A
B
C
D

Pick a letter

Answer:

-1/2

Step-by-step explanation:

cos(-360+60)=-1/2

[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]

In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5

The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form

So basically, the general vertex form of any equation is x = a(y - k)² + h

⇒ y²-4y-x+9 = 0

Shifting the x to RHS,

⇒ x = y²- 4y + 9

Writing y²- 4y in the form of (a-b)²,

⇒ x = y²- 4y + 4 + 5

⇒ x = 1×(y - 2)² + 5,

Hence the equation is now converted to vertex form

⇒ where a = 1, k = 2 and h = 5

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Answer:

The small bamboo plant is 5.5 feet tall

Step-by-step explanation:

I  (1) = 16.5 ft, 3 times as tall as II

II (2) = ? ft

Let the first be x and the second be y, Than

x = 16.5 ft

x = 3y

y = x / 3

y = 16.5 / 3

y = 5.5 ft

Answer:

(C) 29

Step-by-step explanation:

Answer:

the least possible number of marbles in the bag is 12.

Step-by-step explanation:

As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.

The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.

To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.

So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.

Therefore, the least possible number of marbles in the bag is 12.

The population increased by 18 million at the end of one year at the rate of 1.8%.

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. Alternatively put, it is the relationship between a component and a whole in which the value of "whole" is always assumed to be 100.

For instance, if a student receives 15 out of 50 in math, one can determine the relevant percentage by expressing "marks earned" as a fraction of "total marks" and multiplying the result by 100. i.e., the percentage of marks is equal to 15 / 50 100, or 30%.

Given that, population of India is one billion.

The rate of increase is 1.8%.

After one year the population will be:

P = (1000000000)(1.8/100)

P = 18000000

Hence, the population increased by 18 million at the end of one year at the rate of 1.8%.

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Answer:

3,641 cups drank

Step-by-step explanation:

A quart is 4 cups

At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups

At the end of the party, only 7 cups remained

3648 - 7 = 3,641 cups drank

7x² + 48xy - 7y² is the simplified expression

Polynomial is an equation described as the sum of terms in the form of

k[tex]x^n[/tex].

where,

k and n =  positive integers.

Example:

2x³ + 4x² + 3x + 5 is a polynomial.

We have,

(x + 7y) (7x − y)

Distribute the addition over subtraction.

x (7x - y) + 7y (7x - y)

7x² - xy + 49xy - 7y²

Add like terms.

7x² + 48xy - 7y²

We can not further simplify.

So,

7x² + 48xy - 7y² is the final expression.

Thus,

7x² + 48xy - 7y² is the simplified expression

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The complete question.

Find the product (x+7y) (7x−y)

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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The measure of angle the value of x =-96.

What is parallelogram?

A parallelogram is a special kind of quadrilateral composed of parallel lines. Any angle between the adjacent sides of a parallelogram is allowed as long as the opposite sides are parallel. A quadrilateral is a parallelogram if its two opposite sides are parallel and congruent. A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel and equal.

With the use of alternate interior angles, we can quickly resolve this. Right, the interior of a parallelogram is always 360 degrees.

(-x-6)° = 90

x = -96

Hence The measure of angle the value of x =-96.

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The graph of the quadratic function can be seen on the image at the end.

The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.

To find the points we need to evaluate the quadratic equation.

if x = 0

y = 5*0^2 + 2 = 2

So we have the point (0, 2)

if x = 1

y = 5*1^2 + 2 = 7

So we have the point (1, 7)

if x = -1

y = 5*(-1)^2 + 2 = 7

So we have the point (-1, 7)

And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.

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The sinusoidal expression of the function is D(t) = -cos(3t)

A sinusoidal alternating current can be represented by the equation i = I sin ωt, where i is the current at time t and I the maximum current. In a similar way we can write for a sinusoidal alternating voltage v = V sin ωt, where v is the voltage at time t and V the maximum voltage.

here, we have to,

to determine the sinusoidal expression:

When he pushes off, he is 1 m behind the center.

This means that:

Amplitude, a = 1.

But we use, a = -1 because he is behind

The graph has a minimum point at (0,-1) and then intersects its midline at (π/6, 0).

So, the period B is: 2π/B = 4 * π/6 and the vertical shift (d) is 0

Simplify 2π/B = 4 * π/6

2π/B = 2π/3

By comparison, we have:

B = 3

The function is given as:

a cos(Bt) + d

Substitute the calculated values

D(t) = -cos(3t)

Hence, the sinusoidal expression of the function is D(t) = -cos(3t)

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Answer:

period and he completes a swing in ten seconds

Answer:

Step-by-step explanation:

200-14=186

Frank still needs to give 186

The demand function of the question is expressed as;

D(q) = -²/₅₀₀₀q + 14.6

The formula to find the slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

The coordinates we are given are;

(28000, 9) and (33000, 7)

Thus;

Slope; m = (7 - 9)/(33000 - 28000)

m = -2/5000

Now, the equation of a line in point slope form is;

y - y1 = m(x - x1)

Where (x1, y1) is (28000, 9)

y - 9 = (-2/5000)(x - 28000)

y - 9 = -²/₅₀₀₀x + 5.6

y = -²/₅₀₀₀x + 14.6

This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6

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The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the points (-11, 12) and (5, 4), we get:

m = (4 - 12) / (5 - (-11)) = -8 / 16 = -1/2

So the slope of the line passing through (-11, 12) and (5, 4) is -1/2.

