The **probability** of the **data** less than or equal to 104 is 84%.

The **probability** of the **data** less than or equal to 104 is calculated by applying **normal distribution** formula.

In a standard **normal distribution curve**, we have the following;

One standard deviation below the mean = M - S.D = 34%

One standard deviation above the mean = M + S.D = 34%

The **number** of **data** that would be at 104 is calculated as;

M + S.D = 98 + 6

M + S.D = 104

So we can see that 104 lie at **one standard deviation** above the mean.

mean = 50%

one standard deviation above the mean = 34%

The total **probability** = 50% + 34% = 84%

P ( x <| 104 ) = 84%

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please answer 5+10+12+6+11+18+17=

**Answer:**

79

**Step-by-step explanation:**

add this you have easily find answer

Find the measure indicated.

27)

T

A) 59⁰

C) 56°

S

80°

20

Q

B) 50°

D) 37°

R

b)50

since its a Equilateral triangle, then the two base angels have the same measure

abd since both triangles are symmetric, they have the same measurements

so 180-80 = 2x

x = 50⁰

if m∠2=3x+14° and m∠4=2x+6°, what is

The **angle** m∠HAT in the** line segment** is 54 degrees.

When line segment intersect,** angle relationships** are formed such as

**vertical angles**, linear angles etc.

Therefore, the angle ∠HAT can be found using the relationship of the angles as follows:

m∠MAH = 3x + 14

m∠HAT = 2x + 6

Therefore,

m∠MAH + m∠HAT = 90 degrees

3x + 14 + 2x + 6 = 90

5x + 20 = 90

5x = 90 - 20

5x = 70

x = 24

Therefore,

m∠HAT = 2x + 6 = 2(24) + 6 = 48 + 6 = 54 degrees

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a number cube is tossed 60 times Determine the experimental probability of landing on a number less than two

**Answer:**

1.67% approx

**Step-by-step explanation:**

To determine the experimental probability of landing on a number less than two when a number cube is tossed 60 times, we need to count the number of times the number on the cube is less than two and divide it by the total number of tosses.

Let's denote the event of landing on a number less than two as "A." We'll count the number of successful outcomes, where the number on the cube is less than two.

Assuming the number cube is fair and unbiased, it has six sides numbered from 1 to 6. Out of these, only one side has a number less than two, which is one.

Now, we can calculate the experimental probability using the formula:

Experimental Probability (P(A)) = Number of successful outcomes / Total number of tosses

In this case, the number of successful outcomes is the number of times the cube lands on a number less than two, which is one. The total number of tosses is given as 60.

Therefore, the experimental probability of landing on a number less than two is:

P(A) = 1 (successful outcomes) / 60 (total number of tosses)

= 1/60

≈ 0.0167 or 1.67%

So, the experimental probability of landing on a number less than two is approximately 0.0167 or 1.67%.

obove answer is correct i think

PLEASE HURRY! When you know the volume of a prism and some dimensions, you can solve for a(n) ____________ dimension.

When you know the **volume **of a prism and some **dimensions**, you can solve for an unknown dimension.

When armed with knowledge about the volume of a prism alongside certain known dimensions, the **possibility** emerges to determine an elusive dimension within the **prism**. By leveraging the given information, the missing dimension can be unearthed, unraveling the intricacies of the prism's complete set of measurements.

This **calculation **empowers us to gain a comprehensive understanding of the geometric structure, further enriching our grasp of its spatial characteristics. The interplay between the volume and the known dimensions acts as a gateway to unlocking the enigma of the **unknown dimension**.

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From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

,

,

The **x-coordinates **where the graphs of the **equations **intersect are x = -1 and x = 3

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

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations **intersect **is when both **equations **are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is **factored**, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the **x-coordinates **are x = -1 and x = 3

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**Question**

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

This figure is a rectangular prism.

Select ALL figures that are NOT formed by a horizontal

slice parallel to the base.

A

B

C

D

square

right triangle

isosceles trapezoid

rectangle

“This figure is a rectangular prism” it says at the top btw”

if u do this ty

The horizontal slice of a **rectangular prism **will always be a rectangle. Therefore, the correct answers are options A, B and C.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

The **horizontal **cross section of a rectangular prism will always be a rectangle.

