the original price was "x", which oddly enough is the 100%.
now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]
9/17 in decimal form rounded to the nearest hundredth
Answer:
0.53
Step-by-step explanation:
0.6 because you divide 9 and 17
HELPPP ASAPPPP PLSSS!!!!!
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}z+6=\frac{3}{2}( z+6)[/tex]
[tex]\displaystyle\\Didtribute\ \frac{3}{2}:\ \frac{1}{2}z+6=\frac{3}{2}z+9[/tex]
[tex]\displaystyle\\Substract\ \frac{1}{2} z\ on\ each\ side:\ 6=z+9[/tex]
[tex]\displaystyle\\Substract\ 9\ on\ each\ side:\ -3=z\\\\[/tex]
[tex]z=-3[/tex]
10 yards is how many inches?
Answer:
360 inches.
Step-by-step explanation:
because 1 yard is 36 inches (3 rulers) so just multiply 36 by your number of yards.
Bob has $2,600 to invest and needs $3,100 in 11 years. What annual rate of return will he need to get in order to accomplish
his goal if interest is compounded continuously?
OA. 2.54%
OB.2%
OC.1.6%
OD. 1.54%
OE.3.54%
On solving the provided question we can say that the answer is - nnual rate of return will he need to get in order to accomplish his goal if interest is compounded continuously is [tex]A(t) = 2800^e(20)t.[/tex]
Difference between compound and simple interest
Simple interest and compound interest are the two methods for calculating interest. Simple interest is computed on a loan's principle, or initial loan amount. Compound interest is sometimes referred to as "interest on interest" since it is computed using both the principal and the accrued interest from prior periods.
What kind of compound interest are there?Formula for Monthly Compound Interest. 12 times a year are used to compute interest that is compounded monthly., Formula for Quarterly Compounding. Four times a year are used to compute interest that is compounded quarterly., Formula for Daily Compound Interest., Formula for Annual Compound Interest.
[tex]3300 = 2800e^20t\\ (33/28) = e^20t\\ ln(33/28) = 20t\\ 0.05ln(33/28 = t.[/tex]
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Find the sum.
(9-6m) + (12m - 8)
Answer:
Step-by-step explanation:
the answer is (6m+1). Hope i helped :)
a certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation. the academic director is concerned that market factors may have adversely affected the full-time placement rate and decides to perform a hypothesis test to see if her concern is warranted. in this situation, explain the meaning of a type ii error.
The type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
It is given to us that -
A certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation.
The academic director wants to perform a hypothesis test to see if her concern is warranted.
We have to explain the meaning of a type II error for this type of hypothetic test.
In Hypothesis test, type II error occurs when the null hypothesis is not rejected even if it is actually false.
When performing hypothesis test, there are two factors that play an important role -
(a) The significance level of the hypothesis test
(b) The p-value obtained
In the given situation,
Null hypothesis, [tex]H_{0}[/tex]: p = the proportion is equal to 87%, i.e., 0.87
Alternative hypothesis, [tex]H_{A}[/tex]: p = the proportion has reduced than 0.87
The type II error may occur when -
the p-value is greater than the significance level
This condition will arise when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
In such situation, we cannot reject the null hypothesis because the p-value must be greater than the significance level.
Thus, the type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
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The type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
What is type II error ?
In Hypothesis test, type II error occurs when the null hypothesis is not rejected even if it is actually false.
When performing hypothesis test, there are two factors that play an important role -
(a) The significance level of the hypothesis test
(b) The p-value obtained
In the given situation,
Null hypothesis, : p = the proportion is equal to 87%, i.e., 0.87
Alternative hypothesis, : p = the proportion has reduced than 0.87
The type II error may occur when -
the p-value is greater than the significance level
This condition will arise when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
In such situation, we cannot reject the null hypothesis because the p-value must be greater than the significance level.
Thus, the type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.
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three multiple-choice tests were constructed to cover the same curriculum area. test a had 20 items, test b had 40 items, and test c had 60 items. what is the most accurate statement that can be made about the reliability of these tests?
Test c had 60 items
It is the most accurate statement that can be made about the reliability of these tests.
The reason that objective tests include so many items is to increase the reliability of the test.
Reliability Test
It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.
Probability
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
A measure of reliability between two variants of the same test is known as alternate forms reliability. The results of two identical (but distinct) tests are correlated, and a reliability coefficient is computed. If variations in one test's observed results correspond to variations in the scores of an equivalent test, the test is said to be dependable. A psychological test's practise effect which is typical of test-retest reliability, can be mitigated by a survey instrument's alternate-form reliability. The goal is to reword the survey questions in a way that makes them functionally identical, or just rearrange the questions in the first and second surveys of the same respondents.
Test c had 60 items
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Which of the following quadratic functions does not have zeros of −15 and 6?
Answer: f(x) = -x^2 - 9x - 90
Correct answer is the last one (D)
Step-by-step explanation:
Graph every single one of them using Desmos Graphing Calculator
Find the slope of the line through each pair of points.
1) (8, 12), (11,-17)
3) (-1, -8), (-20, 19)
5) (2,16), (8, 20)
7) (11,-6), (8,5)
2) (2.-11). (15, 11)
Date
4) (5, -18), (-15, -16)
6) (9, 10), (-12,-4)
8) (11, 8), (-6, 3)
The slope of the line that passes through each pair of points are:
1. -29/3
3. -27/19
5. 2/3
7. -11/3
2. 22/13
4. 1/5
6. 2/3
8. 5/17
How to Find the Slope of the Line?The slope of a line that joins two points can be found by using the formula below:
Slope (m) = change in y / change in x
1. Slope (m) of the line that goes through (8, 12) and (11, -17):
Slope (m) = (-17 - 12) / (11 - 8) = -29/3
3. Slope (m) of the line that goes through (-1, -8) and (-20, 19):
Slope (m) = (19 - (-8)) / (-20 - (-1)) = 27/-19
m = -27/19
5. Slope (m) of the line that goes through (2,16) and (8, 20):
Slope (m) = (20 - 16) / (8 - 2) = 4/6
m = 2/3
7. Slope (m) of the line that goes through (11,-6) and (8,5):
Slope (m) = (-6 - 5) / (11 - 8) = -11/3
2. Slope (m) of the line that goes through (2.-11) and (15, 11):
Slope (m) = (-11 - 11) / (2 - 15) = -22/-13
m = 22/13
4. Slope (m) of the line that goes through (5, -18) and (-15, -16):
Slope (m) = (-16 - (-18)) / (-15 - 5) = 2/10
m = 1/5
6. Slope (m) of the line that goes through (9, 10) and (-12,-4):
Slope (m) = (-4 - 10) / (-12 - 9) = -14/-21
m = 2/3
8. Slope (m) of the line that goes through (11, 8) and (-6, 3):
Slope (m) = (8 - 3) / (11 - (-6)) = 5/17
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Write an equation in slope-intercept form for the line that contains the point (1, -1) and is parallel to y = 3x - 2.
Considering the definition of parallel line, the line that contains the point (1, -1) and is parallel to y = 3x - 2 is y= 3x -4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y= 3x -2
where:
the slope is 3.the ordinate to the origin is -2.Two lines are parallel if they have the same slope. So, the parallel line has a slope of 3.
The line passes through the point (1, -1). Replacing in the expression for a line:
-1= 3× 1 + b
-1= 3 + b
-1-3 = b
-4 = b
Finally, the equation of parallel line is y= 3x -4.
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Find domain and range. Due tmrw!
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
How to find the domain and range of a function?The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
For the graph given, the domain lie across the x-axis.
The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
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Answer:
answer is in explanation
Step-by-step explanation:
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
How to find the domain and range of a function?
The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
For the graph given, the domain lie across the x-axis.
The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
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Determine the coordinates of the triangle to compute the perimeter of the triangle using the distance formula (round to the nearest whole number).
A 37 units
B 48 units
C 40 units
D 30 units
E 35 units
×
c squere=a squer + b squer if the triagle is right angle triangle and c is hypotenuse. see that graph and take the left side if it is our c then the side that down of it take a and the side that nearest from it take bthe same as above do the other sides and add each other finaly you get the perimetr 37 units see the picture above more explain for youCompute The Following. (A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9
The Computation results of given combination and permutation expression,
(A) P(9, 3) = 504
(B) C(9, 3) = 84
(C) P(8,8) = 40,320
(D)P(9,9) = 1
What is Permutations and Combination ?A permutation is an arrangment of arranging objects or numbers in order.
The formula for permutations is
ⁿPᵣ = n!/(n-r)!
Combinations are the way of selecting objects or numbers from a group of objects, in such a way that the order of the objects does not matter.
The formula for combinations is,
ⁿCᵣ = n!/[r! (n-r)!]
ⁿCᵣ represents the number of combinations from “n” objects taken “r” at a time.
We have given some expressions and we shall compute these.
