What should be added to 61.01 to get the smallest three-digit number?

The transformation that would linearize the data for volume and time is ln(Seconds), ln(cm3).

The correct option is (D)

To determine which transformation will linearize the data, we can look at the form of the relationship between volume and time in the scatterplot. Since the pattern is curved, it suggests that the relationship may be exponential. Therefore, we can try taking the logarithm of the volume or the time or both and see which transformation produces a linear relationship.

A) Seconds, cm3: This transformation does not involve taking the logarithm of either variable, so it is unlikely to linearize the relationship.

B) ln(Seconds), cm3: This transformation takes the natural logarithm of the time variable. It may help to linearize the relationship if the relationship is exponential with respect to time.

C) Seconds, ln(cm3): This transformation takes the natural logarithm of the volume variable. It is unlikely to linearize the relationship because it does not address the potential exponential relationship with respect to time.

D) ln(Seconds), ln(cm3): This transformation takes the natural logarithm of both variables. It is a good choice because it can linearize an exponential relationship between the two variables.

Therefore, the transformation that would linearize the data for volume and time is D) ln(Seconds), ln(cm3).

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When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

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Answer:

4/3 seconds

Step-by-step explanation:

Use the kinematic or SUVAT equation that involves initial velocity, final velocity, acceleration and time since these are what we know and what we want to find;

This formula is: v = u + at

v = final velocity

u = initial velocity

a = acceleration

t = time

Then, simply substitute variables with known values and rearrange or solve for t:

4 = 8 + (-3)t

4 = 8 - 3t

3t = 8 - 4

t = 4/3

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

No, none of the transformations could be applied to Circle K to make it match Circle B as a blue circle.

In order for Circle K to match Circle B as a blue circle, certain transformations would need to be applied. However, no single transformation can change the color of a circle from one color to another. Transformations such as translation, rotation, and scaling only affect the position, orientation, and size of an object, but they do not alter its color.

Therefore, applying any of these transformations to Circle K would not result in it becoming a blue circle.

To change the color of Circle K to match Circle B, a different approach would be needed. One possible solution could be to change the fill color or stroke color of Circle K directly. This can be achieved through programming or graphic editing software by modifying the color properties of Circle K.

However, this method does not fall under the category of geometric transformations, which are typically limited to altering the shape, position, or size of an object.

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer: last one i’m pretty sure

Step-by-step explanation:

The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:

x - 5y = 3

x = 5y + 3

Now we can substitute this expression for x into the second equation:

3x - 2y = -4

3(5y + 3) - 2y = -4

15y + 9 - 2y = -4

13y = -13

y = -1

We can now substitute this value for y back into either equation to find the value of x:

x - 5y = 3

x - 5(-1) = 3

x + 5 = 3

x = -2

Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.

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The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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The number of units manufactured at a cost of $9,500 is approximately 141.75 units.

The sunglasses will hit the ground after 100 seconds

The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.

The width of the floor is 6 feet, and the length is 9 feet.

Now we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -15, and c = -9,450.

Plugging these values in:

x = (-(-15) ± √((-15)² - 4(1)(-9,450))) / 2(1)

x = (15 ± √(15 + 18,960)) / 2

x = (15 ± √19,185) / 2

x ≈ 141.75

In order to find when the sunglasses will hit the ground, we need to find the time t when h(t) = 0.

h(t) = -16t + 1600 = 0

Solving for t:

-16t = -1600

t = 100

Therefore, the sunglasses will hit the ground after 100 seconds.

h(t) = -16t² + 80t

96 = -16t² + 80t

0 = -16t² + 80t - 96

0 = -t² + 5t - 6

0 = (t - 2)(t - 3)

The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.

2w² - 3w - 90 = 0

(2w + 15)(w - 6) = 0

If w - 6 = 0, then w = 6, which is a valid solution.

Therefore, the width of the floor is 6 feet, and the length is 2(6) - 3 = 9 feet.

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Answer:

a.- slope= 36

Interpretation : The cable car travels 36 meter per minute

b.- y = 36x + 100

c.- 640 meters

Step-by-step explanation:

a.-

Find slope using the slope formula : \(\frac{y2-y1}{x2-x1}\)

Plug in the two given points: \(\frac{1000-100}{25-0}\)

Subtract the numbers : \(\frac{900}{25}\)

Reduce the fraction : 36

b.-

Using the given y-interspet (100) and the slope create an equation: y = 36x + 100

c.-

Using the equation you created plug in 15 for x to find the

distance: y = 36 (15) + 100

Multiply the numbers : y = 540 + 100

Add the numbers : y = 640

Algorithm Il always works correctly, but Algorithm I only works correctly when the maximum value is greater than or equal to - 1

=====================================================

Explanation:

Let's say we have the data set {-4,-3,-2}. The value -2 is the largest.

