the probability that the card is either a queen or a diamond is: 4/13
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Number of cards, n(S) = 52
Let E = Event of getting a diamond
F = Event of getting a queen
(E ∩ F) = Event of getting a diamond of queen.
Then, n(E) = 13
n(F) = 4 ,
n (E ∩ F)=1
P(E) = 13/52 = 1/4
P (F) = 4/52 = 1/13
P (E ∩ F) = 1/52
(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)
P (E or F) = 1/4 + 1/13 - 1/52
P (E or F) = (13 + 4 - 1)/52
P (E or F) = 16/52
P (E or F) = 4/13
The required probability of getting either diamond or a queen is 4/13
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What are the solutions of the equation 9x4 minus 2x2 7 0?
The solution of the equations are x = √1 = ± 1
Now, According to the question:
The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]
Using the substitution rule we put [tex]x^{2}[/tex] = u .
The given equation now changes to
[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)
Equation(1) is a simple quadratic equation which can be solved by factorization as follows:
[tex]9u^2 - 2u - 7 = 0[/tex]
(9u + 7)(u - 1) = 0
Therefore
9u + 7 = 0 → u = -7/9
u -1 = 0→ u = 1
Since u = [tex]x^{2}[/tex] implies
x = √-7/9 = ± i√7/9
x = √1 = ± 1
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The complete question is this:
What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.
Destiny is 56 3 4 inches tall. Glen is 1 1 2 inches taller than Destiny and Jane is 1 1 5 inches taller than Glen. How tall is Jane
By simple algebra, Jane is 57 9/20 inches taller.
In math, what does taller than mean?If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.
You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:
54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.
Dwight stands at 56 1/4 inches.
Dwight is 1 1/5 inches shorter than Jane, so
56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.
Jane stands at 57 9/20 inches.
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Solve for d: c=πd what is the answer
Answer:c/π=d
Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.
Make
x
the subject of the formula
a = bx + c
Answer: x = a/b - c
Step-by-step explanation:
First divide by b on each side to get the x by itself.
Then subtract c from both sides to make x the subject of the formula.
Step-by-step explanation:
a = bx + c
the goal is to get to a form with "x = ...".
a - c = bx
(a - c)/b = x
done.
Determine if the expression -3z2 is a polynomial or not. If it is polynomial, state
the
type and degree of the polynomial.
Therefore, the equation that best fits these scatter plot facts as the answer to this problem is y=661-0.1x.
Describe a scatter plot.The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.
Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.A scatter plot is a specific type of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that appear showing any associations between the data.
y=661-0.1x is the equation whose solution best fits this data.
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Please Answer ASAP!
Will give 85 points for answer!
Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 13 over 17, what does the ratio 13 over 17 represent?
Answer:
Step-by-step explanation:
Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
What is a Ratio?
This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.
Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
Answer:
Step-by-step explanation:
the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning
Knowing that 6 < x < 7 and 10 < y < 12, find the possible values of x+y,xy,y/x,y-x
16<x+y<19,60<xy<84,10/7<y/x<12/6,3<y-x<6
smallest with the smallest biggest with the biggest, biggest with smallest, smallest with biggest
The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the
denominator, the new fraction obtained is. Find the fraction.
A set of multimedia equipment costs $1900, By setting up an inequality, find the maximum number of sets of
The Fraction for the given word problem is x/y = 9/11
What is Fraction?A fraction, which derives from the Latin word fractus, meaning "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in everyday speech.
Let the fraction be x/y
The numerator of a fraction is 2 minus its denomination.
⇒ x = y - 2 .....(i)
When 3 is subtracted from numerator and from denomination the new fraction obtained is 3/4
⇒ x - 3/y - 3 = 3/4
Can also be written as
⇒ 4(x + 3) = 3(y - 3)
⇒ 4x - 12 = 3y - 9
⇒ 4x - 3y = -9 + 12
⇒ 4x - 3y = 3 .....(ii)
Substitute the value of (i) in (ii)
⇒ 4x - 3y = 3
⇒ 4(y - 2) - 3y = 3
⇒ 4y - 8 - 3y = 3
⇒ y - 8 = 3
⇒ y = 3 + 8
⇒ y = 11
Putting the value of y in (i).
