Which is an equivalent expression for {(5/7)²· (1/3)⁻³}⁻¹ ?

(5/7)² .(1/3)⁻³
(5/7). (1/3)⁻⁴
(7/5)⁻² . (1/3)⁻³
(7/5)² .(1/3)³

The surface area of the prism is 84 square centimeters.

What is a prism?

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

In the figure,

The surface area of the figure consists of 2 triangles, 3 rectangles.

The area of the triangle and rectangle is the surface area of the triangle.

The area of the triangle is (1/2) × base × height

The base of the triangle  ABC is BC and the height is AB.

The area of triangle ABC is (1/2) × 4 × 3 = 6 square centimeters.

The area of triangle DEF is (1/2) × 4 × 3 = 6 square centimeters.

The area of the rectangle ACDE  is 5 × 6 = 30 square centimeters.

The area of the rectangle ABEF  is 4 × 6 = 24 square centimeters.

The area of the rectangle BCDF  is 3 × 6 = 18 square centimeters.

The total surface area of the figure is ( 6 + 6 + 30 + 24 + 18) square centimeters = 84 square centimeters

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Explanation:

The compound interest formula is

A = P*(1+r/n)^(n*t)

where,

The deposit amount is P = 10000 dollars.

The value of r here is r = 0.014 which is the decimal form of 1.4%

n = 4 since we're compounding quarterly, i.e. 4 times a year.

The timespan from when Derrick was 15 to when he became 18 is 18-15 = 3 years, which is the value of t.

Summary of input values:

Let's find the value of "A".

A = P*(1+r/n)^(n*t)

A = 10000*(1+0.014/4)^(4*3)

A = 10428.1800719861

A = 10428.18

Answer: it is equal to 0.76

Answer: 0.76

Step-by-step explanation: 38 ÷ 50 = 0.76

Answer:

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

Given compound inequality:

Solve each inequality:

Solution is:

or

Answer:

  1.8 cans of paint are needed

Step-by-step explanation:

A large statue has a volume of 135 m³ and an area of 81 m², while a small statue has a volume of 5 m³. You want to know the number of cans of paint required to paint the small statue, if each can covers 5 m².

The ratio of linear dimensions on the small statue to those on the large statue is the cube root of their volume ratio:

  sf = ∛(5/135) = ∛(1/27) = 1/3

The area of the small statue is the larger statue's area multiplied by the square of the scale factor:

  smaller area = larger area × (sf)²

  smaller area = (81 m²)(1/3)² = 9 m²

Each can of paint covers 5 m², so the number of cans required is ...

  (9 m²)/(5 m²/can) = 1.8 cans

You will need 1.8 cans of paint to paint the small statue.

__

Additional comment

If you must pay for whole cans of paint, you must buy 2 cans of paint.

The box's volume V expressed as a function of x V(x) =(x+1)(16 -2x) ².

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle having equal length and width.

An equal-length rectangle with two neighboring sides. a quadrilateral having four straight angles and equal sides. a parallelogram with two sides that are equally spaced apart and one right angle. the shape of a right-angled rhombus.

A distance of (x+1) is cut in from both sides, so the base dimensions are

18 - 2(x+1) = 16 - 2x

The depth of the fold is (x+1), so that is the depth of the box.

The volume V(x) = (x+1)(16 -2x)²

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The equations for parallel lines:

y = -1/2 x - 2  ----- y = -1/2 x + 6

y = 1/2 x + 4   ----- y = 1/2 x - 4

y = 2x -4       -----  y =2/1x + 2

y = 5x + 2     -----  y = 5x - 1

y = 1/5 x + 10 ----   y = 1/5 x + 3

What is slope of line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

If an equation in the form y = mx + c then m is the slope of the line.