Therefore, the correct answers are options A, B and C.

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Out of 20 people how many would you expect to say that they like all seasons

**Answer:**

None

**Step-by-step explanation:**

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

**Answer:**

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

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How do I find the possible degree(s) of a function from the graph alone?

The **possible degrees **of a function from it's graph are found with the sum of the multiplicities of each root of the function.

On the **definition **of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

On the **graph**, these are the values of x for which the graph of the function crosses or touches the x-axis.

The **multiplicity **of each root is given as follows:

Hence the **degree **is found with the sum of the multiplicities of the zeros of the function.

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Eye Color of Males Surveyed

Green

Blue

5

16

Brown

27

Eye Color of Females Surveyed

Blue

Brown

19

18

Green

3

What percent of students in the survey are either female or have green eyes? Round your answer to the nearest tenth.

About % are either female or have green eyes.

What percent of students in the survey are males who do not have green eyes? Round your answer to the nearest tenth.

About % are males who do not have green eyes.

Find the sum of these two percents.

The sum of these two percents is %.

The sum of the **percentage** of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.

Percentage of Females: (1918 / (1918 + 516 + 27)) * 100 = (1918 / 2461) * 100 ≈ 78.0%

Percentage of Students with **Green Eyes**: ((516 + 3) / (1918 + 516 + 27)) * 100 = (519 / 2461) * 100 ≈ 21.1%

Percentage of Students who are either Female or have Green Eyes: 78.0% + 21.1% ≈ 99.1%

Therefore, approximately 99.1% of students in the survey are either female or have green eyes.

Percentage of Males with Green Eyes: (516 / (516 + 3)) * 100 = (516 / 519) * 100 ≈ 99.4%

Percentage of Males who do not have Green Eyes: 100% - 99.4% ≈ 0.6%

Therefore, approximately 0.6% of students in the survey are males who do not have green eyes.

To find the sum of these two percentages:

**Sum** of Percentages: 99.1% + 0.6% ≈ 99.7%

Therefore, the sum of the **percentage** of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.

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Here is a rectangle:

2

3

2 cm

Find the area of the rectangle.

cm²

The area of the given **rectangle** with a length of 3 cm and a width of 2 cm is 6 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.

**Area** of the rectangle = Length * Width

Plugging in the given values:

Area = 3 cm * 2 cm

Multiplying 3 cm by 2 cm gives us:

Area = 6 cm²

Therefore, the area of the given **rectangle** with a length of 3 cm and a width of 2 cm is 6 cm².

The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).

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by what percent will a fraction change if its numerator is decreased by 60% and its denominator is decreased by 20%

Let's assume the original fraction is represented as a/b, where "a" is the numerator and "b" is the denominator.

Decrease the numerator by 60%:

The new numerator, after decreasing it by 60%, will be (1 - 0.6) * a = 0.4a.

Decrease the denominator by 20%:

The new denominator, after decreasing it by 20%, will be (1 - 0.2) * b = 0.8b.

Now, we can calculate the new fraction:

New Fraction = (0.4a) / (0.8b) = 0.4a / (0.8b)

To find the percentage change in the fraction, we can compare it to the original fraction:

Percentage Change = ((New Fraction - Original Fraction) / Original Fraction) * 100

Let's substitute the values:

Percentage Change = ((0.4a / (0.8b) - a / b) / (a / b)) * 100

Simplifying the expression:

Percentage Change = ((0.4a - a) / a) * (b / (0.8b)) * 100

Percentage Change = (0.6a / a) * (1.25) * 100

Percentage Change = 0.6 * 1.25 * 100

Percentage Change = 75%

Therefore, the fraction will change by 75% when the numerator is decreased by 60% and the denominator is decreased by 20%.

Decrease the numerator by 60%:

The new numerator, after decreasing it by 60%, will be (1 - 0.6) * a = 0.4a.

Decrease the denominator by 20%:

The new denominator, after decreasing it by 20%, will be (1 - 0.2) * b = 0.8b.

