The probability that a randomly selected student plays a sport, given that the student is a senior will be 0.08. Then the correct option is A.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
At a secondary school, the likelihood that an understudy is a senior is 0.25. The likelihood that an understudy plays a game is 0.20. The likelihood that an understudy is a senior and plays a game is 0.08.
The probability that a randomly selected student plays a sport, given that the student is a senior will be 0.08. Then the correct option is A.
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1. Given: A = {1,2,3}, B = {4,5,6} C = {a,b}
Find:
a. A x B b. B x C c. A x C
2. Given: A = (3,6,9), B = (4,5,6)
a. Find A x B
b. Find the relation that the first component is smaller than the second component.
Using the provided questions with the values of sets A,B and C, Applying the cartesian product, The answer is {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)} and so on.
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.
What do you mean by cartesian product?In set theory, the Cartesian product of two sets A and B, denoted A x B, is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. It is the set of all possible combinations of elements from the two sets. For example, if A = {1, 2} and B = {a, b}, then A x B = {(1, a), (1, b), (2, a), (2, b)}. The Cartesian product is a fundamental concept in set theory and is used in many branches of mathematics, including linear algebra, topology, and graph theory. It can be extended to more than two sets, for example, the Cartesian product of three sets A, B, and C is denoted A x B x C and is the set of all ordered triples (a, b, c) where a belongs to A, b belongs to B, and c belongs to C.
1. A = {1,2,3}, B = {4,5,6} C = {a, b}
a. A x B = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}
b. B x C = {(4,a),(4,b),(5,a),(5,b),(6,a),(6,b)}
c. A x C = {(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)}
2. A = (3,6,9), B = (4,5,6)
a. A x B = {(3,4),(3,5),(3,6),(6,4),(6,5),(6,6),(9,4),(9,5),(9,6)}
b. Required relation = {(3,4),(3,5),(3,6)}
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Ronald Werner purchased a digital surveyor's level for $1,399.99
in Lincoln, Nebraska, where the sales tax rate is 5.5%.
a. What is the sales tax?
b. What is the total purchase price?
The sales tax rate amount is $76.99.
The total purchased amount is $1476.99.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Cost of the digital surveyor's level = $1399.99
Sales tax rate = 5.5%
The amount of sales tax rate.
= 5.5/100 x 1399.99
= $76.99
The total purchased price.
= $76.99 + $1399.99
= $1476.99
Thus,
Sales tax is $76.99
The purchased amount is $1476.99.
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I was wondering if this was correct?
8^2 + 5/3
evaluate show ur work!!:)
Answer:
I need this answer as well l. let me know
Answer:
65.7
Step-by-step explanation:
8^2 + 5/3
64 + 5/3
= 65.7
Write an article for publication in one of the national newspaper on the topic the usefulness of mobile phone this days
The closing price of Stock X changed on each trading day last month. The percent change in the closing price of Stock X from the first trading day last month to each of the other trading days last month was less than 50 percent. If the closing price on the second trading day last month was $ $10.00, which of the following CANNOT be the closing price on the last trading day last month?
A. $3.00
B. $9.00
C. $19.00
D. $24.00
E. $29.00
The closing price on the last trading day of the month cannot be $3.00, $9.00, $19.00, $24.00, or $29.00 since the percentage change in the closing price from the first trading day is less than 50%.
The percent change in the closing price of Stock X from the first trading day to the second trading day is:
Percent Change
= ($10.00 - First Trading Day Closing Price) / First Trading Day Closing Price
Since the percent change is less than 50%, the First Trading Day Closing Price must be greater than $20.00. Therefore, the closing price on the last trading day cannot be $3.00, $9.00, $19.00, $24.00, or $29.00.
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can anyone help with my math hw
The value of x in the inequality will be x ≥ 2
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
5x^2 +3 ≥ 23
5x^2 ≥ 23 - 3
5x^2 ≥ 20
x^2 ≥ 20/5
x^2 ≥ 4
[tex]x \geq \sqrt{4}[/tex]
x ≥ 2
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Graph the solution to this inequality on the number line. 5/8z>5/6
The graph will be of the form of an open circle at the point 1.3 tending towards right.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
The inequality is,
5/8 z > 5/6
Dividing both sides by 5/8,
5/8 z ÷ 5/8 > 5/6 ÷ 5/8
z > 5/6 × 8/5
z > 8/6
z > 4/3
z > 1.33
The graph will be of the form of fourth option where the open circle is at the number 1.3.
