Answer:
15 dog heights; [tex]n=15[/tex]
Step-by-step explanation:
The formula to be used here is [tex]MOE_\gamma=z_\gamma*\sqrt{\frac{\sigma}{n} }[/tex] where:
[tex]\gamma[/tex] is the confidence level[tex]MOE_\gamma[/tex] is the margin of error for a confidence level[tex]z_\gamma[/tex] is the critical value for the confidence level[tex]\sigma[/tex] is the population standard deviation[tex]n[/tex] is the sample sizeWe are given that:
[tex]\gamma=0.95[/tex][tex]MOE_\gamma=1[/tex][tex]z_\gamma=invNorm(0.975,0,1)=1.96[/tex][tex]\sigma=3.7[/tex]To determine the minimum sample size, [tex]n[/tex], we plug our given values into the formula and solve for
[tex]MOE_\gamma=z_\gamma*\sqrt{\frac{\sigma}{n} }[/tex]
[tex]1=1.96\sqrt{\frac{3.7}{n} }[/tex]
[tex]\frac{1}{1.96}=\sqrt{\frac{3.7}{n} }[/tex]
[tex](\frac{1}{1.96}) ^{2}=\frac{3.7}{n}[/tex]
[tex]n=\frac{3.7}{(\frac{1}{1.96})^{2} }[/tex]
[tex]n=14.21392[/tex]
Don't forget to round up here! This means that [tex]n=15[/tex] actually.
Therefore, if we want to be 95% confident that the sample mean is within 1 inch of the true population mean, the minimum sample size that can be taken is 15 dog heights.
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Consider this quadratic equation. x2 + 1 = 2x – 3 Which expression correctly sets up the quadratic formula?
Suppose a random sample of size 50 is selected from a population with μ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). Round your answers to two decimal places.
a. The population size is infinite.
b. The population size is N = 50,000.
c. The population size is N = 5000.
d. The population size is N = 500.
In the question, it's σ = 10 and not μ = 10.
Answer:
A) σ_x = 1.4142
B) σ_x = 1.4135
C) σ_x = 1.4073
D) σ_x = 1.343
Step-by-step explanation:
We are given;
n = 50
σ = 10
A) Formula for standard error of the mean for infinite size is;
σ_x = σ/√n
Thus;
σ_x = 10/√50
σ_x = 1.4142
B) When population is finite, we use correction factor and thus, we have;
σ_x = [√((N - n)/(N - 1)] × σ/√n
N = 50,000
Thus;
σ_x = [√((50000 - 50)/(50000 - 1)] × 10/√50
σ_x = 1.4135
C) N = 5000
Thus;
σ_x = [√((5000 - 50)/(5000 - 1)] × 10/√50
σ_x = 1.4073
D) N = 500
Thus;
σ_x = [√((500 - 50)/(500 - 1)] × 10/√50
σ_x = 1.343
Explain why the sum of the interior angles in a regular pentagon is 540?
Answer:
Step-by-step explanation:
formula to find the sum of interior angle of a regular pentagon is
(n-2)*180 degree
here n means no of sides .since pentagon has 5 sides replace it by 5
=(5-2)*180
=3*180
=540 degree
On a radar screen, a plane located at A(-2, 4) is flying toward B(4,3). Another plane, located at C(-3, 1), is flying toward D(3,0). Are the planes' paths perpendicular?
Answer:
yes they are perpendicular
hope this helps
have a good day :)
Step-by-step explanation:
Helppp me please I need to graduate
(5x³-7)(2x²+1)
OPTION D is the correct answer
Factor 24m - 12p + 72 to identify the equivalent expressions.
CHOOSE TWO ANSWERS!!!
A.6(4m+2p+12)
B.2(12m-6p+36)
C.12(2m-p+6)
D.24(m-12p+3)
Answer:
B and C
Step-by-step explanation:
If you take the least common factor you'd see that it could be factored to 2(12m-6p+36)
If you take the greatest common factor then it could be factored to 12(2m-p+6)
What is the volume of a square pyramid with a height of 4cm and a base with a side of 9 cm?
Answer:
108cm³
Step-by-step explanation:
Seeing that the base is a square, we first have to calculate the area of the base. This is equal to 9x9, in other words 81cm squared. Now, we multiply the base area to the vertical height divided by 3, which becomes 81x(4/3), which is then 108cm³.
:))))))))))
Find the volume of cone pictured below. Use 3.14 for π
.
Round your answer to the nearest hundredth.
Answer:
V≈718.38
Step-by-step explanation:
The volume of this cone is 718.38 cubic centimeters.
Have a nice day!
What is the slope and equation, how much battery does she lose an hour
Answer:
The slope is y=-5x+100 and she loses 5% per hour
Step-by-step explanation:
hope it helps and can you pls give me brainliest im desperate
Two pools are being drained. To start, the first pool had 3650 liters of water and the second pool had 4166 liters of water. Water is being drained from the first pool at a rate of 27 liters per minute. Water is being drained from the second pool at a rate of 39 liters per minute. Let be the number of minutes water has been drained. (a) For each pool, write an expression for the amount of water in the pool after minutes. (b) Write an equation to show when the two pools would have the same amount of water.
