Using the arrangements formula, it is found that they can stand in the line in 80,640 ways.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
The 2 freshmen are in 2! positions, in any of the 8 positions from 1 to 8.The other 7 students are arranged in 7! positions.Hence the number of ways in which they can be lined up is given by:
N = 2! x 8 x 7! = 80,640.
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(c) If f(x) = a^x , then show that f(m +n + p) = f(m). f(x). f(p)
[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]
Find the midpoint of the line segment with end coordinates of:
(-4,-4) and (-4,-8)
Answer:
(-4, -6)
Step-by-step explanation:
(x,y) = ((x1+x2)/2 , (y1+y2)/2)
[substitute the values given]
(x,y) = ((-4+-4)/2 , (-4+-8)/2)
[solve]
(x,y) = (-8/2 , -12/2)
[simplify]
(x,y) = (-4, -6)
THE ANSWER IS (-4, -6) HOPE IT HALP'S MARK IT AS BRAILY.
What is the area of a circular pizza with a radius of 9 cm? b. 28.3c * m ^ 2 od. 1017.9c * m ^ 2 c. 254.5c * m ^ 2 a. 56.5c * m ^ 2
Answer:
254.5 cm²
Step-by-step explanation:
area = πr²
area = 3.14159 × (9 cm)²
area = 254.5 cm²
[tex]\sf\large\green{\underbrace{\red{Question*}}}:[/tex]
[tex] \mathcal \pink{Solve} [/tex]
[tex] \blue{3(x - 2) + 2(x + 1) = 10}[/tex]
[tex]~~~~~~~3(x-2) +2(x +1) = 10\\\\\implies 3x -6 + 2x+2 = 10\\\\\implies 5x -4 = 10\\\\\implies 5x = 10+4\\\\\implies 5x = 14 \\\\ \implies x = \dfrac{14}5 \\\\ \implies x = 2.8[/tex]
[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]
[tex] \sf \red{3(x - 2) + 2(x + 1) = 10}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
In the above question, it is said to find out the value of "x". So, let's solve.First we gonna multiply (x - 2) with 3 and then again (x + 1) with 2.
So, it goes...[tex]3(x - 2) + 2(x + 1) = 10 \\ \\ \implies \: 3x - 6 + 2x + 2 = 10 \\ \\ \implies \: 5x - 4 = 10 \\ \\ \implies \: 5x = 10 + 4 \\ \\ \implies5x = 14 \\ \\ \implies \: x = \frac{14}{5} \\ \\ \implies \: x = 2.8[/tex]
Therefore, we've found the value of "x" and that is 2.8[tex] \boxed{ \frak \pink{Have \: a \: Splendid \: Day}}[/tex]
[tex] \boxed{ \frak \green{Be \: Brainly}}[/tex]
Sana's mother bought produce for Sunday dinner. She bought one more pound of peaches than pounds of tomatoes. She bought 3 times as many pounds of tomatoes as pounds of mushrooms. If peaches cost $6 per lb, tomatoes cost $3 per lb, and mushrooms cost $10 per lb, how many of each did Sana's mother buy for $80?
Using a system of equations, it is found that Sana's mother bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Number of pounds of peaches.Variable y: Number of pounds of tomatoes.Variable z: Number of pounds of mushrooms.She bought one more pound of peaches than pounds of tomatoes, hence:
x = y + 1.
y = x - 1.
She bought 3 times as many pounds of tomatoes as pounds of mushrooms, hence:
x = 3z.
y = x - 1 = 3z - 1.
She spent a total of $80, hence considering the cost per pound of each product we have that:
6x + 3y + 10z = 80.
Considering the values of x and y as function of z and replacing in the equation, we have that:
6(3z) + 3(3z - 1) + 10z = 80
18z + 9z - 3 + 10z = 80.
37z = 83.
z = 83/37
z = 2.24.
Then:
x = 3z = 3 x 2.24 = 6.72.
y = x - 1 = 3z - 1 = 6.72 - 1 = 5.72.
Hence, she bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
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7 lbs peaches, 6 lbs tomatoes, 2 lbs mushrooms
yum!
Pre Calc question, thanks for the help! Question linked in photo below.
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{0} + 3 = 3[/tex]
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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The length of a reclangle can be represented by the expression 2x - 1. The width of the same rectangle can be represented by the expression x^2 - x + 3. Which of the following expressions can represent the area of the rectangle?
