Use the formula for nCr to evaluate the expression. 10c3/6c4
SOLUTION
The given expression is
[tex]\frac{^{10}C_3}{^6C_4}[/tex]Recall the formula for combination
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Solving the given expresssion
[tex]\frac{^{10}C_3}{^6C_4}=\frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!}[/tex]This further gives
[tex]\begin{gathered} \frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!} \\ =\frac{10!}{7!3!}\div\frac{6!}{2!4!} \\ =\frac{10!}{7!3!}\times\frac{2!4!}{6!} \end{gathered}[/tex]This further gives
[tex]\begin{gathered} =\frac{10\times9\times8\times7!}{7!\times3\times2!}\times\frac{2!4!}{6\times5\times4!} \\ =\frac{10\times9\times8}{6\times5\times3} \\ =8 \end{gathered}[/tex]Therefore the solution is 8
Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide whether the law of sines or the law of cosines should be used to begin solving the triangle.B, C and bOption 1: SSA; law of sinesOption 2: SSA; law of cosinesOption 3: SAA; law of cosinesOption 4: SAA; law of sines
Answer:
Explanation:
Express the interval using inequality notation.
(-4, -1)
Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.
In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.
-4 and -1 are exclusive values for the given variable.
Symbol representing open interval is sign of < or >.
Interval (-4,-1) in inequality notation is given by -4 < x < -1.
All values are included between -4 and -1 except -4 and -1.
Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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evaluate x=5 and y=7
y2-x/y+3x
The answer to the given expression is 2
How to solve variables?To "solve" or "isolate" a variable is to place it on its own side of the equation.
All other variables or constants should be moved to the opposite side of the equation using inverse operations. The operations must be applied to both sides of the equation in order to maintain the equation's balance.
Given : x = 5 and y = 7
To find : [tex]\frac{y^{2} - x }{y + 3x}[/tex]
When we substitute the values mentioned above in this above expression we get;
[tex]\frac{7^{2}- 5 }{ 7+ 3X5}[/tex]
⇒ [tex]\frac{49 - 5}{ 7 + 15}[/tex]
⇒ [tex]\frac{44}{22}[/tex]
On dividing it with 22 we get
[tex]\frac{44}{22}[/tex] = 2
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what is the 6th term in the sequence? f(1) = 10 f(n) = f(n-1) + 3
We will investigate the evaluation of recursive sequences.
A iterative sequences are categorized by two values i.e one value preceding and the current value. The current value is evaluated on the basis of the previous value. In other words the current value is a function of preceeding value or depends on it.
All iterative relations of a sequence are expressed mathematically by two values as follows:
[tex]\begin{gathered} f\text{ ( n ): Current nth term value} \\ f\text{ ( n - 1 ): preceeding/ previous value} \end{gathered}[/tex]A iterative relation is a unique mathematical relationship between the current term f ( n ) and the previous value given as follows:
[tex]\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( n ) = f ( n - 1 ) + 3}}[/tex]For this particular relationship the first term value is given as follows:
[tex]\textcolor{#FF7968}{n}\text{\textcolor{#FF7968}{ = 1, f ( 1 ) = 10}}[/tex]We will now start determining the terms in the sequence by plugging the respective term numbers ( n ) and use the mathematical relationship for the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 2,}} \\ f\text{ ( 2 ) = f ( 1 ) + 3} \\ f\text{ ( 2 ) = 10 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 2 ) = 13}} \end{gathered}[/tex]We have evaluated the 2nd term in the sequence as 13. We will repeat the above steps for all term numbers ( n = 3 , 4 , 5 , 6 ).
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 3,}} \\ f\text{ ( 3 ) = f ( 2 ) + 3} \\ f\text{ ( 3 ) = 13 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 3 ) = 16}} \\ \\ \text{\textcolor{#FF7968}{For n = 4,}} \\ f\text{ ( 4 ) = f ( 3 ) + 3} \\ \text{f ( 4 ) = 16 + 3} \\ \text{\textcolor{#FF7968}{f ( 4 ) = 19 }} \\ \\ \text{\textcolor{#FF7968}{For n = 5,}} \\ f\text{ ( 5 ) = f ( 4 ) + 3} \\ f\text{ ( 5 ) = 19 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 5 ) = 22}} \end{gathered}[/tex]And them lastly for the 6th term in the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 6,}} \\ f\text{ ( 6 ) = f ( 5 ) + 3} \\ f\text{ ( 6 ) = 22 + 3} \\ \text{\textcolor{#FF7968}{f ( 6 ) = 25}} \end{gathered}[/tex]Hence, the answer to the 6th term number is:
[tex]\textcolor{#FF7968}{25}[/tex]
given angle <afb and <rst are supplementary and the m<afb = 7x - 18 and the m<rst = 72 - 2x what is the value of x? what is the m<afb and m<rst be sure to show your work and all three answers.
