Which angles are coterminal with 32

The number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.

We are given two animals. The number of penguins is 3. The number of puffins is 6. We need to find out the number of ways that three penguins and six puffins can stand in line so that all the puffins can stand together.

We will use the concepts of permutations and combinations. We will make a bundle of all the puffins as a single entity.

The number of ways to arrange 6 puffins among themselves is 6! = 720. The number of ways to arrange 3 penguins and a bundle of puffins is (3 + 1)! = 4! = 24.

The total number of ways to form the line is the product of the above-mentioned calculation.

N = 720*24

N = 17,280

Hence, the number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.

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When the interest rate is 12.75%, your balance at the conclusion of the third month is $3270.06.

When provided,

P=$3168

R=0.1275/12

= 0.010625

n=3

Interest rate = 12. 75%

Using the formula

A=P(1+r)^n

we can now insert the values

A=3168(1+0.010625)^3 and

A=3270.06

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Answer:

-98

Step-by-step explanation:

a negative plus a positive equals a negative .

You basically minus 412 and 314 and add the negative sign

The set [tex](\sqrt{3}, \sqrt{13}, 4)[/tex]  could be used to form a right triangle.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

Since for the right triangle is a, b, c are three sides of a triangle, where c is the diagonal, then

a^2 + b^2 = c^2

Consider, the set (4, 8, 11)

Here, 4^2 + 8^2 ≠ 11^2

Consider, the set (6, 8, 13)

Here, 6^2 + 8^2 ≠ 13^2

Consider, the set [tex](\sqrt{3} , \sqrt{5} , 8)[/tex]

Here, [tex](\sqrt{3})^2 + (\sqrt{5})^2[/tex] ≠ 8^2

Consider, the set [tex](\sqrt{3} , \sqrt{13}, 4)[/tex]

Here, [tex](\sqrt{3})^2 + (\sqrt{13})^2 = 4^2[/tex]

Hence, the set [tex](\sqrt{3} , \sqrt{13}, 4)[/tex] could be used to form a right triangle.

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The equation that could be used to determine the number of dimes, d, in his pocket is: 0.35d + 0.75 =2.50.

Let the number of dimes be d

Let number of quarters be q

Hence,

d + q = 2.50

q = d+3

1 dimes = $0.10

1 quarters = $0.25

0.10d +0.25q = 2.50

Substitute value of  q into 0.10d +0.25q = 2.50

0.10d +0.25 (d+3) = 2.50

0.10d +0.25d +0.75 = 2.50

0.35d + 0.75 =2.50

Hence, the equation is : 0.35d + 0.75 =2.50.

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Answer:

[tex] \frac{pr}{ \sin(q) } = \frac{rq}{ \sin(p) } = \frac{pq}{ \sin(r) } [/tex]

Answer:

a) R = 47.28 R = 312.73          b) 6.67

Step-by-step explanation:

a)

Use the sine rule to calculate angle PRQ

[tex]\frac{sinQ}{q} = \frac{sinR}{r}[/tex]

[tex]\frac{sin40}{7} = \frac{sinR}{8}[/tex]

[tex]0.091827 = \frac{sinR}{8}[/tex]

[tex]sinR = 0.73461[/tex]

[tex]sininverse(0.73461) = R[/tex]

[tex]R = 47.28[/tex]

2nd angle for PRQ is 360 - 47.28 = 312.73

b) Use the cosine rule to find side p

p² = r² + q² - 2rqcosP

To find the angle of p we will simply subtract angle R and angle Q from 180.

180 - 47.28 - 40 = 92.72

p² = 8² + 7² + 2(8)(7)cos(92.72)

p² = 107.685

p = √107.685

p = 10.38

Let's suppose that the shortest distance of R from PQ is [tex]x[/tex].

look at the diagram I gave

since the line I made makes a right angled triangle, we can use SOH CAH TOA

for the angle 40, [tex]x[/tex] is opposite and 10.38 is hypotenuse

which means we will have to use SOH

sin40 = O/H

sin40 = [tex]x\\[/tex]/10.38

0.6428 = [tex]x[/tex]/10.38

0.6428 × 10.38 = [tex]x[/tex]

[tex]x[/tex] = 6.67

The circumference of circle with the diameter is 62.8cm

The Circumference of the circle is the measurement of the boundary of the circle.

