Answer:
[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]
Step-by-step explanation:
For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.
Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:
[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]
However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]
Therefore, we have:
[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]
Answer:
[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15
Therefore, we have:
\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%
[/tex]
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
Let a submarine be at a constant depth of 5 km. It is headed in the direction of a lighthouse. If the distance between the submarine and the base of the lighthouse is decreasing at a rate of 24 km/h when the sub is 13 km away from the base, then what is the speed of the submarine
Answer:
24 km/h
Step-by-step explanation:
Given:
Constant speed of submarine = 24 km/h
Depth under sea = 5 km
Distance of submarine from lighthouse = 13 km
Find:
Speed of the submarine
Computation:
At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.
So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.
Put these numbers in descending order.
0.308
0.193
0.26
0.6
Answer:
0.6
0.308
0.26
0.193
Step-by-step explanation:
0.6
0.308
0.26
0.193
Craig and Cindy working together can mow the lawn in four hours working alone Cindy takes twice as long as Craig how long does it take Craig to mow the lawn alone
Answer:
12 hours
Step-by-step explanation:
1 : (1/4 : (2 + 1)) = 12
(a) 4x + 3y + 2x + 7y
Answer:
6x + 10y
Step-by-step explanation:
4x + 3y + 2x + 7y
=> (4x + 2x) + (3y + 7y)
=> 6x + 10y
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope-intercept form
A: y= 2/5x -1/5
B: y= 2/5x +1/5
C: y= -2/5x -1/5
Answer:
y = 2/5x + 1/5
Step-by-step explanation:
y = 2/5x + b
-1 = 2/5(-3) + b
-1 = -6/5 + b
1/5 = b
please help me with geometry
Answer:
∠ DBC = 60°
Step-by-step explanation:
BD is an angle bisector , so
∠ DBC = ∠ ABD = 60°
angel ABD =60°
BD line is bisector
angel DBC=60° because both the angel are similar
A box contains orange balls and green The number of more four the number of orange If there 38 balls how many green balls and how balls are there in the box ?
let number of green balls= x
let number of orange balls=x+4
x+x+4=38
2x=38-4
2x=34
x=17
number of green balls=17
number of orange balls=21
Rebecca buys a new couch for $1,200. She plans on making a monthly payment of $75 on the balance, starting the month
after she buys the couch. Which recursive function models the amount of money Rebecca still has to pay for the couch?
The recursive function is A(t + 1) = A(t) - 75
Where;
A(t) = 1,200 - 75×t
The known parameter are;
The amount Rebecca buys the new couch = $1,200
The amount she plans to make as monthly payment = $75
The time she plans to start paying = The month after she buys the couch
Strategy;
Define a recursive function that models the amount of money Rebecca still has to pay
Definition
A recursive function is one which has its own process as an input in the process of its implementation
A recursive function that models the amount of money Rebecca still has to pay for the couch is found as follows;
The amount left for her to pay in the present month = The amount left to pay in the previous month - $75
Let A(t + 1) represent the amount left for her to pay in the present month and let A(t) represent the amount left to pay in the previous month, we get;
A(t) = 1,200 - 75×t
A(t + 1) = 1,200 - 75×t - 75 = A(t) - 75
The recursive function is A(t + 1) = A(t) - 75
The function is recursive because, the function, A(t), is called in as an input to the execution of the function
Learn more about recursive functions here;
https://brainly.com/question/13657607
Answer:
f(1) = 1,200
f(n) = f(n-1) -75 for n > 2
Step-by-step explanation:
Since the initial loan amount is $1,200, f(1) =1200.
And since $75 is deducted from the balance each month starting with n >2 , the common difference, d, is -75 .
Use the general recursive function for an arithmetic sequence,f(n)= f (n - 1 ) +d , for n > 2 to write the recursive function models Rebecca’s situation:
Which of the following is a quadratic function
A quadratic a function has a form of,
[tex]f(x)=ax^2+bx+c,a\neq0[/tex]
The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.
The second function fits the form of a quadratic function perfectly.
The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.
Hope this helps :)
Step-by-step explanation:
f(x) = 4x² + x - 3
[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]
r3t40 is correct
Determine a scalar c so that the angle between a = i + cj and b = i + j is 45°.
Answer:
c=0
Step-by-step explanation:
ATQ a.b=|a||b|sin(45)
1+c=sqrt(1+c^2)*sqrt(2)*1/sqrt(2)
1+c=sqrt(1+c^2)
(1+c)^2=(1+c^2)
2c=0, c=0
The required simplified value of c is zero for which the angle between a and b is 45°.
