how many multiplications will each of the functions power1, power2, and power3 perform when computing 332? 319? e. how many recursive calls will power2 and power3 make when computing 332? 319?
The number of multiplications for the power₁ is 3 multiplication power₂ is one multiplication and power₃ is 5 multiplications and the number of recursive calls will power2 and power3 make when computing 332 and 319 is 5.
First, let's look at power₁. This function can compute the power of a number by repeated multiplication. For example, to compute 3 to the 4th power, power₁ would perform three multiplications: 3 x 3 x 3 x 3 = 81.
Using this approach, we can see that to compute 3 to the 32nd power, power₁ would perform 31 multiplications (3 x 3 x 3... repeated 31 times). Similarly, to compute 3 to the 19th power, power₁ would perform 18 multiplications.
Next, let's consider power₂. This function uses a different strategy for computing powers. It relies on the fact that any number can be expressed as a power of 2
To compute 3 to the 32nd power using power₂, we would first express 32 as a sum of powers of 2:
=> 32 = 2⁵ + 2⁴ + 2³.
Then, we would use the fact that 3 raised to a power of 2 can be computed with just one multiplication: 3² = 9.
Using this fact repeatedly, we can compute 3 to the 32nd power with only 5 multiplications:
=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.
For 3 to the 19th power, power2 would express 19 as 2⁴ + 2¹ and then use 4 multiplications:
=> 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3.
Finally, let's look at power3. This function is similar to power2 but uses a more efficient algorithm called exponentiation by squaring. This algorithm works by repeatedly squaring the base and halving the exponent until the exponent is 1.
To compute 3 to the 32nd power using power₃, we would start with the binary representation of 32 (100000 in binary).
we can see that power₃ will only perform 5 multiplications to compute 3 to the 32nd power.
Similarly, to compute 3 to the 19th power, power₃ would start with the binary representation of 19 (10011 in binary) and use the exponentiation by squaring algorithm to perform only 6 multiplications.
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Complete Question:
How many multiplications will each of the functions power₁, power₂, and power₃ perform when computing 332? 319?
a theater charges $8 for main floor seats and $5 for balcony seats. for a full house, the ticket income is $4,200. at one show, only 25% of the main floor seats and 40% of the balcony seats were sold for a total of $1,200. how many main floor tickets and how many balcony tickets were sold for this show?
By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.
Let x = number of seats on the main-floor
y = number of balcony seats
We know that if all the seats are sold, then the total income is $4,200, we can write the equation:
x*8 + y*5 = $4,200
And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:
0.25*x*8 + 0.4*y*5 = $1,200
x*2 + y*2 = $1,200
2(x + y) = $1200
x + y = $600
x = 600 - y
putting the value of x in equation1)
8(600-y) + 5y = 4200
4800 - 8y + 5y = 4200
3y = 600
y = 200
and x = 600 - 200 = 400
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Rewrite 26/9 as a mixed number. help me
The required mixed number of 26/9 is given as 2 8/9.
What is a mixed number?A mixed number is a number that consists of a whole number and a proper fraction. It is written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the proper fraction, and "c" is the denominator of the proper fraction.
Here,
To rewrite 26/9 as a mixed number, we need to divide the numerator (26) by the denominator (9) and express the result as a whole number and a proper fraction.
26 ÷ 9 = 2 with a remainder of 8
The whole number part is 2, and the proper fraction part is 8/9, since 8 is the remainder and 9 is the denominator.
Therefore, 26/9 as a mixed number is 2 8/9.
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Help, please. 50 points
The trapezoid is made up of a rectangle and a triangle. The total area of the trapezoid is 75 square centimeters. what is the length of the base of the triangle?
Step-by-step explanation:
use the pythagors theorm b square = h2 -p2
then the 10 cm is parallel so use area of right angled triange =1/2 b×p
In the figure below, find mzABC.
B
D
m/ABC=
The measure of angle ABC from the given circle D is 34°.
What is angles in the same segment theorem?The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.
Given that, circle with the center D and measure of arc AC is 34°.
The measure of arc = m∠ABC
m∠ABC =34°
Therefore, the measure of m∠ABC is 34°.
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There are 250 people in a museum
2/5 of the 50 peoples are girls
3/10 of the 50 people are boys
The rest of the 250 people are adults
Work out the number of adults in museum
The number of adults in the museum, using the fractional value of girls and boys, is 75.
What is a fractional value?A fractional value refers to a portion of the total value.
A fractional value can be depicted in fractions, decimals, or percentages.
A fractional value can also be represented as a ratio or proportion.
In this situation, the fractional number of adults is determined using subtraction.
The total number of people in a museum = 250
The fraction of girls in the museum = 2/5
2/5 of 250 = 100 girls
The fraction of boys in the museum = 3/10
3/10 of 250 = 75
Alternatively:
2/5 + 3/10 = 7/10
7/10 of 250 = 175
Therefore, the number of adults = 75 [250 - (100 + 75)]
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Complete Question:There are 250 people in the museum.
