Probability to like both of them is 0.02.
Probability to like neither of the songs is 0.62.
Probability to like at least one of the songs is 0.44
What is probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given Data
The album has 10 songs and
it turns out you really like 5 of them.
a) You like both of them
P(like both of them )
= [tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.02
Probability to like both of them is 0.02.
b )you like neither of the songs
P(like neither of the songs)
= [tex]\frac{8}{10}[/tex] ×[tex]\frac{7}{9}[/tex]
= 0.62
Probability to like neither of the songs is 0.62.
c) you like at least one of the songs
P( like at least one of the songs)
2 ×[tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.44
Probability to like at least one of the songs is 0.44
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8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R
The triangles PTS and POR are similar, so we can take the ratios of the side to order
[tex]\frac{PT}{ST}=\frac{PQ}{SQ}[/tex][tex]\frac{36}{30}\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}[/tex][tex]\begin{gathered} \text{cross multiplying} \\ \\ 30\text{ (6x - 2) = 30 (5x + 13)} \\ \\ \text{Expanding the parenthesis} \\ \\ 30\text{ x 6x - 30 x 2 = 30 x 5x + 30 x 13} \\ \\ 180x\text{ -60 = 150x + 390} \end{gathered}[/tex]We can then solve for x by collecting like terms
180x - 150x = 390 + 60
30x = 450
Divide both sides by 30
x = 450/ 30
x = 15
Match each word with the phrase that best defines it.
insurance
liability
compensate
premium
deductible
to pay the value of something that has been
lost or stolen
the amount of money a consumer must pay
an insurance company
a responsibility to pay for or to fix a problem
a financial service that protects a consumer
in exchange for payments
the money a consumer must pay for a claim
before the policy takes over
Insurance - A financial service that protects a consumer
Liability - A responsibility to pay for or to fix a problem
Compensate - To pay the value of something that has been lost or stolen
Premium - The amount of money a consumer must pay an insurance company
Deductible - The money of a consumer must pay for a claim before the policy takes over
Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses.
Liability is a general phrase that refers to many types of coverages to assist in defending you or your company in the event that a claim or lawsuit is made against you or your organization.
The amount that the insurance provider has agreed to pay for insured losses that are mentioned in your policy is referred to as "compensation."
You pay a premium when you purchase an insurance policy. Your recurring payments for many popular insurance products, such as life, car, business, homeowners, and renters, are known as premiums.
The sum of money you must contribute to an insured loss is known as a deductible.
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A farmer with 1700 m of fancy ones to enclose a rectangular plot the borders on a river if no fence is required along the river what is the largest area that can be enclosed?
Answer
Largest Area that can be enclosed = 361250 m²
Explanation
Let the length of the fencing along the river be L
Let the width of the fencing be W
A sketch of the problem will make it clearer
Perimeter = L + 2W
Perimeter is giving as the total length of the fencing to be 1700 m
L + 2W = 1700
L = 1700 - 2W
The area of the structure is given as
Area = LW
The area is what we want to maximize
Recall, L = 1700 - 2W
Area = LW = (1700 - 2W) × W = 1700W - 2W²
A = 1700W - 2W²
At maximum point, the derivative of any function is zero
Hence,
(dA/dW) = 1700 - 4W
At maximum point,
(dA/dW) = 0
1700 - 4W = 0
4W = 1700
Divide both sides by 4
(4W/4) = (1700/4)
W = 425 m
Recall, L = 1700 - 2W
L == 1700 - 2(425)
L = 1700 - 850
L = 850 m
Maximum Area
= (Length at maximum area) × (Width at maximum area)
= 850 × 425
= 361250 m²
Hope this Helps!!!
What is the congruence, if any , that will prove the given triangles congruent?
Given:
The triangle FTP and triangle JTA is given.
In the given triangles,
[tex]\begin{gathered} \angle P\cong\angle A \\ \angle F\cong\angle J \\ \angle T\cong\angle T \end{gathered}[/tex]As only three angles of both triangles are similar we can not say that the given traingles are congruent.
So, Option A is correct.