Equation of line               slope          Slope parallel line

y = -1/2 x - 2                        -1/2                        -1/2

y = 1/2 x + 4                          1/2                           1/2

y = 2x -4                                2                            2

y = 5x + 2                               5                           5

y = 1/5 x + 10                          1/5                         1/5

Now identify the lines from the option whose slope are  -1/2,  1/2, 2, 5,  1/5.

The slope of the line y = -1/2 x + 6 is  -1/2.

The slope of the line y = 1/2 x - 4 is  1/2.

The slope of the line y = 2x -4 is 2.

The slope of the line y = 5x + 2  is 5.

The slope of the line y = 1/5 x + 10 is 1/5.

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Answer:

$18

Step-by-step explanation:

Ratios are numerical proportions among different values.

Eg. 1 : 4 is 1 to 4.

Given Total Shares = 1 + 4 = 5 = $90

Jacob gets 1 share.

1 Share = $90 ÷ 5 = $18

Therefore Jacob gets $18.

The probability that two students out of 30 students have their birthday on the Same day is 0.706, that is nearly 71%

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability.

the likelihood of the preceding event is multiplied by the probability of the subsequent,or conditional, occurrence to determine the conditional probability.

In a year we have 365 days

probability at least 2 people share the same birthday=1 - probability no people share the same birthday

the first student can be born on any day,so we'll give him a probability of 365/365

the probability of the next born is 364/365

the probability of the third born is 336/365

[tex] \frac{365 \: factorial}{335 \: factorial \: . {365}^{30} } [/tex]

this is the simplified form of the 30 probabilities product.= 0.294

therefore

probability at least 2 people share the same birthday=1 - probability no people share the same birthday

1 - 0.294= 0.706

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Answer:

A=Right, B=Acute, C=Obtuse, D=Obtuse

Step-by-step explanation:

A.right

B.acute

C.obtuse

D.obtuse

Answer:

give the data in the graph form and your answer is right..

Answer:

- 824 ft

Step-by-step explanation:

2 minutes out of 5 is a fraction  2/5

2/5 of the -2060 would be

 2/5 *( -2060) =  - 824 ft

Answer:

uhhh i think -824

Step-by-step explanation:

-2060/5

-412

-412x2

-824

Answer:

Step-by-step explanation:

r2=x2+y2,tanθ=yx,x=rcosθ,y=rsinθ

The value of Lilah's stock after the decrease of 8 % is $ 368

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the initial amount of money Lilah invested in stocks be = A

The value of A is = $ 400

Now , the percentage decrease in the value of stocks = 8 %

So , the equation will be

The value of the stocks after the decrease = initial amount of money Lilah invested in stocks -  ( percentage decrease in the value of stocks x initial amount )

Substituting the values in the equation , we get

The value of the stocks after the decrease = 400 - ( 8/100 ) x 400

The value of the stocks after the decrease = 400 - ( 8 x 4 )

The value of the stocks after the decrease = 400 - 32

The value of the stocks after the decrease = $ 368

Therefore , the value of A is $ 368

Hence , The value of Lilah's stock after the decrease of 8 % is $ 368

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the value of arc length = 3.14 and the area of the sector = 4.71cm²

The formula for the area of the sector of a circle is /360° (r2) where r is the radius of the circle and is the angle of the sector.

Arc length is the distance between two points along a section of a curve. It is given as

/360°×2r

= 180°, therefore /3 = 180/3= 60°

arc length = 60°/360 × 2×3.14×3

arc length = 3.14cm

The area of the sector = /360°×r²

60/360×3.14×3²

sector area = 3.14×3÷2

sector area = 4.71cm²

therefore the length of the arc and the area bounded by the arc and radius(sector) is 3.14cm and 4.17cm².

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Answer:the value of arc length = 3.14 and the area of the sector = 4.71cm²

Step-by-step explanation:

the value of arc length = 3.14 and the area of the sector = 4.71cm²

Answer: 0

Step-by-step explanation:

A horizontal line always has a slope of 0

Answer:

slope is 7/4

y intercept (0,2)

Step-by-step explanation:

m= 7/4 y=mx + b to find slope.

