The length of one side of a square table is 3ft. What is the area of the table?
Answers
Answer: 9 sq. ft
The area of a square is: A = a²
A = 3²
A = 9
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Related Questions
60 scholars are dancing at the Snow Ball of the scholars 1/12 are doing the Woah, 2/3 Sare Flossing, 4/30 are Dabbing, and the rest the scholars are doing the Orange Justice. How many scholars are doing the Orange Justice?
Answers
Given:
Total number of scholars = 60
Fraction of scholars doing Woah = 1/12
Fraction of scholars doing flossing = 2/3
Fraction of scholars dabbing = 4/30
The rest of the scholars are doing the Orange Justice.
To find the number of scholars doing Orange Justice, let's first find the number doing Woah, Sare Flossing and dabbing.
\(\text{Number of scholars doing Woah = }\frac{1}{12}\ast60=5\)\(\text{Number of scholars doing Sare Flossing }=\text{ }\frac{2}{3}\ast60=40\)\(\text{Number of scholars dabbing = }\frac{4}{30}\ast60=8\)Number doing Orange Justice = Total - Woah - Sare Flossing - Dabbing =
60 - 5 - 40 - 8 = 7
Therefore, 7 scholars are doing the Orange Justice.
ANSWER:
7
. If sin(x + y)=sin x.cos y+cos x.sin y, then find the value of sin 75 degrees
Answers
Answer:
\(\sf \dfrac{\sqrt{6}+\sqrt{2}}{4}\)
Step-by-step explanation:
Trigonometry:75 = 45 + 30
Sin (x + y) = Sin x *Cos y + Cos x * Sin y
Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30
\(\sf =\dfrac{1}{\sqrt{2}}*\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}* \dfrac{1}{2}\\\\\\=\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}\\\\\\=\dfrac{\sqrt{3}*\sqrt{2}}{2*\sqrt{2}*\sqrt{2}}+\dfrac{1*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\\\=\dfrac{\sqrt{6}}{2*2}+\dfrac{\sqrt{2}}{2*2}\\\\\\=\dfrac{\sqrt{6}+\sqrt{2}}{4}\)
Suppose that we have two events, A and B, with P(A) = .50, P(B) = .50, and P(A ∩ B) = .20.
a. Find P(A | B) (to 4 decimals).
b. Find P(B | A) (to 4 decimals).
c. Are A and B independent? Why or why not?
Answers
To find P(A | B), first we use the formula P(A | B) = P(A ∩ B) / P(B).To find P(B | A), we use the formula P(B | A) = P(A ∩ B) / P(A). To determine if A and B are independent, we need to compare P(A ∩ B) with P(A)P(B). If P(A ∩ B) = P(A)P(B), then A and B are independent. If P(A ∩ B) ≠ P(A)P(B), then A and B are dependent.
a. Plugging in the given values, we have:
P(A | B) = 0.20 / 0.50 = 0.40
So, P(A | B) = 0.4000 (to 4 decimals).
b. Plugging in the given values, we have:
P(B | A) = 0.20 / 0.50 = 0.40
So, P(B | A) = 0.4000 (to 4 decimals).
c. Given values are:
P(A) = 0.50
P(B) = 0.50
P(A ∩ B) = 0.20
Calculating P(A) * P(B):
0.50 * 0.50 = 0.25
Since P(A ∩ B) ≠ P(A) * P(B), events A and B are not independent. The occurrence of one event affects the probability of the other event occurring.
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A restaurant offers a special pizza with any 5 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible?
Answers
By permutation without repetition, there are 524160 possible different special pizzas.
The possible special pizzas can be calculated with permutation without repetition. The formula of permutation without repetition can be written as
P = n! / (n - k)!
where P is all of the possible combinations, n is the number of objects or elements, and k is how many numbers should be chosen.
From the question above, we know that :
n = 16
k = 5
By substituting the parameters, we can determine all of the possible different pizzas
P = n! / (n - k)!
P = 16! / (16 - 5)!
P = 16! / 11!
P = 16 x 15 x 14 x 13 x 12 x 11! / 11!
P = 524160
Hence, there are 524160 possible different special pizzas
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Hurryyyy please u don’t have time I will give brainlist
This table shows the results of rolling a number cube with sides
labeled 1 through 6 several times.
