Answer:
Approximately 56.7%.
Step-by-step explanation:
Choose two people at random from the crowd and there will be two cases:
Zero or one out of the two person was rooting for the champion, or both were rooting for the champion.There's no third possible outcome. In other words, the two cases are mutually exclusive. Either the first or the second event is expected to happen. The sum of their probabilities shall equal to 1.
66 out of that 100 were rooting for the champion. The probability that both were rooting for the champion will be easier to find. The probability that the first person is rooting for the champion is equal to [tex]66/100[/tex].
After that first person was chosen from the crowd, the 65 out of the remaining 99 person in the crowd were chanting. The probability that the second person is rooting as well will equal to [tex]65/100[/tex].
Both event shall take place. The probability that both were rooting for the champion will equal to
[tex]\displaystyle \frac{66}{100} \times \frac{65}{99}[/tex].
The probability that one or zero out of the two persons were rooting will equal to
[tex]\displaystyle 1 - \frac{66}{100} \times \frac{65}{99} \approx \frac{17}{30} = 56.7\%[/tex].
Answer:
56.7% is correct.
Step-by-step explanation:
All rhombus have all sides that are equal in length but which one are rhombus or not. Need help on this.
Answer:
I think that the first one is not a rhombus but the last two are.
The city of Odessa, Texas is building a wheelchair ramp to make their courthouse accessible for persons in a wheel chair. The Americans with Disabilities Act (ADA) requires that a wheelchair ramp have an angle of elevation of 4.8°. The ADA guidelines also allow a maximum run of 30 feet of ramp before installing a rest platform. At the Odessa courthouse, the ramp must rise 2.5 feet to reach the top of the steps. Will they have to install a rest platform on their ramp?
Answer:
No they will not have to install a rest platform.
The ramp will be 29.88 feet long so they will not have to install a rest platform.
Step-by-step explanation:
The mean number of births per minute in a country in a recent year was about three. Find the probability that the number of births in any given minute is (a) exactly four, (b) at least four, and (c) more than four.
Final answer:
To find the probability, we use the Poisson probability formula with a mean of three. The probability of exactly four births is 0.168, the probability of at least four births is 0.361, and the probability of more than four births is 0.193.
Explanation:
To find the probability in each case, we will use the Poisson probability formula since the number of births per minute in a country follows a Poisson distribution with a mean of three.
(a) Exactly four births in a minute:
The probability of exactly four births in a minute can be calculated using the Poisson probability formula:
P(X = 4) = (e⁻³* 3⁴) / 4! = 0.168
(b) At least four births in a minute:
The probability of at least four births in a minute is the complement of the probability of having three or fewer births in a minute:
P(X ≥ 4) = 1 - P(X ≤ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)) = 1 - (0.049 + 0.147 + 0.221 + 0.222) = 0.361
(c) More than four births in a minute:
The probability of more than four births in a minute is the complement of the probability of having four or fewer births in a minute:
P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)) = 1 - (0.049 + 0.147 + 0.221 + 0.222 + 0.168) = 0.193
Geometry
The picture below shows the question and answer choices for the questions.
Look at the table for the people that used Lithium.
There are 18 relapses, 6 No relapses with a total of 24 people.
The relative frequency for relapse, would be dividing the number of relapses by the total number of people.
This would be D. 18 / 24 = 75%
In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
A.
m∠1 = m∠7
B.
m∠3 = m∠6
C.
m∠5 + m∠8 = 90°
D.
m∠6 + m∠7 = 180°
Answer:
The correct answer is option B.
m<3 = m<6
Step-by-step explanation:
From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.
To find the correct option
From the given figure we get
Corresponding angles are,
<1 & <5, <2&<6, <2&<7 and <4 &<8
Alternate interior angles are,
<3 & <6 and <4 &<5
Alternate interior angles are equal.
m<3 = m<6
Therefore the correct answer is optionB
The yearly profit or loss for a clothing store is shown for a period of three years. Use a calculator to determine the clothing strore’s overall profit or loss in the three years.
Answer:
loss of $12,481.38
Step-by-step explanation:
It is usually a good idea to follow directions. (See attached.)
