Answer:
56.52
Step-by-step explanation:
The formula for circumference is C=2πr
So, C=2(3.14)(9)
C=56.52 answer
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
A 2-column table with 6 rows. Column 1 is labeled x with entries 25, 28, 30, 31, 33, 40. Column 2 is labeled y with entries 7.5, 6, 5.5, 5, 4.5, 4.5.
The regression line shows a:
negative trend line with a strong relationship.
negative trend line with a weak relationship.
positive trend line with a strong relationship.
positive trend line with a weak relationship.
Finding the correlation coefficient, it is found that the regression line shows a:
negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.
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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures the correlation between two variables, assuming values between -1 and 1.
If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.
Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.
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Find a coterminal angle between 0° and 360°.
780
for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.
An arithmetic sequence is defined as follows:
a₁ = 92
a₁ = a₁-1-8
Find the sum of the first 28 terms in the sequence.
Answer:
-448
Step-by-step explanation:
The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.
Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d
__
series sumUsing the above formula with a1=92, d=-8, and n=28, the sum is ...
S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448
The sum of the first 28 terms of the sequence is -448.
The lines below are parallel. If the slope of the green line is -3, what is the slope of the red line?
Answer:
The lines would be equal, meaning the slope of the red line is also -3.
Step-by-step explanation:
SIMPLE:
Parallel lines have the same slope.
Hola alguien me podría ayudar con este problema :< porfa
Answer:
8= 24b
8/8=24b/8
b=3
Step-by-step explanation:
Based on my own learning
y=-3³ +4
step by step of the rules and formula of this equation
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
The solution to the given system of equation is (4, 4)
Factorizing quadratic functionsFrom the solved steps, the final quadratic functions is given as;
x^2 - 8x + 16 = 0
Factorize to have;
x^2 - 4x - 4x + 16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0
x = 4 and 4
Hence the solution to the given system of equation is (4, 4)
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solve the following absolute value equation.
−8 − 2 |5X – 17| = −14
If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to
-8 - 2 (5x - 17) = -14
-8 - 10x + 34 = -14
-10x = -40
x = 4
If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have
-8 - 2 (-5x + 17) = -14
-8 + 10x - 34 = -14
10x = 28
x = 2.8
What is the solution to this equation?
X/-3=-6
A. x = -2
x|
OB. x=2
OC. x = 18
OD. x= -18
Answer:
Choice C
Step-by-step explanation:
Given equation,
X/-3=-6To Find:
value of xSolution:
=>x/-3=-6
Transpose 3 from LHS to RHS,make sure to change the sign from ÷ to *.
=>x = -6*-3
=>x = 18
Hence, the value of x is 18.
Choice C is correct & accuratethe function f and g are defined follows. f(x)= x+6/x^2-12x+36 g(x) = x+7/x^2-49 for each function, find the domain. write each answer as an interval or union of intervals
Domain of f(x) is {x | x ≠ 6} and Domain of g(x) is {x | x ≠ +7 and x ≠ +7}.
How to find the domain of a function?The domain of a function is the set of all input values that make the function possible.
Now, for f(x) = (x + 6)/(x² - 12x + 36)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 12x + 36 = 0
Solving this using quadratic formula gives; x = 6. Thus, domain of f(x) is;
Domain = {x | x ≠ 6}
Now, for g(x) = (x + 7)/(x² - 49)
To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;
x² - 49 = 0
Solving this using quadratic formula gives; x = +7 or -7. Thus, domain of g(x) is; Domain = {x | x ≠ +7 and x ≠ +7}
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Carlos invests $4540 at a rate of r% per year compound interest.
At the end of 10 years he has earned $1328.54 in interest.
Calculate the value of r.
Answer:
Initial balance$1000
interest rate 8%
Term 20yrs
Step-by-step explanation:
The final balance is $4,926.8.The total compound interest is $3,926.8.
The value of r is 2 %.
What is simple & compound interest?Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.
Given:
Principal(P)= $4540
Rate = ?
Time=10 years
CI=$1328.54
We have to find the value of r.
According to given question we have
By the use of compound interest we have
[tex]CI=p((1+\frac{r}{100} )^{10} -1)\\\\1328.54 =4540 ((1+\frac{r}{100} )^{10} -1)\\\\\0.292= ((1+\frac{r}{100} )^{10} -1)\\[/tex]
After simplifying we get,
r=2 %
Therefore, the value of r is 2 %.