2/5 of the 250 people are girls.
3/10 out of the 250 people are boys.
The rest of the 250 people are adults.
Work out the number of adults in the museum.
A football coach is trying to decide what team is ahead lay in the girl with strategies better play the regular Defense play a prevent DFS the guards or against lol games, but make sure Gaines easier the coach of use the outcome of 100 games
The greater probability is the probability of winning through the use of regular defense.
How to solve for the probabilityIf out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well
Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.
The probability to win by regular is 38 / 50 = 0.76
the probability to win by prevent defense is 29 / 50 = 0.58
0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.
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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?
Play the "regular" defense.
Play a "prevent" defense that guards against long gains but makes short gains easier.
The coach reviews the outcomes of 100 games.
Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.
y-x²-14x=54
43=y-6x
non linear simultaneous equations
Solution of the system of equations y - x²- 14x = 54 and 43 = y - 6x are
x = -4 ± √5 and y = ± 6√5 + 19
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given equations
y - x²- 14x = 54
y = x² + 14x + 54 -------------(1)
43 = y - 6x
y = 6x + 43 ------------(2)
By equation (1) and (2)
6x + 43 = x² + 14x + 54
x² + 14x + 54 - 6x -43 = 0
x² + 8x + 11 = 0
a = 1, b = 8, c = 11
x = (-b ± √(b² - 4ac))/2a
x = (-8 ± √(64 - 4.11))/2
x = -4 ± √16-11
x = -4 ± √5
Putting value of x in equation (2)
y = 6(-4 ± √5) + 43
y = -24 ± 6√5 + 43
y = ± 6√5 + 19
Hence, x = -4 ± √5 and y = ± 6√5 + 19 are the solutions of equations
y - x²- 14x = 54 and 43 = y - 6x.
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an exponential function passes through the points (0, 11) and (3, 1375). what are the values of and ?
The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.
To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.
Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:
11 = [tex]a * b^0[/tex]
Since [tex]b^0[/tex] = 1 for any value of b, we have:
11 = a * 1
So a = 11.
Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:
1375 = [tex]11 * b^3[/tex]
Dividing both sides of the equation by 11, we have:
125 = [tex]b^3[/tex]
By combining the cube roots of the two sides, we obtain:
b = 5
So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].
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The complete question is:
an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?
if a t test yields p > 0.05 the null hypothesis would normally be: select one: a. accepted. b. rejected. c. accepted under certain conditions. d. there is not enough information for you to evaluate the findings.
if a t test yields p > 0.05 the null hypothesis would normally be option (A) accepted
The null hypothesis defined as the types of hypothesis that do not have any statistical significance exist in the given set of observation.
The p value is defined as the measurement that is used to validate the hypothesis using the observed data. The range of the p value varies from zero to one. Zero means no chance and 1 means absolute certainty
If a t test yields a p-value greater than 0.05, it means that there is insufficient evidence to reject the null hypothesis, and the results are not statistically significant. Therefore, the null hypothesis is accepted.
Therefore, the correct option is (A) accepted
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4 Bob makes dry concrete by mixing cement, sand and stone in the ratio 1:2:3 by weight.
He buys the cement, sand and stone in bags as shown in this table.
Cement
Sand
Stone
Weight of bag
(kg)
25
20
15
Cost per bag
(£)
5.50
2.00
3.90
ratios
He packs the dry concrete into 30 kg bags.
Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.
(a) Show that Bob buys 500 kg of sand.
Bob needs to buy 500 kg of sand.
What is the ratio?
A ratio is a quantitative relationship between two numbers, quantities, or values that expresses how many times one is contained in the other. Ratios are typically expressed in the form of "a to b" or "a:b" and can be represented as fractions or decimals.
Since the ratio of cement to sand to stone is 1:2:3 by weight, the total weight of the ingredients needed to make one bag of dry concrete is:
Cement: 1/6 of 30 kg = 5 kg
Sand: 2/6 of 30 kg = 10 kg
Stone: 3/6 of 30 kg = 15 kg
To make 50 bags of dry concrete, Bob will need 50 times these amounts:
Cement: 5 kg x 50 = 250 kg
Sand: 10 kg x 50 = 500 kg
Stone: 15 kg x 50 = 750 kg
Hence, Bob needs to buy 500 kg of sand.
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
You have 4/6 cup of oatmeal in your cupboard. A recipe for cookies calls for 1/4
cup of oatmeal. How much oatmeal would you have left if you made the
cookies
Answer:
5/12
Step-by-step explanation:
4/6 - 1/4 The common denominator would be 12
8/12 - 3/12 = 5/12
Answer:
5/12
Step-by-step explanation:
mark me please
4. The table shows the number of beads used to make a necklace. Ginger wants to make a smaller necklace using the same ratio of pink to white beads. How many different necklaces could Ginger make? How do you know?
