The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).
What is the simplified form of the expression?Given the expression in the question;
(x² + 7x) / (9 - x²)
To simplify, first factor out x form x² + 7x
(x × x + 7 × x) / (9 - x²)
Factor out x
x (x + 7) / (9 - x²)
Next, simplify the denominator
x (x + 7) / (9 - x²)
Rewrite 9 as 3²
x (x + 7) / (3² - x²)
Now, since both terms are perfect squares
a² - b² = (a + b)(a - b)
Hence,
x(x + 7) / ( 3 + x )( 3 - x )
Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).
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i need to add this fraction i need to know the explantion and answer Add: 3 38
+ 7 34
The addition of the given fraction numbers 3(3/8) and 7(3/4) is, 89/8
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
Two fraction numbers,
3(3/8) and 7(3/4)
The addition of two fraction number is,
⇒ 3(3/8) + 7(3/4)
In simple form it can be written as,
⇒ 24+3/8 + 28+3/4
⇒ 27/8 + 31/4
LCM Of 8 & 4
= 8
⇒ 27/8 + 31×2/4×2
⇒ 27/8 + 62/8
⇒ (27 + 62)/8
⇒ 89/8
Hence, the result is 89/8
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simplyfy
(2/x)/(1-4/x)
The result = 2/ (x-4) is obtained by simplifying the provided equation (2/x)/(1-4/x)
What is meant by fraction?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.A portion of something is called a fraction. When the numerator and denominator are split, a number is represented mathematically as a quotient. In a simple fraction, both are integers.A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator. In mathematics, there are three primary fraction types.There are three types of them: mixed fractions, improper fractions, and proper fractions. Fractions are terms with a numerator and a denominator.Given,
[tex]$\frac{\frac{2}{x}}{1-\frac{4}{x}}[/tex]
Use the fractional rule : [tex]$\frac{\frac{a}{b}}{c}=\frac{a}{b \cdot c}$[/tex]
[tex]$=\frac{2}{x\left(1-\frac{4}{x}\right)}[/tex]
Simplify [tex]$x\left(1-\frac{4}{x}\right): \quad x-4$[/tex]
Then we get,
[tex]$=\frac{2}{x-4}[/tex]
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find the area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10).
The area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10) is √336≈18.34 units.
A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram.
Calculate the length of PQ → Position vector of Q - Position vector P
PQ→ (5-3)i + (6-3)j + (4-2)k
PQ→ 2i + 3j + 2k
Calculate the length of PS →Position vector of S - Position vector P
PQ→ (7-3)i + (7-3)j + (10-2)k
PQ→ 4i + 4j + 8k
Area of parralelogram = [tex]\left[\begin{array}{ccc}i&j&k\\2&3&2\\4&4&8\end{array}\right][/tex]
= √16² + 8² + 4²
=√336
=18.34 units
The area of a parallelogram is the region bounded by the parallelogram's four sides. It is measured in square units like cm2, m2, and inch2 and can be computed if we know the size of the parallelogram's base and height.
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HELPP PLSS What is the measurement of ∠Z
Answer:
Z = 155
Step-by-step explanation:
You know all the angles inside the triangle.
180 - 65 - 90 = X
X = 25
Thus using the supplementary rule (All straight lines have degree of 180), then you can get Z
180 - X = Z
180 -25 = Z
Z = 155
Question in picture, pls help
No, there do not exist nonzero constants a and b such that a p(x)+b.
What is nonzero constants?Nonzero constants are numerical values used in mathematical equations which cannot be reduced to zero. They are also referred to as non-zero numbers or constants. Non-zero constants can take on any real or complex number value that is not equal to zero. Non-zero constants are used in various areas of mathematics including linear algebra, calculus, statistics, geometry and trigonometry.
No, there do not exist nonzero constants a and b such that a p(x)+b. q(x) is a polynomial with degree 1. This is because the degree of the polynomial P(x) is 1 and the degree of the polynomial Q(x) is 2, so the degree of the sum of the two polynomials (a p(x)+b. q(x)) must be 2 or greater.
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Please any assistance
Answer: y=-4x+4
Step-by-step explanation: the "+4" represents the y intercept, so (0,4)
Answer:
Step-by-step explanation:
3) The following are the trial balance and other information related to Soft Tech, a
consulting engineer.
