Another representation, in polar coordinates, of the point (157) is -18 6 117 6
Answers
Recall that in polar coordinates:
\((r,\theta)=(-r,\theta+\pi)\text{.}\)1) Notice that:
\(\frac{11\pi}{6}=\frac{5\pi+6\pi}{6}=\frac{5\pi}{6}+\pi\)2) Using the first equation we get:
\((1,\frac{5\pi}{6})=(-1,\frac{5\pi}{6}+\pi)=(-1,\frac{11\pi}{6})\text{.}\)Answer: -1.
Related Questions
What are the coordinates of R' for the dilation D(0.5. p)(PQRS)?
Answers
Answer:
\(R' = (-1,-0.5)\)
Step-by-step explanation:
See attachment for complete question.
From the attachment:
\(P = (-3,-3)\)
\(R = (1,2)\)
Dilation:
\(D_{(0.5,P)}\)
Required
Determine R'
First, subtract the coordinates of P from R. This means that R is measured from P.
\(R = (1-(-3),2-(-3))\)
\(R = (1+3,2+3)\)
\(R = (4,5)\)
Next, apply dilation factor 0.5
\(R' = R * 0.5\)
\(R' = (4,5) * 0.5\)
\(R' = (4* 0.5,5* 0.5)\)
\(R' = (2,2.5)\)
Lastly, measure R' from the origin by adding the coordinates of P to R'
\(R' = (2+(-3),2.5+(-3))\)
\(R' = (2-3,2.5-3)\)
\(R' = (-1,-0.5)\)
Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.
The coordinate of the R' after the dilation is (-1,-0.5)
What is dilation?Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.
Given information-
The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).
The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,
\(Q'=Q-P\\Q'=(-3-(-3), 2-(-3))\\Q'=(0,5)\)
Similarly,
\(R'=R-P= (1-(-3),2-(-3))=(4,5)\\P'=P-P=(-3-(-3), 3-(-3)=(0,0)\\S'=S-P=(1-(-3),-3-(-3))=(4,0)\\\)
As the dilation factor is 0.5. Thus, the point of Q is,
\(Q"=(0.5)\times(0,5)=(0,2.5)\)
Similarly,
\(R"=(0.5)\times(4,5)=(2,2.5)\\P"=(0.5)\times(0,0)=(0,0)\\S"=(0.5)\times(4,0)=(2,0)\\\)
Add the points P back, to the above coordinate plane to get the dilation point. Thus the point of Q is,
\(Q'''=(0,+(-3), 2.5+(-3))\\Q'''=(-3,-0.5)\)
Similarly,
\(R'''=(2+(-3),2.5+(-3))=(-1,-0.5)\\P'''=(0+(-3),0+(-3))=(-3,-3)\\S'''=(2+(-3),0+(-3))=(-1,-3)\\\)
Thus the coordinate of the R' after the dilation is (-1,-0.5)
Learn more about the dilation here;
https://brainly.com/question/10253650
Planes A and B are shown.
m
n
B
MA
If a new line, p, is drawn parallel to line /, which
statement is true?
O
Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line /
O Line p must be drawn in the same plane as line n.
Answers
The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, so option C is correct.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
The given planes are A and B,
A new line, p, is drawn parallel to line l,
Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.
To know more about the line:
https://brainly.com/question/2696693
#SPJ1
The image of the remaining question is attached below.
For questions 1 – 6, find the area of the circle to the nearest hundredth.
Any help will be appreciated thank you!
Answers
Answer:
1. 232.35 cm²
2. 52.81 cm²
3. 373.25 cm²
Step-by-step explanation:
1. Area of circle = πr²
radius (r) = 8.6
Area = π*8.6²
Area = 232.35 cm²
2. Area of circle = πr²
radius (r) = 4.1 cm
Area = π*4.1²
Area = 52.81 cm²
3. Area of circle = πr²
radius (r) = 10.9 cm
Area = π*10.9²
Area = 373.25 cm²
7
5
+
3
2
1 A 3 B(4,0) 6 7
12,0
-7
-5
D(1,2)
C(5-2)
.
