a random sample of size 36 is taken from a population with mean 17 and standard deviation 6. the probability that the sample mean is greater than 18 is?

Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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The surface area of the triangular prism is 136 square units

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

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

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

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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Answer:

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

  c² = a² +b²

  RQ² = PQ² +PR²

  RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

__

Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]

This mean there are infinite solutions.

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Indigo goes out to lunch.

The bill, before tax and tip, was $10.85.

A sales tax of 3% was added on.

Indigo tipped 18% on the amount after the sales tax was added.

The amount after adding sales tax is,

$10.85 x 3% = 0.3255

⇒ $10.85 + 0.3255 = $11.1755

Now to find the amount after tipped 18% on the amount after the sales tax was added.

$11.1755 x 18% = 2.01159

⇒ $11.1755 + 2.01159 = $13.18709

Hence, the amount  after tipped 18% on the amount after the sales tax was added is $13.18709.

Let x be the percent of more than the cost of the bill of $13.18709.

⇒

[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]

Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

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Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

Answer:

see below

Step-by-step explanation:

A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.

The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.

The two largest two digit prime numbers are: 89 and 97.

89×97=8633

The value of x for the expression is equal to -5 and -2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,

log₂ (x+4) + log₂ (x + 3) = 1

log₂ { (x+4)(x + 3) } = 1

x² + 7x + 12 = 2

x²+ 7x + 10 = 0

Solve the above quadratic equation,

x²+ 7x + 10 = 0

x² + 5x + 2x + 10 =0

x ( x + 5 ) + 2 ( x + 5 ) = 0

(x + 5 ) ( x + 2 ) = 0

x  = -5 and -2

The values of x are -5 and -2.

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Answer:

$9,712.12 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]

[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]

[tex]\implies A=9544\left(1.017615179\right)[/tex]

[tex]\implies A=9712.119269[/tex]

The balance of the account at the end of August will be $9,712.12 (nearest cent).

The only two options with equations that are true for x = –2 and x = 2 are;

Option A: x² - 4 = 0

Option D: 4x² = 16

The domain of a function is the set of all input values  for which the function is possible.

Now, we are given the domain values as  x = –2 and x = 2.

a) x² - 4

f(-2) = (-2)² - 4

= 0

f(2) = (2)² - 2

= 0

b) x² = -4

f(-2) = (-2)²

= 4

f(2) = (2)²

= 4

c) 3x² + 12

f(-2) = 3(-2)²  + 12

= 24

f(-2) = 3(2)²  + 12

= 24

d) 4x²

f(-2) = 4(-2)²

= 16

f(2) = 4(2)²

= 16

e) 2(x - 2)²

f(-2) = 2(-2 - 2)²

= 32

f(2) = 2(2 - 2)²

= 0

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The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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Answer:

(2½,1)

Step-by-step explanation:

(-1+6/2,5+-3/2)

(5/2,2/2)

(2½,1)

The graphed two lines will have one solution.

Any line that isn't twisted or bent is said to be straight.

Intersecting lines are two or more lines that have exactly one point in common. The point of junction is this central location that connects all of these lines.

A system of Intersecting Lines will have one unique solution

Lines that are parallel to one another on a plane do not overlap or meet at any point. They are always parallel and equally spaced from one another.

A system of Parallel Lines will have no solution

Here we have

System of equations

Given that the two lines are not parallel line

As we can see that both lines meet at a point

So here we can conclude that both lines are Intersecting Lines

Therefore,

The graphed two lines will have one solution.

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

The significant figure by multiplying 101 with 52 is 5000.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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Average rate of growth over this period is 0.4%.

Average rate of growth over a period is given by:

A=P[tex]e^{rT}[/tex] where,

A- Population at time T

P- Initial population

r-average rate of growth

T-Time period

Now, P=250,000, A=310,000 and T=21 (2000-1980+1)

therefore, putting values in the equation, we get:

310,000=250,000[tex]e^{21r}[/tex]

⇒ [tex]e^{21r}[/tex] = 1.24

⇒ 21r = log(1.24)

⇒ r = 0.0044 or 0.4%.

so, the average rate of growth over this time period is 0.4%.

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The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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If ABCD is a parallelogram, then the measure of D is 68

        9x + 5 + 16x(<DAB) = 180 ....... because it is straight line.

        25x + 5 = 180

        25x = 180 - 5

        25x = 175

            x = 7

          <ADC+ <DAB= 180

          <ADC+ 112 = 180

          < ADC= 180 - 112

          < ADC = 68

Therefore, the measure of D is 68

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The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

The equation of the line, in slope-intercept form,  that passes through the given points, (6,-4) and (6,5) is: x = 6.

An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.

The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.

Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.

Therefore, the value of a is 6. The equation of the line would be x = 6.

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The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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Answer:

Step-by-step explanation:

it is c

The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).

Does the order of transformations matter in functions?

Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.

The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

rotation 90° CCW about the point (-1, -1)

Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

reflection across the line y=x

reflection across the line x=-1

Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.

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The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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