Each pizza slice has an area of approximately 12.82 square inches, rounded to the nearest hundredth.
To find the area of each pizza slice, we first need to find the total area of the pizza and then divide it by the number of slices.
The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( \pi \)[/tex] is approximately 3.14 and r is the radius of the circle.
Given that the radius of the pizza is 7 inches, we can calculate the total area of the pizza:
[tex]\[ A_{\text{total}} = \pi \times (7)^2 \]\[ A_{\text{total}} = 3.14 \times 49 \]\[ A_{\text{total}} \approx 153.86 \text{ square inches} \][/tex]
Now, to find the area of each pizza slice, we divide the total area by the number of slices (12):
[tex]\[ A_{\text{each slice}} = \frac{A_{\text{total}}}{12} \]\[ A_{\text{each slice}} \approx \frac{153.86}{12} \]\[ A_{\text{each slice}} \approx 12.82 \][/tex]
So, the area of each pizza slice is approximately 12.82 square inches.
Simplify (3x2 - x + 7) + (6x2-3)
Answer: [tex]9x^2-x+4[/tex]
Combine Like Terms
[tex]3x^2+-x+7+6x^2+-3\\(3x^2+6x^2)+(-x)+(7+-3)\\9x^2+-x+4[/tex]
Ethan borrowed $2,190 for a new dirt bike. He will pay the money back in 3 years with a simple interest rate of 2.5%. How much interest will he pay?
Answer:
The interest ethan will pay is $164.25Step-by-step explanation:
To calculate the interest paid by ethan on the borrowed bike using the formula.
Simple Interest = Principal * rate * time/100
Principal = $2,190, rate = 2.5%, time = 3years
On substitution
SI = [tex]\frac{2190*3*2.5}{100}[/tex]
[tex]SI = \frac{16,425}{100}\\ SI= $164.25[/tex]
The interest ethan will pay is $164.25
Ethan will pay $164.25 in interest for the loan he took for a new dirt bike, calculated using the formula for simple interest (I = PRT) with P as the principal ($2,190), R as the rate (2.5% or 0.025), and T as the time (3 years).
Explanation:To calculate simple interest, you can use the following formula: I = PRT, where I is the Interest, P is the principal amount (original amount borrowed), R is the interest rate (in decimal form), and T is the time in years. In this case, the principal amount is $2,190, the interest rate is 2.5% or 0.025 as a decimal, and the time is 3 years.
You would then plug these values into the formula to get:
I = 2190 * 0.025 * 3
After calculating that, we would find that Ethan will pay $164.25 in interest.
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Which of the following is equal to the rational expression when x*-2 or 3?
X^2 +5x+6/X^2-X-6
Answer:
i am very sorry but i am trying to solve it so wait a few minutes please
Step-by-step explanation:
Answer: D
x+3/x-3
Step-by-step explanation:
If you toss a coin 4 times, what is the probability of landing heads, heads, tails, heads and then heads?
Answer: 0%
Step-by-step explanation:
if you toss a coin 4 times you cant get 5 results.
PLease help, I need this in 2 minutes!
y÷2.3+5.69=7.58
Answer:
y=4.347
Step-by-step explanation:
To solve for y in the equation:
[tex]\dfrac{y}{2.3}+5.69 =7.58[/tex]
First, subtract 5.69 from both sides
[tex]\dfrac{y}{2.3}+5.69-5.69 =7.58-5.69\\\dfrac{y}{2.3}=1.89\\$Cross Multiply\\y=1.89 X 2.3\\y=4.347[/tex]
.
Alec Tomita's savings account statement is shown below. What is his new balance?
Previous Balance
Interest
Deposits
Withdrawals
$568.23
$2.37
$562.32
$874.36
$877.99
$2007.28
$628.56
$258.56
If the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that,
Previous Balance=$568.23
Interest=$2.37
Deposits=$562.32
Withdrawals=$874.36
We have to apply the addition and subtraction operations in order to find the new balance.
New balance = Previous Balance+Interest+Deposits-Withdrawals
New balance = $568.23+$2.37+$562.32-$874.36
New balance =$258.56
Thus, if the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.
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A bag contains yellow marbles and green marbles, 38 in total. The number of yellow marbles is 6 less than 3 times the number of green marbles. How many yellow marbles are there?