The sum of the three profit values is -$12,481.38, indicating a loss in the 3-year period.
What is the simplified form of the quantity x over 3 plus y over 4 all over the quantity x over 4 minus y over 3? the quantity 4x plus 3y all over the quantity 3x minus 4y the quantity 4x minus 3y all over the quantity 3x plus 4y the quantity 3x plus 4y all over the quantity 4x minus 3y the quantity 3x minus 4y all over the quantity 4x plus 3y
Answer:
Option A) [tex]\frac{4x+3y}{3x-4y}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}[/tex]
Taking LCM in upper and lower fractions, we get:
[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}\\\\ =\frac{\frac{4x+3y}{12}}{\frac{3x-4y}{12}}\\\\\text{Cancelling out the common factor 12, we get:}\\\\ =\frac{4x+3y}{3x-4y}[/tex]
Therefore, the option A gives the correct answer.
I need help with this problem.
Answer: y = -1/4x - 4
Step-by-step explanation:
y = (-1/4)x + 2 (This is the first linear function.)
(4,3) has slope of (-1/4)x or (1/-4)x
4(y2) - 4(y1= the new y -1(x2) -3(x1) = new x which leads to (0,-4) so y-intercept = -4
so all in all, y = (-1/4)x -4 is the answer
Hopefully, you're able to understand this. It's difficult to explain through typed words rather than visually and through a written example.
Same y intercept as x+4y=8 through (4,3)
Y intercept is when x=0, so 4y=8, so y=2 and the y intercept is (0,2)
Answer for y intercept: (0,2)
So we need the line through (0,2) and (4,3). Point-point form says the line through (a,b) and (c,d) is
(c-a)(y-b) = (d-b)(x-a)
(4 - 0)(y - 2) = (3 - 2)(x - 0)
4y - 8 = x
Answer for the line: x - 4y = -8
Check:
(0,2) is on the line: 0-4(2) = -8 check
(4,3) is on the line 4 - 4(3) = -8 check
I need your help badly. I get confused with recursive
Check the picture below.
the first one is simply a serie, using the previous term - 3 times the one after it.
the second one is just an arithmetic sequence, where you add the previous term plus the ordinal position.
the third one is also an arithmetic sequence, simply adding the previous term with 1.4.
recall that an arithmetic sequence is adding up, a geometric sequence is multiplying about.
The length of the major axis of the ellipse below is 13. What is the sum of the lengths of the red and blue line segments
Answer:
13
Step-by-step explanation:
If the length of a major axis of an ellipse is 13, the sum of the lengths of the red and blue line segments is 13.
P = point in the figure
F1 = focus
F2 = focus
PF1 + PF2 = 13
If two planes are perpendicular to the same line, then
A. they are perpendicular to each other
B. not enough information
C. they form a straight line
D. they are parallel
Answer:
D. they are parallel
Step-by-step explanation:
A plane can be defined by a point and a direction vector that is perpendicular to the plane. If two planes have the same direction vector (perpendicular line), then they are either the same plane or they are parallel.
If two planes are perpendicular to the same line, then they must also be parallel to each other.
If two planes are perpendicular to the same line, then they are also parallel to each other. This is because any line that intersects two parallel planes will be perpendicular to both planes.
To illustrate this, imagine two planes, A and B, that are perpendicular to the same line, L. If we draw a line, M, that intersects both planes, then M will be perpendicular to both planes A and B. This is because lines A and B are parallel to each other, and any line that intersects two parallel lines will be perpendicular to both lines.
Therefore, if two planes are perpendicular to the same line, then they must also be parallel to each other. The answer is D. they are parallel.
