Answer:
[tex]\textsf{a)} \quad T_n=-n^2+n+20[/tex]
[tex]\textsf{b)} \quad T_{12}=-112[/tex]
[tex]\textsf{c)} \quad \sf 8th\;term[/tex]
a) Second difference is 2.
b) First term is 10.
Step-by-step explanation:
The given number pattern is:
20, 18, 14, 8, ...To determine the type of sequence, begin by calculating the first differences between consecutive terms:
[tex]20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8[/tex]
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
[tex]-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is -2, the coefficient of the n² term is -1.
Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
Therefore, the expression to find the the nth term of the given quadratic sequence is:
[tex]\boxed{T_n=-n^2+n+20}[/tex]
To find the value of T₁₂, substitute n = 12 into the nth term equation:
[tex]\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}[/tex]
Therefore, the 12th term of the number pattern is -112.
To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:
[tex]\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}[/tex]
As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.
[tex]\hrulefill[/tex]
Given terms of a quadratic number pattern:
T₂ = 1T₃ = -6T₅ = -14We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:
[tex]T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14[/tex]
From this we can create three equations:
[tex]T_1-a=1[/tex]
[tex]-6-b=T_4[/tex]
[tex]T_4-c=-14[/tex]
The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).
[tex]-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c[/tex]
From this we can create three equations:
[tex]-a+x=-7[/tex]
[tex]-7+x=-b[/tex]
[tex]-b+x=-c[/tex]
Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:
[tex]-c=(-7+x)+x[/tex]
[tex]-c=2x-7[/tex]
Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:
[tex]\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}[/tex]
[tex]\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}[/tex]
Solve for x by equating the two equations for T₄:
[tex]\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}[/tex]
Therefore, the second difference is 2.
Substitute the found value of x into the equations for -a, -b and -c to find the first differences:
[tex]-a+2=-7 \implies -a=-9[/tex]
[tex]-7+2=-b \implies -b=-5[/tex]
[tex]-5+2=-c \implies -c=-3[/tex]
Therefore, the first differences are:
[tex]T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14[/tex]
Finally, calculate the first term:
[tex]\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}[/tex]
Therefore, the first term in the number pattern is 10.
[tex]10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14[/tex]
Note: The equation for the nth term is:
[tex]\boxed{T_n=n^2-12n+21}[/tex]
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
6 m, 24 m
Step-by-step explanation:
area of kite = (diagonal 1 × diagonal 2) / 2
Let the length of the shorter diagonal = x.
The length of the longer diagonal is 4x.
The area is the product of the diagonals divided by 2.
area = 4x × x / 2 = 4x²/2 = 2x²
The area is 72 m².
Therefore, 2x² must equal 72 m².
2x² = 72 m²
Divide both sides by 2.
x² = 36 m²
Take the square root of both sides.
x = 6 m
The short diagonal has length 6 m.
The long diagonal is 4x long.
4x = 4(6 m) = 24 m
Answer: 6 m, 24 m
Answer:
6 metres and 24 metres
Step-by-step explanation:
The kite will be composed of two smaller triangles and two larger triangles.
Let's call the shorter diagonal (across the kite) W.
So the longer diagonal (top to bottom of kite) will be 4W.
area = (L X W)/2
= (4W X W)/2
= 4W²/2
= 2W².
2W² = 72
W² = 36
W = 6 metres.
so the shorter diagonal is 6 metres.
the longer diagonal is 4 X 6 = 24 metres
Which statements are true of the graph of h(x) = 3√x-4? Check all that apply.
The domain of h(x) is the set of all real numbers.
The range of h(x) is the set of all real numbers.
For all points (x, h(x)), h(x) exists if and only if x - 4
2
O The graph of h(x) is a translation of f(x) down 4 units.
O The graph of h(x) intercepts the x-axis at (4, 0).
The true statements about the graph of h(x) = ∛(x-4) are:
The domain of h(x) is the set of all real numbers.
