To raise 4 to the 13th power using regular exponentiation, a total of 12 multiplications are required.
How many multiplications are required to raise 4 to the power of 13 using regular exponentiation?To raise 4 to the 13th power using regular exponentiation, we can start by multiplying 4 by itself 13 times. However, this would require a total of 13 multiplications, which is not the most efficient way to calculate 4^13.
Instead, we can use a method called "exponentiation by squaring", which reduces the number of multiplications required. Here's how it works:
Start by writing the exponent (13) in binary form: 13 = 1101 (in binary).
Starting with the base (4), square it repeatedly, each time moving from right to left in the binary representation of the exponent.
Whenever we encounter a "1" in the binary representation of the exponent, we multiply the current result by the base.
Using this method, we can calculate 4^13 with the following steps:
Start with 4.Square 4 to get 16.Square 16 to get 256.Multiply 256 by 4 to get 1024.Square 1024 to get 1,048,576.Multiply 1,048,576 by 4 to get 4,194,304.Square 4,194,304 to get 17,592,186,044,416.Multiply 17,592,186,044,416 by 4 to get 70,368,744,177,664.So, using exponentiation by squaring, we only needed a total of 7 multiplications instead of 13, which is much more efficient.
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A_____is a ratio that compares two measures
Answer:
rate
Step-by-step explanation:
A rate is a ratio that compares two different quantities that have different units of measure.
Mrs. Wilson wants to buy a portable TV for her kitchen. She has space on her counter for a TV that is 18 inches high by 15 inches wide. The store salesperson asks for the length of the diagonal. What should she tell him?
Halla el Perímetro y Area de las siguientes figuras: 1) Triángulo de lados 6 cm × 8 cm × 5 cm, con base en 8cm y altura de 3,73 cm. 2) Circunferencia de diámetro 4,5 cm.
Answer:
1) El triángulo tiene un perímetro cuyo valor es 19 cm y un área de 14,92 cm²
2) La circunferencia tiene un perímetro cuyo valor es 14,14 cm y un área de 15,90 cm²
Step-by-step explanation:
El perímetro es una medida de la distancia alrededor de una figura y el área da una idea de qué tanta superficie cubre dicha figura.
Entonces, el perímetro es la medida obtenida como resultado de la suma de los lados de una figura geométrica plana. Es decir, el perímetro es lo que mide el contorno de la figura.
El área de un triángulo es igual a base por altura dividido por 2.
Siendo r el radio de la circunferencia, el perímetro será calculado como:
P=2*π*r
y el área será:
A=π*r²
1) En este caso, el perímetro es calculado como:
P= 6 cm + 8 cm + 5 cm= 19 cm
Y el área del triángulo es calculada como:
[tex]A=\frac{base*altura}{2} =\frac{8 cm*3.73 cm}{2}[/tex]
A= 14,92 cm²
El triángulo tiene un perímetro cuyo valor es 19 cm y un área de 14,92 cm²
2) Siendo el diámetro un segmento de recta que va desde un punto de la circunferencia a otro y pasa por el centro del círculo y l radio la distancia desde el centro del círculo hasta un punto de la circunferencia, entonces, el radio es la mitad del diámetro.
Siendo el diámetro de la circunferencia 4,5 cm, entonces el radio r tiene un valor de 2,25 cm.
Entonces el perímetro será calculado como:
P=2*π*2,25 cm
P= 14,14 cm
y el área será:
A=π*(2,25 cm)²
A= 15,90 cm²
La circunferencia tiene un perímetro cuyo valor es 14,14 cm y un área de 15,90 cm²
Sandy has 10 roses, 2 daisies, and 8 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?
Answer: The greatest number of flowers that could be in a bouquet = 2
Step-by-step explanation:
Given: Sandy has 10 roses, 2 daisies, and 8 tulips.
Each bouquet has the same number of flowers and the same type of flower.