The most appropriate choice for supplementary angle will be given by-
x = 25.2°
∠AFB = 158.4°
∠RST = 21.6°
What is supplementary angle?
Angle is formed when two straight lines meet at a common point.
The common point is the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if their sum is 180°
Here,
∠AFB = 7x - 18
∠RST = 72 - 2x
Sum = 7x - 18 + 72 - 2x
= 5x + 54
By the problem,
[tex]5x +54=180\\5x = 180-54\\5x =126\\x= \frac{126}{5}\\x = 25.2[/tex]
∠AFB = [tex]7 \times 25.2 -18\\[/tex]
= [tex]176.4 - 18\\[/tex]
= [tex]158.4^{\circ}[/tex]
∠RST =
[tex]72 - 2\times 25.2\\72 - 50.4\\21.6^{\circ}[/tex]
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f(x) = x2 − 5.) Multiply by 3, then subtract 2.
The required expression is f(x) = (3x - 2).
A linear expression is an algebraic equation of highest degree 1 and it contains only one variable. A quadratic expression is an algebraic expression in which the variable has highest degree of 2. In a quadratic equation the two values of variable which satisfies the equation ax² + bx + c = 0 is called the roots of the given equation. According to the given question Square then subtract 5 is expressed as the function f(x) = x² - 5
∴ The function Multiply by 3, then subtract 2 will be expressed as
f(x) = (3x - 2).
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Complete question:
Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function f(x) = (x2 − 5.)Multiply by 3, then subtract 2.
Jackson is packing a moving truck with cube-shaped boxes that each have a side length of 1.5 square feet. The moving truck is 8 feet long, 6.5 feet wide, and 6.25 feet tall. What is the greatest number of boxes that Jackson can fit in the moving truck?
Answer:
96 boxesStep-by-step explanation:
the volume of the box: (cubes have all equal sides)
"cube-shaped boxes that each have a side length of 1.5 square feet."
V = lwh
V = 1.5 * 1.5 * 1.5
V = 3.375 cubic feet
the space inside the truck:
"The moving truck is 8 feet long, 6.5 feet wide, and 6.25 feet tall."
V = lwh
V = 8 * 6.5 * 6.25
V = 325 cubic feet
Now we see how many boxes we can fit, by dividing the size of the truck, by the boxes:
325 ÷ 3.375 = 96.2962963
96.2962963 boxes BUT you can't have .2962963 (part) of a box so you can only fit...
96 boxesDetermine whether the graph represents a function.
The given graph representing function is a relation.
What is meant by relation and function?A function is a relation that states that there must be only one output for every input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the connection between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.(INPUT, OUTPUT): An ordered pair is depicted as (INPUT, OUTPUT):For the given question,
For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.
Thus, the graph shows the relation of the function.
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2. Maryse went for a bike ride. She rode at a constant speed, an she traveled 7 miles in one hour.Maryse wrote the equation y=7x to model her bike ride, where x is the time Maryse spent riding,and y is the distance she traveled.a. Maryse uses her equation to estimate that she rode 14 miles in the first two hours of her trip.Did she use her equation correctly? Explain why or why not. Ensure to write the equation withthe appropriate numbers plugged in.b. Maryse uses her equation to predict that she would travel 40 miles if she rode for four hours.Did she use her equation correctly? Explain why or why not.
ANSWER
1.) YES! Maryse used her equation correctly.
2.) NO! Maryse did not use her equation correctly.
EXPLANATION
Given:
A bike ride model: y = 7x
where:
1). x is the time Maryse spent riding,
2). y is the distance she traveled
Now, she rode 14 miles in the first two hours of her trip
That is:
y = 7x
where y = 14 miles and x = 2 hours
14 = 7(2)
14 = 14
She indeed used her equation correctly.
When she predicted that she would travel 40 miles if she rode for four hours.