For all points (x, h(x)), h(x) exists if and only if x - 4≥0
The graph of h(x) intercepts the x-axis at (4, 0).
The domain of h(x) is the set of all real numbers since there are no restrictions on the input variable x.
For all points (x, h(x)), h(x) exists if and only if x - 4 ≥ 0. This is because the cube root function is only defined for non-negative values, and the expression inside the cube root, x - 4, must be non-negative for h(x) to exist.
The graph of h(x) intercepts the x-axis at (4, 0) since plugging in x = 4 into the equation gives h(4) = ∛(4-4) = ∛0 = 0. This means that the point (4, 0) lies on the graph.
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A dance team is made up of 9 girls and 3 boys. Two of the girls and 1 of the boys are also on the debate team. What percent of the dance team is also on the debate team? Enter your answer in the box.
Answer:
25%
Step-by-step explanation:
9+3=12 dance people total
divide 3 by 12 to determine debate members over dance members
=.25 or 25%
Find the values of m and n. Give the answer in simplest radical form.
PLS HELP ASAPP!!!!!!
The values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin60° = √3/2 and sin30° = 1/2
sin 60° = m/(24√3) {opposite/hypotenuse}
√3/2 = m/(24√3)
m = (24√3 × √3)/2 {cross multiplication}
m = 12 × 3
m = 36
sin 30° = n/(24√3)
1/2 = n/(24√3)
n = 24√3/2 {cross multiplication}
n = 12√3
Therefore, the values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
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Maria is selling chips and candy bars. If she wants to sell each bag of chips, c, for $1.50 and each
candy bar, b, for $1.20, which equation would represent her possible sales, S(c,b)?
○ S(c, b) = c+b
O S(c, b) = 0.30cb
O S(c, b) = 0.30(c+b)
O S(c, b) = 1.50c + 1.206
The The equation that would represent Maria's possible sales, S(c, b), is:
S(c, b) = 1.50c + 1.20b
The term 1.50c represents the total revenue from selling bags of chips.
The term 1.20b represents the total revenue from selling candy bars.
So, the equation can be written as
S(c, b) = 1.50c + 1.20b
This equation represents the total sales amount (S) based on the quantities of bags of chips (c) and candy bars (b) sold.
The equation calculates the sales by multiplying the number of bags of chips (c) by their price of $1.50 each and the number of candy bars (b) by their price of $1.20 each.
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The circle below has center D. Suppose that m BC = 42°. Find the following.
The measure of angle BDC is 42° and the measure of angle BAC is 21°.
Given that, the measure of arc BC of circle = 42°.
An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
From the given circle,
The measure of arc BC = Angle BDC = 42°
Here, Angle BDC = 2×Angle BAC
42° = 2×Angle BAC
Angle BAC = 21°
Therefore, the measure of angle BDC is 42° and the measure of angle BAC is 21°.
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The perimeter of the rectangle below is 202 units. Find the value of x.
5x +3
4x - 1
Solve the following equation by Graphing:
0 = x^2 - 6x + 7
Answer:
See below
Step-by-step explanation:
Where the graph crosses the x-axis will solve the equation
Match the trigonometric expressions to their solutions.
cos [140°- (50° +30°)]
√3
tan 240°
-√6-√2
cos 150°
1
Reset
Next
sin 255
Hi,
cos[140˚- ( 50˚ + 30˚)] = 1/2
tan 240˚ = √3
cos 150˚ = -√3/2
sin 255˚ = -√6 - √2/4
Those above should be the correct ones
XD
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The distance between the side AB are 314.2 ft.
In a triangle ABC AC = 200 ft, m ∠A = 72°, and m ∠B = 37°. we need to find the measure of the side AB,
So,
Using sine law.
