John spent equal amounts of money on 6 robots and 7 dolls. each robot costs $12 more than each doll. How much did John spend in all?

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer: 5/2x-3

Step-by-step explanation: you would subtract 6 from both sides.

5x = 2y + 6

-6            -6

6-6=0 so they would cross out. and you can't subtract 5x from 6 because they aren't like terms. Your new equation would look like 5x-6 = 2y.

Now you need to get the y alone. To do that you need to divide everything by 2 so that the 2y crosses out. 5x-6 = 2y

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

                                                                             2    2    2

I'm trying to visually show it sorry if it looks weird. one you divide everything. (5/2) (-6/2) (2/2) you'll need to clean everything up.

Since you can't simply 5/2 leave it as a fraction. Which makes your answer: 5/2x - 3 = y or y = 5/2x - 3

The sample size is 56.

As per the given question, we need to calculate the sample size. We are given the following information:

Expected population deviation rate (EPDR) = 1.00

Tolerable deviation rate (TDR) = 6%

Control risk = 5%

The formula to calculate the sample size is:

Sample size = (Z² * EPDR * (1-EPDR)) / [(TDR/EPDR)² + (Z² * EPDR * (1-EPDR))]

Where Z = 1.65 for a 5% risk of assessing control risk too low

Putting the values in the formula, Sample size = (1.65² * 1.00 * (1-1.00)) / [0.06² + (1.65² * 1.00 * (1-1.00))]

Sample size = 55.08≈ 56 (approx)

Hence, the sample size is 56.

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Answer:

y=93/5x+3

Step-by-step explanation:

Answer:

25 cups and 10 teaspoons

Step-by-step explanation:

The two triangles are similar If they have the same shape, but their sizes are different.

Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

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Answer:

As x --> ∞, then y --> - ∞

Step-by-step explanation:

As the value of x increases(as the graph goes right), the graph seems to go down, meaning the y-values are getting more an more negative. This means that as x approached infinity, the y values approach negative infinity ( x --> ∞, y --> - ∞ ).

As the value of x decreases(going to the left), the graph seems to go higher and higher. Therefore, as x approaches negative infinity, the y-value approach infinity. ( x --> - ∞, y --> ∞ )

Out of the options given, the one As x --> ∞, then y --> - ∞ is true.

Answer:

The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.

Step-by-step explanation:

To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:

s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)

= (96 +/- sqrt(9216 + 4352)) / -32

= (96 +/- sqrt(13,568)) / -32

Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:

s = (96 + sqrt(13,568)) / -32

= (96 + 120) / -32

= 0.5625 seconds

Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.

To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.

Answer:

Mean: 20

Median: 16

Mode: No mode

Step-by-step explanation:

For the mean:

44 + 4 + 27 + 5 = 80

80/4 = 20

For the median:

5 + 27 = 32

32/2 = 16

For the mode:
None of the numbers are repeated.

The answer to the question is C, which is integers 4,5 or -4,-3.

Let's call the first integer x and the second integer x+1 (since they are consecutive).
According to the problem, we can set up the following equation:
x(x+1) = x + (x+1) + 19
We can simplify this equation by expanding the left side and combining like terms on the right side:
x^2 + x = 2x + 20
Now we can move all the terms to one side and get a quadratic equation:
x^2 - x - 20 = 0
We can factor this equation as (x-5)(x+4) = 0, which means the solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The long answer includes all the steps of solving the quadratic equation:
x^2 - x - 20 = 0
We can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a=1, b=-1, and c=-20.
x = (1 ± √(1 - 4(1)(-20))) / 2(1)
x = (1 ± √81) / 2
x = (1 ± 9) / 2

The two solutions for x are 5 and -4.
Therefore, the two consecutive integers are either 4,5 or -4,-3.
The product of two consecutive integers is 19 more than their sum. To find the integers, let's represent them as x and x+1.

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9514 1404 393

Answer:

  12 ft

Step-by-step explanation:

We can let x represent the average of length and width. Then the length is x+2, and the width is x-2. Then the area is ...

  (x +2)(x -2) = 96

  x^2 = 100

  x = √100 = 10

The length is x+2, so ...

  the length of the garden is 12 feet.

Answer:

No solution equation

Step-by-step explanation:

bshs

Answer:

Step-by-step explanation:

4 (2x + 3) = (2x - 2) + 2 (3x + 7)

=> 8x + 12 = (2x - 2) + (6x + 14)

=> 8x + 12 = 8x + 12

Since, both the equations are same, it is more than 1 solution or  infinite solutions.

Answer:

\(m=\frac{-5}{3}\)

Step-by-step explanation:

We want to find the slope between the points (-2,5) and (1,0).

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

We are already given the values of the points, but let's label their values to avoid any confusion and mistakes.

\(x_1=-2\\y_1=5\\x_2=1\\y_2=0\)

Now, substitute into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{0-5}{1--2}\)

Simplify this to:

\(m=\frac{0-5}{1+2}\)

\(m=\frac{-5}{3}\)

The slope is -5/3.

Answer:

y = -x + 7

Step-by-step explanation:

owa owa

Answer:x+6y=5

4x−5+y=0

3x+y=16

Step-by-step explanation:

Have a great day! <3

Answer:

the third one

Step-by-step explanation:

8x + 40 ≥ 0

8x ≥ -40

x ≥ -5

Answer:

the answer is A i take a test on it i hope it help

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

A) Acute angle

Step-by-step explanation:

Because it measures not greater than 90°

Answer:

The answer is A) acute

Step-by-step explanation:

hope this helps!