The greatest number of flowers that could be in a bouquet = GCD (10,2,8)
Since 10=2 x 5, 8 = 2 x 2 x 2
GCD (10,2,8) =2
Then, The greatest number of flowers that could be in a bouquet = 2
answer the quetions please look below
Answer:
38 in^2 and 26 in^2
Step-by-step explanation:
1. The formula of the area of a trapezoid is [tex]A = \frac{1}{2} (b_{1} + b_{2})h[/tex] where b = base and h = height.
So, [tex]A = \frac{1}{2} (7+12)(4)[/tex] = 38 [tex]in^{2}[/tex]
2. [tex]A = \frac{1}{2}(5+8)(4)[/tex] = 26 [tex]in^{2}[/tex]
No, Betsy is not correct. She likely forgot to multiply by 1/2 when calculating the area. The correct answer is 26 inches squared.
A(n)______ contains variables,numbers, and at least one operation.
Answer:
algebraic expression. An expression that contains at least one variable, at least one numbers and at least one operation.
Step-by-step explanation:
Answer:
expressions
Step-by-step explanation:
this is how a definition in a textbook would be written. they just put a blank in
can you say it in order
Ribbon costs $1.25 per meter. What would be the cost of 250 centimeters rounded to the nearest cent? HINT:
centimeters to meters before calculating the price
Answer:
The answer should be $3.125 or $3.13 rounded.
Step-by-step explanation:
First I divided 1.25 by 100 because 1 meter equals 100 centimeters.
1.25 ÷ 100 = 0.0125
Now that we know that it costs 0.0125 for 1 centimeter we multiply it by 250.
0.0125 * 250 = 3.125
Since it says to round to the nearest cent, the answer should be 3.13
Hope this helps! :)
What is Turtle divided by Kitten? YALL I NEED HELP ASAP ON THIS!!!!!!1
Answer:
rabbit!
Step-by-step explanation:
:-)
Your family is on the way to Disneyland! On the freeway you have driven for 120 minutes at a constant speed of 65 miles per hour before you stop for lunch. After lunch you get back on the freeway with a bit of traffic and drive at a constant speed of 40 miles per hour for 30 minutes before stopping for gas. How far did you drive in all? Use a ratio method.
Answer:
150 miles
Step-by-step explanation:
PLEASE HELP ASAP!!!!! 50 POINTS!!!!
Which of the following measurements, in centimeters (cm), could be the lengths of the sides of a triangle? Select all that apply.
Answer:
6m,6m,13m
Step-by-step explanation:
Someone plz help me I will give brainliest:)
"If we leave now," she said. "We'll be right on time."
"Do you have dear Mr. Henshaw? Alice, ask the clerk."
Blvd.
add ness to strange making it strangeness
I think that the broken tv is the subject
Answer:
1) "If we leave now" she said, "We'll be right on time.
2) "Do you have deer, Mr. Henshaw?" Alice asked the clerk.
3) blvd.
4) Er (Strang-er)
5) Television
Step-by-step explanation:
Hope this Helps!!:D
A real estate agent earns 3% commission for the sale of a $575,000 home. What is the commission earned?
A computer store pays $150 for a computer. The percent of markup is 45%.
What is the markup of the computer? What is the selling price of the computer?
A video game that regularly sells for $55 is on sale for 25% off.
What is the discount? What is the sale price of the video game?
Step-by-step explanation:
For the real estate agent: To find percent of a number, you can just divide by 100 and times it by the percent number, in this case it is 3.
$575,000 / 100 = $5,750
$5750 * 3 = $17,250
The agent earns $17,250.
For the computer store: Use the percentage and multiply it by 0.45, or whatever the percentage is.
150 * 0.45 = 67.5. This is the markup.
Now add the original value back to the markup.
150 + 67.5 = 217.5. This is the selling price of the computer.
For the video game: Use the percentage and multiply it by 0.25, or whatever the percentage is.
$55 * 0.25 = $13.75. This is the discount.
Now subtract the discount from the first value.
$55 - $13.75 = $41.25. This is the sale price.
Find q.
60 °
30 °
4
q
Write your answer in simplest radical form.
Answer:
q = 4√3
Step-by-step explanation:
the value of q = 4. root 3 = 4√3 units .
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hope this will be helpful to you .
Write an recursive formula for a_n and the n^th term of the sequence 3, -18, 108, If You answer this, you might become Brainliest
Answer:
an=a1+(n-1)*-6
Step-by-step explanation:
a1= 3
the recursive formula is an= a1+ (n-1)d
d= how you get from one to the other
to get from 3 to -18 you could either subtract 21 or multiply it by -6
to find which one you have to look at the next number which is 108
to get from -18 to 108 you would either add 126 or multiply it by -6
since multiplying by -6 is in both that is the answer
d= -6
an=a1+(n-1)*-6
Can someone help me thank you I have to show my work for these problems
Answer:
4. perimeter = 232cm
area = 1600cm²
5. perimeter = 30m
width = 8m
Step-by-step explanation:
Perimeter is the sum of the all the sides of a figure.
