Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that:
Complete question is;
In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.
Answer:
P(has diabetes | positive) = 0.442
Step-by-step explanation:
Probability of having diabetes and being positive is;
P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)
We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.
Thus;
P(positive & has diabetes) = 0.08 × 0.95 = 0.076
P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)
P(negative & has diabetes) = 0.004
P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)
We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease
Thus;
P(positive & no diabetes) = 0.92 × 0.1 = 0.092
P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)
P(negative &no diabetes) = 0.828
Probability that a person selected having diabetes actually has the disease is;
P(has diabetes | positive) =P(positive & has diabetes) / P(positive)
P(positive) = 0.08 + P(positive & no diabetes)
P(positive) = 0.08 + 0.092 = 0.172
P(has diabetes | positive) = 0.076/0.172 = 0.442
Using formula:
[tex]P(\text{diabetes diagnosis})\\[/tex]:
[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]
[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]
[tex]\text{P(have been diagnosed with diabetes)}[/tex]:
[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]
[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]
Learn more about the probability:
brainly.com/question/18849788
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
Find the equation of the line.
Use exact numbers.
y=
Answer:
y = 2x+4
Step-by-step explanation:
First we need to find the slope using two points
(-2,0) and (0,4)
m = (y2-y1)/(x2-x1)
m = (4-0)/(0--2)
= 4/+2
= 2
we have the y intercept which is 4
Using the slope intercept form of the line
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a
Answer:
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]
Step-by-step explanation:
The expression is:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
Collect the like terms as follows:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]
[tex]=12a^{2}b+18ab+18a-b-8[/tex]
Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].
Answer:
The CORRECT answer is B
Step-by-step explanation:
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due today
Answer:
25%
Step-by-step explanation:
The last percentile always contains 25% of the observations.
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
What is the answer? x^2-y^2=55
Answer:
To solve for x we can write:
x² - y² = 55
x² = y² + 55
x = ±√(y² + 55)
To solve for y:
x² - y² = 55
y² = x² - 55
y = ±√(x² - 55)
Please help me find Jebel dhanna in UAE map.
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
What is the area of the triangle below?
18
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]