Answer:
2x^3 - 3x^2 + 7x - 3
Step-by-step explanation:
Area = length * width
= (2x - 1)(x^2 - x + 3)
= 2x(x^2 - x + 3) - 1(x^2 - x + 3)
= 2x^3 - 2x^2 + 6x - x^2 + x - 3
= 2x^3 - 3x^2 + 7x - 3
Expand each expression In 4y5/x2
Answer:
[tex]\ln 4 -2 \ln x +5 \ln y[/tex]
Step-by-step explanation:
[tex]\ln \dfrac{4y^5}{x^2}\\\\=\ln(4y^5) - \ln(x^2)~~~~~~~~~~~;\left[ \log_b\left( \dfrac mn \right) = \log_b m - \llog_b n \right]\\\\=\ln 4 + \ln y^5 - 2\ln x~~~~~~~~~~~~;[\log_b m^n = n \log_b m ~\text{and}~\log_b(mn) = \log_b m + \log_b n ]\\\\=\ln 4 + 5 \ln y -2 \ln x\\\\=\ln 4 -2 \ln x +5 \ln y[/tex]
Answer: Answer B
Step-by-step explanation: Let's begin
Answer: B in 4 - 2 in x + 5 in y
If $3840 is deposited into a bank account at a 5% interest rate how long will it take the account to make $960 in interest?
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]
ACTIVITY #1
Try It!
A. Write the definition, property, postulate or theorem that will prove each of the given statements.
What completes the proof are:
1. LC ≅ CU; CU ≅ UK
2. Given
3. Unequal angle theorem (Aa → Ss)
What is the Unequal Angle Theorem?The unequal angle theorem states that the longer side of a triangle will always be directly opposite the largest angle measure. This implies that, if an angle that is opposite a side is greater than another another, the side it is opposite will also be longer than the side opposite the other angle (Aa → Ss).
From the image given, statement 1 was given as well as statement 2.
Statement 1 would be: LC ≅ CU; CU ≅ UK.
The reason for statement 2 will also be "given".
Then, UL > CK using the unequal angle theorem (Aa → Ss).
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The equation of line A is y = 5 - 2x Line B is parallel to line A. Line B passes through the point (-3,7)
Work out the coordinates of the point where line B intersects the x-axis.
Answer:
The answer is (0.5, 0)
Step-by-step explanation:
The number of slugs in a garden t days from now is p, where
Po = 100
P1+1= 1.06pt
Work out the number of slugs in the garden 3 days from now.
The number of slugs in the garden 3 days from now is 119
How to determine the number of slugs?The function is given as:
Po = 100
[tex]P_{t+1} = 1.06P_t[/tex]
When t = 0, we have:
[tex]P_{0+1} = 1.06P_0[/tex]
[tex]P_1 = 1.06 * 100\\[/tex]
[tex]P_1 =106[/tex]
When t = 1, we have:
[tex]P_2 = 1.06 * 106[/tex]
[tex]P_2 = 112.36[/tex]
When t = 2, we have:
[tex]P_3 = 1.06 * 112.36[/tex]
[tex]P_3 = 119.1016[/tex]
Approximate
[tex]P_3 = 119[/tex]
Hence, the number of slugs in the garden 3 days from now is 119
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What is 7 to the 2018th power
Answer: infinity
the answer should be infinity since the number 7 will have to be multiplied with itself 2018 times.
hope that helps....
Please help, i need right answers and be help if it with proof, ty! Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.
Which sequence of transformations will produce the same results?
a reflection over the y-axis and then a rotation 90degree clockwise about the origin
a reflection over the x-axis and then a rotation 90degree clockwise about the origin
a 180degree rotation about the origin
a reflection over the y-axis and then a reflection over the x-axis
Answer:
A. A reflection over the y-axis and then a rotation 90 degree clockwise about the origin.
Step-by-step explanation:
Given information: Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.
This means Figure H is made by G rotated CLOCKWISE and reflected over the X-AXIS.A sequence of transformations to produce the same results could be the opposite of this, wherein Figure H undergoes a series of transformations to form Figure G.
A reflection over the y-axis flips figure H like folding a piece of paper in half vertically. To help visualize, the point (5, -2) becomes (-5, -2). A 90 degree clockwise turn about the origin makes the point (-5, -2) on figure H to become (-2, 5). Figure G has the same point at (-2, 5).so, a reflection of figure H over the y-axis and then a rotation 90 degree clockwise about the origin will form figure G, thus producing the same results.5 feet to 31 inches write the ratio of the first measurement to the second measurement compare in inches
Answer:
60:31
Step-by-step explanation:
30-60-90 Triangle Practice
I need help with this, I do not understand anything.
(Teacher just give us hw expecting to know it already.)
Answer:
When there are numbers like that next to the radical it means multiply. like this: 2√9. You would first figure out the square root. Square root of 9 is 3. 2 times 3 is 6.
After you figure out those problems, you just need to put the number, x, and y in an equation with 2 unknowns.
Step-by-step explanation:
Answer:
When there are numbers like that next to the radical it means multiply. like this: 2√9. You would first figure out the square root. Square root of 9 is 3. 2times 3 is 6.
Step-by-step explanation:
What is the value of X?
Answer:
C
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
x² = 40² + 9² = 1600 + 81 = 1681 ( take square root of both sides )
x = [tex]\sqrt{1681}[/tex] = 41
What is startfraction 3 pi over 4 endfraction radians converted to degrees? if necessary, round your answer to the nearest degree.