Area is given as length times breadth
message me for the rest of the answers and explanation
What is x- intercept of the equation 7x + 3y = 21
Answer:
no c xd estoy en séptimo no en otra cosa xd
A fruit sekker buts 50 boxes of mangoes each containing 100 m mangoes at the rate of ₹1200 per box he sells each mangoes for ₹20 find his total profit and profit %
Answer:
₹40000, 66.6%
Step-by-step explanation:
Given data
Number of boxes= 50
Cost per box= ₹1200
Total cost= 50*1200= ₹60000
Total number of mangoes in all 50 boxes= 50*100= 5000 mangoes
Cost price per mago= 60000/5000= ₹12
Selling price per mango= ₹20
profit = selling price- cost price
profit= 20-12
proft= ₹8
Total profit = 8*5000
Total profit= ₹40000
%profit = 40000/60000*100
%profit= 0.666*100
%profit= 66.6%
The scalene triangle ABC is translated 2 units to the right on a coordinate plane to form the scalene triangle DEF. The measure of segment AB=6 units, the measure of segment BC=5 units, the measure of segment CA=4 units, and m∠ABC=41°. Which of the following is a corresponding measure of triangle DEF?
Answer:
C: EF = 4 Units
Step-by-step explanation:
If the length of a basketball court is 32 meters and the width is 9 meters, what is the diagonal of the basketball court? Round to the nearest tenth, if needed.
A. 33.2
B. 23
C. 30.7
D. 41
Answer:
the answer is a
Step-by-step explanation:
En el puenlo de tamalemeque desean construir un parque de forma rectangular con un camino diagonal cuanto debe medir el camino si el parque deberia tener de 80 metros de largo y 60 de ancho como se puede determinar la medida,argumente su respuesta utilizando lo que sabe de matematicas
Answer:
El camino diagonal debe medir 100 metros de largo.
Step-by-step explanation:
Podemos encontrar el camino usando Pitágoras:
[tex] D^{2} = L^{2} + A^{2} [/tex]
En donde:
D: es el camino diagonal = hipotenusa
L: es el largo = 80 m = cateto
A: es el ancho = 60 m = cateto
Entonces, el camino diagonal es:
[tex] D = \sqrt{L^{2} + A^{2}} = \sqrt{(80 m)^{2} + (60 m)^{2}} = 100 m [/tex]
Por lo tanto, el camino diagonal debe medir 100 metros de largo.
Espero que te sea de utilidad!
An arc is 70.7 meters long and is intercepted by a central angle 5pi/4 radians. Find the diameter of the circle
Answer:
36.008 or 36
Step-by-step explanation:
Use the equation for the length of any circular arc
s = r(radians)
s - length of a circular arc
r - radius
radians - radian measure of the central angle
Then, set-up the equation:
s = r(radians)
70.7m = r(5pi/4)
Get variable "r" on one side by multiplying both sides by 4/5pi, which should result in the following:
r = 70.7m x 4/5pi
then solve for r
r = 282.8/5pi = 18.004
The radius is half the diameter therefore just multiply the radius by 2
d = 18.004 x 2
= 36.008 or 36
The diameter of the circle is 36 meters.
What is an arc?The arc is a portion of the circumference of a circle.
We have been given that an arc is 70.7 meters long and is intercepted by a central angle of 5π/4 radians.
We have to determine the diameter of the circle
For the length of the circular arc, use the equation.
⇒ 70.7 m = R(5π/4)
Multiply both sides by 4/5π to get the variable "R" on one side, which should get the following:
⇒ R = 70.7 m × 4/5π
⇒ R = 282.8/5π
∵ π = 3.14
⇒ R = 282.8/5(3.14)
⇒ R = 18.004
Since the radius is equivalent to half the diameter, simply double the radius by 2.
⇒ D = 18.004 × 2
⇒ D = 36.008 ≈ 36
Hence, the diameter of the circle is 36 meters.
