Ashely is studying circle O, shown below.She wrote the steps below.Step 1: θ/2pi= s/2pirStep 2: θ(2pir)/2piStep 3: s= θrwhat did Ashley derive?A. that all circles are similarB. that a central angle has the same measure as the arc it subtendsC. the formula for arc lengthD. the formula for the area of a sector of a circle
the steps that she made are to derivate the formula dor arc length.
Find the nth term for the following question: -5,-2,3,10,19
Answer:
\(T_n = 2n - 1 + T_{n-1}\)
Step-by-step explanation:
Given
\(Sequence: -5,-2,3,10,19\)
Required
Find the nth term
We have:
\(T_1 = -5\)
\(T_2 = -2 = 3 - 5 = 3 + T_1\)
\(T_3 = 3 = 5 - 2 = 5 + T_2\)
\(T_4 = 10 = 7 + 3 = 7 +T_3\)
\(T_5 = 19 = 9 + 10 = 9 + T_4\)
This gives:
\(T_2 = 3 + T_1 = 4 - 1 + T_1\)
\(T_3 = 5 + T_2 = 6 - 1 + T_2\)
\(T_4 = 7 +T_3 = 8 - 1 + T_3\)
\(T_5 = 9 + T_4 = 10 - 1 + T_4\)
---
Solving further, we have:
\(T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1\)
\(T_3 = 6 - 1 + T_2 = 2 * 3 + T_2\)
\(T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3\)
\(T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4\)
Following the above sequence: the nth term is:
\(T_n = 2n - 1 + T_{n-1}\)
Find non-invertible matrices A,B such that A+B is invertible. Choose A,B so that (1) neither is a diagonal matrix and (2) A,B are not scalar multiples of each other.A = [_____ _____][_____ _____]B = [_____ _____][_____ _____]
Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:
Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is
\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)
Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)
Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:
\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)
Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:
det(A+B) = (1)(1) - (1)(1) = 0
Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.
Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).
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A chemical plant manufactures fertilizer. A particular fertilizer recipe calls for 2 units of potash for every 3 units of urea. The potash is shipped to the plant in modular pallets with dimensions (x+6) by (x-2). The urea is shipped to the plant in modular pallets with dimension (x-2) by (x+1). Assuming equal molar density in each product, calculate x such that there is no material left over after manufacturing the fertilizer.
The value of x such that no meterial left over after manufacturing the fertilizer is 1
How to calculate for x?The area of a place is the floor space occupied by an object. we are to determine the value of x in the length and width of the floor to be used by the manufacturer
The givn parameters are the use of
2 units of potash and
3 units of urea.
Recall that the area of a rectangular floor space is (L*W).
This implies that (x+6)(x-2)=2
x²-2x+6x-12=2
x²+4x-10=0 .......................... (1)
Also, for the urea
Area= (x-3)(x+1)=3
x²+x-2x-2=3
x²-x-2-3=0
This implies that
x²-x-5=0 .............................(2)
Assuming equal molar density in each product,
equations 1 and 2 are equal
x²+4x-10=x²-x-5
Collecting like terms
x²-x+4x+x-10+5=0
5x-5=0
5x=5
x=1
Therefore, assuming equal molar density in each product the value of x=1
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This graph shows how fast a commuter train travels on its route in an urban area. What is the meaning of the point with an x-coordinate of 4
The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.
From the graph, the x coordinate 2, have a y coordinate of 120. Hence:
The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.
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I need the correct answer please I will give you the options as well
Step 1:
Write the coordinates of the vertices of the quadrilateral PQRS.
P = (-3,7)
S = (-3, 7)
R = (4, -2)
Q = (4,12)
Step 2:
To shift the figure to the right by 6 units.
P' = (-3+6,7) = (3,7)
S' = (-3+6, -7) = (3,-7)
R' = (4+6, -2) = (10 . -2)
Q' = (4+6,12) = (10, 12)
Step 3:
Rule : When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.
P'' = (3,7) = (7 , -3)
S'' = (3,-7) = (-7 , -3)
R' = (10 , -2) = (-2 , -10)
Q' = (10, 12) = (12 , -10)
Final answer
P' 7, -3
S' = (-77,37)
R' = (-2 , -10)
Q' =(-12, 10)
Determine the surface area and volume
The surface area of the cone is: 213.66 cm²
The volume of a cone is: 7.33 cm³
How to find the surface area and volume?The formula for the surface area of a cone is:
T.S.A = πrl + πr²
where:
r is radius
l is slant length
From the diagram and using Pythagoras theorem,we have:
l = √(7² + 5²)
l = √74
Thus:
TSA = (π * 5 * √74) + (π * 5²)
TSA = 213.66 cm²
Formula for the volume of a cone is:
V = ¹/₃πr²
V = ¹/₃π * 7
V = 7.33 cm³
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Sarah’s grades on her first four math quizzes are 80, 86, 82, and 94. What grade on the fifth quiz will give her a quiz average of exactly 88
Answer:
Sarah would need to get a 98 on her fifth quiz to get her average to be an 88.
