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Answer: A

Step-by-step explanation:

The cosine of an angle is equal to the sine of its complement, and vice versa.

The graph that can represent the area of each rectangle in terms of the change in the length and width is C. A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.

It should be noted that a graph gives a diagrammatic representation of an information.

Here, the rectangles are formed by decreasing the length and increasing the width, each by the same amount.

Thai can be illustrated by the third graph in the option as the line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.

In conclusion, the correct option is C.

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Answer:

(っ◔◡◔)っ ♥ the answer is C ♥

Step-by-step explanation:

got it right on edge

The required a) assessed value = $21600,
                    b) tax rate = 0.0855,
                    c) real estate tax = $1836.

Cost price is that price for buyer which he pays to seller for an object or product.

a) assessed value = 72000 x 30/100
 =  $21600
b) tax rate = 85.5/1000
    =  0.0855
c) real estate tax = 0.855 x 21600
   =  $ 1836

Thus, the required values of a) assessed value, b) tax rate as a decimal, and c) real estate tax is  $21600, 0.085 and $1836 respectively.

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Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.

The order is important, as one player is the pitcher and the other is the catcher, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

2 players are taken from a set of 25, hence the number of ways is given by:

[tex]P_{(25,2)} = \frac{25!}{23!} = 600[/tex].

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Answer:

See below for step-by-step proof.

Step-by-step explanation:

[tex]\textsf{Given expression}:[/tex]

[tex]\cos^6 \theta+\sin^6 \theta[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3[/tex]

[tex]\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):[/tex]

[tex]\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)[/tex]

[tex]\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:[/tex]

[tex]\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)[/tex]

[tex]\implies 1-3 \cos^2 \theta\sin^2 \theta[/tex]

[tex]\implies 1-3 (\cos \theta\sin \theta)^2[/tex]

[tex]\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:[/tex]

[tex]\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2[/tex]

[tex]\implies 1-\dfrac{3}{4} \sin^2 2 \theta[/tex]

[tex]\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta[/tex]

[tex]\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)[/tex]

[tex]\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]

[tex]\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]

[tex]\textsf{Factor out }\dfrac{1}{4}:[/tex]

[tex]\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)[/tex]

[tex]\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:[/tex]

[tex]\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)[/tex]

[tex]\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)[/tex]

[tex]\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)[/tex]

[tex]\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)[/tex]

[tex]\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)[/tex]

The original price of the wheelbarrow is £75

Let the original price be x.

From the question, the amount paid is:

Amount paid = 54

The reduced price is calculated as:

Reduced = Original price * (1 - discount)

This gives

x * (1- 20%) = 54

Evaluate the difference

x * 0.8 = 54

Divide by 0.8

x = 67.5

Hence, the original price is $67.5

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Complete question

The price of a wheelbarrow is reduced by 20%. During the sale, Carly pays $54 for a wheelbarrow. What was the original price?

By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number [tex]0.\overline{333}[/tex]

The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.

[tex]\frac{1}{3} = 0.\overline{333}[/tex]

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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.

Quotient is described as the quantity produced by the division of two numbers.

Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;

0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.

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The principal value of arc sin(0.98)=78.5°.

The value of the inverse function at a place that falls within the range of the unit of the principal value is the primary value of the trigonometric function at that point.

Trigonometric function solutions with a value between 0 and 2π are known as principal values of trigonometric functions. The primary values of trigonometric functions are values smaller than 2π, which is the interval at which the trigonometric function's value repeats.

The principal value of the inverse trigonometric function is always the positive value whenever any positive value and the negative value are presented in a way that these two values are equal.

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you can reduce it to factors of degree 2 or less).

The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.

Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).

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Answer:

-¾

Step-by-step explanation:

Slope=m

(-1,9) (3,6)

m= Y2-Y1 / X2-X1

m=6-9/3-(-1)

m=-3/3+1

m=-3/4

The given expression in simplified form is x - 5

From the question, we are to simplify the given expression

The given expression is

-4x -3 + 5x -2

To simplify the expression, we collect like terms and then simplify

That is,

-4x + 5x -3 -2

= x - 5

Hence, the given expression in simplified form is x - 5

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In constructing 98% confidence intervals for means, it is true that the statistic is good enough, and is less uncertain.