Step-by-step explanation:
(a) Let's start with the first pool. It has 3650 liters of water. For every minute, 27 liters are being drained. Thus, we can write its equation as 3650 liters - 27 liters per minute = end amount of liters. If we write minutes as m, we can say 3650-27m is our expression. Similarly, for the second one, we have 4166-39m as our answer
(b) For this, we just have to make the two expressions equal, so
4166-39m = 3650-27m
The solution is:
(a)
Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes
Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes
(b)
3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here, we have,
(a) With x being the minutes after which you want to calculate the amount of water in the pool, to calculate this amount of water you must subtract the water drained from the initial amount of water that the pool contains.
Knowing that, for example, the water from the first pool drains at a rate of 27 liters per minute, then after x minutes, the total water drained will be 27 liters per minute * x minutes. Then:
Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes
Reasoning in the same way:
Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes
(b) Now want to know when the two pools would have the same amount of water. If they have the same amount of water then you can express:
Amount of water in the first pool = Amount of water in the second pool
Replacing the expressions found in (a):
3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes
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Two dice are thrown together. Use a tree diagram to find the probability that both numbers are less than 5
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
2 dice = 12 numbers
1, 2, 3, 4 and 1, 2, 3, 4 are less than five.
This is a total of 8 numbers.
[tex]\frac{8}{12} =\frac{8/4}{12/4}=\frac{2}{3}[/tex]
The probability that both numbers are less than 5 on throwing 2 dices is given by P ( A ) = 4/9 = 44.44 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that both numbers are less than 5 on throwing 2 dices be represented as P ( A )
Now , the total number of outcomes for throwing 2 dices = 36 outcomes
And , out of these 36 possible outcomes, there are 16 outcomes where both numbers are less than 5
{(1,1), (1,2), (1,3), (2,1), (2,2), (2,3),
(3,1), (3,2), (3,3), (4,1), (4,2), (4,3),
(1,4), (2,4), (3,4), (4,4)}
So , the number of possible outcomes = 16
And , probability P ( A ) = 16/36
P ( A ) = 4/9
Hence , the probability is 4/9
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Which ordered pairs would appear on the graph of the equation y = 1/2x +
6?
(-6, 3) and (0,6)
(10, 8) and (0,6)
(6, 3) and (0,6)
(10, 11) and (0,6)
Substitute the value of the variable and then simplify
Answer:
y=2*(4)^2-3
y=2*16-3
y=32-3
y=29
Step-by-step explanation:
From her eye, which stands 1,61 meters above the ground, Savannah measures the
angle of elevation to the top of a prominent skyscraper to be 24°. If she is standing at
a horizontal distance of 340 meters from the base of the skyscraper, what is the
height of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary
Answer:
152.99 m
Step-by-step explanation:
Using the solution diagram attached below :
We can obtain the height, h of skyscraper to the position of her eye level using trigonometry ;
Tan θ = opposite / Adjacent
Tan 24 = h / 340
h = tan 24 * 340
h = 151.37775
Hence, the height will be (h + distance from eyelevel to ground)
151.37775 + 1.61
= 152.98775
= 152.99 m
Answer:
132.6 meters tall
Step-by-step explanation:
it gave me the answer
In an experiment, the population of bacteria is increasing
at the rate of 100% every minute. The population is
currently at 50 million.
How much was the population of bacteria 1 minute
ago?
million
25 million
number of bacteria doubles every minute
A public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds. A sample of 15 babies is studied. Round the answers to three decimal places. Part 1 of 4 (a) What is the probability that exactly 5 of them weigh more than 20 pounds
Answer:
0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.
Step-by-step explanation:
For each baby, there are only two possible outcomes. Either they weigh more than 20 pounds, or they do not. The probability of a baby weighing more than 20 pounds is independent of any other baby, which means that the binomial probability distribution is used 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 public health organization reports that 30% of baby boys 6 - 8 months old in the United States weigh more than 20 pounds.
This means that [tex]p = 0.3[/tex]
A sample of 15 babies is studied.
This means that [tex]n = 15[/tex]
What is the probability that exactly 5 of them weigh more than 20 pounds
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.3)^{5}.(0.7)^{10} = 0.206[/tex]
0.206 = 20.6% probability that exactly 5 of them weigh more than 20 pounds.
The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed. Suppose, that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.4 fluid ounce. (a) At what value should the mean be set so that 99.9% of all cans exceed 12 fluid ounces
Answer: At a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.
Step-by-step explanation:
Let us assume that X is a normal rando variable with a mean value [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].
Hence, random variable Z will be introduced as follows.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
(a) Set the value [tex]\sigma = 0.1[/tex] and the equation will be written down as follows.