Sin A / CB = Sin B / AC = Sin C / AB
Using the angle sum property of a triangle we find the value of angle C,
∠C = 180° - (∠A + ∠B)
∠C = 180° - (72° + 37°)
∠C = 180° - 109°
∠C = 71°
So,
Sin 37° / 200 = Sin 71° / AB
AB = 200 / Sin 37° × Sin 71°
AB = 314.2 ft
Hence the distance between the side AB are 314.2 ft.
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the expression 2x+4 is equal to what for x = 3
Answer:10
Step-by-step explanation: You plug in 3 for x so you get the equation 2(3)+4
Which becomes 6+4
Which equals 10
Question: Which expression is undefined in the set of real numbers? A √-4 B 0/-4 с 0-4 D - 4x0
The expression that is undefined in the set of real numbers would be = 0/-4. That is option B.
What are real numbers?Real numbers are those numbers that can either be positive or negative and that are rational or irrational numbers which are different from complex numbers.
An expression can be said to be an undefined set of real numbers when it's numerator = 0 as seen in 0/-4.
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Use the given proof to answer the question below:
Given ABCD is a parallelogram.
Prove: ADCB
D
A
1
2
3
4
S
6
Statements
ABCD is a parallelogram
ABI CD and AD IBC
and
AC = AC
ADCA ABAC
AD CB
Which of the options below complete the proof?
A. Statement 3: LBACZCAD and ZBCA LDCA
Reason 5: A.A.S. Postulate
B. Statement 3: LBACCAD and ZBCA = LDCA
Reason 5: A.S.A Postulate
C. Statement 3: LBAC LDCA and LBCA LDAC
Reason 5: A.A.S. Postulate
D. Statement 3: ZBAC LDCA and LBCA LDAC
Reason 5: A.S.A Postulate
Reasons
Given
Definition of parallelogram
Alternate interior angles theorem
Reflexive property
C.P.C.T.C.
The correct option is D.
Given that ABCD is a parallelogram, we need to prove AD ≅ CB.
So,
Properties of a parallelogram =
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Statement Reason
1. ABCD is a parallelogram Given
2. AB║CD and AD║BC Definition of parallelogram
3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC Alternate interior angles theorem
4. AC ≅ AC Reflexive property
5. ΔBAC ≅ ΔDCA A.S.A Postulate
6. AD ≅ CB CPCTC
Hence the correct option is D.
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Which graph is most often used to show change in data across time?
The graph most often used to show change in data across time is the line graph.
The graph most often used to show change in data across time is the line graph. A line graph is an effective visualization tool that displays data points as a series of connected data markers, forming a line.
It is commonly used to illustrate trends, patterns, or fluctuations in data over a continuous time interval.
The x-axis represents time, while the y-axis represents the variable being measured. By plotting data points and connecting them with lines, line graphs provide a clear visual representation of how the data changes over time, allowing for easy identification of trends, seasonality, growth, or decline in the data series.
Line graphs are widely utilized in various fields, including economics, finance, science, and social sciences, to present temporal data in a comprehensive and understandable manner.
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Find the measure of the each angle to the nearest degree. cos−11013
Which of the following statements are true? Check all of the boxes that apply.
f(x) = 2√x has the same domain and range as f(x)=√x
f(x) = -2√x has the same domain and range as f(x)=√x
f(x) = -√x has the same domain as f (x)=√x, but a different range.
f(x)=√x has the same domain as f(x)=√x, but a different range
0 0 0 0
DONE ✔
Intro
15 of 19
The correct statements regarding the domain and the range of the functions are given as follows:
f(x) = 2√x has the same domain and range as f(x)=√xf(x) = -√x has the same domain as f (x)=√x, but a different range.How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.For the square root function, we have that:
The domain is x >= 0.The range is y >= 0.Hence if we multiply the function by a negative number, the domain of the function remains constant, but the range is changed.
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You empty a 2-liter bottle every 8 seconds into tanks that hold 50 gallons. How long will it take you to fill 11 tanks? (3.8 l = 1 gallon)(Convert 11 tanks to hours)
It will take approximately 2.32 hours to fill 11 tanks.
