7
7
^
Why is randomization important?
Select the statement that best answers the question.
to ensure all treatment groups receive experimental units
to ensure all treatment groups are roughly equivalent regarding the experimental units
to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units
4) Intro
English

Answer:

17.65%

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve

Answer:

Aisha, Arsenio

Step-by-step explanation:

Because it adds up to a total of 180 degrees

Answer:

y = 15, x = 4

Step-by-step explanation:

Hope this helped!

Answer:

y+15x=4

Step-by-step explanation:

Answer:

The conclusion on the additive inverse is correct while the conclusion on the multiplicative inverse is incorrect

Step-by-step explanation:

Here, we want to find out if what Angie is saying is correct or not.

The equation we are considering is m(t) = (-28/5)t

Let’s start with the additive inverse

When we talk of the additive inverse, we mean that particular value which when added to the original equation will give the identity element 0

She said this value is (28/5)t

This is actually correct. This is because when we add (-28/5)t to (28/5)t , we will get 0

Let’s look at the multiplicative inverse

When we talk of the multiplicative inverse, we are referring to that value, such that when we multiply it by the original expression, we will have a value of 1

This is actually incorrect. This is because an expression cannot be a multiplicative inverse of itself. Looking at the values given for the number and its multiplicative inverse, we can see that these values are actually the same which is not supposed to be so and hence, the two cannot be multiplicative inverse of each other.

Answer:

Angie is correct about the additive inverse only.

Step-by-step explanation:

Answer: 2x7=14

Step-by-step explanation:

There are only three numbers that go with each equation, all you have to do is eliminate the ones that don't match.

Answer:

There is significant preference among the 3 designs

Step-by-step explanation:

Given :

Design 1 Design 2 Design 3

54 38 28

H0 : no significant preference among the 3 designs

H1 : The preference among the designs are different

To test, we use the Chisquare test for independence ;

χ² = (observed - Expected)² / Expected

The sample size, n = 120

Expected = 120 / number of designs = 120 / 3 = 40

(54-40)^2/ 40 + (38 - 40)² / 40 + (28 - 40)² / 40

= 4.9 + 0.1 + 3.6

= 8.6

The Chisquare critical value at 95% = 5.99

Since ;

|χ² critical| < χ² statistic ; we reject the null and conclude that there is significant preference among the 3 designs

Answer:

A) D: 4.6

B) C: 5.12

Step-by-step explanation:

A) From the given options, the smallest number is 4.6 which is option D.

Due to the fact that the decimal sides from options A to the last are; 602, 620, 666..., 600.

This is because after the number 6, the remaining digits are assumed to be zero because there is no number attached again. The one that has 6 with dot above it means that it is a recurring decimal with 6. Thus, it can't be the smallest.

B) The largest is option C which is 5.12.

Because on the decimal sides, ranking from highest to lowest we have;

120, 111..., 102, 100. A number with dot on it means recurring decimal.

The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

The proof is given as:

Statement Reason

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The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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There are 2100 workers in​ the company

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since 85​% of the workers are women, we can say:

The percentage of worker that aren't women = 100% - 85​% = 15​%

Let N represent the number of all workers. If 315 people work for the company who​ aren't women. We can say:

15​% of N = 315

15/100 × N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

Method 2:

We can write:

N - 0.85N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

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Answer:

the first and third equation

Step-by-step explanation:

when you divide 1/4 by 5, you get 1/20. dividing 1/4 by 5 is also the same as multiplying 1/4 by 1/5.

Step-by-step explanation:

Confidence interval = 90% = 0.90.

1 - 0.90 = 0.10

Mean of 15 batch:

724+718+776+760+745+759+795+756+742+740+761+749+739+747+742 = 11253/15

= 750.2

Mean of second batch:

735+775+729+755+783+760+738+780

= 6055/8

= 756.875

Sd = 20

Z-alpha/2 = 1.64

= (750.2-756.875)-1.64*√20²/15 + 20²/8

= -21.0348

(750.2-756.875)+1.64*√20²/15 + 20²/8

= 7.68

2. The upper limit of the interval is less than 10 so in conclusion the difference in mean batch viscosity is about 10 or less than 10

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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The explicit formula is \(an = 275 (0.91)^n-1\)

After the eight hour we would have 142.11 mg

The explicit formula for decay is a mathematical formula that, given a substance's initial quantity and decay rate, predicts how much of a material will be left behind after a specified period of time.

The formula shows that the amount of the substance remaining after a certain amount of time is exponentially decreasing.