Unit conversion is a way of converting some common units into another without changing their real value. The value of (3π/4) radian converted to a degree is 135°.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
Since π radian is equal to 180°. Therefore, the value of (3π/4) radian is equal to,
1 radian = 180°/π
(3π/4) radian = (3π/4) × (180°/π) = 135°
Hence, the value of (3π/4) radian converted to a degree is 135°.
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Answer:
option 2
Step-by-step explanation:
Mary O’Connell is earning a weekly salary of $521.60 as a payroll clerk. She has accepted a new assignment in the tax processing department. In her new position, she will be paid an annual salary of $30,534. How much more will she earn per week in her new position
Answer:
$ 65.59 more per week
Step-by-step explanation:
Assuming she worked 52 weeks a year as a clerk :
30534 - 52 * 521.6 = $ 3410.80 more per year
now each WEEK that is 3410.80 / 52 = 65.59
the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
How to determine the radius of the smaller circle
In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:
[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]
2 · r² = (9-r)²
2 · r² = 81 - 18 · r + r²
r² + 18 · r - 81 = 0
The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
Remark
The image is missing and is thus included in the figure attached below.
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Consider the expression below.
9 + 4(x + 2) – 3x
Select the term that best describes "3" in the given expression.
A.
exponent
B.
variable
C.
coefficient
D.
constant
Answer:
the term that best describes 3 is a coefficient because a
Step-by-step explanation:
Coefficient is a number that is being multiplied by the variable.
(3x+43)^((2)/(3))+22=38
Answer:
X = 7 and -35.6666
Step-by-step explanation:
This chart shows the result of an experiment conducted to see the effect of different brands of fertilizers on the growth of a bean plant.
Which of the following ranges would be appropriate to use in order to represent the numerical data in centimeters on the vertical axis of a Line Graph?
A. 0.0 to 26.0
B. 0.0 to 25.0
C. 14.0 to 25.2
D. 0.0 to 20.0
The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.
What is a line graph?
A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.
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Please do both you get 100 points!!
#6
Sum of exterior angles of any polygon=360°
sides=6
Measure of one angle
360/660°Option D
#7
4ft=1cm
32ft=32/4=8cmand
60ft=60/4=15cmDimensions are 8cm and 15cm
Option B
Answer:
6. d. m∠YXZ = 60°
7. b. 8 cm x 15 cm
Step-by-step explanation:
Question 6
∠YXZ is the exterior angle of a regular polygon
Exterior angle of a regular polygon = 360° ÷ number of sides
⇒ ∠YXZ = 360° ÷ 6
⇒ ∠YXZ = 60°
Question 7
Scale 1 cm : 4 ft
Therefore, to convert actual dimensions in feet to sketch dimensions in centimeters, divide dimensions in feet by 4:
⇒ width = 32 ft
⇒ width = 32 ÷ 4 = 8 cm
⇒ length = 60 ft
⇒ length = 60 ÷ 4 = 15 cm
Therefore, the dimensions of the sketch are 8 cm x 15 cm
Which number produces a rational answer when added to 0.85
The number that produces a rational answer when added to 0.85 is; 193/180
How to identify rational numbers?A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or not infinitely long. If they aren't, then these are called irrational numbers.
Now, let us convert 0.85 to a fraction. Thus;
0.85 = 85/100 = 17/20
From the given options, the only one that when added to 0.85 will yield a rational number is 2/9. This is because;
17/20 + 2/9 = 193/180
193/180 is a rational number.
The missing options are;
A. 2/9
B. 0.2645751311...
C. √2
D.
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A ser of esta consists of four scores…
Answer:
x4 = 8
Step-by-step explanation:
To find the mean, add the values and divide by the number of values.
mean = (x1 + x2 + x3 + x4)/4
(3 + 12 + 7 + x4)/4 = 8
x4 + 22 = 32
x4 = 10
Answer:
x4 = 8
Step-by-step explanation:
Solve for the h in the triangle below. Round to the nearest tenth. 90⁰ 6.0 Oh-13.3 Oh 5.5 Oh 8.0 53%
Answer:
h=8.0
Step-by-step explanation:
law of sines
sinA/a=sinB/b
b/a=sinB/sinA
b = a times sinB/sinA
b = 10 times sin53/sin90
on a calculator type sin53 in degrees
b = 10 times 0.7986/1
b = 7.986
Bob's family pays $50.37 at the pizzeria. This included a 19% tip. What was the cost of the bill without the tip percentage. (Please include how to solve it)
Answer:
$43.33
Step-by-step explanation:
50.37/119 = ?/100
cross multiply,
? = 43.3277
Give brainliest, please!
Hope this helps :)
asap need help quick
Answer:
Answer:11
Step-by-Step Answer:
When we multiply 11 with 1\2 then thier answer will be 11\2
This graph talks about supply and demand can I get some help with it?
well that's Economics not Mathematics