Outcome
Number of times outcome occurred
1
10
What is the experimental probability of rolling a 2 or a 4?
2
6
Enter your answer as a fraction in simplest form in the box.
3
4
4
8
5
Basic
6
6
6
7
8
8
9
-
y
10
✓
.
4
1
5
6
х
Х
x
1
2.
3
<
>
+
$
0
+
+
%
0
.
:
A
&
=
=
TO
TT
Answers
Answer:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
18. 3
+
11
17
3
4
co
loo
8
Step-by-step explanation:
12. 5
11.
10
10
15. 7
14. 11
A drawer contains a dozen each of red,blue,green,ad white socks,all unmatched.Laura takes socks out at random in the dark.How many socks must laura take to be sure she has 2 pairs of white socks
Answers
Answer:
40 socks
Step-by-step explanation:
There are 48 socks in total inside the drawer. 2 pairs of white socks means four white socks. The worst possible scenario (however unlikely it is) is that Laura takes all of the red, blue and green socks before picking any white sock. From that point on, Laura has to pick four more socks in order to have two white pairs. In this scenario, there are 8 socks left in the drawer, all white. Therefore, the minimum number of socks that Laura must take to be sure that she has two pairs of white socks is:
\(n=(12*4) - 8\\n=40\ socks\)
She must take at least 40 socks.
Can we draw a triangle with sides 3cm 3.5 cm and 6.5 cm?
Answers
No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.
Let's understand the concept behind this:
Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.
We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.
Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.
AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.
AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.
AB + BC = 3 + 3.5 cm = 6.5 cm = AC.
However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.
Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.
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.Un recipiente cilíndrico de 5cm de radio y 10cm de altura se llena de agua. Si la masa del recipiente lleno es de 2kg, ¿cuál es la masa del recipiente vacío?
Answers
Answer:
La masa del recipiente vacío es 1,2146 kg.
Step-by-step explanation:
La densidad se define como la propiedad que tiene la materia, ya sean sólidos, líquidos o gases, para comprimirse en un espacio determinado. En otras palabras, la densidad es una magnitud que permite medir la cantidad de masa que hay en determinado volumen de una sustancia. Entonces, la expresión para el cálculo de la densidad es el cociente entre la masa de un cuerpo y el volumen que ocupa:
\(densidad= \frac{masa}{volumen}\)
Entonces la masa puede ser expresada como:
masa= densidad*volumen
En este caso:
densidad del agua= 1000 \(\frac{kg}{m^{3} }\)volumen del recipiente cilíndrico= π*radio²*altura= π*(5 cm)²* 10 cm= π*(0,05 m)²*0,1 m= 7,854*10⁻⁴ m³Reemplazando:
masa= 1000 \(\frac{kg}{m^{3} }\) * 7,854*10⁻⁴ m³
masa=0.7854 kg
Si la masa del recipiente lleno es de 2 kg, entonces se le resta la masa de agua calculada:
2 kg - 0,7854 kg= 1,2146 kg
Entonces, la masa del recipiente vacío es 1,2146 kg.
In a sale, the price of a book is reduced by 25%.
The price of the book in the sale is £12
Work out the original price of the book
Answers
Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book
Answer: £16
Step-by-step explanation:
To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.
75% of x = £12
To solve for x, we can set up the equation:
0.75x = £12
To isolate x, we divide both sides of the equation by 0.75:
x = £12 / 0.75
x = £16
Therefore, the original price of the book was £16.
Use basic integration formulas to compute the following antiderivatives of definite integrals or indefinite integrals. ∫(e−x−e4x)dx
Answers
The antiderivative of the function f(x) = e^(-x) - e^(4x) is given by -e^(-x) - (1/4)e^(4x)/4 + C, where C is the constant of integration. This represents the general solution to the indefinite integral of the function.
In simpler terms, the antiderivative of e^(-x) is -e^(-x), and the antiderivative of e^(4x) is (1/4)e^(4x)/4. By subtracting the antiderivative of e^(4x) from the antiderivative of e^(-x), we obtain the antiderivative of the given function.
To evaluate a definite integral of this function over a specific interval, we need to know the limits of integration. The indefinite integral provides a general formula for finding the antiderivative, but it does not give a specific numerical result without the limits of integration.
