Answer:
40320
Step-by-step explanation:
There are 8 different people we could assign to the first task. Now there are 7 tasks and 7 people left. There are 7 different people we could assign to the next task. And so on
8 *7*6*5*4*3*2*1
8!
40320
Final answer:
The professor can assign eight different tasks to her eight teaching assistants in 40,320 different ways, calculated by the factorial of eight (8!).
Explanation:
The question pertains to the number of ways to assign eight different tasks to eight teaching assistants. This problem can be solved using the concept of permutations, which is a fundamental principle in combinatorics, a branch of mathematics.
To find the number of different permutations of eight distinct items (the tasks), we would calculate 8!, which signifies factorial of eight. This represents the product of all positive integers up to 8:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320Therefore, there are 40,320 different ways the professor can make the assignments to her eight teaching assistants.
David performed the following mathematical operation .
Answer:
C: x = 1/2
Step-by-step explanation:
Set the divisor, 2x - 1, equal to zero and solve for x: 2x = 1, so x = 1/2. Statement C is true.
Answer:
The correct option is C.
Step-by-step explanation:
If a function f(x) is completely divisible by (x-a), it means (x-a) is a factor of f(x) and x=a is a root of that polynomial.
The given polynomial is
[tex]P(x)=2x^2+9x-5[/tex]
It is given that when David divide the above polynomial by (2x-1), then he get
[tex]Quotient=x+5[/tex]
[tex]Remainder=0[/tex]
Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).
[tex]2x-1=0[/tex]
Add 1 on both the sides.
[tex]2x=1[/tex]
Divide both sides by 2.
[tex]x=\frac{1}{2}[/tex]
It means [tex]\frac{1}{2}[/tex] must be a root of the polynomial [tex]2x^2+9x-5[/tex].
Therefore, the correct option is C.
Using complete square to slove for x in the equation (x+7) (x-9)=25
Answer:
[tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Step-by-step explanation:
Apply Distributive property:
[tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex]
Add like terms and then add 63 to both sides of the equation:
[tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex]
Pick the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{2}{2})^2=1[/tex]
Add it to both sides of the equation:
[tex]x^2-2x+1=88+1[/tex]
Rewriting the left side as a squared binomial, we get:
[tex](x-1)^2=89[/tex]
Apply square root to both sides:
[tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex]
And finally we need to add 1 to both sides of the equation. Then we get:
[tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]
Find the value of this expression if x=-1 and y=-5 x^2y/4
Answer:
[tex]\large\boxed{-\dfrac{5}{4}=-1\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Put the values of x = -1 and y = -5 to the expression}\ \dfrac{x^2y}{4}:\\\\\dfrac{(-1)^2(-5)}{4}=\dfrac{(1)(-5)}{4}=\dfrac{-5}{4}[/tex]
each cookie sells for $0.50 Sam spent $90 on baking supplies and each cookie cost $0.25 to make how many cookies does Sam need to sell before making a profit formula: sales>cost
Answer:he needs to sell 180 cookies or more
Step-by-step explanation:
90.00/.50=180
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f + g)(x).
Answer:
[tex]\large\boxed{(f+g)(x)=5x+3}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x-6,\ g(x)=3x+9\\\\\text{Substitute:}\\\\(f+g)(x)=(2x-6)+(3x+9)\\\\=2x-6+3x+9\qquad\text{combine like terms}\\\\=(2x+3x)+(-6+9)\\\\=5x+3[/tex]
1. In a 30-60-90 triangle, the leagoo the hypotenuseis 6. What is the leaga of the shortest
a2
6.3
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
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Assuming that there are 20. drops in 1.0 mL, how many drops are in 3.9 gallons?
drops
Answer:
295261.98 or just 295.2962 (rounded).
Step-by-step explanation:
You have to figure out how many ml are in a gallon. Then multiply that by 3.9 gallons.
Each month, Anna pays $630 in rent. How much rent does she pay over the course of 18 months?
Answer:
$11,340
Step-by-step explanation:
1 month: 630
18 months: 18×630=11,340
Anna pays a total of $11,340 in rent over the course of 18 months by multiplying her monthly rent of $630 by 18.
To find out how much rent Anna pays over the course of 18 months, we need to multiply her monthly rent by the number of months. Anna pays $630 each month, so over 18 months, she would pay:
$630 times 18 = $11,340.
Therefore, Anna pays a total of $11,340 in rent over the course of 18 months.
Cone A has a surface area of 384 ft2 and Cone B has a surface area of 96 ft?. What is the ratio of their volume?