For such more question on perpendicular
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Find the cosine of angle Z
Answer:
[tex]cosZ=\frac{3}{5}[/tex]
Step-by-step explanation:
Cos of an angle by definition of its ratio is side adjacent/hypotenuse. The side adjacent to angle Z cannot be the hypotenuse, so it has to be 6. The hypotenuse is 10. Therefore,
[tex]cosZ=\frac{6}{10}=\frac{3}{5}[/tex]
NEED HELP PLEASE ANSWER THIS MATH QUESTION
Answer:
Δ ABC was dilated by a scale factor of 1/2, reflected across the y-axis
and moved through the translation (3 , 2)
Step-by-step explanation:
* Lets explain how to solve the problem
- The similar triangles have equal ratios between their
corresponding side
- So lets find from the graph the corresponding sides and calculate the
ratio, which is the scale factor of the dilation
- In Δ ABC :
∵ The length of the horizontal line is x2 - x1
- Let A is (x1 , y1) and B is (x2 , y2)
∵ A = (-4 , -2) and B = (0 , -2)
∴ AB = 0 - -4 = 4
- The corresponding side to AB is ED
∵ The length of the horizontal line is x2 - x1
- Let E is (x1 , y1) , D is (x2 , y2)
∵ E = (5 , 1) and D = (3 , 1)
∵ DE = 5 - 3 = 2
∵ Δ ABC similar to Δ EDF
∵ ED/AB = 2/4 = 1/2
∴ The scale factor of dilation is 1/2
* Δ ABC was dilated by a scale factor of 1/2
- From the graph Δ ABC in the third quadrant in which x-coordinates
of any point are negative and Δ EDF in the first quadrant in which
x-coordinates of any point are positive
∵ The reflection of point (x , y) across the y-axis give image (-x , y)
* Δ ABC is reflected after dilation across the y-axis
- Lets find the images of the vertices of Δ ABC after dilation and
reflection and compare it with the vertices of Δ EDF to find the
translation
∵ A = (-4 , -2) , B = (0 , -2) , C (-2 , -4)
∵ Their images after dilation are A' = (-2 , -1) , B' = (0 , -1) , C' = (-1 , -2)
∴ Their image after reflection are A" = (2 , -1) , B" = (0 , -1) , C" = (1 , -2)
∵ The vertices of Δ EDF are E = (5 , 1) , D = (3 , 1) , F = (4 ,0)
- Lets find the difference between the x-coordinates and the
y- coordinates of the corresponding vertices
∵ 5 - 2 = 3 and 1 - -1 = 1 + 1 = 2
∴ The x-coordinates add by 3 and the y-coordinates add by 2
∴ Their moved 3 units to the right and 2 units up
* The Δ ABC after dilation and reflection moved through the
translation (3 , 2)
1. Write 3,876,943,000 using scientific notation.
Use the 1x10^6 style format for entering your answer. No spaces between characters.
2. Write 0.0007317 using scientific notation.
Use the 1x10^-6 style format for entering your answer. No spaces between characters.
Answer:
3.876943x10^9
7.317x10^-4
Step-by-step explanation:
3,876,943,000
Put the decimal at the end
3,876,943,000.
Move it so only 1 number is before the decimal
3.876943000
We moved it 9 places, so that is the exponent
We moved it to the left, so the exponent is positive
The three zeros at the end can be dropped because they are the last numbers to the right of the decimal
3.876943x10^9
0.0007317
Move it so only 1 number is before the decimal
00007.317
We moved it 4 places, so that is the exponent
We moved it to the right, so the exponent is negative
The four zeros at the left can be dropped because they are the last numbers to the left of the whole number
7.317x10^-4
If ax*x + bx + c = 0, then what is x?
Answer:
Quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Step-by-step explanation:
If you want to solve something that looks like [tex]ax^2+bx+c=0[/tex], the answer will have this form [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
This is called the quadratic formula.
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.
A.) 3
B.) 1/3
C.) -1/3
D.) -3
Answer:
-3 is the value of k in g(x)=kf(x)
Step-by-step explanation:
Both functions cross nicely at x=-3 so I'm going to plug in -3 for x:
g(x)=kf(x)
g(-3)=kf(-3)
To solve this for k we will need to find the values for both g(-3) and f(-3).
g(-3) means we want the y that corresponds to x=-3 on the curve/line of g.
g(-3)=-3
f(-3) means we want the y that corresponds to x=-3 on the curve/line of f.
f(-3)=1
So our equation becomes:
g(-3)=kf(-3)
-3=k(1)
-3=k
So k=-3.