The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.
How to find the number of necklaces ?To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.
Pink beads : White beads
30 : 35
( 30 / 5 ) : ( 35 / 5 )
6 : 7
To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:
= 30 / 6
= 5 necklaces
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Discuss THREE ways on how bad behaviour in sport in a country can
dampen nation building.
(3 x 2) C
Fynlain
ba
ode
f
othie
in.
enorts can encourage positive
Answer:
Step-by-step explanation:
chicken
There are 10 people in a group. 3 are red and 7 are blue. They vote yes or no.
What is probability that all 3 red people vote no and all 7 blue people vote yes?
Answer:70% chance they vote yes
Step-by-step explanation:
Answer:
3/10 for red people and 7/10 for blue people.
Step-by-step explanation:
which of the following is the best interpretation of the power of a significance test? responses power is the probability of detecting an effect if no effect exists. power is the probability of detecting an effect if no effect exists. power is the probability of detecting an effect if an effect exists. power is the probability of detecting an effect if an effect exists. power is the probability of detecting an effect whether or not an effect exists. power is the probability of detecting an effect whether or not an effect exists. power is the probability of not detecting an effect if no effect exists. power is the probability of not detecting an effect if no effect exists. power is the probability of not detecting an effect if an effect exists.
The power in a significance test is the probability of detecting a true effect, while the probability of making a type II error is the complementary probability of power.
A significance test is a statistical method used to determine whether an observed difference or effect is statistically significant or simply due to chance.
Power is defined as the probability of detecting an effect in a significance test if an effect truly exists. In other words, it is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. The null hypothesis assumes that there is no significant difference between two groups, while the alternative hypothesis states that there is a significant difference.
Mathematically, power is calculated using the following formula:
Power = 1 - β
Where β is the probability of making a type II error, which is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. In other words, it is the probability of not detecting an effect when an effect truly exists.
Therefore, power and β are complementary probabilities. If power is high, β is low, and vice versa. A significance test with a low power has a higher chance of making a type II error, meaning that it can fail to detect a real effect. Conversely, a test with a high power has a lower chance of making a type II error, meaning that it can detect a real effect more accurately.
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What is the graph of the following function? Click on the graph until the correct one appears.
g(x) = {<1}X-2, X21-4x+3, x < 1
Pls i need help !!!
The graph of the piecewise function is given by the image presented at the end of the answer.
How to graph the piecewise function?A piecewise function is a function that has multiple definitions, according to it's input values.
The two definitions for this problem are given as follows:
Until x = 1.Right of x = 1.For the values until x = 1, we have an increasing linear function, with intercept of y = -2, and finishes at the point (1,-1).
For the values greater than x = 1, the function is a linear function, starting at the point (1,-1), and decaying.
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I need help
I'm confused
According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...
How to identify the sequences that belong to each category?To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.
On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:
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You are building a ramp that must cover a horizontal distance of
exactly 13 feet. The angle of the ramp from the ground is 8°.
Determine the length of the ramp, in feet. Round to two decimal
places as needed.
The length of the ramp that must cover the horizontal distance is 13.13 feet.
What is the length of the ramp, in feet ?Given the data in the question, this forms a right-triangle.
Angle θ = 8°Adjacent of angle θ = 13ftLength of the ramp = hypotenuse = ?To solve for the length of the ramp, we use trigonometric ratio
Cosine = Adjacent / Hypotenuse
Plug in the values
cos( 8° ) = 13ft / hypotenuse
Hypotenuse = 13ft / cos( 8° )
Hypotenuse = 13.13 ft
Therefore, the ramp's length is 13.13 ft.
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Select the correct answer.
If f(x) = 3x+2 and g(x) = 2x - 2. what is (f- g)(x)?
OA. X+4
OB. X-2
OC. X
OD. 5x-2
O E.
X-4
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1
= 3x + 2 - 2x + 2 ← collect like terms
= x + 4
Next
Save
1
The distance between Dallas and Houston is about 364 kilometers. There are approximately
measurement is closest to the number of miles between these two towns?
Answer
A 227.5 miles
B 582.4 miles
C 40 miles
D 372 miles
In a case whereby the distance between Dallas and Houston is about 364 kilometers the approximately measurement is closest to the number of miles between these two towns is A 227.5 miles.
How can the the approximately measurement be determined?The concept that will be used here is unit conversion. It should be noted that 1 Mile = 1.609344 kilometres.
Then Xmile = 364 kilometers
We can cross multiply to have
Xmile =364 kilometers/1.609344 kilometres.
=226.179
Hence the closest to the number of miles is A 227.5 miles
Therefore, option A is correct.