Answer:
8 : 1
Step-by-step explanation:
Given ratio of sides = a : b, then
ratio of area = a² : b²
ratio of volumes = a³ : b³
Given
ratio of areas = 384 : 96 = 4 : 1 ← in simplest form, then
ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{1}[/tex] = 2 : 1
Hence
ratio of volumes = 2³ : 1³ = 8 : 1
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
Answer:
Option D is correct.
Step-by-step explanation:
The length of 2 sides of triangle are given i.e 10 cm and 16 cm.
We need to find the range of the values of length of the third side.
Sum of 2 sides of triangle is greater than the 3rd side
so, 10+16 = 26
So, the length of third side should be less than 26
and we know that the length of third side should be greater than the absolute difference of other two sides
16-10 = 6
So, the length of third side should be greater than 6
Combining both we get 6<x<26
Hence Option D is correct.
The range of possible values for the third side of the triangle is 6 < x < 26
How to find third side of the triangleSide 1 = 10 cmSide 2 = 16 cmSide 3 = x cmSum of two sides is greater than third side10 + 16 = 26 cm
Length of third side is greater than difference between the two sidesDifference = 16 cm - 10cm
= 6 cm
Therefore, the range of value of the third side is x is greater than 6cm less than 26cm
6 < x < 26
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Simplify the expression (x^1/6)3
Answer:x^1/2
Step-by-step explanation:
x^1/6*3=
x^3/6=
x^1/2
Factor completely: 2x2 + 10x + 12
[tex]\bf 2x^2+10x+12\implies 2(x^2+5x+6)\implies 2(x+3)(x+2)[/tex]
recall that 3 * 2 = 6, and 3x + 2x = 5x.
Answer:
Step-by-step explanation:
It is a little easier if you take out the two.
2*(x^2 + 5x +6)
The numbers that multiply to 6 and adds to 5 are 3 and 2
2*(x + 3)(x + 2)
So that's how the trinomial factors.
How do you calculate a weighted grade into a percentage?
For example, 64.97/ 75
Answer:
86%
Step-by-step explanation:
64.97/ 75 = 0.8662...
0.8662 x 100 = 86%
but it weighted so:
0.8662 x actual weighted % = % got out of weighted %
example:
Test is Weighted 25% out of 100%
0.8662 x 25% = 21 %
this case you got 21% out of 25% for the test
Write a function to represent the set of ordered pairs. {(2, -8), (3, -18), (4, -32), (5, -50)}
Answer:
y = -2x²
Step-by-step explanation:
The set of ordered pairs is:
(x₁, y₁) = (2, -8)
(x₂, y₂) = (3, -18)
(x₃, y₃) = (4, -32)
(x₄, y₄) = (5, -50)
First let's check if this is linear. For even increments of x, Δy is:
Δy₂₁ = y₂ − y₁ = -18 − -8 = -10
Δy₃₂ = y₃ − y₂ = -32 − -18 = -14
Δy₄₃ = y₄ − y₃ = -50 − -32 = -18
Δy isn't constant, so this isn't linear. However, the difference of the differences is constant:
Δy₃₂ − Δy₂₁ = -14 − -10 = -4
Δy₄₃ − Δy₃₂ = -18 − -14 = -4
So this is a quadratic.
y = ax² + bx + c
To find the coefficients of a, b, and c, we can either plug in three points from the set and solve the system of equations:
-8 = a(2)² + b(2) + c
-18 = a(3)² + b(3) + c
-32 = a(4)² + b(4) + c
Or, if it's simple, we can use a little trial and error.
-8 = -2 (2)²
-18 = -2 (3)²
-32 = -2 (4)²
So the function is:
y = -2x²
Find The area of the trapezoid
Please help with questions 25-26
Answer:
Part 1) [tex]A=96\ cm^{2}[/tex]
part 2) [tex]A=40.8\ ft^{2}[/tex]
Step-by-step explanation:
Part 1)
we know that
The area of a trapezoid is equal to
[tex]A=(1/2)[b1+b2]h[/tex]
In this problem we have
[tex]b1=12\ cm[/tex]
[tex]b2=6+12+2=20\ cm[/tex]
[tex]h=6\ cm[/tex] ----> perpendicular distance between the two bases
substitute
[tex]A=(1/2)[12+20](6)[/tex]
[tex]A=96\ cm^{2}[/tex]
Part 2)
we know that
The area of a kite is equal to
[tex]A=(1/2)[D1*D2][/tex]
we have
[tex]D1=10.2\ ft[/tex]
[tex]D2=8\ ft[/tex]
substitute
[tex]A=(1/2)[10.2*8][/tex]
[tex]A=40.8\ ft^{2}[/tex]
Answer:
25) 96 cm²
26) 40.8 ft ²
Step-by-step explanation:
25) To find the area of trapezoid
Area of trapezoid = h(a + b)/2
Here a = 6 + 12 + 2 = 20 cm
b = 12 cm and h = 6
Area = h(a + b)/2
= 6(20 + 12)/2
= 96 cm²
26) To find the area of kite
Area of kite = pq/2
Where p and q are the two diagonals
Here p = 10.2 ft and q = 8 ft
Area = pq/2
= (10.2 * 8)/2 = 40.8 ft²
3x – 10xy + 13y – 4xy + 2x2
Answer:
3x-14xy+13y+4
Step-by-step explanation:
3x – 10xy + 13y – 4xy + 2x2
= 3x-14xy+13y+4
Simplification of the expression [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex] is [tex]3x - 14xy + 13y + 2x^{2}[/tex] .