First, we need to convert the capacity of the tanks from gallons to liters, as the rate at which we empty the bottle is given in liters. Since 1 gallon is equal to 3.8 liters, the capacity of each tank is 50 gallons * 3.8 liters/gallon = 190 liters.
Now, let's calculate the time it takes to fill one tank:
The bottle is emptied at a rate of 2 liters every 8 seconds. To find the time it takes to fill one tank, we divide the capacity of the tank (190 liters) by the rate at which we empty the bottle (2 liters/8 seconds):
Time for one tank = 190 liters / (2 liters/8 seconds) = 190 liters * (8 seconds/2 liters) = 760 seconds.
Next, we need to find the total time required to fill 11 tanks. Since each tank takes 760 seconds to fill, we multiply this by 11 to account for the 11 tanks:
Total time to fill 11 tanks = 760 seconds/tank * 11 tanks = 8,360 seconds.
Finally, we convert the total time from seconds to hours. There are 60 seconds in a minute and 60 minutes in an hour, so:
Total time to fill 11 tanks = 8,360 seconds * (1 minute/60 seconds) * (1 hour/60 minutes) = 2.32 hours (rounded to two decimal places).
Therefore, it will take approximately 2.32 hours to fill 11 tanks.
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3500pounds is placed into a savings account that pays interest at arate of 1.5% compounded annually.
Calculate the total compound amount at the end six years of investment, rounded to 2 decimal places.
Answer:
$3827.00
Step-by-step explanation:
To calculate the total compound amount at the end of six years with an interest rate of 1.5% compounded annually, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Total compound amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $3500
r = 1.5% = 0.015 (as a decimal)
n = 1 (compounded annually)
t = 6 years
Substituting these values into the formula, we have:
A = 3500 * (1 + 0.015/1)^(1*6)
Calculating this expression, we get:
A ≈ 3500 * (1.015)^6 ≈ 3500 * 1.093717 ≈ 3827.00
Rounding the total compound amount to 2 decimal places, the final value is approximately $3827.00
6. Prove that linear functions grow by equal differences over equal intervals.
Part I. This is the graph of. Use the graph to show that equal intervals of x-values have equal differences
of y-values.
a) Think about an interval on the x-axis starting with p and ending with p + k. What is the difference
between the x-values? What is the difference between the y-values for these x-values? Complete the
tables using.
The linear function equation, y = m·x + c, indicates;
6. The growth in the y-values over each unit x-value interval is a difference of m units.
Part I. Please find attached the graph of y = x + 3, created with MS Excel, which shows that the differences between the y-values is 2 units over each x-value interval of 2 units.
a) The difference between the x-values is; k
The difference between the y-values is; m·k
The difference in the y-value is; m·k
Please find attached the completed tables in the following section
What are linear functions?The equation of a linear function is; y = m·x + c
Where;
m = The slope of the graph = (y₂ - y₁)/(x₂ - x₁)
(x₁, y₁), and (x₂, y₂), are ordered pair of data on the graph of the linear function
c = The y-intercept of the linear function
(y₂ - y₁)/(x₂ - x₁) = m
(y₂ - y₁) = m × (x₂ - x₁)
Δy = m × Δx
When Δx = 1, we get;
Δy = m
Therefore, the y-value of a linear function increases by m, the slope value, when the x-value increases by 1, which indicates that the linear function grows by equal differences over the same interval of the input value of the function
Part I; Please find a graph of the linear function, y = 1·x + 3, which shows that each equivalent interval of 2 units in the x-axis, produces a difference in the y-value or y-axis of 2 units.
