Please help need urgent

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$14500\\ P=\textit{initial amount}\dotfill &\$22500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6\\ \end{cases}[/tex]

[tex]14500=22500(1 - \frac{r}{100})^{6}\implies \cfrac{14500}{22500}=\left( \cfrac{100-r}{100} \right)^6\implies \cfrac{29}{45}=\left( \cfrac{100-r}{100} \right)^6 \\\\\\ \sqrt[6]{\cfrac{29}{45}}=\cfrac{100-r}{100}\implies 100\sqrt[6]{\cfrac{29}{45}}=100-r \\\\\\ r=100-100\sqrt[6]{\cfrac{29}{45}}\implies r\approx \stackrel{\%}{7.06}[/tex]

Answer:

Step-by-step explanation:

Finding the hypotenuse of the triangular side :

Finding Surface Area :

Finding Volume :

Answer: The surface area is 173.2 mm²

Step-by-step explanation: If the four triangles are equilateral and one of the sides is 10 then all the other sides must be 10 as well, meaning that the surface area of each triangle is 43.3 mm². That means that to find the surface area of the whole pyramid you must multiply 43.3 by 4 because there are 4 separate triangles.

43.3 × 4 = 173.2

Answer:

[tex]3x + y = -4[/tex]

Step-by-step explanation:

We were given to points on the line we are trying to find, hence we are able to determine the slope/gradient.

[tex]( - 1, \: 1) \: and \: (1, \: 7) \\ slope = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \\ \\ s = \frac{7 - 1}{1 - ( - 1)} \\ s = \frac{6}{2} [/tex]

Slope is equal to 3.

Since we have the value for the slope, we can now use one of the points on the line to determine the equation of the line.

note that the coefficient of x is the slope. In this case the A from the standard form (Ax + By= C) is the slope.

[tex] \\ let \: us \: use \: the \: point \: ( - 1, \: 1) \\ a = 3 \: \: \: \: y = 1 \: \: \: x = - 1\\ ax + by = c \\ 3( - 1) + 1 = c \\ - 3 + 1 = c [/tex]

[tex] - 2 = c \\ therefore \: the \: equation \: of \: the \\ \: line \: is \\ ax + by = c \\ 3x + y = - 4[/tex]

[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]

Absolute value of a graph formula:

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

 [tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]

Join them to build the equation:   [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]

Answer:

[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

-----------------------------------------------------------------------------------------

Parent function:  [tex]f(x)=|x|[/tex]

[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]  

From inspection of the graph, the vertex of the transformed function is at (6, -7).  Therefore, there has been a translation of:

[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]

[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]

The line goes through point (0, -3)

Substituting this point into the above equation to find [tex]a[/tex]:

[tex]\implies a|0-6|-7=-3[/tex]

[tex]\implies 6a=4[/tex]

[tex]\implies a=\dfrac{2}{3}[/tex]

Therefore,

[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Using the confidence interval, it is found that the correct option regarding the valid conclusion they can make is given by:

b. Because the confidence interval includes 0, we don't have convincing evidence that there is a difference in reaction time.

At the null hypothesis, it is tested if there is not a difference in reaction times, that is:

[tex]H_c - H_d = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is:

[tex]H_c - H_d \neq 0[/tex]

The interval contains 0, hence there is not enough evidence to reject the null hypothesis, which means that option B is correct.

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Answer:

[tex]\frac{8}{30}[/tex]

Step-by-step explanation:

Card(AUBUC)= Card(A)+card(B)+card(C)-Card (A∩B) -Card( A∩C)-Card(B∩C) +Card(A∩B∩C)

= 21 + 14 + 15 - 10 - 8 - 4 + 2

= 30

Then

Card(AUBUC) = 30

Card( A∩C) = 2 + 6 = 8

[tex]p\left( A\cap C\right) =\frac{card\left( A\cap C \right) }{card\left( A\cup B\cup C \right) }[/tex]

               [tex]=\frac{8}{30}[/tex]

Answer:

inscribed angle

Step-by-step explanation:

That is an inscribed angle in a circle ....

Answer:

inscribed angle

Step-by-step explanation:

The vertex (point, corner) of the angle is ON the circle, this is an inscribed angle.

The statement about the graphs is true is:  Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

Graph curve is above the horizontal axis.

Let determine the area under the curve using this formula

Base of left and right triangle

Left  

Base = -3 - (-5)

Base= 2

Right

Base= 3 - (-3)

Base= 6

Right and left height

Height= 0.25

Hence:

Total area=(base× height)/2

Total area=[ (2×0.25)/2] + (6×0.25)/2

Total area=0.25+0.75

Total area=1

Therefore  Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.

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Answer:

9

Step-by-step explanation:

because 3*4=12 then divide 108 by 12 giving you 9

Answer:

B. 11

Step-by-step explanation:

Hope this helps! ;-)

Answer:

11

Step-by-step explanation:

15-12/3

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

15-4 = 11

Answer:

b

Step-by-step explanation:

4 - 8 = -4 times 2 = -8

Answer:

Area=154.062 [tex]m^{2}[/tex]

Step-by-step explanation:

As Circumference of a circle is given by;

[tex]C=2\times \pi\times r[/tex]

As the circumference is 44m so we can calculate the value of r by using the above formula.

[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]

Now to Calculate the Area of a Circle.

As the area of a circle is,

[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]

Answer:a function whose value decreases as the independent variable increases over a given range.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the question, it is given that a right cone has a radius of 15 units and volume of 3000π units³ and we have to find the height of the cone.