If we follow algorithm 1, then the max will erroneously be -1 after all is said and done. This is because the max is set to -1 at the start even if -1 isn't in the data set. Then we see if each data value is larger than -1.

Each statement being false means we do not update the max to its proper value -2. It stays at -1.

This is why we shouldn't set the max to some random value at the start.

It's better to use the some value in the data set to initialize the max. Algorithm 2 is the better algorithm. Algorithm 1 only works if the max is -1 or larger.

The slope of a line perpendicular to the line whose equation is 3x+y=8 is 1/3.

The slope of a line perpendicular to the line whose equation is 3x+y=8 can be found by first finding the slope of the given line and then taking the negative reciprocal of that slope.

To find the slope of the given line, we can rearrange the equation to solve for y:

3x+y=8

y=-3x+8

Now we can see that the slope of the given line is -3. To find the slope of a line perpendicular to this one, we take the negative reciprocal of -3, which is 1/3.

Therefore, the slope of a line perpendicular to the line whose equation is 3x+y=8 is 1/3.

Answer: 1/3

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The expression of "21 equal negative 3 over 4 y" in algebraic notation is 21 =-3/4y

From the question, we have the following parameters that can be used in our computation:

21 equal negative 3 over 4 y

negative 3 over 4 y means -3/4y

So, we have the following

21 equal -3/4y

equal means =

So, we have

21 =-3/4y

Hence, the expression in algebraic notation is 21 =-3/4y

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The sum and difference of two cubes are written as follows

x³ + 8 = (x + 2)(x² - 2x + 4).

64x³ - 27 = (4x - 3)(16x² + 12x + 9).

54x³ - 2 - cannot be factored

x³ - 8 = (x - 2)(x² + 2x + 4).

The sum and difference of two cubes are written as follows

x³ + 8:

This can be factored as (x + 2)(x² - 2x + 4).

64x³ - 27:

This can be factored as (4x - 3)(16x² + 12x + 9).

54x³ - 2:

This cannot be factored using the sum or difference of two cubes formula. However, it can be factored as 2(27x³ - 1).

x³ - 8:

This can be factored as (x - 2)(x² + 2x + 4).

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Answer:

5.2

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

\(71\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ 172\% = \frac{172}{100} = 1.72 \\ 6\% = \frac{6}{100} = 0.06\)

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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Answer:

-g(x), g(2x), g(-x)

Step-by-st-ep explanation:

if f (–x) = f (x), so all of the signs are the same

you can also try on desmos, the graph is more helpful than words explain sometimes

The functions that are odd are -g(x), g(2x), and g(-x). The correct option is A, B, and E.

A function assigns the value of each element of one set to the other specific element of another set.

For an odd function, -f(x) = f(-x).

Given that the function, g(x) = 3x³ + x is an odd function. Therefore, the transformation of the function that will again result in an odd function is,

A.)  –g(x)

-g(x) = -(3x³ + x) = -3x³ - x

g(-x) = 3(-x)³ + (-1x = -3x³ - x

Thus, this is an odd function.

B.)  g(2x) ⇒ Since this will result in the same function, the only difference will be that the function will be vertically stretched.

E.)   g(–x)

-g(x) = -(3x³ + x) = -3x³ - x

g(-x) = 3(-x)³ + (-1x = -3x³ - x

Thus, this is an odd function.

Hence, the functions that are odd are -g(x), g(2x), and g(-x).

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Answer:

Step-by-step explanation:

Here in this given sequence, -16; -9; -2: _

a=-16

d=-9-(-16)=7

so,The 4th term=

Answer:

given sequence, -16; -9; -2: _

first term(a)=-16

common difference(d)=-9-(-16)=7

next term is 4

so

4th term=a+(n-1)d

=-16+(4-1)7=-16+21=5

c.5

Given:

\(3x+2x=34-5-4\)

\(5x=29-4\)

\(5x=25\)

\(x=25\div5\)

Answer:

x = 5

Given: 3x+4+2x+5=34

first combine similar values,

3x + 2x and 4 + 5

5x + 9 = 34

time for substitution

5x + 9 - 9 = 34 - 9

5x = 25

divide by the value of x in this instance it is 5

5x = 25 / 5

x= 5

now to check we will plug in 5 for x

3(5) +4+2 (5) +5=34

15 + 4 + 10 + 5 = 34

19 + 15 = 34

34 = 34✓

Hope this helps, happy learning =D

Answer: 32

Step-by-step explanation:

From the question, we are informed that Tenisha successfully made 24 out of 30 free throws during the first half of her basketball season. The fraction for her successful free throws will be:

= 24/30

= 4/5

If she shoots 40 free throws during the second half of the season and she continues to make them at the same rate, the number of free throws that she should Tenisha expect to make during the second half of the season will be:

= 4/5 × 40

= 32

The given expression is

- 36 > 6x + 12

By subtracting 12 from both sides of the inequality, we have

- 36 - 12 > 6x + 12 - 12

- 48 > 6x

Dividing both sides of the inequality by 6, we have

- 48/6 > 6x/6

- 8 > x

We can write this as

x < - 8

The effect of tripling the sample size while keeping the confidence level the same would be to reduce the margin of error from 0.09 to 0.049, and to narrow the confidence interval from (0.23, 0.41) to (0.263, 0.361).