(A) P(9, 3) , here n = 9 and r = 3
=> P(9, 3) = 9!/(9-3)! = 9!/6! = 9×8×7×6!/6!
P(9, 3) = 9×8×7 = 504
(B) C(9, 3) = 9!/3!(9-3)! = 9!/6!×3!
= 9×8×7×6!/6!(3×2×1) = 9×8×7/6 = 84
(C) P(8, 8) = 8!/(8-8)!
= 8!/0! = 8! = 8×7×6×5×4×3×2×1 = 40,320
(D) C (9, 9) = 9!/9!(9-9)!
= 9!/9! 0! = 1
Hence ,we get all the values of given expression.
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PLEASE HELP ITS A TIMED QUESTION Evaluate 5-4 and 5-2
The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ -(5⁻⁴)(5²)
Simplify the expression, then we have
⇒ -(5⁻⁴)(5²)
⇒ -(1/5⁴)(5²)
⇒ -(5² / 5⁴)
⇒ - 25 / 625
⇒ - 1/25
The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.
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How do you simplify (1/8)^(4/3) ?
Answer:
1/16
Step-by-step explanation:
Rational Exponents can be rewritten as Radicals:
[tex](\frac{1}{8})^{\frac{4}{3}}=\sqrt[3]{\frac{1}{8}}^{4}[/tex]
Take the cube root of 1/8 = 1/2.
Raise (1/2) to the 4th power
Step-by-step explanation:
the numerator (top part) of a fractional exponent means "to the power of ...".
the denominator (bottom part) of a fractional exponent means "the ...th root".
so,
(1/8)^(4/3) means the cubic root of 1/8 to the power of 4.
these 2 operations can be done in any sequence.
it is the same if we first put 1/8 to the power of 4 and then get the cubic root, or if we first get the cubic root of 1/8 and then put that result to the power of 4.
to keep the numbers small, I prefer here to start with the cubic root :
cubic root (8) = 2, because 2³ = 8.
and so, cubic root (1/8) = 1/2
(1/2)⁴ = 1/16
that's it.
(1/8)^(4/3) = 1/16
if b is an integer how would you represent the next 6 even integers
Answer:
Below
Step-by-step explanation:
IF b is even : b+2 b+4 b+6 b+8 b+10 b+12
If b is ODD : b+1 b+3 b+5 ..... b+11
suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean (parameter of interest). what is the probability the researcher will make a type i error?
The probability the researcher will make a type i error 0.10
The hypothesis testing, type I error involves rejecting true null hypothesis also referred to as 'false-positive' conclusion and type II error occurs when false null hypothesis is not rejected. It is also known as 'false negative' conclusion. And they are opposite to each other.
Here we have given that suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean
And we need to find the probability the researcher will make a type i error
While looking into the given question,
We know that,
Significance level = 5%
alternative value of the mean = 0.90
Then the probability the researcher will make a type i error is calculated as,
mean = 1 - error
0.90 = 1 - error
=> error = 0.10
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use the discriminant to determine how many and what kind of solutions the quadratic equation 3x2 4x=-5 has
The correct option B. two complex (nonreal) solutions, for the given quadratic equation.
Explain the term discriminant?Any equation of the type ax² + bx + c = 0; In which, x is variable and a, b, and c are any real values where a ≠ 0 is called a quadratic equation.The section of a quadratic formula following the square root symbol, b2-4ac, is the discriminant. The discriminant informs us if there exist two solutions, single solution, or even no solutions.The given quadratic equation is-
3x² + 4x = - 5
3x² + 4x + 5 = 0
So, D = b² - 4ac
In which, b = 4, a = 3, c = 5
D = (4)² - 4(3)(5)
D = 16 - 60
D= -44
D < 0
2 complexes (nonreal) solutions are found for the given quadratic equation.
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The correct question is-
Use the discriminant to determine how many and what kind of solutions the quadratic equation 3x² + 4x = - 5 has.
A. one real solution
B. two complex (nonreal) solutions
C. no real or complex solutions
D. two real solutions
a local movie theater found that if the price of admission was $17, the attendance was about 1150 customers per day. when the price of admission was dropped to $12, attendance increased to about 1250 per day. write a linear equation for the attendance in terms of the price, p. ( a
According to the point-slope form, the linear equation for the attendance in terms of the price is given as [tex]y=-20p+1490[/tex].
It is given to us that -
If the price of admission was $17, the attendance was about 1150 customers per day
When the price of admission was dropped to $12, attendance increased to about 1250 per day
We have to write a write a linear equation for the attendance in terms of the price.
