Solving the first problem: n=15 and p=0.4.
Explanation:
Step 1. We are given the number of trials n
[tex]n=15[/tex]And the probability of success:
[tex]p=0.4[/tex]We need to find the probability of 4 successes P(4).
Step 2. Since it s a problem where the outcome is either success or failure, we use the binomial distribution formula:
[tex]p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}[/tex]Where p(x) is the probability of x successes. x is the number of successes, and q is the probability of a failure.
Step 3. In this case, x is 4:
[tex]x=4[/tex]The probability of failure is defined as follows:
[tex]\begin{gathered} q=1-p \\ \downarrow \\ q=1-0.4 \\ \downarrow \\ q=0.6 \end{gathered}[/tex]Step 4. Substituting the known values into the binomial distribution formula:
[tex]\begin{gathered} p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x} \\ \downarrow \\ p(4)=\frac{15!}{(15-4)!(4!)}(0.4)^4(0.6)^{15-4} \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} p(4)=\frac{15!}{(11)!(4!)}(0.0256)(0.6)^{11} \\ \downarrow \\ p(4)=\frac{15!}{(11)!4!}(0.0256)(0.003628) \end{gathered}[/tex]Step 5. Solving step by step and simplifying the factorial expressions, the result is:
[tex]\begin{gathered} p(4)=\frac{15!}{(11)!4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12\times11!}{(11)!4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12}{4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12}{4\times3\times2\times1}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{32760}{24}(0.0256)(0.003628) \\ \downarrow \\ p(4)=(1365)(0.0256)(0.003628) \\ \downarrow \\ p(4)=0.126776 \end{gathered}[/tex]The probability is 0.126776
Answer:
[tex]P\left(4successes\right)=0.126776[/tex]I have tried to solve this multiple times and keep getting different answers please help me
Given:
The measure of the central angle O = 10
And the area of the circle = 20 square inches
We will find the area of the sector subtended by ∠O using the ratio and the proportional as follows:
Area of the circle : Area of the sector
20 A
360° 10°
Using the cross product, we will find the value of A
[tex]A=\frac{10*20}{360}=\frac{5}{9}\approx0.55555_-[/tex]Rounding to the nearest tenth
So, the answer will be Area of the sector = 0.6 square inches
Hassan and Eva rode their bikes from the same starting point. Hassan rode his bike 5/6 of a mile, while Eva rode hers4/7 of mile. Which equation shows the mileage difference, d, in the distances they rode?A. 5/6 + d = 4/7B. d / 4/7 = 5/6C. d - 5/6 = 4/7D. 5/6 - d = 4/7
Solution
It is given that; Hassan and Eva rode their bikes from the same starting point.
Hassan rode his bike 5/6 of a mile
Eva rode hers 4/7 of a mile.
the mileage difference, d = 5/6 - 4/7
=> d + 4/7 = 5/6
=> 5/6 - d = 4/7
The correct option is D
write an equation for the line parallel to the given line that contains C C(2,4); y= -4x+7y=(type your answer in slope-intercept form)
Answer
The equation of the line is
y = -4x + 12
Explanation
Two straight lines that are parallel to each other normally have the same slopes.
So, to write the equation for our required line, we need to extract the slope from the line that is parallel to it.
To do that, we will note that
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, comparing this with y = -4x + 7
We can see that the slope of our required line is -4
To now write its equation, we will use the form of the equation of a straight line that uses the slope of the line and the coordinates of a point on the line.
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
For this line,
m = -4
(x₁, y₁) = (2, 4)
x₁ = 2
y₁ = 4
y - y₁ = m (x - x₁)
y - 4 = -4 (x - 2)
y - 4 = -4x + 8
y = -4x + 8 + 4
y = -4x + 12
Hope this Helps!!!
z InstructionsO ptsQuestion 1What is the y-intercept?- 101X25у678No new data to save. Last checked at 4:51 pmSubmit
To find the y-intercept we need to remember that this happens when x=0. Then, in our case, the y-intercept is 6.
Evaluate each using the values given. 4(x + z); use x = 3, and z = 1
Evaluate each using the values given. 4(x + z); use x = 3, and z = 1
we have
4(x + z)
For x=3 and z=1
substitute the given values in the expression
so
4(3+1)
4(4)
16
Plot the midpoint m of 21 and 22.ImAO 098+72176-54321+A++++++-9-8-7-6 -5 -4 -3-2+++++ +++ Re1 2 3 4 5 6 7 8 972-2-1-3 +-4-1-51-6-7-1-8.