Soft Tech, Consulting Engineer
Trial Balance
December 31, 2022
Debit Credit
Cash Br. 59,000
Accounts Receivable 99,200
Allowance for Doubtful Accounts Br. 1,500
Supplies 3,920
Prepaid Insurance 2,200
Equipment 50,000
Accumulated Depreciation—Equipment 12,500
Notes Payable 14,400
Share, Capital 104,020
Dividend 34,000
Service Revenue 200,000
Rent Expense 19,500
Salaries and Wages Expense 61,000
Utilities Expense 2,160
Office Expense 1,440
Br. 332,420 Br. 332,420
Other data:
1. Fees received in advance from clients Br.12,000.
2. Services performed for clients that were not recorded by December 31,
Br.9,800.
3. Bad debt expense for the year is Br.2,860.
4. Insurance expired during the year Br.960.
5. Equipment is being depreciated at 10% per year.
6. Fine Tech gave the bank a 90-day, 10% note for Br.14,400 on December 1,
2022.
7. Rent of the building is Br.1,500 per month. The rent for 2022 has been
paid, as has that for January 2023.
8. Salaries and wages earned but unpaid December 31, 2022, Br.5,020.
Instructions
a. From the trial balance and other information given, prepare annual
adjusting entries as of December 31, 2022.
b. Prepare the worksheet
c. Prepare an income statement for 2022, a statement of owner’s equity,
and a classified statement of financial position.
d. Maintain the necessary closing entry.
Finney & Associates is an interior decorating firm in Tucson. The following costs were incurred in a project to redecorate the mayor's offices. • Direct material: $29,000 • Direct professional labor: $42,000 The firm's budget for the year included the following estimates: • Budgeted overhead: $800,000 • Budgeted direct professional labor: $640,000 Overhead is applied to contracts by using a predetermined overhead rate that is based on direct professional labor cost. Actual professional labor during the year was $655,000 and actual overhead was $793,000. Question What is the total cost to redecorate the mayor's offices?
The total cost to redecorate the mayor's office by Finney & Associates is $123,500.
How to compute the total production cost:The total production cost consists of direct materials, direct labor, and overhead costs.
The overhead cost can be computed using a predetermined overhead rate or activity-based costing rates.
In this situation, the predetermined overhead rate is the quotient of the budgeted overhead cost and the budgeted direct professional labor cost.
Direct material: $29,000
Direct professional labor: $42,000
Allocated overhead cost: $52,500
Total cost = $123,500
Budgeted overhead: $800,000
Budgeted direct professional labor: $640,000
Predetermined overhead rate = Budgeted overhead/Budgeted direct professional labor cost
= $1.25 ($800,000/$640,000)
Allocated overhead cost = $52,500 ($1.25 x $42,000)
Thus, Finney & Associates can reliably claim that they incurred a total cost of $123,500 in redecorating the mayor's offices.
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What is the Area of this Shape?
Answer:
38.5
Step-by-step explanation:
rectangle = (2.5x2)+1.5=6.5
6.5x5=32.5
both triangle = 4/2 = 2
(1.5x2)x2=6
total area = 32.5 + 6 = 38.5
According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately
two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care
nursery.
Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies
were born deaf. Round answer to four decimal places
Answer:
Step-by-step explanation:
According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery.
Briefly describe each of the six guidelines for establishing causality. Give an example of the application of each guideline. Select the correct answer below
Six guidelines for determining causality:
The first guideline is to look for situations where results correlate with suspected causes, even if other factors differ.The second guideline states that groups that differ only in the presence or absence of the suspected cause should be similarly tested for the presence or absence of the effect.A third guideline states that evidence should be sought that the more suspected causes, the more consequences.The fourth guideline states that if an effect could be produced by other possible causes, it should be confirmed that the effect is still present after considering those other potential causes. I'm here.The fifth guideline states that suspected causes should be tested experimentally. The sixth rule is physical Suspected underlying mechanism The effect must be determined to generate.About causalityCausality is a term that refers to the principle of cause and effect, in which knowledge and information can be known automatically without the need for knowledge and mediation from other sciences. that every action derives its certainty and necessity, and the peculiarity of its existence, from some of the former, are things which are accepted without doubt and require no refutation. The necessity and originality of causal systems are parts of humanity, known collectively and beyond doubt.
