Answer:
10
Step-by-step explanation:
we can solve this using basic algebra
We set up the equation using the info that each video costs $5 and that we but 12 of them
12(1 * 5) + x = 70
(Please note: 1x = x)
12(5) + x = 70
60 + x = 70
60 - 60 + x = 70 - 60
x = 10
Please help me fill in the blank! Thank you!!
Answer:
The fraction of 6% is 6/10 and the model is 10 squares and only color 6 of them
YOU WELCOME :)
Answer:the fraction of 6% is 6/10
Step-by-step explanation:and the model is 10 squares and only color 6 of them
What are the solutions to the equation (2x - 5)(3x – 1) = 0?
x=-zorx=1
O
O x= orx=1
2
O x = 5 or x = 3
O x = 5 or x = 1
HURRY
Answer:
x = \(\frac{5}{2}\) , x = \(\frac{1}{3}\)
Step-by-step explanation:
(2x - 5)(3x - 1) = 0
Equate each factor to zero and solve for x
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = \(\frac{5}{2}\)
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = \(\frac{1}{3}\)
PLSS I NEED HELP.!!
Answer: 30
Step-by-step explanation:
It to be 30 but this look hard so I’m not sure
Does each point lie on the circle, yes or no?
To answer this question we have to evaluate the given equation using each ordered pair and see if it's true:
(0, sqrt(13))
\(\begin{gathered} (0-2)^2+(\sqrt[]{13})^2=13 \\ 4+13=13 \\ 17\ne13 \end{gathered}\)This point does not lie on the circle.
(0, -sqrt(13))
\(\begin{gathered} (0-2)^2+(-\sqrt[]{13})^2=13 \\ 4+13=13 \\ 17\ne13 \end{gathered}\)This point does not lie on the circle.
(4, 3)
\(\begin{gathered} (4-2)^2+(3)^2=13 \\ 4+9=13 \\ 13=13 \end{gathered}\)This point does lie on the circle.
(-2, 1)
\(undefined\)Work out the volume of the cuboid 4cm 10cm 15cm
Answer:
600 m³
Step-by-step explanation:
Attached Below
If it helps, mark as brainliest. : )
you buy 6 apples for $2.70 write and equation that can be used to express the relationship between the total price t and the number of apples a you buy.
1. t= 2.70a
2. t=0.45a
3. t=6a
t= 2.22a
Answer:
The correct answer is: 2. t=0.45a
Step-by-step explanation:
Let t be the price of apples
and a be the number of apples
The price and quantity are directly proportional
\(t \propto a\)
Removing the proportionality symbol introduces a proportionality constant in the equation
\(t = ka\)
So far we know that cost of 6 apples is $2.70
Putting in the equation
\(2.70 = k (6)\\k = \frac{2.70}{6}\\k = 0.45\)
Putting the values of k will give us:
\(t = 0.45a\)
Hence,
The correct answer is: 2. t=0.45a
Solve - x/6 less than or equal to 3
Answer: x is greater than or equal to 18
Step-by-step explanation:
Answer:
x ≤ - 2
Step-by-step explanation:
- x/6 ≤ 3
- x/2 ≤ 1
- x ≤ 2
x ≤ - 2
A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?
The function which represents the cost to drive a car from this agency miles x a day is :
C(x) = 15, if 0 ≤ x ≤ 200
= 15 + 0.05x, if x > 200
Given that,
A car rental agency charges $15 a day for driving a car 200 miles or less.
The function can be written as,
C(x) = 15 if 0 ≤ x ≤ 200
If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.
C(x) = 15 + 0.05x, if x > 200
Hence the correct option is D.
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The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random samples of 100 new homes is taken. A. What is the probability that the sample mean selling price was more than $110,000? b. What is the probability that the sample mean selling price was between $113,000 and $
The probability of getting a sample mean selling price between $113,000 and $117,000 is approximately 0.4332.
A normal distribution with a mean of $115,000 and a standard deviation of - is used to estimate the distribution of the sample mean using the central limit theorem.
= 25,000/√100
= 2,500.
a. To find the probability that the sample means selling price was more than $110,000, we can calculate the z-score:
z = (110,000 - 115,000) / 2,500
= -5,000/2,500
= -2
As per the standard normal distribution table, the probability of getting a z-score of -2 or lower is approximately 0.0228. Therefore, the probability of getting a sample mean selling price of more than $110,000 is approximately 0.0228.
b.
Calculating the z-scores for each value:
z1
= (113,000 - 115,000) / 2,500
= -0.8
z2
= (117,000 - 115,000) / 2,500
= 0.8
The likelihood of receiving a z-score between -0.8 and 0.8, as determined by a typical normal distribution table or calculator, is found to be roughly 0.4332.
