by-step explanation:
A .
1150-1090=60
60feet/5sec = 12feet/sec
B.
yes it's is constant , because is decreasing by 60 feet in every 5 sec
C.1150
which fraction is greater 1/3 or 1/9
Answer:
1/3
Step-by-step explanation:
1/9 is one piece in total of 9 but 1/3 is one piece in total of 3
0.4(20-10m) = 2.5 -2m -12.5
Answer: M=9
Step-by-step explanation:
Which of these relations is a function?
Answer:
The top right
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Because for every x there is a only an y
you order 3 strings of white led lights and 2 strings of colored led lightgs for 66$ In a second order you buy one string of each type for 27$ A. WHICH TYPE OF LED IS MORE EXPENSIVE
The colored type of led is more expensive if you order 3 strings of white led lights and 2 strings of colored led lights for 66$.
What is meant by an equation?An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.
Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.
First type of white led have 3 strings=3x
Second type of colored led have 2 strings and bought only one string=2y
The total cost =3x+2y=66 ----------->(1)
In the second order ,
Each string brought only one=x+y=27 ------->(2)
Solving equations 1 and 2
From eq2, y=27-x
3x+2(27-x)=66
3x+54-2x=66
X=12
Y=27-x=27-12=15
Therefore, the type of colored led are expensive
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Can you help me with these questions please. look at the image.
Using Pythagoras's theorem, the relationships of the sides of the right triangle is x² - 21x + 108 = 0.
The value of x in the right triangle is x = 9 or x = 12.
How to find the sides of a right angle triangle?The right angle triangle is a triangle with one of its angles as 90 degrees. The sides of a right angle triangle can be found using Pythagoras's theorem.
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore, the equation to show the relationships between the three sides can be gotten by applying Pythagoras's theorem.
x² + (21 - x)² = 15²
x² + (21 - x)(21 - x) = 225
x² + 441 - 21x - 21x + x² = 225
2x² - 42x + 441 - 225 = 0
2x² - 42x + 216 = 0
divide through by 2
x² - 21x + 108 = 0
Let's find the value of x by factoring.
x² - 21x + 108 = 0
x² - 12x - 9x + 108 = 0
x(x - 12) - 9(x - 12) = 0
(x - 9)(x - 12) = 0
Therefore,
x = 9 or x = 12
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