Step-by-step explanation:
Sarah needs to get a 58 on the fifth quiz for her quiz average to be exactly 88.Let x be the grade on the fifth quiz. The average of all five quizzes is 88. So we have: (80 + 86 + 82 + 94 + x)/5 = 88
80 + 86 + 82 + 94 + x = 440
x = 440 - 80 - 86 - 82 - 94 = 58
Therefore, Sarah needs to get a 58 on the fifth quiz for her quiz average to be exactly 88.To solve such type of questions, we can follow these steps:Read the problem carefully and identify the given information. In this case, we are given that Sarah's grades on her first four math quizzes are 80, 86, 82, and 94. We are also given that the average of all five quizzes is 88.
Formulate an equation. We can formulate the equation as follows:
Average = (Sum of all grades) / (Number of grades)
88 = (80 + 86 + 82 + 94 + x) / 5
Solve the equation. We can solve the equation by substituting the known values. This gives us:
88 = (80 + 86 + 82 + 94 + x) / 5
440 = 80 + 86 + 82 + 94 + x
x = 440 - 80 - 86 - 82 - 94 = 58
Answer the question. The question is asking what grade Sarah needs to get on the fifth quiz. We know that x is the grade on the fifth quiz, so the answer is 58.
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How do you estimate the intercepts of the graph of the function?
By using the concept of intercept the method of estimation of intercepts has been described below
What are intercepts?
The distance from the origin to the point where the graph cuts the x axis is the x - intercept of the graph
The distance from the origin to the point where the graph cuts the y axis is the y - intercept of the graph
There are two intercepts of a graph, x - intercept and y - intercept
x-axis is the horizontal axis and y axis is the vertical axis of the graph
Let the function be y = f(x)
To find x intercept, we have to substitute y = 0 and solve for x
The value of x will give the x intercept
To find y intercept, we have to substitute x = 0 and solve for y
The value of y will give the y intercept.
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What is the value of this expression: (−2)3 x 30 x (−4)−2
0
-3/2
-3/4
-1/2
3/2
3/4
1/2
The given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
In the above question, the following mathematical expression is given :
(−2)3 x 30 x (−4)(−20)
We need to find the value of the given expression by solving it using the BODMAS rule
According to the rule, first we'll solve the multiplication then subtraction
Therefore, we get
(−2)3 x 30 x (−4)(−20)
(-6) x 30 x (-)(-)80
We know, that (-) x (-) = +
and (-) x (+) = (-)
Therefore, we get
(-6) x 30 x (-)(-)80
(-6) x 30 x 80
-6 x 2400
- 14400
Hence, the given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
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10
Use the cards 1-10. Draw cards without replacing.
A.
B.
CÓ Ư
C.
D.
E.
F.
P(6, then 1)
P(even, then 5)
P(8, then odd)
P(3, then prime)
P(prime, composite)
P(even, then 3, then 5)
4
8
2
6
9
3
10
A. P(6, then 1) = 1/90
B. P(even, then 5) = 1/18
C. P(8, then odd) = 1/18
D. P(3, then prime) = 2/45
E. P(prime, composite) = 4/15
F. P(even, then 3, then 5) = 1/144
Given:
Total number of cards: 10
A. P(6, then 1):
P(6, then 1) = 1/10 x 1/9
= 1/90
B. P(even, then 5):
Number of favorable outcomes: 5 x 1 = 5
P(even, then 5) = 5/10 x 1/9
= 1/18
C. P(8, then odd):
Number of favorable outcomes: 1 x 5 = 5
P(8, then odd) = 1/10 x 5/9
= 1/18
D. P(3, then prime):
Number of favorable outcomes: 1 x 4 = 4
P(3, then prime) = 1/10 x 4/9
= 2/45
E. P(prime, composite):
Number of favorable outcomes: 4 x 6 = 24
P(prime, composite) = 4/10 x 6/9
= 4/15
F. P(even, then 3, then 5):
Number of favorable outcomes: 5 x 1 x 1 = 5
P(even, then 3, then 5) = 5/10 x 1/9 x 1/8
= 1/144
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Solve the linear equation using equivalent equations to isolate the variable. Express your solution as an integer as a simple fraction or as a decimal number.
t-5=9
The solution to the given linear equation is t = 14
Solving Linear equationsFrom the question, we are to solve the given linear equation.
From the given information,
The given linear equation is
t - 5 = 9
To solve the equation, we will use the addition property of equality
Solving the equation
t - 5 = 9
Add 5 to both sides of the equation
t - 5 + 5 = 9 + 5
Simplify
t = 14
Hence, the solution is t = 14
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a 24 foot tall streetlight casts a shadow that is 18 feet long. how long of a shadow is cast by a nearby parking meter post that is 4 feet high?
