Simplify help asap pleaseeeeer I need help asap

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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⁶√5 < √2 < ³√3

Step-by-step explanation:

Given: ⁶√5, ³√3, √2

\( = {5}^{ \frac{1}{6} } , \: {3}^{ \frac{1}{3} } , \: {2}^{ \frac{1}{2} } \\ = {({5}^{ \frac{1}{6} })}^{6} , \: {({3}^{ \frac{1}{3} })}^{6} , \: {({2}^{ \frac{1}{2} })}^{6} \\ = 5, \: {3}^{2} , \: {2}^{3} \\ = 5, \: 9, \: 8 \\ \\ 5 < 8 < 9 \\ = {5}^{ \frac{1}{6} } < \: {2}^{ \frac{1}{2} } \: < {3}^{ \frac{1}{3} } \\ \)

Answer:

Assume that there is a Latin quiz with 10 matching vocabulary questions, and your niece try to match them randomly. Then, the probability that she gets the first item right is

1

10

since there is only one correct answer for this item out of 10 options. Now, the probability that she gets the second item right is

1

9

since there is only one correct option and there is only 9 options left to choose from. So, in a similar fashion, the probability that she will get the third item correct is

1

8

, the fourth item correct is

1

7

and so on. Therefore, the probability that she will match them all correctly (getting a 100 on the quiz) is equal to

1

10

⋅

1

9

⋯

1

2

⋅

1

1

=

1

10

!

=

1

3628800

ANSWER

EXPLANATION

Let the two points be (2, 4) and (3, 9).

The general form of the equation of a straight line is given by:

where m = slope

b = y-intercept

First, we have to find the slope of the line using the formula:

where (x1, y1) and (x2, y2) are the two points that the line passes through

Therefore, the slope of the line is:

Now, we find the equation of the line using the point-slope method:

Therefore, the equation of the line is:

The average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

The function f(x)=80(1.5)x

where x is the time in hours

Then,

f(4)=80(1.5)4=480

f(8)=80(1.5)8=960

f(0)=80(1.5)0=0

Then the average rate of change between 4 and 8 hours =\(\frac{960-480}{4}\)

=120 units per hour

The average rate of change between 0 and 4 hours=\(\frac{480-0}{4}\)

=120 units per hour

Hence, the average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

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Answer:

\(8v^{3} +27=(2v)^{3} +3^{3}=(2v+3)(4v^{2} -6v+9)\\\)

Step-by-step explanation:

from  formula a³ – b³ = (a – b) (a² + ab + b² )

Answer:

sorry I can't understand hahahhaha

Step-by-step explanation:

Speak korean po

Part D: x= -b/2a

(-1/3, -4/3)

im sorry if this is wrong ;'(

Answer:D

Step-by-step explanation:

D will go with each funcuation.

Option C) is the correct graph that best represents the combination of both functions.

The graph, which plots time on the x-axis and temperature on the y-axis, displays an increasing function that depicts the temperature. The graph is divided into two sections: one shows a straight line with a positive slope to reflect the heater's contribution, and the other shows a curve to show the sun's contribution.

Option A) depicts a straight line that illustrates the rise in temperature brought on by the heater, but it omits the sun's influence. The intersection of these two functions is not depicted in this graph.

Option B) displays a curve that depicts the rise in temperature brought on by the sun, but it omits the impact of the heater. The intersection of these two functions is not depicted in this graph.

The sum of the two functions h(t) and s(t), which model the rise in pool temperature, can be written as follows:

c(t) = h(t) + s (t)

The specific functions h(t) and s(t) and their values at various times t would affect the graph of c(t).

Both the function h(t) and the function s(t) model the rise in temperature brought on by the sun and the heater, respectively.

As a result, Option C) is the correct graph that accurately depicts the union of the two functions.

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Answer:

Its A.

Step-by-step explanation:

it just looks like a combination of the other 2

The confidence interval for the population mean is 35.316 and 42.684.

The 80% confidence interval for the population mean can be calculated using the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, we need to determine the critical value corresponding to an 80% confidence level. Since the sample size is relatively large (n = 31) and assuming the data follows a normal distribution, we can use the Z-distribution.

The critical value can be obtained from a standard normal distribution table or using statistical software. For an 80% confidence level, the critical value is approximately 1.282.

Next, we calculate the standard error using the formula:

Standard Error = standard deviation / √(sample size)

Plugging in the values, we have:

Standard Error = 16 / √(31) ≈ 2.872

Now we can calculate the confidence interval:

Confidence Interval = 39 ± (1.282 * 2.872)

Calculating the values, we get:

Confidence Interval = 39 ± 3.684

Rounding to three decimal places, the 80% confidence interval for the population mean is approximately 35.316 to 42.684.