[tex] \: [/tex]

To Find the height of the cone, we must know this formula :

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi {r}^{2}h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times {(15)}^{2} \times h = 3000 \pi}}}}}}} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times {(15)}^{2} \times h = 3000 \cancel\pi}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times 225 \times h = 3000}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{225}{3} \times h = 3000}}}}}}} \\ \\[/tex]

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf 75 \times h = 3000}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf h = \frac{3000}{75} }}}}}} \\ \\[/tex]

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h =40 }}}}}}} \\ \\[/tex]

Therefore,

A diagram of parallelogram MNOP is attached below

We have side MN, || side OP, and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.

∠N and ∠O are supplementary by the rules of angles in parallel lines

∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

∠M ≅ ∠O; ∠N ≅ ∠P

An ERRAND is a chore, but it is not a game and A CONNECTION is a bond, but it is not a separation.

An ERRAND is a chore, but it is not a game.

The correct vocabulary word from each drop-down menu that correctly complete the first sentences is errand.

A CONNECTION is a bond, but it is not a separation

The correct vocabulary word from each drop-down menu that correctly complete the second sentences is connection.

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Answer:

Yes, by ASA congruence.

Step-by-step explanation:

Solving :

Hence, as 2 angles and a side of the triangles are equal, we can say they are congruent by ASA congruence.

[tex]\huge\underline{{\sf Answer}}[/tex]

[tex] \textbf{Let's check if the two triangles are } [/tex][tex] \textbf{congruent} [/tex] ~

[tex] \large\textsf{Given information } [/tex]:

[tex] \textsf{Two angles of a triangle is equal to corresponding} [/tex] [tex] \textsf{two angles of another triangle, and they} [/tex][tex] \textsf{have one side in common (should be equal} [/tex][tex] \textsf{for both) } [/tex]

[tex] \textsf{So, after analyzing this information, we can } [/tex][tex] \textsf{conclude that the two triangles are congruent by} [/tex][tex] \textsf{AAS congruency criteria.} [/tex]

[tex] \texttt{[ since two angles are equal and one} [/tex][tex] \texttt{non included side is common/equal ]} [/tex]

[tex]f(x) = 3^x + \ln x -108 x\\\\f'(x) = 3^x \ln 3 + \dfrac 1x - 108\\\\f''(x) = 3^x \cdot 0+ \ln 3\cdot 3^x\cdot \ln (3)-x^{-1-1}-0= 3^x \cdot \ln^2 3 -x^{-2}\\ \\f'''(x) = 3^x \cdot 0 + \ln^2 (3) \cdot 3^x \cdot \ln (3) +2x^{-2-1} = 3^x \ln^3 (3)+2x^{-3}\\\\f''''(x) = 3^x \cdot 0 + \ln^3 (3) \cdot 3^x \ln(3) -3\cdot 2 x^{-3-1} = 3^x\ln^4 (3)-6x^{-4} \\\\\text{Hence the fourth derivative of f(x) is}~~ 3^x\ln^4 (3)-6x^{-4}.\\\\[/tex]

[tex]\textbf{Note:}\\\\\dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v\dfrac{du}{dx}\\\\\dfrac{d}{dx} \ln (x) = \dfrac 1x\\\\\dfrac{d}{dx} a^x = a^x \ln a\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} (\text{Constant}) = 0[/tex]

The quadrants in which the tangent is positive are I and III.

Option B is the correct answer.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle.

It is positive when the opposite side and the adjacent side are both positive or both negative.

In the first quadrant (I), both the opposite and adjacent sides are positive, so the tangent is positive.

In the second quadrant (II), the opposite side is positive and the adjacent side is negative, so the tangent is negative.

In the third quadrant (III), both the opposite and adjacent sides are negative, so the tangent is positive.

In the fourth quadrant (IV), the opposite side is negative and the adjacent side is positive, so the tangent is negative.

Therefore,

The quadrants in which the tangent is positive are I and III.

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The probability that it will not rain on both Saturday and Sunday will be 0.2268.

From the information, meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.

The probability that it will not rain on both Saturday and Sunday will be:

= (1 - 42%) × (1 - 54%)

= 0.58 × 0.46

= 0.2268

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Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Suppose that we're taking about

It means, we divide p into q equal parts.

And each part is of value p/q

Statement 7 is given below.

5x - 10 = 0

Then statement 8 is given by the division property of equality.

5x = 10

 x = 10/5

 x = 2

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Answer:

x = 27.19

Step-by-step explanation:

Sin(54) =22/x

0.81=22/x

x0.81= 22

x = 27.19

Probability that the next person will purchase more than one costume as a fraction in simplest form is; 11/113

We are given the data for number of people who visited the website and the number of costumes purchased in a single day as;

Number of visitors that purchased no costume = 27 visitors

Number of visitors that purchased exactly one costume = 75

Number of visitors that purchased more than one costume = 11

Total number of visitors = 27 + 75 + 11 = 113

Thus;

Probability that the next person will purchase more than one costume as a fraction in simplest form is;

P(purchase more than one costume) = 11/113

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3:7 =

3/7

3/7 = x/35

7x = 105

x = 15

answer : clara borrowed 15 books

I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.

The expression for the amount of Meghan's newspaper for three months will be T = C - (9.95 x  3).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, expansion and division.

The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months.

T = C - (9.95 * 3)

The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.

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Answer:

Your kid will be 9 years old.

Step-by-step explanation:

It's not relevant, that you are 14 now.

Answer: 9

Step-by-step explanation: Regardless of if you are 14 or not, 30-21=9