This is about interpretation of graphs.
Option C is correct.
From the graph, we can see the 2 lines representing function f(x) and function g(x). Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.We see that the best point for that is where x = -3.
For f(x), when x = -3, y = 1For g(x), when x = -3, y = -3we can rewrite them as;
x = -3, f(-3) = 1 and x = -3, g(-3) = -3
Let us plug in the relevant values into g(x) = k⋅f(x) to get;-3 = k(1)
Thus; k = -1/3
Read more at; https://brainly.com/question/13903701
I need some help with graphing again.
To find the x intercepts, we need to put the standard form equation into factored form.
Which two numbers multiply to -8 and add to -2?
[tex]-4*2=-8[/tex]
[tex]-4+2=-2[/tex]
So the factored form is
[tex](x-4)(x+2)[/tex]
That means the x intercepts are at [tex]x=4,-2[/tex]
So now we have the x intercepts.
To find the vertex, we need to convert the standard form equation into vertex form.
The formula of vertex form is [tex]y=a(x-h)^2+k[/tex]
Since the a value in the standard form equation is 1, the a value in vertex form is also one.
The h value can be found using the formula [tex]h=\frac{-b}{2a}[/tex]
Which comes out to [tex]\frac{2}{2}[/tex] or 1.
To find the k value, we can just plug in what we got for h back into the equation.
[tex](1)^2-2(1)-8=-9[/tex]
So the vertex is [tex](1,-9)[/tex].
This also means the axis of symmetry is [tex]x=-1[/tex]
Finally, to find the y intercept, we plug in 0 for x and solve.
[tex](0)^2-2(0)-8=-8[/tex]
So the y intercept is [tex](0,-8)[/tex].
Please assist me with this problem.
Answer:
4
(We didn't even need to use (9,6) )
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
We are given the line we are looking for has the same y-intercept as x+2y=8.
So if we put x+2y=8 into y=mx+b form we can actually easily determine the value for b.
So we are solving x+2y=8 for y:
x+2y=8
Subtract x on both sides:
2y=-x+8
Divide both sides by 2:
y=(-x+8)/2
Separate the fraction:
y=(-x/2)+(8/2)
Reduce the fractions (if there are any to reduce):
y=(-x/2)+4
Comparing this to y=mx+b we see that b is 4.
So the y-intercept is 4.
Again since we know that the line we are looking for has the same y-intercept, then the answer is 4 since the question is what is the y-intercept.
4
Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?
32%
68%
95%
99.7%
Answer: Second Option
68%
Step-by-step explanation:
First we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=27[/tex]
The standard deviation is:
[tex]\sigma=3[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=24 the Z-score is:
[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]
For x=30 the Z-score is:
[tex]Z_{30}=\frac{30-27}{3}=1[/tex]
Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of pizzas are delivered between 24 and 30 minutes
URGENT NEED THIS ANSWER SOON FOR THIS MATH QUESTION
Answer:
22.2 ft²
Step-by-step explanation:
The area (A) of the sector is
A = area of circle × fraction of circle
= πr² × [tex]\frac{50}{360}[/tex]
= π × 7.13² × [tex]\frac{5}{36}[/tex]
= π × 50.8369 × [tex]\frac{5}{36}[/tex]
= [tex]\frac{50.8369(5)\pi }{36}[/tex] ≈ 22.2 ft² ( nearest tenth )
Answer:
Area of smaller sector = 22.2 ft²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
To find the area of circle
Here r = 7.13 ft
Area = πr²
= 3.14 * 7.13²
= 159.63 ft²
To find the area of smaller sector
Here central angle of sector is 50°
Area of sector = (50/360) * area of circle
= (50/360) * 159.63
= 22.17 ≈ 22.2 ft²
When the women's soccer team won the state championship, the parent boosters welcomed the team back to school with a balloon bouquet for each of the 18 players. The parents spent a total of $94.32 (excluding tax) on foil balloons that cost $1.94 each and latex school-color balloons that cost $0.17 each. Each player received 10 balloons, and all the balloon bouquets were identical. How many of each type of balloon did each bouquet include?