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Pi/6 is the reference angle for:
A 13pi/6
B 5pi/6
C 3pi/6
D 8pi/6
Check all that apply
will give brainliest
geometry
50 points
The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.
How to determine the perimeter and the area of a composite figure
In this case we have a composite figure formed by six triangles and two rectangles. The perimeter is the sum of the side lengths and the area is the sum of the areas of the triangles and rectangles. The perimeter of the entire figure is described below:
p = AB + BC + CD + DE + EF + FG + GA
p = 5√2 + √10 + √10 + 5 + √10 + 5 + 2√10
p = 10 + 5√2 + 5√10
p = 10 + 5 · (√2 + √10)
p = 10 + 5√2 · (1 + √5)
p = 5 · [2 + √2 · (1 + √5)]
And the area of the composite figure is determined by the following expression:
A = 0.5 · (3) · (1) + (3) · (4) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 2 · (3) · (1) + (3) · (4) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 33.5
The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.
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Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (8 points) Part B: Find (a - b) (x). Show your work. (8 points) Part C: Find (a - b)(x). Show your work. (9 points) Part D: Find a(b(x)]. Show your work. (10 points)
a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]
b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]
If f(x) = 2x² +5 and g(x)=x2-2, find (f-g)(x).
A. x^2+3
B. 3x^2+3
C. 3x^2+7
D. x^2+7
Answer:D. x^2+7
Step-by-step explanation:
If f(x) = 2x² +5 and g(x)=x2-2, find (f-g)(x).A. x^2+3B. 3x^2+3C. 3x^2+7D. x^2+7
The diagram shows a right angled triangle. 7cm and 11cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
The size of the unknown angle "x".
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question we'll have to use cos because hypotenuse and adjacent is given.
[tex]\large\boxed{cos(A)=\frac{adj}{hyp}}[/tex]
Substitute according to the formula.
[tex]cos \: x= \frac{7}{11}[/tex]
We'll have to use cos inverse.
[tex]x={cos}^{-1}(\frac{7}{11})[/tex]
[tex]x=50.47880364[/tex]
[tex]\large\boxed{x=50.5°}[/tex]
Therefore, the size of the unknown angle "x" is 50.5°
The required measure of the angle x is given as 50°.
Given that,
The diagram shows a right-angled triangle. 7cm and 11cm and x degrees.
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,
Apply cosine equation,
cosx = 7 / 11
cosx = cos50
x = 50°
Thus, the required measure of the angle x is given as 50°.
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Question 3
Points 2
Answered On: 06/15/2022 09:40 AM
A boa constrictor slithers 1/3 feet in 3/4 second. What is its speed in terms of
feet per second?
Reset
Reset
comp
Answer:
18 inches = 1.5 feet
8 inches = 2/3 foot
y = 1.5 + (2/3)x
Find the area of ABCD. Type the answer in the box below
Answer:
The Area is 25
Step-by-step explanation:
You will need distance formula for this questions
for AD, (0,4) and (4,7)
The formula is here
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
which gives you
[tex]\sqrt{\left(4-0\right)^2+\left(7-4\right)^2} = 5[/tex]
for AB
(0,4),(3,0)
[tex]\sqrt{\left(3-0\right)^2+\left(0-4\right)^2}=5[/tex]
The answer will be 5*5, which is 25
Evaluate 2Tu when T =5 and u=9
Answer:
2Tu = 90
Step-by-step explanation:
You can substitute the values T = 5 and u = 9 into the expression to get: 2 × 5 × 9 which is 90 (2 × 45 = 90)
Hope this helps!
The final result is 90 when T = 5 and u = 9.
Here, we have to evaluate 2Tu when T = 5 and u = 9, we substitute the values of T and u into the expression and perform the operations accordingly.
Given expression: 2Tu
T = 5
u = 9
Now, let's substitute the values:
2 * 5 * 9
Next, perform the multiplication:
2 * 5 = 10
10 * 9 = 90
So, when T = 5 and u = 9, the value of 2Tu is 90.
