Isabella recently opened her online candle shop, Spectacular Scents. Her sales in the first
week were $86. After advertising her new shop on social media, her sales increased by 20%
the following week and continued to increase at that rate.
Write an exponential equation in the form y = a(b)* that can model Isabella's weekly sales, y,
x weeks after opening her shop.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

The values of triangle ABC are

The angles in triangle ABC is calculated using the sine rule which sates that the ratio of a side and the opposite angles are equal to  each other

This represented by the formula

Sine A / a = Sine B / b = Sine C / c

applying the formula for the problem

Sine B / b = Sine C / c

Sine 48 / 121 = Sine C / 162

cross multiplying

Sine C = 162 * Sine 48 / 121

Sine C = 0.99495

C = arc sine (0.99495)

C = 84.2

Applying sum of angles in a triangle

< A + < B + < C = 180

< A + 48 + 84.2 = 180

< A = 180 - 48 - 84.2

< A = 47.8 degrees

side a

Sine A / a = Sine B / b

Sine 47.8 / a = Sine 48 / 121

121 * sine 47.8 / Sine 48  =  a

a = 120.6

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Answer:

Step-by-step explanation:

If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.

275 - 6 = 269

Use tangent with the given angle and the new height. The distance is x.

tan15 = 269/x

x = 269/tan15

x = 1004ft

The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.

Hence option C is correct.

According to the information given,

We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.

Carlos's height of 6 feet can be used as one side of the triangle,

And we can use the tangent function to find the length of the adjacent side.

A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).

So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:

tan(15) = height of the tree / distance from Carlos to the tree

Distance from Carlos to the tree = height of the tree / tan(15)

Plugging in the values given:

Distance from Carlos to the tree = 275 / tan(15)

                                                      ≈ 1026

Therefore,

The nearest foot to the distance from Carlos to the tree is option C. 1026.

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Answer:

60 people

Step-by-step explanation:

Before

C:A

2:3

After

C:A

3:2

We know that the number of adults never change.

Before

C:A

4:6

After

C:A

9:6

difference in units of children= 9-4

= 5

5 units= 30

1 unit= 30÷5

= 6

total units [before]= 4+6

= 10

10 units= 6×10

=60

The answer is Relational operators, they are binary operators that evaluate the truthhood or falsehood of a relationship between any two arguments, and that produce  value of true (1) or false (0) as a result.

This is usually done by checking whether a variable is true or false. True values ​​are true values. For example Non-zero numbers, strings, and objects. Incorrect values ​​are the values ​​that correspond incorrectly. lets take 0, empty strings and undefined. By testing whether a variable is true or false, we can also determine whether it equals 1 or 0 without explicitly comparing it to 1 or 0.

This is a useful way to determine the value of a variable without having to write a comparison statement and useful way for determining the value of any variable without being written any comparison statement.

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If she makes 135 attempts, the number of throws will be 40.5 .

Number of free throws made by a basketball player varies directly with number of attempts the player has.  If she makes 12 out of 40 attempts, the amount of throws she will make during the season if she made 135 total attempts can be calculated as follows:

Therefore,

y ∝ x

y = kx

where

Therefore,

12 = 40k

k = 12 / 40

k = 6 / 20 = 3 / 10

Hence,

y = 3 / 10 × 135

y = 405 / 10

y = 40.5

Therefore, the number of throws will be 40.5.

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Answer:

3 cm

Step-by-step explanation:

Given

Triangle ABC and Triangle DEF are similar

BC=4cm

EF = 16cm

FD = 12cm

ED = 10cm

Since we know that the triangles are similar,

AB/DE = BC/EF = CA/FD as they are the corresponding sides of the similar triangles

or

BC/EF = AC/FD

or

4/16 = AC/12

1/4 = AC/12

12/4 = AC

3 = AC

Therefore the value of AC is 3 cm

He stands 6 feet tall, and his shadow extends 9 feet. if the building's shadow extends for 322.5 feet.

Now 6/9 = X/322.5

9X = 1935

X = 215ft

The Height of the building = 215ft

Consider an object AB of height h such that its shadow of length s is formed and angle of elevation is θ.

The object AB depicts a right triangle in which ∠ABO = 90o.