Which of the following is the image of C after a rotation of 180° about the origin?
(-5.2)
0 (-5,-2)
(-2.5)
Answers
Answer:
can you take a picture of you problem
PLS HELP The histogram displays donations in dollars to a charity. A histogram titled Donations to Charity In Dollars with the x-axis labeled Donations. The x-axis has intervals of 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Number of Donations and starts at 0 with tick marks every one unit up to 5. There is a shaded bar above 10 to 19 that stops at 4, above 20 to 29 that stops at 3, above 30 to 39 that stops at 1, and above 50 to 59 that stops at 1. There is no shaded bar for 40 to 49. Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 49. This might happen if the charity suggested donation minimum of $35 and donors followed that.
The data is skewed, with a maximum range of 49. This might happen if the donations were only allowed in cash and many donors did not have much cash on them.
The data is bimodal, with a maximum range of 49. This might mean that the most popular amounts to donate were between 10 and 19 and 51 and 59 dollars.
The data is symmetric, with a maximum range of 59. This might happen if everyone donated a percent of their salaries.
Answers
Based on the given histogram, the data is skewed with a maximum range of 49.
This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.
One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.
Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.
Learn more about histogram here:
https://brainly.com/question/30354484
#SPJ1
Write an exponential function in the form y=ab^x that goes through points (0,10) and (9, 5120).
Answers
The form \(y=ab^x\) has two unknowns, namely \(a\) and \(b\), so you would need to have two points to find the equation (which you do). Once you have your two points, you can create a system of equations by plugging in the x and y coordinates like below:
\(\left \{ {{10=ab^0} \atop {5120=ab^9}} \right.\)
One thing you may remember is that ANY number to the power of 0 equals 1. Knowing that, we can replace \(b^0\) in the first equation with 1. Since 1 multiplied by any number is just that same number, that leaves \(a\) alone in the first equation.
\(\left \{ {{10=a} \atop {5120=ab^9}} \right.\)
The first equation now tells us that \(a\) is 10, so we can plug 10 in for \(a\) in the other equation.
\(5120=10b^9\)
Now we can divide both sides by 10 to isolate \(b^9\).
\(512=b^9\)
To get \(b\) alone, we have to take the 9th root of both sides.
\(\sqrt[9]{512} =\sqrt[9]{b^9}\)
That gives us:
\(2=b\)
We can now plug \(a\) and \(b\) into the form they gave us to get:
\(y=10*2^x\)
when four coins are tossed simultaneously then what is the probability of getting two heads and two tails
Answers
Answer:
50% chance
Step-by-step explanation:
4 * 50% = 2
The ratio of blue chairs to red chairs in Ms. Vickers' class is 2 to 5. Which of the following cannot represent the total number of chairs in Ms. Vickers' class? A 14 C 28 B 20 D 35
Answers
Answer:
I would say B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Graph the line with slope -6 and y-intercept 3.
Answers
Answer:
See Attachment.
Genera Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define variables
Slope m = -6
y-intercept b = 3
Step 2: Write linear equation
Substitute into general form.
Slope-Intercept Form: y = -6x + 3
Step 3: Graph
Answer:
*See Below*
Step-by-step explanation:
It was hard to find this answer. Sorry if the graph glitches.