Therefore, the confidence interval for the population mean is 35.316 and 42.684.

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The boundaries of the class 1.87-3.43 are D) 1.865-3.435. The lower boundary is 1.865 and the upper boundary is 3.435.

The boundaries of the class 1.87-3.43 can be determined by subtracting and adding half of the smallest possible unit of measurement to the given class limits. In this case, since the given class limits are 1.87 and 3.43, we need to find the boundaries by subtracting and adding half of the smallest possible unit of measurement.

Let's assume the smallest possible unit of measurement is 0.01.

To find the lower boundary:

Lower Boundary = Lower Limit - (0.01/2)

Lower Boundary = 1.87 - 0.005

Lower Boundary = 1.865

To find the upper boundary:

Upper Boundary = Upper Limit + (0.01/2)

Upper Boundary = 3.43 + 0.005

Upper Boundary = 3.435

Therefore, the boundaries of the class 1.87-3.43 are:

D) 1.865-3.435

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When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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Answer:

1x + 2y = 177 (price)

x + y= 114 (rentals)

Step-by-step explanation: x= movies y= video games

Answer:

56

Step-by-step explanation:

add and then multiply

To determine whether a vector is in V, we need to check if it can be expressed as a linear combination of the vectors in the spanning set of V.

The spanning set of V is given as:

V = Span { (1, 2, 3), (2, 2, 2), (1, -5, 5) }

Let's check whether each of the given vectors is in V and express them as linear combinations of u, v, and w:

(a) a = (1, 4, 0)

To express a as a linear combination of u, v, and w, we need to find scalars x, y, and z such that:

a = xu + yv + z*w

Substituting the values:

(1, 4, 0) = x*(1, -2, 3) + y*(2, 2, 2) + z*(1, -5, 5)

This gives us a system of equations:

x + 2y + z = 1

-2x + 2y - 5z = 4

3x + 2y + 5z = 0

Solving this system of equations, we find x = 1, y = -1, and z = -2.

Therefore, a = 1u - 1v - 2*w.

(b) b = (0, 0, 0)

To express b as a linear combination of u, v, and w, we need to find scalars x, y, and z such that:

b = xu + yv + z*w

Substituting the values:

(0, 0, 0) = x*(1, -2, 3) + y*(2, 2, 2) + z*(1, -5, 5)

This gives us a system of equations:

x + 2y + z = 0

-2x + 2y - 5z = 0

3x + 2y + 5z = 0

Solving this system of equations, we find that it has infinitely many solutions, indicating that b can be expressed as a linear combination of u, v, and w in multiple ways.

One possible solution is x = 0, y = 0, and z = 0.

Therefore, b = 0u + 0v + 0*w.

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Answer:

\(y=x-8\) or \(y+5=x-3\)

Step-by-step explanation:

To write an equation finding the equation of a line you can use y-y1=m(x-x1)

Step 1: Find the slope using slope formula \(\frac{y_{2} -y_{1}}{x_{2} -x_{1}}\)

\(\frac{-9 -(-5)}{-1 -3}=\frac{-4}{-4} =1\)

Step 2: Plug in numbers to Point Slope Form.

\(y-(-5)=1(x-3)=y+5=x-3\)

Step 3: Depending on what your teacher prefers you can also change it into slope-intercept form

\(y=x-8\)

E = 2400/d is the equation for the illumination, E, in lux as a function of the source's distance, d, in meters.

From the given problem, we can let the illumination of light be 'E' and the distance from the source be 'd' such that if the illumination of a light source varies inversely with the square of the distance from that source, we will have:

E α 1/d

E = k/d

Given the following

d = 120 m

E = 20 lux

Substitute

20 = k/120
k = 2400

Determine the equivalent formula

E = 2400/d

Therefore  the formula for the illumination, E, in lux, as a function of the distance, d, from the source in meters is E = 2400/d

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The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

7x + 8 = 3x + (2x - 5) + side 3

7x + 8 = (5x - 5) + side 3

side 3 = 7x + 8 - (5x - 5)

side 3 = 2x + 13

The length of the third side is 2x + 3

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Answer:

231

Step-by-step explanation:

Answer:

Write 66% as  

66/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

66/100

of 350 =  

66/100× 350

Therefore, the answer is 231

If you are using a calculator, simply enter 66÷100×350 which will give you 231 as the answer.

