Answer:
11/15
Step-by-step explanation:
Romeo is chucking pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall. How fast are the pebbles going when they hit her window?
Answer:
4.45 m/s
Step-by-step explanation:
Vertical distance, Sy = 5m
The speed of pebble when they hit her window :
Vx = Sx / t
We can obtain t using the relation :
Sy = 1/2 * at²
Where, a = acceleration due to gravity = 9.8m/s²
We can obtain t
5 = 1/2 * 9.8 * t²
5 = 4.9t²
t = √5/4.9
t = 1.01 seconds
Hence,
Speed, Vx = Sx / t
Vx = 4.5 / 1.01
Vx = 4.45 m/s
If f(x) = 8x and g(x) = 2x +1 find (f o g) (x)
Answer:
(fog) (x) = 8*(2x+1)=16x+8
Step-by-step explanation:
BRAINIEST AND 10 POINTS
Answer:
16
Step-by-step explanation:
just use a calculator
find the 7th term of the geometric sequence whose common ratio is 1/3 and whose first term is 6.
Answer:
5
Step-by-step explanation:
2
Question
If the average (arithmetic mean) of x, y, and 24 is 10, what is the average of x and y?
02.
03
06
o It cannot be determined from the information given
Answer:
I don't know
Step-by-step explanation:
the answer is 0.2
The average of x and y is 03
How to determine the average?The average of the three numbers is given as:
Average = 10
This means that:
(x + y + 24)/3 = 10
Multiply both sides by 3
x + y + 24 = 30
Subtract 24 from both sides
x + y = 6
Divide by 2
(x + y) = 3
Hence, the average of x and y is 03
Read more about average and mean at:
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Suppose the probability of a false positive result on a mammogram is 7% and that radiologists' interpretations of mammograms are mutually independent in the sense that whether or not a radiologist finds a positive result on one mammogram does not influence whether or not a radiologist finds a positive result on another mammogram. Assume that a woman has one mammogram every year for ten years.
(a) What is the probability (as a %) that she will have no false positive results during that time?
(b) What is the probability (as a %) that she will have at least one false positive result during that time?
(c) What is the probability (as a %) that she will have exactly two false positive results during that time?
(d) Suppose that the probability of a false negative result on a mammogram is 3%, and assume that the probability that a randomly chosen woman has breast cancer is 0.0003.
(i) If a woman has a positive test result one year, what is the probability (as a %) that she actually has breast cancer?
(ii) If a woman has a negative test result one year, what is the probability (as a %) that she actually has breast cancer?
Answer:
a) 48.4%
b) 51.6%
c) 12.3%
d) i) 93.0% ii) 3.0%
Step-by-step explanation:
a)
P(fp) = probability of false positive result
P(fp) = 0.07
P(fp = 0) = (1 - 0.07)¹⁰
P(fp = 0) = 0.4839... ⇒ 48.4%
b)
P(fp = 1) = 1 - 0.4839...
P(fp = 1) = 0.516... ⇒ 51.6%
c)
P(fp = 2) = 10C2(0.07)²(0.93)⁸
P(fp = 2) = 0.123... ⇒ 12.3%
d)
P(fn) = probability of false negative
P(b) = probability a randomly selected woman has breast cancer
P(fn) = 0.03
P(b) = 0.0003
If she has a positive test, it is either a true positive, meaning she actually has breast cancer, or a false positive, meaning she doesn't;
If P(fp) = 0.07, then the probability of a true positive is 0.93 or 93%
ii)
If she has a negative test, a true negative means she doesn't have breast cancer, and a false negative means she does have breast cancer;
The probability of a false negative is 0.03 or 3%
(I'm not entirely sure about part d, but I've answered as I've understood it according to my logic, they seem to be somewhat trick questions unless I've incorrectly understood the questions)
Look at ZV SW and ZTSW in the image below.
Which of the following is the best description for this pair of angles?
O acute
O complementary
O straight
supplementary
Answer:
Supplementary is your answer
The total cost c a roof technician charges to fix a sink in a house depends on the number h of hours it takes to assess the damages to the roof and repair the roof. This situation can be represented by the function rule 32h + 145. What is the total cost the roofer will charge if he works for 19.25 hours?