Now, we can calculate the new fraction:

New Fraction = (0.4a) / (0.8b) = 0.4a / (0.8b)

To find the percentage change in the fraction, we can compare it to the original fraction:

Percentage Change = ((New Fraction - Original Fraction) / Original Fraction) * 100

Let's substitute the values:

Percentage Change = ((0.4a / (0.8b) - a / b) / (a / b)) * 100

Simplifying the expression:

Percentage Change = ((0.4a - a) / a) * (b / (0.8b)) * 100

Percentage Change = (0.6a / a) * (1.25) * 100

Percentage Change = 0.6 * 1.25 * 100

Percentage Change = 75%

Therefore, the fraction will change by 75% when the numerator is decreased by 60% and the denominator is decreased by 20%.

Which is an expression for the volume of the prism (v =lwh)

Show how to calculate the volume in two different ways

The **expression** that shows the** volume** of the** prism** is x³ - x² - 6.

The prism above is a** rectangular prism**. The volume of the prism can be found as follows:

The volume of the prism can be found as follows:

volume of the rectangular prism = lwh

where

l = length of the basew = width of the baseh = height of the prismTherefore,

**volume** of the rectangular prism = (x - 3)(x)(x + 2)

volume of the rectangular prism = (x² - 3x)(x + 2)

volume of the rectangular prism = x³ + 2x² - 3x² - 6

volume of the rectangular prism = x³ - x² - 6

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Find w=a+bi=, where a and b are real numbers

√-8+6i

Given statement solution is :- The given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are** real numbers.**

To find the** complex **number in the form w = a + bi, where a and b are real numbers, we can solve the given expression.

Let's solve √(-8 + 6i) step by step:

First, we can express -8 + 6i in the form a + bi:

-8 + 6i = -8 + 6i + 0i = -8 + 6i + [tex]0i^2[/tex]

Now, we can take the square root of -8 + 6i:

√(-8 + 6i) = √((-8) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-8 + 6i) = √(-8 - 6 + 6i)

= √(-14 + 6i)

Now, we want to express -14 + 6i in the form a + bi:

-14 + 6i = -14 + 6i + 0i = -14 + 6i +[tex]0i^2[/tex]

Taking the square root, we have:

√(-14 + 6i) = √((-14) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-14 + 6i) = √(-14 - 6 + 6i)

= √(-20 + 6i)

Now, we want to express -20 + 6i in the form a + bi:

-20 + 6i = -20 + 6i + 0i = -20 + 6i + [tex]0i^2[/tex]

Taking the square root, we have:

√(-20 + 6i) = √((-20) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-20 + 6i) = √(-20 - 6 + 6i)

= √(-26 + 6i)

Now, we want to express -26 + 6i in the form a + bi:

-26 + 6i = -26 + 6i + 0i = -26 + 6i +[tex]0i^2[/tex]

Taking the square root, we have:

√(-26 + 6i) = √((-26) + 6i + [tex]0i^2[/tex])

Since [tex]i^2[/tex] = -1, we can simplify the expression further:

√(-26 + 6i) = √(-26 - 6 + 6i)

= √(-32 + 6i)

We continue this process until we reach a point where the expression simplifies. However, in this case, we** encounter **an expression that cannot be simplified further, as the square root of a negative number is not defined in the set of real numbers.

Therefore, the given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are** real numbers.**

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What is the meaning of "A function f is one-to-one"?

A function f is said to be one-to-one, o**r injective**, if it has the property that for any two different inputs, it produces two** different outputs**.

More formally, a function f: X -> Y is one-to-one (or injective) if for every x1, x2 in X, if x1 ≠ x2 then f(x1) ≠ f(x2).

This means that no two **different elements** of the domain X map to the same element of the codomain Y. If you were to draw a horizontal line through any point on the graph of a one-to-one function in the Cartesian plane, that line would intersect the graph at most one time. This is known as the "horizontal line test" for one-to-one functions.

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Andrea has a jug that holds 1.5 liters of chocolate milk. She fills one container with 250 milliliters and another container with 0.6 liters. How much chocolate milk is left in the jug in milliliters?