That is:
y = 7x
where y = 40 miles and x = 4 hours
[tex]\begin{gathered} 40\text{ }\ne\text{ 7\lparen4\rparen} \\ 40\ne28 \end{gathered}[/tex]Hence, She indeed used her equation correctly in part one but she did not use her equation correctly in part two.
Which of the folowing expressions is equivalent to 8^3?A 4^3× 4^3B 4^3× 2^3C 8^2× 1^1 D 4^2× 2^1
Convert 50 degrees Fahrenheit to degrees celcius
10 degrees celsius
Explanations:The formula for converting temperature in degree Farenheit to degree Celcius is:
[tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(T_f-32) \\ \text{Where T}_c=\text{ temperature in degr}ees\text{ celcius} \\ T_f=\text{ temperature in degre}es\text{ Fahrenheit} \end{gathered}[/tex][tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(50\text{ - 32)} \\ T_c=\text{ }\frac{5}{9}\times18 \\ T_c=\text{ 5 }\times2 \\ T_c=10^0C \end{gathered}[/tex]A recycling plant processes an average of \frac{{7}}{{8}}
8
7
ton of cardboard each minute. At this rate, how many tons of cardboard does this plant process per day? (1 day = 24 hours)
By taking some products, we will see that the average amount processed per day is 1,260 tons.
How many tons of cardboard the plant process per day?We know that the recycling plant processes an average of 7/8 tons of cardboard each minute.
In one hour we have 60 minutes, so the amount processed per hour is given by the product:
60*7/8 tons = 52.5 tons.
And in one day we have 24 hours, so the total amount processed in one day is 24 times what we got above, which is:
24*52.5 tons = 1,260 tons.
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Practice
Solve each equation. Check your solution (Example 1-3)
1. -2a-9=6a+15
2. 14+3n = 5n-6
3. 1/2 x -5=10 - 3/4 x
4. 7/3 y+1=1/6 y+8
Answer:
a = -3n = 10x = 12y = 42/13Step-by-step explanation:
You want to solve the equations and check the solutions for ...
1. -2a-9=6a+15
2. 14+3n = 5n-6
3. 1/2 x -5=10 - 3/4 x
4. 7/3 y+1=1/6 y+8
Three-step linear equationEach of these equations has both a variable term and a constant term on each side of the equal sign. The usual 3-step solution is ...
Subtract one of the variable terms from both sidesIdentify the constant term on the side with 2 terms and subtract that from both sidesDivide by the coefficient of the variableThis can be made less error-prone by choosing the variable term in Step 1 that has the smallest (least) coefficient. Then the constant in Step 2 will be the constant on the side of the equation that has the variable term with the largest coefficient.
We can do the subtractions of Step 1 and Step 2 both at the same time, reducing the work slightly. Of course, subtraction is the same as adding the opposite. Then what remains is dividing by the coefficient of the variable (or multiplying by its inverse).
1. -2a-9=6a+15Add 2a -15 to both sides:
-24 = 8a
-3 = a . . . . . . divide by 8
check: -2(-3)-9 = 6(-3) +15 ⇒ -3 = -3 . . . checks OK
2. 14+3n = 5n-6Add -3n+6 to both sides:
20 = 2n
10 = n . . . . . . divide by 2
check: 14 +3(10) = 5(10) -6 ⇒ 44 = 44 . . . checks OK
3. 1/2 x -5=10 - 3/4 xAdd 3/4x +5 to both sides:
5/4x = 15
x = 12 . . . . . . multiply by 4/5
check: 1/2(12) -5 = 10 -3/4(12) ⇒ 1 = 1 . . . checks OK
4. 7/3 y+1=1/6 y+8Add -1/6y -1 to both sides:
13/6y = 7
y = 42/13 . . . . . multiply by 6/13
check: (7/3)(42/13) +1 = (1/6)(42/13) +8 ⇒ 98/13 +1 = 7/13 +8
⇒ 8 7/13 = 8 7/13 . . . checks OK
Write the following numbers in order of size.
Start with the smallest number.
0.4
0.38
0.02
0.2
0.113
Answer:
0.02, 0.113, 0.2 0.38 0.4
Step-by-step explanation:
The number of cookies in a shipment of bags are normally distributed with a mean of 58 and a standard deviation of 5. There are normally 800 bags of cookies in a a shipment. How many bags of cookies will contain between 48 and 68 cookies?