Answer:
I believe it is 761 is the cost the roofer will charge.
Step-by-step explanation:
First: Multiply 32 with 19.25 (standing for h), which equals to 616.
Second: Add 616 with 145, which adds up to 761.
what is the best teaching learning material in mathematics for kids?
Answer:
Step-by-step explanation:
Dice, cards, spinners and the like are interactive and engaging math aids to get children involved in learning about probability, chance, number patterns and statistics.
Mary needs a laptop. She decided to barrow one on hire purchase. The marked price of the laptop $100, 200 and she had to pay a deposit of 10% of the marked price. If the total hire purchase price of the laptop is $142, 020 after a 5 year payment plan, how much was Mary’s monthly payments?
Answer:
2, 367
Step-by-step explanation:
142,020 / 5 = 28, 404
28, 404 / 12 = 2, 367
6th work. What measure of Central tendency is calculated by adding all the values and diving the sum by the number of values
A) Median
B) Mean
C) Mode
D) Range
a variable for which no data have been collected but has influence on other variables in the study.
Answer:
Confounding variable
Step-by-step explanation:
Confounding variables also known as lurking or third variable are varibeks which causes an unwanted or spurious association between an independent and dependent variable. This Confounding variable usually has a relationship between not the independent and dependent variable and if not adequately managed or corrected for, they may cause a relationship which is not intended thereby interfering with the outcome of our research. Such is the correlation between ice cream sale and murder rate.
Please help I can't figure it out
Answer:
61.2%
Step-by-step explanation:
Let's start by finding the total area of the circle
it says that the radius is 4 so the total area is 16π
Then let's find the area of the traingle
The hieght is 6.5 and the base is 6
.5*6.5*6=19.5
Let's then find the white area
16π-19.5=30.765
Finally we just have to do (30.765/16π)= 61.2%
what is the least common denominator of 1/3 and 4/7?? plsss explain
Answer:
21
Step-by-step explanation:
The smallest number that can go into both 3 and 7 as our denominators is 21. This can be worked about by multiplying them together.
(FYI: In some cases, if the product is even, it may not always work to multiply them together)
Answer:
21
hope this helps
have a good day :)
Step-by-step explanation:
3 multiples are 3, 6, 9, 12, 15, 18, 21, 24
7 multiples are 7, 14, 21, 28
so would need to change both denominators to 21 and multiple 7 and to 1/3 to get 7/21 and 3 to 4/7 to get 12/21
A local steakhouse served 625 customers over a weekend. The distribution of each customer's food purchase is non-normal. The average cost of each customer's food purchase is 52 dollars, with a standard deviation of 17 dollars. Suppose that a random sample of 315 customers are selected from the weekend's customers. Would it be appropriate to model the distribution of the sample mean with a normal model?
No. The mean distribution theorem states that the sampling distribution of the sample mean can only be modeled by the non-normal model because the population distribution is non-normal.
There is not enough information to make assumptions regarding the distribution of the sample mean.
Yes. The central limit theorem states that the sampling distribution of a sample mean can be modeled by a normal model if the sample size is large enough, regardless of the shape of the population distribution.
No. The central limit theorem states that the sampling distribution of a sample mean can only be modeled by a normal model if the sample size is large enough and the shape of the population distribution is normal.
Yes. The mean distribution theorem states that the sampling distribution of a sample mean can be modeled by a normal model if the sample size is large enough regardless of the population distribution.
Answer:
yes. The central limit theorem states that the sampling distribution of a sample mean can be modeled by a normal model, regardless of the shape of the population distribution.
Step-by-step explanation:
In order for the distribution of the sample mean to be normal, the sample size, n, must be large enough. By the central limit theorem, if n > 30, the distribution of the sample mean can be modeled by a normal distribution.
The answer is yes the central limit theorem states that the sampling distribution of a sample mean can be modeled by a normal model, regardless of the shape of the population distribution.
Option (B) is correct.
It is required to find the appropriate to model the distribution of the sample.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.
Given that:
A local steakhouse served 625 customers over a weekend.
The average cost of each customer's food purchase is 52 dollars, with a standard deviation of 17 dollars. random sample of 315 customers are selected from the weekend's customers.
