The equivalent expressions are:
a) 4*(x + 2) = 4x + 8
b) 4*(2x + 3) = 8x + 12
c) (6 + 8)*x = 14*x
d) 6*(x + y + z) = 6x + 6y + 6z
How to use the distributive property?This is a property of the multiplication, and it says that we can distribute products in the following way:
A*(B + C) = A*B + A*C
So let's do that.
a) 4*(x + 2) = 4*x + 4*2 = 4x + 8
b) 4*(2x + 3) = 4*(2x) + 4*3
= 8x + 12
c) (6 + 8)*x = 6*x + 8*x = 14*x
d) 6*(x + y + z) = 6x + 6y + 6z
These are the equivalent expressions.
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you watch a roulette wheel spin 7 consecutive times and the ball lands on a red slot each time. what is the probability that the ball will land on a red slot on the next spin?
The probability that the ball will fall into a red slot during the following spin is 0.14.
To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. The concepts of probability and odds are distinct. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.
[tex]\frac{1}{7}=0.142857[/tex]
The probability is 0.14
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The probability of the ball landing on a red slot in a single spin of a fair roulette wheel is 1/2, as there are an equal number of red and black slots.
The outcome of each spin is independent, meaning that the outcome of one spin does not affect the outcome of another. Therefore, the probability that the ball will land on a red slot in the next spin is still 1/2, regardless of the results of the previous seven spins.
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find the value of x in the following: 2x - 7 = 13
Answer:
10
Step-by-step explanation:
2x - 7 = 13
+7. +7
2x = 20
20/2x = 10
use the table to complete the statement. (help asap).
The x intercept shown in the table are -2 and 2
The y intercept shown in the table is -4
What are x and y intercepts?The x-intercept of a graph is the point at which the graph crosses the x-axis, i.e., the y-coordinate of the point is 0. In other words, it's the solution to the equation y = 0.
The y-intercept of a graph is the point at which the graph crosses the y-axis, i.e., the x-coordinate of the point is 0. In other words, it's the solution to the equation x = 0.
In the table x- and y-intercepts are the values where the y values and x value are zero
x intercepts = -2 and 2
y intercepts = -4
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The graphs below have the same shape. What is the equation of the blue graph?
The equation of the blue graph is option B. G(x) = (x - 4)² + 1.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
The given function is f(x) = x².
From the figure, we can see that the graph of f(x) is shifted left to 4 units.
Then the function becomes (x - 4)².
Then the function is shifted up to 1 unit.
The resulting function is G(x) = (x - 4)² + 1.
Hence the correct equation of the graph is G(x) = (x - 4)² + 1.
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there are 18 chairs (labeled 1, 2, ... , 18) in a row to seat 5 chemistry majors, 6 mathematics majors, and 7 physics majors. find the number of possible seating arrangements if: a. the mathematics majors occupy the first 6 seats; b. the mathematics majors cannot occupy the first 6 seats; c. students with the same major sit in a block.
The number of possible seating arrangements depends on the conditions specified in the problem is 435,456,000
Permutation is the arrangement of objects in a specific order.
a. The mathematics majors occupy the first 6 seats:
The number of permutations of the mathematics majors is simply 6! (6 factorial), since they all have to sit together in a block. After the mathematics majors are seated, we have 12 chairs left for the chemistry and physics majors, who can be arranged in (5 + 7)! / (5! x 7!) ways.
Finally, the total number of permutations for the mathematics majors to occupy the first 6 seats is
=> 6! x (5 + 7)! / (5! x 7!).
=> 570240
b. The mathematics majors cannot occupy the first 6 seats:
In this case, the number of permutations of the mathematics majors is (18 - 6)! / (6! x (12 - 6)!). This is because they cannot occupy the first 6 seats and have to be arranged in the remaining 12 chairs.
Next, the number of permutations for the chemistry majors is (12 - 6)! / (5! x (12 - 6 - 5)!).
Finally, the number of permutations for the physics majors is (12 - 6 - 5)! / 7!.
The total number of permutations for this scenario is
=> (18 - 6)! / (6! x (12 - 6)!) x (12 - 6)! / (5! x (12 - 6 - 5)!) x (12 - 6 - 5)! / 7!.
=> 668250
c. Students with the same major sit in a block:
In this case, the number of permutations of the chemistry majors is simply 5! since they have to sit together in a block.
Similarly, the number of permutations of the mathematics majors is 6! and the number of permutations of the physics majors is 7!.
Finally, the total number of permutations for students with the same major to sit in a block is
=> 5! x 6! x 7!.
=> 435456000
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phillip writes the expression 2⁷ which is another way to write the same expression using repeated multiplcation?