Complete Question:
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random samples of 100 new homes is taken. A. What is the probability that the sample mean selling price was more than $110,000? b. What is the probability that the sample mean selling price was between $113,000 and $117,000
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4. Find the volume of the solid obtained by rotating the region bounded by the graphs of a. y=x2-9, y=0 about the x-axis, b. y = 16-*, y = 3x +12, x=-1 about the x-axis. c. y=x2 + 2, y = -x + 10, x > 0 about the y-axis.
The volume of the solid obtained by rotating the region bounded by the graphs of:
a. \(y=x^2-9, y=0\) about the x-axis is 0.
b. \(y=16-x,y=3x+12,x=-1\) about the x-axis is (82π / 9) cubic units.
c. \(y=x^2+2, y=x^2+10.x > 0\) about the y-axis is(160π/3) cubic units.
To find the volume of the solid obtained by rotating the region bounded by the given graphs, we can use the method of cylindrical shells. The volume is calculated as the integral of the shell's volume over the specified interval.
a.) For the region bounded by \(y=x^2-9, y=0\) , rotating about the x-axis:
V = ∫[a, b] 2πx * (f(x) - g(x)) dx
where a and b are the x-values where the curves intersect.
To find the intersection points, we set the two functions equal to each other:
x² - 9 = 0
x² = 9
x = ±3
So, a = -3 and b = 3.
V = ∫[-3, 3] 2πx * (x² - 9) dx
V = 2π ∫[-3, 3] (x³ - 9x) dx
= 2π [ (1/4)x⁴ - (9/2)x² ] | [-3, 3]
= 2π [ ((1/4)(3⁴) - (9/2)(3²)) - ((1/4)(-3⁴) - (9/2)(-3²)) ]
= 2π [ (81/4 - 81/2) - (81/4 - 81/2) ]
= 2π (0)
= 0
Therefore, the volume of the solid obtained by rotating the region bounded by y = x² - 9 and y = 0 about the x-axis is 0.
b. For the region bounded by y = 16 - x, y = 3x + 12, and x = -1, rotating about the x-axis:
V = ∫[a, b] 2πx * (f(x) - g(x)) dx
In this case, we have two curves intersecting at x = -1. So, we can split the integral into two parts.
For the first part, we have:
V1 = ∫[-1, a] 2πx * (f(x) - g(x)) dx
where a is the x-value where y = 16 - x and y = 3x + 12 intersect.
The two equations equal to each other:
16 - x = 3x + 12
x = 1
So, a = 1.
The integral becomes:
V1 = ∫[-1, 1] 2πx * ((16 - x) - (3x + 12)) dx
V1 = 2π ∫[-1, 1] (16x - x² - 3x - 12) dx
= 2π [ (8x² - (1/3)x³ - (3/2)x² - 12x) ] | [-1, 1]
= 2π [ (8(1)² - (1/3)(1)³ - (3/2)(1)² - 12(1)) - (8(-1)² - (1/3)(-1)³ - (3/2)(-1)² - 12(-1)) ]
= 2π [ (-19/6) - (49/6) ]
= 2π [ -68/6 ]
= -68π/3
For the second part, we have:
V2 = ∫[a, b] 2πx * (f(x) - g(x)) dx
where b is the x-value where y = 3x + 12 intersects with the x-axis (y = 0).
3x + 12 = 0
3x = -12
x = -4
So, b = -4.
V2 = ∫[1, -4] 2πx * (0 - (3x + 12)) dx
V2 = 2π ∫[1, -4] (3x² + 12x) dx
= 2π [ (x³ + 6x²) ] | [1, -4]
= 2π [ ((-4)³ + 6(-4)²) - (1³ + 6(1)²) ]
= 2π [ 32 - 7 ]
= 50π
The total volume is given by:
V = V1 + V2 = -68π/3 + 50π = (50π - 68π/3) / 3
V = (150π - 68π) / 9 = 82π / 9
Therefore, the volume of the solid obtained by rotating the region bounded by y = 16 - x, y = 3x + 12, and x = -1 about the x-axis is (82π / 9) cubic units.
c. For the region bounded by y = x² + 2, y = -x² + 10, and x > 0, rotating about the y-axis:
To find the volume, we need to determine the limits of integration by finding the x-values where the two curves intersect.
x² + 2 = -x² + 10:
x² = 4
x = ±2
Since we are only interested in the region where x > 0, the limits of integration are from 0 to 2.