How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Regarding perfect squares, it is found that:
A negative constant guarantees that the polynomial is not a perfect square.The polynomial with a constant term of -121 is not a perfect square.Perfect squaresPerfect square expressions are formed with the notable products of the square of the sum or the square of the subtraction, as follows:
(a + b)² = a² + 2ab + b² -> square of the sum.(a - b)² = a² - 2ab + b² -> square of the subtraction.The constant term of perfect squares, in both cases, is given by:
b².
Since the number is squared, it will always be a positive value, meaning that a negative constant term guarantees that the polynomial is not a perfect square.
The polynomial with a negative constant in this problem has a constant of -121, hence it is not a perfect square.
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Forever Flowers, the nursery that sells the peony plants, has an app that uses
equations to help customers order the correct number of plants. The function rule for
peony plants is P = 1.5n where P represents the number of plants needed for n yards.
a. What type of representation is a function rule?
b. State at least one reason why using this type of representation may be more useful
than other representations
a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.
b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.
What is a function rule?The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
f(x), where x is the input value, is how functions are expressed.
All functions have the general form y = f(x)
On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.
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Which Zeros of the polynomial function partially graphed below have even multiplicity?
The Zeros of the polynomial function partially graphed below have even multiplicity are x = -3 and x = 3.
What are the Zeros of the Polynomial?
The zeros of a Polynomial graph are simply the points where the graph curve crosses the x-axis.
In simply terms, the Zeros of a function are the values of the independent variable that make the function equal to 0. Multiplicity just refers to how many copies of a given zero exist.
From the given graph, the zeros of the Polynomial function are x = 2 and x = 3 and x = -3
An odd multiplicity means the graph of the function crosses the x-axis at that point. An even multiplicity means the curve contacts the x-axis at that point and backs instead of crossing.
Thus, the odd multiplicity is at x = 3
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I don't know what any of this means for my son's homework please help
All we simply need to do is to apply the law of indices that states;
[tex](a^b)^c=a^{bc}[/tex]Hence;
[tex](\frac{x^2}{y^4})^3=\frac{x^6}{y^{12}}[/tex]The correct option is
Let 0 be an angle in quadrant
If angle theta is given as;
[tex]\cos \theta=-\frac{4}{5}[/tex]And angle theta is in the third quadrant, then we can find the value of y by using the pythagoras' theorem as follows;
[tex]\begin{gathered} r^2=x^2+y^2 \\ When\text{ cos}\theta=-\frac{4}{5},\text{ and cos}\theta=\frac{x}{r} \\ \text{Then,} \\ x=-4,r=5 \\ \text{Therefore,} \\ 5^2=-4^2+y^2 \\ 25=16+y^2 \\ \text{Subtract 16 from both sides;} \\ 9=y^2 \\ \text{Take the square root of both sides;} \\ y=3 \end{gathered}[/tex]Note also that;
[tex]\sin \theta=\frac{y}{r}[/tex]However, the angle theta is in the third quadrant where y is also negative. Therefore, sin theta would be;
[tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=-\frac{3}{5} \end{gathered}[/tex]Note also that cosec theta is given as;
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \csc \theta=\frac{1}{-\frac{3}{5}} \\ \csc \theta=-\frac{5}{3} \end{gathered}[/tex]Note also that, tan theta is given as;
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]Therefore, we would have;
[tex]\begin{gathered} \tan \theta=-\frac{3}{5}\text{ / -}\frac{4}{5} \\ \tan \theta=-\frac{3}{5}\times-\frac{5}{4} \\ \tan \theta=\frac{3}{4} \end{gathered}[/tex]ANSWER:
[tex]undefined[/tex]5. If c = -1 and d = -2, what is the value of the expression 2c²d-3cd?a. -10b. -24c. 2d. 10e. -2
Recall that to evaluate an expression at some given values, we substitute each variable with the corresponding given value.
Evaluating 2c²d-3cd at c=-1 and d=-2 we get:
[tex]2(-1)^2(-2)-3(-1)(-2).[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 2(1)(-2)-3(-1)(-2), \\ -4-6, \\ -10. \end{gathered}[/tex]Answer: Option a.
Answer:
-10
Step-by-step explanation:
Substitute variable values for variables.