Each bouquet included
nothing foil balloons and
nothing latex balloons.
Answer:
Each bouquet included 2 foil balloons and 8 latex balloons.
Step-by-step explanation:
Let f represent the number of foil balloons in each bouquet. Then 10-f is the number of latex balloons. The problem statement tells us the cost of all of the bouquets is ...
18(1.94f +0.17(10-f)) = 94.32
We can divide by 18 to get ...
1.94f +1.70 -0.17f = 5.24
1.77f = 3.54 . . . . . . . . . . . . subtract 1.70
f = 3.54/1.77 = 2 . . . . . . . . divide by the coefficient of f
The number of latex balloons is 10-2 = 8.
Each bouquet included 2 foil and 8 latex balloons.
I need help with these. They are hard.
Answer:
Find the explicit from for the sequence [tex]t_n=t_{n-1}+4,t=6[/tex]:
[tex]a_n=4n+2[/tex]
This next question I edited a bit. Your question just says find the four terms. I'm assuming they meant the first four. I also changed the c to an [tex]a[/tex].
Find the first four terms of the sequence given by: [tex]a_n=n a_{n-1}-3,a_1=2[/tex]:
a) 2,1,0.-3
You might want to read that second question again because there is errors in the question or things that don't really make sense. I made my own interpretation of the problem based on my own mathematical experience.
Step-by-step explanation:
So your first question actually says that you can find a term by taking that term's previous term and adding 4.
So more terms of the sequence starting at first term 6 is:
6,10,14,18,....
This is an arithmetic sequence. When thinking of arithmetic sequences you should just really by thinking about equations of lines.
Let's say we have this table for (x,y):
x | y
----------
1 6
2 10
3 14
4 18
So we already know the slope which is the common difference of an arithmetic sequence.
We also know point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line. You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.
[tex]y-6=4(x-1)[/tex]
[tex]y=6+4(x-1)[/tex] :I added 6 on both sides here.
[tex]y=6+4x-4[/tex] :I distribute here.
[tex]y=4x+2[/tex] :This is what I get after combining like terms.
So [tex]a_n=y[/tex] and [tex]x=n[/tex] so you have:
[tex]a_n=4n+2[/tex]
---------------------------------------------------------------------------------------
The first four terms of this sequence will be given by:
[tex]a_1,a_2,a_3,a_4[/tex]
[tex]a_1=2[/tex] so it is between choice a, c, and d.
[tex]a_n=na_{n-1}-3[/tex]
To find [tex]a_2[/tex] replace n with 2:
[tex]a_2=2a_{1}-3[/tex]
[tex]a_2=2(2)-3[/tex]
[tex]a_2=4-3[/tex]
[tex]a_2=1[/tex]
So we have to go another further the only one that has first two terms 2,1 is choice a.
A circle has a radius of 10.9 cm. If the area is multiplied by 6, what happens to the radius? HELP ASAP!!
The radius is multiplied by √6
The radius is multiplied by 6.
The radius is multiplied by 36.
Answer:
root 6
Step-by-step explanation:
pi*r^2 = A
6*pi*r^2 = 6A
6*r^2 = new radius squared
root 6 * r = new radius
The correct answer is option 1) The radius is multiplied by [tex]\sqrt{6}[/tex]
[tex]A = \pi r^2[/tex]
where A is the area and r is the radius.
If the area is multiplied by 6, we can represent this with the following equation:
A' = 6A
where A' is the new area and let r' be its radius.
[tex]A' = \pi (r')^2[/tex]
Substituting this into the equation for the new area gives us:
[tex]\pi (r')^2 = 6*(\pi r^2)[/tex]
To solve for r', we can divide both sides of the equation by [tex]\pi[/tex]:
[tex](r')^2 = 6r^2[/tex]
Next, take the square root of both sides to solve for r':
[tex]r' = \sqrt{6}r[/tex]
Therefore, the new radius r' is the original radius r multiplied by [tex]\sqrt{6}[/tex].
Write an equation in standard form for each ellipse with center (0, 0) and co-vertex at (5, 0); focus at (0, 3).
