Evaluate the expression 5 % (8 + 6 – 2).

The surface area of the solid is 281 ft².

Given that, a solid figure made of a rectangular prism and a square pyramid,

We need to find its surface area,

To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,

So,

Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,

= 2×5×5 + 2(4·12+12·5+4·5)-5²

= 50+256-25

= 281 ft²

Hence the surface area of the solid is 281 ft².

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Answer:

50.15

Step-by-step explanation:

250.75-50=200.75

200.75/5=50.15

Answer: The net gain was 3 stocks for these three days.

Explanation

Given

• Monday: lost 8 and 3/8.

• Tuesday: lost 1 and 5/8 points.

• Wednesday: gained 13 points.

Procedure

To calculate the net gain, we have to add all the values we are giving, considering that the stock lost will have a negative sign:

0. Calculating the losses

We have to mixed numbers, for which we can add the whole numbers and the fractions separately.

• Whole numbers

• Fractions

At last, we add both results and we get the losses:

2. Calculating the gains

As we only have one quantity, there is no need for calculations:

3. Calculating net gain

Finally, we put both quantities in the formula:

The domain and range of the function in interval notation are (-∞, ∞) and [-5, ∞) respectively. Option D is correct.

The given function is y = (x+3)^2 - 5.

The domain of the function is all real numbers, since any value of x can be plugged into the function.

To find the range of the function, we can consider the vertex of the parabola, which is (-3,-5) since the coefficient of x^2 is positive. The lowest value of the function occurs at the vertex, which is -5. Therefore, the range of the function is y ≥ -5, meaning that the function can output any value greater than or equal to -5.

Therefore, the domain of the function is all real numbers and the range of the function is y ≥ -5.

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Answer: Number 2

Step-by-step explanation: yes

Answer:

1.9 is the correct answer

Answer: 525

Step-by-step explanation:

3 km =30 hm

35hm*15=525

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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Answer:

\(\huge\boxed{\sf \frac{65}{80} => \frac{13}{16} }\)

Step-by-step explanation:

Obtained Marks = 65

Total Marks = 80

Fraction:

=> \(\sf \frac{65}{80}\)

=> \(\sf \frac{13}{16}\)

Hope this helped!

~AnonymousHelper1807

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Step-by-step explanation:

so 24 batches of muffins are made in 3 hours and in a day 576 batches

Answer:

25

Step-by-step explanation:

\(0.09a=75\\a=\frac{75}{0.09} \\0.03*a=0.03*\frac{75}{0.09} =25\)

Answer:

0.14

Step-by-step explanation:

There are 4.1 mill that are 25-34. That age group over the total should give you the probability. 4.1/30.3

The area of the whole is: 5×3=15

The area of the triangle is: 2×3/2=3

So the area of the shades region is 15-3=12

Three or more line segments that only intersect at their ends form closed, two-dimensional shapes known as polygons.

A polygon is a closed, two-dimensional shape with straight sides that is flat or plane. It has straight sides. Polygons are a different category that belongs to the category of two-dimensional figures because two-dimensional (2D) figures are flat because they lack volume.

Polygons are flat 2D shapes that have straight lines and all lines are closed, meaning that they don't have any disconnected lines. Polygons are a subcategory of 2D figures because they carry all traits of 2D figures but also have special ones of their own. Examples of polygons are squares, rectangles, and triangles. Examples of nonpolygons but still are 2D figures are circles, ovals, and any other flat shape.

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Complete question

How can polygons be considered a subcategory of two-dimensional figures?

The area of rectangle is 96in2 which is option A.

To find the area of the rectangular face, we need to find the length and width of the rectangle, and then multiply them together.

The length of the rectangle is the distance between the points (-5,8) and (3,8), which is 8 - (-4) = 12 inches.

The width of the rectangle is the distance between the points (-5,8) and (-5,-4), which is 3 - (-5) = 8 inches.

Therefore, the area of the rectangular face is 12 x 8 = 96 square inches.

So the answer is 96 in².

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Answer:

slope = -1

Step-by-step explanation:

parallel lines have the same slope,

y = -x – 4

=> y = -1(x) -4

          ↑ slope

y = mx + b

     ↑ slope

Answer:

9/29

Step-by-step explanation:

There are 29 students.  11 don't play a sport, so there are 18 students who play a sport.

The number of students who play both sports is:

18 = 13 + 14 − x

x = 9

So the probability is 9/29.

26.2miles:-

\(\\ \sf\longmapsto 26.2(1.61)\)

\(\\ \sf\longmapsto 42.182\)

\(\\ \sf\longmapsto 42km\)

The given distance to the nearest kilometer is 42 kilometers.

Given that, Sean runs a marathon, which is 26.2 miles long.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, a mile is about 1.61 kilometers.