We have that that after the 8th hour;

a8 = 275(0.91)^8-1

a8 = 142.11 mg

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Answer:

The answer is 7!

Step-by-step explanation:

It's the correct answer, I calculated it.

I hope this helps.

Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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Answer:

answer is false in my opinion not sure

Answer:

4/7

Step-by-step explanation:

5+2=7

7 children

4 boys Out of 7 children

Answer:1/7

Step-by-step explanation:

Khan academy

Each coordinate was multiplied by 2 instead of divided by 2

the correct coordinates are

preimage                                image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we solve with scale factor of 1/2

preimage                                 image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

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Answer:

see explanation

Step-by-step explanation:

given y varies directly as x³ then the equation relating them is

y = kx³ ← k is the constant of variation

to find k use the condition y = 4 when x = 2 , then

4 = k × 2³ = 8k ( divide both sides by 8 )

\(\frac{4}{8}\) = k , that is

k = \(\frac{1}{2}\)

y = \(\frac{1}{2}\) x³ ← equation of variation

Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

\(P(t) = P(0)(1-r)^{t}\)

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that \(P(0) = 750000, P(48) = 250\)

We use this to find r. So

\(P(t) = P(0)(1-r)^{t}\)

\(250 = 750000(1-r)^{48}\)

\((1-r)^{48} = \frac{250}{750000}\)

\(\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}\)

\(1-r = 0.84637\)

So

\(P(t) = 750000(0.84637)^{t}\)

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

\(P(56) = 750000(0.84637)^{56} = 65.83\)

Rounding to the nearest number

There will be 66 bacteria in 8 hours.

Answer:

197,488

Step-by-step explanation:

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.

Identify the variables in the formula.

AA0ktA=250=750,000=?=48hours=A0ekt

Substitute the values in the formula.

250=750,000ek⋅48

Solve for k. Divide each side by 750,000.

13,000=e48k

Take the natural log of each side.

ln13,000=lne48k

Use the power property.

ln13,000=48klne

Simplify.

ln13,000=48k

Divide each side by 48.

ln13,00048=k

Approximate the answer.

k≈−0.167

We use this rate of growth to predict the number of bacteria there will be in 8 hours.

AA0ktA=?=750,000=ln13,00048=8hours=A0ekt

Substitute in the values.

A=750,000eln13,00048⋅8

Evaluate.

A≈197,488.16

At this rate of decay, researchers can expect 197,488 bacteria.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The equation of SQ is y = (-1/2)x + 2.

Given the coordinates of point P and point R as (-8,6) and (8,-2) respectively. Now, we need to find the equation of SQ.

Let's use the slope-intercept form of the equation of a line which is y = mx + b where m is the slope and b is the y-intercept.

Firstly, we need to find the slope of the line passing through the points P and R.

 Slope of a line through two given points (x1,y1) and (x2,y2) is given by,m = (y2 - y1) / (x2 - x1).

Hence, Slope of line PR = mPR= (-2 - 6) / (8 - (-8))= (-8) / 16= -1/2. As the line SQ is parallel to the line PR, the slope of the line SQ will be the same as the slope of line PR. The slope of line SQ = mSQ= mPR= -1/2.

Now, we need to find the equation of line SQ which passes through the point (0,2) and has slope -1/2.

Hence, using the slope-intercept form of the equation of a line, we get the equation of SQ as follows: y = mx + b 2 = (-1/2)(0) + b 2 = b.

Therefore, the equation of line SQ is y = (-1/2)x + 2, where x and y are the coordinates of the points on the line.

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9514 1404 393

Answer:

  a) parallel

  b) not parallel

Step-by-step explanation:

a) Alternate interior angles are congruent where a transversal crosses parallel lines. The marked alternate interior angles are congruent, so the lines are parallel.

__

b) Corresponding angles are congruent where a transversal crosses parallel lines. The marked corresponding angles are not congruent, so the lines are not parallel.

Answer:

a) parallel

b) not parallel

Step-by-step explanation:

a) Alternate interior angles are congruent where a transversal crosses parallel lines. The marked alternate interior angles are congruent, so the lines are parallel.

b) Corresponding angles are congruent where a transversal crosses parallel lines. The marked corresponding angles are not congruent, so the lines are not parallel.

The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.

According to the question,

We have the following system of equations:

x+y = 3 .....(1)

4x-y = 7 ....(2)

Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.

We can solve these equations by adding as follows:

x-y+4x+y = 3+7

5x = 10

x = 10/5

x = 2

Now, we can put the value of x in equation 1 to find the value of y:

2+y = 3

y = 3-2

y = 1

Hence, the correct option is B.

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