V = ∫[0, 2] 2πx * (f(x) - g(x)) dx
V = ∫[0, 2] 2πx * ((x² + 2) - (-x² + 10)) dx
V = 2π ∫[0, 2] (2x² - x² + 12) dx
= 2π [ (2/3)x³ - (1/3)x³ + 12x ] | [0, 2]
= 2π [ (2/3)(2)³ - (1/3)(2)³ + 12(2) - (2/3)(0)³ - (1/3)(0)³ + 12(0) ]
= 2π [ (16/3 - 8/3 + 24) - (0) ]
= 2π [ (24 + 8/3) ]
= 2π [ (72/3 + 8/3) ]
= 2π [ 80/3 ]
= 160π/3
Therefore, the volume of the solid obtained by rotating the region bounded by y = x² + 2, y = -x² + 10, and x > 0 about the y-axis is (160π/3) cubic units.
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Activity 1: Directions: Use the values of a, b and c of each of the following quadratic equations in finding the sum and the product of its roots. By inspection or by any appropriate method, determine the roots. Use the space provided for your solutions and complete the table below.
\(\\ \sf\longmapsto D=b^2-4ac\)
#1
\(\\ \sf\longmapsto x^2+6x+9=0\)
Now
\(\\ \sf\longmapsto D=(6)^2-4(1)(9)=36-36=0\)
Roots are real and equal#2
\(\\ \sf\longmapsto x^2+9x+20=0\)
Now
\(\\ \sf\longmapsto D=(9)^2-4(1)(20)=81-80=1\)
Roots are real and rational#3
\(\\ \sf\longmapsto x^2+6x+3=0\)
Now
\(\\ \sf\longmapsto D=6^2-4(1)(3)=36-12=24\)
Roots are real and distinct and irrational.#4
\(\\ \sf\longmapsto 2x^2-10x+8=0\)
Now
\(\\ \sf\longmapsto D=(-10)^2-4(1)(8)=100-32=68\)
Roots are real and distinct and irrational.#5
x^2+5x+10=0Now
\(\\ \sf\longmapsto D=5^2-4(1)(10)=25-40=-15\)
Roots are not real.#6
x^2-3x+1=0\(\\ \sf\longmapsto D=(-3)^2-4(1)(1)=9-4=5\)
Roots are real and distinct and irrationalAn ice field is melting at the rate M (t)=4-(sin t)³ acre-feet per day, where t is measured in
days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the
beginning of day 4 (t = 3) ?
(A) 10.667
(B) 10.951
(C) 11.544
(D) 11.999
A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.
To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.
First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4
So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)
Integrating this expression with respect to t over the interval [0,3], we get:
\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt
= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]
= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))
= 11.544
Therefore, the answer is (C) 11.544.
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Lina goes to another bank that offers her 7% interest on her $200. After 1 year, how much would she have earned?
Simplify the expression -4.6+( -1.4) .on the test , when maureen simplified the expression she got 3.2 .
Answer:
Step-by-step explanation:
-4.6+( -1.4)=
-4.6-1.4=-6 maureen is wrong, because both have the minus , so she should add with the minus symbol.
Solve the system below
2x+y=3
y=x-3
Answer:
x=2 y=-1
Step-by-step explanation:
2x+x-3=3
3x-3=3
3x=6
x=2
y=2-3
y=-1
1. A savings account earns 8 % Interest each year, compounded quarterly (4 times a year). If a person Invests $100 and makes no further deposits or withdrawals, what is the balance inthe account after 3 years?hpA
So, the formula that we're going to use is:
Compound interest
A = P(1 + r/n)ⁿˣ
Where
A = amount
P = principal = $100
r = rate = 8% = 8 / 100 = 0.08
x = time
In this case, n=4 since it is being compounded quarterly, so:
The answer is $126.82.
Find an expression which represents the difference when (-6x + 5) is subtractedfrom (-2 – 8) in simplest terms.
the given expression is,
= (-2-8) - (-6x + 5)
= -10 + 6x - 4
= 6x - 14
so the simpl
Find X value.
Will rate brainliest for the right ans
Answer:
\(\huge\boxed{x=65}\)
Step-by-step explanation:
Look at the picture.