Now we know that in trigonometry, the tangent ratio for an angle is equal to the opposite side to that angle divided by its adjacent side.

So, for the angle of elevation θ, we have

=> tan θ = AB/OB

Putting AB = h and OB = s, we get

=> tan θ = h/s

=> s/h = 1/tan θ

=> s = h/tan θ

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The equation of the line is y = (3/5)x + 14/5.

This graph is option D.

Option D is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = 3/5

Passes through the point = (-3, 1)

Now,

The equation of the line.

y = mx + c

m = 3/5

(-3, 1) = (x, y)

1 = (3/5)(-3) + c

1 = -9/5 + c

c = 1 + 9/5

c = 14/5

Now,

y = mx + c

y = (3/5)x + 14/5

This graph is option D.

Thus,

The equation of the line is y = (3/5)x + 14/5.

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The best discrete variable of measurement for the situation is an interval.

Finding the scale of measurement for the variables is the next step in selecting a statistical test after identifying the independent and dependent variables. The dependent variable must be measured using an interval or ratio scale for each of the parametric tests that we have covered so far. Many psychologists also subject variables with roughly interval scales of measurement to parametric tests. You must decide whether to use "scale" or "interval" scores when performing parametric tests of means.

Given the condition about whether the race of the defendant has an impact on jury verdicts,

and measure on a 1 (not at all) to 7 (very) scale how guilty the defendant,

The best scale of measurement for the condition is an interval.

Although the interval scale has characteristics of nominal and ordered data, it also allows for the quantification of data point differences. The variables' actual positions in the order as well as their differences are both displayed by this form of data. They can be combined or split, but not added to or subtracted from. 

The fact that zero is an existing variable adds another characteristic to this scale. Zero in the ordinal scale indicates that there is no data.

Hence the scale of measurement is an interval.

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To find 4f(-2) + 5f(1), we need to first find the values of f(-2) and f(1). Using the given equation, we have:

An easy definition of a function

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

f(-2) = -(-2) - 11 = 9

f(1) = -1 - 11 = -12

So, 4f(-2) + 5f(1) = 4 * 9 + 5 * -12 = 36 - 60 = -24.

To find 3f(5) * 2, we need to first find the value of f(5). Using the given equation, we have:

f(5) = -5 - 11 = -16

So, 3f(5) * 2 = 3 * -16 * 2 = -96

To find -5f(12) - 2f(-9), we need to first find the values of f(12) and f(-9). Using the given equation, we have:

f(12) = -12 - 11 = -23

f(-9) = -(-9) - 11 = 2

So, -5f(12) - 2f(-9) = -5 * -23 - 2 * 2 = 115 + 4 = 119

To find f(9)/f(-6), we need to first find the values of f(9) and f(-6). Using the given equation, we have:

f(9) = -9 - 11 = -20

f(-6) = -(-6) - 11 = 5

So, f(9)/f(-6) = -20 / 5 = -4.

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The angle in radians in simplest form is 2π/3 radians.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given the radius of the circle = 8

and length of arc = 16π/3

the relation between angle and arc is given by,

s = rθ

where r = radius, s = arc length and θ = angle in radians,

so, θ = s/r

θ = (16π/3)/8

θ = 2π/3 radians

Hence the angle is 2π/3 radians.

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Answer:

Australian dollar = n * 100 / 88

Step-by-step explanation:

n = American dollars

1 Australian dollar = 88 cents American

Answer:

7 units

Step-by-step explanation:

The point is 4 units from the x axis and 3 units from the y axis.

4 + 3 = 7

[tex]\frac{s}{-2 + 10} = 13[/tex]

To solve this, we first remove any fraction. So we have to multiply "-2 + 10" on each sides:

[tex]s = 13(-2+10)\\s = 13(8)\\s = 104[/tex]

If any step didn't make sense, tell me and I will help you :)

Answer:-0.696

Step-by-step explanation:Let the total daily pocket money of the 35 pupils in the other class "A" and the total daily pocket money of all 80 pupils "B".

