Let a represent the row number in this pattern. Write a rule that tells you the number of dots, d, in row n (Hint: Your rule should begin with "d=") Row 1 Row 2 Row 3 Row 4​

Answer:

[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]

Step-by-step explanation:

          We will use the distance formula to solve.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(1--5)^2 +(-2-5)^2}[/tex]

[tex]\displaystyle d=\sqrt{(6)^2 +(-7)^2}[/tex]

[tex]\displaystyle d=\sqrt{36+49}[/tex]

[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]

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Given data:

Vincent turned his head 30° to the side.

The figure in the option b is the angle that he turned his head.

In order to translate the words into a number sentence, first let's translate each word or expression separately:

Four less than seven: "7 - 4"

Is greater than: ">"

Zero: "0"

Therefore the number sentence will be:

Answer:

Step-by-step explanation:

The smallest value of length AC would be 5 ft - 3 ft = 2 ft while the largest length would be 5 ft + 3 ft = 8ft. The answer will be

2 < Ac < 8

We can calculate the percent of change by means of the following formula:

Where x2 is the new value and x1 is the original value.

In this case, we go from 60 to 24, then the original value (x1) was 60 and the new value (x2) is 24, by replacing these values into the above equation, we get:

Then, the percent of change equals -60%

Okay, here we have this:

Considering the provided inequation, we are going to identify how can be represented on a number line, so we obtain the following:

So the first thing we will do is factor to find the solution intervals, we have:

According to this, we finally obtain that the solution interval is option D, because it satisfies the found interval and its endpoints are closed.

Given:

The set of data is given as

Required:

To find the mean.

Formula:

Explanation:

Mean is the ratio of the sum of the values and the number of values.

No of values in the given data is 7.

Final Answer:

okay so the answer is 9ft so option B

now we can take a look at how we arrived to that answer

do you know the formula for the volume?

the company's profit in 2015 was $89,600,000 (89.6 million dollars)

43%

Profit in 2011 = $128 million

Profit in 2015 decreased by 30%

% decrease = (old price - new price)/old price

old price = Profit in 2011 , new price = Profit in 2015

30% = (128,000,000 - new price)/128000000

Hence, the company's profit in 2015 was $89,600,000 (89.6 million dollars)

Percentage increase = (new price - old price)/old price

new price = 128million dollars , old price = 89.6 million dollars

% increase = [(128 - 89.6)in millions/(89.6) in millions] × 100

% increase = 38.4/89.6 × 100

% increase = 0.43 × 100

% increase = 43%

Hence, the label's profit must increase by 43% from its 2015 value to reach $128 million within the next two years

The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:

If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.

Now let's compare that generic equation with the function given by the question:

One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:

So the initial price was $3000.

Now let's compare the terms inside parenthesis that are raised to t:

As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:

We can substract 1 from both sides of this equation:

And we multiply both sides by 100:

So each year the price increases in a 1.9%.

Then the answers in order are:

$3000

growth

1.9%

The equation of line is [tex]6y=6x$-$12[/tex].

The given slope is [tex]\frac{1}{6}[/tex].

The [tex]y $-$[/tex]intercept is [tex](0, $-$2)[/tex].

We have to write the equation of line using the given slope and [tex]y $-$[/tex]intercept.

The equation of line with the slope m and [tex]y $-$[/tex]intercept of [tex](0,a)[/tex] is [tex]y=mx+a[/tex].

From the question,

The value of  [tex]m=\frac{1}{6}[/tex]

The value of [tex]a= $-$2[/tex]

Now putting the value of [tex]m[/tex] and [tex]a[/tex] in the equation of line.

[tex]y=\frac{1}{6}x+( $-$2)\\y=\frac{1}{6}x$-$2[/tex]

Multiply by [tex]6[/tex] on both side

[tex]y\times6=6\times(\frac{1}{6}x$-$2)\\6y=6\times\frac{1}{6}x$-$6\times2\\6y=6x$-$12[/tex]

The equation of line is [tex]6y=6x$-$12[/tex].