If we open a circle and make a straight line out of it , then its length is circumference.

The circumference of a circle = 2πr

where r is radius of circle

we can write circumference in terms of diameter,

diameter of circle = 2r

so , the circumference = πd

Given in the question,

the diameter of circle = 20cm

Therefore , the circumference will be  πd

taking 3.14 value of π

= (3.14)× 20

=62.8 cm

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The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

56

Step-by-step explanation:

Step-by-step explanation:

54÷3

=18

one is 17

one is 18

the other is 19

Answer:

-7

Step-by-step explanation:

To solve this system of equations, let's solve for x first. We can move 6y to the other side of the first equation by adding it to both sides. Now we know what x equals:

x = 30 + 6y.

Now, we can substitute that equation in for every x in the 2nd equation, then solve for y.

The second equation becomes:

5(30+6y) - 2y = -46

(150 + 30y) - 2y = -46

Simplify.

150 + 28y = -46

Subtract 150 from both sides

28y = -196

Divide by 28 (to get y by itself)

y = -7

Answer:

y = -7

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x-6y = 30\\5x-2y =-46\end{cases}[/tex]

Multiply the first equation by -5:

[tex]\implies -5(x-6y)=-5(30)[/tex]

[tex]\implies -5x+30y=-150[/tex]

Add this to the second equation to eliminate the term in x:

[tex]\begin{array}{crcrcl}& 5x & - & 2y & = & \:\:-46\\+&(-5x&+&30y&=&-150)\\\cline{2-6}&&&28y&=&-196\\ \cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies 28y=-196[/tex]

[tex]\implies \dfrac{28y}{28}=\dfrac{-196}{28}[/tex]

[tex]\implies y=-7[/tex]

The number of people who bought £4 tickets are 139.

Let £4 tickets be x

Let £5 tickets be y.

Therefore based on the information given, this will be:

x + y = 223 ..... i

4x + 5y = 936 ..... ii

From equation i

x = 213 - y

Put this into equation ii

4x + 5y = 936

4(213 - y) + 5y = 936

852 - 4y + 5y = 936

Collect like terms

y = 84

This implies that the number of £5 tickets is 84.

Recall that x + y = 223

x + 84 = 223

x = 223 - 84

x = 139

The number of £4 tickets is 139

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The total weight of 100 trucks in pounds is 300000 pounds.

According to the question,

We have the following information:

A truck weighs approximately 3000 pounds.

We have to find the weight of 100 such trucks.

We know that in order to find the total weight of 100 trucks we will multiply the weight of one truck by 100.

(More to know: we multiply a number when we have to find the weight or cost of more than one product.)

So, we have the following expression:

Weight of 100 trucks = 3,000*100 pounds

Weight of 100 trucks = 3,00,000 pounds

Hence, the total weight of 100 trucks in pounds is 3,00,000 pounds.

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The wavelength of the light is found to be 384.06 nm. The light is coming from the source as sodium bulb.

The distance between two crests or troughs of a light wave is known as the wavelength of light.  

For the stated question-

The wavelength of the light before refraction = 510.8 nm (air).

The refractive index of 1.33.(water).

Thus,

refractive index = wavelength of the light in air/wavelength of the light in water.

μ = λ(air) / λ(water)

1.33 = 510.8 /  λ(water)

λ(water) = 510.8/1.33

λ(water) = 384.06 nm

Thus, the wavelength of the light is found to be 384.06 nm.

The light is coming from the source as sodium bulb (for wavelength of 510.8 nm.)

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Answer:

51.425

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Given equation,

→ 8x - 31 = 5x + 17

Now the value of x will be,

→ 8x - 31 = 5x + 17

→ 8x - 5x = 17 + 31

→ 3x = 48

→ x = 48/3

→ [ x = 16 ]

Hence, the value of x is 16.

Answer:

16 ft

Step-by-step explanation:

We are here given that the side lengths of the state flag are in ratio 4:7 . Let us take the ratio to be [tex] 4x:7x[/tex] .