9514 1404 393
Answer:
3 ft
Step-by-step explanation:
The post is 4/24 = 1/6 as tall as the streetlight, so we expect its shadow to be 1/6 as long as that of the streetlight:
(1/6)(18 ft) = 3 ft
The parking meter post shadow is 3 feet long.
Divide 18 by j. Then, add 7.
Which of the following expressions matches the statement above?
A.
j ÷ 18 + 7
B.
18 ÷ 7 + j
C.
18 ÷ (j + 7)
D.
18 ÷ j + 7
Sam has 26 seashells.
He collects 31 more seashells.
• Then he gives 14 seashells away.
Which equation shows the number of seashells, s, Sam has now?
Answer:
hshs7hhs7bs7bs8be8
Step-by-step explanation:
26+31= 57-14=43
Answer:
26+31-14
Step-by-step explanation:
using pendant you should answer that correctly so...
26+31=57-14 and you should get 43
in written form...
Sam has 31 seashells to his 26 seashells giving him the total of 57. Sam then gave away 14 of the 57 seashells away leaving him with 43 seashells.
hope this helps
Find the value of y.
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?
How many yards are in four and one-half miles?
7,040 yards
7,920 yards
8,448 yards
8,800 yards
Answer:
7,920
Step-by-step explanation:
I took test and got 100%
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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Question content area top
Part 1
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.11°F and a standard deviation of 0.59°F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F?
b.
What is the approximate percentage of healthy adults with body temperatures between 96.34°F and 99.88°F?
Answer:
a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.
b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.
Which of the following shows 12 more than a number, written as an algebraic expression?
A: 12 − n
B: 12 + n
C: n − 12
D: 12n
Answer:
the answer is
Step-by-step explanation:
So 12 more than N would be 12 + N.
Answer:
b) 12 + n
Step-by-step explanation:
The statement is,
→ 12 more than a number.
Now equation will be,
→ 12 + n
≈ (or) n + 12
So, option (b) is correct.
b) The completed construction of a regular hexagon is shown below. Explain why AACF is a 30°-
60°-90° triangle. (10 points)
ACF is a 30º-60º-90º triangle because of the following:
1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)
1 → short leg
2 → hypotenuse
\(\sqrt{3}\) → long leg
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
Using Pythagorean theorem.
\(a^2 + b^2 = c^2\)
\(1^2 + b^2 = 2^2\)
\(b^2 = 2^2 - 1^2\)
\(b^2 = 4 - 1\)
\(b^2 = 3\)
\(\sqrt{b^2} = \sqrt{3}\)
\(b = \sqrt{3}\)
Paige makes bracelets and sells them online for $15 and $20. She buys all of her supplies in bulk. The table shows her sales for the last 3 months. During the 3-month period represented by the table, she ordered supplies twice. Each
A factory uses 3/8 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used ¾ of a barrel of raisins. How many batches of granola bars did the factory make yesterday?
Answer:
2
Step-by-step explanation:
3/4= 6/8 if you need 3/8 for one batch you made two batches. found it on brainly
The graph below is a polynomial function in the form f(x)=(x−a)(x−b). Find suitable real numbers a and b that describe the graph.
For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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Keeping car tires inflated is essential to safe driving. For one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately Normal, with a mean of 35 psi and a standard deviation of 2 psi. What percentage of tires are inflated to a pressure between 33.5 and 36 psi?
Find the z-table here.
22.55%
46.48%
53.52%
77.45%
Answer:
Step-by-step explanation:
The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:
Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ
where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35=−0.75
This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35=0.5
This means that 36 psi is 0.5 standard deviations above the mean.
Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.
Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649
This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.
Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%
The distance travelled by a car during 10 minutes moving with a speed of 10 meter per second is
Answer:6000 meters
Step-by-step explanation:
10 x 60=600
600 x 10=6000
2. A(n) is NOT an example of an agreement. (1 point)
O lease
O month-to-month
O annual
O fine print
An Annual is not an example of an agreement.
Solve Two-thirds x minus one-fifth greater-than 1. x >
Answer:
x > 9/5Step-by-step explanation:
The above statement is written as
\( \frac{2}{3} x - \frac{1}{5} > 1\)
Multiply through by the LCM of 3 and 5 which is 15
So we have
\(15 \times \frac{2}{3} x - 15 \times \frac{1}{5} > 15 \\ \\ 10x - 3 > 15 \\ \\ 10x > 15 + 3 \\ \\ 10x > 18 \\ \\ x > \frac{18}{10} \\ \\ x > \frac{9}{5} \)
Hope this helps you
Answer: The answer is x > 9/5.
Hope this helps!! Also please put as brainlist answer really need it would really aprecite it please.