Find the missing side lengths. Leave your answers as radicals in simplest form.

a. About 50% of the students scored less than 78.

b. Approximately 68% of the students scored between 75 and 78.

c. Approximately 95% of the students scored between 72 and 81.

d. Approximately 99.7% of the students scored between 69 and 75.

a) The normal curve is symmetrical, meaning that the area to the left of the mean is equal to the area to the right of the mean. Since the mean score is 78, 50% of the students scored above 78 and 50% scored below 78.

b) To apply the Empirical Rule, we will assume that 68% of the data falls within one standard deviation of the mean, which in this case is 3 points. So, 68% of the students scored between 75 and 81.

c) The percentage of students who scored between 72 and 81 can be found by subtracting the area to the left of 72 from the area to the left of 81. Using the Empirical Rule, we know that 95% of the observations are within two standard deviations of the mean, so the area between 72 and 81 is equal to 95%.

d) The percentage of students who scored between 69 and 75 can be found by subtracting the area to the left of 69 from the area to the left of 75. Using the Empirical Rule, we know that 99.7% of the observations are within three standard deviations of the mean, so the area between 69 and 75 is equal to approximately 99.7%.

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We can be performed Multiplication on algebraic expressions in the same way as it can be performed on two whole numbers or fractions.

Multiplication of algebraic expressions or variable expressions involves multiplying two expressions combined with various arithmetic operations like addition, subtraction, multiplication, and division and contains constants, variables, terms, and coefficients.

Multiplying the algebraic equation involves the following steps.

1. Multiply the coefficients of the terms, add the powers of the variables with the same base, and obtain the algebraic sum of the like and unlike terms before learning about the multiplication of algebraic expression.

The multiplication of two terms with the same signs is positive, and two terms with different signs are negative.

Example:

−a×−b=ab

a×−b=−ab

We can add the exponents of the same bases in case of multiplication as a^m×a^n=a^m+n

Example:

a^2×a^3=a^2+3=a^5

b^5×b^8=b^5+8=b^13

Algebraic Expression: An algebraic expression is the collection of the constants and the variables connected by fundamental operators like addition (+), subtraction (−), etc.

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Answer:

D) 2x + y = 4

Step-by-step explanation:

slope = -2

y-intercept = 4

slope-intercept form:  y = -2x + 4

standard form:  2x + y = 4

Answer:

60

Step-by-step explanation:

1/6 * 60 = 60/6

60/6 = 10/1 = 10

The number of 1/6 pound servings in 10 pounds of chicken is; 60

We are required to determine how many 1/6 pound servings are in 10 pounds of chicken.

Hence ; we have;

= 60.

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After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer:

5(x+1)=2(x-2)

5x+5=2x-4

5x-2x=-5-4

3x=-9

x=-3

Step-by-step explanation:

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The measure of the frame is 8.5 inches and 11 inches

a) if the frame is 4 papers long then we  have the length of the frame as

11×4=44 inches (since he lays the paper along the edge of frame)

We know 1 inch= 0.0833 foot

Thus      44 inches= 3.66667 foot

b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches

∴25.5 inches= 2.125 feet

Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

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Answer:

1/4, 4/7, 2/3, 1/2

Step-by-step explanation:

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

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Answer:

(0, -6) is the y-intercept.

Answer:

x = 145

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

35+x+35+x = 360

2x+70 = 360

Subtract 70 from each side

2x+70-70 = 360-70

2x = 290

Divide by 2

2x/2 =290/2

x = 145

Answer:

x=145

(145+145+35+35=360)

Step-by-step explanation:

This question is very simple to answer if you remember that all parallelograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral must add up to 360 degrees.

Answer:

  a) N5995.13

  b) N14376.61

  c) N36762.11

Step-by-step explanation:

For repetitive calculations, I like to use a spreadsheet or graphing calculator. __

The formula for the amount is ...

  A = P(1 +r)^t . . . . . . where principal P is invested for t years at rate r compounded annually

The principal being invested is P = 5000. The interest rate is r = 9.5% = 0.095, and the time is t = 2 years. Putting these values into the formula gives ...