Answer:
3n - 6 = 38
3n -6 + 6 = 38 + 6
3n = 44
3n/3 = 44/3
n = 44/3
Step-by-step explanation:
1. set up the equation (the - affect the 6 not the 3)
2. add 6 to both sides
3. divide both sides by 3 to get n
PLEASE HELP I need an explanation please if not thanks anyway
Answer:
V = 24 mi^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 4*3*2
V = 24 mi^3
PLEASE HELP ME!! LIKE I NEED IT NOW!!
A DJ charges $150 for set-up and transportation, plus $65 per hour to entertain at a party. Which equation represents the relationship between the cost, y (in dollars), and the number of hours, x, for which the DJ is hired?
A DJ charges $150 for set-up and transportation, plus $65 per hour to entertain at a party. Which equation represents the relationship between the cost, y (in dollars), and the number of hours, x, for which the DJ is hired?
A. y= 150+65x
B. y= 65+150x
C. y=215x
D. y=65x
Answer:
A. y= 150+65x
Step-by-step explanation:
65 is the only number that changes. The 150 will be the same no matter what.
Evaluate the following
expression if x = 6.
3x
Answer:
3x would equal 18 is x was 6
Step-by-step explanation:
x=6
3*6=18
3x would equal 18
if a=2, b= -1, c= -3 and d= -2 find :
1/2bc-6ac+2ab
1/4(ac)² +1/6ac
Answer:
34
8
Step-by-step explanation:
1/2bc - 6ac + 2ab
(1/2)(-1)(-3) - (6)(2)(-3) + (2)(2)(-1)
(1/2)(4) - (-36) + (-4)
2 + 36 - 4
34
1/4(ac)² + 1/6ac
(1/4)[(2)(-3)]² + (1/6)(2)(-3)
(1/4)(-6)² + (1/6)(-6)
(1/4)(36) + (-1)
9 - 1
8
8y - 1-/2 ( 4y - 16)
Answer:
6y +8
Step-by-step explanation:
8y - 1-/2 ( 4y - 16)
Distribute
8y - 1/2*4y - 1/2 *-16
8y -2y +8
Combine like terms
6y +8
Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Michael and his merciless band of thieves. The Captain has probability 1 2 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability 1 6 6 1 start fraction, 1, divided by, 6, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Answer:
1/12
Step-by-step explanation:
If the Captain hits the pirate ship, it won't affect whether she's also hit by the pirate's cannons (and vice-versa), because they both fired at the same time. So, these events are independent.
Since they are independent, in order to get the probability that both the pirate and the Captain hit each other's ships, we just need to multiply together the probability that the captain hits and the probability that the pirate hits.
The probability that the Captain hits is 1/2
The probability that the pirate hits is 1/6
So, the probability that both the pirate and the Captain hit each other's ships is 1/2 * 1/6 = 1/12
Final answer:
The probability that Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%, calculated by multiplying the individual probabilities of each hitting the other's ship (0.5 for Captain Jessica and approximately 0.167 for the pirate).
Explanation:
To calculate the probability that both Captain Jessica and the pirate Michael hit each other's ships when they fire their cannons at the same time, we must consider each event independently and then multiply the probabilities of the two events since they are independent. Le'ts calculate the combined probability step-by-step.
First, we know that Captain Jessica has a probability of hitting the pirate ship which is ½ or 0.5.
Second, the dread pirate Michael has a probability of hitting the Captain's ship which is ⅙ or approximately 0.167 (1 divided by 6).
Since these are independent events, we multiply the two probabilities to find the combined probability of both events occurring together: 0.5 * 0.167 = 0.0835.
Therefore, the probability that both Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%.
A golfer is standing on a tee with a green in a valley below. If the tee is 43 yards higher
than the green and the direct distance from the green to the hole is 177 yards, find the
angle of depression from the tee to the green.
Answer:
[tex]13.65^0.[/tex]
Step-by-step explanation:
Given,
Height of tee, H = 43 yard
Direct distance of the hole is, D = 177 yards
Now, Angle of depression of tee
[tex]\tan \theta = \dfrac{H}{D}[/tex]
[tex]\tan \theta = \dfrac{43}{177}[/tex]
[tex]\tan \theta =0.2429[/tex]
[tex]\theta = 13.65^\circ[/tex]
Hence, angle of depression from tee to the green is [tex]13.65^0.[/tex]
If a rubber chicken driving an automaric driven telsa car went to mc donalds to buy nuggets which costed 6000 dollars a nugget and the chicken brought 3 nuggets, how much did Mr.rubber chicken pay?
