The length of the major arc WYX is (11/3)π inches or 11.62π inches.
What are the major and minor arcs of a circle?
A minor arc is an arc that is smaller than a semicircle, which means its central angle measures less than 180 degrees and a major arc is an arc that is larger than a semicircle, which means its central angle measures more than 180 degrees.
Since the measure of angle ZVX is 90 degrees (since VX is a radius of the circle), we know that the measure of angle ZVW is 170 - 90 = 80 degrees.
Now, we can use the fact that the sum of the measures of angles in a triangle is 180 degrees to find the measure of angle VWX:
mVWX = 180 - mZVW - mZVX
mVWX = 180 - 80 - 90
mVWX = 10 degrees
Therefore, the length of the minor arc WY is 10/360 times the circumference of the circle:
length of minor arc WY = (10/360) × 2π × 6 in
length of minor arc WY = (1/18)π × 6 in
length of minor arc WY = (1/3)π in
Since the length of the major arc WYX is equal to the circumference of the circle minus the length of the minor arc WY, we have:
length of major arc WYX = 2π × 6 in - (1/3)π in
length of major arc WYX = (11/3)π in
Therefore, the length of the major arc WYX is (11/3)π inches, or approximately 11.62π inches.
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solve: 9^2x+1=81^x-2 /3^x
Answer:
x=-4
Step-by-step explanation:
\( {9}^{2x + 1} = {81}^{x - 2} \div {3}^{x} \)
\( {3}^{2(2x + 1)} = {3}^{4(x - 2)} \div {3}^{x} \)
\( {3}^{4x + 2} = {3}^{4x - 2} \div {3}^{x} \)
\( {3}^{4x + 2} = {3}^{4x - 2 - x} \)
\(4x + 2 = 3x - 2\)
\(4x - 3x = - 2 - 2\)
\(x = - 4\)
(3.1x10^6) x (2.7x10^-2)
The given expression is
(3.1 x 10^6) x (2.7 x 10^-2)
It becomes
3.1 x 2.7 x 10^6 x 10^- 2
8.37 x 10^6 x 10^- 2
By applying the rule of exponents, it becomes
8.37 x 10^(6 - 2)
= 8.37 x 10^4
find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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A population numbers 12,000 organisms initially and grows by 17.5% each year.
Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a â‹… b t where
P =
A population numbers 12,000 organisms initially and grows by 17.5% each year. The growth function of the population is P = 12,000 x 1.175^t
An exponential growth function can be written as:
P = A (1 + r)ⁿ
Where:
P = quantity after n periods
n = number of periods
r = growth rate per period
A = initial quantity
In the given problem, the period is the number of years t
A = 12,000
r = 17.5% = 0.175
Hence, the growth function:
P = 12,000 (1 + 0.175)^t
P = 12,000 x 1.175^t
Your question is incomplete, but most probably your question was:
A population numbers 12,000 organisms initially and grows by 17.5% each year. Suppose P represents population, and t the number of years of growth, write the function in terms of t.
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Click “show your work” and graph the absolute value function shown below.
f(x) =|x +2| - 1
The graph of the function is attached
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = |x - 2| + 1
The equation of the graph is an absolute value graph
An absolute value graph is represented as
y = |x|
The function is shifted right by 1 unit and up by 1 unit
So, we have
f(x) = |x - 2| + 1
Next, we graph the function
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Out of the 10 people in Carla’s office, 6 regularly watch the evening news on TV. a) What fraction of the workers watch the evening news? b) What fraction DO NOT watch the news?
Answer:
3/5 watched the evening news
2/5 did NOT watch the news
Step-by-step explanation:
reduce 6/10 = 3/5
1 - 6/10 = 4/10 = 2/5
A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ŷ=5.3x – 21.9. Use the regression equation to predict the value of y when x=70.392.9Meaningless result402.1349.1
We have the equation, and we will replace the x-value to find the regression value, as follows,
\(\begin{gathered} y=5.3x-21.9 \\ y=5.3(70)-21.9 \\ y=349.1 \end{gathered}\)The answer is d.349.1
I’m confused on this question.
Answer:
The second box plot represents the data
Step-by-step explanation:
A box and whisker plot gives you the five-number summary of the data, which includes:
the minimum (lowest value of the data)
the maximum (highest value of the data)
Q1 (25% of the data lies below this point)
Q3 (75% of the data lies below this point), and
the median (the middle of the data).
The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively. From the data, we see that the minimum is 5 and the maximum is 10.
Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.
El mayor es Novecientos mil cuatrocientos ochenta y nueve , y cuarenta mil dos
El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.
Por otro lado, el número "cuarenta mil dos" se representa como 40,002.
Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.
Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.
Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.
En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.
Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.
Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.
En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.
Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).
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Sarah is tying bows that require a ribbon that is 2 1/5 inches long. If she needs to make 15 bows. What is the total amount of ribbon she will need?
Answer:
Sarah will need 33 inches of ribbon
Step-by-step explanation:
Multiply 2 1/5 or 2.20 (inches) by 15 (bows)
If a three-digit number is divided by 5 or by 6, remainder is 1 in each case. What is the least such three-digit number?
Answer:
The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.
Step-by-step explanation:
This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x-30 > 30
Answer:
\(x > 60\)
Step-by-step explanation:
\(x-30 > 30\)
\(x > 60\) (add 30 onto both sides of the inequality)
This data set represents the widths in yards of pieces of fabric used by a sewing group.
What is the mean of this data set?
{1 1/3, 1/4, 2/3, 1/2, 1 1/4}
Enter your answer as a fraction in simplest form in the box.