Answer:
Explanation:
From the graph, we can see that the coordinate of z2 is (-4, -3) and that of z1 is (1,6) where;
[tex]\begin{gathered} x_1=-4 \\ y_1=-3 \\ x_2=1 \\ y_2=6 \end{gathered}[/tex]We'll go ahead and use the below midpoint formula to determine the coordinates of the midpoint of z1 and z2;
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Substituting the values into the above formula, we'll have;
[tex]\text{Midpoint}=(\frac{-4+1}{2},\frac{-3+6}{2})=(-\frac{3}{2},\frac{3}{2})[/tex]Let's go ahead and plot the above point on the graph;
how is 3^2 different from (-3)^2?
Given the following question:
3^2 = 3 * 3 = 9
(-3)^2 = -3 * -3 = 9
They are different because one is the multiplication of negative integers while the other isn't. Since a negative times a negative is a positive.
They are similar because they both have the same answers.
A triangular prism is 20 millimeters long and has a triangular face with a base of 16 millimeters and a height of 15 millimeters. The other two sides of the triangle are each 17 millimeters. What is the surface area of the triangular prism? A triangular prism is 20 millimeters long and has a triangular face with a base of 16 millimeters and a height of 15 millimeters. The other two sides of the triangle are each 17 millimeters. What is the surface area of the triangular prism?
The surface area of the triangular prism is 1,240 square millimeters.
Given:
A triangular prism is 20 millimeters long and has a triangular face with a base of 16 millimeters and a height of 15 millimeters. The other two sides of the triangle are each 17 millimeters.
we know that :
surface area of triangular prism is SA = 2B + PL
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the triangular prism
The area of the triangular face B = 1/2 base * height.
= 1/2(16 * 15)
= 1/2(240)
= 240/2
B = 120 square millimeters.
The perimeter of triangular face P = 16 + 17 +17
= 33 + 17
P = 50 millimeters.
substitute the values we get,
SA = 2B + PL
= 2(120) + (50)(20)
= 240 + 1000
SA = 1240 square millimeters.
Hence the surface area of the triangular prism is 1,240 square millimeters.
Learn more about the surface area and triangular prism here:
https://brainly.com/question/16765719
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I need to know for each word problem to know if it’s direct , inderect, or parrative and I want to know it because I have a quiz tom Problem number 1.
Recall that proportion is partitive if the word problem can be modeled by an equation of the form:
[tex]x=ky\text{.}[/tex]Where k is a constant. The above equation means that as one variable increases the other one increases too.
In the case of inverse proportion, when one varibale
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than 4". Let B be the event "the outcome is less than or equal to 1". Find P(A or B). Outcome Probability 1 0.29 2 0.07 3 0.53 4 0.05 5 0.05 6 0.01
solution
For this case we want to find this probability:
P(A)= P(outcome is greater than 4)
And replacing we got:
P(A)= 0.05+0.01= 0.06
P(A)= 0.06
2. Carole was scuba diving and descending 4.5 feet per second. If she stopped to look at coral that are 36.9 ft below the surface, how long did it take?
Speed = distance / time
time = distance / speed
Distance = 36.9 ft
Speed = 4.5 feet per second
Replacing:
Time = 36.9 / 4.5 = 8.2 seconds
Factor the given expression by determining any common monomial factorsthat may exist 6k2m - 3k + 9km2 - 12k2m2
ANSWER
[tex]=3k\left(3m^2+2km-4km^2-1\right)[/tex]EXPLANATION
Given;
[tex]6k^2m-3k+9km^2-12k^2m^2[/tex]The common factor is 3k;
Hence, factor out the common term;
[tex]\begin{gathered} =3k\left(2mk-1+3m^2-4m^2k\right) \\ =3k\left(3m^2+2km-4km^2-1\right) \end{gathered}[/tex]Your bill at PF chang’s was 58.74. You are leaving a 20 percent tip how much is the tip ?
We remember that for calculating percentages, we take the percent as a fraction. And that it becomes a multiplication between the fraction and the number. For example, 15% represents:
[tex]15\%=\frac{15}{100}=\frac{3}{20}[/tex]When we simplify the last fraction.