A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.

Your level of confidence in your findings is shown by the confidence interval. You can never be certain that your results will hold for future surveys or experiments. In statistics, being 95% or 98.5% certain is typically seen as "good enough."

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The confidence interval for the mean usage of water is (18.7,20.5).

Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.

We have to find the confidence interval for the mean usage of water.

To find out the confidence interval we have to first find margin of error.

μ=19.5

σ=2.4

α=0.98

α/2=0.49

We have to find the z value for the p value 0.49 which is z=2.33

Margin of error=z*μ/[tex]\sqrt{n}[/tex]

=2.33*19.5/[tex]\sqrt{3034}[/tex]

=0.82

lower level=mean -m

=19.5-0.82

=18.68

after rounding upto 1 decimal

=18.7

upper mean = mean+m

=19.5+0.82

=20.52

Hence the confidence interval for the usage of water is (18.7,20.52).

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The volume of the cylinder whose radius is 5x-1 unit is 25x²πh + πh - 10xπh.

Suppose that the radius of the considered right circular cylinder is 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

The right circular cylinder is the cylinder in which the line joining centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given that the radius of the cylinder is (5x-1), while the height of the cylinder is h. Therefore, the volume of the cylinder is,

The volume of the cylinder = π × (5x-1)² × h

                                            = (25x² + 1 - 10x)πh

                                            = 25x²πh + πh - 10xπh

Hence, the volume of the cylinder is 25x²πh + πh - 10xπh.

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Answer:

No.

Step-by-step explanation:

The ratio of the lengths of the vertical sides from A to B is 2/4 which equals 1/2.

The ratio of the lengths of the horizontal sides of A to B is 4/11.

Since 4/11 is not equal to 1/2, figure B is not a scale copy of figure A.

Answer:

Perimeter:12cm

Area:5cm²

Step-by-step explanation:

Perimeter is the total distance around the figure ie sum of all sides of figure

∴Perimeter of triangle equals 2cm plus 5cm plus 5cm

∴The perimeter equals 12cm

Area of triangle equals 1/2×base×height,where base is 2cm & height is 5cm

(Inserting values)

∴Area of the triangle equals 1/2×2cm×5cm which equals 5cm²

The solution is given below:

An index number expressing the level of a group of commodity prices relative to the level of the prices of the same commodities during an arbitrarily chosen base period and used to indicate changes in the level of prices from one period to another.

Given:

Comm.         p0        q0       p1       q1       p0q0    p1q0       p1q1        p0q1

     A           25      750       30    960    18750      750       28800     24000

    B             30      450       25    550    13500     750       13750      16500

    C             5        250        6     360      1250     30        2160          1800

    D              6        90         7       210      540       42        1470           1260

    E               10        140       10     190     1400      100       1900          1900

     F                 4         48       5     65      192          240        365         260

Now,

[tex]\sum[/tex]p0q0 = 35632

[tex]\sum[/tex]p1q0 = 1912

[tex]\sum[/tex]p1q1 = 48445

[tex]\sum[/tex]p0q1= 45720

1) P01(L) = [tex]\sum[/tex]p1q0/[tex]\sum[/tex]p0q0 * 100

             = 5.36

2) P01(L) = [tex]\sum[/tex]p1q1/[tex]\sum[/tex]p0q1 * 100

            = 105.96

Dorbish- Bowley

= 5.36+ 105.96/2

=55.66

Marshall- Edgeworth

=  1912+  48445/35632 + 45720

= 50357/ 81352

= 0.619 *100= 61.9

Fisher's price index

=( 5.36 * 105.96 )^ 0.5

=23.831

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The ratio x:y as required in the task content is; 25:18.

It follows from the information given in the task content that;

The area of rectangle P is; 40x.

The area of rectangle Q is; y × (1.25 × 40) = 50y.

Hence, since the area of Q is 10% less than the area of P, it follows that A(q) = 0.9A(p).

And, A(p)/A(q) = 10/9

Hence, 10/9 = 40x/50y

x/y= 50/36 = 25/18

Hence, the required ratio is; 25: 18.

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Answer:

a

Step-by-step explanation:

a is the anwer because b/c it has a constant rate of change unlike the others

The surface area of the spherical ball is given as follows:

[tex]635.04\pi[/tex] yd².

