Answer: (4x - √3)(4x + √3).
Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.
So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).
During a game, a spinner landed on several different colors. During a game, a spinner landed on several different colors.
Considering this data, how many of the next 13 spins should you expect to land on purple?
First, we need to find the experimental probability (probability using the provided data) of landing on purple.
Experimental probability of purple = # of purple / total #
Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)
Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.
Answer: 1 spin
Hope this helps!
The following playing cards are used in a game. 1, 2, 3, 4, 5, 6, 7
Find the P (not prime)
When a number is selected at random, the probability that a number that is not a prime number would be selected would be = 3/7.
How to determine the probability of a non prime numbers?Prime numbers are defined as those numbers that are greater than one that cannot be divided by a whole number apart from themselves without a remainder.
To calculate the probability of non prime numbers from a game of cards the formula for probability should be used. That is;
Probability = possible outcome/sample space
The possible outcome = 1,4,6 = 3
The sample space = 7
Therefore probability = 3/7
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Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound=0.640, upper bound=0.910, n=1200
The point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample are:
margin of error = 0. 135point estimate = 0. 775 x = 930 peopleHow to find the parameters ?The point estimate of the population proportion:
= (lower bound + upper bound) / 2
= (0.640 + 0.910) / 2
= 0. 775
The margin of error for the confidence level :
= p - hat - lower bound
= 0. 775 - 0. 640
= 0. 135
The number of individuals in the sample with the specified characteristic (x ) :
= n x p - hat
= 1, 200 x 0. 775
= 930 people
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The table describes the quadratic function p(x). x p(x) -4 24 -3 9 -20 -1 -3 0 2 0 What is the equation of p(x) in vertex form? Op(x) = 2(x - 1)² - 3 p(x) = 2(x + 1)² - 3 Op(x) = 3(x - 1)² – 3 p(x) = 3(x - 1)² – 3
The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.
Option C is the correct answer.
Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.
where k and n are positive integers.
We have,
From the table,
From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.
So,
The vertex is (- 1, -3).
The vertex form of p(x).
p(x) = a ( x - h)² + k
Where (h, k) is the vertex.
Now,
(-1, -3) = (h, k)
Make (- 2, 0) = (x, p(x))
0 = a (- 2 + 1)² + (-3)
0 = a x 1 - 3
a = 3
Thus, The vertex equation of p(x).
p(x) = 3(x + 1)² - 3
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the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
Need the right answer for problem 12
The distance of the point from the line is d =
Given data ,
Let the point be P ( 1 , 1 )
Let the equation of line be represented as e
where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line
So , slope m = ( 0 + 2 ) / ( -5 - 1 )
m = 2/-6
m = -1/3
So , the equation of line is
y - 0 = ( -1/3 ) ( x + 5 )
y = ( -1/3 ) ( x + 5 )
( 1/3 )x + y + 5/3 = 0
Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
On simplifying , we get
D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]
D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]
D = 3 / ( 10 ) / 9
D = 27/10
D = 2.7 units
Hence , the distance is 2.7 units
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
-3, √3, 13/3
The other zeros are
(Use a comma to separate answers.)
Answer:
{-3, √3, -√3, 13/3}
Step-by-step explanation:
Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.
We can write the polynomial with these zeros as:
p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)
where a is some constant coefficient. Multiplying out the factors, we get:
p(x) = a(x + 3)(x^2 - 3)(x - 13/3)
To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:
a(x + 3)(x^2 - 3)(x - 13/3) = 0
This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:
(x + 3)(x^2 - 3)(x - 13/3) = 0
Expanding the quadratic factor, we get:
(x + 3)(x - √3)(x + √3)(x - 13/3) = 0
Canceling out the (x - √3) and (x + √3) factors, we get:
(x + 3)(x - 13/3) = 0
Solving for x, we get:
x = -3 or x = 13/3
Therefore, the other zeros are -3 and 13/3.
The complete set of zeros is {-3, √3, -√3, 13/3}.
Hope it helps^^
If sun x= 4/5 what is the value of b? 22.5 3b
By following trigonometry identities we get b equals **7**
Define trigonometry identities?Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.
There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.
Some of the most popular trigonometric identities are listed below:
sin²(x) + cos²(x) = 1
- tan(x) = sin(x)/cos(x)
- cot(x) = cos(x)/sin(x)
- sec(x) = 1/cos(x)
- csc(x) = 1/sin(x)
- sin(2x) = 2sin(x)cos(x)
- cos(2x) = cos²(x) - sin²(x)
- tan(2x) = (2tan(x))/(1 - tan²(x))
The use of these identities
.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .
In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).
LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:
b cos(x°) = √(506.25 + 9b²)
Substituting x = arcsin(4/5), we get:
b cos(arcsin(4/5)) = √(506.25 + 9b²)
Simplifying this equation using trigonometric identities, we get:
b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)
b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)
b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)
b× (√(9/25)) = sqrt(506.25 + 9b²)
3b/5 = √(506.25 + 9b²)
Squaring both sides of the equation, we get:
9b²/25 = 506.25 + 9b²
Solving for b, we get:
b = 7
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Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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There are 6 bottles of water.
Each bottle is 1/2 full. If you
were to combine all the
water, how many full bottles
of water would there be?
Answer:3
Step-by-step explanation: 1/2 X 6 = 3
Answer:
6 x 1/2 = 3 full bottles
Step-by-step explanation:
Solve by using a system of equations.
A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?
The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:
Let the variable y represent the quantity of first alloy (30% gold).Let the variable x represent the quantity of second alloy (80% gold).Therefore, a system of linear equations to describe this situation can be written as follows;
x + y = 40 .....equation 1.