⇒ x = y - 2
⇒ x = 11 - 2
⇒ x = 9
Hence, Fraction = x/y = 9/11
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Please help ASAP. Which of the following are solutions of the system of linear inequalities? y > 4x+1 y≥x+4.
Using graphical method, the solution to the system of linear inequality (x, y) are (1, 5)
What is System of Linear InequalityA mathematical statement called a linear inequality depicts the relationship between two different variables, typically on a graph. A line or border that divides the area of all the points that fulfill the inequality from the areas of the points that do not constitutes the graph of a linear inequality. A set of lines in the coordinate plane that represent the equations of a system of linear inequalities is called a graph. The region of the coordinate plane where each of the inequalities holds can be seen by joining these lines to create a graph.
The inequality given are;
y > 4x + 1y ≥ x + 4This can be solved using a graphing calculator;
The point of intersection shows the solution to the graph
The solution to the linear inequalities (x, y) are (1, 5)
The broken lines in the graph is from the greater than inequality, while then straight unbroken lines is the inequality with greater than or equal to sign.
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What is Y 1 on a graph?
The graph of y is a straight line parallel to the x−axis through the point (0,1)
Now, According to the question:
Let's know:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The equation is Y = 1
A straight line in slope (m) and intercept (c) form is:
y = mx + c
y is a straight line of slope 0 and y- intercept of 1
y = 0.x + 1
y = 1
Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)
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. Which of the following equations
represents an identity? Justify your
choice.
1) 2x+1=3x+4
2) 4x-3=2(2x+7)
3) 6x+3=2x+10
4) 4(5x+2) = 20x+8
The correct equation which represent an identity will be;
⇒ 4(5x+2) = 20x+8
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.
Given that;
All the equations are,
1) 2x + 1 = 3x + 4
2) 4x - 3 = 2(2x + 7)
3) 6x + 3 = 2x + 10
4) 4(5x + 2) = 20x + 8
Now,
Solve each equation and find an identity as;
1) 2x + 1 = 3x + 4
⇒ 1 - 4 = 3x - 2x
⇒ - 3 = x
⇒ x = -3
Thus, It is not represent an identity.
2) 4x - 3 = 2(2x + 7)
⇒ 4x - 3 = 4x + 14
⇒ - 3 ≠ 14
Thus, It shows no solution.
3) 6x + 3 = 2x + 10
⇒ 6x - 2x = 10 - 3
⇒ 4x = 7
⇒ x = 7/4
Thus, It is not represent an identity.
4) 4(5x + 2) = 20x + 8
⇒ 20x + 8 = 20x + 8
⇒ 20x - 20x = 8 - 8
⇒ 0 = 0
Clearly, '0' is an additive identity.
Thus, This equation shows an identity.
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What are the 3 ways to find x-intercept?
The three ways of finding the x-intercept are:
Using a Graph of a Line.Using the Equation of the Line.Using the Quadratic Formula.By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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Interpreting Graphs-DeltaMath Interpret the graph of a Function
The function is (linear, or nonlinear). The function is negative where x (<, or >) (any number) and where x (<, or >) (any number). There (is, or isn't) an extrema. The maximum is located at x=(any number). As the x-value (increases, or decreases) the y-value (increases, or decreases).
Everything in the parenthesis is the drop down menus or pick a number off of the graph.
The function in the attached graph is nonlinear
The function is negative where x < 0 and where x > 0.
There is an extrema.
The maximum is located at x = 0.
As the x-value decreases the y-value decreases for x < 0
As the x-value increases the y-value decreases for x > 0
How to determine the characteristics of the functionThe function is not a straight line graph, because of this, it is a non linear function
The extrema refers to points of maximum or minimum values. The function on the graph has a maximum value at (0, 0)
The end behavior of the function is described as
x ⇒ ∞ f(x) ⇒ - ∞
x ⇒ -∞ f(x) ⇒ -∞
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can someone help me with this but please with details on how u got the answer:
The function’s average rate of change over the interval from x: 1 to x:2 is:
The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have the interval from x = 1 to x = 2.