Hence the graph will be of the form of fourth line at the point 1.3 tending towards right.
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Problem
Pat can drive 363636 kilometers for every 333 liters of gas they put in their car.
Complete the table using equivalent ratios.
The numbers that correctly complete the ratios if Pat drives 36 kilometers for every 3 liters of gas are 4 and 11.
What is a ratio?A ratio is an expression commonly used in mathematics to show the relationship or proportion between two elements. For example, the proportion of cats to dogs might be expressed as 10:12, which means there are 10 dogs for every 12 cats.
How to complete the missing ratios?The ratio given is 3 liters of gas to 36 kilometers, which means that to drive 36 kilometers 3 liters of gas are required. Let's simplify this expression:
36 / 3= 12. This means that for every liter you can drive 12 kilometers. Based on this let's find the new ratio:
48 kilometers / 12 = 4 liters of gas
132/ 12 = 11 liters of gas
This means that to drive 48 kilometers Pat needs 4 liters of gas and to drive 132 kilometers she needs 11 liters of gas.
Note: This question is incomplete and it has some errors; here is the complete correct question:
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if I tested 300 g of gold ore and it contained 0.08 of gold how much gold would I have if I had 1 ton
Answer:
1g or 1 gram
Step-by-step explanation:
Decide whether the quadrilateral is a parallelogram. Explain your answer.
A ship is sailing due north. At a certain point, the bearing of a lighthouse 6.5 km away is N39.4°E. Later on, the captain notices that the bearing of the lighthouse has become S39.4°E. How far did the ship
travel between the two observations of the lighthouse?
The ship travelled ? km between the two observations
(Do not round until the final answer. Then round to the nearest tenth as needed)
The two types of figures are open and closed, geometric figures respectively. Figures that don't end where they begin are said to be open figures.
what is geometric figures ?Closed geometric shapes are made up of points, line segments, circles, and curves. All around us, we can observe these types of shapes. Circle, rectangle, triangle, and other geometric shapes are a few examples. The triangle-shaped slices of a pizza are round.
Straight lines have been drawn on the floor, the door, the window, and the zebra crossing by the roadside in the classrooms. Even though angles are used in building construction, they also have connections to disciplines like physics and chemistry.
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Consider the quadratic function 1(x) = #x2 - 5x + 12. Which statements are true about the function and its
graph? Select three options.
A. The value of f(-10) = 82
B. The graph of the function is a parabola.
C. The graph of the function opens down.
D. The graph contains the point (20, -8).
E. The graph contains the point (0, 0).
Answer:
B. The graph of the function is a parabola.
C. The graph of the function opens down.
E. The graph contains the point (0, 0).
Step-by-step explanation:
The reason why option (A) is incorrect is because f(-10) [tex]\neq[/tex] 82. We can see: [tex]= x^2 - 5x + 12\\= (-10)^2 - 5(-10) + 12\\= 100 + 50 + 12\\= 162 \neq 82[/tex]
The reason why option (D) is incorrect because the graph does not contain the point (20, -8). You can verify this by plugging the x-value of 20 into the equation for f(x) and solving for y:
If the sum of a, b and c is twice the sum of a-b and a-c and the difference of a+b and a-c is 3 the value of a is?
The value of a is (5c-9)/3
What is word problem?Word problem is expressing a mathematical problems in words . Looking at the problem above
the sum a,b,c is twice the sum a-b and a-c.
This means that a+b+c = 2( a-b+a-c)
a+ b + c = 2( 2a-b-c)
a+b+c = 4a-2b -2c
collect like terms
3a = 3b + 2c
a = b+⅔c
and the difference of a+b and a-c is 3. Therefore,
a+b-(a-c) = 3
a+ b - a + c = 3
b+ c = 3
b = c-3
therefore substitute c-3 for b in 3a = 3b + 2c
3a =3( c-3) + 2c
3a = 3c - 9 +2c
3a = 5c -9
Therefore the value of a
a = (5c -9)/3
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The tape diagram shows that there are 90 teeth on a comb.
90
Complete the table to show different percentages of the teeth on the comb.
Teeth
90
100%
9
27
Percentage
% of 90 teeth
% of 90 teeth
% of 90 teeth
On solving the provided question, we can say that - the value of the percentage will be is = x = 10
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
X% of 90 is 9
[tex]x/100 X 90 = 9\\x = 9/90 X 100\\x = 10[/tex]
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What are the dimensions of the following matrix?
