Complete the pattern.

___, ___, ___, 0, 2, 4, 6

-1, -2, -3
-2, -4, -6
-6, -4, -2

Answer:

36 ft

Step-by-step explanation:

The ratio of the lengths of the sides is the same as the ratio of the perimeters.

Just like one side (15 ft) of triangle ABC is 3 times as long as the corresponding side (5 ft) of triangle DEF, the perimeter of triangle ABC is also 3 times the perimeter of triangle DEF.

15/5 = x/12

3 = x/12

x = 36

Answer: 36 ft

Answer:

Point slope form is the best form to use for this particular question.

We reflect point slope form as:  \(y-y_{1} =m(x-x_1)\)

M reflects the slope, and the X and Y values are the coordinates given.

M = -2, X = 4, Y = 2

This should result in an equation that looks like this:

\(y-2=-2(x-4)\)

Now, if we want to turn this equation into slope-intercept form, we have to do some calculations. First of all, we have to multiply -2 with (x-4) to get

\(y-2=-2x+8\)

Next, we add two on both sides to isolate the Y variable.

Therefore, the slope-intercept equation would be: \(y=-2x+10\)

The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

The required answer is the series ∑ln(6k)4k diverges.

determine whether the series ∑ln(6k)4k converges or diverges.

To analyze the convergence or divergence of the given series, we can use the Ratio Test:

1. Find the ratio of consecutive terms: a_(k+1)/ask
  In this case, a_k = ln(6k)4k.

2. Compute the limit as k approaches infinity: lim(k->∞) (a_(k+1)/a_k)
  a_(k+1) = ln(6(k+1))4(k+1) and a_k = ln(6k)4k

3. Compute the ratio: (ln(6(k+1))4(k+1))/(ln(6k)4k)

4. Find the limit as k approaches infinity: lim(k->∞) [(ln(6(k+1))4(k+1))/(ln(6k)4k)]

5. Apply L'Hopital's rule for indeterminate forms (0/0 or ∞/∞) if needed.

If limit exist and partial sum converges or individual term approaches zero then series is convergent otherwise divergent and further checked by methods explained below.
In this case, however, we notice that the terms in the series do not go to zero, since ln(6k)4k will always grow larger as k increases. This implies that the series does not converge.

Thus, the series ∑ln(6k)4k diverges.

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fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer:

Answer:

c

Step-by-step explanation:

because c is the answer lady

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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Answer: A

Step-by-step explanation:

Unit means per 1, there are 4 units. 2.12 divided by 4 is 0.53

The series is convergent with sum 5/8

A series is said to be convergent, if it converges to a value as the terms of series tends to infinity.

A series is said to divergent, it it does not converge to a value but keeps on either increasing or decreasing as the terms of series tends to infinity.

In the question ,

\(\frac{1}{3} +\frac{2}{9} + \frac{1}{27} +\frac{2}{81}+..\) is given series

dividing the series into two parts ,

\((\frac{1}{3} +\frac{1}{27} +\frac{1}{243}+..)\) + \((\frac{2}{9} + \frac{2}{81} + \frac{2}{729}+...)\)

Using infinite geometric series formula both the side ,

=> \(\frac{\frac{1}{3}}{1- \frac{1}{9}} + \frac{\frac{1}{2}}{1- \frac{1}{9}}\)

=> \(\frac{1/3}{8/9}+ \frac{1/2}{8/9}\)

=>  \(\frac{3}{8} + \frac{1}{4}\)

=> \(\frac{5}{8}\)

Hence , the series is convergent.

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The dimensions are 3 inches, 10 inches, and 13 inches.

It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.

Therefore,

(2x + 6)²

4x²+ 24x + 36

Reduce to lowest term

x² + 6x + 9

x² + 3x + 3x + 9

x(x + 3) - 3(x + 3)

(x - 3) = 0

x = 0 + 3 = 3

Therefore x = 3

Therefore the dimensions will be:

x = 3

2x + 4 = 2(3) + 4 = 10

2x + 6 = 2(3) + 6 = 12

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Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

Recall that the function for the trapezoid area is:

A(x)=(B+b)*h/2

where

B and b are the bases and

h is the height.

Thus, given a height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x) * 14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

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Answer:

1. 18/800×100%

=2.25%

2. 288/360×100%

=80%

3. 33/132×100%

=25%

4. 18/72×100%

=25%

5. 20/32×100%

=62.5%

6. 55/250×100%

=22%

Answer:

160 times X

Step-by-step explanation:

160 is the number of pencils in each box.

And

X is how many boxes there are.