The surface area of a sphere of radius r is given as follows:

[tex]S = 4\pi r^2[/tex].

In this problem, the diameter is of 25.2 yd, hence the radius is given by:

r = 0.5 x 25.2 yd = 12.6 yd.

Then the surface area in yd² is:

[tex]S = 4\pi (12.6)^2 = 635.04\pi[/tex].

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The correct answer is option A which is ZA = 3 cm

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The triangle is shown below.

From the triangle, A  is the concurrency point of angle bisectors of all vertices.

Consider ΔAYD,

Using the Pythagorean theorem,

AD² = AY² + YD²

5² = AY² + 4²

25 = AY² + 16

AY² = 25 - 16

AY² = 9

AY = √9 = 3 cm

Consider triangles ADY and ADZ.

∠AYD ≅∠AZD=90

∠ADY≅∠ADZ ( Angle bisector)

AD ≡ AD (common side)

The two triangles are congruent by the AAS postulate.

Therefore, by CPCTE, AY=ZA=3 cm

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Answer:

I'm not sure if B. is incorrectly written but the answer would be

65c + 90s [tex]\geq[/tex]600

Step-by-step explanation:

since he needs AT LEAST 600$ then the sign should look like that. 65 dollars per car, and c represents the amount of cars, and 90 per SUV and s represents how many SUVS

B. 65c + 90s ≥ 600 is the correct option.

Our friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns.

Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

If he gets paid $65 to detail a car and $90 to detail an SUV

The inequality form for above condition so he can earn at least $600

= 65c + 90s ≥ 600, where c = cars and s = SUV

Thus, the required inequality is given by 65c + 90s ≥ 600.

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The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

From the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle

From the given information,

Line DE is about half the length of line DF

That is,

ED = 1/2 DF

Also,

Line FE is about one-third of the length of line DF

That is,

EF = 1/3 DF

Then, we can write that

ED + EF = 1/2DF + 1/3DF

ED + EF = 5/6 DF

Since,

5/6 DF < DF

Then,

ED + EF < DF

Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

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Based on Pythagoras' theorem, EB is equal to 38.7 and DY is 17.7.

The length of the sides EB and DY are obtained using Pythagoras theorem.

Since EY is a perpendicular bisector;

EB = √(64.2² - 51.2²)

EB = 38.7

Since, DY is a perpendicular bisector;

DY = √64.2² - 61.7²)

DY = 17.7

Therefore, EB is equal to 38.7 and DY is 17.7.

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The value of y by virtue of the circle description above is; 0.8.

By definition, a unit circle is a circle whose radius is 1 and has its center at the origin (0,0).

On this note, the value of y can be evaluated as;

1² = (-3/5-0)² + (y-0)²

1 -0.36 = y²

0.64 = y²

±0.8 = y.

However, since point P is in the 2nd quadrant where y is positive, the value of y is 0.8.

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The greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.

let

number of children tickets = x

number of adult ticket sold = 1 / 3 x

The greatest number of adult tickets sold if the box office receipts was not more than $3,190 can be calculated as follows:

The equations that represent the situation is as follows:

5.50x + 8.50 (1/3 x) = 3190

5.50x + 2.83333333333x = 3190

8.33333333333x = 3190

x = 3190 / 8.33333333333

x = 982.839313573

x ≈ 983

Therefore,

adult ticket = 983/3 = 328

Therefore, the greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.

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The product of the given function is x^5 + 5x^4 + 7x^3

The leading degree of a polynomial function is always greater than or equal to 2.

Given the products below;

x^3 (x^2 + 5x + 7)

Expand

(x^3)(x^2) + 5x(x^3) + 7x^3

Simplify

x^5 + 5x^4 + 7x^3

Hence the product of the given function is x^5 + 5x^4 + 7x^3

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The equivalent expression of  x³(x² + 5x + 7) is  x⁵ + 5x⁴ + 7x³

The equivalent expression of the expression can be found as follows;

x³(x² + 5x + 7)

let's open the bracket by multiplying.

Therefore,

x³(x² + 5x + 7) = x⁵ + 5x⁴ + 7x³

Hence,

The equivalent expression of  x³(x² + 5x + 7) is  x⁵ + 5x⁴ + 7x³

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