0.3x + 0.8y = 0.6(40) .....equation 2.
From equation 2, we have the following:
0.3x + 0.8y = 24
0.3x + 0.8(x - 40) = 24
0.3x + 32 - 0.8x = 24
-0.5x = -8
x = -8/-0.5
x = 16 grams.
y = 40 - x
y = 40 - 16
y = 24 grams.
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
1+2i, 1+√5
The other zeros are
(Use a comma to separate answers.)
Answer:
The other zeros are:
1 - 2i, 1 - √5
please help, due in an hour !!
Answer:
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
what will the coordinates be if Point A (-4,-5) of the trapezoid was reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction.
Answer:
If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).
Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":
A" = (4 - 6, -5 + 7) = (-2, 2)
Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).
Step-by-step explanation:
Answer:
(-2, 2)
Step-by-step explanation:
I did the test
Hope this helps :)
Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answer:
Answer is D.
Please mark my answer as Brainliest if you found this one helpful.
the diagram below shows all the possible totals from adding the results of rolling a two fair dice.
a) whats the probability of rolling a total of 5? give ur answer as a fraction in its simplest form.
b) if you rolled a pair of fair dice 180 times, how many times would you expect to roll a total of five?
Answer:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20
Step-by-step explanation:
The diagram is not visible in the question. However, I can provide a general method to solve the problem.
a) To find the probability of rolling a total of 5, we need to count the number of ways we can get a sum of 5 and divide it by the total number of possible outcomes. From the diagram, we can see that there are four ways to get a sum of 5: (1,4), (2,3), (3,2), and (4,1). Since each die has six equally likely outcomes, there are 6 x 6 = 36 possible outcomes in total. Therefore, the probability of rolling a total of 5 is:
Probability of rolling a total of 5 = Number of ways to get a total of 5 / Total number of possible outcomes
= 4/36
= 1/9 (in its simplest form)
b) If we rolled a pair of fair dice 180 times, the expected number of times we would roll a total of 5 can be calculated as follows:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20
someone help i really need help with this
Answer:
29
Step-by-step explanation:
she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.
i need an answer for this with explanation
Answer: 76
Step-by-step explanation:
The surface area is all of the area faces added together
The blue is 5*4 but I have 2 of those faces so I multiply by 2
(5*4*2)=40
The red is 4*2 but I have 2 of those faces so I multiply by 2
(4*2*2)=16
The green is 5*2 but I have 2 of those faces so I multiply by 2
(5*2*2)=20
Add those together
A=40+16+20=76
what is 9v+–3v+–4v–2+1 simplified
Answer:
2v-1
Step-by-step explanation:
9v+-3v+-4v-2+1
=9v-3v-4v-1
=6v-4v-1
=2v-1
Find the value of 11 3/8 -7/8
The value of 11 3/8 -7/8 is 10 1/2
What is subtraction?Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60
Solving 11 3/8 -7/8
= 91/8 - 7/8
= (91-7)/8
= 84/8
= 21/2
= 10 1/2
Therefore the value of 11 3/8 -7/8 is 10 1/2
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The prism below is made of cubes which measure
1
4
of an inch on one side. What is the volume?
A 3D illustration view of a blank tabular with 5 rows and 2 columns.
Note: Figure is not drawn to scale.
A.
15
32
cubic in
B.
5
2
cubic in
C.
30
cubic in
D.
15
2
cubic in
The volume of the prism is B. 2.5 cubic inches.
How to calculate the volumeAccording to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:
Length = 2 × 1/4
Width = 5 × 1/4
Height = 3 × 1/4
= 2/4 + 5/4 + 3/4
= 2 2/4
= 2.5 cubic inches.
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v=? image attached please help
Answer:
v=12
Step-by-step explanation:
9/v = 6/8
9 = 6v/8
72= 6v
v= 12
Answer:
v = 12
Step-by-step explanation:
Now we have to,
→ Find the required value of v.
Given proportion,
→ (9/v) = (6/8)
Then the value of v will be,
→ (9/v) = (6/8)
→ 9 × 8 = 6 × v
→ 72 = 6v
→ 6v = 72
→ v = 72/6
→ [ v = 12 ]
Hence, the value of v is 12.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
9.6
Step-by-step explanation:
sin(angle)= opposite/hypotenuse
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
Answer:
Step-by-step explanation:
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
Describe two trends you can find in the graph below. Use calculations and numbers to support your thinking.
The two trends on the graph are:
Positive correlationNegative correlationDescribing the two trends on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The two trends on the graph are:
Positive correlationNegative correlationFor the positive correlation, we have
Upward trend from January till August
This is because the function values increase approximately in this domain
For the negative correlation, we have
Upward trend from August till December
This is because the function values decrease approximately in this domain
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What are the values of x and y?
X=
Y=
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
Select the correct answer from each drop-down menu.
Consider the expression below.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.
What is like term?In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).
The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.
Simplifying the expression we het 10 x + 5.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.
2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.
3. If the expression is set equal to -10x + 5, there would be only one solution.
10x + 5 = -10x + 5
20x = 0
x = 0
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Please answer if you know this one with the steps thank you.
Step-by-step explanation:
T = 5200 = .2 ( E - 10600)
5200 / .2 = E - 10600
E = 5200/.2 + 10 600 = 36600 pounds
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
HELP ASAP WILL GIVE BRAINLIEST
Use the graph to answer the question.
2
O
21/1/201
O
D'
IN
A
2
Determine the scale factor used to create the image.
C'
2.5
B'
D
A
11
C
2
В
B
Answer:
1/4
Step-by-step explanation:
The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.