What percentage of the questions did he get right
Answers
Question Help When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 36 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 3000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answers
Answer:
The probability is \(P(X \le 2 ) = 0.9072\)
The company will accept 90.72% of the shipment and will reject \((100 -90.72) = 9.2\%\) of the shipment , so many of the shipment are rejected
Step-by-step explanation:
From the question we are told that
The sample size is n = 36
The proportion that did not meet the requirement is \(p = 0.03\)
Generally the probability that the whole shipment is accepted is equivalent to the probability that there is at most 2 batteries that do not meet the requirement , this is mathematically represented as
\(P(X \le 2 ) = [ P(X = 0 ) + P(X = 1 ) + P(X = 0)]\)
=> \(P(X \le 2 ) = [ [^{n}C_0 * (p)^{0} *(1-p)^{n-0} ] + [^{n}C_1 * (p)^{1} *(1-p)^{n-1} ] + [^{n}C_2 * (p)^{2} *(1-p)^{n-2} ]]\)
Here C stands for Combination (so we will be making the combination function in our calculators )
So
=> \(P(X \le 2 ) = [ [^{36}C_0 * (0.03)^{0} *(1-0.03)^{36-0} ] + [^{36}C_1 * (0.03)^{1} *(1-0.03)^{36-1} ] + [^{36}C_2 * (0.03)^{2} *(1-0.03)^{36-2} ]]\)
=> \(P(X \le 2 ) = [ [1 * 1 * 0.3340 ] + [36* 0.03 *0.3444 ] + [630 * 0.0009 *(0.355 ]]\)
=>\(P(X \le 2 ) = 0.9072\)
The company will accept 90.72% of the shipment and will reject \((100 -90.72) = 9.2\%\) of the shipment , so many of the shipment are rejected
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.) 0.84 mile(s) down the coast
Answers
Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.
As given in the question,
Nearest point on the coast is 2 miles far away
rate of the row = 1mile per hour
Walk at the rate of 3 miles per hour
Let 'x' hours be the least time to reach point Q.
Time = distance / speed
Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3
Time taken to reach the coast = (√ 4 + x² ) / 1
Total time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
To find least time dt/dx = 0
t = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )
⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )
Squaring both the side we get,
x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )
⇒3x² -24x +36 =0
⇒ x² -8x + 12 = 0
⇒ x = 2 or 6 hours
Therefore , the least time taken to reach the point Q is equal to 2 hours.
Learn more about least time here
brainly.com/question/17429465
#SPJ4
Joseph is buying tomato seed packets and cucumber seed packets at the store. He plans to buy 7 seed packets of EACH type of plant. Cucumber seed packets cost $1.89 each.
Joseph spends a total of $23.24 on all the seed packets. Which of the following equations can be used to find how much each tomato seed packet (t) costs? Select ALL that apply.
A
23.24=1.89(7)+t
B
7(1.89)+7t=23.24
C
7t=10.00
D
23.24−13.23=7t
Answers
Answer:
B
Step-by-step explanation:
Elimanited C and D
Linda walked 1/6 mi to the park and then another 4/9 mi to the cafe. How far did she walk in total?
Answers
Answer:
could you show the answers
Step-by-step explanation:
= 1/6 mi + 4/9mi
= 9 + 24
54
=33/54mi
= 9.444444...
Use the hundredth grids to answer the question.
Which equation is shown by the model?
See picture below
Answers
Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).
How to identify the correct equation?To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.
In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.
On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:
1.23 - 0.35 = 0.88 (option B).Learn more about equations in: https://brainly.com/question/29538993
#SPJ1
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.
In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was Xbar=282. We want to estimate the mean score in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation =40.
If we take many samples, the sample mean Xbar varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score in the population. What is the standard deviation of this sampling distribution?
Give your answer to four decimal places.
Answers
The standard deviation of the sampling distribution is approximately 0.3292.
What is central limit theorem?The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.
Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.
The standard deviation is given by the formula:
SD = σ/√(n)
Now, substituting the value of σ = 40, n = 147,400 we have:
SD = σ/√(n) = 40/√(147400) ≈ 0.3292
Hence, the standard deviation of the sampling distribution is approximately 0.3292.
Learn more about central limit theorem here:
https://brainly.com/question/18403552
#SPJ1
What are the square roots of 100?
Answers
Answer:
10 and -10.
Step-by-step explanation:
10 * 10 = 100
-10 * -10 = 100.
Alonzo drove 136.75 miles in 2.5 hours. How many miles did Alonzo drive in an hour?