Here, number of kilometers = 26.2×1.61

= 42.182 kilometers

≈ 42 kilometers

Therefore, the given distance to the nearest kilometer is 42 kilometers.

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Answer:

h

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The proportion of Asian Treasure is the difference in price of the mix and Paradise tea, divided by the difference in price of Asian Treasure and Paradise tea. So the amount of Asian Treasure is ...

  (6.00 -5.00)/(7.50 -5.00)(60 ounces) = 24 ounces . . . Asian Treasure tea

The remaining 60-24 = 36 ounces will be Paradise tea.

__

Using an equation

You can get the same result if you define a variable (a) to the amount in ounces of the higher-priced contributor. Then the lower-priced contributor will be in the amount (60-a) ounces. The total cost of the mix is ...

  7.50a +5.00(60 -a) = 60(6.00)

  (7.50 -5.00)a +60(5.00) = 60(6.00) . . . rearrange the left side

  (7.50 -5.00)a = 60(6.00 - 5.00) . . . . . .  subtract 60(5.00)

  a = 60(6.00 -5.00)/(7.50 -5.00) . . . . . . divide by the coefficient of 'a'

Note that this last expression is identical to the one we used above to find the quantity of Asian Treasure tea.

a/b The decay can be modeled by this equation, (1 - r), the r being the rate of decay. So it would be 1-0.115. (0.115 is your answer for a) You have to convert the percent into a decimal by moving the deicmal place two places to the left. 0.885 is your answer for b.

c. For function notation, that just means write an equation. So you want your decay times your inital.  V(t)=15000(0.885)^x. We get the V(t) from the directions that they want us to put it in; it's basically y.

d. Since it's two years, plug in 2 for x. This shows the decay after two years

V(t)=15000(0.885)^2

e. As with d, plug in 10 for x. V(t)=15000(0.885)^t

Answer:

The cash flow statement paints a picture as to how a company’s operations are running, where its money comes from, and how money is being spent. So i think D is the answer

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

x = 6.8

Step-by-step explanation:

7x + 36 = 12x + 2 (alternate interior angles are congruent)

Collect like terms

7x - 12x = -36 + 2

-5x = -34

Divide both sides

-5x/-5 = -34/-5

x = 6.8

Answer:

h ≈ 209 ft

Step-by-step explanation:

The illustration forms 2 right angle triangle with same height , which is the height of the pyramid.

The first triangle has an unknown adjacent side and height but the angle is 31° 10'. The larger triangle has adjacent side of 120 ft plus the adjacent side of the smaller triangle.

let

the adjacent side of the smaller triangle = a

recall both triangle have same height = h

Therefore,

tan 31° 10' = opposite/adjacent = h/a

tan 31.167 = h/a

h = a tan 31.167

h = 0.6048345941  a

The larger triangle

adjacent side = 120 + a

height = h

tan 24° 10' = h/120 + a

convert the minutes to degree

tan 24.167° = h/120 + a

cross multiply

120 + a tan 24.167 = h

120 + a (0.44872570999 ) = h

h = 53.8470851998  + 0.44872570999a

Therefore,

0.6048345941  a  = 53.8470851998  + 0.44872570999a

0.6048345941  a  - 0.44872570999a = 53.8470851998

0.1561094942 a = 53.8470851998

divide both sides by 0.1561094942

a = 53.8470851998 / 0.1561094942

a = 344.931520506

a ≈ 345 ft

The height can be computed as

tan 31.167 = h/a

h = 345 × tan 31.167

h = 345 × 0.6048345941

h = 208.667934967

h ≈ 209 ft

The functions (f.g)(x) and (g.s)(x) are illustrations of composite function

The values of the composite functions are:

(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10

The equation of the functions are given as:

f(x) = 3x - 8

g(x) = -2x + 5

s(x) = 4x^2 - 9x + 2

.

The composite functions are calculated using:

(fg)(x) = f(x) * g(x)

So, we have:

(f g)(x) = (3x - 8) * (-2x + 5)

Evaluate the product

(fg)(x) = -6x^2 + 15x + 16x - 40

Evaluate the like terms

(fg)(x) = -6x^2 + 31x - 40

Also, we have:

(gs)(x) = g(x) * s(x)

So, we have:

(gs)(x) = (-2x + 5) * (4x^2 - 9x + 2)

Expand

(gs)(x) = -8x^3 + 18x^2 -4x + 20x^2 - 45x + 10

Collect like terms

(gs)(x) = -8x^3 + 18x^2 + 20x^2-4x - 45x + 10

Evaluate the like terms

(gs)(x) = -8x^3 + 38x^2 -49x+ 10

Hence, the values of the composite functions are:

(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10

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