Cause and effect are defined by the relationship between one event (cause) and another event (effect), where the second event is understood as the result of the first.
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Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible. (6,2); 3x−2y=7 please help me with this, it’s due tomorrow!!?
The equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
What is slope-intercept form?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point
Given that, a line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7, we need to find the equation of the line,
The line is
3x-2y = 7
Converting into slope-intercept form,
3x-2y = 7
2y = 3x - 7
y = 3x/2 - 7/2
We know that, the slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line = -2/3
Therefore, the equation of the asked line is, y = -2x/3 + c....(I)
Put x = 6 and y = 2 in equation to find c,
2 = -4 + c
c = 8
Therefore, put c = 8 in equation (i)
y = -2x/3 + 8
Hence, the equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
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Triangle ABC is defined in the coordinate plane by the points A(1, 2), B(4, 3), and C(4, 0).
Under which transformations will the image of triangle ABC be similar to the preimage?
select all that apply
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
According to the figure AB=1. AC=4
A'B' = 3, A'C' = 12
FAB'=3AB [A'C' = BAC
So, the scale factor is 3
Dilation is a method for producing comparable numbers. By increasing distances by the scale factor, each point is extended outwards from the center point D. (If the scale factor is more than one, go outwards.)
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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
A. [tex]$T(x, y) \rightarrow(-x, -y)$[/tex]
This is a reflection to the origin that does not preserve angles or aspect proportions. Therefore, triangle ABC under this transformation does not resemble that image.
Example: [tex]$T(x, y) \rightarrow(x, x-y+1)$[/tex]
This is a shear transformation that does not preserve angles or aspect ratio. Therefore, triangle ABC under this transformation does not resemble that image.
C. [tex]$T(x, y) \rightarrow(x+3, y)$[/tex]
This is a translation that preserves angles and aspect ratio. So the triangle ABC under this transformation resembles that image.
D. [tex]$T(x, y) \rightarrow(0.2x, 4y)$[/tex]
This stretches by a factor of 0.2 in the x direction and 4 in the y direction, preserving angle and horizontal proportions. So the triangle ABC under this transformation resembles that image.
E. [tex]$T(x, y) \rightarrow(2x, 2y)$[/tex]
This is a stretch by a factor of 2 in both the x and y directions, preserving the proportions of the angles and sides. So the triangle ABC under this transformation resembles that image.
F. [tex]$T(x, y) \rightarrow(3x, 4y)$[/tex]
This stretches by a factor of 3 in the x direction and 4 times in the y direction, preserving the proportions of angles and sides. So the triangle ABC under this transformation resembles that image.
Therefore, the similarity-preserving transformations between triangle ABC and its image are C, D, E, and F.
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a raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep. find the volume of soil that it holds in cubic yards round to 1 decimal place. please explain
The volume of the soil that it holds in cubic yards is 11.1.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep.
In yards,
a raised flower bed is 8.33 yards long, 2.67 yards wide, and 0.5 yards deep.
The volume of the soil that it holds,
= 8.33 x 2.67 x 0.5
= 11.10 cubic yards.
Therefore, the volume is 11.1 cubic yards.
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A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48-ounce sample?
Step-by-step explanation:
1 ounce = 28 grams
48 ounce = 1344 grams
So, 1344 grams would be in a 48-ounce sample.
A monument is constructed by first laying a row of 60 bricks at ground level. A second row, with two fewer bricks, is centered on that; a third row, with two fewer bricks, is centered on the second; and so on. The top row contains 10 bricks. How many bricks are there in the monument?
Let's call the number of bricks in the ith row as B_i. Then, B_i = 60 - 2 * (i - 1) for i = 1, 2, ..., n, where n is the number of rows.
The number of bricks in the monument can be found by summing up the bricks in each row. So, the total number of bricks is:
T = B_1 + B_2 + … + B_n
= 60 + (60 - 2) + (60 - 4) + … + (60 - 2 * (n - 1))
= 60 * n + (-2) * (1 + 2 + … + (n - 1))
To find the sum of 1 to (n-1), we can use the formula for the sum of an arithmetic series: S_n = n * (a_1 + a_n) / 2, where a_1 = 1 and a_n = n - 1.
Substituting these values into the formula, we get: S_n = (n - 1) * (1 + (n - 1)) / 2 = (n - 1) * n / 2.
