Answers
Answer:
12 cm
Step-by-step explanation:
The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.
For the tangent the "two" intersection points with the circle are the same point, so ...
product of tangent lengths = product of secant lengths
(8 cm)(8 cm) = (4 cm)(4 cm +x)
Dividing by 4 cm gives ...
16 cm = 4 cm + x
12 cm = x
Related Questions
Please answer this correctly
Answers
Answer:
676
Step-by-step explanation:
lxw
14x35
4x24
6x15
676
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77° when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre.
Answers
Answer:
Height of the Dom is 112.18 m.
Step-by-step explanation:
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :
[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]
So, the height of the Dom is 112.18 m.
1. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n=1 n^2 + 1 / 2n^3 - 1
2. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 n / √n^5 + 5
3. Use direct comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 4 + 3^n / 2^n
Answers
Answer:
1. Diverges
2. Converges
3. Diverges
Step-by-step explanation:
Solution:-
Limit comparison test:
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = c
Where,
1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.
2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.
3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.
a) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n^2+1}{2n^3-1} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]
- Apply the limit ( n - > ∞ ):
(n = 1) ∑^∞ [tex][ \frac{1}{2n}][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.
Answer: Diverges
b)
The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]
- Apply the limit ( n - > ∞ ) in the denominator for ( 5 / n ), only the dominant term n^(3/2) is left:
(n = 1) ∑^∞ [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][\frac{1}{1 + 0}][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.
Answer: converges
Comparison Test:-
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).
-Then the following conditions are applied:
1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges
2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges
c) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]
- Apply the limit ( n - > ∞ ) in the numerator for ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:
(n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] ... The comparative series ( ∑[tex]b_n[/tex] )
- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):
[tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )
- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:
∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] diverges
- The first condition is applied when ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.
Answer: Diverges
he dot plot shows how many swimmers are in each line at a waterpark: Is the median or the mean a better measure of center for these data and why? Median, because the data are skewed and there is an outlier Median, because the data are symmetric and there are no outliers Mean, because the data are skewed and there is an outlier Mean, because the data are symmetric and there are no outliers
Answers
Answer:
Step-by-step explanation:
There's no plot, but I can give you this: Median is better with a large outlier, while mean is better for symmetry. Therefore, the correct answer would be either the first or fourth. Ofc, we can't see the plot so that's all I can give you.
Hope that helped,
-sirswagger21
A gum ball machine has 22 red 18 white 10 blue and 23 green. What chances of pulling out a red
Answers
Step-by-step explanation:
Total gum balls = 22 + 18 + 10 + 23 = 73
Probability of red gum = 22/73
a pail holds 3 1/2 gallons of water. How much is it in cups
Answers
Answer:
3 1/2 gallons of water is 56 cups
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
1 gallon=4cups
1/2 gallon=2cups
3*4=12
or 4cups+4cups+4cups=12
12+2=14
Louis had 19 dogs. He feeds them with 38 pounds of biscuits. If there are 4 more
dogs, then how much more pounds of biscuit are needed?
Answers
Answer:
14
Step-by-step explanation:
Answer:
Which of these factors will affect the friction on a road
Step-by-step explanation:
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!
Answers
Answer:
B. 1 over 8
Step-by-step explanation:
To determine the probability of the spinner landing on 5, we need to first know what probability is,
probability = required outcome/all possible outcome
since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner. This implies that all possible outcome = 64
In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.
This implies that the required outcome = 8
but
probability = required outcome/all possible outcome
probability (of the spinner landing on 5) = 8/64 =1/8
Answer:
b
Step-by-step explanation:
A bicycle ramp used for competitions is a triangle prism. The volume of the ramp is 313.2 cubic feet. Write and solve an equation to find the the width of the ramp.
Answers
Answer:
8.7 ft
Step-by-step explanation:
The diagram of the ramp is attached below.
Volume of a Triangular Prism = Base Area X Width
From the diagram:
Base of the triangle = 6 ft
Height of the Triangle = 12 ft
Therefore:
Base Area of the Prism [tex]=\frac{1}{2}X 12X6=36$ ft^2[/tex]
From the diagram, Width of the ramp =x
Given that the volume of the ramp is 313.2 cubic feet.
Therefore, substituting into the formula for Volume of a Triangular Prism
[tex]313.2=36 X x\\x= 313.2 \div 36\\$Width of the ramp, x=8.7 ft[/tex]
Answer:
8.7
Step-by-step explanation:
What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?
Answers
Answer:
24
Step-by-step explanation:
That would be:
(3/8)(30)
---------------
(15/16)(1/2)
This can be reduced in various ways. First, divide that 30 by 15, obtaining:
6/8
-----------
1/32
Now invert the divisor (1/32) and multiply:
(6/8)(32/1)
This reduces to 6*4, or 24.
A student takes a multiple-choice test that has 11 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. (a) Find P (6). (b) Find P (More than 3). Round the answers to at least four decimal places.
Answers
Answer:
a) P(6) = 0.0097
b) P(More than 3) = 0.1611
Step-by-step explanation:
For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A student takes a multiple-choice test that has 11 questions.
This means that [tex]n = 11[/tex]
Each question has five choices.
This means that [tex]p = \frac{1}{5} = 0.2[/tex]
(a) Find P (6)
This is P(X = 6).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]
P(6) = 0.0097
(b) Find P (More than 3).
Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So
[tex]P(X \leq 3) + P(X > 3) = 1[/tex]
We want P(X > 3). So
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]
[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]
[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]
[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]
Then
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]
P(More than 3) = 0.1611
The given line segment passes through the points (0, -3) and (-5, -4).
What is the equation of the line that is parallel to the given line and passes through the point (-2, 2)?
