Toheebah ran round the playground 12 times. the playground is 240m by 160m.What distance did she cover?
​

Answer: To prove the given identity:

(cosec A - sec A)(cot A - tan A) = (cosec A + sec A)(sec A cosec A - 2)

We will start by simplifying both sides of the equation.

Left-hand side (LHS):

(cosec A - sec A)(cot A - tan A)

Using trigonometric identities, we can rewrite cosec A, sec A, cot A, and tan A in terms of sin A and cos A:

Substituting these values into the LHS:

(cosec A - sec A)(cot A - tan A)

= (1/sin A - 1/cos A)(cos A / sin A - sin A / cos A)

= ((cos A - sin A) / (sin A * cos A)) * ((cos A^2 - sin A^2) / (sin A * cos A))

= (cos^2 A - sin^2 A) / (sin^2 A * cos^2 A) [Using the difference of squares identity: a^2 - b^2 = (a + b)(a - b)]

= ((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A)

Right-hand side (RHS):

(cosec A + sec A)(sec A cosec A - 2)

Again, using the same trigonometric identities:

Now, we need to show that the LHS is equal to the RHS:

((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A) = (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)

To prove this, we can cancel out the common factors in the numerator and denominator of the LHS:

(cos A - sin A) = 1 - 2sin^2 A * cos^2 A

Next, we'll simplify both sides individually:

Therefore, the LHS is equal to the RHS, and the given identity has been proven.

Answer:

3)  B = 37.2°, C = 32.8°, c = 8.1

4)  A = 34.4°, C = 35.6°, a = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for angle B:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]

[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{9}{\sin B}[/tex]

[tex]\implies 14\sin B=9\sin 110^{\circ}[/tex]

[tex]\implies \sin B=\dfrac{9\sin 110^{\circ}}{14}[/tex]

[tex]\implies B=\sin^{-1}\left(\dfrac{9\sin 110^{\circ}}{14}\right)[/tex]

[tex]\implies B=37.1632517...^{\circ}[/tex]

[tex]\implies B=37.2^{\circ}[/tex]

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies C=180^{\circ}-A-B[/tex]

[tex]\implies C=180^{\circ}-110^{\circ}-37.1632517...^{\circ}[/tex]

[tex]\implies C=32.8367482...^{\circ}[/tex]

[tex]\implies C=32.8^{\circ}[/tex]

Finally, substitute the values of a, A, and C into the Law of Sines formula and solve for side c:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{c}{\sin 32.8367482...^{\circ}}[/tex]

[tex]\implies c=\dfrac{14\sin 32.8367482...^{\circ}}{\sin 110^{\circ}}[/tex]

[tex]\implies c=8.07866414...[/tex]

[tex]\implies c=8.1[/tex]

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula and solve for angle C:

[tex]\implies \dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{21}{\sin 110^{\circ}}=\dfrac{13}{\sin C}[/tex]

[tex]\implies 21 \sin C=13\sin 110^{\circ}[/tex]

[tex]\implies \sin C=\dfrac{13\sin 110^{\circ}}{21}[/tex]

[tex]\implies C=\sin^{-1}\left(\dfrac{13\sin 110^{\circ}}{21}\right)[/tex]

[tex]\implies C=35.5712205...^{\circ}[/tex]

[tex]\implies C=35.6^{\circ}[/tex]

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies A=180^{\circ}-B-C[/tex]

[tex]\implies A=180^{\circ}-110^{\circ}-35.5712205...^{\circ}[/tex]

[tex]\implies A=34.4287794...^{\circ}[/tex]

[tex]\implies A=34.4^{\circ}[/tex]

Finally, substitute the values of b, B, and A into the Law of Sines formula and solve for side a:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]

[tex]\implies \dfrac{a}{\sin 34.4287794...^{\circ}}=\dfrac{21}{\sin 110^{\circ}}[/tex]

[tex]\implies a=\dfrac{21\sin 34.4287794...^{\circ}}{\sin 110^{\circ}}[/tex]

[tex]\implies a=12.6349923...[/tex]

[tex]\implies a=12.6[/tex]

Answer:

2/3

Hope this helps

Answer:

Approx. 0.2079

Step-by-step explanation:

To find the value of sin 78°, we can use a scientific calculator or a trigonometric table. However, I can provide an approximate value using the trigonometric identity:

sin(90° - θ) = cos(θ)

In this case, we can use the identity sin(90° - 78°) = cos(78°). Since the cosine of 78° can be determined more easily, we can calculate that instead.

cos 78° ≈ 0.2079

Therefore, sin 78° is approximately equal to 0.2079.