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What is the difference in finding the exact vs approximate volume?
Answer:
An exact number is one that has no uncertainty. An example is the number of tires on a car (exactly 4) or the number of days in a week (exactly 7). An approximate number is one that does have uncertainty. ... The number can be the result of a measurement.
Step-by-step explanation:
What is the equation for a line that passes through the points (-4,-3) and (8,12)?
Answer:
y = 1.25x + 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
( -4 , -3 ) ( 8 , 12 )
12 + 3 15 = 5
8 + 4 12 = 4
↑ slope = 5/4
↓ point slope form: y - y₁ = m ( x - x₁ )
y + 3 = 5/4 ( x + 4 )
y + 3 = 5/4x + 5
-3
y = 5/4x + 2
Jim mad 2/3 of a pound weighed pizza. He gave the pizza to 6 friends. What was the weight of pizza each friend got?
Olive has 600 fruit trees. Some of the trees are apple trees. The rest of the trees are pears trees and plum trees in the ratio of 7:5 there are 175 plum trees what is the fraction of apple trees
Answer: 3/10
Step-by-step explanation:
Since the rest of the trees are pears trees and plum trees in the ratio of 7:5 and there are 175 plum trees, the number of pear trees will be:
= 175 ÷ 5/7
= 175 × 7/5
= 245
Plum trees = 175
Pear trees = 245
Apple trees = 600 - (175 + 245)
= 600 - 420
= 180
Fraction of apple trees = Number of apple trees / Total number of trees
= 180/600
= 3/10
A surveyor at point S locates a tree 200 meters away, at point T. The surveyor turns 120 degrees counterclockwise and locates a rock formation 150 meters away, at point R. Find the distance between the tree and the rock formation.
This will require using the law of cosines.
Answer:
190
Step-by-step explanation:
The distance between the tree and the rock formation is approximately 304.14 meters.
To find the distance between the tree (point T) and the rock formation (point R), we can use the law of cosines. The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Let's denote the unknown distance between the tree and the rock formation as 'd.'
We have a triangle with sides of lengths 200 meters (side ST), 150 meters (side SR), and d meters (side TR). The angle opposite side ST is 120 degrees.
According to the law of cosines:
d² = 200² + 150² - 2 * 200 * 150 * cos(120°)
Now, we can calculate this expression to find the value of d:
d² = 40000 + 22500 - 60000 * cos(120°)
Using the value of cos(120°) ≈ -0.5, we have:
d² = 40000 + 22500 - 60000 * (-0.5)
d² = 40000 + 22500 + 30000
d² = 92500
Taking the square root of both sides to solve for d:
d = √92500
d ≈ 304.14
Therefore, the distance between the tree and the rock formation is approximately 304.14 meters.
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Three friends are comparing their weekly paychecks. Donald discovers that he earned one-third of Michael's paycheque, and $80 less than Jacob's paycheque. Together, the three friends earned $2920 in one week. How much did each friend earn?
Answer: Michael's paycheque = $ 1704
Donald's paycheque = $ 568
Jacob's paycheque = $ 648
Step-by-step explanation:
Let x = Michael's paycheque
Donald's paycheque = [tex]\dfrac13x[/tex]
Jacob's paycheque = [tex]\dfrac 13 x+80[/tex]
Together, the three friends earned $2920 in one week.
[tex]\Rightarrow\ x+\dfrac13x+\dfrac13 x+80=2920\Rightarrow\ (\dfrac{3+1+1}{3})x=2920-80\\\\\Rightarrow\ \dfrac{5}{3}x=2840\\\\\Rightarrow\ x=2840\times\dfrac{3}{5}\\\\\Rightarrow\ x=1704[/tex]
Michael's paycheque = $ 1704
Donald's paycheque = [tex]\dfrac{1704}{3}=\$ 568[/tex]
Jacob's paycheque = $ 568+80 = $ 648
Hayden reaches into his dresser and pulls out a red shirt, but does not like it and throws in onto the bed. What is the chance that the next shirt he pulls out of the dresser will be Purple?
A. 2/10
B. 4 in 10 chance
C. 4 in 9 chance
D. 1/9 chance
Answer:
how many of each color are in the dresser?
Step-by-step explanation:
verify the segments are parallel
Step-by-step explanation:
I don't have a answer but try photo math app it might help you a lil