Let us say that -
Price of admission is given as "p"
and, attendance of customers is given as "q"
It is given to u that -
For p = $17, q = 1150 customers per day
For p = $12, q = 1250 customers per day
We know that the point-slope form of a linear equation can be represented as -
[tex]y-y_{1} =m(x-x_{1} )[/tex] ------ (1)
where,
([tex]x_{1} ,y_{1}[/tex]) = initial coordinates of the point
m = slope of the linear equation = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ----- (2)
From the given information, we can represent the points as -
([tex]x_{1} ,y_{1}[/tex]) = (17, 1150)
and, ([tex]x_{2} ,y_{2}[/tex]) = (12, 1250)
Substituting the values of ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) in equation (2), we have -
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\= > m = \frac{1250-1150}{12-17}\\= > m = \frac{100}{-5} \\= > m = -20[/tex]------ (3)
Now, substituting the values of ([tex]x_{1} ,y_{1}[/tex]) and m from equation (3) in the point-slope form of the linear equation (1), we have
[tex]y-y_{1} =m(x-x_{1} )\\= > y-1150=(-20)(x-17)\\= > y-1150=-20x+340\\= > y=-20x+340+1150\\= > y=-20x+1490[/tex]
In terms of price, p we can write the above linear equation as -
[tex]y=-20p+1490[/tex]
Thus, the linear equation for the attendance in terms of the price is given as [tex]y=-20p+1490[/tex].
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a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 31 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 8% rate of defects?
The probability that the shipment is accepted is 0.278685
The following problem is a problem of the binomial distribution. Here,
n = 31
p = probability of pills being a defect = 0.08
We need to find the probability that the batch is affected.
This means we need to find
P(X≤1)
PMF of Binomial is given by
P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
= P(X = 0) + P(X = 1)
= ³¹C₀ 0.08⁰ 0.92³¹ + ³¹C₁ 0.08 X 0.92³⁰
= 0.92³⁰(0.92 + 31X0.08)
= 0.92³⁰ X 3.4
=0.278685
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I need help with this
By using the concept of percentage, it can be calculated that
65% people are completely satisfied with the car
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 2% means [tex]\frac{2}{100}[/tex]. Here, 2 is expressed as a fraction of 100.
This is a word problem on percentage
Number of people who are completely satisfied with the car = 1495
Total number of people surveyed = 1495 + 210 + 595 = 2300
Percentage of people who are completely satisfied with the car = [tex]\frac{1495}{2300}\times 100[/tex]
= 65%
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If you have two main effects, and one main effect is significant, this means that a. The other main effect may or may not be significant but the interaction effect is definitely significant b.The other main effect and the interaction effect are not significant
c. The other main effect and the interaction effect are significant d. The other main effect and the interaction effect may or may not be significant
If you have two main effects, and one main effect is significant, this means that d. The other main effect and the interaction effect may or may not be significant
What exactly is a significant effect in research?A statistically significant result indicates that it is unlikely to be explained solely by chance or random factors. In other words, if there is no true effect in a research study, a statistically significant result has a very low chance of occurring.
The significance level is the threshold at which one can accept whether an event is statistically significant. Researchers use the p-value to determine statistical significance: if the p-value is less than the significance level, the result is statistically significant.
If you have two main effects and one of them is significant, the other one and the interaction effect may or may not be significant.
In conclusion, based on the information illustrated, the correct option is D.
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Statistics is the science of conducting studies to: Select one: a. Solve a system of equations b. Collect; organize, summarize; analyze; and draw conclusions from data Hypothesize; experiment and draw conclusions d. Monitor; study, and report on a subject
The science of conducting studies to gather, arrange, summarize, analyze, and draw conclusions from data is known as statistics.
Survey responses are analyzed using statistics. Understanding the phrases and ideas is crucial in order to fully comprehend what is being represented (or misrepresented) by a given statement.
Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activities and census data. Both theoretical and practical advancements in statistics have been sparked by the current need to transform the vast volumes of data accessible in many application domains into valuable information.
Option B is the proper response, thus.
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tickets for a play cost $ 7 for students and $ 10 for adults. on opening night, all 380 seats were filled, and box office revenue was $ 3290.00. how many adults attended at the play?
The total number of adults who attended the play are 210.
Here, we are given that tickets for a play cost $ 7 for students and $ 10 for adults.