What is a vector?Vector is defined as the quantities that have both magnitude and direction are called a vector quantity and the nature of the quantity is called a vector.
Here,
scaler product is given as,
a . b = |a|.|b|cos45
(i + cj). (i + j) = √[1² + c²] . √[1²+1²] × 1/√2
1 + c = √1 + c²
Squaring both sides
(1 + c)² = 1 + c²
1 + c² + 2c =1 + c²
2c = 0
c = 0
Thus, the required simplified value of c is zero for which the angle between a and b is 45°.
Learn more about vectors here,
https://brainly.com/question/13322477
#SPJ2
sold 72 books, if ratio of books to bookmarks sols was 9:2, how many bookmarks sold?
16 book marks has been sold
Answer:
16 bookmarks
Step-by-step explanation:
9/72 = 2/x
72/9 = 8
2 x 8 = 16
hope this helps
Use formula autocomplete to enter a sum function in cell B7 to calculate the total of cells in B2:B6
Excel enables the users to perform mathematics basic and advanced function with just one formula.
The formula for sum of entire row or column can be done with just entering a single formula and results are shown in seconds.
The formula for sum of few column cells is,
=SUM(B2:B6)
The spreadsheet allows the user to enter various formula and results are displayed withing seconds.
There are formulas for basic math functions and there are also formulas for advance mathematics calculations. For addition of values of many cells sum formula is used and range is assigned for reference.
The formula adds all the values of selected cells and displays the results in different cell.
Learn more at https://brainly.com/question/24365931
What two numbers add to 13 and multiply to -48?
Answer:
16 x -3 and 16-3
Step-by-step explanation:
If you multiply 16 and -3 you get -48 and if you subtract 3 from 16 you get 13 (hope this helped) :)
Mason conducted a survey of his class to determine if they prefer to use pens or pencils for their math homework. Out of the 30 students in his class, 12 of them are male. A total of 21 students said they prefer pencils, and 12 of those students are female.
Fill in the missing joint and marginal frequencies in the table.
Pencils Pens Total
Male
% 10% 40%
Female
% 20%
%
Total 70%
% 100%
Answer:
Step-by-step explanation:
-Total column
30 students in the class
12 male , so 30-12 = 18 female
-Pencils column
21 students prefer pencils
12 female that prefer pencils , 21-12 = 9 male that prefer pencils
-Total row
21 students prefer pencils
30 students total, 30-21 = 9 students prefer pens
-Pens column
12 students male -9 students male prefer pencil =3 students male prefer pens
18 students female -12 students female prefer pencil =6 students female prefer pens
-to calculate the % always find the equivalent fraction of
30 students/ 100% = number of students you have / ?%
example: for male that prefer pencils we have 30/100 = 9/? so
? = 100*9 /30 =30%
how would i find the area of the blue region and the perimeter of the outer window frame
Answer:
The diameter is 6. The radius is 3. For the half of the orange circle.
The area of the half of the small orange circle is = pi*r*r = pi*3*3.
The diameter is 24. The radius is 12.
The area of the half of the light orange circle and the other colors is = pi*r*r = pi*12*12
The area of dark orange, light blue, purple and green figures = pi*12*12 – pi*3*3 = 135*pi
To get the area of the blue figure we need to divide 135*pi into ¼ and you will get the area of the blue figure.
The area of the blue figure =( ¼ )*135*pi *(1/2) = ¼ *1/2 = 1/8
The area of the blue figure is = 135pi / 8
B) outside perimeter of the window frame = 28 +pi*14 = 71.98
Hope this helps you :)
Question 4
A sector of a circle has a diameter of 16 feet and an angle of 2pi 5 this is a fraction by the way) radians. What is the area of the sector?
Answer:
40.2
Step-by-step explanation:
Diameter = 16, Radius = 16/2 = 8
Central angle = 2π/5 radians = 72°
Sector area,
8²π×(72/360)
= 64π/5
= 40.2 (rounded to the nearest tenth)
Answered by GAUTHMATH
Which set of angles are complementary
Answer:
A. <ECF and <BCF
Step-by-step explanation:
Complementary angles are angles that add up to give 90°
m<BCE = m<BCA = 90° (right angles)
m<ECF + m<BCF = m<BCA
m<ECF + m<BCF = 90° (Substitution)
Therefore, <ECF and <BCF are complementary angles.
