There are 181440 number of different 10 letter words , (real or imaginary) that can be formed from the given letters .
In the question ,
it is given that ,
the letters are X, W, C, V, R, Z, W, U, M, A ,
since the total number of letters = 10 ,
So , 10 letter can be arranged in 10! ways = 362880 ways
and we can also see that the letter W is repeated 2 times
So it can be arranged in 2! ways = 2 ways .
So , the total number of different 10 letters words that can be formed is calculated by dividing total number of possible arrangements by arrangement of each repeated letter ,
that is ,
= 362880 / 2
= 181440 .
Therefore , There are 181440 number of different 10 letter words (real or imaginary)that can be formed from the given letters .
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For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 6 or greater than 9.
The probability that the sum will be less than 6 or greater than 9 is
The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).
What is the likelihood of rolling two dice together?The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.
I am assuming that you are rolling two dice.
Probability of even: 18 "evens" out of 36 total outcomes = 18/36
→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)
Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36
→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)
Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36
→(4,6), (5,5), (6,4), (6,6)
evens OR >9s NOT both
18/36 + 6/8 - 4/36 = 20/36 = 5/9.
The probability that the sum is 5/9.
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The box plot shows the times for sprinters on a track team.
(A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.)
What is the value of the upper quartile?
The five number from the box plot is presented as follows:
Minimum value: 44.First quartile: 48.Median: 50.5.Third quartile: 53.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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what is the total cost of cake option 1
Answer:
give me the question dude......
Step-by-step explanation:
Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return
The statement that is not true about body mass index is B. measures the percentage of one's body fat directly
What is Body mass index?The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.
The majority of the time, total body fat and BMI are correlated.
The Body mass index (BMI) formula
= weight in kilograms / square of height in meters
BMI Categories values are classified below
Underweight ≤ 18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
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Answer:B
Step-by-step explanation:
Which equation is equivalent to the given equation?
x²- 10x = 14
-
(x - 10)² =-86
(x - 5)² = 39
(x - 5)²= = -11
(x-10)²= 114
The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V = 70 cm^3 when T = 420 kelvin and P = 18 kg/cm^2. Find the pressure when T = 140 kelvin and V = 60 cm^3.
The pressure of the gas is 7kg/cm^2.
How to determine the pressure of the gas?Joint Variation is a situation in which the value of one variable depends on two, or more, other variables when the other variables are held constant
Given that: The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. This can be written as:
VαT and Vα 1/P
Combining the two relations gives:
Thus Vα T/P
V = kT/P (where k is a constant)
PV=kT
k = PV/T
P =kT/V
Given: V = 70 cm^3
when T = 420 kelvin
P = 18 kg/cm^2
k = 18×70 / 420
k = 1260/420
k = 3
Given: T = 140 kelvin and
V = 60 cm^3.
Find the pressure
P = kT/V
P = 3×140/60
= 420/60
= 7kg/cm^2
Therefore, the pressure when T = 140 kelvin and V = 60 cm^3 is 7kg/cm^2.
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The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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In a factory, 40% of k liters of acid are added to 60% of w liters of water.
Express the total volume of the solution as an algebraic expression. Pls help
Answer: (0.4k+0.6w)
Step-by-step explanation:
the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.
The total volume of the solution as an algebraic expression is
0.4k + 0.6w.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount of acid added to the solution = 40% of k
Amount of water added to the solution= 60% of w
Now,
The total volume of the solution.
= 40% of k + 60% of w
= 40/100 x k + 60/100 x w
= 0.40k + 0.60w
Thus,
The volume is 0.4k + 0.6w.
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ASAP Write an equation of a quadratic formula with the given properties: f(3)=f(-5)=0;f(-6)=-36
The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).
How to derive a quadratic equation that contains three points
In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:
y = a · x² + b · x + c
Where:
x - Independent variable.y - Dependent variable.a, b, c - Real coefficients.We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:
9 · a + 3 · b + c = 0
25 · a - 5 · b + c = 0
36 · a - 6 · b + c = - 36
Then, the solution to the system is found by numerical methods:
(a, b, c) = (- 4, - 8, 60)
The equation that contains the three points is y = - 4 · x² - 8 · x + 60.
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8.7% increase of 525 what is answer
Answer:
Step-by-step explanation:
570.675
Given that (x - 2) is a factor of x³ + x² - 5ax + 2a², 'a' can take the value of 2 or which other number?
well now, let's recall the remainder theorem, check your textbook since we know you're Da Bomb and love to check that theorem.
well, we know a factor is (x-2) for the polynomial f(x), that means that f(2) = 0, so let's use that
[tex]f(x)=x^3+x^2-5ax+2a^2\hspace{5em}\stackrel{\textit{a factor of f(x)}}{(x-2)}\qquad thus\qquad f(2)=0 \\\\\\ 0=(2)^3+(2)^2-5a(2)+2a^2\implies 0=8+4-10a+2a^2 \\\\\\ 0=2a^2-10a+12\implies 0=2(a^2-5a+6) \\\\\\ 0=a^2-5a+6\implies 0=(a-2)(a-3)\implies a= \begin{cases} 2\\ 3 \end{cases}[/tex]
Write a proof for the statement.