The mean daily pocket money of the 35 pupils in the other class is m cents, so:

A = 35 * m

The mean daily pocket money of all 80 pupils is 72.25 cents, so:

B = 80 * 72.25

Since we know the total pocket money of both classes, we can use this information to solve for m:

A + B = 115 * m

35 * m + 80 * 72.25 = 115 * m

35 * m = 115 * m - 80 * 72.25

35 * m = 115 * m - 5780

5780 = 115 * m - 35 * m

5780=80 * m

Finally, we can solve for m:

m = 5780/80

m = 72.25

Answer:x=\frac{b-1}{a-d}

Step-by-step explanation:

Arun walked 5 km to east and then 12km to north. By joining the starting point and the end point by straight line we will get a right angled triangle, hypotenuse of which will tell how far is he from his starting point.

The square on the hypotenuse's area is equal to the sum of the two squares on the legs (a and b) (c). Pythagoras, a Greek philosopher who was born in 570 BC, is honored by having his theorem named after him. The theorem has already been shown more than once through various techniques, possibly greater than any other mathematical theorem. The hypotenuse side of a right-angled triangle's square is equal to the total of its other two sides, according to Pythagoras' Theorem. These right triangle three sides are known as the Perpendicular, Base, and Hypotenuse.

So Pythagoras theorem,

H²= 5² + 12²

H²= 25 + 144

H² = 169

H = 13

So, he will be 13 km far away from his starting point.

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The rate of change of the table is 3

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

The table of values

On the table, we have the following ordered pairs

(9, -6)  and (11, -12)

The rate of the table is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (9, -6)  and (11, -12)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-12 + 6)/(11 - 9)

Evaluate

Slope = -3

Hence, the rate of the table is -3

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Answer:

Step-by-step explanation:

You want the domain and range of the function ...

  F(x) = (x -6)/(x² -3x -18)

We can simplify the function to ...

  [tex]F(x) = \dfrac{x-6}{x^2-3x-18}=\dfrac{x-6}{(x-6)(x+3)}\\\\F(x)=\dfrac{1}{x+3}\quad x\notin\{-3,6\}[/tex]

The domain is the set of x-values for which the function is defined. It is undefined where the denominator is zero. So, x=-3 and x=6 are excluded from the domain, which would otherwise be all real numbers.

The range is the set of values that the function may have. Here, the function can have any y-value except 0 (the value of the horizontal asymptote), and 1/9, the location of the "hole" at x=6.

The range is all real numbers except 0 and 1/9.

The approximate percent increase in consumption from 1986 to 1997 is:

B. 20%

The initial consumption level for the year, 1986 is 62 million barrels per day and by 1997, the percent increase in consumption shot up to 74 million barrels per day.

When we subtract the latter consumption levels from the former, we will have a total of 12 million barrels per day. So, the percentage increase will be:

12 million barrels per day/ 62 million barrels per day × 100

= 19.35 %

Thus, we can arrive at the conclusion that the total consumption levels per day increased by 19.35%, which is approximately 20%.

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The timesheet of Rick's working hours is given below.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

From the given data points of Rick's working hours:

Date      Start Time     End Time  Time away  Regular hours

Dec. 9,   7:30 am        4:30 pm     30 minutes     8.5  

Dec. 10,  7:00 am        4:30 pm     30 minutes     8.5

Dec. 11,   11:30 am        5:00 pm      -                       5.5

Dec. 12,   7:30 am        5:30 pm      60 minutes      9

Dec. 13,   7:30 am        7:00 pm      90 minutes       10

Dec. 14,   8:00 am        5:00 pm      90 minutes       4.9

Dec. 15,    -                       -                   -                      -

Therefore, the timesheet is given.

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The complete question:

Make a timesheet for the following dates and times: Dec. 9, Rick...

Make a timesheet for the following dates and times:

Dec. 9, Rick worked from 7:30am to 4:30 p.m. He took a 30 min lunch break

Dec. 10, Rick worked from 7 am to 4:30 p.m. He took a 30 min lunch break

Dec. 11, Rick worked from 11:30 am to 5:00 p.m. He didn't take a lunch break

Dec. 12, Rick worked from 7:30 am to 5:30 p.m. He took an hour lunch break

Dec. 13, Rick worked from 7:30 am to 7:00 p.m. He took an hour and a half lunch break

Dec. 14, Rick worked from 8 am to 5 p.m. He took an hour and a half lunch break

Dec. 15,  Rick did not work.