Now, in our exerciseIn this exercise, we have to calculate the tip, which is the 20% of the total bill. As we see before, we just have to calculate the fraction and make the multiplication between that fraction and the bill value (58.74).
[tex]\begin{gathered} 20\%\text{ of 58.74}=\frac{20}{100}\cdot58.74 \\ =\frac{1}{5}\cdot58.74 \\ =\frac{58.74}{5} \\ =11.748 \end{gathered}[/tex]This means that the tip will be $11.748.
Use special right triangle ratios to find the length of the hypotenuse.OA. 30O B. 15√/3O C. 15O D. 15√/245°1545
Given:
The given triangle is right angled triangle.
The angle is 45 degrees.
The adjacent side is 15.
Required:
We need to find the hypotenuse of the given triangle.
Explanation:
Consider the cosine formula.
[tex]cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex][tex]Substitute\text{ }\theta=45\degree\text{ and adjacent side=15 in the formula.}[/tex][tex]cos45\degree=\frac{15}{hypotenuse}[/tex][tex]hypotenuse=\frac{15}{cos45\degree}[/tex][tex]Use\text{ }cos45\degree=\frac{\sqrt{2}}{2}\text{ in the equation.}[/tex][tex]hypotenuse=\frac{15}{\frac{\sqrt{2}}{2}}[/tex][tex]hypotenuse=15\times\frac{2}{\sqrt{2}}[/tex][tex]hypotenuse=15\times\frac{\sqrt{2}\times\sqrt{2}}{\sqrt{2}}[/tex][tex]hypotenuse=15\times\sqrt{2}[/tex][tex]hypotenuse=15\sqrt{2}[/tex]Final answer:
[tex]hypotenuse=15\sqrt{2}[/tex]if Maria's garden is 5 feet long and 3 feet wide what is the area of her garden
Assuming that the garden is rectangular.
Area of the garden = length*width = 5*3 = 15 square feet
After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to the surface of the water. They start 1500 feet underwater. After ascending for 6 hours, they are 1380 feet below the surface of the water. (Note: under the water is negative)Write and equation to model this situation (use d for depth in meters and x for hours).
Variables
d: depth, in ft
x: time, in hours
The first point is (0, -1500) that is, at zero hours, they were 1500 ft underwater
The second point is (6, -1380), that is, at six hours, they were 1380 ft underwater
The slope of the line that connects these two points is:
[tex]m=\frac{-1380-(-1500)}{6-0}=\frac{120}{6}=20\frac{ft}{h}[/tex]From the point (0, -1500) the y-intercept of the line is b = -1500
Using the slope-intercept form of the line we get:
y = mx + b
d = 20x - 1500
If New York is 2 inches from Chicago, what is the distance between the two cities?
Since the picture is giving you the information about the scale equivalence in which
[tex]1inch=557\text{miles}[/tex]use this information to obtain what is 2 inches
[tex]2inches\cdot\frac{557miles}{1inch}=1,114miles[/tex]the distance between the 2 cities will be 1,114 miles
In order to start a small business, a student takes out a simple interest loan for $2000.00 for 3 months at a rate of 12.25% The amount of interest is $61.25 The future value is?
Hello!
The formula to calculate the future value is:
[tex]A=P\cdot(1+\frac{r}{100}\cdot t)[/tex]As we know the values, let's replace them:
[tex]\begin{gathered} A=2,000\cdot(1+0.1225\cdot0.25) \\ A=2,000\cdot(1+0.030625) \\ A=2,0000\cdot1.030625 \\ A=61.25 \end{gathered}[/tex][tex]\begin{gathered} FV=i\cdot(1+(r\cdot t)) \\ FV=62.25\cdot(1+(0.1225\cdot0.25)) \\ FV=62.25\cdot(1+0.030625) \\ FV=62.25\cdot1.030625 \\ FV\cong64.156 \end{gathered}[/tex]Andrew can paint the neighbour's house 3 times as fast as Bailey. The year Andrew in Bailey work together, it took them 4 days. How long would it take each to paint the house?
Andrew can paint the neighbour's house 3 times as fast as Bailey. The year Andrew in Bailey work together, it took them 4 days. How long would it take each to paint the house?