Answer:
multiply 2, 7 times
Step-by-step explanation:
2 x 2 x 2 x 2 x 2 x 2 x 2
= 128
Part A:
Determine 3 angles between 0° and 360° which have the same reference angle as a rotation angle of 72°. Name at least 1 angle greater than 360° with this same reference angle.
Part B:
What if the given rotation angle in quadrant 1 is n°. Determine 3 angles between 0° and 360° which have the same reference angle as a rotation angle of n°. Explain how you determined these angle measures.
the expression $y^2 10y 33$ can be written as a combination of a square of a binomial and an integer. find the integer.
When the expression y² + 10 y + 33 is written as a combination of a square of a binomial expression and an integer, the value of the integer is 8
We are given an expression y² + 10 y + 33 and this expression can be written as a combination of a square of a binomial and an integer. we need to find the value of the integer.
= y² + 10 y + 33
Write 10 y = 2 (5) (y)
= y² + 2 (5) (y) + 33
Write 33 = 25 + 8
= y² + 2 (5) (y) + 25 + 8
Write 25 = 5²
= y² + 2 (5) (y) + 5² + 8
Write y² + 2 (5) (y) + 5² = (y + 5)²
= (y + 5)² + 8
So, here (y + 5)² is the square of the Binomial expression and 8 is the integer.
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suppose there is a 10% chance of raining, and there is a 2% chance that the midterm exam is cancelled. assume that these two events (raining and cancelling the exam) are independent. what is the probability that neither events happen? please select the best answer.
TLDR: 88%
The probability of neither event happening is the complement of the probability of either event happening, which is 100 - 12 = 88.
Cheers,
qxxi
Please I need help on this immediately!!!
The value of the element t11 is 34 and the value of the element at d12 is 15.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
M + W = Indoor= [26 55] Outdoor = [32 49]
The value indicates the sum of the indoor volunteers ages 18-39,\
34.
To create a matrix by subtracting the women's matrix from the mens matrix.
Now the difference;
M – W = Indoor = 8 15 Outdoor = -16 3
This value indicates the difference of the volunteers indoors 40 so
Therefore the value would be 15.
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I WILL MARK BRAINLIST AND SET THIS 100 POINTS BUT PLS ANSWER CORRECTLY.THIS IS GRADED OUT OF 100% I need 80% to pass for an A- PLS YALL!
Answer:
The third angle is 60
Step-by-step explanation:
The interior angle of a triangle is equal to the 180 minus the exterior angle.
[tex]180-80= 100[/tex]
So one of the interior angles is equal to 100
All of the interior angles of a triangle add up to 180
[tex]180=100+20+x[/tex]
[tex]x=60[/tex]
Gracie's grandmother gave her 40 stamps.
Then, each month Gracie adds 30 stamps to her collection.
Coordinate grid labeled points (0, 40), (1, 70), (2, 100) and (3, ?)
Part A
How many stamps does Gracie have after 3 months?
Enter your answer in the box.
stamps
Part B
What does the point
(
2
,
100
)
represent on the graph?
A.
The number of months since Gracie began adding to her stamp collection.
B.
The number of stamps in the collection after 2 months is 100.
C.
The number of stamps Gracie added to her collection in 2 months is 100.
D.
The number of stamps collected in 2 weeks is 100.
A)
Gracie has 130 stamps after 3 months.
B)
The point (2, 100) represents that the number of stamps after 2 months is 100.
Option C is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Coordinate grid labeled points (0, 40), (1, 70), (2, 100).
Each month Gracie adds 30 stamps to her collection.
So,
(3, 130)
Now,
A)
130 stamps after 3 months.
B)
(2, 100) represents that the number of stamps after 2 months is 100.
Thus,
130 stamps after 3 months.
(2, 100) represents that the number of stamps after 2 months is 100.
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There will be 130 stamps Gracie have after 3 months,
and (2, 100) represents the number of stamps in the collection after 2 months is 100.
What is the coordinate grid?A coordinate grid has two perpendicular lines, or axes labeled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.
Given Gracie's grandmother gave her 40 stamps.
Then, each month Gracie adds 30 stamps to her collection,
Coordinate grid labeled points (0, 40), (1, 70), (2, 100), and (3, ?)
A: since she adds 30 stamps each month,
stamps in 3rd month are 100 + 30 = 130.
130 stamps in 3rd month.
B: What does the point (2, 100),
the graph is plotted between the number of stamps and months,
which gives the change of stamp each month,
the coordinates (2, 100) say that Gracie has 100 stamps in 2 months.
so option B is correct.
Hence There will be 130 stamps Gracie have after 3 months,
and The number of stamps Gracie added to her collection in 2 months is 100.