Answer:
The required standard form of ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].
Step-by-step explanation:
The standard form of an ellipse is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where, (h,k) is center of the ellipse.
It is given that the center of the circle is (0,0), so the standard form of the ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] .... (1)
If a>b, then coordinates of vertices are (±a,0), coordinates of co-vertices are (0,±b) and focus (±c,0).
[tex]c^2=a^2-b^2[/tex] .... (2)
If a<b, then coordinates of vertices are (0,±b), coordinates of co-vertices are (±a,0) and focus (0,±c).
[tex]c^2=b^2-a^2[/tex] .... (3)
It is given that co-vertex of the ellipse at (5, 0); focus at (0, 3). So, a<b we get
[tex]a=5,c=3[/tex]
Substitute a=5 and c=3 these values in equation (3).
[tex]3^2=b^2-(5)^2[/tex]
[tex]9=b^2-25[/tex]
[tex]34=b^2[/tex]
[tex]\sqrt{34}=b[/tex]
Substitute a=5 and [tex]b=\sqrt{34}[/tex] in equation (1), to find the required equation.
[tex]\frac{x^2}{5^2}+\frac{y^2}{(\sqrt{34})^2}=1[/tex]
[tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex]
Therefore the required standard form of ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].
find all solutions of each equation on the interval 0 ≤ x < 2 pi.
tan^2 x sec^2 x +2 sec^2 x - tan^2 x=2
SOMEONE PLEASE HELPPP!!
Answer:
[tex]x = 0 , \pi , 2\pi[/tex]
Step-by-step explanation:
The given equation is:l
[tex] \tan^{2} (x) \sec^{2} x + 2 \sec^{2} x - \tan^{2} x = 2[/tex]
Add -2 to both sides of the equation to get:
[tex] \tan^{2} (x) \sec^{2} x + 2 \sec^{2} x - \tan^{2} x - 2 = 0[/tex]
We factor the LHS by grouping.
[tex]\sec^{2} x(\tan^{2} (x) + 2 ) - 1( \tan^{2} x + 2) = 0[/tex]
[tex](\sec^{2} x - 1)(\tan^{2} (x) + 2)= 0[/tex]
We now apply the zero product property to get:
[tex](\sec^{2} x - 1) = 0 \: \: or \: \: (\tan^{2} (x) + 2)= 0[/tex]
This implies that:
[tex]\sec^{2} x = 1 \: \: or \: \: \tan^{2} (x) = - 2[/tex]
[tex] \tan^{2} (x) = - 2 \implies \tan(x) = \pm \sqrt{ - 2} [/tex]
This factor is never equal to zero and has no real solution.
[tex]\sec^{2} x = 1[/tex]
This implies that:
[tex]\sec \: x= \pm\sqrt{1} [/tex]
[tex] \sec(x) = \pm - 1[/tex]
Recall that
[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]
We reciprocate both sides to get:
[tex] \cos(x) = \pm1[/tex]
[tex]\cos x = 1 \: or \: \cos x = - 1[/tex]
[tex]\cos x = 1 \implies \: x = 0 \: or \: 2\pi[/tex]
[tex]\cos x = - 1 \implies \: x = \pi[/tex]
Therefore on the interval
[tex]0 \leqslant x \leqslant 2\pi[/tex]
[tex]x = 0 , \pi , 2\pi[/tex]
Noam chose 3 songs from a pile of 20 songs to play at a piano recital. What is the probability that she chose The Entertainer, Something Doing, and The Ragtime Dance?
[tex]|\Omega|={_{20}C_3}=\dfrac{20!}{3!17!}=\dfrac{18\cdot19\cdot20}{2\cdot3}=1140\\|A|=1\\\\P(A)=\dfrac{1}{1140}\approx0.09\%[/tex]
Answer:
0.014%
Step-by-step explanation:
To calculate the probability that she chooses that exact songs for the piano recital, you just first calculate the probability of her choosing one of them:
[tex]Probability of 1=\frac{1}{20}=.05[/tex]
This is 5%, now you multipy this with the probability of the second song after this one, since there is one less song, the total number of outcomes should be reduced to 19:
[tex]Probability of 2nd=(.05)(\frac{1}{19}[/tex]
[tex]Probability of 2nd=(0.05)(0.052}[/tex]
[tex]Probability of 2nd=0.002[/tex]
This would be .26%
To calculate the probability of the third song being chosen after the first two, we have 2 less outcomes possibles, so the total number of possibilities now is reduced to 18.
