Suzie's Slushes has increasing profits each week during the hot summer months. Suzie finds that each week during the summer her profits increase by 30% over what they were the previous week. In her first week of business, her profits were $300. How much money will she make in all over 4 weeks

Answer:

Important: 3

6

looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3

6

.

To find an equivalent fraction to 3

6

, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By dividing the original fraction by 3, we get:

3 ÷ 3

6 ÷ 3

= 1

2

By multiplying the original fraction by 2, we get:

3 × 2

6 × 2

= 6

12

Step-by-step explanation:

[tex]\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=\dfrac{1}{\cos x}- \dfrac{\sin x }{ \cos x } \cdot \sin x\\\\\\=\dfrac 1{\cos x} - \dfrac{\sin^2 x}{\cos x}\\\\\\=\dfrac{1- \sin^2 x}{\cos x}\\\\\\=\dfrac{\cos^2 x}{\cos x}~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}[/tex]

Answer:

4.14

Step-by-step explanation:

3x : -2

-8 14

cross multiply

3x × 14 : -2 × 8

42 + 14x : -16

42+ 16 : 14x

58 : 14x

58 : x

14

4.14 : x

A force F, of 25 newtons pulls at an angle of 20° above due east

A force F₂ of 35 newtons pulls at an angle of 55° below due west

Find the magnitude and direction of the resultant force

The angle the longer chain makes with the ceiling is 38.5°

The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle

The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that

a/sinA = b/sinB = c/sinC

Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.

So, a/sinA = b/sinB  where

Making A subject of the formula, we have

A = sin⁻¹(asinB/b)

So, substituting the values of the variables into the equation, we have

A = sin⁻¹(asinB/b)

A = sin⁻¹(46 cm × sin60/64 cm)

A = sin⁻¹(46 cm × 0.8660/64 cm)

A = sin⁻¹(39.84 cm/64 cm)

A = sin⁻¹(0.6225)

A = 38.49°

A ≅ 38.5°

So, the angle the longer chain makes with the ceiling is 38.5°

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Answer:

hope you can understand

Answer:

Step-by-step explanation:

angle c

The angle of the triangle with the greatest measure is ∠A

A triangle is a polygon with three sides and three angles.

Analysis:

For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.

In conclusion, the angle with the greatest measure is ∠A

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The equation of the tangent to the curve at the point corresponding to the given value of the parameter will be x + y = c.

The curves are given below.

x = t⁵ + 1 and y = t⁶ + t

Then differentiate the functions with respect to t, then we have

[tex]\rm \dfrac{dx}{dt} = 5t^4\\[/tex]   ...1

and

[tex]\rm \dfrac{dy}{dt} = 6t^5 + 1[/tex]   ...2

Divide equation 2 by equation 1, then we have

[tex]\rm \dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } = \dfrac{dy}{dx} = \dfrac{6t^5 + 1}{5t^4}[/tex]

Then the slope of the equation at t = −1, then we have

dy/dx = [6(-1)⁵ + 1]/[5(-1)⁴]

dy/dx = (-6+1)/5

dy/dx = -5/5

dy/dx = -1

Then the equation of the tangent line will be

y = -x + c

x + y = c

Where c is a constant.

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Answer:

The meal was $20

Step-by-step explanation:

20%= 1/5

1/5=4/? ---> one converts to four by multiplying it by 4 so you should do the the same with the denominator which is five.

5×4= 20

Answer:

[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.

That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).

Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.

[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]

I've marked corresponding sides and angles in the attached picture.

The data value that is an outlier in the data for boxes of cookies is: E. 56.

The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.

Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:

First Quartile (Q1) = 15.5

Third Quartile (Q3) = 22.5

Interquartile Range (IQR) = 22.5 - 15.5 = 7

Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5

Q3 + 1.5 × IQR = 33

None of the values are lower than 5.

However, the only value that is greater than 33 is 56.

The outlier in the data is: E. 56.

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Answer:

(1) 1 and 7

Step-by-step explanation:

Hello!

We can solve by isolating the variable.

There are two solutions, 1 and 7.

The answer is option 1: x = 7, x = 1.

Answer:

Step-by-step explanation:

8

Answer:

x = 19/2 or 9.5

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve.