The percent of bags of cookies will contain between 48 and 68 cookies is 68.29%.
What is mean?The average of the specified collection of numbers is what is referred to as mean. It indicates that values in a particular data set are distributed equally.
μ = 58, σ = 5,
Z₁ = X₁ - (μ/ σ)
= 48 - (58/5)
= 36.4
again,
Z₂= X₂ - (μ/ σ)
= 68 - (58/5)
= 56.4
Thus, we know P( 48 < X < 68)
= p(-1 < Z < 1)
= 0.6829
= 68.29%
68.29% bags of cookies will contain between 48 and 68 cookies.
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The economy's real GDP was $100 billion in 2019 and $240 billion in 2020. Its
population was 15 million in 2019 and 15 million in 2020.
What is the growth rate of real GDP per capital from 2019 to 2020?
The growth of the real GDP per capita from 2019 to 2020 is 1.4.
How To calculate the growth rate of real GDP?It also calculates the amount of money spent on finished goods and services or the income generated from that production.GDP = private consumption + gross private investment + government investment + government spending + (exports – imports).GDP can be assessed in a variety of methods. The most popular techniques include Nominal GDP, Real GDP, Actual GDP, and Potential GDP.One of the key metrics used to assess the general health of a nation's economy and standard of life is its gross domestic product (GDP), which reflects economic growth and productivity. GDP growth rate is one approach to assess how well a nation's economy is doing. This rate indicates changes in the proportion of economic output over the course of a month, a quarter, or a whole year.Therefore, the formula to compute real GDP per capita = Real GDP / Population.
The real GDP in 2019 is $100B.
And the real GDP in 2020 is $240B.
Real GDP per capita of 2019 = 100B/15M. = 6666.6Real GDP per capita of 2020 = 240B/15M = 16000The growth rate of real GDP = current value - previous value / previous value
The growth rate of real GD P= 1.4Therefore, the growth of the real GDP per capita from 2019 to 2020 is 1.4.
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WILL GIVE BRAINLIEST
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Decorations for the dance cost $120
the club is charging $10 per student that attends.
In the graph, the x axis is labelled with number of students and the y axis with amount of money collected
As they spend $120 for the decorations of the dance the starting point for the money raised is -120, upon charging 2 students the money they will get is 2 x 10 = 20
So the money raised will be
-120 + 20 = -100
The line will pass from point (0, -120) through (2, -100)
Therefore, graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100 is correct.
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Answer:
Step-by-step explanation:
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
I rlly need help on this problem-
Two factors are multiplied and their product is 34.44. One factor is a whole number. What is the least number of decimal places in the other factor?
The least number of decimal places in the other factor is 2
What is a factor?A factor simply means the number that can b multiplied with another number to get the original number.
Based on the question asked, lat the whole number be represented as 2. In this case the multiplication will be:
= 2 × 17.22
=34.44
In this case, one can see that 17.22 has 2 decimal places.
Therefore, the correct option is 2.
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A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function Inverse of S is equal to the quantity t squared plus 3 times t minus 4 end quantity over the quantity t squared minus 6 times t plus 6 end quantity
Which equation represents the average sales each day for the real estate company?
An inverse function which represents the average sales each day for the real estate company is: D. S⁻¹ = (t + 4)/(t - 5).
How to determine equation?In order to determine equation which represents the average sales each day for the real estate company, we would factorize the numerator and denominator of the given inverse function as follows:
Numerator = t² + 3t - 4
Next, we would solve the quadratic equation by using the factorization method:
t² + 3t - 4 = t² + 4t - t - 4
t² + 4t - t - 4 = t(t + 4) - 1(t + 4)
t² + 4t - t - 4 = (t - 1)(t + 4)
Numerator = (t - 1)(t + 4)
For the denominator, we have:
t² - 6t + 5 = t² - 5t - t + 5
t² - 5t - t + 5 = t(t - 5) - 1(t - 5)
t² - 5t - t + 5 = (t - 1)(t - 5)
Denominator = (t - 1)(t - 5)
Now, we would rewrite the inverse function as follows:
S⁻¹ = Numerator/Denominator
S⁻¹ = (t - 1)(t + 4)/(t - 1)(t - 5)
S⁻¹ = (t + 4)/(t - 5)
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Answer the image here
Answer:
1/100 or -1/100
Step-by-step explanation:
the two solutions are
0.01 = 1/100
-0.01 = -1/100
5. When purchasing a new video game system, thestore charges 9% on tax. What decimal isequivalent to 9%?
The decimal that is equivalent to 9% is:
[tex]\frac{9}{100}=0.09[/tex]Then, the decimal which is equivalent to 9% is 0.09.
i need help :). it sure how to do synethetic división so it would help if u showed me how
The dividend is
and the divisor is
x+2
We begin by arranging them as follows:
now, we divide the leading term in the dividend by the leading term in the divisor to get the first term of the quotient: 4x^2 / x = 4x.