[tex]Probability of 3rd=(.0026)(\frac{1}{18}[/tex]
[tex]Probability of 3rd=(.0026)(0.055)[/tex]
[tex]Probability of 3rd=0.00014[/tex]
The probability of Noam choosing the three songs would be: 0.014%
AC, DF, and GI are parallel. Use the figure to complete the proportion. (7)
Answer:
The answer is
C.) BE
AD/AG=BE/BH
Answer:
Option C
Step-by-step explanation:
We have to find the value in the blank space
We are given that AC,DF and GI are parallel
We know that by middle splitting theorem
We have
[tex]\frac{JD}{AD}=\frac{JE}{BE}[/tex]
Because AC is parallel to DF and A and B are the mid points of JD and JE
[tex]\frac{JD}{GD}=\frac{JE}{EH}[/tex]
Because DF is parallel to GI
Divide equation one by equation second then we get
[tex]\frac{GD}{AD}=\frac{EH}{BE}[/tex]
Adding one on both sides then we get
[tex]\frac{GD}{AD}+1=\frac{BE}{EH}+1[/tex]
[tex]\frac{GD+AD}{AD}=\frac{BE+EH}{BE}[/tex]
[tex]\frac{AG}{AD}=\frac{BH}{BE}[/tex]
Because BE+EH=BH and AD+GD=AG
Reciprocal on both sides then we get
[tex]\frac{AD}{AG}=\frac{BE}{BH}[/tex]
Hence, option C is true.
The simple interest formula is l=prt where l represents simple interest on an amount p for t years at a rate of r where r is expressed as a decimal. What is the amount of money p that will generate $40 in interest at a 10% interest rate over 5 years
Answer: $80
Step-by-step explanation:
Given : Interest amount : [tex]T=\$40[/tex]
The rate of interest : [tex]r=10\%=0.1[/tex]
Time period : [tex]t=5[/tex] years
The simple interest formula is
[tex]l=prt[/tex], where l represents simple interest on an amount p for t years at a rate of r where r is expressed as a decimal.
Substitute all the values in the formula , we get
[tex]40=p(0.1)(5)\\\\\Rightarrow\ p=\dfrac{40}{0.1\times5}=80[/tex]
Hence, the amount of money p that will generate $40 in interest at a 10% interest rate over 5 years= $80
The amount of money (p) required to generate $40 in interest at a 10% interest rate over 5 years is $80.
What is the principal needed?Given the parameters:
Simple interest l = $40
Interest rate r = 10% = 10/100 = 0.10
Time t = 5 years
To determine the amount of money (p) that will generate $40 in interest at a 10% interest rate over 5 years, we use the simple interest formula:
I = P × r × t
Solve for p:
P = I / rt
Plug in the values
P = $40 / ( 0.10 × 5 )
P = $40 / 0.5
P = $80
Therefore, the value of the principal is $80.
Learn more about simple interest here: brainly.com/question/25845758
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NEED HELP!!!