What is the simplification of the given expression ?Given expression is [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]
Grouping the like terms from the expression, results -
= [tex]3x - (10xy - 4xy) + 13y + 2x^{2}[/tex]
Simplification of the expression is -
= [tex]3x - 14xy + 13y + 2x^{2}[/tex]
Thus, simplification of the expression [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex] is [tex]3x - 14xy + 13y + 2x^{2}[/tex] .
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Y=8x+40 substitute 3 for x
Answer:
[tex]\displaystyle 64 = y[/tex]
Step-by-step explanation:
[tex]\displaystyle y = 8[3] + 40; y = 24 + 40; 64 = 24 + 40[/tex]
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which congruency theorem can be used to prove that triangle abd is congruent to triangle dca
Answer:
SAS
Step-by-step explanation:
we know that
Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles
so
In this problem
we have that
the pair of corresponding sides AB with DC and AD with DA and their included angles ∠ BAD with ∠CDA are equal
therefore
Triangle ABD is congruent with triangle DCA by SAS congruency theorem
Answer:
sas
Step-by-step explanation:
i just did the assignment. please mark me brainliest!!!!!
Converting 5/9 to whole number
The answer to your question is 0.55555555555
Solution: You simply divide 5 by 9 to get your whole number. In other words, 5/9 =0.55555555555
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The fraction 5/9 cannot be converted into a whole number because it results in a decimal number (approximately 0.55) upon division.
Explanation:In Mathematics, we have different types of numbers - whole numbers, fractions, decimals, etc. Here, you are asked to convert a fraction 5/9 into a whole number. However, it's essential to understand, that 5/9 cannot be converted into a whole number because it is less than 1.
For general understanding, a whole number can only be a non-negative number without any fractional or decimal parts, such as 0, 1, 2, 3, 4, and so forth. A fraction like 5/9 implies division, and when you divide 5 by 9, you get a decimal number (approximately 0.55), which is not a whole number.
Thus, the fraction 5/9 cannot be precisely converted into a whole number without rounding it off.
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John has consumed 1,600 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,800 calories per day. How many calories does he have left to consume for the day? Is 1,000 a viable solution to this problem?
Answer:
No; 1,000 will cause him to exceed 1,800.
Step-by-step explanation:
Given,
The consumed calories = 1,600,
Burned calories = 400,
Thus, the remaining calories = 1600 - 400 = 1200
Since, 1,800 calories per day would be like to keep,
Also, 1200 < 1800
Hence, remaining calories is less than the required calories,
And, the calories left to consume for the day = Required calories - remaining calories
= 1800 - 1200
= 600
Therefore, 600 is the viable solution to this problem.
Note : If 1,000 a viable solution to this problem then the required calories will be more than 1800 or exceed 1800.
Which graph represents the function g(x) = |x + 4| + 2? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]g\left(x\right)=\left|x+4\right|+2[/tex]
The vertex of the function is the point (-4,2)
The y-intercepts is the point (0,6)
using a graphing tool
see the attached figure
Answer:
It is the second graph
Look at the picture that's attached to that is the answer
Find -x + 10 subtracted from 0.
-* +10
0X-10
Answer:
x-10
Step-by-step explanation:
we know that
(-x+10) subtracted from 0 is equal to
0 minus (-x+10)
so
0-(-x+10)=0+x-10
=x-10
Answer:
x-10
Step-by-step explanation:
Solve the inequality 6x − 8 > 4x + 26
Hi.
Answer:
[tex]\boxed{x>17}\checkmark[/tex]
The answer should have positive sign but not negative.
Step-by-step explanation:
First, you add by 8 from both sides.
[tex]6x-8+8>4x+26+8[/tex]
Then, simplify.
[tex]6x>4x+34[/tex]
Next, you do is subtract by 4x from both sides.
[tex]6x-4x>4x+34-4x[/tex]
Simplify.
[tex]2x>34[/tex]
Therefore, you divide by 2 from both sides.