[tex]0.999 = P (X \geq 12) \\= P (Z \geq \frac{12 - \mu}{0.1})\\= 1 -\phi (\frac{12 - \mu}{0.1})\\\phi (\frac{12 - \mu}{0.1}) = 0.001[/tex]
According to the tables,
[tex]\frac{12 - \mu}{0.1} = -3\\\mu = 12.3[/tex]
Thus, we can conclude that at a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.
Solve rational equations 5/6+3/b=1/3
The measure of an angle ABC is 50°,AD bisects angle BAC, and DC bisects angle BCA. The measure of angle ADC is what?
9514 1404 393
Answer:
115°
Step-by-step explanation:
Let A, B, C represent the vertex angle measures of ΔABC. Then the sum of angles in ΔADC is ...
A/2 +∠ADC + C/2 = 180°
Multiplying by 2 gives ...
A + C + 2×∠ADC = 360°
From the given information, we know ...
A + C + 50° = 180° . . . . . sum of angles in ΔABC
This lets us write an expression for (A +C):
A + C = 130° . . . . . . . . subtract 50° from the previous equation
Substituting for A+C, we get ...
130° + 2×∠ADC = 360°
2×∠ADC = 230° . . . . . . . . . subtract 130°
∠ADC = 115° . . . . . . . . . . . divide by 2
Find a solution to the linear equation −2x−2y=−12.
A sandwich costs $4.20 and a fruit drink costs $1.80. There is a 8% tax. How much
change will you get from a $10 dollar bill after purchasing both the sandwich and drink
(and paying tax of course)?
A. $6.48
B. $3.52
C. $3.70
D. $3.90
Answer:
B. 3.52
Step-by-step explanation:
4.20+1.80=6.00
6.00 x .08 (8% tax)=.48 tax
6.00+ .48=6.48 total cost
10.00-6.48=3.52 change from a $10 bill
A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 14.12. The camera is 190.0 cm above the
surface. How far is the camera from the rock?
The camera is cm from the rock
Round to the nearest tenth as needed.)
Answer:
778.1 cm
Step-by-step explanation:
The solution triangle attached below :
Using trigonometry :
θ = 90 - 14.12 = 75.88°
Cos θ = Adjacent / hypotenus
Cos 75.88 = 190 / d
d = 190 / cos 75.88
d = 778.83
Rock is 778.8 cm from the camera
What is the value of 2 - 1.25 as a fraction?
Answer:
3/4
Step-by-step explanation:
2 - 1.25 - 0.75
0.75 = 3/4
Your answer is 3/4.
I hope this helps, have a nice day.
Answer:
[tex] \frac{3}{4} [/tex]Step-by-step explanation:
[tex]2 - 1.25[/tex]
[tex]0.75[/tex]
[tex]0 \frac{75}{100} [/tex][tex] \frac{75}{100} [/tex][tex] \frac{25(3)}{25(4)} [/tex][tex] \frac{25 \times 3}{25 \times 4} [/tex][tex] \frac{3}{4} [/tex]Hope it is helpful...Solve for y.
O 10
O 12
O 15
O 18
Answer:
first option
Step-by-step explanation:
3x = 90 degree (being perpendicular)
x = 90/3
x = 30 degree
substitute the value of x
2x + 3y = 90 degree (being perpendicualr)
2*30 + 3y = 90
60 + 3y = 90
3y = 90 - 60
y = 30/3
y = 10 degree
Answer:
that's easy its letter a number 10
what is equivalent to 4 to the power of 3
Answer:
64
Step-by-step explanation:
because you multiply 4 by it self
What is 1/8 * 1/8 in fraction? PLEASE HELP
Answer:
1/64
Step-by-step explanation:
See image below:)
Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second city. Let x represent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation
Answer:
827
Step-by-step explanation:
this is the answer !!
Determine whether the triangles are similar. If so, write a similarity
statement.
Answer:
[tex]\triangle FED\sim \triangle JEH[/tex]
Step-by-step explanation:
Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity. [tex]\implies \boxed{\triangle FED\sim \triangle JEH}[/tex]
9514 1404 393
Answer:
ΔDEF ~ ΔHEJ
Step-by-step explanation:
The vertical angles at E are congruent, and the marked angles at F and J are congruent. The two triangles are similar by the AA postulate.
The given portion of the similarity statement names the angles in the order "unspecified", "vertical", and "50°". If we name those angles in the same order in the other triangle, the similarity statement becomes ...
ΔDEF ~ ΔHEJ
What is the probability of the spinner landing on 1 or 3
Answer:
Assuming there are 3 possibilities for the spinner, the answer is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Find the degree measure of the indicated angle.
?
22
135°
Answer:
measure of the indicated angle
=180-(135+22)
=180-157
=23°
the first option is the answer
Answer:
23
Step-by-step explanation:
135+22 = 157
all angles add up to 180 degrees so
180-157 is 23