Therefore, T = 60 * n + (-2) * (n - 1) * n / 2 = 30 * n^2 + 30 * n.
Finally, to find the number of bricks for n = 10 rows, we substitute n = 10 into the equation:
T = 30 * 10^2 + 30 * 10 = 300 + 300 = 600
So, there are 600 bricks in the monument.
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The quotient of -20 and the sum of u and v
Answer:
-20 ÷ (u +v) or -20/(u +v)
Step-by-step explanation:
You want an expression that represents the quotient of -20 and the sum of u and v.
SumThe sum of two quantities is indicated with a plus (+) sign.
"The sum of u and v" is written in symbols as ...
u + v
QuotientThe wording "the quotient of a and b" means "a divided by b". It is written in symbols using a division sign or fraction bar:
a ÷ b or a/b
The desired quotient can be written as ...
-20 ÷ (u +v) or -20/(u +v)
__
Additional comment
The parentheses are needed so that the sum is computed before the quotient is computed. If the expression is typeset, the division bar does the grouping:
[tex]\dfrac{-20}{u+v}[/tex]
A water tank is being filled with water. Before water is pumped in, the water level in the tank is 14 inches high. After 20 minutes, the water level is 52 inches high.If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?A. h= 39+13tB. h=1.95t-13C. h=1.95t+13
The equation which can be used to model this situation is equals to the h = 1.9t + 14 , where h represents the water level , t represents the time in minutes.
We have, A water tank which is filled with water. Before pumping the water,
The level i.e., high of water in water tank
= 14 inches
After 20 minutes, the level of water in tank = 52 inches
We have to determine the equation to model this situation in form of time "t" in minutes. Let "h" be level of water increases from initial point/ level in t minutes. As the change in water level from initial to after 20 minutes = 52 inches - 14 inches = 38 inches
That is, water level increased 38 inches in 20 minutes. Then rate of increase in level = 38/20 = 1.9 inches per minutes
Now, the for time 't' the equation is formed by multiplying the rate of chenge of water level with 't' and adding initial water level.
=> h = 1.9t + 14
which is linear equation in two variables,i.e., h and t . Hence,the required equation model is h = 1.9t + 14 .
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esc Calculate the wavelength in meters of electromagnetic radiation that has a frequency of 1.82 x 10^8 s-1¹. (c = 3.00 X 10^8 m/s) k C #C [] CA 9 %
The wavelength in meters of electromagnetic radiation that has a frequency [tex]2.5[/tex] × [tex]10^{5}[/tex] .
How can you determine the electromagnetic radiation's wavelength at different frequencies?The wavelength in meters of electromagnetic radiation that has a frequency of [tex]1.82[/tex] ×[tex]10^{8}[/tex] s-1¹. (c = 3.00 X [tex]10^{8}[/tex] m/s) k C #C [] CA 9 %
The frequency f of electromagnetic waves, or, equivalently, the wavelength c/f, is used to classify them.
The characteristics of electromagnetic radiation include amplitude (brightness), wavelength, frequency, and period. We have shown that the frequency of a light wave is related to its energy by the equation E = h v E=hnu E=h.
v=1.210 3 Hz and
e=310 8 m/s equal v and e, respectively.
3×[tex]10^{8}[/tex]
λ = 2.5 ×[tex]10^{5}[/tex].
The wavelength in meters of electromagnetic radiation that has a frequency 2.5 × [tex]10^{5}[/tex].
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the difference of two times a number and five is eight
Please help, I am trying to get this question answered.
They are similar by the property of SAS and the factor by which the triangle grows is 1.25
15. ______________________ a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact
Experimentation is a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact.
What is experimentation in scientific method?Experimentation in the scientific method is the process of testing a hypothesis or theory through the process of collecting data and making observations.
This involves designing and performing experiments to test the hypothesis or theory, and then analyzing the results to determine whether the hypothesis or theory is supported by the data or not.
Experimentation allows for the collection of direct evidence about the hypothesis or theory being tested, which can then be used to make informed decisions about the hypothesis or theory.
Experimentation is the ultimate test of a hypothesis or theory and is fundamental to the scientific method.
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None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, none of the students taking rhetoric are taking physics.
Which one of the following statements follows logically from the statements above?