The system of linear equations shown in the graph has no solution.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the coordinates of two lines,

line 1: line passes from (0, 3) and (3, 2)

and slope of the line is given by,

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 3)/(3 - 0)

m = -1/3

Line 2: line passes from (0, -2) and (3, -3)

slope =  (y₂ - y₁)/(x₂ - x₁)

m = (-3 - (-2))/(3 - 0)

m = -1/3

since both, the lines have the same slope so both lines will be parallel,

If two lines are parallel, they will never intersect and so there is no solution to the given system of equations.

Hence lines will have no solution.

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The examination of the results of the two numerical articulations, 72 × 3 and 72 × 7, can be resolved utilizing the duplication administrator (×). 72 × 3 = 216 and 72 × 7 = 504.

While contrasting the results of these two expressions, we can see that 504 is more prominent than 216. This can be addressed as 504 > 216.

This implies that when 72 is duplicated by 7, the outcome is more prominent than when 72 is increased by 3.

This is on the grounds that 7 is a bigger number than 3, and thus, when it is increased by 72, the outcome will be bigger. All in all, the expression 72 × 7 delivers a more noteworthy worth than the expression 72 × 3.

All in all, the examination between 72 × 3 and 72 × 7 outcomes in 72 × 7 being more prominent than 72 × 3, or 504 > 216.

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The root mean square speed of a carbon dioxide molecule at mentioned average kinetic energy is 1.57× [tex] {10}^{-11} [/tex].

The formula to find root mean square speed of carbon dioxide molecule using average kinetic energy is as follows -

c = ✓2KE/m, where c is root mean square speed, KE is kinetic energy and m is molecular mass

Keep the values in formula to find the root mean square speed.

c = ✓2×5.44×[tex] {10}^{-21} [/tex]/44

Performing multiplication and division on Right Hand Side of the equation

c = ✓2.47×[tex] {10}^{-22} [/tex]

Taking square root on Right Hand Side of the equation

c = 1.57× [tex] {10}^{-11} [/tex]

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Answer:

Below

Step-by-step explanation:

If the men are indistinguishable   and the women are too, then

6 w  5 m    

7 w 4 m

8 w   3 m

      3 ways

IF they ARE distinguishable it becomes a much larger, complex calculation:

8 C 6 * 10 C 5   +  8 C 7 * 10 C 4   +  8 * 10 C 3  

  ( is THIS what you are studying ? )

5% as a ratio not in simplified form is 5/100 or 5:100.

To write a percent as a ratio, we can divide it by 100 and express the result as a fraction. For example, 5% can be written as 5/100.

So, according to the U.S. Census Bureau, 5% of Americans age 25 or older had completed a bachelor's degree or higher in 1940 can be written as a ratio as:

= 5/100

This fraction represents the ratio of Americans age 25 or older who had completed a bachelor's degree or higher in 1940 to the total number of Americans age 25 or older.

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Answer:Not to simplify

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

9/10 is already in its simplest form. It cannot be further simplified as it is a fraction with two prime numbers in its numerator and denominator.

Antonia will have to wait 42 days before she gets to do both activities on the same day again.

The smallest positive integer that is a multiple of both 6 and 7 is the least common multiple (LCM) of 6 and 7. This is the number of days that will pass before Antonia does both of these activities on the same day again.

We can find the LCM of 6 and 7 using the formula as follows -

LCM(6, 7) = 6 * 7 / GCD(6, 7)

where GCD is the greatest common divisor.

The GCD of 6 and 7 is 1, so we can write -

LCM(6, 7) = 6 * 7 / 1 = 42

Therefore, Antonia will have to wait 42 days before she gets to do both activities on the same day again.

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Answer:

Step-by-step explanation:

that is incorrect.

if it were to be equal, one side should equal each other when multiplied to make the ratio equal.

20-5x=40-10x (when multiplied by 2 on each side)

It CANNOT equal 50, if it were there would not be -10x

20-5x=100-25x

DIVIDE BY 2 to get 50 WOULD GIVE:

20-5x=50-17.5x

Answer:

Yes

Step-by-step explanation:

solve the equation for x , then evaluate and compare both sides

20 - 5x = 50 - 10x ( add 10x to both sides )

20 + 5x = 50 ( subtract 20 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

then

left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10

right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10

since both sides are equal then

20 - 5x = 50 - 10x is true