see picture*****
Answer:
1. -10
2. [tex]x=1\pm\sqrt{2}i[/tex]
3. -1+2i
4. -3-7i
5. 13
6. rectangular coordinates are (-4.3,-2.5)
7. rectangular coordinates are (-2.5,4.3)
8. x^2 + y^2 = 8y
9. Polar coordinates of point (-3,0) are (3,180°)
10. Polar coordinates of point (1,1) are (√2,45°)
Step-by-step explanation:
1) Simplify (2+3i)^2 + (2-3i)^2
Using formula (a+b)^2 = a^2+2ab+b^2
=((2)^2+2(2)(3i)+(3i)^2)+((2)^2-2(2)(3i)+(3i)^2)
=(4+12i+9i^2)+(4-12i+9i^2)
We know that i^2=-1
=(4+12i+9(-1))+(4-12i+9(-1))
=(4+12i-9)+(4-12i-9)
=(-5+12i)+(-5-12i)
=5+12i-5-12i
=-10
2. Solve x^2-2x+3 = 0
Using quadratic formula to find value of x
a=1, b=-2 and c=3
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(3)}}{2(1)}\\x=\frac{2\pm\sqrt{4-12}}{2}\\x=\frac{2\pm\sqrt{-8}}{2}\\x=\frac{2\pm2\sqrt{-2}}{2}\\x=\frac{2\pm2\sqrt{2}i}{2}\\x=2(\frac{1\pm\sqrt{2}i}{2})\\x=1\pm\sqrt{2}i[/tex]
3. If u =1+3i and v =-2-i what is u+v
u+v = (1+3i)+(-2-i)
u+v = 1+3i-2-i
u+v = 1-2+3i-i
u+v = -1+2i
4. if u = 3-4i and v = 3i+6 what is u-v
u-v = (3-4i)-(3i+6)
u-v = 3-4i-3i-6
u-v = 3-6-4i-3i
u-v = -3-7i
5. if u=(3+2i) and v=(3-2i) what is uv?
uv = (3+2i)(3-2i)
uv = 3(3-2i)+2i(3-2i)
uv = 9-6i+6i-4i^2
uv = 9-4i^2
i^2=-1
uv = 9-4(-1)
uv = 9+4
uv = 13
6. Convert (5, 7π/6) to rectangular form
To convert polar coordinate into rectangular coordinate we use formula:
x = r cos Ф
y = r sin Ф
r = 5, Ф= 7π/6
x = r cos Ф
x = 5 cos (7π/6)
x = -4.3
y = r sin Ф
y = 5 sin (7π/6)
y = -2.5
So rectangular coordinates are (-4.3,-2.5)
7. Convert (5, 2π/3) to rectangular form
To convert polar coordinate into rectangular coordinate we use formula:
x = r cos Ф
y = r sin Ф
r = 5, Ф= 2π/3
x = r cos Ф
x = 5 cos (2π/3)
x = -2.5
y = r sin Ф
y = 5 sin (2π/3)
y = 4.33
So rectangular coordinates are (-2.5,4.33)
8. Convert r=8cosФ to rectangular form
r.r = (8 cos Ф)r
r^2 = 8 (cosФ)(r)
Let (cosФ)(r) = y and we know that r^2 = x^2+y^2
x^2 + y^2 = 8y
9. Convert(-3,0) to polar form
We need to find (r,Ф)
r = √x^2+y^2
r = √(-3)^2+(0)^2
r =√9
r = 3
and tan Ф = y/x
tan Ф = 0/-3
tan Ф = 0
Ф = tan^-1(0)
Ф = 0°
As Coordinates are in 2nd quadrant, so add 180° in the given angle
0+180 = 180°
So,Polar coordinates of point (-3,0) are (3,180°)
10) Convert (1,1) to polar form
We need to find (r,Ф)
r = √x^2+y^2
r = √(1)^2+(1)^2
r =√2
and tan Ф = y/x
tan Ф = 1/1
tan Ф = 1
Ф = tan^-1(1)
Ф = 45°
As Coordinates are in 1st quadrant, so Ф will be as found
So,Polar coordinates of point (1,1) are (√2,45°)
Only the function represented by graph has an inverse function.
Answer:
2
Step-by-step explanation:
Only graph 2 shows a function that passes the horizontal line test. The other graphs will cross a horizontal line multiple times, meaning the function does not have an inverse.
Answer:
Graph 2: the linear function.Step-by-step explanation:
A function is invertible if its bijective: injective and surjective at the same time. But, graphically exist the horizontal line test to know if the function is injective, i.e., one to one: one element of the domain has a unique element in the image set.
So, in this case, the only function that can be cut once by a imaginary horizontal line is graph number 2. If we draw a horizontal line in other options, it will cut them in more than one point, meaning that they are not injective, therefore, not invertible.