Quadrilateral IJKL is similar to quadrilateral MNOP. Find the measure of side PM. Round your answer to the nearest tenth if necessary.

The dilutions in one step, or have to do serial dilutions.

There is a limit to how much can dilute a sample in one step.

Dilute by more than a factor of 100 in a single step, because that a large volume of dilute solution.

Rather, use the serial dilution technique.

Remember the formula for dilution factor (DF):

DF =Vf /Vi

, where

Vi = aliquot  volume

and Vf = final volume = aliquot volume + diluent volume

a) DF = 50

For a single dilution.

This time  add 0.2 mL of sample to 9.8 mL of saline.

Vf = 0.2 mL + 9.8 mL= 10.0 mL

DF = Vf/Vi = 10.0mL 0.2mL= 50

b) DF = 100

For a single dilution.

This time  add 0.1 mL of sample to 9.9 mL of saline.

Vf = 0.1 mL + 9.9 mL=10.0 mL

DF =Vf/Vi = 10.0mL/0.1mL = 100

c) For a serial dilution.

The formula for serial dilutions is

DF =DF1×DF2×DF3×…

about a 1:100 dilution followed by a 1:2 dilution

(1) Add 0.1 mL of sample to 9.9 mL of diluent.

DF1 = 100 Call this "Solution 1".

(2) Add 5 mL of Solution 1 to 5 mL of saline. Call this "Solution 2".

Vi = 5 mL

Vf = 5 mL + 5 mL= 10 mL

DF2 = Vf/Vi = 10mL/5mL=2

DF = DF1×DF2 = 100 ×2= 200

DF = 50

DF = 100

DF = 200

The dilutions in one step, or  have to do serial dilutions.

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The Least common denominator of the given fractions is 12.

What is least common denominator?

The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.

Consider the given fraction, 3/4 and 1/6

The denominator are 4 and 6.

The multiples of 4 are, 4, 8, 12, 16, 20.

And the multiples of 6 are, 6, 12, 18, 24, 30.

From the above listed multiples of 4 and 6, 12 is the least common multiple of both the numbers.

Hence, the Least common denominator of the given fractions is 12.

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The given equation that should be in the standard form should be like a 4.5 x 10¹¹.

The equation in standard form:

Since

The equation is (5 x 10³) x (9 x 10⁷)

Now here we use the commutative property

So,

45 x (10³ x 10⁷)

45 x 10¹⁰

4.5 x 10¹¹

Here, we multiply the number in the 1st bracket, then add, it, and then finally in standard form.

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Answer:

Step-by-step explanation:

(5*10^3)*(9*10^7)

(5*1000)*(9*10000000)

5000*90000000

450000000000

The factorization of the given  polynomial by greatest monomial factor is given as 3b⁵(1 + 5b - 6b²).

The factorization of a polynomial can be done by taking out the common part to all of its terms and then expressing it as the product of those parts.

The given polynomial is 3b⁵ + 15b⁴- 18b⁷

It can be factorized as follows,

The largest factor common for all the terms of 3b⁵ + 15b⁴- 18b⁷ is 3b⁵.

Then, the given expression can be written as,

3b⁵ + 15b⁴- 18b⁷

= 3b⁵(1 + 5b - 6b²)

Hence, the given polynomial can be factorized as 3b⁵(1 + 5b - 6b²).

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Answer:

21%

Step-by-step explanation:

Step-by-step explanation:

1) divide 134 by 106

106/134 is about 0.79

2) Multiply by 100 to find the percentage

0.79(100)= 79%

3) Subtract 79% from 100% to find the percentage difference

100%-79%= 21%

Therefore, the percent of change between 134 and 106 is 21%.

Answer:

$361,660

Step-by-step explanation:

(a)

the original value represents 100%

an increase of 7% is then 100% + 7% = 107% = [tex]\frac{107}{100}[/tex] = 1.07 then

new value = 1.07 × old value

(b)

new value = 1.07 × $338,000 = $361,660

Answer:  m∠5 = 116°

Step-by-step explanation:

Because m∠4 and m∠6 are consecutive interior angles, then we know

         m∠4 + m∠6 = 180

(106 - y) + (3y - 10) = 180

   104 - y + 3x - 10 = 180

                96 + 2y = 180

                         2y = 84

                           y = 42

And also the m∠4 and m∠5 are alternate interior angles, we get:

m∠5 = m∠4 = 3y - 10

Since we also calculate what y is, we just plugin.

mm∠5 = m∠4 = 3(42) - 10 = 126 - 10 = 116

The two plans will cost the same when Lucy has driven 550miles. ($55 + $0.50 x 550)= $330

(0.6*550)=$330

The difference between both the trip rate is .10$

and the difference between initial fee is 55$

so after 1 mile the difference is .10$

the 55$can be earn after

55*10=550 mile.