If 1 box contains 160 pencils then the equation which represents the total number of pencils is y=160x.

An equation is a relationship between two or more variables where variables represent some quantity . It is mostly found in equal to form. It is equated to find the value of variables.

Equation form :y=a+bx

There are 160 pencils in one box and x represents the number of boxes. So the equation that represents the total number of pencils can be found by product of x and 160.

Equation will be x*160=160x.

Hence the equation which represents the total number of pencils is y=160x.

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The standard equation of the circle with endpoints of a diameter (−6, 7) and (−4, 3) can be expressed as (x+5)^2+(y-5)^2 = 13.

First, calculate the midpoint of the two points given, which can be calculated by taking the average of the x-coordinates and the average of the y-coordinates. The midpoint is then (-5,5).
Then, calculate the radius of the circle by taking the distance between the midpoint and one of the given points, which in this case is the distance between (-5,5) and (-6,7). Using the distance formula, the radius of the circle is √10.
Finally, use the general equation of a circle to find the standard equation of the circle that satisfies the criteria given. The general equation of a circle is (x−h)^2+(y−k)^2=r^2, where (h,k) is the center of the circle and r is the radius of the circle. Since the center of the circle is (-5,5) and the radius is √10, the equation can be rewritten as (x+5)^2+(y-5)^2 = 13.

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Step-by-step explanation:

\( \frac{3}{9} = \frac{5}{y} = \frac{x}{12} \\ \frac{3}{9} = \frac{5}{y} \\ 3y = 45 \\ y = 15 \\ \\ \frac{3}{9} = \frac{x}{12} \\ 9x = 36 \\ x = 4\)

Arithmetic expressions can be used as control expressions in programming languages when a control structure, such as an if statement or a loop, expects a condition to determine the flow of execution

Arithmetic expressions can be used as control expressions in certain programming languages or contexts where a control structure expects a conditional expression to determine the flow of execution.

Typically, control expressions are used in decision-making structures such as if statements, while loops, for loops, and switch statements.

In most programming languages, the control expression must evaluate to a boolean value (true or false) in order to determine the execution path. However, some languages allow arithmetic expressions to be used in control structures, considering a value of zero as false and any non-zero value as true.

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The time series component which reflects gradual shifts or movements to relatively higher or lower values over a longer period of time is a trend pattern. (Option D)

A time series refers to a collection of observations of well-defined data items obtained through repeated measurements over time. Generally, a time series is a sequence taken at successive equally spaced points in time and thus it is a sequence of discrete-time data. An observed time series comprises of three components: the trend (long term direction), the seasonal (systematic, calendar related movements) and the irregular (unsystematic, short term fluctuations). A trend pattern occurs when there is a long-term increase or decrease in the series. It is the gradual shifts or movements to higher or lower values over a period.

Note: The question is incomplete as it is missing options which are A) seasonal pattern. B) cyclical pattern. C) trend and seasonal pattern. D) trend pattern.

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The simplified expression is\($-11p^2-8p+\frac{7}{3}$, where $a=-11$ and $b=\frac{7}{3}$.\)

To simplify the given expression, let's break it down step by step.
Step 1: Simplify the expressions inside the parentheses:
\($((5p+1)-2p\cdot4)(3)(4-1\div3)(6p-9)$$=(5p+1-8p)(3)(4-\frac{1}{3})(6p-9)$$=(-3p+1)(3)(\frac{11}{3})(6p-9)$\)
Step 2: Simplify the expression in the first set of parentheses:
\($=(-3p+1)(\frac{11}{3})(6p-9)$\\\)
Step 3: Expand the expression using the distributive property:
\($=-\frac{33}{3}p^2+11p+6p-\frac{11}{3}-18p+6$\)
Step 4: Combine like terms:
\($=-11p^2-8p+\frac{7}{3}$\\\)
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Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

The value of Fx(-5,2) is -30. To find Fx(-5,2), we first need to take the partial derivative of F with respect to x.

F(x,y) = 3x^2 + 5y^2

Taking the partial derivative of F with respect to x, we get:

Fx(x,y) = 6x

Now, to find Fx(-5,2), we simply plug in -5 for x and 2 for y:

Fx(-5,2) = (6 * -5)

Fx(-5,2) = -30

Therefore, the value of Fx(-5,2) is -30.

In the given function F(x,y) = 3x^2 + 5y^2, the partial derivative Fx indicates how much the function changes with respect to changes in x while keeping y constant. In other words, it measures the instantaneous rate of change of the function in the x-direction at the given point (-5,2). A negative value for Fx(-5,2) indicates that the function is decreasing in the x-direction at that point.