Answer:
\( \frac{4}{5} \)
Simplify this expression 10⁰
Answer:
0
Step-by-step explanation:
10 to the power of zero is zero
Answer:
1
Step-by-step explanation:
Anything with an exponent of zero always equals 1
HELP ASAP
FIRST GET BRAINIEST
I LOVEEE ALL YALL !!!!
the last net, it's the only one with a rectangle and 4 triangels
Answer:
D
Step-by-step explanation:
Again all it takes is for you to image wat the shape would fold into.
Hope this helps!
Brainliest please!
Please fully rate!
Have a great day!
Happy to help! :)
Can someone please help, ty!!
Please help solve this
Answer:
BC~=AD (GIVEN )
CBA=CDA (altanate angles BC=AD)
C=A (altanate angles (BC=AD)
AAS
brainyliest please
The arc length of this circle is 9.42 inches. Determine the length of the radius.PC90ABComplete your work in the space provided.
We know that:
\(S=\theta\times r\)Then:
\(r=\frac{S}{\theta}\)So:
\(90\degree\times\frac{\pi}{180\degree}=1.571rad\)Now:
\(r=\frac{9.42in}{1.571rad}=5.996\text{ in}\)Can you please answer this question?
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $113,100?
Answer:
850
Step-by-step explanation:
Current profit per year = $ 20
Number of subscribers = 3000
For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.
So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)
Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:
Total profit = Number of subscribers x Profit per each subscriber
Total profit = (3000 + x)(20 + 0.01x)
We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:
Using quadratic formula, we can solve this equation as:
x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.
Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725
Lyla goes out to dinner with her freinds where the subtotal is $23.89. A 7% tax and 18% tip is added to the subtotal. How much did she pay in total?
Lyla pays $ 24.14 in total.
What is the total amount?
To add two or more numbers and determine the final total, use the sum. A series of any form of numbers, known as addends or summands, is added; the outcome is their sum or total.
Here, we have
Given: Lyla goes out to dinner with her friends where the subtotal is $23.89. A 7% tax and 18% tip are added to the subtotal.
we have to find out how much did she pay in total.
= $23.89 + 7% + 18%
= $23.89 + 7/100 + 18/100
= $23.89 + 0.07 + 0.18
= $ 24.14
Hence, Lyla pays $ 24.14 in total.
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Which expression is always equivalent to sin x when 0° < x < 90°?
(1) cos (90°- x)
(3) cos (2x)
(2) cos (45° - x)
(4) cos x
The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1
To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.
Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.
Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.
On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.
Option 1 is correct.
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i need help with graphing
Answer:
Pls mark brainleist
Step-by-step explanation:
Graphing formula: y = mx + b
y and x always stay in the equation
m is the slope
and b is the y intercept
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The length KL is 8 units
The value of x is undefined
The length KL is 12 units
Calculating the length KLFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
DK = 8
A rhombus is a quadrilateral with all sides equal.
So, we have
KL = 8
Calculating the value of xHere, we have
SKAL = 2x - 8
There is no point S on the rhombus
This means that
x = undefined
Calculating the length KLHere, we have
DM = 5y + 2 and DK = 3y + 6
A rhombus is a quadrilateral with all sides equal.
So, we have
5y + 2 = 3y + 6
Evaluate
2y = 4
Divide
y = 2
So, we have
KL = 5 * 2 + 2
KL = 12
Hence, the length KL is 12 units
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What is the sum?
7
7
8
+
4
3
8
PLEASE HELP Evaluate: (-2)5
Answer:
-10
Step-by-step explanation:
Given f (x) = 4x-3, g(x) = x^3 +2x
Find (f-g) (4)
Answer:
\((f-g)(4) = -59\)
Step-by-step explanation:
We are given the two functions:
\(f(x)=4x-3\text{ and } g(x) = x^3 +2x\)
And we want to find the value of:
\((f-g)(4)\)
Recall that this is equivalent to:
\((f-g)(4) = f(4) - g(4)\)
Find f(4):
\(f(4) = 4(4)-3 = 13\)
And find g(4):
\(g(4) = (4)^3 + 2(4) =72\)
Substitute:
\((f-g)(4) = (13)-(72)\)
And subtract. Hence:
\((f-g)(4) = -59\)
Step-by-step explanation:
I love this question!
So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.
Subtracting First
The first option is taking f(x) and g(x) and subtracting them, then introducing the number.
The calculation:
f(x) - g(x)
Substitute.
4x - 3 - (x^3 + 2x)
Multiply out the negative.
4x - 3 - x^3 - 2x
Rewrite.
-x^3 + 4x - 2x - 3
Simplify.
-x^3 + 2x - 3
Then, replace x with 4.
-(4)^3 + 2(4) - 3
Simplify.
-64 + 8 - 3
Add.
-59
Making x = 4 first
Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.
f(x) = 4x - 3
f(4) = 4(4) - 3
f(4) = 16 - 3
f(4) = 13
Then find g(4):
g(x) = x^3 + 2x
g(4) = (4)^3 + 2(4)
g(4) = 64 + 8
g(4) = 72
Then, subtract these two:
f(4) - g(4) = 13 - 72
f(4) - g(4) = -59
Answer:
Either way, the answer is -59
In this picture, the measure of angle ois 1 radian.
A. True
B. False
Answer: the answer is true I think
Step-by-step explanation:
Dertermine the quotient of 3/7 divided by 2/3 pls help
Answer: 9/14
Step-by-step explanation:
hope this helps!
On a test of 40 problems joe got 50% of this prolem correct. How many did he get correct?
Answer:
20 questions
Step-by-step explanation:
50% of 40 is 20