A. There are students who are taking art but not literature.
B. None of the students taking literature are taking art.
C. There are students who are taking rhetoric but not literature.
D. None of the students taking rhetoric are taking literature.
E. There are students who are taking both art and literature.
The correct option is (A).
The following statements follows logically from the statements is there are students who are taking art but not literature.
"None of the students taking literature are taking physics."
So: if you are student taking literature, then you are not taking physics.
⇒TL=Taking Literature
⇒TP=Taking Physics
⇒TA=Taking Art
⇒TR=Taking Rhetoric
P1: TL ==> not TP
TP ==> not TL
"but several of the students taking physics are taking art."
So: some of the students taking physics are also taking art.
Q1: TP-some-TA
TA-some-TP
"In addition, none of the students taking rhetoric are taking physics."
So: if you are a student taking rhetoric, then you are not taking physics.
P2: TR ==> not TP
TP ==> not TR
Answer choice (A) states: "There are students who are taking art but not literature."
So: some students who are taking art are not taking literature.
(A): TA-some-not TL
not TL-some-TA
Can we logically infer this from the statements above? Yes.
Remember we can combine a quantifier statement with a Sufficient & Necessary statement if the right-hand side variable of the quantifier statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have that with P1 and Q1.
So, we can combine Q1 to P1 like so: TA-some-TP ==> not TL to infer: TA-some-not TL, so the correct option is (A).There are students who are taking art but not literature.
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Please help me with this question.
The value of x is in the quadrilateral PQRS is 1.6
What are similar quadrilateral?Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
The ratio of the corresponding angle of a similar quadrilateral are equal.
This means that all quadrilateral are not similar if the ratio of their corresponding sides are not equal
Therefore AD/PS = DC/ SR
= 4/3.2 = 2/x
4x = 2× 3.2
4x = 6.4
divide both sides by 4
x = 6.4/4
x = 1.6
Therefore the value of x or line RS in the quadrilateral PQRS = 1.6
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bgrvfecdwxsafecdwxstcrefdxwsza
The value of x in the triangle is 23.83
How to determine the value of x in the triangleFrom the question, we have the following parameters that can be used in our computation:
A right triangle
The value of x can be calculated using the following tangent equation
tan(40) = 20/x
Make x the subject of the equation
x = 20/tan(40)
Evaluate
x = 23.83
Hence, the value of x is 23.83
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indicate which of the following sentences are statements. (select all that apply.) A. 1,024 is the smallest four-digit number that is a perfect square. B.he is a mathematics major. C.128=26 D.X=26
D. X=26 is a mathematical statements, since it can be either correct or incorrect.
To comprehend any mathematical statement, we must first understand what mathematics is all about. When we answer a math problem, the solution is either correct or incorrect. There is no midway to the problems! Any mathematical statement is in the same scenario. A mathematical statement is either correct or incorrect.
In this scenario, the statement, 'A. 1,024 is the smallest four-digit number that is a perfect square.', and 'B. He is a mathematics major.' are correct statements. And 'C. 128=26' is a incorrect statement. Therefore, these options are not the mathematical statements because A and B is correct statement and C is a false statement. Meanwhile, D. X=26 is a mathematical statement because it is either correct or incorrect, depending on the given problem. Therefore D. X=26 is the correct answer for a mathematical statement.
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Table bellow shows the number of cups of coffee people drink completely the table and work out the mean number of cups of coffee
The mean number of cups of coffee will be 4.
How to calculate the meanThe sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
The mean number of cups of coffee will be:
= 140 / 35
= 4.
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In a poker hand consisting of 5 cards, find the probability of holding a. 3 kings b. 4 hearts and 1 diamonds Expert's answer A poker hand consists of 5 cards. The sample space has (52/5) possible outcomes. a. Choose 3 kings from 4 kings. From the remaining 52−4=48cards choose 2 non-kings to make a five-card poker hand P(3 kings)=(43)(52−45−3)(525)=P(3 kings)=(552)(34)(5−352−4)= =4!3!(4−3)!⋅48!2!(48−2)!52!5!(52−5)!==5!(52−5)!52!3!(4−3)!4!⋅2!(48−2)!48!= =2(48)(47)(120)52(51)(50)(49)(48)=9454145≈0.001736=52(51)(50)(49)(48)2(48)(47)(120)=5414594≈0.001736 b. There are total 13 hearts and 13 diamonds. Choose 4 hearts from 13 hearts (134)(413) Choose 1 diamonds from 13 diamonds (131)(113) P(4 hearts and 1 diamonds)=(134)(131)(525)=P(4 hearts and 1 diamonds)=(552)(413)(113)= =13!4!(13−4)!⋅13!1!(13−1)!52!5!(52−5)!==5!(52−5)!52!4!(13−4)!13!⋅1!(13−1)!13!= =13(12)(11)(10)(5)(13)52(51)(50)(49)(48)=14339984≈0.003576=52(51)(50)(49)(48)13(12)(11)(10)(5)(13)=39984143≈0.003576
In a poker hand consisting of 5 cards, the probability of holding 3 kings is 0.0009 .