(2, 11) is the vertex of f(x) = 4(x - 2)² +11.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given equation is f(x) = 4(x - 2)² +11.

The vertex form is y=a(x-h)²+k

y=a(x-h)²+k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h, k) is the vertex.

(h, k) are the vertices of the given equation.

a=4,

h=2 and

k=11

so the (2,11) is the vertex of the function.

Hence, the vertex of f(x) = 4(x - 2)² +11 is (2, 11).

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Answer:

? understand whatt I think you ment to put a picture or something

Using percentages, we know that Emika's monthly budget is $50.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without dimensions and without a standard measurement.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

So, if we multiply a fraction of a number by 100, you get a percentage. % is the symbol used to denote percentages.

Let x stand in for Emika's monthly cell phone budget.

Divide $60 by 120% to find his monthly spending limit.

x = $60 / 120%

x = $60 / 1.20

x = $50

Therefore, using percentages, we know that Emika's monthly budget is of $50.

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Answer: 27/16

Step-by-step explanation: evaluate

Answer:

see explanation

Step-by-step explanation:

N(t)=4|t+5|+3, evaluate N(2).

Evaluate: Plug in a number for each variable.

4(|t+5|)+3

t=2

Evaluate for t=2

4(|2+5|)+3

4(|2+5|)+3

=31

(Hope this answer does you some good )

Answer:

630 people could ride the Ferris wheel in 6 hours.

Step-by-step explanation:

First, let's find the people-per-hour amount:

Since there are 3 "20 minutes" in an hour, we multiply the amount it can accommodate by 3 as well:

35 * 3 = 105

Next, since we have 6 hours, we multiply our people-per-hour by 6:

105 * 6 = 630 people in 6 hours, final answer.

Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].

What is the trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}[/tex]

As we know,

[tex]sec(x)=\frac{1}{csc(x)}\\\\\\1-1csc^2(x)=cot^2(x)\\\\\\1+csc^2(x)=cot^2(x)[/tex]

So,

[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}\\\\\\=\frac{\frac{1}{csc(x)}-csc(x)}{\frac{1}{csc(x)}+csc(x)}\\\\\\=\frac{\frac{1-csc^2(x)}{csc(x)}}{\frac{1+csc^2(x)}{csc(x)}}\\\\\\=\frac{{1-(1)csc^2(x)}}{{1+csc^2(x)}}\\\\\\=\frac{cot^2(x)}{cot^2(x)}\\\\\\=1[/tex]

Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].

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Answer: 2 is equal to or less than 5

Step-by-step explanation:

When the dot is colored in that means it’s equal to or _, while when it’s hollowed out it’s equal to a simple greater or less than symbol.

Answer:

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

We know parallel lines have equal slopes.

Find the slope of the given line:

The slope is - 3.5.

Use point-slope equation to find the equation of the parallel line.

Convert it to standard form:

Answer:

Step-by-step explanation:

You want cost equations and the cheaper company for driving 5 miles when A charges $85 plus $1.50 per mile, and B charges $65 plus $2.50 per mile.

In each case, the cost is the sum of the initial fee and the mileage charge. The mileage charge is the cost per mile, multiplied by the number of miles (x). Using the given fees and costs per mile, we have ...

  A = 85 +1.50x

  B = 65 +2.50x

The difference in fees is $85 -65 = $20. The difference in mileage charges is $2.50 -1.50 = $1.00 (per mile). Then the two companies will charge the same for $20/($1 /mile) = 20 miles.

Five miles is less than that "break even" mileage, so the cheaper company will be the one with the lower initial fee. (The graph shows the charges for each company for 5 miles.) For more than 20 miles, the cheaper company is the one with the lower mileage charge.

Company B will be cheaper for a drive of 5 miles.

Answer:

Step-by-step explanation:

The function for f(x)=8(x+10) is;

B. f^-1(x)=x-10/8