A model of a dinosaur skeleton was made using a scale of 1 in : 15 in in a museum. If the size of the dinosaur’s tail in the model is 8 in, then find the actual length of dinosaur’s tail.

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.

The areas and volumes are given as follows:

a) Area of the four sides to be painted: 2448 m².

b) Area to be covered with shingles: 1140 m².

c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.

d) Total surface area: 5878.4 m².

The sides painted are divided as follows:

Hence the total area to be painted is found as follows:

Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².

(Area rectangle = base x height)

This part of the problem seems incomplete, however the answer is correct.

The volume is given by:

Volume = base area x height.

Hence:

Hence the volume is given by:

V = 26 x 42 x 0.16 = 174.72 m³.

The base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:

Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².

The top is composed by:

Hence:

Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².

Then the total surface area is:

Total surface area = 4632 + 1246.4 = 5878.4 m².

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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.

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%

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

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

Rs. 3125 is equivalent to 50 units of the foreign currency.

Step-by-step Explanation

The exchange rate of the foreign currency in Indian Rupee is Rs. 62.50

This means that

1 unit of that foreign currency = Rs. 62.50

Or better written as

Rs. 62.50 = 1 unit of the foreign currency

So, we are then told to find how much Rs. 3125 is in the foreign currency

Let Rs. 3125 be equal to x units of the foreign currency

Rs. 62.50 = 1 unit of the foreign currency

Rs. 3125 = x units of the foreign currency

A simple mathematics relation obtained by cross multiplying will give us the value of x

After cross multiplying

62.50 × x = 3125 × 1

62.50x = 3125

Divide both sides by 62.50

(62.50x/62.50) = (3125/62.50)

x = 50

Therefore, Rs. 3125 is equivalent to 50 units of the foreign currency.

Hope this Helps!!!

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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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:

To solve for the equation of the line parallel :

For parallel line equation:

Slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept

First let's find the slope of the line.

To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates.

Slope= 5

The y-intercept is (0, b). The equation passes through the origin, so the y-intercept is 0.

Hence the

Answer:

Step-by-step explanation:

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:

Step by step explanation:

We can solve this situation by the theorem of the angle formed outside of a circle by intersection:

*For two tangents:

Then, if m

[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]

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

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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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%

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

Postulates and Theorems of Parallel Lines

First, we need to know what type of angles are <3 and <7. Following the definition:

If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.

Angles 3 and 7 are corresponding angles and they are told to be congruent.

Now we apply the postulate that reads:

The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate

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:

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:



Answer: the width, length and height

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

Answer: 47+13 =60

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

Step-by-step explanation:

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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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:

solve for x

answer: C. 9

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

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.

1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:

2) So, based on that constant of proportionality (k) we can find the missing leg.

Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.

To find the slope of the line we have to use this equation:

Now we have to replace two coordiantes in the line, so I was able to see the coordinates: (0,40) and (20,50), sothe equation become:

and we simplify so:

So the slope is 1/2