In order for the distribution of the sample mean to be normal, the sample size, n, must be large enough. By the central limit theorem, if n > 30, the distribution of the sample mean can be modeled by a normal distribution.
So, the answer is yes the central limit theorem states that the sampling distribution of a sample mean can be modeled by a normal model, regardless of the shape of the population distribution.
Learn more about arithmetic here:
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find the equation of the striaght line passing through (3, 5) which is perpendicular to the line y=3x+2
Answer:
pls provide with a graph
Solve using the quadratic formula
Answer:
-5, -1/2
Step-by-step explanation:
I could only show half of the steps, but you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps.
What is the tangent of 0?
Step-by-step explanation:
tan 0 = 5/ √11 = 5√11 /11
__________
Answer:
5 / √11
Step-by-step explanation:
tan θ = opposite side / adjacent side
tan θ = 5 / √11
reduce the 24 hour clock times in 12 hour clock time add am or pm
Answer:
1) 1:04 am
2) 6:22 pm
3) 6:42 pm
4) 1:30 pm
5) 12:40 pm
6) 5:35 pm
7) 3:24am
8) 11:25 am
9) 6:42 am
10) 9:20 am
Which statement implies that A and B are independent events?
O A. P(B|A) = P(B N A)
O B.
P(BA) = P(B)
P(A)
O C.
P(B|A) = P(A)
OD.
P(BA) = P(B)
Answer:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both A and B happening is the same as the probability of A happening multiplied by the probability of B happenings, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
The statement is [tex]P(A \cap B) = P(A)P(B)[/tex]
Geometry work HELP ASAP trying to find the measure of a circumference!!
Answer:
65 degrees
Step-by-step explanation:
Since it is given that AB=DC
then we know that AO=DO and BO=CO because it is the radius of a same circle.
Hence the shapes are equal and thus DOC=65 degree as it serves as a corresponding angle to AOB
4 to the power of -3 as fraction
Answer:
Step-by-step explanation:
4^-3
=1/4^3
=1/64
Answer:
[tex]\frac{1}{64}[/tex]
Step-by-step explanation:
[tex]4^{-3} = 0.015625[/tex]
[tex]0.015625 = \frac{1}{64}[/tex]
from 5 metres of cloth Alexa cut 217 cm how much cloth remaining after cutting
Answer:
2.83 meters
Step-by-step explanation:
Change 217 cm to meter
217 * 1 m/ 100 cm = 2.17 m
5 meter - 2.17 m = 2.83 meters
Answer:
283 cm Or 2.83 m of cloths remaining after cutting.
Step-by-step explanation:
Alexa have a cloth measures 5 metre and she cut 217 cm clothes.As we know that
1 m = 100 cm
so, 5 m = 5 × 100 = 500 cm
Alexa cut 217 cm of clothesSubtract 217 cm from 500 cm
➛ 500 - 217
➛ 283 cm Or 2.83 m
Plz Help more than one !!!!!!!!!!!!!!!!!!
Answer:
The correct option is (b).
Step-by-step explanation:
We need to find the equivalent to -2(4-3x)+(5x-2)
Using the associative property,
-2(4-3x) = -2(4)+2(3x)
= -8+6x
So,
-2(4-3x)+(5x-2) = -8+6x +5x-2
taking like terms together,
-2(4-3x)+(5x-2) = 6x+5x-8-2
= 11x-10
The equivalent expression is equal to (11x-10).
The functions f(x) and g(x) are shown on the graph. f(x)=x² what is g(x)?
[tex]a. \: \: g(x) = ( x - 2) {}^{2} [/tex]
[tex]b. \: \: g(x) = 2 {x}^{2} [/tex]
[tex]c. \: \: g(x) = ( \frac{1}{2} x) {}^{2} [/tex]
[tex]d. \: \: g(x) = (x + 2) {}^{2} [/tex]
9514 1404 393
Answer:
b. g(x) = 2x²
Step-by-step explanation:
The vertices of the two curves are in the same place, so no translation has taken place. This eliminates choices 'a' and 'd'.
A point on the curve g(x) is given. You can test to see which of choices 'b' and 'c' it satisfies.