0.65 mL

249.1 mL

450 mL

650 mL

**Answer:**

correct answer is 650ml

Multiply

19(x + 1 + 9z)

The **product **of the **expressions **19(x + 1 + 9z) is 19x + 19 + 171z

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

19(x + 1 + 9z)

When the **brackets **are **opened**, we have

19(x + 1 + 9z) = 19 * x + 19 * 1 + 19 * 9z

**Evaluate **the products of the expression

So, we have the following representation

19(x + 1 + 9z) = 19x + 19 + 171z

Hence, the product of the **expressions **19(x + 1 + 9z) is 19x + 19 + 171z

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Solve for a. Round your answer to the nearest tenth if necessary. 10.7 N X P 22.2 R 17.8

**Answer:**

**Step-by-step explanation:**

the answer is 69 the if we round of

Find the number that belongs

in the green box.

37⁰

64°

[?]

30

Round your answer to the nearest tenth.

**Answer:**

? ≈ 20.1

**Step-by-step explanation:**

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]

with a = ? , b = 30 , ∠ A = 37° , ∠ B = 64° , then

[tex]\frac{?}{sin37}[/tex] = [tex]\frac{30}{sin64}[/tex] ( cross- multiply )

? × sin64° = 30 × sin37° ( divide both sides by sin64° )

? = [tex]\frac{30sin37}{sin64}[/tex] ≈ 20.1 ( to the nearest tenth )

Mrs. Brown wants to assign eight homework

problems to her Algebra 1 class tonight. If

there are eleven problems she could choose

from, how many different homework sets

could she assign?

A

88

B

165

C

495

D

990

Mrs. Brown can **assign** 165 different **homework** sets to her Algebra 1 class.

We have,

The number of different homework sets Mrs. Brown could assign can be calculated using the **combination** **formula**.

In this case, she wants to choose 8 problems out of 11 available problems. The formula for **combinations** is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of items to choose from and r is the number of items to be chosen.

Using this formula:

C(11, 8) = 11! / (8! x (11 - 8)!)

C(11, 8) = 11! / (8! x 3!)

Simplifying the factorial expressions:

C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)

The factorial terms cancel out:

C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)

C(11, 8) = 165

Therefore,

Mrs. Brown can **assign** 165 different **homework** sets to her Algebra 1 class.

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how to find x values

**Answer:**

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find

Un camión va cargado con 3796 kg de patatas. En una frutería descarga 6 sacos de 50 kg cada uno. ¿ Cuanto pesa ahora la carga del camión?

The** current weight** of the truck is given as follows:

3496 kg.

How to obtain the current weight of the truck?The current weight of the truck is obtained applying the **proportions **in the context of the problem.

The **initial **weight of the truck is given as follows:

3796 kg.

The **weight **removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the** current weight** of the truck is given as follows:

3796 - 300 = 3496 kg.

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6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable

The **equation **6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has **no solution **for the variable x.

Given the **equation **in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To **solve **the **equation **6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is **no solution**.

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The roof gable on Charlene's house has two

equal sides. One angle measures 110.4°. The

other two angles are equal to each other.

Estimate the measure of each of the other

two angles.

Each of the other two **angles** in the roof gable measures approximately 34.8°.

If the roof **gable** on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a **triangle** is always 180°.

Let's denote the measure of the other two angles as x.

Since the two equal sides of the gable form an isosceles triangle, the two **angles** opposite those sides are equal.

Therefore, we have:

x + x + 110.4° = 180°

Combining like terms:

2x + 110.4° = 180°

Now, let's solve for x:

2x = 180° - 110.4°

2x = 69.6°

x = 69.6° / 2

x = 34.8°

Therefore, each of the other two **angles** in the roof gable measures approximately 34.8°.

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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.” Here is a dot plot of their responses.

in the **dot plot** given, A rating of 6 is not a good description of the center of this **data set **because it does not accurately represent the most common or **typical response.**

To determine the **center of data** set, we typically look for the measure of central tendency, such as the mean, **median**, or mode.

From the dot plot, we can observe that the **mode** is at the **rating of 10**, with six students giving this highest rating. In contrast, the rating of 6 has only two students, making it **less representative **of the center.