We get, to evaluate 2Tu, we first multiply T and u together, and then multiply the result by 2.
In this case, we have T = 5 and u = 9.
So, we perform the following steps:
Multiply T and u: 5 * 9 = 45
Multiply the result by 2: 2 * 45 = 90
Thus, the final result is 90 when T = 5 and u = 9.
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A circle has a radius of 3 units and is centered at (-2,-2)) Write the equation of this circle
Answer:
The area is: 28.26 units^2
The diameter is: 18.84 units
Step-by-step explanation:
Area A=pie(3.14)R^2
Diameter D=pie(3.14)R2
Joshua has a ladder that is 15 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.2 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78°.
Will the ladder be safe at this height? Show your work and label the diagram to support your answer.
Yes the ladder be safe at this height.
What is angle of elevation?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given:
ladder = 15 ft long.
top of the ladder is 14.2 ft above the ground.
Using trigonometry,
sin x = 14.2/15
sin x = 0.947
x= 71.262°
As, 78 > 71.262°
Hence, it would be safe to use the ladder of 15 ft long.
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e^In(8) use the properties of natural logarithms to simplify the expression
[tex]\text{Let,}\\\\~~~~~~~~~y = e^{\ln 8}\\\\\implies \ln y = \ln \left( e^{\ln 8} \right)\\\\\implies \ln y = \ln 8( \ln e)\\\\\implies \ln y = \ln 8\\\\\implies y = 8\\\\\implies e^{\ln 8} = 8\\\\\text{Hence,}~~ e^{\ln 8 } = 8[/tex]
Answer:
8
Step-by-step explanation:
One of the properties of natural logs is that
[tex]e^{lnx} = x\\\\So,\\\\e^{ln8} = 8[/tex]
Please HELP what are the lengths
What is the perimeter of this composite figure?
4 cm
6 cm
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
x>3
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she strikes it. How long does Marsha have to
react, before the volleyball hits the ground? Round your answer to two decimal
Answer:
0.98 seconds
Step-by-step explanation:
We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.
__
motion equationThe general form of the equation of height for ballistic motion is ...
[tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]
The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.
For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...
h(t) = -16t² +10.5t +5
__
reaction timeMarsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...
a = -16b = 10.5c = 5The solution is ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]
The positive solution is ...
t ≈ 0.976327 ≈ 0.98
Marsha has about 0.98 seconds to react before the volleyball hits the ground.
_____
Additional comment
After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.
according to the graph what is the value of the constant in the equation below
Answer:
6
Step-by-step explanation:
hope it helps
please help i need it
Answer:
[tex]4\frac{7}{8}[/tex]
Step-by-step explanation:
The three heaviest eggs are between [tex]1\frac{1}{2}[/tex] and [tex]1 \frac{3}{4}[/tex]
[tex]1\frac{1}{2} +1 \frac{3}{4}/2[/tex][tex]1+1+\frac{2}{4}+\frac{3}{4}/2[/tex][tex]2\frac{5}{4}/2[/tex][tex]1\frac{5}{8}[/tex][tex]1\frac{5}{8}*3=\frac{13}{8}*3=\frac{39}{8} = 4\frac{7}{8}[/tex]Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
A rectangular parking lot has a length that is 5 yards greater than the width the area of the parking lot is 300 yd.² find the length and width
Answer:
width=5yd and length=10yd
Step-by-step explanation:
To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)
We know that Area (A) = Length (L) * Width (W)
You know Area (A) = 50 sq. yds.
You don't know anything about the width, so let's just say Width (W) = x
And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd
Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.
Well, now just plug in. What does W equal and L equal?
From above we plug in and can say that 50 sq yd = x * (x + 5 yd).
Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).
Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:
0 = x^2 + 5x - 50
Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.
I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that
0 = x^2 + 5x - 50 = (x + 10)(x - 5)
And so you know that x = -10 or 5.
Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.
mark me brainlistSimplify the following
(3a 2b ×2a 6b)
Answer:
3a 2b ×2a 6b = 72a²b² = 72× (ab)²Step-by-step explanation:
3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b) [commutative property]
= (6×ab) × (12×ab) [associative property]
= (6×12) × (ab×ab) [commutative + associative]
= (72) × (ab)²
= 72× (ab)²
= 72a²b² [exponent property]