Answers
Answer:
54.7
Step-by-step explanation:
all you have to do id divide 136.75 by 2.5
Hope tis helps
In a class of 30 students, 16 have a cat and 15 have a dog. There are 11 students who have a cat and a dog. what is the probability that a student has a dog given that they do not have a cat?
Answers
For every 5 football teams in the state, there are 9 baseball teams. What is the ratio of football teams to total sports team in the state
Answers
Answer:
5:14
Step-by-step explanation:
total number of teams is 5+9
Suppose that a sample is taken from a population whose mean value is 76.
As the sample size increases, the sample mean will approach which value?
Answers
Answer:
The sample mean will approach 76
Step-by-step explanation:
Refer to Law of large numbers (LLN) and the central limit theorem (CLT)
For random sample, with sample size n, in population with expected value μ, the sample mean converge almost surely to the expected value μ as n -> ∞
Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (0, b) at (0, 6) and blue line s intercepts (c, 0) at (2, 0) and (0, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality Which step of the proof contains an error? A. Step 5 B. Step 6 C. Step 2 D. Step 4
Answers
Answer:
transitive property
Step-by-step explanation:
Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?
Answers
785.4 cubic feet
Step-by-step explanation:Step 1: Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Step 2: For Emma’s cylindrical storage tank, the radius of the base is 5 feet. Substitute this value in the formula and calculate the area of the base, which is equal to: A = π*5² = 78.54 square feet.
Step 3: Now we need to calculate the volume of the cylindrical storage tank. The volume of a cylinder is calculated by: V = π*r²*h, where r is the radius of the circle and h is the height of the cylinder. For Emma’s tank, the height is 10 feet. Substitute these values in the formula and calculate the volume, which is equal to: V = π*5²*10 = 785.4 cubic feet.
Step 4: Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
If you have any additional questions or need further assistance, please let me know.
How many strings can be formed by ordering the letters MISSISSIPPI which
contain the substring of MISS?
Answers
Answer:
1680 is the answer.
Step-by-step explanation:
Here, we have 11 letters in the word MISSISSIPPI.
Repetition of letters:
M - 1 time
I - 4 times
S - 4 times
P - 2 times
As per question statement, we need a substring MISS in the resultant strings.
So, we need to treat MISS as one unit so that MISS always comes together in all the strings.
The resultant strings will look like:
xxxxMISSxxx
xxMISSxxxxx
and so on.
After we treat MISS as one unit, total letters = 8
Repetition of letters:
MISS - 1 time
I - 3 times
S - 2 times
P - 2 times
The formula for combination of letters with total of n letters:
\(\dfrac{n!}{p!q!r!}\)
where p, q and r are the number of times other letters are getting repeated.
p = 3
q = 2
r = 2
So, required number of strings that contain MISS as substring:
\(\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680\)
So, 1680 is the answer.
An election ballot asks voters to select four city commissioners from a group of
twelve candidates. In how many ways can this be done?
Answers
Answer:
Step-by-step explanation:
C(16, 4) = 1820 ways
16
C
4 = (16x15x14x13) / (4x3x2x1)
he figure shows a parallelogram inside a rectangle outline:
A parallelogram is shown within a rectangle. The length of the rectangle is 3 over 5 foot, and the width of the rectangle is 2 over 5 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 5 foot.
What is the area of the parallelogram?
1 over 25 square foot
11 over 25 square foot
3 over 25 square foot
4 over 25 square foot
Answers
Answer:
4/25 foot²
Step-by-step explanation:
Refer to attachment*
Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having
\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}\)
\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)
Hence, Option D) is correct
Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have
\({:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}\)
\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}\)
\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)
This also, proves that the correct answer is D)
Cory is a bird watch he estimated that 30% of the birds American , 20 % ne eyed , and 20 designs n simulation Let , 1 and 2 represent American robins Let and 4 represent -eyed Let and 6 represent song sparrows Let 78and 9 represent other birds The table shows the simulation results. 05716 16803 965683217733855 76635 922908886472794 14333 0594377510 7405187238 79019 97895 8648794036 1274924005 According to this simulation, what is the probability that at least one of the next five birds he sees is a robin? O A. 0.45 B. 0.6 C. 0.75 D. 0.3
Answers
Answer:
I believe the answer is C. 0.75
Step-by-step explanation:
The probability that at least one of the next five birds he sees is a robin is 0.75.