The solution is: the value of x in this triangle is x = 83°.

Here, we have,

given that,

the angles of a triangle are:

44, 53 and x

now, we have to find the value of x in this triangle.

we know that,

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

so, we have,

44 +  53 + x = 180°

or, x=  83

Hence, The solution is: the value of x in this triangle is x = 83°.

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The amount of wrapping paper which Elijah used is equal to 812 m².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a right rectangular prism, we have the following;

Surface area of a right rectangular prism = 2[3 × 10 + (10 × 12 × 2) + (13 × 12 × 2)]

Surface area of a right rectangular prism = 812 m².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability of a student being female given that they got a 'B' is 87/315.

We can use Bayes' theorem to find the probability of a student being female given that they got a 'B'. Let's first find the total number of students who got a 'B':

Total number of students who got a 'B'

= 7 + 9 + 6 + 13 + 16 + 12

= 63

Out of these 63 students, the number of females who got a 'B' is:

Number of females who got a 'B' = 13 + 16 = 29

So, the probability of a student being female given that they got a 'B' is:

P(Female | B) = P(B | Female) x P(Female) / P(B)

From the given data, we can calculate these probabilities as follows:

P(B | Female) = 29/25

P(Female) = 25/63

P(B) = 63/175

Plugging in these values, we get:

P(Female | B)

= (29/25) x (25/63) / (63/175)

= 87/315

Therefore, the probability of a student being female given that they got a 'B' is 87/315.

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The area of the given figure is 27.5 square centimeter which has a rectangle and triangles

The given figure has a rectangle and triangles

The area of rectangle is length times width

Area of rectangle =5×4

=20 square centimeter

Area of triangle =1/2×base×height

=1/2×2.5×3

=7.5/2

=3.75 square centimeter

As there are two triangle = 2(3.75)

=7.5 square centimeter

Total area = 7.5+ 20

=27.5 square centimeter

Hence, the area of the given figure is 27.5 square centimeter

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The outside border of the garden would have walked around approximately  58%.

Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.

Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:

P = 2L + 2W

If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.

To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:

Percentage walked = (S1 + S2) / P * 100%

Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:

Percentage walked = (2L + W) / (2L + 2W) * 100%

Simplifying this expression, we get:

Percentage walked = (2L + W) / (2(L + W)) * 100%

Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:

Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%

For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:

Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%

= 7/12 * 100%

= 58.3%

So the outside border of the garden would have walked around approximately  58%.

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The required sine function is

y = 2 sin (3π/4 (x) + 3

For given function,

A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4

A = 2

T = 3π/4

Since we know

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

In this case, the midline is 3

⇒ D = 3

Using the generalized equation of sine function,

y = A sin (B (x + C)) + D

y = 2 sin (3π/4 (x + 0) + 3

y = 2 sin (3π/4 (x) + 3

Therefore, the required sine function is

y = 2 sin (3π/4 (x) + 3

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The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer: 0

Step-by-step explanation: It is furthest away from the other numbers with a difference of at least 5. If plotted in a table it would visually be seen to be further away from the general trend.

Answer to the given Hypotheses is : The current shortage in the new car market has made it quicker to sell a car.

In this scenario, we have to determine if the current shortage in the new car market has affected the time it takes a car dealership to sell a new car. To answer this question, we will use the p-value approach.

First, we will determine the null and alternative hypotheses. The null hypothesis (H₀) is that the average time it takes to sell a car has not changed, while the alternative hypothesis (H₁) is that the current shortage in the new car market has made it quicker to sell a car.