Answers
Answer:
y= 1/5x + 12/5
Step-by-step explanation:
Points: (0, -3) and (-5, -4)Line: y= mx+bSlope: m=(y2-y1)/(x2-x1)= (-4+3)/(-5-0)= -1/-5= 1/5Y-intercept: -3= 0*1/5+b ⇒ b= -3So the line is: y= 1/5x - 3Parallel line to this has same slope and passes through the point (-2, 2)
Its y- intercept is: 2= 1/5(-2)+b ⇒ b= 2+2/5= 12/5The required equation in slope- intercept form is:
y= 1/5x + 12/5What’s the correct answer for this question?
Answers
Answer:
A.
Step-by-step explanation:
In the attached file
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answers
Answer:
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
Step-by-step explanation:
I am going to say that:
The speed of the first plane is x.
The speed of the second plane is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x. We could also say that x = 2y.
Two airplanes leave an airport at the same time, flying in the same direction
They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, they will be x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149149 freshmen students, 3232 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alphaαequals=0.100.10 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choos
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149 freshmen students, 32 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alpha = 0.01 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choose the correct answer below. H_0: p = 0.20 H_a: p not equal to 0.20 H_0: p not equal to 0.20 H_a: p = 0.20 H_0: p = 0.20 H_a: p 0.20 If alpha = 0.05, find the rejection region for the test. Choose the correct answer below. z > 1.645 z > 1.96 z
Solution:
We would set up the null and alternative hypothesis. The correct options are
For null hypothesis,
p ≥ 0.2
For alternative hypothesis,
p < 0.2
This is a left tailed test.
Considering the population proportion, probability of success, p = 0.2
q = probability of failure = 1 - p
q = 1 - 0.2 = 0.8
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 32
n = number of samples = 149
P = 32/149 = 0.21
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.21 - 0.2)/√(0.2 × 0.8)/149 = 0.31
The calculated test statistic is 0.31 for the right tail and - 0.31 for the left tail
Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Therefore, the rejection region is z > 1.96
g A two-tailed test is one where: Select one: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis
Answers
Answer:
c. results in either of two directions can lead to rejection of the null hypothesis.
Step-by-step explanation:
A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.
If triangles DEF and NPQ are similar, what is the length of side d? As fraction or whole number.
Answers
The length of the side d would be 77/18.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
If triangles DEF and NPQ are similar, then
7/9 = d/ (11/2)
By cross multiply
9d = 7 x 11/2
d = 77/2 ÷ 9
d = 77/18
Thus, The length of the side d would be 77/18.
Learn more about ratios here:
brainly.com/question/186659
#SPJ2
Use slope-intercept form to write the equation of a line
that has a slope of -3 and passes through the point
(1,-5).
Use the drop-down menus to select the proper value
for each variable that is substituted into the slope-
intercept equation
y =
X
DPM
m =
Answers
Answer:
y=-3x-2
Step-by-step explanation:
There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.
Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]
We are given the slope of -3 and the point of (1,-5).
[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]
Convert into Slope-Intercept Form:
[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]
In 2 + In 8 - In 4
In 4
In 6
In 64
DONE
Answers
Answer:
ln 4
Step-by-step explanation:
plus(+) will become times and minus(-)will become divide. Combine all together as all are in terms of ln
ln (2x8)/4
=ln 4
Answer: In 4
Step-by-step explanation: edge 2021
Please answer this correctly
Answers
Answer:
21-25 = 4
26-30 = 3
Step-by-step explanation:
16-20 (4)= 17 17 17 18
21-25 (4)= 21 22 24 25
26-30 (3)= 26 27
30
31-35 (3)= 32 35 35
36-40 (5)= 36 37 37 38 39
41-45 (2)= 41 42
sorry it’s hard to see. please help!!!
Answers
3/11 ÷ 3/11
and
9/10 ÷ 3/5
PLZ HELP ME
Answers
Answer:
3/11 divided by 3/11 is 1
9/10 divided by 3/5 is 1 1/2 (1.5)
Step-by-step explanation:
Answer:
1
1.5
Step-by-step explanation:
3/11 ÷ 3/11 = 1
9/10 ÷ 3/5 = 3/2 ≈ 1.5
If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function
Answers
Answer:
g(X)=3(2^x)
Step-by-step explanation:
please very soon I offer the crown !!! + 10 points urgently !!!
Answers
Answer:
d. 10th e. 26th
Step-by-step explanation:
22-12=10
12+14=26
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answers
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
write any two numbers less than 15 , which has exactly four factors
Answers
Answer:
4 can be divided by 1 and 2
6 can be divided by 1 and 2
12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4
Step-by-step explanation:
A=(-2,-7) B=(-6,4) C=(-2,7) D=(2,4) What is the perimeter?
Answers
[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]
.
[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]
.
[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]
.
[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]
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[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]
In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.93. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places) 4.56
Answers
Answer:
1.54
Margin of error M.E = 1.54
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that
Standard deviation r = 1.93
Number of samples n = 6
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96×1.93/√6) = 1.544321633166
M.E = 1.54 (to 2 decimal place)
Margin of error M.E = 1.54
During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00
Answers
Answer:
Exponential; $376.32
Step-by-step explanation:
Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.
The same would be true for the second month, so the overall multiplier for the two months is ...
(1.12)(1.12) = 1.12^2 = 1.2544
This makes the food bill for the second month amount to ...
1.2544 × $300 = $376.32
_____
As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.
If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.
On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h
Answers
Answer:
d = 48 h
Step-by-step explanation:
Lamar's distance traveled is directly proportional to the number of hours be drove.
So distance (d) ∝ hours (h)
Lamar traveled 288 miles in 6 hours
Since d ∝ h
then d = kh [ where k is the proportionality constant ]
if 288 = k × 6
k = =288/48
Therefore, equation will be d = 48 h will be the equation