The probability of holding 3 kings in a poker hand of 5 cards can be calculated as follows:
The number of ways to choose 3 kings from a deck of 4 kings is= ⁴C₃ = 4.
The number of ways to choose 2 other cards from the remaining 48 cards is = ⁴⁸C₂ = 1128.
The total number of 5-card hands from a standard deck of 52 cards is = ⁵²C₅ = 2598960.
So , the probability of holding 3 kings in a 5 card hand is
⇒ (4 × 1128)/2598960
⇒ 4512/2598960 .
⇒ 0.00085148 .
Therefore , probability of holding 3 kings in a 5card hand is approximately 0.0009 .
The given question is incomplete , the complete question is
In a poker hand consisting of 5 cards, find the probability of holding 3 kings .
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A and B are points on a polygon. A’ and B are the points under a translation. Find B’
By translation the point B' on the polygon is (0, -8).
What is translation?If the point (x, y) is translated h unit to the right and k unit to the up, its image is (x + h, y + k) and the translation is (h, k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y + k) and the translation is (-h, k)If the point (x, y) is translated h unit to the right and k unit to the bottom, its image is (x + h, y - k) and the translation is (h, -k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y - k), and the translation is (-h, -k)Let us try to answer the question.
The coordinates of point A are as follows: (4, 5)
x = 4 and y
The coordinates of point A' are as follows: (9, -1)
x' = 9 and y' = -1
That is, in the third case above, x increased and y decreased.
The point A has been moved to the right and down.
Using the third rule above (x + h, y - k),
x + h = 9
x = 4
Multiply x by 4.
4 + h = 9
Subtraction of 4 from both sides
4 - 4 + h
= 9 - 4
h = 5
y - k = -1
y = 5
Substitute 5 for y
5 - k = -1
Subtraction of 5 from both sides
5 - 5 - k = -1 - 5
-k = -6
Divide each side by -1.
k = 6
In the third case, the translation is (h, -k).
h = 5 and k = 6
The literal translation is (5, -6)
To find B' the image of the point B
B = (-5, -2)
B' = (x + h, y - k)
B' = (-5 + 5, -2 - 6)
B' = (0, -8)
The complete question is :
" A and B are points on a polygon. A' B' are points of the polygon under a translation. Find B'.
A(4,5) A' (9,-1)
B (-5,-2) B' (0,-8)."
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a grocery store sells bananas for 0.70 per pound if the store sells 1/2 ton of bananas how much money will the store receive
Answer:
A ton is equal to 2000 pounds. So half a ton is equal to 2000/2 = 1000 pounds.
If the store sells 1000 pounds of bananas at a price of $0.70 per pound, the total revenue the store will receive is 1000 * $0.70 = $700.
Step-by-step explanation:
In a year when the maximum income for Social Security was $118,500, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222.
Both of his employers took out Social Security tax. As a result, Bart had paid excess Social Security tax, and the government must return some of it to him. How
much does the government owe him for excess Social Security paid?
Answer:
The government owes Bart the excess Social Security tax that he paid, which is the amount of tax he paid on his income above the maximum income for Social Security. In this case, that would be $118,500 (the maximum income for Social Security) minus $99,112 (what he earned at his first job) minus $56,222 (what he earned at his second job) = $13,166. So the government owes Bart $13,166 for the excess Social Security tax he paid.
Answer:
Step-by-step explanation:
He earned a total of 155,334.
99112 plus 56222.
subtract the max income from the income total
155,334 - 118500 = 36834
He is owed the social security tax he paid on 36834.
The problem does not give the social security rate.