Answer:
cannibalism
Step-by-step explanation:
11. The measure of an angle formed by two tangents to a circle is 90. If the radius of the circle
is 8 centimeters, how far is the vertex of the angle from the center of the circle?
Vertex of the angle is 11.31 cm far from the center of the circle.
Given in the question,
Measure of angle formed by two tangents of the circle (∠PVQ) = 90°Measure of the radius (OP)= 8 cmIn ΔOPV and ΔOQV,
OP ≅ OQ (Radii of the circle)
PV ≅ QV (Tangents from a point outside the circle)
OV ≅ OV (Reflexive property)
ΔOPV ≅ ΔOQV (SSS property of congruence)
Therefore, m∠PVO = m∠QVO = 45°
By triangle sum theorem,
m∠POV + m∠PVO + m∠OPV = 180°
m∠POV + 45° + 90° = 180°
m∠POV = 45°
Hence, ΔOPV is an isosceles triangle.
OP = PV = 8 cm
By applying Pythagoras theorem in ΔOPV.
OV² = OP² + PV²
OV² = 8² + 8²
OV = √128
OV = 11.31 cm
Therefore, vertex V is 11.31 cm from the center of the circle.
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The distance from the vertex of the angle to the center of the circle is 0 centimeters.
Explanation:In this problem, we have two tangents to a circle, and we are given that the angle between them is 90 degrees. We need to find the distance from the vertex of the angle to the center of the circle.
Since the angle between the tangents is 90 degrees, the tangents are perpendicular to each other. This means that the vertex of the angle is located on the circumference of the circle, and it forms a right triangle with the center of the circle and one of the points where the tangents intersect the circle.
Using the Pythagorean theorem, we can find the distance from the vertex to the center of the circle. Let's call this distance x. We know that the radius of the circle is 8 centimeters, so one leg of the right triangle is 8 centimeters. The other leg is x centimeters, and the hypotenuse is the radius of the circle plus x centimeters.
Applying the Pythagorean theorem, we have:
x^2 + 8^2 = (8 + x)^2
Simplifying the equation, we get:
x^2 + 64 = 64 + 16x + x^2
Cancelling out x^2 terms, we have:
64 = 64 + 16x
Subtracting 64 from both sides, we get:
0 = 16x
Dividing both sides by 16, we get:
x = 0
Since we cannot have a distance of 0, the equation does not have a solution. This means that the vertex of the angle is located at the center of the circle, and the distance is 0 centimeters.
Kyle is painting the front door of his house. The dimensions of the door are 80 inches by 36 inches by 2 inches. If he paints all of the surfaces, how much area will he paint?
Answer:
its 5760ins
Step-by-step explanation:
80 inches * 36 inches * 2 inches = 5760 inches3
good day, and be safe
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⊕ΘΞΠΤ⊕
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PARA HORNEAR UN PASTEL DE UN KILO SE NECESITA ENTRE OTROS INGREDIENTES UN TERCIO DE HARINA Y 3 CUCHARADAS DE VAINILLA CUANTA VAINILLA ES NECESARIA 3 KILOS Y MEDIO
Answer: 10 + 1/2 spoons of vanilla.
Step-by-step explanation:
This question says:
For 1kg of cake, we need 1/3 kg of flour and 3 spoons of vanilla.
How much vanilla do we need if we want to make a cake of 3 + 1/2 kg?
Ok, if for 1kg we need 3 spoons, then for (3 + 1/2)kg we need (3 + 1/2) times 3 spoons, this is:
(3 + 1/2)*3 spoons
=3*3 + 3/2 = 9 + 3/2 = 9 + 2/2 + 1/2 = 10 + 1/2
We need 10 + 1/2 spoons of vanilla.
What is the power of 1^5
Answer:
1x1x1x1x1
Step-by-step explanation:
1^5 is the same as 1x1x1x1x1 because a power multiplies a number by itself
Answer:
1x1x1x1x1
Step-by-step explanation:
1^5 = 1x1x1x1x1 = 1
(happy to help!!!)
The price of an item has been reduced by 70%. The original price was $31. What is the price of the item now?
Answer:
$9.3 dollars.
Step-by-step explanation:
To solve this question, you will need to begin by finding the percentage left of the original value:
100%-70%= 30% left.