[tex]\frac{2x}{2}>\frac{34}{2}[/tex]
Finally, you solve and simplify.
[tex]34/2=17[/tex]
[tex]x=17\checkmark[/tex]
X=17 is the correct answer.
Hope this helps you!
Have a nice day! :)
Answer:
The solution for the inequality is x>17
Step-by-step explanation:
Consider the provided inequality.
[tex]6x - 8 > 4x + 26[/tex]
Subtract 4x to both the sides.
[tex]6x -4x- 8 > 4x-4x + 26[/tex]
[tex]2x- 8 > 26[/tex]
Add 8 to the both sides.
[tex]2x- 8+8 > 26+8[/tex]
[tex]2x > 34[/tex]
Divide both the sides by 2.
[tex]x > 17[/tex]
Hence, the solution for the inequality is x>17
In a bouquet of 24 roses, sixteen are red and the rest are pink. What is the ratio of pink to red roses?
Answer: 1:2 ratio
Step-by-step explanation:
Total-red roses=pink roses
24-16=8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink:red
The ratio of pink to red roses 1:2 ratio
Total-red roses=pink roses
24-16= 8
8:16
GCF: 8
16/8=2
8/8=1
1:2 ratio
pink : red
A ratio indicates how many times one number contains another.
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
ReductionRatios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.
Thus, the ratio 40:60 is equivalent in meaning to the ratio 2:3, the latter being obtained from the former by dividing both quantities by 20. Mathematically, we write 40:60 = 2:3, or equivalently 40:60∷2:3. The verbal equivalent is "40 is to 60 as 2 is to 3."
Irrational ratiosRatios may also be established between incommensurable quantities (quantities whose ratio, as the value of a fraction, amounts to an irrational number). The earliest discovered example, found by the Pythagoreans, is the ratio of the length of the diagonal d to the length of a side s of a square, which is the square root of 2, formally.
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What is the following product? 3 sqrt 16x7 . 3 sqrt 12x9
Answer: The required product is [tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.[/tex]
We will be using the following property of exponents :
[tex](i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.[/tex]
The required multiplication is as follows :
[tex]P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.[/tex]
Thus, the required product is [tex]4x^5\sqrt[3]{3x}.[/tex]
If $190 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in 4 years? Use the continuous compound interest formula: A = Pert.
Answer:
295.01
Step-by-step explanation:
Use A = Pe^(rt)
$294.88 is the worth of the investment after 4 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that $190 is invested at an interest rate of 11% per year and compounded continuously.
We need to find the worth of the investment after 4 years.
[tex]A=Pe^{rt}[/tex]
A is the final amount
p is the principal amount
r is the rate of interest
t is the time.
[tex]A=190e^{0.11(4)}[/tex]
[tex]A=190e^{0.44}[/tex]
A=190×1.552
A=294.88
Hence, $294.88 is the worth of the investment after 4 years.
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A mover in a moving truck is suing a rope to pull a 400-pound box up a ramp
that has an incline of 25o. What is the force needed to hold the box in a
stationary position to prevent the box from sliding down the ramp?
Answer:
Step-by-step explanation:
The pulling force
Answer:
F = -52.8 N
Step-by-step explanation:
Given :
Inclination angle : 25°
Weight, W = 400 lb
The force N will push the box against the ramp.
Therefore, Force F will prevent the box from sliding down the ramp.
F = W sin 25°
= 400 x (-0.132)
= -52.8 N ( negative sign shows that the force applied in the opposite direction )
what is the slope of the line that passing through point (2,3) and (-2,5)?
Answer:
[tex]\displaystyle \boxed{-\frac{1}{2}}[/tex]
Step-by-step explanation:
Slope formula:
↓
[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex]
[tex]\displaystyle Y_2=5\\\displaystyle Y_1=3\\\displaystyle X_2=(-2)\\\displaystyle X_1=2\\[/tex]
[tex]\displaystyle \frac{5-3}{(-2)-2}=\frac{2}{-4}=\frac{2\div2}{-4\div2}=\frac{1}{-2}=-\frac{1}{2}[/tex]
Therefore the slope is -1/2.
-1/2 is the correct answer.
Hope this helps!
Solve the inequality -1+4y<_31.
Answer:
[tex]\large\boxed{y\leq8\to\{y\ |\ y\leq8\}\to y\in(-\infty,\ 8]}[/tex]
Step-by-step explanation:
[tex]-1+4y\leq31\qquad\text{add 1 to both sides}\\\\-1+1+4y\leq31+1\\\\4y\leq32\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}\leq\dfrac{32}{4}\\\\y\leq8[/tex]
Can someone help me plz
The correct answer: D