Area of composite figures worksheet. How do you solve it. Step-By-Step​

Answer:

adjacent angle .................

Answer:

0.9817.

Step-by-step explanation:

We are going to assume that this data is distributed based on the normal distribution.

Mean (population)= μ= $190

Standard deviation= σ= $12

n= 50

Meaning of "sample mean falls within $4": Sample value is between $186 and $194.

Check image below to see the calculation process:

Note: These values for probabilities can also be found in tables provides by book authors. You may ask your teacher/tutor about the and they will probably know where to find them.

The graph is not a direct variation because the line does not go through the origin; option C.

A direct variation is a relationship between two or more quantities in which as one quantity increases, the other quantity also increases. Similarly, if the other quantity decreases, the other decreases as well.

For the graph of a direct variation, the line must pass through the origin.

Therefore, the graph does not represent a direct variation because the line does not go through the origin.

In conclusion, direct variation involves a corresponding increase or decrease in two related quantities.

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Answer:

16 shirts = GH¢256

Step-by-step explanation:

If 5 shirts cost GH¢80​

Let's determine the price of 16 shirts by cross multiplying the values

This method of evaluating answers is one of the essential methods .

It's just Making sure that the values within each side of the wall to symbol crosses each other.

But one shirt = GH¢80​/5

one shirt = GH¢16

So

5 shirts= GH¢80​

16 shirts = (16 shirts * GH¢80​)/5 shirts

16 shirts = GH¢1280/5

16 shirts = GGH256

Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches,  the area is 260.1 inches.

Step-by-step explanation:

25.5/5=5.1

5.1*2=10.2

The width is 10.2 inches

25.5*2+10.2*2=71.4

The perimeter is 71.4 inches

20.5*10.2=260.1

The area is 260.1

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in.

\(P=2\times(l+w)\)

where, 'l' is the length of the rectangle

'w' is the width of the rectangle

\(A=l\times w\)

For given example,

The sides of a rectangle are in the ratio 2:5

The longer side of the rectangle is 25.5 in.

This means the length of the rectangle is \(l=25.5~in.\)

Let 'x' represents the width of the rectangle.

⇒ \(\frac{2}{5} =\frac{x}{25.5}\)

⇒ 2 × 25.5 = 5 × 'x'

⇒ 51 = 5x

⇒ x = 51/5

⇒ x = 10.2 in.

This means the width of the rectangle is 10.2 in.

⇒ \(l=25.5~in,~w=10.2~in.\)

Using the formula of perimeter of the rectangle,

⇒ P = 2 × (25.5 + 10.2)

⇒ P = 2 × 35.7

⇒ P = 71.4 in.

Using the formula of area of the rectangle,

⇒ A = 10.2 × 25.5

⇒ A = 260.1 sq. in.

Therefore, the width of the rectangle is 10.2 in.

The perimeter of the rectangle is 71.4 in.

The area of the rectangle is 260.1 sq.in.

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To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer:

C

Step-by-step explanation:

The last part is -8, which means 8 fewer.

As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer:

\(\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha\)

Step-by-step explanation:

Step(i):-

Given that the trigonometric function

            \(\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha }\)

  we know that    sin²∝ + cos²∝ = 1

                      ⇒    sin²∝ = 1- cos²∝

Now we have to simplify the given trigonometric function

                =       \(\frac{cosec\alpha(sin^{2} \alpha ) }{sin\alpha cos\alpha }\)

               =       \(\frac{cosec\alpha(sin \alpha ) }{ cos\alpha }\)

Step(ii)

         we know that  cosec∝ = 1/ sin∝

              = \(\frac{\frac{1}{sin\alpha } (sin \alpha ) }{ cos\alpha }\)

    After cancellation sine function, we get

          =  \(\frac{1 }{ cos\alpha } = sec\alpha\)

Final answer:-

\(\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha\)

The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.

Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.

Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.

Every function has a domain (input variable) and a range (output variable) or codomain.

Constant donation = $7

Variable donation per mile = $0.25

Function, F(d) = 7 + 0.25m

where d = the total amount donated

m = the total miles the person walks

Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.

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Answer:

OK so he gets 3000 a year

so 3000t is what we need. thats 3000 times the number of years.

His starting salary is 41250, so we would add that on.  

K = 3000t + 41250.

Step-by-step explanation:

The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:

The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.

Therefore, we find ƒ(-4) = -51.

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Answer:

|.25|

Step-by-step explanation:

Answer:

-1 / 4 = 0.25

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

HEHEHEHEHEHEHE

The transformation function can be represented as vwxyz \($\rightarrow$\)qrstu = (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u).

This algebraic representation of the transformation of pentagon vwxyz into pentagon qrstu is using the notation of a function. A function takes an input (in this case, the coordinates of pentagon vwxyz) and produces an output (in this case, the coordinates of pentagon qrstu). This transformation can be represented by the notation (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u). This notation means that the coordinates (v,w,x,y,z) are being transformed into the coordinates (q,r,s,t,u). This notation is a concise way of expressing the transformation of pentagon vwxyz into pentagon qrstu. It is important to note that the transformation itself is not specified; the notation is simply used as a way of representing the transformation.

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Answer:

width = y - 5

Step-by-step explanation:

area = y^2 + 4y - 45

(y + 9)(y - 5)

Answer:

45°

Step-by-step explanation:

I assume you meant 45°, not 45%.

90-45=45

If it is actually 45%, then the answer would be:

90x.55=49.5°

Answer:

13) x = 19

14) x = 12.4

Step-by-step explanation:

So, for 13, we know that the whole thing is 90 degrees, a right angle.

So, (4x - 17) + 31 = 90

Now, we'll subtract 31 from 90 to figure out the other angle.

4x - 17 = 59

Now, add seventeen to both sides to get 4x alone...

4x = 76

Divide each by four!

x = 19

Now, to check, we plug this x value into our first equation:

(4(19) - 17) + 31 = 90

(76 - 17) + 31 = 90

(59) + 31 = 90

90 = 90 :: true!

________________________________________

For 14, we know that the total must be 180, because it's a straight angle.

So, (5x + 22) + 96 = 180  
Again, subtract the known angle from each side:

5x + 22 = 84

Subtract 22 from each side to get the exponent by itself...

5x = 62

Divide each side by 5:

x = 12.4

Now, plug it in to check.....

(5*12.4) + 22 + 96 = 180

62 + 22 + 96 = 180

84 + 96 = 180

180 = 180 :: true!

After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.

Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):

t = t(0.05, 8) = 1.860

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

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Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Answer:

Step-by-step explanation:

Answer:

i am pretty sure is t = -0.9

Step-by-step explanation:

-1(t+8) = -7.1

(t+8) = 7.1

t = -0.9

Answer:

\(y+5=-\frac{3}{4}(x-8)\)

Step-by-step explanation:

\(4x-3y=15 \\ \\ 3y-4x=-15 \\ \\ 3y=4x-15 \\ \\ y=\frac{4}{3}x-5\)

The slope of the given line is \(4/3\). So, the slope of the line that we need to find is \(-3/4\).

Using point-slope form, the equation is \(y+5=-\frac{3}{4}(x-8)\).

Answer:

-108

Step-by-step explanation:

\( - 3 \times { (2 - ( - 4)) }^{2} = \\ - 3 \times ( {2 + 4})^{2} = \\ - 3 \times 36 = - 108\)

Answer:

108 is correct hjgbjbvmbhbjnnn

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4