To compute the antiderivative of the function f(x) = e^(-x) - e^(4x), we can use basic integration formulas.
∫(e^(-x) - e^(4x))dx
Using the power rule of integration, the antiderivative of e^(-x) with respect to x is -e^(-x). For e^(4x), the antiderivative is (1/4)e^(4x) divided by the derivative of 4x, which is 4.
So, we have:
∫(e^(-x) - e^(4x))dx = -e^(-x) - (1/4)e^(4x) / 4 + C
where C is the constant of integration.
This gives us the indefinite integral of the function f(x) = e^(-x) - e^(4x).
If we want to compute the definite integral of f(x) over a specific interval, we need the limits of integration. Without the limits, we can only find the indefinite integral as shown above.
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.A crocodile opens his jaws at a 36° angle. He closes his jaws, then opens them
again at a 30° angle. In which case is the distance between the tip of his upper
jaw and the tip of his lower jaw greater?
Answers
Answer:
I would guess the 30 degree one.
Step-by-step explanation:
WILL GIVE BRAINLIEST PLS HELP!
sean solved the equation below to determine the solution. 3x-8= -x+4(x-2) How many solutions does sean have?
Answers
Answer:
Step-by-step explanation:
no solution
Solve each problem. Be sure to include the correct sign in your answer.
a. 8 × 3 = ?
b. –7 × 5 = ?
c. –6 × (–9) = ?
d. 8 ÷ (–2) = ?
e. –24 ÷ (–3) = ?
f. –36 ÷ 6 = ?
Answers
The solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Solve as shown below,
(a) 8 × 3 = 24
(b) –7 × 5 = -35
(c) –6 × (–9) = -(-54) = 54
(d) 8 ÷ (–2) = 8 × 1 / (-2) = - 4
(e) –24 ÷ (–3) = -24 × 1 / (-3) = 8
(f) –36 ÷ 6 = -36 × 1 \ 6 = -6
Therefore, the solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.
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Please show how to solve step by step with instructions and what formulas in Excel to use. Thank you.
Powder Puffs sells pom-poms to schools internationally. It has an offer from a private
buyer and the owners would like to know the value of each share of common equity so
they don't undervalue their shares. The cost of capital for this firm is 6.65% and there are
60,797 common shares outstanding. The firm does not have any preferred equity, however, it
has outstanding debt with a market value of $3,833,340. Use the DCF valuation model based
on the expected FCFs shown below; year 1 represents one year from today and so on. The
company expects to grow at a 2.2% rate after Year 5. Rounding to the nearest penny, what is the
value of each share of common stock?
Answers
The value of each share of common stock, rounded to the nearest penny, is approximately $66.61 according to the given information and values in the question.
step by step:
To calculate the value of each share of common stock using the Discounted Cash Flow (DCF) valuation model, we need to discount the expected future cash flows to their present value and subtract the market value of the outstanding debt. The formula for calculating the value of each share of common stock is:
Value per Share = (Present Value of Future Cash Flows - Debt) / Number of Common Shares
To calculate the present value of future cash flows, we discount each cash flow using the cost of capital.