Then we multiply the divisor by 4x and subtract
the result from the dividend. That is:
We repeat the same procedure: using the last line -3x - 6 as the dividend:
So, the leading term of -3x-6 is -3x, so we have -3x/x = -3. Then we multiply the divisor by -3 and subtract the result from the dividend. That is:
Because the remainder is 0, we have finished the division. So the correct answer will be 4x-3
Simplify the following expressions by using the properties of exponents. Assume none of the denominators is zero.
a^3 (2a^2 + 4bc^4)^ 0
The total value of the exponential expression is a³
What is Exponentiation ?
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Now, The given expression is :
a^3 (2a^2 + 4bc^4)^ 0
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Hence, The total value of the exponential expression is a³
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20. A room is 24 feet long and 15 feet wide. How much will it cost to cover the floorwith carpet costing $36 a square yard if an extra 4 square yards must be purchasedfor matching?Answer
At first, we will change the feet to the yard because the cost of carpet is per square yard
Since 1 yard = 3 feet, then
Divide each dimension by 3 to change it from feet to yard
Since the length of the room = 24 feet, then
The length of the room = 24/3 = 8 yards
Since the width of the room = 15 feet, then
The width of the room = 15/3 = 5 yards
The rule of the area of the rectangle is
Area = Length x width, then
The area of the room = 8 x 5 = 40 square yards
Since we will add extra 4 square yards to it, then
The total area needs to cover = 40 + 4 = 44 square yards
Since the cost of 1 square yard = $36, then
Multiply the area by the cost to find the cost of the carpet
The total cost = 44 x 36 = 1584
The cost of the carpet is $1584
6 less than the number x
Find the perimeter and area of the shaded figure below.
The perimeter of the shaded figure is 12 units
The area of the shaded figure is 8 square units
Given,
Length of the shaded figure = 4 units
Width of the shaded figure = 2 units.
The shaded figure resembles a rectangle
So,
Perimeter of the shaded figure = 2( length + width)
Perimeter, P = 2 ( 4 + 2)
P = 2 × 6
P = 12 units
Now,
Area of the shaded figure = length × width
Area, A = 4 × 2
A = 6 square units
Therefore,
The perimeter of the shaded figure is 12 units
The area of the shaded figure is 8 square units
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775,710 teenagers voted for their favorite singer on a TV show. Each singer received the exact same number of votes. How many singers could there have been?a) 5b) 2c) 6d) 9
There could have been 2,5,6, and 9 singers
1) Regarding 775,710 as an even number then for sure there could have been 2 singers on this TV Show
[tex]775710\colon2=387,855[/tex]2) On the other hand, 775710 is also divisible by 5, for its last number is 0. So there could also have been 5 singers.
[tex]775710\colon5=155,142[/tex]3) This number of teenagers can also be divided by 6 (for it is divisible by 2 and by 3) and by 9 as well ( the sum of the digits of 775710, 7+7+5+7+1+0=27 is also divisible by 9).
Hence, there could have been 2,5,6, and 9 singers since 775,710 can be divided exactly by 2,5,6, and 9.
triangle DEF is rotated 90 to the right to format the triangle with the side lengths shown below
Problem
Solution
For this case we can conclude that:
DE = r
DF= s
EF= t
You have been given $10,000 to invest. Safe investments, like certificates of deposit, pay about 5.5% interest. The stock market is much riskier but pays about 12%. If you would like to earn about 10% a year on these investments, how much would you invest in CDS and how much should you invest in stocks?
will give brainliest ty
Answer:
Let x = amount in low risk account, then 10000-x is amount invested in high risk account. To earn 10% of 10000:
(.10)(10000) = (.055)x + .12(10000-x)
1000 = 1200 -.045x
x = 4444.44 in low risk and 5555.56 in high risk