ProbabilityBased on the stimulation result shown on the table we can seen that other birds appeared at least 15 times.
Hence:
P(A)=15/20
P(A)=0.75
Therefore the probability that at least one of the next five birds he sees is a robin is 0.75.
Learn more about probability here: https://brainly.com/question/24756209
#SPJ2
Solve the following equations. Round your answers to the nearest hundredth as needed.
9.13b-1.93=10.05
Answers
Answer:
b = 1.31
Step-by-step explanation:
Step 1: Add 1.93 to both sides.
\(9.13b-1.93+1.93=10.05+1.93\) \(9.13b=11.98\)Step 2: Divide both sides by 9.13.
\((9.13b)/9.13 = 11.98/9.13\) \(b = 1.31215..\)Step 3: Round to the nearest hundredth.
1.31215.. ≈ 1.31Therefore, b = 1.31.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
b = 1.31
Step-by-step explanation:
9.13b - 1.93 = 10.05(Move 1.93 to the other side to isolate b which changes the sign to positive)
9.13b = 10.05 + 1.93
9.13b = 11.98
Divide by 9.13 to get b
\(\frac{9.13b}{9.13} = \frac{11.98}{9.13} \\\)
b = 1.31
find x on the following figure
Answers
If the perpendicular from chord is x, the length of cord is 11.3 and diameter be 15.5 then the value of x is 4.54.
Given Perpendicular from center to chord is x. The length of cord be 11.3 and the diameter be 15.5.
Perpendicular means a line on other line making an angle of 90 degrees. Cord is the length of line joining two points on a circle and is different from radius or diameter. We know that the formula of calculating the length of chord is as under:
l=\(2\sqrt{r^{2} -d^{2} }\)
now put the value of l=11.3 and r=15.5/2=7.25
11.3=\(2\sqrt{7.25^{2} -x^{2} }\)
11.3/2=\(\sqrt{52.5625-x^{2} }\)
5.65=\(\sqrt{52.5625-x^{2} }\)
squaring both sides
\(5.65^{2} =52.5625-x^{2}\)
31.9225=52.5625-\(x^{2}\)
31.9225-52.5625=-\(x^{2}\)
-20.64=-\(x^{2}\)
20.64=\(x^{2}\)
x=4.54
Hence if the length of cord is 11.3 and diameter is 15.5 then the value of x is 4.54.
Learn more about circle at https://brainly.com/question/24375372
#SPJ10
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in firecontrol by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
Required:
a. What is the probability that all of the sprinklers will operate correctly in a fire?
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
c. What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?
Answers
Answer:
0.028 ; 0.649 ; 4
Step-by-step explanation:
P(correctly activation), p = 0.7
Number of sprinklers, n = 10
q = 1 - p = 1 - 0.7 = 0.3
Using the binomial probability relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Probability that all sprinklers activate correctly;
P(x = 10) = 10C10 * 0.7^10 * 0.3^0
P(x = 10) = 1 * 0.0282475249 * 1
P(x = 10) = 0.028
Probability that atleast 7 will operate correctly :
P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)
P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028
P(x ≥ 7) = 0.649
3.)
Probability of atleast 1 operates :
P(x ≥ 1) = 0.98
1 - probability of 0 operates
1 - p(x =0)
P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02
Recall :
nC0 = 1 ;
1 - p(x = 0)
P(x = 0) = 1 * 1 * 0.3^n = 0.02
0.3^n = 0.02 - - - (1)
0.3^3.24 = 0.02 - - - (2)
Comparing (1) and (2)
n = 3.24
Since, n cannot be a fraction ;
Then n is rounded to the next whole number = 4