[tex]2(-1)^2(-2) - 3(-1)(-2)[/tex]
Simplify
2(1)(-2) - 6
-4 - 6
-10
Question 4c. Want to clarify something I want to ask right why does it become 3y square +6y-y-2
Answer:
Explanation:
Given the expression:
[tex]3y^2+5y-2[/tex]We want to write the given expression in the form:
[tex](ay-b)(y+c)[/tex]That is, to factorize the expression.
When an expression is to be factorized, follow the steps below:
Step 1: Multiply the coefficient of x² and the constant.
[tex]-2\times3y^2=-6y^2[/tex]Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6
[tex]\begin{gathered} 6y\times-1y=-6y^2 \\ 6y+-y=5y \end{gathered}[/tex]Step 3: Rewrite the middle term, 5y with those numbers.
[tex]\begin{gathered} 3y^{2}+5y-2 \\ =3y^2+6y-y-2 \end{gathered}[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =3y(y+2)-1(y+2) \\ =(3y-1)(y+2) \end{gathered}[/tex]1,-4,16 what is the 15th term
The sequence has its 15th term to be 268435456
What is the 15th term of the sequence?From the question, the given parameters are
1, -4, 16
The above sequence is a geometric sequence, with the following parameters
First term, a = 1Common ratio, r = -4/1Evaluate the quotient
So, we have
r = -4
The nth term of a geometric sequence is
Tn = a * r^(n-1)
Where
a = 1 and r = -4
Also, we have n = 15
Substitute a = 1 and r = -4 in the equation Tn = a * r^(n-1)
So, we have
Tn = 1 * (-4)^(n-1)
Substitute 15 for n
Tn = 1 * (-4)^(15-1)
Evaluate
Tn = 268435456
Hence, the 15th term of this sequence is 268435456
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Sketch the graph of of the linear inequality: y<2x
Ive attached it on this photo. ur welcome :)
Answer:
Step-by-step explanation:
Solve The Equation
-1.9 = 0.5(p +1.7)
Whoever answer first gets brainliest!
Answer:
p=-5.5Step-by-step explanation:
To solve this equation, use the distributive property. Isolate the difference between the numbers from one side of the equation.
Distributive property:
A(B+C)=AB+AC
-1.9 = 0.5(p +1.7)
First, switch sides.
0.5(p+1.7)=-1.9
Divide by 0.5 from both sides.
[tex]\sf{\dfrac{0.5\left(p+1.7\right)}{0.5}=\dfrac{-1.9}{0.5}}[/tex]
Solve.
-1.9/0.5=-3.8
p+1.7=-3.8
Then, you subtract by 1.7 from both sides.
p+1.7-1.7=-3.8-1.7
Solve.
Add or subtract the numbers from left to right.
-3.8-1.7=-5.5
[tex]\rightarrow \boxed{\sf{p=-5.5}}[/tex]
Therefore, the correct answer is p=-5.5.
I hope this helps, let me know if you have any questions.
The value of p on the equation - 1.9 = 0.5(p +1.7) is - 5.5.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, we have to solve for p in the equation - 1.9 = 0.5(p +1.7).
0.5(p + 1.7) = - 1.9
First, we'll distribute the terms.
0.5p + 0.85 = - 1.9.
0.5p = - 1.9 - 0.85.
0.5p = - 2.75.
p = - 2.75/0.5.
p = - 5.5
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50 POINTS HELP PLEASE
Write the equation of the line given the following slope and y-intercept
m=4
b=−1
y=
(note for people answering and admins the y is supposed to be blank and its the answer box dont take it down pls,thank you)
Answer:
y = 4x - 1===========================
Given Slope m = 4,y-intercept b = - 1Equation of a line in slope-intercept formy = mx + bSubstitute the values to gety = 4x - 12sinxcosx/sin^2x+cos^2x-1=1
The simplified equation is sin(2x) = 2
How to determine the value of the trigonometry formula?The trigonometry ratio is given as
2sinxcosx/sin^2x+cos^2x-1= 1
Rewrite the equation of the trigonometry formula properly
So, we have the following equation
2sin(x)cos(x)/sin^2(x)+cos^2(x) -1 = 1
Add 1 to both sides of the equation
So, we have the following equation
2sin(x)cos(x)/sin^2(x)+cos^2(x) = 2
Express 2sin(x)cos(x) as sin(2x)
So, we have the following equation
sin(2x)/sin^2(x)+cos^2(x) = 2
Express sin^2(x)+cos^2(x) as 1
So, we have the following equation
sin(2x)/1 = 2
Multiply both sides by 2
So, we have the following equation
sin(2x) = 2
Hence, the simplified equation of the trigonometry formula is sin(2x) = 2
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What is the slope of the line on the graph
Mellisa is buying party favors to make gift bags
Which probability distribution table corresponds with this frequency distribution table?