Answer:

The answer is "\(22^{\circ}\)"

Step-by-step explanation:

Please find the question image file in the attachment:

In this question, \(\angle B =90^{\circ}\), that is made up of the two complementary angles that are 57 and 3x.

So, the equation is:

\(\to 57+3x=90\\\\\to 3x=90-57\\\\\to 3x= 33\\\\\to x=\frac{33}{3}\\\\\to x= 11\)

In \(\Delta ABC\):

BC=2x

put the value of x in above then \(BC= 2\times 11^{\circ} =22^{\circ}\)

The remainder when f(x) is divided by (x+5) is -4645.  This result is obtained by applying the Remainder Theorem, which provides a convenient and efficient way to determine the remainder of a polynomial division without actually performing the division process.

Using the Remainder Theorem, we can find the remainder when a polynomial, f(x), is divided by a linear divisor, (x-c).

In this case, f(x) = x^5 - 6x^4 + 2x^3 + 4x – 5 and the divisor is (x+5), so c = -5.

The Remainder Theorem states that if f(x) is divided by (x-c), the remainder is f(c). Therefore, we need to find the value of f(-5) to determine the remainder when f(x) is divided by (x+5).

f(-5) = (-5)^5 - 6(-5)^4 + 2(-5)^3 + 4(-5) - 5
      = -3125 - 6(625) + 2(-125) - 20 - 5
      = -3125 - 3750 - (-250) - 20 - 5
      = -3125 - 3750 + 250 - 20 - 5
      = -4870 + 250 - 25
      = -4645

Hence, the remainder when f(x) is divided by (x+5) is -4645. This result is obtained by applying the Remainder Theorem, which provides a convenient and efficient way to determine the remainder of a polynomial division without actually performing the division process.

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Answer:

Answer is A

Step-by-step explanation:

(14x^4y^6)/(7x^8y^2)

because everything is one term, you can split into three terms

14/7, x^4 / x^8 , and y^6/y^2

multiplying these three terms will get us the starting term

14/7 = 2

x^4 / x^8

with division of exponents, you subtract the smaller exponent (4), from the big exponent (8), and leave it on the same side (bottom) as the big exponent

1/x^4

same thing with our y's

y^6/y^2

this time, the term stays on the top

y^4

take the simplified terms and multiply them together

(2) * (1/x^4) * (y^4) =

A: (2y^4) / (x^4)

The value of the expression 6×(0.7 + -0.8) ÷ -2 is 0.3.

To calculate the expression 6×(0.7 + -0.8) ÷ -2

we can follow the order of operations (PEMDAS/BODMAS) which states that we should first perform any calculations within parentheses

Evaluate any exponents or multiplication/division operations from left to right, and finally perform addition/subtraction operations from left to right.

Let's break down the expression step by step:

Calculate the sum within the parentheses:

0.7 + -0.8 = -0.1

Multiply the result by 6:

6 × (-0.1) = -0.6

Finally, divide the result by -2:

-0.6 ÷ -2 = 0.3

Therefore, the value of the expression 6×(0.7 + -0.8) ÷ -2 is 0.3.

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Answer:

60 local calls

Step-by-step explanation:

Total price minus the long-distance charges: 54.35 - 8.35 = $46.00

46 minus the fixed per month cost: 46-31 = $15

15 divided by the cost of each local call: 15/0.25 = 60 calls

Answer:

6+1.25t

Step-by-step explanation:

W(in the 1st month)=6+1.25

W(in the 2nd month)=6+1.25+1.25

W(in the 3rd month)=6+1.25+1.25+1.25

W(in the t months)=6+t(1.25)

Step-by-step explanation:

the slow intercept form is

y = ax + b

the slope is always the factor a of x (in every line equation).

it is defined as the ratio y/x expressing how many units y changes, when x changes a certain amount of units - e.g. when going from one point on the line to another.

so, for the given 2 points x changes by -5 (from 7 to 2), and y changes by +10 (from 2 to 12).

therefore, the slope is 10/-5 = -2

our line equation looks more like

y = -2x + b

to get b we use the coordinates of one of the points.

e.g. 7, 2

2 = -2×7 + b = -14 + b

b = 16

or full line equation is

y = -2x + 16

Answer:

D

Step-by-step explanation:

In a boxplot, potential outliers are data points that are more than 1.5 Interquartile Ranges (IQRs) from the edges of the box. A boxplot visually represents the distribution of a dataset, with the box containing the middle 50% of the data and the edges representing the lower and upper quartiles.

To answer your question, potential outliers in a boxplot are points that are more than 1.5 times the interquartile range (IQR) away from the edges of the box. The IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of the data. The box in a boxplot represents the IQR, with the median (50th percentile) marked by a line inside the box. The whiskers of the boxplot extend to the minimum and maximum values that fall within 1.5 times the IQR from the edges of the box. Any points outside this range are considered potential outliers and are plotted as individual points beyond the whiskers. However, it is important to note that potential outliers do not necessarily indicate errors or incorrect data, and further investigation may be needed to determine their validity. Overall, boxplots are a useful tool for visualizing the spread and distribution of numerical data.

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Answer:

4⁴⁰

Step-by-step explanation:

just multiple 5×8

that's it