If a quadrilateral is a square, then the quadrilateral is a rectangle.
Proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.
Explain quadrilaterals.A quadrilateral is a closed shape created by uniting four points, any three of which cannot be collinear. Four sides, four angles, and four vertices make up a quadrilateral.
Quadrilaterals have a few characteristics. The list is as follows.
Each side has four sides.
Each of them has four vertices.
Two diagonals are present.
360 degrees is the sum of all interior angles.
Given, to prove if a quadrilateral is a square, then the quadrilateral is a rectangle.
The Square has four equal sides, and all four angles are right-angled.
Rectangle has equal opposite sides, and all four angles are the right angle.
Here, the two sides of the square can be increased to form a rectangle.
Hence, proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.
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What is the slope-intercept form of the equation of the line shown in the graph?
An equation of this line shown in the graph in slope-intercept form is y = 0.75x + 5 or 3x/4 + 5.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following parameters:
Point (x, y) = (60, 50)
Point (x, y) = (20, 80)
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (80 - 50)/(20 - 60)
Slope, m = 30/40
Slope, m = 3/4 or 0.75
At point (60, 50), the intercept is given by:
y = mx + c
50 = 0.75(60) + c
50 = 45 + c
Intercept, c = 50 - 45
Intercept, c = 5.
Now, we can write the equation of this line in slope-intercept form as follows:
y = 0.75x + 5 or 3x/4 + 5.
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Jolyn's points per basketball game are normally distributed with a standard deviation of 7 points. If Jolyn scores 48 points, and the z-score of this value is 3, then what is her mean points in a game?
If Jolyn scores 48 points, and the z-score of this value is 3, then her mean points in this normally distributed game is equal to 27.
How to calculate the mean points?In a normal distribution, the relative score or z-score can be calculated by using this formula:
[tex]z=\frac{x\;-\;u}{\sigma}[/tex]
Where:
x represents the sample score.u represents the mean point.σ represents the standard deviation.Making mean (μ) the subject of formula, we have:
μ = x - zσ x
Substituting the given parameters into the formula, we have;
Mean point, μ = 48 - (3 × 7)
Mean point, μ = 48 - 21
Mean point, μ = 27.
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Write an equation of the parabola in vertex form.
Amusement Park Ride
Height (feet)
YA(0, 180)
(1, 164)
160
80
0 2 4
Time (seconds)
Equation:
Equation of parabola in vertex form is :
[tex](x-h)^{2} = 4a(y-k)[/tex]
[tex](x-0)^{2} = 4a(y-180)[/tex]
it passing through (1,164)
∴ [tex](1-0)^2=4a(164-180)[/tex]
[tex]1 = 4a(-16)[/tex]
⇒ [tex]-64a = 1[/tex]
⇒ [tex]a = -\frac{1}{64}[/tex]
∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]
[tex]x^2 = -\frac{1}{16}(y-180)[/tex]
[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]
Here, the equation of parabola in vertex form is:
[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]
What is Parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.
What is cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.
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The following number is shown in expanded form:
1 1
4x1+8 x 100 + 9 × 1000
What is the decimal form of the number?
The decimal form of the number is :
9804.0
What is the decimal number?
Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
If the question is,
4x1+8 x 100 + 9 × 1000, then simplify it first
4x1+8 x 100 + 9 × 1000=4+800+9000=9804
So, the decimal form is :
9804.0
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The equation y = 11x represents a proportional relationship. What is the
constant of proportionality?
A.11
B.x
C.1/11
D.0
The constant of proportionality in the equation y = 11x is 11 , the correct option is (a) .
in the question ,
it is given that
the equation is y = 11x
also given that the equation is proportional relationship ,
we need to find constant of proportionality .
we know that the proportional equation is written as y = k*x
where k is the constant of proportionality , on comparing it with the equation y = 11x
, we get k = 11 ,
So , the constant of proportionality is = 11 .
Therefore , The constant of proportionality in the equation y = 11x is 11 .
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33 is 15 less than k
A car can travel
198 miles on 9
gallons of
gasoline. How
much gasoline will
it need to go 462
miles?
Answer:
21 gallons
Step-by-step explanation:
[tex]\frac{9}{198} \times 462 \\ \\ =\frac{462}{22} \\ \\ =21[/tex]
A total of 600 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the
number of adult tickets sold. How many adult tickets were sold?