Let's calculate the present value of future cash flows and the value per share of common stock:
Year 1: FCF = $250,000
Year 2: FCF = $300,000
Year 3: FCF = $350,000
Year 4: FCF = $400,000
Year 5: FCF = $450,000
\(Year 6 onwards: FCF = $450,000 * 1.022^(Year - 5)\)
Cost of Capital = 6.65%
Outstanding Debt = $3,833,340
Number of Common Shares = 60,797
First, let's calculate the present value of future cash flows:
\(PV = FCF / (1 + r)^n\)
where:
PV = Present Value
FCF = Future Cash Flow
r = Cost of Capital
n = Number of years
\(Year 1:PV1 = $250,000 / (1 + 0.0665)^1 ≈ $234,837.45Year 2:PV2 = $300,000 / (1 + 0.0665)^2 ≈ $268,084.17Year 3:PV3 = $350,000 / (1 + 0.0665)^3 ≈ $301,706.42Year 4:PV4 = $400,000 / (1 + 0.0665)^4 ≈ $335,693.63Year 5:PV5 = $450,000 / (1 + 0.0665)^5 ≈ $369,035.06Year 6 onwards:PV6 = $450,000 * 1.022^(Year - 5) / (1 + 0.0665)^Year\)
Now, let's calculate the total present value of future cash flows:
\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)\)
∑(PV6) represents the sum of present values for Year 6 onwards, up to infinity. Since we have a constant growth rate of 2.2%, we can use the perpetuity formula to calculate this sum:
\(∑(PV6) = PV6 / (r - g)\)
where:
r = Cost of Capital
g = Growth rate
\(∑(PV6) = PV6 / (0.0665 - 0.022) = PV6 / 0.0445Now, let's calculate PV6 and ∑(PV6):PV6 = $450,000 * 1.022^1 / (1 + 0.0665)^6 ≈ $303,212.65∑(PV6) = $303,212.65 / 0.0445 ≈ $6,820,510.11\)
Next, let's calculate the total present value:
\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)Total PV = $234,837.45 + $268,084.17 + $301,706.42 + $335,693.63 + $369,035.06 + $6,820,510.11Total PV ≈ $8,329,866.84\)
Finally, let's calculate the value per share of common stock:
Value per Share = (Total PV - Debt) / Number of Common Shares
Value per Share = ($8,329,866.84 - $3,833,340) / 60,797
Value per Share ≈ $66.61
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Suzy's Sculpting gym charges a $10 application fee and $12 per month for membership. Tami's Toning does not charge an application fee, but charges $14 per month for membership. After how many months will the total cost of membership be the same for both gyms?
Answers
Answer:
Total cost of membership will be the same for both gyms after 5 months.
Step-by-step explanation:
Given: Suzy's Sculpting gym charges a $10 application fee and $12 per month for membership.
Tami's Toning does not charge an application fee, but charges $14 per month for membership.
To find: After how many months will the total cost of membership be the same for both gyms
Solution:
Let \(t\) denotes number of months after which total cost of membership will be the same for both gyms
For Suzy's Sculpting gym,
Total charges \(= 10+12t\)
For Tami's Toning,
Total charges \(=14t\)
Now solve \(10+12t=14t\)
\(10+12t=14t\\10=14t-12t\\10=2t\\t=\frac{10}{2}\\ t=5\)
So, total cost of membership will be the same for both gyms after 5 months.
) 1. The table below shows a relationship between x and y.
ху
D»
O
y-2x-5
-2 1-5
y" 3x: 1
0 1
2
7
20
o
y = x+1
4
13
Which of the following equations best represents this relationship?
D
y=3x+1
Answers
Basically just try and follow rise over run or try and place numbers in the following formula
y2- y1
x2- x1
f(x)=3x-4 and g(x) = x2 find the value of f(3)-g(2)
show all work
Answers
Answer: 1
f(x) = 3x - 4 => f(3) = 3.3 - 4 = 9 - 4 = 5
g(x) = x² => g(2) = 2² = 4
=> f(3) - g(2) = 5 - 4 = 1
Step-by-step explanation:
I help video
Find the length of the third side. If necessary, write in simplest radical form.
Answer:
4
8
Submit Answer
Answers
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
6^2 + (2√7)^2 = c^2
36 + 28 = c^2
64 = c^2
c = 8
A movie theater has a seating capacity of 183. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
1316, How many children, students, and adults attended?
children attended.
Answers
Using simplification, if the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
From the given question,
We know that the capacity of movie theater is 183.
The theater charges $5.00 for children, $7.00 for students and $12.00 of adults.
There are half as many adults as there are children.
If the total ticket sales was $1316, then we have to find how many children, students, and adults attended.
Let the number of children that attended = x
Since, there are half as many adults as children.