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2 A motorcycle can go 1/4 of a mile on 1/168 of a gallon of
gas. How far can the motorcycle go on 3 gallons of gas?
Answer:
Multiply 1/4*3= 3/4. So a motorcycle can go 3/4 of a mile on 3 gallons of gas
Step-by-step explanation: Hope this helps!!, Mark me Brainliest, :)))
suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. based on this information alone, is the system consistent or inconsistent? why or why not?
Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.
The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.
In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.
So, Based on the information provided, it is consistent.
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Choose ALL answers that describe the polygon KLMN if KL = 10, LM = 17, MN = 10, NK = 17, KL // MN, and LM // NK
In the polygon KLMN KL = 10, LM = 17, MN = 10, NK = 17 and
KL || MN, and LM || NK hence the polygon KLMN is a parallelogram.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
Given, A polygon in which KL || MN, and LM || NK and also from the given information opposite sides are of equal length.
We know in a parallelogram opposite sides are parallel and equal in length.
Now, If in this parallelogram all individual interior angles measures
90° then this parallelogram would be a rectangle.
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what is the area of a circle with a diameter of 15.8 cm? use 3.14 for pi and round your final answer to the nearest hundredth. enter your answer in the box.
The required area of the circle with diameter 15.8 cm is 196.06 cm^2.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
According to question:To find the area of a circle, we use the formula: pi * (radius)^2. The diameter of the circle is given as 15.8 cm,
so the radius can be calculated by dividing the diameter by 2,
giving us a radius of 15.8 cm / 2
= 7.9 cm.
Plugging the radius into the formula, we get:
pi * (7.9 cm)^2
= 3.14 * 62.41.
Finally, rounding the answer to the nearest hundredth, we get: 62.41 * 3.14
= 196.06 cm^2.
Thus, requi9red answer is 196.06 cm^2.
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Y is inversely proportional to the square of x. If Y = 6 when x = 2, then Y =1/2 when x is ______.
question is in the screenshot
The graph in option - B represents the correct alternative.
What is a function? What is a quadratic function?A function describes a relationship between a dependent and independent variable. Example -
y = f(x) = 5x + 9
Given is the function as -
f(x) = 12(1/3)ˣ
At {x = 0}, we get -
y = 12 x 1 = 12
The {y - intercept} would be at (0, 12).
It is a exponential function of the form -
y = A(B)ˣ.
Refer to the graph attached. We can conclude that option B is the correct graph.
Therefore, the graph in option - B represents the correct alternative.
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help please !! this is algebra just in case !
Answer: The answer to this equation is 50.
Step-by-step explanation:
Evaluate the equation like this using PEMDAS.
2 x (1 + 4) ^2
2 x ( 5 ) ^ 2
2 x 25
50
Therefore, the answer to this equation is 50.
Hope this helps!
given that the mean number of book read per child is 1, the value of x.
Since the mean number of book read per child is 1, the value of x is 4.
What is a mean?In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the mean for the number of book read?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of books, we have;
Total number of book = 0(4) + 12(1) + 2(x)
Total number of book = 12 + 2x
Mean = (12 + 2x)/(16 + x)
1 = (12 + 2x)/(16 + x)
16 + x = 12 + 2x
2x - x = 16 - 12
x = 4.
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Can you answer this question?
What is BD?
20. A hollow spherical vessel has internal and external radii of 6 cm and 6.4 cm respectively. Calculate the mass of the vessel if it is made of metal of density 10 g/cm³. nuorted cone of diameter and height
The mass of the vessel if it is made of metal of density 10 g/cm³ is 1993 g.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
Volume of sphere = 4/3 πr³
Hence, For internal;
⇒ Volume of sphere = 4/3 πr³
⇒ Volume of sphere = 4/3 × 3.14 × (6)³
⇒ Volume of sphere = 904.32 cm³
For external;
⇒ Volume of sphere = 4/3 πr³
⇒ Volume of sphere = 4/3 × 3.14 × (6.4)³
⇒ Volume of sphere = 1097.5 cm³
Thus, Volume of sphere between sphere is,
⇒ 1097.5 - 904.32
⇒ 193.2 cm³
Here, it is made of metal of density 10 g/cm³.
Hence, the mass of the vessel is,
⇒ 193.2 × 10
⇒ 1932 g
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#15 picture is in the description !!100 POINTS!! BRAINLIEST
Answer:
SOH-CAH-TOA, the rest are just reciprocals of these
Step-by-step explanation:
sinY= o/h = 6/√61
cosY= a/h = 5/√61
tanY =o/a = 6/5
cosecY = h/o = √61/6
secY = h/a = √61/5
tanY = a/o = 5/6
Answer:
Step-by-step explanation:
Sin = 6/[tex]\sqrt{61][/tex]
Cos=5/[tex]\sqrt{61[/tex]
tan=6/5
cosec= [tex]\sqrt{61\\[/tex]/6
sec=[tex]\sqrt{61\\[/tex]/5
cot= 5/6
Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
A . graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 20
B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
C. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one third comma 0
D. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 40
The graph represents this situation:
B) graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y= 30+ 10x
Now, take x= 0
y= 30
and, x= 1
y= 30+ 10
y= 40
and, x= 2
y= 30+ 20
y= 50
and, graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars.