Divide the overall distance traveled by the time period to find the average speed. An someone traveling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, would be driving 20 miles north and then 20 miles south to arrive at the same location (60 mph)

The overall distance traveled by an object over the total amount of time is the thing's average speed. The average speed v of an object during a motion that covers a total distance of d and a total duration of t can be estimated using the formula v = d t.

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Answer:

7a+9b

Step-by-step explanation:

Answer:

A. Prime factorisation method

Step-by-step explanation:

❌The answer is not A because:

You don't need to write a quadratic equation in terms of its prime factors to solve the quadratic equation.

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I have earned 10 college credit hours before end of my high school graduation date.

A credit hour is an approach to estimating how much credit an understudy gets for going to a course which relates to the hours out of each week spent in that course. Dissimilar to numerous conventional secondary school courses that expect understudies to go to class consistently, school courses may just meet a few times each week.

Each hour that an understudy spends in the class regularly compares to a credit hour. For instance, on the off chance that an understudy signs up for a class that meets for one hour on Monday, Wednesday, and Friday, that course would be worth three credit hours, which is normal of numerous school courses.

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The value of x and y are (11.66,5)

Given that,

3x-30=y-----------1

7y-6=3x-----------2

Now, putting the value of equation 1 in equation 2 we get

⇒7(3x-30)-6=3x

⇒21x-210=3x

⇒21x-3x=210

⇒18x=210

⇒x=11.66

now put the value of x in equation 1 we solved earlier we get

⇒3×11.66-30=y

⇒35-30=y

⇒y=35-30

⇒y=5

Therefore the value of x is 11.66 and the value of y is 5

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It will take 8 days for the average charge per day for company a to be the same as the average charge per day for company b.

The charges incurred by these companies are given by the word expression -

Total charge = Service fee + Fee per day. Equating the expressions by keeping values of both companies. Let us represent each day by z.

80 + 22x = 0 + 32x

Rewriting the equation

32x - 22x = 80

Performing subtraction on Left Hand Side of the equation

10x = 80

Shifting 10 to Right Hand Side of the equation

x = 80/10

Performing division on Right Hand Side of the equation x = 8

On eight days, the charge will be equal.

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Answer:

186- none of those answers are correct, the right answer is one hundred eighty six miles

Step-by-step explanation:

623

-437

____

186

Answer:

The difference in the number of miles run by Kiki during practice is 186 miles.

Step-by-step explanation:

Given that Kiki runs 437 miles during the first week of track practice and she runs 623 miles during the second week of track practice.

The difference in miles will be:

= 623 - 437 = 186 miles.

Answer:

9z^2 -7

Step-by-step explanation:

(z9z−5)−2.

(9z^2−5)−2.

9z^2-5 -2

9z^2-7

Write the problem as a mathematical expression.

Multiply

z9 by z  by adding the exponents.

Subtract

2 from  −5  .

ANSWER:

z^10 − 7

Answer:

2, 3, 4

Step-by-step explanation:

The term "at least" interprets as "greater than or equal to".

Because George has a Maximum of 300 hours left to complete sculptures and paintings, the Sum of the Hours (30x and 15y) must be Less Than, or can be Equal to 300.

The best-subset method builds the best 1-variable model, the best 2-variable mode, ... , the best k-variable model.

The best subsets regression is a s model selection approach that consists of testing all possible combination of the predictor variables, and then selecting the best model according to some statistical criteria.

Best subset regression is an exploratory model building regression analysis. It compares all possible models that can be created based upon an identified set of predictors.

The goal of attribute subset selection is to find a minimum set of attributes such that dropping of those irrelevant attributes does not much affect the utility of data and the cost of data analysis could be reduced. Mining on a reduced data set also makes the discovers pattern easier to understand.

Best subset selection is a method that aims to find the subset of independent variables that best predict the outcome and it does so by considering all possible combinations of independent variables.  

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Answer:

From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%

Step-by-step explanation:

How it decreased by 30%

V2-V1/V1x100

V2=3.5 V1=5

=(3.5−5)|5|×100
=−1.55×100

=−0.3×100

=−30%change

=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5

=(5.3−3.5)|3.5|×100

=1.83.5×100

=0.514286×100

=51.4286%change

=51.4%increase

The average rate of change of the function at the interval -2 < x < 8 is 1.5

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

g(x) = 3/2x + 1

The interval is given as

-2 < x < 8

This interval can be represented as

x = -2 and x = 8

Substitute the known values in the above equation, so, we have the following representation

g(-2) = 3/2(-2) + 1 = -2

g(8) = 3/2(8) + 1 = 13

This means that

g(-2) = -2 and g(8) = 13

The average rate of change is then calculated as

Average rate of change = [g(8) - g(-2)]/[8 + 2]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [13 + 2]/[8 + 2]

Evaluate the expression

Average rate of change = 1.5

Hence, the rate is 1.5

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Answer:

what are you asking?!?