The probability distribution table corresponds with the given frequency distribution table is option (D)
Probability is defined as the ratio of number of favorable outcome to the total number of outcomes. The value of the probability varies from 0 to 1.
Probability = Number of favorable outcomes / Total number of outcomes
The total frequency = 3+7+2+3+5
= 20
The probability of each outcomes
Substitute the values in the equation
p(1) = 3/20 = 0.15
p(2) = 7/20 = 0.35
p(3) = 2/20 = 0.1
p(4) = 3/20 = 0.15
p(5) = 5/20 = 0.25
Hence, the probability distribution table corresponds with the given frequency distribution table is option (D)
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Determine the intervals on which the function is strictly decreasing. Write your answer as an interval or a list of intervals. When writing a list of intervals make sure to separate it into roll with a comment to use his feet and triples as possible.
Given graph shown a function plotted.
The aim is to determine where the function is strictly decreasing.
The interval where the function is strictly decreasing is given by the union of intervals where the graph is descending from a point.
From the graph, it is clear that the function decreases from
[tex](-5,3)\text{ to (-2,-4)}[/tex]and again from
[tex](2,3)\text{ to (6,-1)}[/tex]Therefore, the intervals where the function is strictly decreasing is:
[tex](-5,-2)\cup(2,6)[/tex]Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, and D as the possible answers.
By definition, a sample space is a collection or a set of possible outcomes of a random experiment. In our problem, we have four different outcomes. A, B, C and D. This is our sample space
[tex]S=\lbrace A,B,C,D\rbrace[/tex]Determine the value for m in the equation 1.4m = 0.42.
0.30
0.03
5.88
2.80
Determine the value for j in the equation 13 over 20 equals j plus 9 over 20.
4 over 20
4 over 40
2 over 20
22 over 40
Which statement correctly applies mathematical reasoning to find the possible values for x in the equation x − 1.3 = 1.5?
x is greater than 1.5
x is less than 1
x is between 0.1 and 1.5
x is less than 0.1
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
Determine the value for k in the equation k − 173.54 = 294.57.
121.03
589.14
347.08
468.11
Answer:
1. 0.30
2.4 over 20
3. x is greater than 1.5
4. 19.2
5. 468.11
Step-by-step explanation:
1) 1.4m = 0.42.
Divide both sides by 1.4
1.4m/1.4 = 0.42/1.4
m = 0.30
2) 13/20=j+9/20
Flip equation
j + 9/20 = 13/20
Substract 9/20 from both sides
j + 9/20 - 9/20 = 13/20 - 9/20
j = 13 - 9/20
j = 4/20
3) x − 1.3 = 1.5?
Add 1.3 to both sides
x - 1.3 + 1.3 = 1.5 + 1.3
x = 2.8
So, x is greater than 1.5
4) x/6 + 0.4 =3 + 0.6
Substract 0.4 from both sides
x/6 + 0.4 - 0.4 = 3 + 0.6 -0.4
x/6 = 3 + 0.2
x/6 = 3.2
Multiply both sides by 6
x/6 • 6 = 3.2 • 6
x = 19.2
5) k − 173.54 = 294.57.
Add 173.54 to both sides
k - 173.54 + 173.54 = 294.57 + 173.54
k = 468.11
The value of m from the given equation is 0.3.
The given equation is 1.4m = 0.42.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
1) 1.4m = 0.42
⇒ m = 0.42/1.4
⇒ m = 0.3
2) 13/20 = j+9/20
⇒ j = 13/20 - 9/20
⇒ j = 4/20
⇒ j = 1/5
3) x - 1.3 = 1.5
⇒ x = 1.5 + 1.3
⇒ x = 2.8
4) x/6 + 4/10 = 3 + 6/10
⇒ x/6+0.4=3.6
⇒ x/6 = 3.2
⇒ x = 19.2
5) k − 173.54 = 294.57
⇒ k = 294.57+173.54
⇒ k = 468.11
Therefore, the value of m from the given equation is 0.3.
