There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.
P=13/52*12/51=1/4*4/17=1/17.
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can someone please help me solve, it's on factor theorem, I got most of the answer it's just for the remainder what is it? is what I'm doing correct?
Answer:
remainder: 3/4
Step-by-step explanation:
You want to divide the polynomial (2x^4-9x^3-x^2+2) by (2x-1).
Polynomial long divisionThe attachment shows the division worked out.
Your work has a sign error in the second product: (-4x²)(2x-1) should be (-8x³+4x²).
Factor theoremThe factor theorem tells you that if division by (2x-1) gives a remainder of 0, then (2x-1) is a factor of the dividend polynomial. Alas, here, the remainder is not zero, so 2x-1 is not a factor.
Remainder theoremThe remainder theorem tells you that the remainder of p(x) divided by (x-a) is p(a). We can evaluate the polynomial for x=1/2, the value that makes the divisor zero:
f(1/2) = ((2(1/2) -9)(1/2) -1)(1/2)^2+2 = ((-8)(1/2) -1)(1/4) +2 =(-5)(1/4) +2 = 3/4
The remainder from division by (2x -1) is 3/4.
__
Additional comment
We did the polynomial evaluation by writing it in Horner form. This minimizes the number of arithmetic operations required, and generally makes them simpler.
surface area of a shape with the measurements 4 mm, 8 mm, 2 mm
Answer:
112 mm^2.
Step-by-step explanation:
Total surface area
2(4*8 + 4*2 + 2*8)
= 2 * 56
= 112 mm^2.
What is the correct form of the partial fraction decomposition for the expression StartFraction 7 x + 18 Over x squared + 9 x EndFraction?
The correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x is 2/x + 5/(x + 9).
What is the Fraction?
The numerator and the denominator are the two components of a fraction. The number displayed above the fractional bar is known as the numerator. As an illustration, the numerator in 6/7 is 6. Denominator: The fractional bar's lowermost number is designated as the denominator.Here,
x ² + 9x = x (x + 9), so the partial fraction decomposition would be
(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)
where a, b are some constants. To find them, multiply both sides by x ² + 9x :
7x + 18 = a (x + 9) + bx
Solve for a and b :
7x + 18 = (a + b) x + 9a
[ a + b = 7
[ 9a = 18
→ a = 2, b = 5
So
(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)
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Write the equation of the line through each point. Use slope-intercept form.
(-7,10) ; parallel to 2x - 3y = -3 .
The equation of the line in slope-intercept form passing through the point (-7 , 10) and parallel to 2x - 3y = -3 is y = (2/3)x + 44/3.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is parallel to 2x - 3y = -3, then their slopes are equal. First, express the equation in slope-intercept form y = mx + b to get the slope, m.
2x - 3y = -3
-3y = -2x - 3
y = -2/-3 x - 3/-3
y = 2/3 x + 1
m = 2/3
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
10 = 2/3(-7) + b
b = 44/3
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (2/3)x + 44/3
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An airplane flying at an altitude of 30,000 feet flies up to avoid a storm. Immediately after passing the storm, the airplane returns to its original altitude.
A. What interger represents the airplane's change in altitude to avoid the storm.?
B. What integer represents the airplanes change in altitude immediately after passing the storm?
C. Use appropriate tools, draw a number line to represent the airplanes changed altitude.
Answer: The number 8,000 represents the change in height necessary to dodge the storm.
The integer representing the altitude after passing the storm is 30,000
Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000
Step-by-step explanation:
In the picture that is attached, the diagram for this query is displayed.
We are informed that the aircraft's starting height was 30,000 feet.
A. What integer represents the airplane's change in altitude to avoid the storm.?
During the storm:
The plane flew at at altitude of 38,000 feet
We will deduct the end altitude from the starting altitude to obtain the change in altitude.
change of altitude = final altitude - initial altitude
change of altitude = 38,000 - 30,000
= 8,000 ft
Therefore, the integer representing the change of altitude to avoid the storm is 8,000
B. What integer represents the airplanes change in altitude immediately after passing the storm?
After the storm:
We are aware that the aircraft returned to its original height following the storm.
The number reflecting the altitude after passing the storm would be 30,000 ft given that the starting altitude is 30,000 ft.
C. Use appropriate tools, draw a number line to represent the airplanes changed altitude.
See a picture.
Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000
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Write a function for the height, T of the taller candle in terms of the number of hours it has burned, h.
The linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
What is the missing information?The missing information is that a 18 inch candle is burning at a rate of 3.1 inches an hour.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The initial height of 18 inches is the intercept.The burning rate is the slope, as a negative, as burning means that the height of the candle is decreasing.Hence the linear function for the height of the taller candle after t hours is given by:
h(t) = 18 - 3.1t.
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Please help! The object shown below has a mass of 5 kg and starts at rest. What is the acceleration of the object?
A.
20 m/s2
B.
2 m/s2
C.
50 m/s2
D.
150 m/s2
The acceleration of the object is 2 m/s²
Calculating AccelerationFrom the question, we are to determine the acceleration of the object
From Newton's second law of motion, we have that
F = ma
∴ a = F/m
Where F is the net force
m is the mass
and a is the acceleration
From the given information,
m = 5kg
From the diagram,
Net force = 30 N - 20N
Net force = 10 N
Then,
a = F/m
a = 10/5
a = 2 m/s²
Hence, the acceleration of the object is 2 m/s²
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: Write in standard form
(a) 567000
..... (1 mark)
The standard form of a given number is scientific notation which is given by the form of exponents of ten and written as 5.67 ×10⁵.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
What is the standard form?Standard form is a way of writing down in the easy form very large or very small numbers.
Let E is the standard form of a given number
E = 567000
E = 500000 + 67000 + 7000
E = 0.567 × 10⁶ = 5.67 ×10⁵
E = 5.67 × 10⁵
Hence, the standard form of a given number is 5.67 ×10⁵.
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Anyone pls help me rq
Answer:
m<LHK = 101
Step-by-step explanation:
Ok, so the straight line is equal to 180 degrees. And we already know the side of one angle, that is 79 degrees. So, simply subtract 79 from 180, and you get 101 degrees. I took geometry last year, and this might not be the "correct" way to do it, but it is easier and you get the same correct answer
Answer:
<LHK = 101
Step-by-step explanation:
angle on a straight line add up to 180
180 - 79 = 101
y varies directly with x .If y = (3/4) when x = (1/2) , find y when x=3
The direct variation is y = 3/2 x, the value of y for x = 3 is 9/2.
What is direct variation?A direct variation is defined as having variables that are directly proportional. When one variable's value rises, the other variable's value rises as well, and vice versa. Assuming k is constant, the following is how a direct variation is expressed:
y=kx
As y varies directly with x,
using direct variation,
y = kx
given, y = 3/4 when x = 1/2,
⇒ 3/4 = k 1/2
⇒ k = 3/2
when x = 3,
the value of y will be -
y = kx
⇒ y = 3/2. 3
⇒ y = 9/2
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i need help solving this
Answer:
x = 9.
Step-by-step explanation:
12x + 7 = 115
12x + 7 - 7 = 115 - 7
12x = 108
x = 9.
If angle A is 4x+2 and angle B is 11x, what is the value of x? (round to the nearest tenth)
The value of the x in the vertical angles are the 7/2.
According to the statement
We have to find that the value of the x in the given angles.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint.
From the given information:
If angle A is 4x+2 and angle B is 11x.
Then from the given figure, The given angles are the verticals.
We know that the Verticals angles are equal.
Then
4x+2 = 11x
7x = 2
x = 2/7.
Here the values of the x in the given vertical angles are 7/2.
So, The value of the x in the vertical angles are the 7/2.
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Years ago, a cell phone plan cost $70 per month for unlimited calling plus $0.10 per text message.
Answer:
so the cell phone plan is $70 per month
Step-by-step explanation:
solution in question
What are the coordinates of D'' if -CD with vertices C(2,4) and D(8,7) is translated along <-6,2> and then reflected over the y -axis?
The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)
What does coordinate mean in this case?
To coordinate is to make plans for things to come together or to collaborate with another person to achieve a goal. Coordination occurs when all the details of a journey are planned. When you and a friend divide up a large science project and decide who will do what, that is an example of coordination.We want to find the coordinates of Parallelogram CDEF with vertices C(2, -1), D(7,1), E(6,-2), and F(1,-4) after a reflection across y = x.
We can find these coordinates by following the following rule:
Reflection over y = x rule : ( x , y ) ---> ( y , x )
the x and y values simply swap places .