B: g(2) = 2(2²) = 8 . . . . matches point (2, 8)
C: g(2) = (1/2·2)² = 1² = 1 . . . . does not match point (2, 8)
The function g(x) is ...
g(x) = 2x²
Help please!! Step by step!!
Answer:
[tex]P(Ice Cream|Frogtown) = 67.4\%[/tex]
Step-by-step explanation:
Given
The attached plot
Required
P(Ice Cream|Frogtown)
This is calculated as:
[tex]P(Ice Cream|Frogtown) = \frac{P(Ice\ Cream\ n\ Frogtown)}{P(Frogtown)}[/tex]
From the attachment;
[tex]P(Ice\ Cream\ n\ Frogtown) = 0.31[/tex]
[tex]P(Frogtown) = 0.31 + 0.15 = 0.46[/tex]
So, we have:
[tex]P(Ice Cream|Frogtown) = \frac{P(Ice\ Cream\ n\ Frogtown)}{P(Frogtown)}[/tex]
[tex]P(Ice Cream|Frogtown) = \frac{0.31}{0.46}[/tex]
[tex]P(Ice Cream|Frogtown) = 0.6739[/tex]
Express as percentage
[tex]P(Ice Cream|Frogtown) = 0.6739 * 100\%[/tex]
[tex]P(Ice Cream|Frogtown) = 67.39\%[/tex]
[tex]P(Ice Cream|Frogtown) = 67.4\%[/tex] -- approximated
Pleas help will mark brainlist!
Geometry
This makes a cube because a cube has 6 faces, 8 vertices, and 12 edges.
What is 5x5 answer for a cookie
Answer:
25
Step-by-step explanation:
a rectangular container of length 40cm and width 36cm was filled with 57600cm of water. find the depth of the water in the container.
Answer:
40 cm
Step-by-step explanation:
57600 is the volume here
Because "was filled with 57600cm of water."
- NOTE : Volume can Never change unless There is a Subtracted amount of water That's Removed36 x 40 x n = 57600
n = 40
Determine the values of the parameter s for which the system has a unique solution, and describe the solution. x 1 - 5 sx 2
Answer:
[tex]s \ne \±2[/tex]
[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]
[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]
Step-by-step explanation:
Given
[tex]3sx_1 +5x_2 = 3[/tex]
[tex]12x_1 + 5sx_2 =2[/tex]
Required
Determine the value of s
Express the equations as a matrix
[tex]A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right][/tex]
Calculate the determinant
[tex]|A|= (3s*5s -5 *12)[/tex]
[tex]|A|= (15s^2 -60)[/tex]
Factorize
[tex]|A|= 15(s^2 -4)[/tex]
Apply difference of two squares
[tex]|A|= 15(s -2)(s + 2)[/tex]
For the system to have a unique solution;
[tex]|A| =0[/tex]
So, we have:
[tex]15(s -2)(s+2) = 0[/tex]
Divide both sides by 15
[tex](s -2)(s+2) = 0[/tex]
Solve for s
[tex]s -2 = 0\ or\ s +2 = 0[/tex]
[tex]s = 2\ or\ s = -2[/tex]
The result can be combined as:
[tex]s =\±2[/tex]
Hence, the system has a unique solution when [tex]s \ne \±2[/tex]
Next, we solve for s using Cramer's rule.
We have:
[tex]mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right][/tex]
Calculate the determinant
[tex]|x_1| = (3 * 5s - 5 *2)[/tex]
[tex]|x_1| = 15s - 10[/tex]
So:
[tex]x_1 =\frac{|x_1|}{|A|}[/tex]
[tex]x_1 = \frac{15s - 10}{15(s -2)(s+2)}[/tex]
Factorize
[tex]x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}[/tex]
Divide by 5
[tex]x_1 = \frac{3s - 2}{3(s -2)(s+2)}[/tex]
[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]
Similarly:
[tex]mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right][/tex]
Calculate the determinant
[tex]|x_2| = 3s * 2 - 3 * 12[/tex]
[tex]|x_2| = 6s- 36[/tex]
So:
[tex]x_2 =\frac{|x_2|}{|A|}[/tex]
[tex]x_2 = \frac{6s- 36}{15(s -2)(s+2)}[/tex]
Factorize
[tex]x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}[/tex]
Divide by 3
[tex]x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}[/tex]
[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]