Total number of seats = 380
Box office revenue on opening night = $ 3290
Let the number of adults be x
Then, the number of students will be = (380 - x)
thus, we can form the following equation-
10x + 7(380 - x) = 3290
10x + 2,660 - 7x = 3290
3x + 2,660 = 3290
3x = 3290 - 2660
3x = 630
x = 630/3
x = 210
Thus, the total number of adults who attended the play are 210.
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a recent study of minimum wage earners found that 55% of them are 16 to 24 years old. suppose a random sample of 12 minimum wage earners is selected. what is the probability that exactly 7 of them are 16 to 24 years old.
The probability that exactly 7 of them are 16 to 24 years old is 0.222
In this question we have been given a recent study of minimum wage earners found that 55% of them are 16 to 24 years old.
A random sample of 12 minimum wage earners is selected. we need to find the probability that exactly 7 of them are 16 to 24 years old.
Here, n = 12
p = 0.55
1 - p = 0.45
x = 7
Using binomial distrubution the required probability would be,
P = 12C7 * (0.55)^7 * (0.45)^(12 - 7)
P = 792 * 0.01522 * (0.45)^5
P = 792 * 0.01522 * 0.01845
P = 0.2224
Therefore, the required probability is 0.222
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you are dealt five cards from a thoroughly shuffled standard deck of cards. what is the probability that you get a full house. (full house
The probability of getting a full house is 0.001441 or 0.14%.
When you dealt five cards from a thoroughly shuffled standard check of cards then for the probability of getting a full house we need to know the total number of full house combinations and possible cards hands.
This is calculated by taking the number of possible full house combinations (3,744) and dividing it by the total number of possible 5-card hands (2,598,960). This can be written as :
Mathematically, this can be expressed as:
P(Full House) = 3,744 / 2,598,960 = 0.001441 or 0.14%
Therefore the probability of getting a full house is 0.001441 or 0.14%
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Amrit’s income is
32
%
more than Bethan’s income.
Amrit and Bethan’s combined income is
£
54
868
.
Calculate Amrit's income.
Amrit's income is £27434.16.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let the Bethan's income be x
Amrit's income is 32% more than Bethan's income.
So, Amrit's income=x+32%
Amrit and Bethan's combined income is £54868.
According to given question we have
x+x+32%=£54868
2x+32/100=£54868
2x=54868-0.32
2x=54867.68
x=27433.84
Bethan's income=£ 27433.84
Amrit's income
=x+32%
=£ 27433.84+0.32
=£27434.16
Therefore, Amrit's income is £27434.16.
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What is the actual distance between Toledo and Colubus?
The equation is y = 2.5. And the actual distance in the third case and the distance on the map in the fourth case will be 120 miles and 90 mm, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the distance on the map and 'y' be the actual distance. Then the equation of the line is given as,
(y - 25) = [(50 - 25) / (20 - 10)](x - 10)
y - 25 = 2.5x - 25
y = 2.5x
If x = 48 mm, then the actual distance is given as,
y = 2.5(48)
y = 120 miles
If y = 225 miles, then the distance on the map is given as,
225 = 2.5x
x = 90 mm
The graph is given below.
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what is the equation of this line in standard form? responses 6x−11y=−13 6 x minus 11 y equals negative 13 11x−6y=13 11 x minus 6 y equals 13 6x−11y=13 6 x minus 11 y equals 13 6x−7y=17
6x - 11y = - 13 is the the equation of this line in standard form that is option A from the group of choices.
What is equation?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Coefficients, variables, operators, constants, terms, expressions, and an equal to sign are all components of an equation. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.
Here,
6x - 11y = - 13 is the the equation of this line in standard form that is option A from the set of possibilities.
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How do you find the sum of the infinite geometric series given 16+12+9+...?
The sum of the infinite geometric series 16 + 12 + 9 + ... is 64.
To find the sum of an infinite geometric series, you can use the formula:
sum =[tex]\frac a{(1 - r)}[/tex]
where "a" is the first term in the series and "r" is the common ratio between terms.
In this case, the first term is 16 and the common ratio is 3/4, so the sum is:
sum [tex]= \frac{16}{(1 - \frac{3}4)} =\frac{16}{(\frac{1}4)} = 64[/tex]
Therefore, the sum of the infinite geometric series 16 + 12 + 9 + ... is 64.
Note that this formula is only valid if the absolute value of the common ratio is less than 1. If the absolute value of the common ratio is 1 or greater, the series will either converge to a finite value or diverge to infinity, and the sum cannot be calculated using this formula.
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