Let
x -----> Andrew's time to paint the house
y ----> Balley's time to paint the house
we have that
x+y=4 ------> equation A
x=y/3 -----> equation B
substitute equation B in equation A
(y/3)+y=4
solve for y
(4/3)y=4
y=3 days
x=3/2=1 day
therefore
Andrew's time to paint the house is 1 day
Balley's time to paint the house is 3 days
s 1 05 1 -1.5 -05 0.5 1 -0.5 -1.5 If the cosine of in this unit circle is a, what would be true of the cosine of in a circle with a radius of 2?
In the unit circle
[tex]\cos ^2x+\sin ^2x=1[/tex][tex]x^2+y^2=r^2[/tex]Where r is the radius of the circle
x- coordinate represents cos angle
cos angle = x/r
Since r = 2
cos angle = x/2
y-coordinate represents sin angle
sin angle = y/r
sin angle = y/2
Because the question is incomplete
we can not find which is true
Which answer represents the domain of the logarithmic function given below?F(x) = log7 xA.x 0B.x < 0C.x > 0D.All real numbers
ANSWER
C. x > 0
EXPLANATION
The argument of a logarithm must be positive - i.e. it is not defined for negative values or zero.
In this case, the argument of the logarithm is x so, the domain of this function is x > 0.
Write the equation of the line perpendicular to y=5/3x+2 that passes through the point (-3,5)
Answer
The equation of the line in point-slope form is
y - 5 = (-3/5) (x + 3)
We can simplify this to obtain the slope-intercept form
y - 5 = (-3/5) (x + 3)
y - 5 = (-3x/5) - (9/5)
y = (-3x/5) - (9/5) + 5
y = (-3x/5) + (16/5)
Then, to put the whole thing in a simplified equation form, we multiply through by 5
y = (-3x/5) + (16/5)
5y = -3x + 16
3x + 5y = 16
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
So, we just need to compute the slope of this line since a point on the line has already been provided (-3, 5)
For two lines with slopes m₁ and m₂ that are perpendicular to each other, the slopes are related through the relation
m₁m₂ = -1
And the slope-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, the slope of the line whose equation is given in the question is
m₁ = (5/3)
This is obtained by comparing y = mx + b with y = (5/3)x + 2
So, we can obtain the slope of the line that we need
m₁m₂ = -1
m₁ = (5/3)
m₂ = ?
m₁m₂ = -1
(5/3) × m₂ = -1
(5m₂/3) = -1
Cross multiply
m₂ = (-3/5)
So, we can write the equation in point-slope form now
Recall that
y - y₁ = m (x - x₁)
m = slope = (-3/5)
Point = (x₁, y₁) = (-3, 5)
x₁ = -3
y₁ = 5
y - y₁ = m (x - x₁)
y - 5 = (-3/5) (x - (-3))
y - 5 = (-3/5) (x + 3)
Hope this Helps!!!
Select the correct answer.For 2 =2cis , find in rectangular form.O A. 16731673 - 161ОВ.16V3 + 161OC. –32/3 – 321OD.-1673 - 161O E. -1673 + 161|
To raise a complex number to a power, we use the De Moivre's Theorem.
Given,
[tex]z=2cis\frac{\pi}{6}[/tex]We can expland and write in >>>
[tex]\begin{gathered} 2(\cos \theta+i\sin \theta) \\ =2(\cos \frac{\pi}{6}+i\sin \frac{\pi}{6}) \end{gathered}[/tex]De Moivre's theorem tells us >>>>
[tex]\lbrack r(\cos \theta+i\sin \theta)\rbrack^n=r^n(\cos n\theta+i\sin n\theta)[/tex]Let's raise the complex number given to the fifth power >>>>
[tex]\begin{gathered} \lbrack2(\cos \frac{\pi}{6}+i\sin \frac{\pi}{6})\rbrack^5 \\ =2^5(\cos \frac{5\pi}{6}+i\sin \frac{5\pi}{6}) \\ =32(-\frac{\sqrt3}{2}+i\frac{1}{2}) \\ =-16\sqrt[]{3}+16i \end{gathered}[/tex]Can you pls help me with number 11 thank you
Following the PEMDAS order:
3[2 + 3(2² + 6)] + 3³ =
3[2 + 3(4 + 6)] + 27 =
3[2 + 3 x 10] + 27 =
3[2 + 30] + 27 =
3 x 32 + 27 =
96 + 27 =
123
What is the change in y direction? (Blue arrow)? What is he change in x direction ( green arrow)?