a) Considering the interval p and p + k, let y₁ represent the y-value at p and let y₂ represent the y-value at p + k, we get;
Slope, m = (y₂ - y₁)/((p + k) - p) = (y₂ - y₁)/k
Therefore;
(y₂ - y₁)/k = m
(y₂ - y₁) = m × k
Therefore, the increase in the y-value, for an increase in the x-value of k is a constant, m·k = (y₂ - y₁)
Therefore the difference in the y-value for the specified x-values is a constant m·k
The possible equation in the question obtained from a similar question on the website is; y = -(1/2)·x + 10
The completed tables are;
[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 2& p+ k = 6&\\ \cline{1-4}x-value & 2 & 6 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (2)+10 =9 & y = (-1/2)\cdot (6)+10=\underline{7} & -2 \\\cline{1-4}\end{tabular}[/tex]
[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 10& p+ k = 14&\\ \cline{1-4}x-value & 10 & 14 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (10)+10 =\underline{ 5 }& y = (-1/2)\cdot (14)+10=3 & -2 \\\cline{1-4}\end{tabular}[/tex]
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What is the perimeter of the figure? In Units
The sales tax for an item was $20 and it cost $500 before tax. Find the sales tax rate. Write your answer as a percentage.
Answer: To find the sales tax rate as a percentage, we can use the following formula:
Sales Tax Rate = (Sales Tax / Cost Before Tax) * 100%
In this case, the sales tax is given as $20, and the cost before tax is $500. Plugging these values into the formula, we have:
Sales Tax Rate = ($20 / $500) * 100%
Simplifying the expression:
Sales Tax Rate = (0.04) * 100%
Sales Tax Rate = 4%
Therefore, the sales tax rate for the item is 4%.
Step-by-step explanation:
What is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The Option D.
What is the area of the rhombus?To get area of a rhombus, we will use the formula: Area = (d₁ * d₂) / 2 where d₁ and d₂ are the lengths of the diagonals.
Given that the horizontal diagonal length is 25 millimeters (d₁ = 25 mm) and the vertical diagonal length is 8 millimeters (d₂ = 8 mm.
We will substitute values into the formula:
Area = (25 mm * 8 mm) / 2
Area = 200 mm² / 2
Area = 100 mm².
Full question:
A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
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Assume 0 is an acute angle.
cot 0 =
4
3
The value of the angle csc θ of the given problem is: 5/4
How to solve the trigonometric ratios?There are different trigonometric ratios such as:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, we are given that:
cot θ = 4/3
We know that cot θ = 1/tan θ
Thus:
tan θ = 3/4
Since θ is an acute angle, it means it is less than 90 degrees. Thus, using Pythagoras theorem, we can find the third side which is the hypotenuse to be 5
Now, csc θ = 1/sin θ
Thus: sin θ = 4/5
csc θ = 5/4
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Find the missing angle and side measures of Delta*ABC , given that
m angle A = 50 deg , m angle C = 90 deg , and CB = 16
The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.
To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.
Given:
∠A = 50°
∠C = 90°
CB = 16
We can start by finding the measure of ∠B:
∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)
50° + ∠B + 90° = 180°
∠B + 140° = 180°
∠B = 180° - 140°
∠B = 40°
Now, using Sine law
CB/ sin A = AB / sin C
16 / sin 50 = AB / sin 90
16 / 0.766044 = AB
AB = 12.25
Again 12.25 = AC/ sin B
12.25 = AC / sin 40
AC = 19.068
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April can buy a package of 10 folders for $1.20 or a package of 8 folders for $1.12. What is the unit price, per folder, in each package?
Each folder in the package of 10 costs $
Each folder in the package of 8 costs $
Answer:
Step-by-step explanation:
For the package of 10 folders: Unit price = $1.20 / 10 = $0.12 For the package of 8 folders: Unit price = $1.12 / 8 = $0.14
Andre is making a quilt with blue and green fabrics. He has 15 options for the blue portion of the quilt and wants to use 4 different fabrics. How many different ways are there for Andre to select the blue fabrics?
There are 1365 different ways for Andre to select the blue fabrics for his quilt.