Therefore, a rating of 6 does not accurately capture the overall sentiment or the **central tendency **of the data set.

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**Full Question:**

Please see the attached.

A collection of coins consists of nickels dimes and quarters. There are four fewer quarters than nickels and 3 more dimes than quarters. How many of each kind of coin are in the collection if the total value of the collection is $6.5?

There are 19 nickels, 15 quarters, and 18 dimes in the **collection**.

Let's assume that there are n **number** of nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4.

There are 3 more dimes than quarters, so the number of dimes will be (n - 4) + 3 = n - 1.

The value of each nickel is $0.05, the value of each dime is $0.10, and the value of each quarter is $0.25.Using this information, we can form the following equation to **represent** the total value of the collection:

0.05n + 0.10(n - 1) + 0.25(n - 4) = 6.5Simplifying this equation, we get:0.05n + 0.10n - 0.10 + 0.25n - 1 = 6.50.40n - 1.10 = 6.50

Adding 1.10 to both sides, we get:0.40n = 7.60Dividing both sides by 0.40, we get:n = 19

Therefore, there are 19 nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4 = 19 - 4 = 15.

There are 3 more dimes than **quarters**, so the number of dimes will be (n - 4) + 3 = 15 + 3 = 18.

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Fluency in the conversion of the metric system to the Imperial System is an essential skill in the nursing profession. Think of a situation in which negative effects have occurred due to incorrect dosage calculations? This situation could be a personal experience, the experience of someone you know, or a hypothetical. Explain how this error could have been avoided. How will you ensure that you avoid dosage errors due to metric conversions in your future career as a nurse?

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will **double**-**check **my calculations, use reliable conversion charts or **tools**, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent **errors **in the future.

*~~~Harsha~~~*

2. Find the area of the figure below.

1.3 cm

1.3 cm

3 cm

4.2 cm

6.8 cm

5 cm

The **area **of the figure as shown in the diagram is** 30.64 cm².**

The **area **of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². **Area** of a shape is a two dimensional quantity.

To calculate the **area **of the figure, we use the formula below

Formula:

A = 2LW+l²................... Equation 1Where:

A =From the diagram,

Given:

L = 5 cmW = 1.3 cml = 4.2Substitute these values into equation 1

A = (2×5×1.3)+4.2²A = 13+17.64A = 30.64 cm²Learn more about **area **here: https://brainly.com/question/28470545

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How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the square tiles has an edge of 3/4 ft. Show your work

Area of the floor: 14ft x 6ft = 84

Area of tiles: 3/4 x 3/4 =.5625

84/.5625= 149 1/3

Area of tiles: 3/4 x 3/4 =.5625

84/.5625= 149 1/3

Solve the following equations. Check the solutions. 8x^2 + 11 = 191 + 3x^2, 7x^2 - 15 = 49 + 3x^2, 14x^2 - 157 = 333 + 4x^2

The **solutions **to the **equations **are:

x = 6, x = 4, x = 7.

1. 8x² + 11 = 191 + 3x²

**Rearranging **the equation:

8x² - 3x² = 191 - 11

5x² = 180

Dividing both sides by 5:

x² = 36

Taking the square root of both sides:

x = ±6

Checking the solution:

8(6)² + 11 = 191 + 3(6)²

288 + 11 = 191 + 108

299 = 299

The solution x = 6 satisfies the equation.

2. 7x² - 15 = 49 + 3x²

Rearranging the equation:

7x² - 3x² = 49 + 15

4x = 64

**Dividing **both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Checking the solution:

7(4)² - 15 = 49 + 3(4)²

112 - 15 = 49 + 48

97 = 97

The **solution **x = 4 satisfies the equation.

3. 14x² - 157 = 333 + 4x²

**Rearranging **the equation:

14x² - 4x^2 = 333 + 157

10x² = 490

Dividing both sides by 10:

x² = 49

Taking the square **root **of both sides:

x = ±7

Checking the solution:

14(7)² - 157 = 333 + 4(7)²

686 - 157 = 333 + 196

529 = 529

The solution x = 7 **satisfies **the equation.

Therefore, the **solutions **to the **equations **are:

x = 6, x = 4, x = 7.

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