\(m\angle VUP=180^o-2\cdot60^o=180^o-120^o=\boxed{60^o}\\\\m\angle UPQ=360^o-2\cdot60^o=360^o-120^o=\boxed{240^o}\\\\m\angle QRM=180^o-2\cdot60^o=180^o-120^o=60^o\\\\m\angle RMQ=180^o-135^o=45^o\\\\in\ \triangle QRM:\ m\angle MQR=180^o-(60^o+45^o)=180^o-105^o=75^o\\\\m\angle PQW=360^o-(2\cdot60^o+75^o+80^o)=360^o-(120^o+155^o)\\\\=360^o-275^o=\boxed{85^o}\\\\m\angle UVW=\boxed{90^o}\)
VWQPU is the pentagon. The sum of interior angles in a pentagon is equal 540°. Therefore:
\(x^o=540^o-(90^o+60^o+240^o+85^o)=540^o-475^o=65^o\)
Show that there exist a rational number a and an irrational number b such that a^b is irrational.
Answer:
In explanation below.
Step-by-step explanation:
Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.
Which statements about the fraction bar diagram shown at left are true? Check all that apply.
The entire fraction bar represents 1 whole.
The fraction bar is divided into six parts.
The shaded portion represents 1 whole.
The fraction bar is divided into equally sized parts.
Six parts of the whole are shaded orange.
Answer:
1,2,4 and 5
Step-by-step explanation:
those are correct
Triangle ABC is rotated by 135 degrees about point S to create A'B'C' what is the perimeter of ABC
Answer: 12.9
Step-by-step explanation:
5.1 + 2 + 5.8 = 12.9
The perimeter of the triangle ABC is 12.9 units.
What is the perimeter of a triangle?The perimeter of a triangle is the sum of length of three sides of the triangle.
Given, the triangle ABC is rotated by 135 degrees about point S to create the triangle A'B'C'.
We know, after rotation of a figure, the whole dimension of the figure remains the same.
Therefore, AB = A'B' = 5.1 units
BC = B'C' = 2 units
CA = C'A' = 5.8 units
Hence, the perimeter of the triangle ABC
= (5.1 + 2 + 5.8) units
= 12.9 units
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write an equation for the number 40 is 5 times as many as 8 PLEASE HURRY????
Answer:
40=5×8
Step-by-step explanation:
I think, hope this helps
The equation for the number 40 is 5 times as many as 8 is; 40=5×8
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given that the number 40 is 5 times as many as 8
40 is 5 times as many as 8 means
5×8 = 40
Then the equation will be;
40=5×8
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Which of the following are solutions to the equation below?
Check all that apply 25x(squared) - 16 = 0
\(~~25x^2-16=0\\\\\implies (5x)^2 -4^2 =0\\\\\implies (5x+4)(5x-4)=0\\\\\implies x = -\dfrac{4}5, ~~~x=\dfrac 45\)
which expressions are equivalent to 2(4f 2g)2(4f 2g)2, (, 4, f, plus, 2, g, )? choose 3 answers: choose 3 answers: (choice a) 8f 2g8f 2g8, f, plus, 2, g a 8f 2g8f 2g8, f, plus, 2, g (choice b) 2f(4 2g)2f(4 2g)2, f, (, 4, plus, 2, g, )b 2f(4 2g)2f(4 2g)2, f, (, 4, plus, 2, g, )(choice c) 8f 4g8f 4g8, f, plus, 4, g c 8f 4g8f 4g8, f, plus, 4, g (choice d) 4(2f g)4(2f g)4, (, 2, f, plus, g, )d 4(2f g)4(2f g)4, (, 2, f, plus, g, )(choice e) 4f 4f 4g4f 4f 4g4, f, plus, 4, f, plus, 4, g e 4f 4f 4g4f 4f 4g4, f, plus, 4, f, plus, 4, g
The expressions that are equivalent to 2(4f + 2g)², (4, f, plus, 2, g) are:(a) 8f² + 8g² + 16fg (8, f, squared, plus, 8, g, squared, plus, 16, f, g) (b) 2f(4f + 2g) · 2f(4f + 2g) (2, f, times, the quantity, 4, f, plus, 2, g,
end the quantity, times, 2, f, times, the quantity, 4, f,
plus, 2, g) (d) 4(2f + 2g)² (4,
times, the quantity, 2, f, plus, 2, g,
end the quantity, squared)In summary,
the three correct expressions equivalent to
2(4f + 2g)², (4, f, plus, 2, g) are:
8f² + 8g² + 16fg, 2f(4f + 2g) ·
2f(4f + 2g), and 4(2f + 2g)².