Now, to find the exact value of the discounted item, you will solve for 30% (0.3) of $31:
0.3×31= $9.3 dollars.
Manesh is putting new tile on a kitchen counter. Each sheet of tile will cover 1.5 \text { ft}^21.5 ft
2
Answer: the answer is 12
Please help out before 8pm !!
Answer:
170 degrees
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary, meaning that they add up to 180 degrees. This means that x+10=180, or that x=170 degrees. Hope this helps!
If you know a length in a scale drawing and its corresponding length in the original drawing, how can you determine the relationship between the areas of the drawings? Explain. (Lesson 13,14 & 15 of module 4)
Answer:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
Step-by-step explanation:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
For example:
Given a scale factor of 25%, would the quotient of the area of the scale drawing to the area of the original drawing be?
Answer:
The quotient of the areas would be equal to the square of the scale factor. Therefore, the quotient of the scale drawing to the original in this example would be equal to [tex](\frac{1}{4}) ^{2}[/tex]
Hope it will find you well.
Teorema de pitágoras. Las medidas de los lados y la diagonal de un rectángulo son tres números impares consecutivos.
Hallar los valores de estos elementos.
Answer:
This question says:
"the lenghts of the sides and the diagonal of a rectangle are 3 odd consecutive numbers".
This means that if x is an odd number, then the meassures are:
x, x + 2, x + 4.
We add 2 in each case, because the next consecutive number of, for example, 3 is 3 + 2 = 5, and so on.
Now, from the Pitagoras theorem we know that, for a triangle rectangle, we have
A^2 + B^2 = H^2
where A and B are the cathetus, and H is the hypotenuse.
In our case the smaller odd numbers will be the cathetus and the larger one will be the hypotenuse.
x^2 + (x + 2)^2 = (x + 4)^2
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16
x^2 - 4x -12 = 0
now we need to solve this for x
we know that for a quadratic equation of the form:
ax^2 + bx + c = 0
the solutions are:
[tex]x = \frac{-b +- \sqrt{b^2 -4ac} }{2a}[/tex]
in our case we have:
[tex]x = \frac{4 +- \sqrt{16 +48} }{2} = \frac{4+-8}{2}[/tex]
The only positive value is x = 12/2 = 6
but 6 is not odd, so we can never have that the sides and the diagonal are odd consecutive numbers.
[tex]f(x)=\sqrt x+2[/tex]
What is the inverse?
Answer:
[tex](x-2)^2[/tex]
Step-by-step explanation:
To find the inverse of this function, you need to replace the location of the x and the y.
You start with [tex]y=\sqrt{x}+2[/tex]. Now, replace the x and the y, and try to isolate the y.
[tex]x=\sqrt{y}+2\\x-2=\sqrt{y}\\y=(x-2)^2[/tex]
Hope this helps!
HELP ASAP GIVING BRAINLIST AND A LOT OF POINTS!!!!!
Tara starts with $20, in which she buys 2 items for d amount. Subtract 2d from the total for your answer.
1) 20 - 2d
To find the average distance, add all the numbers together, and divide by the amount of numbers there are:
3) (t + w)/2
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chapter 8 question 7
please help wil mark brainlyest
Answer:
0.72
Step-by-step explanation:
[tex] \cos \: 44 \degree = 0.7193398003 \\ \cos \: 44 \degree =0.72[/tex]
For breakfast, Sarah can choose eggs, granola, or oatmeal as a main course, and orange juice or milk for a drink. How many possible outcomes are there in the sample space?
Answer:
6 outcomes
Step-by-step explanation:
3 (main courses) x 2 (drinks) = 6 outcomes
eggs - orange juice
granola - orange juice
oatmeal - orange juice
eggs - milk
granola - milk
oatmeal - milk
A 10-foot ladder leans against the side of a house with its base 2.2 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth. The ladder reaches feet high.
Answer:
Ladder reaches 9.76 high.
Step-by-step explanation:
From the figure attached,
Ac is the ladder which reaches at the point A when leans against the side of a house.
Length of the ladder = 10 feet
Distance of the ladder form the base of a house = 2.2 ft
By Pythagoras theorem,
AC² = AB² + BC²
(10)² = h² + (2.2)²
h² = 100 - 4.84
h = √95.16
h = 9.755 feet
≈ 9.76 feet
Therefore, the ladder reaches the 9.76 high.
The answer is 9.7 feet
Find the surface area