Applying rule to coordinates:
C(2,-1) --- swap 2 and - 1 ---> C'(-1,2)
D(7,1) --- swap 7 and 1 ---> D'(1,7)
E(6,-2) --- swap 6 and -2 ---> E'(-2,6)
F(1,-4) --- swap 1 and -4 ---> F'(-4,1)
The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)
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Traveling carnivals usually shut down for the winter months. Suppose a traveling carnival decided to instead remain open for business indefinitely in its last stop of the season. Assume its usual revenue projections hold($15,000 on the first nigh, and each night's revenue after the first night will be about 75% of the previous night revenue). To the nearest dollar, what is the maximum amount of revenue the carnival can expect in the town?
The maximum amount of revenue the carnival can expect in the town in the 5th night is; $4746.093.
How to solve Geometric Progression?A geometric progression is defined as a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
We are told that Revenue in the first night = $15000
Now revenue of new night is 75% of the previous night. Thus;
2nd night = 15000 × 75/100 = $11250
3rd night = $11250 × 75/100 = 8437.5
Therefore, the given geometric sequence is ;
15000, 11250, 8437.5 ...
First term; a = $15000
Common ratio (r) = 11250/15000 = 0.75
The formula for the nth term of a GP is given by ;
aₙ = arⁿ ⁻ ¹
Thus, revenue for the 5th night is;
a₅ = ar⁵⁻¹
a₅ = 15000(0.75)⁴
a₅ = 4746.093
We conclude that the revenue in the 5th night in two will be $4746.093.
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Which parent function is represented by the graph?
O A. Absolute value parent function
• B. Quadratic parent function
• C. Linear parent function
• D. Reciprocal parent function
Answer: D, reciprocal parent function
Step-by-step explanation:
The temperature in the mountains at 3 PM is 5°C. By 8 PM, the temperature has fallen 7°. What is the temperature at 11PM?
Answer:
-6.2
=
7°c ÷ 5hrs (difference between 3pm to 8pm)= 1.4
3×1.4= 4.2
7+4.2=11.2
5-11.2=-6.2
(sorry if it's wrong)
20. The difference between the compound interest and the simple interest on a certain
Sum at 9% per annum for 2 years is 324. Find the sum.
The sum is 40,000.
The difference between compound interest and simple interest is 324 on a certain sum at 9% for 2 years.
So,
Compound interest - Simple interest = 324
C.I - SI = 324
The formula for compound interest is given as:
C.I = P( 1 + r/100 )ⁿ - P
Where P is the principal amount, r is the rate and n is the time in years.
Therefore,
C.I = P( 1 + 9/100)² - P
C.I = P( 1 + 0.09)² - P
C.I = P(1.09)² - P
C.I = 1.1881P - P
C.I = 0.1881P
Now, the formula for simple interest is given as:
S.I = ( P × R × T / 100 )
Where P is the principal amount, R is the rate and T is time in years.
Therefore,
S.I = ( P × 9 × 2 / 100 )
S.I = 18P / 100
S.I = 0.18P
Now,
C.I - S.I = 324
0.1881P - 0.18P 324
0.0081P = 324
P = 324 / 0.0081
P = 324 × 10000 / 81
P = 4 × 10000
P = 40000
Hence, the principal amount is 40,000.
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Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x-4
O h(x) = 3/4x
O h(x) = 1/4x
the answer to this question is
O h(x) = 1/4x
What is the rate of change? x intercept is (-1,0) and b is -4 if that helps at all
Answer:
-4
Step-by-step explanation:
In this case, rate of change will be equivalent to the gradient of the line.
Standard form of Equation of Line:
y = mx + c
where
m = Gradient
c = y - intercept
From the given information, we can substitute x = -1 and y = 0, and c = b = -4 (y-intercept) to find m (Gradient)
0 = -1m - 4
m = -4
Therefore, the rate of change is -4.
is it possible for a system of lineaf equations to have no solutions
yes
when equations are parallel
&
when you solve the equations you have
DIFFERENT NUMBERS on either side of the equal sign
for example when you do the math you would end up with something like :
7 = 0
mrviolamath
khan academy
The population of China is about 1.4 x 109
people, while the population of South Korea is
approximately 50,000,000 people. How many
times greater is the population of China than
the population of South Korea?
The population of China is 28 times greater than that of South Korea, calculated using solving of basic linear equation.
As per the question statement, the population of China is about (1.4 × 10⁹) people, while that of South Korea is approximately 50,000,000 people.
We are required to calculate that, by how many times is the is the population of China greater than that of South Korea.
To solve this question, let us assume that, the population of China is "x" times greater than that of South Korea. Hence, we will form a linear equation of single variable (x) and solving for "x", we will obtain our desired answer.