Assuming that the sample is a simple random sample, we can use the formula for the confidence interval for a proportion:

Confidence interval = sample proportion ± margin of error

where the margin of error is:

Margin of error = z* (standard error)

and z* is the z-score corresponding to the desired level of confidence (in this case, 90%). For a 90% confidence interval, the z* value is 1.645.

The formula for the standard error is:

\(Standard error = \sqrt{[(sample proportion \times (1 - sample proportion)) / sample size]}\)

Using the information given, we can write:

0.23 ≤ sample proportion ≤ 0.41

z = 1.645

We can solve for the sample proportion as follows:

\((sample proportion \times (1 - sample proportion)) / sample size = (1.645 / 2.0)^2\)

Solving this equation gives:

\(sample size = (1.645 / 0.09)^2 \times (0.41 * 0.59)\)

So, tripling the sample size would give us a new sample size of 3 * 50 = 150.

Using the same formula for the confidence interval, but with the new sample size, we get:

\(Margin of error = 1.645 \times \sqrt{ [(sample proportion \times (1 - sample proportion)) / sample size]}\)

Setting the margin of error equal to 0.09 (the margin of error for the original sample), we can solve for the new sample proportion:

0.09 = 1.645 * sqrt [(sample proportion * (1 - sample proportion)) / 150]

Solving for the sample proportion gives:

sample proportion = 0.312

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The unknown angles are as follows:

An angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

In other words, a line that splits an angle into two equal angles.

Therefore, a bisector of an angle 120 degrees bisect the angle into 60 degrees.

Hence, FH bisect ∠EFG into the angles m∠EFH  and  m∠GFH .

Therefore,  m∠GFH  and m∠EFH are congruent.

m∠EFG = 119°

Hence,

m∠EFH = m∠GFH

Therefore,

m∠EFH  = 119 / 2

Hence,

m∠EFH  = 59.5°

m∠GFH  = 59.5°

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The largest palindrome made from the product of two 3-digit numbers is 906609.

To find the largest palindrome made from the product of two 3-digit numbers, we can start by considering all possible products of two 3-digit numbers, ranging from 100 to 999. We can then check if each product is a palindrome.

A palindrome is a number that reads the same forwards and backwards. We can iterate through the products in decreasing order and check if each product is a palindrome. If we find a palindrome, we compare it with the current largest palindrome found and update it if necessary.

Starting from 999 and iterating downwards, we multiply each number by all the 3-digit numbers below it. For example, we multiply 999 by 999, 998, 997, and so on. We continue this process until we find the largest palindrome.

After checking all possible products, we find that the largest palindrome made from the product of two 3-digit numbers is 906609. This palindrome is obtained by multiplying 993 by 913.

Therefore, the largest palindrome made from the product of two 3-digit numbers is 906609.

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Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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The equation of the line that is parallel to the line y = x 4 and passes through the point (6, 5) is y = x - 1

The line y = x + 4 has a slope of 1 because it is in the form y = mx + b, where m is the slope of the line. To find a line parallel to this line, we need to use the same slope of 1.

Now, we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (6, 5) with a slope of 1:

y - y1 = m(x - x1)

where m = 1, x1 = 6, and y1 = 5.

Plugging in the values, we get:

y - 5 = 1(x - 6)

Simplifying, we get:

y - 5 = x - 6

y = x - 1

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The economic order quantity is approximately 355 units, which corresponds to option D) 355 units.

To find the economic order quantity (EOQ), we can use the following formula:

EOQ = sqrt((2 * Annual Demand * Fixed Ordering Cost) / Carrying Cost per Unit)

Given information:

Annual Demand = 3,000 units

Fixed Ordering Cost = $30

Carrying Cost per Unit = $1.43

Substituting the values into the formula:

EOQ = sqrt((2 * 3,000 * 30) / 1.43)

EOQ = sqrt(180,000 / 1.43)

EOQ = sqrt(125,874.125)

EOQ ≈ 354.91

Rounding the EOQ to the nearest whole number, we get:

EOQ ≈ 355 units

Therefore, the economic order quantity is approximately 355 units, which corresponds to option D) 355 units.

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