Percentages are:

Middle school

Spring = 75%    Winter = 25%

High school

Spring = 40%     Winter = 60%

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the per cent sign, "%".  A percentage is a number without dimensions and without a standard measurement.

Given,

Middle school

Number of students preferring spring = 93

Number of students preferring winter = 31

High school

Number of students preferring spring = 36

Number of students preferring winter = 54

Total  number of middle school students =  93 + 31 = 124

Percentage of middle school students who prefer spring =  [tex]\frac{93}{124} * 100[/tex]

                                                                                     = 75%

Percentage of middle school students who prefer winter = [tex]\frac{31}{124} * 100[/tex] = 25%

Total number of high school students = 36+54 = 90

Percentage of high school students who prefer spring = [tex]\frac{36}{90} * 100[/tex]

                                                                                             =  40%

Percentage of high school students who prefer winter = [tex]\frac{54}{90} *100[/tex]

                                                                                            = 60%

Therefore the above is the percentage of students who prefer spring and winter.

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The linear equation for the parallel line will be y=6x-3.

What exactly is a linear equation?

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

Line parallel to line y=6x-7 will have same slope which will be m=6

as general equation is y=mx+c where m=slope and c=constant.

For parallel line c will be as it is passing through (2,9)

9=6*2+c

c=9-12

c=-3

then the equation will be y=6x-3

Hence,

           The equation for the parallel line will be y=6x-3.

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Step-by-step explanation:

you have to find your five number summary

The value of the exterior angle x of the quadrilateral is equal to

The sum of the exterior angles of any convex quadrilateral is 360 degrees so we have that:

65 + 106 + 78 + x = 360

simply the left hand side of the equation

249 + x = 360

subtract 249 from both sides of the equation

249 - 249 + x = 360 - 249

x = 111°

In conclusion, since the sum of the exterior angles of a quadrilateral is s 360°, we have got the measure of one the the exterior angle x to be equal to 111°

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The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;

A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.

The coordinates of the vertices of the triangle are;

X(0, 5), Y(10, 3), Z(4, -1)

The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;

The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;

Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))

The coordinates of the point Y(4, -1) following the composite transformation is therefore;

Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)

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The probability that exactly 4 out of 7 seeds planted do not grow is 0.0007 (approximately), given that each seed has a 95% chance of growing into a healthy plant.

The probability that a seed doesn't grow is 1 - 0.95 = 0.05.

To calculate the probability that exactly 4 seeds don't grow out of 7, we need to use the binomial distribution formula, which is:

P(X=k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]

where:

X is the random variable representing the number of seeds that don't grow.

k is the specific number of seeds that don't grow (in this case, k=4)

n is the total number of seeds planted (n = 7)

p is the probability that a seed doesn't grow (p=0.05)

C(n,k) is the number of ways to choose k items out of n, also known as the binomial coefficient.

Plugging in the values, we get:

P(X=4) = C(7,4) * 0.05⁴ * 0.95³

          = 35 * 0.00000625 * 0.857375

          = 0.0006522

Rounding to four decimal places, the probability that exactly 4 seeds don't grow is 0.0007 (approximately).

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You would earn $0.006 for recycling 24 iced tea cans.

To determine the amount earned from recycling 24 iced tea cans, we need to find the total weight of the aluminum used in those cans and then convert that weight to pounds.

The total weight of the aluminum used in 24 cans as follows:

24 cans * 0.01 ounce per square inch = 0.24 ounces

Converting ounces to pounds, using a conversion factor of 1/16:

0.24 ounces / 16 ounces per pound = 0.015 pounds

The total amount earned:, since each pound is $0.40

0.015 pounds * $0.40 per pound = $0.006

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Answer:

$121.00

Step-by-step explanation:

y = 18.50x + 47.00

y = the total amount in the account

x = the number of weeks

y = 18.50(4) + 47.00

y = 74.00 + 47.00

y = 121

The solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.

What is quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic equation is:

ax^2 + bx + c = 0

where x is the variable, and a, b, and c are constants, with a not equal to 0. The quadratic equation can have two solutions, one solution, or no real solutions, depending on the values of a, b, and c.

Starting with the given equation:

25 = (x + 9)²

We can start by taking the square root of both sides of the equation, which gives us:

±5 = x + 9

Next, we can isolate x by subtracting 9 from both sides of the equation:

x = -9 ± 5

This gives us two solutions:

x = -9 + 5 = -4

or

x = -9 - 5 = -14

Therefore, the solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.

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Answer:

3 and 1/12 left

Step-by-step explanation:

The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°

Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°

W =25.0277

Now,
Area of the triangle is given as
= 1/2 UW sinv

= 1/2× (25.027)×(6.7)×(sin156°)

= 34.1 square inch

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Answer:

x = 5/2

y = 1/2

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = - 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]

That's our required ratio ~

There are 16% of the Green were Planes.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of all planes = 1550

The percent of green planes = (number of green planes/number of total planes ) x 100

The percent of green planes = (250/1550) x 100

The percent of green planes = 0.1612 x 100

The percent of green planes = 16.129

Round to the nearest percent, and we get

The percent of green planes = 16%

Thus, 16% of the Green were Planes.

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Answer:

28

Step-by-step explanation:

IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS

CROSS MULTIPLY

Answer:

20 gallons / 5 seconds = 4 gallons / second

Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.

Step-by-step explanation: