There are 180 different starting lineups that can be created for the college team.To find the number of different starting lineups that can be created for the college team, we need to use the combination formula.
The number of ways to choose k items from a set of n distinct items is given by the formula:
nCk = n! / (k! * (n-k)!)
where "!" denotes the factorial function, which means the product of all positive integers up to that number.
In this case, we want to choose 2 guards out of 5, 2 forwards out of 4, and 1 center out of 3. So the total number of different starting lineups that can be created is:
(5C2) * (4C2) * (3C1)
= (5! / (2! * 3!)) * (4! / (2! * 2!)) * (3! / (1! * 2!))
= (10) * (6) * (3)
= 180
Therefore, there are 180 different starting lineups that can be created for the college team.
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0.5 + 0.163 (3 has a line over it) and i need to find it in a fraction
Answer:
[tex]\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}[/tex]
Step-by-step explanation:
[tex]0.16\bar{3} = 0.16333333333\\[/tex]
the 3 repeats until infinity
Let's multiply this by 100 to move the non-repeating part to the left of the decimal point
0.1633333333...... x 100 = 16.333333333333333...
.333333 = 1/3
Therefore the recurring number multiplied by 100 is
[tex]16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}[/tex]
Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333
[tex]\dfrac{49}{3} \div 100[/tex]
To divide by a number, multiply by the reciprocal of that number
Reciprocal of 100 is 1/100:
[tex]\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}[/tex]
(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring
We want to add 0.5 to this.
0.5 = [tex]\dfrac{1}{2}[/tex]
so
0.5 + 0.16333333 = 0.6633333
[tex]= \dfrac{1}{2} + \dfrac{49}{300}[/tex]
We can write [tex]\dfrac{1}{2}[/tex] as [tex]\dfrac{150}{300}[/tex] by multiplying numerator and denominator by 150
So we get
[tex]0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}[/tex]
If you perform this division on a calculator you will get the answer as 0.663333 = [tex]0.66\bar{3}[/tex] which is what you get when you add 0.5 and [tex]0.16\bar{3}[/tex]
Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Answer:
The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.
This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.
Answer:
Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Step-by-step explanation:
In this question that you have put:
7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =
Vertical Angles Theorem ( Or in similar terms VAT )
Make sure that you remember the following:
vertical angles are the angles that are opposite each other when the two line " meet together "
Thus, your answer to your questions is.
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
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Find (1/3x−3)+(−3/4x−5)
Answer:
-5x-96/12
Step-by-step explanation:
Firstly we want ot combine the multiplied terms into one fraction:
(1x/3-3)+(-3/4 x-5)
Then we multiply by 1:
(x/3-3)+(-3/4 x-5)
Find common denominator:
(x/3+3(-3)/3)+(-3/4 x-5)
Combine fractions with common denominator:
(x+3(-3)/3)+(-3/4 x-5)
Multiply the numbers:
(x-9/3)+(-3/4 x-5)
Combine multiplied terms into a single fraction:
x-9/3+(-3x/4 -5)
Find common denominator:
x-9/3+(-3x/4 + 4(-5)/4)
Combine fractions with common denominator:
x-9/3+(-3x + 4(-5)/4)
Multiply the numbers:
x-9/3 + (-3x-20/4)
Find common denominator:
4(x-9)/12 + 3(-3x-20)/20
Combine fractions with common denominator:
4(x-9)+3(-3x-20)/12
Distribute:
4x-36+3(-3x-20)/12
Distribute:
4x-36-9x-60/12
Subtract the numbers:
4x - 96 - 9x/12
Combine like terms:
-5x - 96/12
Answer: -5x-96/12
b³+b²+4b factorize this
Answer: b (b²+b+4)
Step-by-step explanation:
b²=bb
b³=b²b
=b²b+bb+4b
=b(b²+b+4)
You and your friend just finished playing a game. Your final score was 24 and her final score was -13. By how many points did you win
Answer: 37 points
Step-by-step explanation:
Y-1= -1/3(x-6) in standard form
Answer:
x + 3y = 9
Step-by-step explanation:
Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
The solution is Option E.
The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , -4 )
Let the second point be Q ( 7 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = 10 / 10 = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 6 = 1 ( x - 7 )
y - 6 = x - 7
y = x - 1 be equation (1)
Now , the point of intersection of lines is at ( 3 , 2 )
Substitute the value of x and y in the equation , we get
when x = 3 , y = 2
2 = 3 - 1
2 = 2
Hence , the solution to the equation is ( 3 , 2 )
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Please help need help asap :))
The side of the triangle from shortest to longest can be arranged as,
ACABBCWhat is a triangle?A triangle is a polygon with three sides such that the sum of all the interior angles is always 180°.
In a triangle, the side opposite to the biggest angle is always the lengthiest, while the side opposite to the smallest angle is the shortest.
Given that the measure of ∠A is 100°, therefore, the length of the side BC will be the lengthiest.
Also, the measure of ∠B is 20°, therefore, the length of the side AC will be the shortest.
Hence, BC > AB > AC.
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for which type of function does linear approximation always give the exact value of f ( x ) for x near the starting point? linear quadratic exponential logarithmic linear approximation never gives the exact value.
By applying the slope of the function at that point, linear approximation provides an estimate of the value of a function close to a beginning point.
When estimating the value of a function at a nearby location, linear approximation uses the slope of the function at a particular position. In order to arrive at the starting position, it first calculates the difference between the two points, multiplies it by the slope, and adds it. This provides a rough estimate of the function's value at the new location. A technique for calculating a function's value close to a beginning point is called linear approximation. It is predicated on the notion that a linear function can be used to roughly approximate the function close to the point of interest. This indicates that the value of the function at surrounding places can be inferred from the slope of the function at the point in question.
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0/1
12. Ashton picked 6 pounds of pecans. He used of the pecans in a soup recipe. Ashton then
splits the pecans that are left in pound bags. How many bags of pecans does he have?
Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags
What is Fraction?A fraction represents a part of a whole.
If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.
To find out how many pounds of pecans he has left.
we can multiply the original amount of pecans by 3/4:
3/4 x 6 pounds = 4.5 pounds
So Ashton has 4.5 pounds of pecans left to split into bags.
If he splits the remaining pecans into 1-pound bags, then he has:
4.5 pounds ÷ 1 pound/bag = 4.5 bags
Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags
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The complete question
Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have
Meredith's new Pomeranian puppy is 7 inches tall and 9 inches long. She wants to make a drawing of her new Pomeranian to put in her locker. If the sheet of paper she is using is 3 inches long by 5 inches, find an appropriate scale factor for Meredith to use in her drawing. (please answer I need help)
Answer:
2.3333 inches
Step-by-step explanation:
To find the appropriate scale factor, we need to determine how many times smaller the piece of paper is compared to the dog. We can start by finding the ratio of the length of the paper to the length of the dog:
3 inches / 9 inches = 1/3
Similarly, the ratio of the width of the paper to the height of the dog is:
5 inches / 7 inches = 5/7
So, the smaller of these two ratios, 1/3, is the appropriate scale factor for Meredith to use in her drawing. This means that the length of the dog in the drawing will be 9 inches * 1/3 = 3 inches, and the height will be 7 inches * 1/3 = 2.3333 inches.
A baker uses the equation y=12x to predict the revenue generated from selling x cakes she uses equation y=450+4.5x to model the cost to produce x cakes.
The complete question:
A baker uses the equation y = 12x to predict the revenue generated from selling a cakes. She uses equation y= 450 +4.5x to
model the cost to produce a cakes:
What does (60, 720), the solution of the system -450 +4.5x &
y=12x represent?
Solution:-
The solution of the system (-450 + 4.5x, y = 12x) at (60, 720) represents :
a. The point where the revenue generated from selling 60 cakes is 720 dollars
b. The cost to produce those 60 cakes is 720 dollars.
What is a system of equations?In geometry, A system of equations is a collection of two or more equations with the same set of unknown variables. In solving a system of equations, we try to calculate values for each of the unknowns that will satisfy each and every equation in the system.
The given system of equations is:
y = 12x (equation 1)
y = 450 + 4.5x (equation 2)
where x represents the number of cakes produced and sold, y represents the revenue generated from selling x cakes, and 450 + 4.5x represents the cost to produce x cakes.
To find the solution of the system, we can substitute equation 1 into equation 2, and solve for x as follows:
12x = 450 + 4.5x
7.5x = 450
x = 60
Substituting this value of x into equation 1 gives us:
y = 12(60)
y = 720
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6.RP.3d-2016 (#39) Fei Yen's dog eats 8 ounces of dog food each day. Fei Yen bought a 28-pound bag of dog
food. How many 8-ounce servings are in a 28-pound bag of dog food?
A 14
B 56
C 224
D 448
There are 56 servings in a 28 pound bag of dog food.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
And we know that 1 pound = 16 ounces
Then ,the food in ounces
= 28 x 16
= 448 ounces
Now, the number of 8 ounces servings are in a 28 pound bag of dog food
= 448 / 8
= 56
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The start of a quadratic sequence is shown
below.
What is the nth term rule for the sequence?
-5, -2, 3, 10, 19,
Answer:
nth term = n²-6
Step-by-step explanation:
we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.
In this series,
-5, -2, 3, 10, 19....
a=1, b=0, c=-6
nth term = n²-6
if n=1 then,
nth term=1²-6
⇒nth term=-5
which expression is equivalent to 5^6
a.125 x 125 b. 6 x 5 c. 35 x 6 x 6 x 6 d. 25 x 5 x 5 x 5
The expression that is equivalent to 5^6 is A.125 x 125
What are index forms?Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.
Other terms for index forms are called standard forms or scientific notations.
They are also described as numbers or variables that are raised to an exponent.
From the information given, we have that;
5⁶
This is replicating 5 in 6 places, we have the representation as;
5 × 5 × 5 × 5 × 5 × 5
Hence, the expression is 125 x 125
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There were 230,600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%.
Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014.
Answer:
J(t) = 230,600(1.009)^t
Step-by-step explanation:
J(t) = 230,600(1 + 0.009)^t, or
J(t) = 230,600(1.009)^t If this is Wrong ill do. it again!!
Point D is the centroid of ABC, BD = 4x + 2 and DF = 3r. Find the value of x
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and the value of x is -1
Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
we know that,
BD = 4x+2
DF = 3x
So by the given formulae, we used to solve the x value as,
BD = (1/(3/2)) [DF]
BD = (2/3)[DF]
4x+2 = (2/3)(3x)
4x+2 = 2(x)
4x+2 = 2x
4x-2x = -2
2x = -2
x = -1
Therefore, the value of x is x = -1
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A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answer is Below ------v
1. clockwise
2. 3
1. (y, -x)
2. (3x,3y)
dave wants to buy a new collar for each of his 5 cats. the collars come in a choice of 9 different colors. step 1 of 2 : how many selections of collars for the 5 cats are possible if repetitions of colors are allowed?
If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:
9 x 9 x 9 x 9 x 9 = 59,049
In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:
Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
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two numbers are in the ratio 5:4 if the smaller is 32 find the greater one.
Answer:
The greater number is 40.Step-by-step explanation:
Greetings!!!
The given two numbers ratio.
[tex] \frac{5}{4} [/tex]
The smaller number is 32
[tex] \frac{5}{4} \times 32[/tex]
convert elements into fraction
[tex] \frac{5}{4} \times \frac{32}{1} [/tex]
Apply fraction rule
[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]
Multiply the numbers
[tex] \frac{5 \times 32}{4 \times 1} [/tex]
Divide the numbers
[tex] \frac{32}{8} = 8 \\ 8 \times 5 = 40[/tex]
Hope it helps!!!
pls help me i need now and if the answer is correct i give free BRAINLIEST HERE!!!!
THANK YOU
The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;
m∠1 = 47.5°[tex]m\widehat{BD}[/tex] = 110°m∠COD = 55°[tex]m\widehat{CD}[/tex] = 20°m∠AOC = 100°m∠APB = 25°m∠ADB = 25°[tex]m\widehat{CD}[/tex] = 90°[tex]m\widehat{AB}[/tex] = 70°[tex]m\widehat{CD}[/tex] = 100°What is a secant of a circle?A secant is a line that has two points of intersection on a circle.
The specified parameters are;
1. The measure of arc [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°
Angle at the center of the circle = 2 × Angle at the circumference
Angle at the center of the circle = The arc angle of the circle
Therefore;
m∠DAC = 15°/2 = 7.5°
m∠ACO = 80°/2 = 40°
The external angle of a triangle theorem, indicates that we get;
m∠1 = 40° + 7.5° = 47.5°
m∠1 = 47.5°
2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°
The intersecting chords theorem indicates that we get;
m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])
[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°
[tex]m\widehat{BD}[/tex] = 110°
3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°
Therefore; m∠ACO = 90°/2 = 45°
m∠DAC = 20°/2 = 10°
The external angle theorem indicates that we get;
m∠COD = 45° + 10° = 55°
m∠COD = 55°
4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;
m∠ACO = 50°/2 = 25°
m∠CAO = 35° - 25° = 10°
[tex]m\widehat{CD}[/tex] = 2 × m∠CAO
Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°
[tex]m\widehat{CD}[/tex] = 20°
5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°
m∠AOC = 100°
6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°
The external secant, tangent theorem, indicates that we get;
m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])
m∠APB = (1/2) × (70° - 20°) = 25°
m∠APB = 25°
7. [tex]m\widehat{AB}[/tex] = 50°,
The angle at the center of a circle is twice the angle subtended at the circumference, therefore;
m∠ADB = 50°/2 = 25°
m∠ADB = 25°
8. m∠CAD = 45°
The angle formed by an arc at the center of a circle theorem, indicates that we get;
[tex]m\widehat{CD}[/tex] = 2 × m∠CAD
[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°
[tex]m\widehat{CD}[/tex] = 90°
9. m∠ACB = 70°
m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference
Therefore;
[tex]m\widehat{AB}[/tex] = 2 × m∠ACB
[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°
[tex]m\widehat{AB}[/tex] = 70°
10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°
m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])
Therefore; m∠(AOB) = 80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°
[tex]m\widehat{CD}[/tex] = 100°
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Select the correct answer.
Consider this function.
f(x) = 6log₂x - 3
Over which interval is function f increasing at the greatest rate?
OA. [2, 6]
OB. [1/8, 1/2]
OC. [1, 2]
OD. [1/2,1]
The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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Write an inequality for the graph below.
Answer:
Y < (1/3) x - 5
Luis wants to buy a skateboard that usually sells for $79.86. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 8.25%. Round your intermediate calculations and answer to the nearest cent.
The total cost of the skateboard is $
The total cost of the skateboard is $76.07.
What is the total cost of the skateboard?The first step is to determine the price of the skateboard after the 12% discount. A discount reduces the price of an item.
Price after discount = price before discount x (1 - percent discount)
$79.86 x (1 - 12/100)
$79.86 x (1 - 0.12)
$79.86 x 0.88
= $70.28
Price after the sales tax = (1 + sales tax) x price after discount
= (1 + 8.25/100) x $70.28
(1 + 0.0825) x $70.28
1.0825 x $70.28 = $76.07
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If f(x) = 2x - 9 and g(x) = x² + 3, what is (f + g)(4)?
question 8
help me asap
The sector area of the sector defined by the minor arc CB is given as follows:
7.5 cm².
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
We have that the radius is half the diameter, hence it's measure is given as follows:
r = 3 cm.
The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.
CB + 84º = 180º.
CB = 96º.
An entire circle has an angle of 360º, hence the area of the sector is given as follows:
A = 96/360 x π x 3²
A = 7.5 cm².
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The width of a rectangle is the length minus 8 units. The area of the rectangle is 9 square units. What is the length, in units, of the rectangle?
Answer: The length is 9 units and the width is 1 unit
Step-by-step explanation:
We can use the formula for the area of a rectangle to solve this problem. The formula is A = l * w, where A is the area, l is the length, and w is the width.
We have A = 9, and we know that w = l - 8. Substituting this into the formula, we get:
9 = l * (l - 8)
We can rearrange this to solve for l:
9 = l^2 - 8l
Adding 8l to both sides of the equation, we get:
9 + 8l = l^2
Subtracting 9 from both sides, we get:
8l = l^2 - 9
We can factor this to get:
l(l - 9) = 0
Since the product of two numbers is zero only when one of them is zero, we can set each factor equal to zero and solve:
l = 0 or l - 9 = 0
Adding 9 to both sides of the second equation, we get:
l = 9
Therefore, the length of the rectangle is 9 units.
D. A car dealer purchased 40 new cars at
$6500 each. He sold 40% of them at
$8000 each and the rest at $9000 each.
What was his total profit?
40%=
5
2
5
2
⋅40=16 cars at 8000 each =128,000 in sales
40−16=
24 cars at 9000 each
=216,000 in sales
Total sales: 128,000+216,000=344,000
Total expense: 6500⋅40=260,000
Total profit: 344,000−260,000=84,000
Answer:
$84000
Step-by-step explanation:
40% of the cars would be 16 cars that are sold for $8000 each.
16×$8000=$128000
The remaining 60% of cars would be 24 cars to be sold at $9000 each.
24×$9000=$216000
The total profit = the sum - the amount he paid for all cars.
total profit = ($128000+$216000) - (40×$6500)
total profit = $344000 - $260000
total profit = $84000
a radioactive substance decays exponentially. a scientist begins with 100 milligrams of a radioactive substance. after 29 hours, 50 mg of the substance remains. how many milligrams will remain after 38 hours?
After 38 hours, there will be 43.1 mg of the radioactive substance remaining.This means that the amount of a radioactive substance decreases exponentially over time
Radioactive decay follows an exponential decay curve. This means that the amount of a radioactive substance decreases exponentially over time. The equation for this is: [tex]A(t) = A0*e^(-λ*t\\[/tex])Where A(t) is the amount of substance at time t, A0 is the initial amount of substance, and λ is the decay constant. In this problem, A0 = 100 mg, t = 29 hours, and A(t) = 50 mg. We can use this to solve for λ:50 mg = 100 mg * [tex]e^(-λ*29)λ =[/tex] -0.027Now that we have the decay constant, we can calculate the amount of substance remaining after 38 hours:A(38) = 100 mg * [tex]e^(-0.027*38[/tex]).A(38) = 43.1 mg.Therefore, after 38 hours, there will be 43.1 mg of the radioactive substance remaining.
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a poker hand consists of ive cards drawn from a standard 52-card deck. find the expected number of aces in a poker hand given that the irst card drawn is an ace.
The expected number of aces in a poker hand given that the first card drawn is an ace is 0.235.
If the first card drawn is an ace, then there are only 3 aces left in the deck of 51 cards from which to draw the remaining 4 cards. Therefore, we can model the number of aces in the poker hand as a binomial random variable with parameters n = 4 (the number of cards after the first ace) and p = 3/51 (the probability of drawing an ace from the remaining deck).
The expected number of aces in a poker hand given that the first card drawn is an ace can be calculated as follows:
E(X) = np = 4 * 3/51 = 12/51 = 0.235
Therefore, the expected number of aces in a poker hand given that the first card drawn is an ace is approximately 0.235.
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____ The given question is incorrect, the correct question is given below:
A poker hand consists of five cards drawn from a standard 52-card deck. find the expected number of aces in a poker hand given that the first card drawn is an ace.