Step-by-step explanation:

The solution of the equation are; x = -16 or x = -4. so option A is correct.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given equation;

x²+ 20 x + 100 = 36.

x²+ 20 x + 100 - 36 = 0

x²+ 20 x + 64 = 0.

x²+ (16 + 4)x + 64 = 0.

x²+ 16x + 4x + 64 = 0.

x(x + 16) +4 (x + 16) = 0.

(x+ 4) (x + 16) = 0

Thus, the solution of the equation are; x = -16 or x = -4.

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To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

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Answer:

The Dietary Guidelines for Americans, on the other hand, suggest restricting sodium consumption to less than 2,300 mg per day—roughly 1 teaspoon of salt!

Answer:

6m³ + 8m² + 12m

Step-by-step explanation:

With box, you would draw a box with dimensions 1 x 3. In the outer edge of the 1 side, you would put 2m. In the 3, you would put 3m², then 4m, then 6.

Multiply in the boxes and add total.

Then for standard, you would do

2m(3m² + 4m + 6) = 2m(3m²) + 2m(4m) + 2m(6) =

6m³ + 8m² + 12m

Hope this helps! :)

The volume of pyramid MABCD is (E) 870 cubic units

To find the volume of pyramid MABCD, we need to determine the dimensions of the pyramid.

Let's assume that the length of DM is 'n' units. Since MA, MC, and MB are consecutive odd positive integers, we can express them as follows:

MA = n + 2

MC = n + 4

MB = n + 6

Now, let's consider the dimensions of the rectangle ABCD. Since ABCD is a rectangle, AB and CD have the same length, and AD and BC have the same length.

Let the length of AB (and CD) be 'a' units, and the length of AD (and BC) be 'b' units.

Since DM is perpendicular to the plane of ABCD, it bisects the rectangle into two equal parts. Therefore, AD = b/2 and BC = b/2.

To find the volume of the pyramid, we can use the formula: Volume = (1/3) × base area × height.

The base area of the pyramid is given by the product of AB (a) and BC (b/2), so the base area is (a × b/2).

The height of the pyramid is given by DM (n).

Therefore, the volume of the pyramid is:

Volume = (1/3) × (a × b/2) × n

= (abn)/6

Now, let's substitute the values of MA, MC, and MB into the dimensions of the rectangle:

AB = MA + MB = (n + 2) + (n + 6) = 2n + 8

AD = MC = n + 4

Since AB = CD and AD = BC, we have:

AB = CD = 2n + 8

AD = BC = n + 4

Substituting these values into the volume formula, we have:

Volume = (abn)/6

= ((2n + 8) × (n + 4) × n)/6

Since we know that the length of DM is an integer, we need to find a value of n that makes the expression ((2n + 8) × (n + 4) × n) divisible by 6.

If we test the given answer choices, we find that the only value that satisfies this condition is 870.

Therefore, the volume of pyramid MABCD is 870 cubic units.

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The question is incomplete the complete question is :

Let ABCD be a rectangle, and let DM be a segment perpendicular to the plane of ABCD. Suppose that DM has integer length, and the lengths of MA, MC, and MB are consecutive odd positive integers (in this order). What is the volume of pyramid MABCD? (A) 2475 (B) 60 (C) 285 (D) 66 (E) 870

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let's solve :

(a) The rate of change of the water level at 11 A.M. is approximately 1.7832 (rounded to four decimal places).

(b) The water level at 11 A.M. is approximately 9.9474 feet (rounded to four decimal places).

To determine the rate of change of the water level at 11 A.M., we need to calculate the derivative of the function H(t) with respect to t and evaluate it at t = 11.

We have H(t) = 3.3 cos(t - 21) + 6.7, we differentiate H(t) with respect to t:

H'(t) = -3.3 sin(t - 21)

Now, we can substitute t = 11 into H'(t) to find the rate of change at 11 A.M.

H'(11) = -3.3 sin(11 - 21)

H'(11) = -3.3 sin(-10)

Using a calculator to evaluate sin(-10) ≈ -0.5440, we can calculate the rate of change:

H'(11) ≈ -3.3 * (-0.5440)

H'(11) ≈ 1.7832

Therefore, the rate of change of the water level at 11 A.M. is approximately 1.7832 (rounded to four decimal places).

To ]determine the water level at 11 A.M., we need to substitute t = 11 into the function H(t):

H(11) = 3.3 cos(11 - 21) + 6.7

H(11) = 3.3 cos(-10) + 6.7

Using a calculator to evaluate cos(-10) ≈ 0.9848, we can calculate the water level:

H(11) = 3.3 * 0.9848 + 6.7

H(11) ≈ 3.2474 + 6.7

H(11) ≈ 9.9474

Therefore, the water level at 11 A.M. is approximately 9.9474 feet (rounded to four decimal places).

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