  A = 5000(1 +0.095)^2

  = 5000(1.199025) = 5995.125

This rounds to an account balance after 2 years of N5995.13.

The calculations for the other amounts and time periods are done the same way, but for different values of P and t. You can do these calculations by hand, but it is generally much easier to use a calculator, spreadsheet, or other tool.

The attachment shows use of a tool that lets a function be defined that takes P and t as arguments. It is shown as being evaluated for the different values of P and t in this problem.

  A = N10,000(1 +0.095)^4 = N10,000(1.43766095) = N14376.6095

This rounds to an account balance after 4 years of N14376.61.

  A = N28000(1.095)^3 ≈ N36762.11

Answer:

ooo acellus its A

Step-by-step explanation:

Answer:

A.

The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

The required probability is 0.1422.

The probability of those that paid with credit card is: 0.2952 around 0.20

The correct option is  (b) i.e.,0.30

Probability that drivers filled their vehicles with regular gasoline P(R) = 88% = 0.88

Probability that drivers purchased midgrade gas P(M) = 2% = 0.02

Probability that bought premium gas P(P) = 10% = 0.10

Let A be the given event that it is paid with credit card.

Probability that who bought regular gas paid with credit card P(A|R) = 285

Probability that who bought midgrade gas with credit card P(A|M) = 34% = 0.34

Probability that who bought premium gas with credit card P(A|P) = 42%

= 0.42

According to Bayes theorem, we get that

P(P|A) is given by:

\(\frac{P(A).P(A|P)}{P(R).P(A|R)+P(M).P(A|M)+P(P).P(A|P)}\)

= (0.1 × 0.42)/ 0.88 × 0.28 + 0.2 × 0.34 +0.1 × 0.42

= 0.042/ 0.2952

= 0.1422

To find the probability that the customer paid with a credit card, we can use the law of total probability.

The probability of those that paid with credit card is given as

= 0.2464 + 0.0068 + 0.042

= 0.2952

The correct option is 0.30

Hence, the required probability is 0.1422.

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The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.

The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.

If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).

Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.

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Answer:

Step-by-step explanation: it’s D on edge

The inverse function is,

⇒ k⁻¹ (x) = -16 (x + 8)

What is Inverse function?

The inverse function returns the  original value for which a function gave the outputs.

Given that;

The function is,

k (x) = -1/16 x - 8

Now, Find the inverse function as;

k (x) = -1/16 x - 8

Substitute k (x) = y,

y = -1/16 x - 8

Find the value of x in terms of y,

y = -1/16 x - 8

y + 8 = -1/16 x

16 ( y + 8 ) = -x

x = -16 ( y + 8 )

Replace x and y,

y = -16 ( x + 8 )

Thus, The inverse function is,

⇒ k⁻¹ (x) = -16 (x + 8)

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Answer:

n=−3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

13−2n=19

13+−2n=19

−2n+13=19

Step 2: Subtract 13 from both sides.

−2n+13−13=19−13

−2n=6

Step 3: Divide both sides by -2.

−2n/−2=6/−2

\(13 - 2n = 19\)

Subtract sides -13

\(13 - 13 - 2n = 19 - 13\)

\( - 2n = 6\)

Divided sides by -2

\( \frac{ - 2}{ - 2}n = \frac{ 6}{ - 2} \\ \)

\(n = - 3\)

Done....♥️♥️♥️♥️♥️

Answer:

5.1%

Step-by-step explanation:

percent = part/whole × 100%

percent = 85/1675 × 100%

percent = 5.1%

The percentage of earnings that Charlotte spends on cosmetics to the nearest tenth of a per cent is 5.1%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Charlotte earns $1675 every month of which she spends $85 on cosmetics.

The percentage will be calculated as,

Percent = part/whole × 100%

Percent = 85/1675 × 100%

Percent = 5.1%

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer:

C? I have no clue sorry :(((