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Explanation

Step 1

Let

A whole pizza = 1 pizza

Dexter eats 1/2

Landry eats 1/3

x= fraction of the pizza remains

Step 2

the r

1) Let's start out isolating the cosine by dividing both sides by 2

2) From that we can find two general solutions in which the cosine of theta yields the square root of 3 over two:

But not that there is a restraint, so we can write out the solution as:

The formula for determining the nth term of a geometric sequence is expressed as

Tn = ar^(n - 1)

Where

a represents the first term

r represents the common ratio.

n represents the number of terms

From the information given,

a = 2, r = 3

Thus, the rule for the nth term of the geometric sequence is

Tn = 2 x 3^(n - 1)

To determine the fifth term, we would substitute n = 5 into the equation. It becomes

T5 = 2 x 3^(5 - 1)

T5 = 2 x 3^4

T5 = 162

The fifth term is 162

Answer:

y = 11

Step-by-step explanation:

Hello!

We can utilize the slope formula to create the equation for y:

The value of y is 11.

SOLUTION:

Step 1:

In this question, we are given that;

If a red and a blue fair six-sided die are rolled.

What is the probability the result is 8 or divisible by 3?

Step 2:

The table for the two dice rolled together is as shown below:

Green 1 2 3 4 5 6

Red

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Step 3:

The probability that the result is 8 =

Next,

The probability that the result is divisible by 3

=

Finally, the probability that the result is 8 or divisible by 3, we have that:



Weight required to destroy a bridge cable (in ponds) The type of variable is Nominal Categorical

A frequently used category variable is gender. Categorical variables can either be ordinal or numeric.

The closing price (in dollars) of the stock is a quantitative variable, and since the price involves an absolute zero, the scale of measurement is a ratio scale

Pounds is what type of variable?

Weight is a prime example of a ratio variable (e.g., in pounds). With certainty, we may state that 20 pounds weigh twice as much as 10 pounds. Ratio variables also have an important zero-point (e.g., exactly 0 pounds means the object has no weight)..

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Solution:

Let's find a expression such that if you apply the distributive property to your expression it would give the same result presented:

• 8x + 12 = 2 (4x + 6)

• 8x + 12 = 4 (2x + 3)

• 8x + 12 = 8 (x + 1.5)

Any of these expressions could be the solution to the question.

Given: Different statement relating different quadrilateral

To Determine: If true or false statement

Solution

The image below summarizes the properties of a quadrilateral

From the above, we can conclude that

Answer: 47+13 =60

60 as a fraction should be 3/5 in simplest form.

Step-by-step explanation:

Given the graph of f(x):

Where the points A, B, and C have the coordinates:

Now, the transformation -f(x) is just a reflection about the x-axis. This is equivalent to a change of sign on the y-coordinate. The new points A', B', and C' are:

And the graph looks like this:

Now, for the f(x) - 2 transformation, we see that this is just a shift of 2 units down. Then:

Where:

Solution;

Given the results:

From the above data:

A) The low-end value is

B) The high end value is

C) Does this data set have outlier?

D) Outlier:

We should know that :

1 pound = 16 ounces

The question is :

Which is more, 1/2 of a pound or 6 ounces?

so,

1/2 of a pound = 1/2 x 16 = 8 ounces

So,

8 ounces > 6 ounces

so, the answer is option 1

The more is 1/2 of a pound

A linear function or a direct variation function is represented by:

where k is the constant rate of chante, in this case $15 per hour.

s=y= salary of Lindsay

h=x= hours she has worked

Then, the equation that represents the situation would be:

Answer:

Step-by-step explanation:

7(x+2) = 7x+14

7(x+2)=7x+7 times 2

4(x+4)= 4x+16

4 times x = 4x

4 times 4 = 16

= 4x+16

9(x+6) = 9x+54

9 times x = 9x

9 times 6 = 54

= 9x+54

Answer: the width, length and height

Step-by-step explanation: multiply the width length and height of a cube and you get the area

solve for x

answer: C. 9

Answer:

Lower limit: 11.7 cm

Upper limit: 16.263

Explanation:

The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :

Where:

• μ = sample mean

• σ = sample standard deviation

• Z* = critical value of the z-distribution

• n = is the sample size

In this case:

• μ = 14cm

• σ = 4cm

• n = 12

The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96

Now, we can use the formula above to find the upper and lower limit:

Thus:

Rounded to one decimal:

Lower limit: 11.7cm

Upper limit: 16.3cm