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if you generate multiple datasets from a distribution with a given mean and variance, the mean and variance that you calculate from the generated data will always be the exact same as the original?
If we generate the multiple datasets from a distribution with a given mean and variance , then mean and variance of from generated data will not be same .
The sample mean and the variance are random variables that vary from sample to sample, even if the samples are drawn from the same population.
When we generate a sample from a distribution with a known mean and variance, the sample mean and variance will be estimates of the population mean and variance ;
So , because of sampling variability, the estimates obtained from different samples may differ from one another and from the true population parameters.
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Select the correct answer.
What is the value of x in the triangle?
7√3
60°
OA. 21
OB. 10
O C.
C. 7
O D. 7√3
30%
The value of x in the triangle is equal to: A. 21.
What is a 30-60-90 triangle?In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).
Note: x is the side opposite to the 60° angle.
The side opposite to the 60° angle, x = 7√3 × √3
The side opposite to the 60° angle, x = 7 × 3
The side opposite to the 60° angle, x = 21 units.
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Sarah charges $12 an hour when she
babysits. She also charges a non-refundabl
$5 fee just for showing up. What equation
could be used to represent the relationship
between x, the number of hours she
babysits, and y, the amount of money she
makes? jo
The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.
What is the relationship between x and y as described?It follows from the task content that the relationship between y and x is to be.
By comparison with the slope-intercept equation; y = mx + c.
Since, slope, m is the rate of change; m = 12$ per hour.
Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.
Therefore, the required equation is;
y = 12x + 5.
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what’s (-3x^5)^2 times 4x^3
Answer:36x^13
Step-by-step explanation:
We can solve this problem using the rule of exponents: (am)n = amn.
First, let's simplify the exponent on the first term:
(-3x^5)^2 = (-3x^5) × (-3x^5)
Next, let's multiply this by 4x^3:
(-3x^5)^2 × 4x^3 = (-3x^5) × (-3x^5) × 4x^3
Now, let's multiply the coefficients and combine the exponents:
(-3 × -3)x^(5 + 5 + 3) = 36x^13
Therefore, the answer is 36x^13.
Please help asap!!! :) 84 points if done correctly.
Answer:
[tex]\boxed{\checkmark}\;\;52 = 8n + 4[/tex]
[tex]\boxed{\checkmark}\;\;4(2n + 1) = 52[/tex]
[tex]\boxed{\checkmark}\;\;4 = 52 - 8n[/tex]
[tex]\boxed{\phantom{\checkmark}}\;\;4n = 48[/tex]
[tex]\boxed{\checkmark}\;\;n = 6[/tex]
Step-by-step explanation:
To determine if the equations are equivalent, solve the equations for n.
Option 1
[tex]\begin{aligned}\implies 52&=8n+4\\52-4&=8n+4-4\\48&=8n\\48\div 8&=8n \div 8\\6&=n\\n&=6\end{aligned}[/tex]
Option 2
[tex]\begin{aligned}\implies 4(2n+1)&=52\\8n+4&=52\\8n+4-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]
Option 3
[tex]\begin{aligned}\implies 4&=52-8n\\4+8n&=52-8n+8n\\4+8n&=52\\4+8n-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]
Option 4
[tex]\begin{aligned}\implies 4n&=48\\4n \div 4&=48 \div 4\\n&=12\end{aligned}[/tex]
Option 5
[tex]n=6[/tex]
Therefore, the equations that are equivalent are:
52 = 8n + 44(2n + 1) = 524 = 52 - 8nn = 6A system of equations is shown.
y=x+1
x-2y=-4
Which represents the solution of this system?
O(-2, -3)
O(-2, 3)
(2, -3)
(2, 3)
Find the area under the standard normal distribution curve between =z−1.97 and =z1.21. Use The Standard Normal Distribution Table and enter the answer to 4 decimal places.
What is the percent of change from 90 to 18?
* 80% increase
*80% decrease
*75% decrease
*75% increase
*25% increase
The percent of change is the change in value in percent from 90 to 18 that is an 80% decrease.
To calculate the percent change from 90 to 18, we first need to find the difference between the two values:
Change = Final Value - Initial Value
Change = 18 - 90
Change = -72
The negative sign indicates that there has been a decrease in value.
To find the percent change, we can use the following formula:
Percent Change = (Change / Initial Value) x 100%
Percent Change = (-72 / 90) x 100%
Percent Change = -80%
So there is decrease in percent from 90 to 18 that is by 80%.
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what's the rate of change of -7≤x≤-2
Answer:
4
Step-by-step explanation:
Rate of change forumla
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
We have our X points, -7 and -2. Now to find the Y value at those places.
For -7, Y is 5
For -2, Y is 25
Now we plug this into the equation
[tex] = \frac{25 - 5}{ - 2 - ( - 7)} = \frac{20}{5} = 4[/tex]