Explanation:
The graph given is a straight line with a positive gradient. This means as x increases, y increases.
The direction of the change in y and the change in x is in the direction of the blue and green arrows respectively.
Answer: Change in y: up
Change in x: to the right
Identify the two tables which represent quadratic relationships.*01UNلیا انу34Х0123Eу-4-8-10-10х1230 4у-4-44Х13NONICOу-4-16X01AN00 Wy12X0123у-2.024
In a quadratic relationship, the magnitud of y grows more and more.
A linear relationship, for example, is different because it always grows the same.
Their graphs look like:
Let's find how the magnitude of y change on each table:
First choice
From y = 3 to y = 4, it changes 1,
from y = 4 to y = 5 it changes 1
from y = 5 to y = 6 it changes 1.
CONLUSION: it always change the same, that is why it is a linear relationship
Second choice
From y = -4 to y = -8, it changes 4 unities,
from y = -8 to y = -10 it changes 2
from y = -10 to y = -10 it changes 0.
find the horizontal and vertical asymptots,b) find the continuity intervalc) find discontinuity and type of discontinuity
The function given is,
[tex]f(x)=\frac{1}{\sqrt[]{x+1}}[/tex]The graph of this function:
We can also find the asymptotes the following way:
Horizontal Asymptote
[tex]\begin{gathered} f(x)=\frac{1}{\sqrt[]{x+1}} \\ y=\frac{1}{\sqrt[]{x+1}} \\ y=\frac{\frac{1}{x}}{\sqrt[]{\frac{x}{x}+\frac{1}{x}}} \\ y=\frac{\frac{1}{x}}{\sqrt[]{1+\frac{1}{x}}} \\ as \\ x\rightarrow\infty \\ y\rightarrow0 \end{gathered}[/tex]As for Vertical Asymptote,
[tex]\begin{gathered} x+1\neq0 \\ x\neq-1 \\ ------- \\ VA\rightarrow x=-1 \end{gathered}[/tex](a)From the graph, we can see that horizontal asymptote is at y = 0
And, the vertical asymptote is at x = -1
The graph below (with asymptotes showing):
(b)As seen from the graph, the function is continuous from x > -1
There aren't any function at x = -1 and less
So, the continuity interval is
[tex]x>-1[/tex](c)The function is discontinuous at x = -1
This is an infinite discontinuity because it's a vertical asymptote.
4 minutes 45 seconds = ?
In order to express the 4 minutes and 45 seconds in seconds, we just have to follow these steps:
1 . Note that one part of the time is already in seconds (45 seconds), then we leave it the way it is and just convert the part in minutes.
4 minutes + 45 seconds
2. convert the time in minutes to seconds, one minute is equivalent to 60 seconds, then 4 minutes is equivalent to 4 times 60 seconds, then we get:
4×60 seconds + 45 seconds
240 seconds + 45 seconds
3. Add 240 and 45
240 + 45 = 285
Then, 4 minutes 45 seconds = 285 seconds
prove the kites have a pair of congruent opposite angles given kits is a kiteprove angle kit is congruent to angle KET
Let us make a drawing to understand the situation:
By the definition of kites, we have that the red sides are congruent (namely, they have the same length), and the black sides are congruent as well. Then, the triangles
[tex]\bigtriangleup ABD\cong\bigtriangleup CBD[/tex]are congruent (SSS criteria). When two triangles are congruent, corresponding angles are congruent as well. Then, for angle A and angle C are corresponding angles, we have
[tex]\measuredangle A\cong\leq C[/tex]Please help me with this problem.3.Gavin deposited money into his savings account with an annual interest rate of 9%. Gavin thought the equivalent quarterly interest rate would be 2.25%. Is Gavin correct? If he is, explain why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your answer.Answer:
Solution
Annual interest rate = 9%
Note that the annual interest rate is the interest for the whole year.
Now, let us fnd the equivalent quarterly interest rate
For quarterly interest rate, we have
[tex]\frac{1}{4}\times9=\frac{9}{4}=2.25[/tex]Quarterly interest rate is 2.25%
Therefore, Gavin is correct