To determine the number of different ways Andre can select the blue fabrics for his quilt, we can use the concept of combinations.
Andre wants to select 4 different fabrics from a pool of 15 options for the blue portion of the quilt. This can be calculated using the formula for combinations:
C(n, r) = n! / (r! × (n-r)!)
where n is the total number of options and r is the number of selections.
In this case, we have:
n = 15 (number of options for blue fabrics)
r = 4 (number of fabrics to be selected)
Plugging in these values into the combination formula, we get:
C(15, 4) = 15! / (4! × (15-4)!)
Simplifying the equation, we have:
C(15, 4) = 15! / (4! × 11!)
Now, let's calculate the factorial terms:
15! = 15 × 14 × 13 × 12 × 11!
4! = 4 × 3 × 2 × 1
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Substituting these factorial terms into the equation:
C(15, 4) = (15 × 14 × 13× 12 × 11!) / (4 × 3 × 2 × 1 × 11!)
Simplifying further:
C(15, 4) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)
C(15, 4) = 1365
Therefore, there are 1365 different ways for Andre to select the blue fabrics for his quilt.
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Pedro observed what customers ordered at his ice cream shop and found the following probabilities:
�
(
vanilla
)
=
0.3
�
(
sundae
)
=
0.2
�
(
vanilla and sundae
)
=
0.15
P(vanilla)=0.3
P(sundae)=0.2
P(vanilla and sundae)=0.15
Find the probability that a customer ordered vanilla ice cream given they ordered a sundae.
The probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
To find the probability that a customer ordered vanilla ice cream given they ordered a sundae, we can use the concept of conditional probability.
The conditional probability of an event A given event B is denoted as P(A|B) and is calculated as the probability of both events A and B occurring divided by the probability of event B.
In this case, we want to find P(vanilla|sundae), which represents the probability of a customer ordering vanilla ice cream given that they ordered a sundae.
Using the given probabilities:
P(vanilla) = 0.3
P(sundae) = 0.2
P(vanilla and sundae) = 0.15
The probability of a customer ordering a sundae is the denominator for the conditional probability. Therefore, P(sundae) will be the denominator.
P(vanilla|sundae) = P(vanilla and sundae) / P(sundae)
Substituting the given values:
P(vanilla|sundae) = 0.15 / 0.2
Now we can simplify:
P(vanilla|sundae) = 0.15 / 0.2
= 0.75
Therefore, the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
In conclusion, based on the given probabilities, there is a 75% chance that a customer who ordered a sundae also ordered vanilla ice cream.
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100 Points! Geometry question. Photo attached. Find the measure. Please show as much work as possible. Thank you!
Answer:
The answer would lie within 31 degrees of MP and also as in PM.
Answer:
central m arc MP=118°
Step-by-step explanation:
here
central m arc MN=2* inscribed m arc MN=2*31=62°
again
central m arc MN+ central m arc MP=180° being linear pair
substituting value
62°+central m arc MP=180°
central m arc MP=180°-62°
central m arc MP=118°
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in the given right triangle HJK include the following: C. 10.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse, x = 5 × 2
Hypotenuse, x = 10.
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Can u help me find the value of x
The numerical value of x in the dimensions of the rectangle is 9.
What is the numerical value of x?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
Area of a rectangle is expressed as;
A = length × width
From the diagram:
Wdith of the rectangle = x - 2
Length of the rectangle = x + 5
Area = 98 ft²
Since area of a rectangle = length × width:
98 = ( x - 2 )( x + 5 )
Simplify
( x - 2 )( x + 5 ) = 98
Apply distributive property:
x² + 3x - 10 = 98
x² + 3x - 10 - 98 = 0
x² + 3x - 108 = 0
Factor using AC method:
( x - 9 )( x + 12 ) = 0
Hence:
x - 9 = 0 or x + 12 = 0
x = 9 or x = -12
Since, we are dealing with dimensions, we take the positive value.
Hence, the value of x is 9.
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