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds. A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss when combining their special diet with running a mile a day over a period of two weeks. Interested in studying the dietitian's article further, you ask friends who have tried the dietitian's new program and you determine their weight loss to be 3.0 pounds in a two week period, on average. As you set up a hypothesis test to determine if the dietitian's article is correct, what is the dietitian's claim?
a. Adults should run every day to lose weight.
b. The average amount of weight loss is less than 2.52.5 pounds.
c. The average amount of weight loss is greater than 3.03.0 pounds.
d. The average amount of weight loss is greater than 2.52.5 pounds.
Answer:
d. The average amount of weight loss is greater than 2.5 pounds.
Step-by-step explanation:
After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds.
At the null hypothesis, we test if this mean is of 2.5, that is:
[tex]H_0: \mu = 2.5[/tex]
A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss.
With the additional weight loss, the dietitian claims that the mean is more than the value presented at the null hypothesis, that is, more than 2.5, and thus, the correct answer is:
[tex]H_1: \mu > 2.5[/tex]
And thus, the correct option is given by option d.
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value used is [tex]T_c = 2.132[/tex]
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 5 - 1 = 4
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357
The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
(-4/9)*3×(-27/20)*4=
(-4/9)*3×(-27/20)*4= 7.2
Step-by-step explanation:
here's the answer to your question
Which equation is equivalent to 24% = 82-3?
0 24x _ 22x-3
O 24% = 22%-6
O 24% = 23x-3
O 24% – 23%-9
Answer:
the 4th option
Step-by-step explanation:
8 = 2³
so, when we convert
[tex] {8}^{x - 3} [/tex]
into a "2 to the power of" expression, we get therefore
[tex] ({2}^{3}) ^{x - 3} [/tex]
and when we have an exponent of an exponent, we can simplify by multiplying these two exponents.
3×(x-3) = 3x - 9
and therefore we get
[tex] {2}^{3x - 9} [/tex]
and by the way, we can now even easily solve this for x, as we know
[tex] {2}^{4x} = {2}^{3x + x} [/tex]
after all, because 4x = x + x + x + x = 3x + x = ...
and because we got also
[tex] {2}^{4x} = {2}^{3x - 9} [/tex]
we know that 3x + x = 3x - 9
and that gives us x = -9
Instructions: Determine whether the lines
passing through the pairs of points are
parallel, perpendicular or neither.
• Line a: (5,3) and (5,7)
• Line b: (2,7) and (-1,7)
Select one:
O Perpendicular
Neither
Parallel
Answer: Perpendicular
Explanation
the gradient of line b is (7-7)/(-1-2) = 0/-3 = 0
Therefore it means that it is a horizontal line
Must click thanks and mark brainliest
Question 12 plz show ALL STEPS
9514 1404 393
Answer:
θ = 1.5 radians ≈ 85.9°
Step-by-step explanation:
The arc length in terms of central angle and radius is ...
s = rθ
where θ is the central angle in radians. Here, we want to find θ, so we have ...
θ = s/r . . . . divide by r
For the given numbers, ...
θ = (6 cm)/(4 cm) = 3/2 = 1.5 . . . radians
I radian is 180°/π, so 3/2 radians is ...
(3/2)(180°/π) = 270°/π ≈ 85.9°
Last year, Singh had $20,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 6% simple interest per year. After one year, he received a total of $1280 in interest. How much did he invest in each account?
Answer:
8000 and 12000 respectively
Step-by-step explanation:
Let the amount invested in first account be x and y be the amount invested in the second account.
ATQ, x+y=20000 and 1280=(7/100)*x+(6/100)*y
x=8000 and y=12000.
the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
Which table represents a linear function
Answer:
3rd option (top right)
Step-by-step explanation:
3rd option represents a linear equation
y = -2x-1
Answered by GAUTHMATH
find the supplement of 158 degrees and 17 minutes
Answer:
supplement of 158 degree
x+158=180
x=180-158
x=22 degree.
Step-by-step explanation:
This graph shows a portion of an odd function.
Use the graph to complete the table of values.
X
f(x)
-2.
-3
-4
-6
DONE
9514 1404 393
Answer:
-2-1-2-3Step-by-step explanation:
An odd function is symmetrical about the origin:
f(-x) = -f(x)
So, ...
f(-2) = -f(2) = -2
f(-3) = -f(3) = -1
f(-4) = -f(4) = -2
f(-6) = -f(6) = -3
Answer:
-2
-1
-2
-3
I did it on edge2020 and got it right