Move all x terms to one side and integer terms to the other

Rounded to the nearest whole number, the standard deviation of the data is 29.

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where:

n = number of values = 4

x = each value

Therefore, we have:

Mean = (65 + 75 + 100 + 130) / 4 = 92.50

Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) =  2,525 / 3 = 841.666666666667

Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882

Rounding to the nearest whole number, we have:

Standard deviation = 29

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Answer:

The answer is C. 100

Step-by-step explanation:

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the objects. The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The polar coordinate of the coordinate (1, -3) are,

r = √(x² + y²) = √[(1)²+(-3)²] = √10

θ = tan⁻¹(-3/1) = -71.565 = 288.435

Hence, The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

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We need radius

Let that be r

Answer:

12 feet

Step-by-step explanation:

It asks how many feet away from the sprinkler can water be spread. Therefore, in this scenario, we require the radius.

Area of a circle :

Area (circle) = πr²

Solving :

⇒ 452.16 = 3.14 × r²

⇒ r² = 452.16 ÷ 3.14

⇒ r = √144

⇒ r = 12 feet

Answer:

[tex]\sf M=\left(-\dfrac{1}{2},0\right)[/tex]

Step-by-step explanation:

Let (x₁, y₁) = Point A = (-2, 1)

Let (x₂, y₂) = Point B = (1, -1)

[tex]\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)[/tex]

Answer:

y=-x+6

Step-by-step explanation:

Start by graphing y=-x+5.  Then mark the point (2,4) for easier reference.  A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.

Step-by-step explanation:

2×length + 2×width = 45

length = 4×width

now, we are using the second equation (a variable identity) in the first equation

2×4×width + 2×width = 45

8×width + 2×width = 45

10×width = 45

width = 45/10 = 4.5 in

length = 4×width = 4×4.5 = 18 in

the area of the rectangle is

length × width = 18 × 4.5 = 81 in²

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trendline and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that an equation for the line of best fit is given by:

y = 22.214x + 291.27

Since the slope of the equation for the line of best fit is positive, the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

Next, we would predict the restaurant's sales for the Monday of the 20th week as follows:

y = 22.214x + 291.27

y = 22.214(20) + 291.27

y = 444.28 + 291.27

y = $735.55.

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Answer:

63

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

Answer:

$301

Step-by-step explanation:

 Charge for 1 hour = $ 72

To find the cost for 3 hours, multiply hourly rate ($72) by 3

Charge for 3 hours = 72 * 3  = $ 216

Now, to find the total cost, add the charge for 3 hours and the fixed rate.

Total cost = fixed rate + charge for 3 hours

                = 85 + 216

                = $ 301

The slope of the line is [tex]\frac{6-0}{0-6}=-1[/tex]. so in point-slope form, the equation of the line is [tex]y=-x+6[/tex].

In standard form, this is [tex]\boxed{x+y=6}[/tex]

Answer: Choice A

The two characteristics here are:

The graph of choice B is [tex]y \le 2x-3[/tex] since we have a solid line and shading below the solid line. This time points on the boundary are part of the solution set.

Answer: 24.15

Step-by-step explanation:

Answer:

6 hours 30 minutes

Step-by-step explanation:

10 subtract 4 is 6

55 subtract 25 is 30

Answer:

The correct answer is B.

Step-by-step explanation:

Pay per month depends on hours of training, so hours of training is the domain, and pay per month is the range.

When we try to compute gamma, for this problem, the value of gamma is 1

To answer the question, we need to know what time dilation is.

Time dilation is a phenomenon in special relativity in which there is an elongation of time due to the motion of an object.

Now, the time is given by t = γt₀ where

Since we need to compute gamma when the speed of the automobile moving past you is 30 m/s.

Given that

Substiting these into γ, we have

γ = 1/√[1 - (v/c)²]

γ = 1/√[1 - (30 m/s/3 × 10⁸ m/s)²]

γ = 1/√[1 - (1/1 × 10⁷)²]

γ = 1/√[1 - (1 × 10⁻⁷)²]

γ = 1/√[1 - (1 × 10⁻¹⁴)]

γ = 1/√[1 - 0.00000000000001]

γ = 1/√0.99999999999999

γ = 1/1

γ = 1

So, when we try to compute gamma, the value of gamma is 1

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