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Write the sentence as an equation (type the numbers as numbers not words and do not include spaces in your answer). 336 is 230 decreased by q
The value of q is -106 and the required equation is given by q=-106
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: The statement of an equation" 336 is 230 decreased by q"
230 is decreased by q is equivalent to 230 substracted by q and the number obtained by the above operation is equal to 336
Thus we have the equation as follows
230-q=336
q=230-336
q=-106
Hence, The value of q is -106 and the required equation is given by q=-106
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Seema likes to grow bright flowers, so she buys 32 daffodil bulbs. She plants 12 bulbs in her front yard. Then Seema evenly divides the rest of the bulbs into 4 pots.
Answer:
5
Step-by-step explanation
32 -12 =20 divided by
4= 5
Instructions: Before you get started, answer the following items on a separate sheet of paper. This will help you assess your prior knowledge and practice some skills that you will need in studying this lesson. Show your complete solution.
Consider having numbers from 1–20. Write the ratio representing the following (express in the simplest term, if possible):
1. Odd numbers to all numbers involved
2. Numbers divisible by 5 to even numbers
3. Numbers greater than 7 to numbers less than 12
4. Even numbers greater than 5 but less than 17 to all numbers involved
the ratio representing the above-described number are given as follows;
In mathematics, parity refers to whether an integer is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, 82 are even because 3, 5, 7, and 21 are all odd numbers.
With regard to the above ratios:
1) Odd numbers to all numbers involved:
There are 10 odd numbers from 1 to 20 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). So, the ratio of odd numbers to all numbers involved is 10/20 = 1/2.
2) Numbers divisible by 5 to even numbers:
There are 4 numbers from 1 to 20 that are divisible by 5 (5, 10, 15, 20). Out of these 4 numbers, 2 are even (10, 20). So, the ratio of numbers divisible by 5 to even numbers is 4/2 = 2/5.
3) Numbers greater than 7 to numbers less than 12:
There are 4 numbers less than 12 (1 to 7) and 5 numbers greater than 7 (8 to 20). So, the ratio of numbers greater than 7 to numbers less than 12 is 5/4.
4) Even numbers greater than 5 but less than 17 to all numbers involved:
There are 6 even numbers greater than 5 but less than 17 (6, 8, 10, 12, 14, 16). So, the ratio of these even numbers to all numbers involved is 6/20 = 3/10 = 1/2 * 3/5 = 3/10.
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Elam is packing his room to move into a new house. A small box can hold 8 books without breaking, while a large box can hold 12 books without breaking. He has at most 160 books to pack and less than 30 boxes total. Let s represent the number of small boxes and l represent the number of large boxes.
The inequalities s ≥ 0 and l ≥ 0 are part of the system that models this scenario.
Which inequalities complete the system?
a:s – l < 30
b:8s – 12l ≤ 160
c:s + l < 30
d:8s + 12l ≤ 160
s + l > 30
8s + 12l ≤ 160
s + l < 30
8s + 12l ≥ 160
Answer:
The complete system of inequalities to model this scenario is s ≥ 0, l ≥ 0, 8s + 12l ≤ 160, and s - l < 30.
Step-by-step explanation:
Answer: 8s + 12l ≤ 160.
Step-by-step explanation: I would explain.. but I figured maybe I'd spare you the struggle and give you the answer. If you NEED steps, DM me.
find the value of MN in all 4 circles.
The measures of the arcs MN in the circles are 105, 100, 106 and 66
How to determine the measures of arcs MNCircle 1
From the question, we have the following equation that can be used in our computation:
MN = PQ
This means that
2MN + 85 + 65 = 360
So, we have
2MN = 210
Divide by 2
MN = 105
Circle 2
Here, we have
MN = 2MP
Also, we have
MP + MQ = 180
So, we have the following equation
1/2MN + 130 = 180
So, we have
MN = 100
Circle 3
Here, we have
PR = 74
So, we have the following equation
MN + 74 = 180
So, we have
MN = 106
Circle 4
Here, we have
PN = PM = 147
So, we have the following equation
MN + 2 * 147 = 360
So, we have
MN = 66
Hence, the measures of the arcs are 105, 100, 106 and 66
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Had to take another picture