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Answer:

4 x 10^5

Step-by-step explanation:

To divide (4.8x10^3) by (1.2x10^-2), we need to divide 4.8 by 1.2, and then multiply the result by 10^3 / 10^-2.

4.8 divided by 1.2 is 4.

10^3 / 10^-2 can be simplified as 10^3 * 10^2 = 10^(3+2) = 10^5.

So, the expression can be written as:

(4.8x10^3) / (1.2x10^-2) = (4 / 1.2) x 10^5

= 4 x 10^5

The standard form of this expression is 4 x 10^5.

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Given statement solution is :- The set of ordered pairs (-1, -3) and (5, 5) determine a line with a slope of 4/3, according to the given statement's answer.

To determine the slope of a line given two ordered pairs (x1, y1) and (x2, y2), we use the formula:

slope is equal to y2 - y1 / x2 - x1.

Let's calculate the slopes for each set of ordered pairs:

A. (5, -3) (2, 3)

slope = (3 - (-3)) / (2 - 5)

= 6 / (-3)

= -2

B. (3, 10) (-3, -2)

slope = (-2 - 10) / (-3 - 3)

= -12 / (-6)

= 2

C. (3, -5) (-3, -7)

slope = (-7 - (-5)) / (-3 - 3)

= (-2) / (-6)

= 1/3

D. (-1, -3) (5, 5)

slope = (5 - (-3)) / (5 - (-1))

= 8 / 6

= 4/3

Option D's set of ordered pairs, (-1, -3) and (5, 5), results in a line with a slope of 4/3.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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Answer:

The sum of the series is 44.

Step-by-step explanation:

Sigma notation. I just had a test on this, so this is pretty good timing.

Below the sigma, we see that k = 1. This means that 1 is the number you would substitute for k into the expression on the right to get the first term. In this case, the first term is -2. (2(1)² - 4)

Now, we can also find out the number of terms in the series by subtracting 1 (taken from k = 1) from the number on top of the sigma, 4, and then adding 1 to it.

4 - 1 + 1 = 4. This means there are 4 terms in the series.

See the remaining work in the attached file. You should get that the sum of the series is 44.

Hope this helps!

Answer:

Store 1

Step-by-step explanation:

Given

See attachment

Required

Determine the store with the best price per unit

It should be noted that the store with the best has the least price per unit.

So, we have:

Store 1

\(Quantity = 10\ ft\)

\(Price = \$2.50\)

The unit rate is:

\(Rate = \frac{Price}{Quantity}\)

\(Rate = \frac{\$2.50}{10\ ft}\)

Rate = $0.250 per feet

Store 2

\(Quantity = 2\ yd\)

\(Price = \$1.85\)

Convert quantity to feet

\(Quantity = 2 * 3ft = 6ft\)

The unit rate is:

\(Rate = \frac{Price}{Quantity}\)

\(Rate = \frac{\$1.85}{6\ ft}\)

Rate = $0.308 per feet

Store 3

\(Quantity = 12\ ft\)

\(Price = \$3.40\)

The unit rate is:

\(Rate = \frac{Price}{Quantity}\)

\(Rate = \frac{\$3.40}{12\ ft}\)

Rate = $0.283 per feet

Store 4

\(Quantity = 5\ yd\)

\(Price = \$4.00\)

Convert quantity to feet

\(Quantity = 5 * 3ft = 15ft\)

The unit rate is:

\(Rate = \frac{Price}{Quantity}\)

\(Rate = \frac{\$4.00}{15\ ft}\)

Rate = $0.267 per feet

From the calculations above; store 1 has the least unit rate.

Hence, store 1 has the best price per unit

At this rate, Paula will use 35 oz of sauce and 28 oz of cheese to make 7 pizzas.

To determine how much sauce and cheese Paula's Pizza Parlor will use to make 7 pizzas, we need to first find the rate at which the ingredients are used. From the given information, we can see that 3 pizzas require 15 oz of sauce and 12 oz of cheese. This means that each pizza requires 5 oz of sauce and 4 oz of cheese.

To find the total amount of sauce and cheese needed for 7 pizzas, we can simply multiply the amount needed for one pizza by 7. This gives us a total of 35 oz of sauce and 28 oz of cheese needed to make 7 pizzas.

It is important to accurately calculate the amount of ingredients needed for a given amount of pizzas to ensure that there is enough to satisfy demand without wasting excess ingredients. This can help businesses like Paula's Pizza Parlor manage their inventory and expenses efficiently.

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