A=
[-1 5 -7 0]
[6 3 -4 -3]
Answer: 2 x 4
Reason:
There are 2 rows and 4 columns. The number of rows is listed first, followed by an "x", then the number of columns is listed.
4
Use the drawing tools to form the correct answer on the number line.
Graph the solution set to this inequality.
-2(x + 6) > -4x
On solving the provided question we can say that the value of the inequality equation will be -2(x + 6) > -4x => x<-1
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
The inequality equation is
-2(x + 6) > -4x
-2x -6 > -4x
-6x > 6
-x>1
x<-1
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Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3
The True statements are:
A ) D ( x ) is a function.D ) D ( x ) is a direct variation.E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).What is a Function?Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
For D (x) = 2 x:
- x is the independent variable,
- D ( 6 ) = 2 · 6 = 12.
10 = 2 · 5, 12 = 2 · 9, - 4 = 2 · ( - 2 ).
True statements are:
A ) D ( x ) is a function.
D ) D ( x ) is a direct variation.
E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).
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find the coordinate of a triangle a(1,3) , b(2,5) and c(3,3) after being rotated about fixed point p(2,4) by 45 in clockwise direction and then translate (3,4) .
After the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121).
STEPS FOR FIND THE COORDINATEThe coordinates of a triangle after rotation and translation can be found using the following steps:
Rotation: To rotate a point (x, y) about a fixed point (a, b) by an angle θ (in this case, 45 degrees in the clockwise direction), you can use the following formulas to find the new coordinates:x' = (x - a) * cos(θ) - (y - b) * sin(θ) + a
y' = (x - a) * sin(θ) + (y - b) * cos(θ) + b
Translation: To translate a point (x, y) by a distance (dx, dy) in the x and y direction, you can use the following formulas to find the new coordinates:x' = x + dx
y' = y + dy
So for the first vertex of the triangle(1,3) after being rotated about fixed point p(2,4) by 45 in clockwise directionx' = (1 - 2) * cos(45) - (3 - 4) * sin(45) + 2 = -1.121 + 1.121 + 2 = 2.000
y' = (1 - 2) * sin(45) + (3 - 4) * cos(45) + 4 = -0.707 - 0.707 + 4 = 2.586
And after the translation (3,4) for point Ax' = 2 + 3 = 5
y' = 2.586 + 4 = 6.586
similarly for point B(2,5) will be (5.121,7.121)
and for point C(3,3) will be (6.121,5.121)
So after the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121)Learn more about coordinate of a triangle here:
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1. A radio whose cash price is Shs 180,000 can also be bought on hire purchase by paying a deposit of 35% of the cash value followed by 6 equal monthly instalments of Shs 24,500. Find the: (i) hire purchase price of the radio (ii) extra amount paid over the cash price using hire purchase
What is /25x2y2/xyin simplest form? Assume x>0 and y>0.
The expression 25x²y²/xy in the simplest form is 25xy
How to evaluate the expression in the simplest formFrom the question, we have the following parameters that can be used in our computation:
/25x2y2/xy
Express the exponents as proper superscript
So, we have
25x²y²/xy
Divide x²y² by x
So, we have the following representation
25x²y²/xy = 25xy²/y
Divide xy² by y
So, we have the following representation
25x²y²/xy = 25xy
The expression cannot be further simplified
Hence, the solution is 25xy
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A triangle has sides with lengths of 9 and 11 inches. The angle across from the 11 inch side has a measure of 65 degrees
The angle across from the 9 inch side has a measure of 47.8 degress
How to find the angle of the triangle?To find the angle across from 9 we make use of the sine rule
The sine rule states that
Let the vertices of the triangle be XYZ
Applying the sine rule we have
Sinx/9 = sin 65/11
Cross and multiply to get
11sinx = 9*sin65
⇒sin x = (9*0.9063)/11
This is given as sin x= 8.1567/11
Sin x = 0.7415
X = Sin⁻¹0.7415
m<X=47.8⁰
The angle that is proportional to 9 inch is 47.8 degress.
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please help me!!
this is due soon
In the given parallelogram, the value of a is 40 and b is -10.
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
Given a parallelogram ABCD
Since, two opposite angles of Parallelogram is equal
Thus, ∠ B = ∠ D and ∠ A = ∠ C
From above equations
3a + b = 110....(1)
Since, sum of all angles in quadrilateral is 360
Thus,
110 + 3a + b + 2(a - 3b) = 360
110 + 110 + 2(a -3b) = 360
2 (a - 3b) = 360 - 220 = 140
a- 3b = 70.....(2)
From equation 1 and equation 2
Multiply with 3 in equation 1 and then add with equation 2
9a + 3b + a - 3b = 330 + 70
10a = 400
a = 40
From equation 2
40 - 3b = 70
b = -10
therefore, The value of a is 40 and b is 10 in the given parallelogram.
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When the net is folded into the rectangular prism shown beside it, which letters will be on the front and left side of the rectangular prism?
A. The letter on the front will be A.
The letter on the left side will be D.
B. The letter on the front will be C.
The letter on the left side will be F.
C. The letter on the front will be C
The letter on the left side will be E.
D. The letter on the front will be F.
The letter on the left side will be A.
SOMEONE HELP! QUICK!
The letters on the front side and left side of the rectangular prism when it is folded are;
C. The letter on the front will be C. The letter on the left side will be E.
What is a rectangular prism?A rectangular prism is a three dimensional figure with six faces, such that each face is parallel to the opposite face and all the faces are rectangles.
The volume of a rectangular prism is the product of its three dimensions of length, width and height, while the surface area is twice the sum of the surface area of the three perpendicular faces.
The letters on the six faces of the rectangular prism are;
A, B, C, D, E, and F
When the net is folded into the rectangular prism shown in the figure, the sides with letter B is on top and the side with letter F in front.
The face of the net that will be on the front of the rectangular prism when it is folded is therefore, adjacent to the letter B, which is the face with letter C and the face to the left of the rectangular prism is the face adjacent to the face in front, which is the face with the letter E.
The correct option is therefore option C.
C. The letter on the front will be C. The letter on the left side will be E.
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Work out the total cost of the bottles of orange squash Jill needs to buy.
The total cost of squash needed for the 50 people is £10
How to solve an equationJill makes orange juice for 50 people. Each person would need 2 full glasses, hence:
Total glasses of juice = 50 people * 2 glasses per person = 100 glasses
Each glass is 250 milliliters, hence:
Total volume of juice = 100 glasses * 250 ml per glass = 25000 ml
1000ml = 1l
25000 ml = 25000 ml * 1l per 1000ml = 25 liters
1 part of orange squash is mixed with 4 part of water, hence:
Amount of squash = (1/5) * 25 liters = 5 liters
1 liter of squash cost £2
5 liters = 5 liters * £2 per liter = £10
The total cost of squash is £10
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The time on the clock is correct at 8:00 a.m. The clock loses 5 minutes every hour. What time would the clock show when the correct time is 3:00 p.m.?
Answer:
2:25
Step-by-step explanation:
Answer:
2:25 pm
Step-by-step explanation:
7 hours from 8 AM to 3 PM* 5 mins= 35 mins :)))))))))
3:00 pm - 35 mins= 2:25 pm
Find the following.
Please help asap due soon!
The numeric value of each composite function is given as follows:
(q ∘ p)(8) = 9.(p ∘ q)(8) = 25.How to obtain the composite functions?The functions in this problem are defined as follows:
p(x) = x² + 9.[tex]q(x) = \sqrt{x + 8}[/tex]From the composition of q and p, we have that:
[tex](q \circ p)(x) = q(p(x)) = q(x^2 + 9) = \sqrt{x^2 + 9 + 8} = \sqrt{x^2 + 17}[/tex]
At x = 8, the numeric value is found replacing the lone instance of x by 8, hence:
[tex]\sqrt{8^2 + 17} = \sqrt{81} = 9[/tex]
From the composition of p and q, we have that:
[tex](p \circ q)(x) = p(q(x)) = p(\sqrt{x + 8}) = (\sqrt{x + 8})^2 + 9 = x + 8 + 9 = x + 17[/tex]
At x = 8, the the numeric value is found replacing the lone instance of x by 8, hence:
8 + 17 = 25.
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please help i will mark you brainliest
Answer:
Below
Step-by-step explanation:
A vertical line is of the form x = ....
For this question it would just be x = 8
this line will go through ALL values of 'y'
PLEASE HELP MEEEEEEEeEEE
a
its just counting
i think its a
Find the ratio in simplest form.
30 minutes to 2 hours
1/4
15/1
1/15
Answer:
1/4
Step-by-step explanation:
1 hour = 60 minutes
2 hours = (2 x 60) minutes
= 120 minutes
Hence, ratio of 30 minutes : 2 hours
= 30 : 120
= 1 : 4