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Find each value.Show calculations for each problem
In the given expression :
[tex]a_n=-8n[/tex]we need to find the value of n at which, an = -24
[tex]\begin{gathered} \text{Substitute the value of a}_n=-24\text{ in teh express}ionofa_n \\ a_n=-8n \\ -24=-8n \\ or \\ -8n=-24 \\ \text{Dividing both side by (-8)} \\ \frac{-8n}{-8}=\frac{-24}{-8} \\ n=3 \end{gathered}[/tex]Thus, at n=3, the an = -24
Write an equation for the line point slope form and slope intercept formSlope= -6Passing through -3,-7
For this question, we recall the point-slope form of the equation of a line:
[tex]y-y_0=m(x-x_0)[/tex]and the slope-intercept form:
[tex]y=mx+b[/tex]Therefore for the given data, the point-slope form is:
[tex]\begin{gathered} y-(-7)=-6(x-(-3)) \\ y+7=-6(x+3) \end{gathered}[/tex]and the slope-intercept form is:
[tex]\begin{gathered} y=-6x-18-7 \\ y=-6x-25 \end{gathered}[/tex]ONLY #11 please show work THANK YOU
The sketch of the given parametric equations is as appended.
Given parametric equations,
x(t) = 1+2t
y(t) = [tex]t^{2}[/tex]
y = [tex]\frac{(x-1)^{2}}{4}[/tex]
For bounding range of -2 ≤ t ≤ 2, corresponding values of x are as follows,
x = 2t + 1
For t = -2, x = 2(-2) + 1 = -3
For t = 2, x = 2(2) + 1 = 5
Hence the graph has been drawn with bounding limits of -3 ≤ x ≤ 5
The outcome is a parabola with vertex at (1,0) and open upwards. The curve moves towards infinity in upwards direction if there are no bounds / range.
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Find the measure of <1 and <2
Answer:
150°
Step-by-step explanation:
Both the measure of <1 and <2 are 150°
A ball is dropped from a height of 180 inches onto a level floor. After the second bounce it is still 5 inches off the ground. Presuming that the height the ball bounces is always the same fraction of the height reached on the previous bounce, what is that fraction?
The fraction which is a constant is equal to 1/6
How to find the fraction of the bouncing ballGiven data
A ball is dropped from a height of 180 inches
After the second bounce it is still 5 inches
the height the ball bounces is always the same fraction of the height reached on the previous bounce
Let the first height be x, this the initial drop height = 180
Let the second height be, the first bounce y
Let the third height be w, the second bounce = 5
the fraction is said to be:
height of y / height of x = height of w / height of y
y / x = w / y
y / 180 = 5 / y
y^2 = 180 * 5
y^2 = 900
y = √900
y = 30
the fraction is then 30 / 180 = 1 / 6
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Zachary has a container of worms for fishing. When empty, the mass of the container is 225 grams. With the worms in it, the container has a total mass of 751.4 grams. Each worm has a mass of 11.2 grams. How many worms are in the container? Write and solve an equation to model this equation.
Solving a linear equation we will see that there are 47 worms in the container
How many worms are in the container?We know that the mass of the container is 225 grams, and the mass of each worm is 11.2 grams.
Then if there are x worms on the containers, the total mass is:
M(x) = 225g + x*11.2g
In this case, we know that the total mass is 751.4 grams, then we can write:
751.4 g = 225g + x*11.2g
Solving this linear equation we get:
751.4g - 225g = x*11.2g
526.4g = x*11.2g
526.4g/11.2g = x = 47
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Melissa wants to pour 30.78 grams of salt into a container. So far, she has poured 19.1 grams. How much more salt should Melissa pour?
Answer:
She should pour 11.68 more grams
Step-by-step explanation:
If Melissa wanted to pour 30.78 grams of salt into a container and already has poured 19.1 grams she should pour 11.68 grams more
The expression below is scientificnotation for what number?9.9x10^7
To change the number from scientific notation to normal number multiply 9.9 by 10^7
[tex]9.9\times10,000,000=99,000,000[/tex]The number is 99,000,000