Therefore number of adults = 1/2x =0.5x
We know there are total of 183 tickets
Therefore number of students = 183 - x - 0.5x
number of students = 183 - 1.5x
Each children ticket costs = $5
Then the price of children tickets = 5x
Similarly for adults each ticket costs = $12
So total cost of adult ticket = 12×0.5x = $6x
Now the cost of student tickets = 7(183 - 1.5x)
As given that
Total cost of all tickets = $1316
So the expression should be
5x + 6x + 7(183 -1.5x) = 1316
Simplifying
11x + 1281 - 10.5x = 1316
Subtract 1281 on both side
11x + 1281 - 10.5x-1281 = 1316-1281
Simplifying
0.5x = 35
Divide by 0.5 on both side we get
x = 70 children
Now finding the number of adults
= 0.5x
= 0.5×70
= 35 adults
Now finding the number of students
= 183 - 1.5x
= 183 - 1.5×70
= 183 - 105
= 78 students
Hence, If the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
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Work out the area of a rectangle with base, b = 14mm and perimeter, P = 30mm
Answers
Answer:
14 mm squared is the area
Step-by-step explanation:
Does anyone know the answer so this question
Answers
Step-by-step explanation:
f(3)= -2*3^2 +3 -5
= -2*9 +3 -5
= 16
At noon, Trevor and Kim start running from the same point. Trevor runs east at a speed of 8 km/h and Kim runs west at a speed of 6 km/h. At what time will they be 21 km apart?
Answers
Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.
To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.
Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.
Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:
Total distance = 8t + 6t
We want to find the time when this total distance equals 21 km:
8t + 6t = 21
Combining like terms, we have:
14t = 21
To solve for t, we divide both sides of the equation by 14:
t = 21 / 14
Simplifying, we find:
t = 3 / 2
So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.
Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.
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Compare -4 and -9
Greater than or less than
Answers
-4 is closer to 0 than -9
it is further right on the number line
Which statement is correct?A. -1.5 < -2, B. 2.5 < -3 ,C, 3.5 <2.5 D, 2<-1
Answers
What is the НСF of
4725
5850
Answers
Answer:
433345344 Answer
Step-by-step explanation:
type in symbols to make 2,3,7, and 12 equal 55
Answers
Answer: 3(7+12) - 2
Step-by-step explanation:
Which expression is equivalent to is Measure of angle 4? A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6. Measure of angle 2 measure of angle 3 Measure of angle 1 measure of angle 2 Measure of angle 1 measure of angle 3 Measure of angle 5 measure of angle 6.
Answers
Answer: Measure of angle 2 + measure of angle 3
Step-by-step explanation:
The expression is equivalent to is Measure of angle 4 is ''Measure of angle 2 + measure of angle 3''.
Given
A triangle has angles 1, 2, 3.
The exterior angle to angle 1 is 4, angle 2 is 5, to angle 3 is 6.
Exterior angle;An exterior angle is an angle that is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side.
The,
The measure of the angle 4 is;
The measure of angle 2 + measure of angle 3
Hence, the expression is equivalent to is Measure of angle 4 is ''Measure of angle 2 + measure of angle 3''.
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Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)
Answers
Answer:
y - 6 = -1 (x+5)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula \(m = \frac{y_2-y_1}{x_2-x_1} \\\). Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:
\(m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1\)
So, the slope of the line is -1.
2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula \(y-y_1 = m (x-x_1)\) and substitute real values for the \(m\), \(x_1\), and \(y_1\).
Since \(m\) represents the slope of the line, substitute -1 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:
\(y-6 = -1(x+5)\)
Please help answer this question!! 20 points!!!!
Answers
Answer:
Relative to such interrogate proposed, the answer is identified as 5520, if quantities ‘a’ and ‘b’ were to subject to define, given such conditions.
Step-by-step explanation:
Understood:
- Such quantity is a four (4) digit number, as explicitly stated.
- The value must be divisible by three (3). Thus, once the digits are summed, such quantity must be able to divide, and distribute evenly, into three (3).
- Likewise, such number is obligated to be divisible by five (5). Thus, the last digit of such quantity must end in either a ‘5’ or a ‘0’.
We were given the mathematical expression: 5a2b
5 + 2 = 7 + x = a number that is divisible by three, as stated in the problem.
X could be a list of differentiated number(s), although for a simplicity, x could be equated to as 5 to produce 12 (which is a factor of three, hence, divisible by three).
Now that ‘a’ has been substituted, ‘b’ must be substituted, similarly:
With ‘b’, we could appoint any number, so long that is either a 5 or 0 in the last digit, hence producing a value divisible my five.
For simplicity, which choosing either 5 or 0 does not make a difference, I will choose zero.
Thus, the rectified answer to such an interrogate is 5520. The difference between the largest of such number and the smallest is their abilities to become divisible by a certain constant ‘a’ and ‘b’.
*I hope this helps.
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