Since the population of China is assumed to be "x" times greater than that of South Korea,
[tex](50000000*x)=1.4*10^{9}\\ or,5*10^{7}*x=1.4*10^{9}\\or,5x=\frac{1.4*10^{9}}{10^{7}} \\or, 5x=1.4*10^{2}\\ or,5x=1.4*100\\or,5x=140\\or,x=\frac{140}{5}\\ or,x=28[/tex]
That is, The population of China is 28 times greater than that of South Korea.
Linear Equation: As the name itself suggests, a linear equation is an equation between variables, (typically Two) that gives a straight line when plotted on a graph, and also has a degree of 1.To learn more about Linear Equations, click on the link below.
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Find x. 30² + 35² = x²
The unknown variable's result of the equation 30² + 35² = x² is 46.10
To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.30² + 35² = x²
900 + 1225 = x²
x² = 2125
x = [tex]\sqrt{}[/tex]2125
x = 46.10
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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can someone please help meee
From the figures and the properties of the parallelogram was possible to find that: UT=27, ST=18, RV=7 and US=14.
Quadrilaterals
There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, the opposite sides are equal and parallel, for a parallelogram. In a parallelogram is noted too that the opposite angles and the diagonals are equal.
From the properties: the opposite sides are equal and parallel for a parallelogram. It is possible to find:
UT=RS=27
ST=RU=18
Considering that UV=7, then VS= 7 since V is the midpoint of the diagonal US. Therefore, US=14.
From the property: the diagonals are equal for a parallelogram. It is possible to find:
US=RT=14
RV=RT/2=14/2=7
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Please help me with this
The complete table for the electrician charges is shown below:
x y
1 125
2 175
3 225
4 275
How to complete a table with two variables
According to the statement, there are two variables. First, the number of hours of work (x) and, second, the total fee. The total fee changes linearly with the number of hours and the expression is defined below:
y = x' + (Δy / Δx) · x (1)
Where:
x' - Base fee, in dollars.Δx - Change in time, in hoursΔy - Change in total fee, in dollars.x - Time, in hours.If we know that x' = 75, Δx = 1 h and Δy = 50, then the values of the table are shown below:
x = 1
y = 75 + 50 · 1
y = 125
x = 2
y = 75 + 50 · 2
y = 175
x = 3
y = 75 + 50 · 3
y = 225
x = 4
y = 75 + 50 · 4
y = 275
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The volume of a sphere is a function of its radius, V = (4/3) πr³ . Evaluate the function for the volume of a volleyball with radius 10.5cm .
[tex]V = 1.17 * 10^{-29} m^{3}[/tex] is volume of a sphere is a function .
What is surface area of volume?
The quantity of surface area per unit volume of an object or collection of objects is known as the surface-area-to-volume ratio, sometimes known as the surface-to-volume ratio and variously abbreviated as sa/vol or SA:V.
Convert the radius from picometers to meters
r = 141 pm = 1.41 * [tex]10^{-10} m[/tex]
V = 4/3 π r³
= 4/3 π ( 1.41 * [tex]10^{-10}[/tex])³
[tex]V = 1.17 * 10^{-29} m^{3}[/tex]
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I need done before school please help!!
Factor completely. 2x³ - 4x² 30x
A (x+3)(x - 5)
B 2x(x² - 2x - 15)
2x(x+3)(x - 5)
- 5)
D 2x(x-3)(x
-
Hi! I'm just answering questions for points.
yael used to have a square garage with 356ft ^2 of floor space. She recently built an addition to it. The garage is still a square but it now has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
The answers are given below:-
The length of one side of the garage originally was 17.9 ft.
The length of one side of the garage now is 21.9 ft.
The percent increase in the length of one side was 22.35%.
What is the area of a square?The area of a square of side s is given by s squared, that is:
A = s².
The original area was 320 ft², hence the original length was:
s² = 320
s = √(320)
s = 17.9 ft.
The area increased by 50%, hence the new area is:
A = 1.5 x 320 = 480 ft².
The current length of one side is:
s² = 480
s = √(480)
s = 21.9 ft.
The percent increase is the change divided by the initial length and multiplied by 100%, hence:
(21.9 - 17.9)/17.9 x 100% = 22.35%.
The percent increase in the length of one side was 22.35%.
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i need help solving this angle problem
Answer:
corresponding angles are equal
Step-by-step explanation:
89*=(6x+5)*
89-5=6x
84=6x
x=14
I hope I could help.