Now we are given that the flag is 28 ft. long. So ;

[tex]\longrightarrow 7x = 28\\[/tex]

Divide both sides by 7 ,

[tex]\longrightarrow x = 4 [/tex]

Therefore the height of the flag will be ,

[tex]\longrightarrow h = 4x [/tex]

Substitute for x ,

[tex]\longrightarrow h = 4(4) ft [/tex]

Multiply,

[tex]\longrightarrow\underline{\underline{ h = 16ft}} [/tex]

And we are done!

The equation to find n is given by, n/2 + 50 = 176.

And the solution i.e. the number of African animals in zoo is 252.

Given that the variable for number of African animals in zoo is n.

Now given that there are 176 South African animals in zoo and which is 50 more than half the number of African animals in zoo.

So half of African animals in zoo = n/2

50 more than half African animals in zoo = n/2 + 50

According to condition, the suitable equation to find the value of n is given by,

n/2 + 50 = 176

n/2 = 176-50 = 126

n = 126*2 = 252

Hence the number of African animals in the zoo is 252.

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Answer:

2w+12

Step-by-step explanation:

twice a number: doubled or multiplied by 2

Increased: means to add

Hopes this helps please mark brainliest

Answer:

W2+12

Step-by-step explanation:

twice a number means to multiply by two

increased by 12 means to add 12

so W2+12 is the answer

Camilla have total of 7 dogs.

acc to our question-

hence,Camilla have total of 7 dogs.

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Answer:

[tex]14x+14y+4[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

In math there is a general rule is  "Like adds like"

1. Identify your common variables (x,y,z)

2. add the common variables

Solution

6x + 5y + 8x -2y +11y +4

x and y variables add

(6x+8x) + (5y-2y + 11y) + 4

14x + 14+ + 4

We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.

Given,

The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.

In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.

To report the large-sample z statistic and its p-value,

Null hypothesis,

H₀ : p = 0.79

Alternative hypothesis,

Ha : p < 0.79

Level of significance, α = 0.01

Under H₀

Test statistic,

[tex]Z_0= \frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

Z₀ = -7.948

The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by

P-value = P(z <-7.945)

            = 0.000     (from z-table)

Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.

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Answer:

2y= -8 is the correct answer

A square root of 7, then 2.8, then 3.14 aka pi, then square root of 17, and lastly 4.6

Step-by-step explanation:

Answer:

12.

Step-by-step explanation:

[tex]\text{let } x = \text{ number of people who participated in the survey}[/tex]

3 = 25% of x. We can rewrite that as an equation.
[tex]\frac3x \times 100 = 25 \text{ // Divide by 100}\\ \\\frac3x = \frac14 \text{ // Cross multiply}\\\\12 = x[/tex]

The value of x that is a counterexample to the student's conjecture is of:

x = 0.

A counter example to a conjecture is a statement that makes the conjecture false.

In the context of this problem, the conjecture is presented as follows:

x + 5 < x².

The conjecture is only true for non-negative numbers, hence the counter example also has to be a non-negative number, meaning that these following options are removed, as they are negative numbers:

For x = 0, the conjecture is given as follows:

0 + 5 < 0²

5 < 0

Which is a false statement, hence x = 0 is the counterexample to the student's conjecture.

At x = 5, the conjecture is given as follows:

5 + 5 < 5².

10 < 25.

Which is true, however, the conjecture has already been shown to be false at x = 0.

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Answer:

The answer for the question mark is 1.

Step-by-step explanation:

The rule of the 0 exponent applies here. Since x is 0, the question mark would be 3⁰, and every number to the 0th power is 1, so the answer is 1.

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The image point of (0,3) after these set of transformation, rotation of 90° (R90°) reflection across the y-axis (∘r) is (-3, 0).

In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).

By applying a rotation of 90° about the center of rotation to this point, the following coordinates would be produced:

(x, y)                                    →              (y, -x)

Ordered pair = (0, 3)      →      Ordered pair = (3, 0)

Next, we would apply a reflection across the y-axis as follows:

(x, y)                   →                           (-x, y)

Ordered pair = (3, 0)      →      Ordered pair = (-3, 0)

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The area of the floor not covered by the rug is 450 square feet

The floor has a rectangular shape while the rug has a circular shape

The area not covered by the rug

=  area of the room -  area of the rug

= length * width - pi * diameter^2 / 4

= ( 25 * 20 ) - ( 22 / 7 * 8^2 / 4 )

= 500  - 50.265

= 449.735

≅ 450 square feet

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