Step-by-step explanation:

The length of WX = 25, WY = 25, XY = 17.

Isosceles triangles have two sides that have the same length.

 ABC, if it is an isosceles triangle then AB=AC

Properties of isosceles triangle used in this question:

In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal and its reverse also hold.

ABC is an isosceles triangle AB=AC then

                                 ∠B =∠C

Given: ΔWXY, ∠X = ∠Y

       Therefore, WX = WY

WX = 9x-11

WY = 7x-3

XY = 4x=1

9x-11 = 7x-3

9x-7x = -3+11

2x = 8

x = 4

We can calculate easily all the side with the help of x value

WX = 9x-11 = 9*4 -11 = 26-11

                        = 25

WY = 7 x (-3) = (7×4)– 3 = 28-3

                       = 25

XY = 4x=1 = (4×4) +1 = 16+1

                       = 17

Hence, we get all the sides.

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Any data collection whose metrics of central placement only have the letter A as a value.Mode and median

For any given data set, the mode and median are the two measures of central location that have just one value. The mode is the most commonly occurring value in a given data set, while the median is the middle value in the data set when it is sorted in order from least to greatest. The mean, on the other hand, is an average of all the values in the data set, and the standard deviation is a measure of how much the values in the data set differ from each other. So, the answer is A. Mode and median.

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Answer:

x=−2

Step-by-step explanation:

x2+5x+4−(2x2−10)=2x2−10−(2x2−10)

−x2+5x+14=0

(−x−2)(x−7)=0

−x−2=0

Hence B is the correct option

On simplifying the trigonometric expression [tex](1-sin^2x)cosx[/tex]  we get  [tex]cos^3x[/tex].

there are many ways to simplify trigonometric expressions. The simplest one is to use trigonometric identities.

                                                  [tex](1-sin^2x)cosx[/tex]

now, accordingly, we use the following identity of trigonometry to simplify

                                               [tex]sin^2x+cos^2x=1\\\\[/tex]

subtract sin^2x on both sides of this trigonometric identity we get

                                      [tex]sin^2x-sin^2x+cos^2x=1-sin^2x[/tex]

so by canceling similar terms from the left side we get

                                              [tex]1-sin^2x=cos^2x[/tex]

so by putting it in the first expression we get  

                                              [tex](1-sin^2x)cosx[/tex][tex]=cos^2x(cosx)[/tex]

finally, we get

                                                                          [tex]=cos^3x[/tex]

so by simplifying the trigonometric expression [tex](1-sin^2x)cosx[/tex]   using trigonometric identities we get  [tex]cos^3x[/tex].

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This probability means that in a very long series of hands of poker, about 8.8% of the time we will get 4 of a kind.

The results of a chance process are unpredictable, yet they follow a predictable distribution over a large number of repeats. The frequency of a particular occurrence happening across many repeats approaches a single number, according to the law of large numbers. The likelihood of a chance result is determined by its long-term relative frequency. The probability given in the question is 88/1000, which means that we should anticipate 88 poker hands with a four-of-a-kind for every 100 hands with a pair.

The probability stated in the question for different Texas hold'em poker games has this meaning. Because it is also possible that 87 or 89 of 1000 such hands will have four of a kind, this probability does not guarantee that exactly 88 of those hands will contain four of a kind. There are frequently more than 88 fours of a kind, though this isn't always the case.

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The test statistic would be a two-sample t-test, which compares the means of two independent samples by calculating the difference in means between the two samples and dividing the difference by the standard error of the difference.

In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

Describe a percentage example.

The hundredth component, one percent (symbolized as 1%), is expressed as 100 percent, and 200 percent denotes double the quantity specified. For example, 1% of 1,000 chickens equals 1/100 of 1,000, or 10 chickens, and 20% of the total is equal to 20% of 1,000, or 200.

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Answer: decimal 0.03 fraction 3/10

Step-by-step explanation:

Answer: 15x15

Step-by-step explanation:

I'm assuming this is an optimization problem in a Calculus class, if not just disregard all of this and be happy with the answer.

We can write two equations for the value of x and y lengths of this rectangle.

2y+2x=60

xy=A

Solve our perimeter equation for y, y=30-x.

This gives us x(30-x)=A, and 30x-x²=A.

Find the derivative of the area function: A'=30-2x

To maximize we set A' to 0: 0=30-2x, x=15

Plug back into our perimeter formula: 2y+2(15)=60, y=15

So both sides will be 15 inches.