To find the function’s average rate of change over the interval from x = 1 to x = 2 is:
We interpreted the interval in the coordinate form.
The curve from (1, 2) to (2, 0) is a straight line.
And the slope of the line is the average rate of change of the function.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (0-2) / (2-1)
m = -2/1
m = -2
Therefore, the average rate of change is -2.
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Similar figures review - Question 1
For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm
What is proportions?In general, the term proportion refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal.
How to find the length of the houseThe length of the house on the map is calculated using equality in proportions as follows
The required proportion is
= height of the house / length of the house
= 6 / 4.5
= 4/3
Using this proportion, the length of the house in the drawing is
= 30 mm / 4/3
= 22.5
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auggie bought 8 books. Some books cost $13 each and the rest of the books cost $24 each. They spent a total of $159. Write a system of linear equations that could represent the given situation
Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:
x + y = 8 (the total number of books Auggie bought is 8)
13x + 24y = 159 (the total amount of money Auggie spent is $159)
This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.
The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.
Step-by-step explanation:
7. $5,000 was invested at a simple interest
rate. In 15 years, the account was worth
65 hundred dollars. What was the interest
rate?
A 0.2%
B 1.5%
C 2%
D 2.15%
Answer:
C. 2%
Step-by-step explanation:
(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%
A saw mill cuts boards that are 16 ft long. After they are cut, the boards are inspected and
rejected if the length has a percent error of 1. 5% or more. The saw mill also cuts boards that are 10, 12, and 14 feet long. An inspector rejects a board that
was 2. 3 inches too long. What was the intended length of the board?
Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet
Some board lengths to reject are: 14.8 ft, 17.20 ft and 12.10 feetThe intended lengths are 10.19, 12.19 and 14.19 feetNow, According to the question:
Board lengths that should be accepted
From the question, we have the following parameters that can be used in our computation:
Length = 16 ft
Percent error = 1.5%
This means that the acceptable lengths are
Acceptable = Length ± Percent error * Length
Substitute the known values in the above equation, so, we have the following representation
Acceptable = 16 ± 1.5% * 16
So, we have
Acceptable = 16 ± 0.24
Evaluate
Acceptable = 15.76 to 16.24
Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet
Board lengths that should be rejected
In (a), we have
Acceptable = 15.76 to 16.24
Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet
The intended lengths of the boards
Here, we have
Lengths = 10, 12 and 14 feet
Length too long = 2.3 inches
Convert to inches
Length too long = 0.19
So, we have
Intended lengths = (10, 12 and 14 feet) + 0.19
Evaluate
Intended lengths = 10.19, 12.19 and 14.19 feet
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Mr Espinoza randomly chooses one of five toll booths when entering a toll road when driving to work. What is the probability he will select the middle toll booth on Monday and Tuesday
The probability that Mr. Espinoza will select the middle toll booth on Monday and Tuesday is 8%.
What is the probability?Probability refers to the odds of Mr. Espinoza selecting the middle toll booth on Monday and Tuesday when he could have selected toll booths 1, 2, 4, or 5.
The chances of selecting one out of five toll booths = 1/5 or 0.2
The likelihood of Monday and Tuesday out of the five working days = 2/5 or 0.4
The probability of selecting the middle toll booth on Monday and Tuesday = 1/5 x 2/5
= 0.2 x 0.4
= 0.08
= 8%
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PLS HELP QUICK
give two different first steps you could use to solve this equation
-3(2x+6)=12
There are two steps of solving the equation -3(2x+6)=12.
The steps are given below.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given equation:
-3(2x+6)=12
The first step:
Solving the parenthesis first,
-6x -18 = 12
Adding 18 to both sides,
-6x = 30
Divide by -6,
x = -5
The alternate step:
-3(2x+6)=12
Divide by -3,
2x + 6 = -4
2x = -10
x = -5
Therefore, x = -5 is the solution of the equation.