Answer:
150 adult tickets where sold
Step-by-step explanation:
If we multiply 150 times 3 that gives us 450, which acounts for all the students. And 150 is the number thats left of adults that adds up to 600.
Two numbers have these properties.
Both numbers are greater than 6.
Their highest common factor (HCF) is 6.
Their lowest common
multiple (LCM) is 60.
Find the two numbers, writing your
answers on one line in the form,
The two numbers are .
and .. .
12 and 30 are the two numbers are greater than 6 with HCF 6 and LCM 60.
What is Highest common factor and Least Common Multiple?
Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.
Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.
HCF x LCM = Product of the numbers.
6 x 60 = 6a x 6b
10 = a x b
10 can be written as, 1 x 10 and 2 x 5.
But a and b > 1.
So, 10 = 2 x 5
a = 2, b = 5
Therefore, the two numbers are,
6a = 6(2) = 12 and
6b = 6(5) = 30
Hence, the two numbers with HCF 6 and LCM 60 are 12 and 30.
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
The final solution of the inequality –2(5 – 4x) < 6x – 4 is x < 3.
How to solve inequality?Inequalities are expressions that have the <, >, ≤ and ≥ signs.
Therefore, let's solve the given inequality as follows:
–2(5 – 4x) < 6x – 4
open the brackets on the left side
–2(5 – 4x) < 6x – 4
-10 + 8x < 6x - 4
add 10 to both sides of the inequality
-10 + 8x < 6x - 4
-10 + 10 + 8x < 6x - 4 + 10
8x < 6x + 6
subtract 6x from both sides of the inequality
8x < 6x + 6
8x - 6x < 6x - 6x + 6
2x < 6
divide both sides of the inequality by 2
2x < 6
2x / 2 < 6 / 2
x < 3
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A car dealership decreased the price of a certain car by 5%. The original price was $47,200.
What is the new value and the original value?
Answer:
New: $44,840 Original: 47,200
Step-by-step explanation:
You have to multiply 47,200 by 95% or 0.95
Salina and Nessa combined like terms using the same expression. Salina’s answer differs from Nessa’s. The table shows both of their solutions.
Salina
Nessa
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + x squared y + 2 x y squared + 2 x y
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + 2 x y squared + 2 x y
Which statement is correct regarding their solutions?
Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
Salina did not add the constant terms correctly.
Nessa combined the constants correctly but then left the Plus 2 x y squared term in her answer
Nessa did not combine the x squared y terms correctly.
The statement that is correct regarding their solutions is A. Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
How to illustrate the expression?From the information, Salina and Nessa combined like terms using the same expression.
The expression given is illustrated as.
6x²y - 3 + x²y + 2xy² + 2xy - 6
It should be noted that the like terms are:
6x²y and x²y as well as -3 and -6.
Combine the like terms
6x²y + x²y = 7x²y
Also, -3 + (-6) = -9
Therefore, the value will be 7x²y + 2xy² + 2xy - 9
The correct option is A as it illustrated the mistake Salina made.
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Answer:
A is the answer
Step-by-step explanation:
Evaluate the expression when m = -3.
2
m² -7m+6
Answer:
36
Step-by-step explanation:
substitute m = - 3 into the expression
m² - 7m + 6
= (- 3)² - 7(- 3) + 6
= 9 + 21 + 6
= 36
10. Brock bought a bicycle that cost $40.00 when it was new. If he eventually sold it for 10%
of the original cost, how much was it sold for?
Answer:IT WOULD BE 60.00
Step-by-step explanation:
BC 40 = 60
Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
The scatter plot shows the relationship between the number of coffee drinks sold and the total expenses of a coffee shop.
The slope of the line is....
The intercept of the line is.....
The regression equation is
For the linear function built from the scatter plot, it is found that:
The slope of the line is of: 5.The intercept of the line is of: b = 500.The equation is of: y = 5x + 500.What is a linear function?The slope-intercept representation of a linear function is the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the numeric value of the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the numeric value of the output variable y when the input variable x has a value of 0.From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:
b = 500.
When the input increases by 200, the output increases by 1000, hence the slope is:
m = 1000/2 = 5.
Thus the equation is:
y = 5x + 500.
Missing InformationThe graph is given by the image at the end of the answer.
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Evaluate the expression when a=5 and b=1/2: 13/2 - 7/2 -b( 2/3) + 4/8 - ab
f(x)=x² +6
Find an equation for the tangent line to the graph of f(x) = x² +6 at (5,31).
y=
Answer:
y = x^2 + 6 given equation
y = m x + b equation of straight line required
dy/dx = 2 x tangent to given curve
dy/dx = slope = 2 * 5 = 10
Thus our line must be of the form
y = 10 x + b
31 = 10 * 5 + b at the point required
b = 31 - 50 = -19
Then our final equation becomes
y = 10 x - 19