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A mass attached to a spring is pulled toward the floor so that its height above the floor is 10 mm (millimeters). The mass is then released and starts moving up and down reaching maximum and minimum heights of 20 and 10 mm , respectively, with a cycle of 0.8 seconds.
a) Assume that the height h(t) of the mass is a sinusoidal function, where t is the time in seconds, sketch a graph of h from t = 0 to t = 0.8 seconds. t = 0 is the time at which the mass is released.
b) Find a sinusoidal function for the height h(t).
c) For how many seconds is the height of the mass above 17
a) The graph of h(t) from t = 0 to t = 0.8 seconds is a sinusoidal curve that starts at 10 mm, reaches a maximum of 20 mm at t = 0.4 seconds, and returns to 10 mm at t = 0.8 seconds.
b) The sinusoidal function for the height h(t) is \(h(t) = 5 \times sin(5\pit) + 15.\)
c) The height of the mass is above 17 mm for approximately 0.133 seconds.
a) To sketch a graph of h from t = 0 to t = 0.8 seconds, we need to consider the given information:
The maximum and minimum heights of the mass and the time for one complete cycle.
The maximum height is 20 mm, the minimum height is 10 mm, and the time for one cycle is 0.8 seconds.
We can start by plotting the maximum and minimum heights on the y-axis and marking the time for one cycle on the x-axis.
At t = 0 seconds (when the mass is released), the height is 10mm.
At t = 0.4 seconds, halfway through the cycle, the height is the average of the maximum and minimum heights, which is (20 + 10) / 2 = 15 mm.
At t = 0.8 seconds, the height is 10 mm again, completing one full cycle.
Using this information, we can sketch a sinusoidal graph that starts at the minimum height, increases to the maximum height, and then decreases back to the minimum height within one cycle.
b) To find a sinusoidal function for the height h(t), we can use the general form: \(h(t) = A \times sin(2\pi / T \times t + \phi) + C,\)
where A is the amplitude, T is the period, φ is the phase shift, and C is the vertical shift.
In this case, the amplitude is (20 - 10) / 2 = 5 mm (half the difference between the maximum and minimum heights).
The period is 0.8 seconds, which is the time for one complete cycle.
Since the mass starts at the minimum height at t = 0, there is no phase shift (φ = 0). The vertical shift (C) is 10 mm, the minimum height.
Therefore, the sinusoidal function for the height h(t) is: \(h(t) = 5 \times sin(2\pi / 0.8 \times t) + 10\)
c) To find for how many seconds the height of the mass is above 17 mm, we can set up an inequality using the sinusoidal function h(t) and solve for t.
h(t) > 17
5 \(\times\) sin(2π / 0.8 \(\times\) t) + 10 > 17
5 \(\times\) sin(2.5π \(\times\) t) + 10 > 17
Subtracting 10 from both sides:
\(5 \times sin(2.5\pi \times t) > 7\)
Now, we can solve for t by taking the inverse sine (arcsine) of both sides:
2.5π \(\times\) t > arcsin(7/5)
Dividing both sides by 2.5π:
t > (1 / (2.5π)) \(\times\) arcsin(7/5)
Approximately, t > 0.285 seconds.
Therefore, the height of the mass is above 17 mm for more than 0.285 seconds.
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frustrated freight may never reach the intended recipient T/F
True, Frustrated Freight is any freight or shipment that it has been halted from moving.
Generally speaking, the elements that make a bundle quit moving or being shipped to the normal beneficiary are issues to do with marking, bundling, as well as making.
Frustrated Freight alludes to products that can't be conveyed to the expected beneficiary because of different reasons like an erroneous location, beneficiary inaccessibility, or harm during travel.
This can prompt the shipment never arrive at its expected objective, causing disillusionment for the shipper and beneficiary, and possibly bringing about monetary misfortunes.
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If hector is 8 years old and Marry is 3 years old, how old will marry be when hector is 16.
Find the range of the function.
Answer:
equation of the line passing through two points
we can chose two points from the graph
I took (5,0) and (0,5)
x-x1/x2-x1=y-y1/y2-y1
x-5/0-5=y-0/5-0
(x-5)*5=y*(-5)
x-5=-y
y+x=5
Step-by-step explanation:
range of the function is [- infinite, infinite]
if x is determined as R number then even range of the function will be R ,real numbers.
How many different ways can six friends stand in line at the movies if Alice and David refuse to stand next to each other
Step-by-step explanation:
Let the other 4 friends arrange themselves first. There are 4! ways to do so.
Now there are 3 spaces between the 4 friends, and 1 at each end (total 5 spaces)
Example: _F_F_F_F_
Alice can choose to stand in any of the 5 spaces. David can choose to stand in any of the 4 remaining spaces (now Alice and David are not next to each other)
Total number of ways = 4! * 5 * 4 = 480.
What's -1/15t =7
please help
Answer:
t=-105
Step-by-step explanation:
divide 7 by -1/15 to get t separated