H₀: μ = 20

H₁: μ < 20

Second, we will choose the appropriate test statistic and determine the level of significance. In this case, we will use a one-sample t-test, as the population standard deviation is known, and you will use a 5% level of significance (α = 0.05).

Third, we will calculate the test statistic and the p-value. The test statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the mean.

t = (x' - μ) / (σ / √n)

t = (15 - 20) / (12 / √30)

t = -2.89

Using a t-distribution table with 29 degrees of freedom, the p-value is 0.004.

Since the p-value is less than the level of significance, we reject the null hypothesis and conclude that the current shortage in the new car market has made it quicker to sell a car.

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Given is a circle with center Z, we need to find the measure of the angle YZU,

We know that,

In a circle, the length of an arc and the length of the corresponding central angle are inextricably linked and equal.

Also,

The whole circle measures 360°.

So,

arc YU + arc UV + arc VX + arc YX = 360°.

10x+9 + 90° + 34° + 6x-13 = 360°

16x = 240°

x = 15

So, arc YU = 10(15) + 9

arc YU = 159°

Since arc YU = ∠ YZU

Therefore the measure of the angle YZU is 159°

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1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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Answer:2x-14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

the probability that either event will occur is 0.92

Step-by-step explanation:

the probability that either event will occur is 0.92

What is the probability that either event will occur?

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 15

Other Events = 3

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 15 + 3

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 15/36

For either events, we have

P(A or B) = 33/36 = 0.91666

Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)

The solution is: the dimensions of the flag in inches is:

40 inches by 55 inches.

The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;

L is the length of the flag

W is the width of the flag

From the diagram, L = y and W = 11y/8

Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.

190 = 2(y+11y/8)

190 = 2y + 11y/4

multiply through by 4

760 = 8y+11y

760 = 19y

y = 760/19

y = 40

The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.

Hence, the dimensions of the flag in inches is 40 inches by 55 inches.

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complete question:

Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

No explanation is needed because there is no question.

Answer:

you got it

Step-by-step explanation:

no explanation needed

Your ability to borrow money at lower rates improves as your credit score increases. Option D.

Your ability to borrow money at lower rates improves as your credit score increases.

A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.

Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.

While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer: x=6.6

Step-by-step explanation:

The is a 30-60-90 triangle, which means it falls into the special right triangles category

That means that the hypotenuse (x) is the smaller leg (sqrt11) multiplied by 2.

Sqrt11 times 2 is 6.6332495807108

Rounded to the nearest tenth would turn out to be 6.6

Answer

The order of the number from greatest to least is 1.62, 15/20, 16.2%

Step-by-step explanation

Given: 1.62 16.2% 15/20​

To order these data in descending order (i.e. from highest to least), follow the steps below

1. Convert all numbers to decimals

1.62

16.2% = 16.2/100

16.2% = 0.162

15/20 = 0.75

So, the number are 1.62, 0.162, 0.75

2. Compare the three decimals and arrange in descending order

1.62 > 0.75 > 0.162

This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162

By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is

1.62, 15/20, 16.2%

Answer:

138ft^2

Step-by-step explanation:

9x2=18

10x12=120

18+120=138ft^2

The triangles are similar and

Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem

Given data ,

Let the first triangle be ΔPSQ

Let the second triangle be ΔRST

Now , the corresponding sides are

PS / RS = QS / TS

where the corresponding sides of similar triangles are in the same ratio

And , the common angle to both the triangles is m∠S

So , ∠S ≅ ∠S and PS / RS = QS / TS

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , the triangles are similar

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Answer:

is every whole number a natural number

As all sides of a Rhombus are of equal length, the length of the missing sides are 82

The property of a Rhombus required for answering this question is associated with the length of it's sides. A Rhombus has four sides with the length of all these sides being equal.

This means that with the length of one of it's sides being 82 , the length of the remaining 3 sides would be 82 as well.

The length of sides x = y = z = 82. Hence, x, y and z are 82

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Answer:

=

Step-by-step explanation:

0.67 is the same as 0.670