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I NEED HELP PLS PSSSSSSSSSSSSSSS
Answer:
240
Step-by-step explanation:
The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday
Answer:
278
Step-by-step explanation:
average = sum/count
count = 7 (7 days)
monday = 150
tuesday = 250
wednesday = 200
thursday = 250
friday = 350
saturday = 450
sunday = 300
sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950
mean = 1950/7 = 278.571428571 ≈ 278
Cari says if a triangle has the side lengths of 3, , and 9, then the triangle is a 30-60-90 triangle. Dana says if a triangle has the side lengths of 2, , and 4, then the triangle is a 30-60-90 triangle. Who is correct and why
A high school has a population of 2035 students and is increasing by 3% each year.
Write an exponential function to model the student population in terms of the number of years from now.
Answer:
Y=7x+67
Step-by-step explanation:
Find the value of 'x', round to 4 decimal places.
The value of x is 14.7224.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Sin 60° = x/17 ____(1)
Sin 60° = √3/2 _____(2)
From (1) and (2) we get,
√3/2 = x/17
x = 17√3/2
x = 17 x 1.73205 / 2
x = 14.7224
Thus,
The value of x is 14.7224.
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Simplifying algebraic expression
4-6 = -2
x/7-6
Substitute
28/7-6
PEMDAS
28/7 = 4
4-6 = -2
(If you're looking for the expression, it's 4-6. But if straight answer, -2)
Answer:
[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]
Step-by-step explanation:
Given information,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: x = 28[/tex]
Now the value of expression is,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]
[tex] \sf \rightarrow \: 4 - 6[/tex]
[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]
Therefore, the answer is -2.
Is x 3 a factor of the polynomial x^3 3x^2 4x 12?
(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.
To solve the problem, recall the factor theorem.
Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0
The given function is:
f(x) = x³ - 3x² + 4x - 12
To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).
Substitute x = 3 into f(x):
f(3) =3³ - 3(3)² + 4(3) - 12
f(3) = 27 - 27 + 12 - 12
f(3) = 0
Since f(3) = 0, then x -3 is a factor of x³ - 3x² + 4x - 12
Your question is incomplete, but most probably your question was:
Is x - 3 a factor of the polynomial x³ - 3x² + 4x - 12?
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Help asappppp please
Answer:
the answer is a
and the correct answer is letter C
Step-by-step explanation:
I don't know that is the answer
[Please help me on this- I will give you brainlist!!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
The degree of polynomial is 2 and leading coefficient is 3.
What are polynomial?A polynomial is a mathematical expression made up of one or more terms. The phrases "poly" and "nominal," for example, are whence the name "polynomial" arose. The words "poly" and "nominal" both signify many. A polynomial is an algebraic expression with two or more algebraic terms, to put it simply. It has exponents, operators, coefficients, coefficients, variables, and constants.
Given polynomials 9, 3x², 8x
standard form of polynomial; The value of the largest exponent in a polynomial is known as its degree. However, it differs between a polynomial with just one variable and one with multiple variables. The degree of a polynomial for a single variable is equal to the variable's highest power in the polynomial.
the standard form is 3x², 8x, 9
degree of polynomial is 2.
and leading coefficient is the constant term followed by the variables with highest power,
LC = 3.
Hence degree = 2 and leading coefficient = 3.
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From midnight to 2:00 am, the temperature dropped 1.4 °c each hour. If the temperature at 2:00am was 11.2 °c, what was the temperature at midnight
The temperature at midnight as required to ve determined in the task content is; 14°C.
What is the temperature at midnight as required to be determined from the given information.According to the task content; the temperature was 11.2°C at 2 : 00am.
However, since the temperature dropped 1.4 °c each hour; we have that;
In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.
On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.
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make N the subject of formulaP=N+2/d
Answer:
N = Pd - 2
Step-by-step explanation:
P = N + 2/d
Pd = N + 2
Pd - 2 = N
N = Pd - 2