Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
31 feet
25 feet

Similar triangles are those triangles whose corresponding sides are in the same ratio. The triangles that are similar to ΔABC are ΔDEF and ΔJKL.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.

For two triangles to be similar there sides should be in the same ratio.

For ΔABC ~ ΔMNO,

AB/MN should be equal to BC/NO,

AB/MN = 15/35 = 0.4286

BC/NO = 8/12 = 0.66

Thus, there are not similar triangles.

For ΔABC ~ ΔDEF,

AB/MN should be equal to BC/NO,

AB/DE = 15/22.5 = 0.66

BC/EF = 8/12 = 0.66

Thus, there are similar triangles.

For ΔABC ~ ΔGHI,

AB/GH should be equal to BC/HI,

AB/MN = 15/77 = 0.1948

BC/NO = 8/36 = 0.222

Thus, there are not similar triangles.

For ΔABC ~ ΔJKL,

AB/MN should be equal to BC/NO,

AB/JK = 15/60 = 0.250.25

BC/KL = 8/32 = 0.66

Thus, there are similar triangles.

Hence, the triangles that are similar to ΔABC are ΔDEF and ΔJKL.

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Answer:

415

Step-by-step explanation:

20x20=400+15= 415

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{20^2 + 15^1}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{20^2 + 15^1}[/tex]

[tex]\mathbf{= 20\times 20 + 15\times 1}[/tex]

[tex]\mathbf{= 400 + 15}[/tex]

[tex]\mathbf{= 415}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{415}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The true statement about this function is that: B. the function is negative for all real values of x, where x < -3 and where x > 1.

A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.

By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.

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The changes that transform C(t) to F(t) is that the function C(t) is stretched vertically to form the function F(t)

The Fahrenheit function

The Celsius  function is given as:

C(t) = -0.30 (t – 12)² + 40  

The conversion from Celsius to Fahrenheit is

F(t) = 9/5 * C(t)

Hence, the Fahrenheit function is F(t) = 9/5 * C(t)

Convert values from Celsius to Fahrenheit

The values are t = 0, 12 and 24.

So, we have:

F(0) = -0.54(0 - 12)² + 72 = -5.76

F(12) = -0.54(12 - 12)² + 72 = 72

F(24) = -0.54(24 - 12)² + 72 = -5.76

The new function F(t)

The conversion from Celsius to Fahrenheit is

F(t) = 9/5 * C(t)

So, we have:

F(t) = 9/5 * (-0.30 (t – 12)² + 40)

Expand

F(t) = -0.54(t – 12)² + 72

Hence, the new function is F(t) = -0.54(t – 12)² + 72

The graph of function F(t)

See attachment for the graph of function F(t)

The changes that transform C(t) to F(t)

We have:

C(t) = -0.30 (t – 12)² + 40  

F(t) = 9/5 * C(t)

The above implies that the function C(t) is stretched vertically to form the function F(t)

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Answer:

k+i =290

Step-by-step explanation:

The three angles added together form a circle, which is 360 degrees

k+i + 70 = 360

We want to find the sum of k+i, so we subtract 70 from each side

k+i + 70-70 = 360-70

k+i =290

Answer: 9/110

Step-by-step explanation:

11*20=220

3*3/2*4=18

18/220=9/110

Answer:

P = 9/110

Step-by-step explanation:

Area of all triangles

[tex]4(\frac{(3)(3)}{2}) =4(\frac{9}{2}) =18[/tex]

Area of the rectangle

[tex](20)(11)=220[/tex]

Probability of hit

[tex]P=\frac{18}{220}= \frac{9}{110}[/tex]

Hope this helps

Answer:

I think it's 87.5 or 87½

Step-by-step explanation:

I hope it helps you.

Answer:

A

Step-by-step explanation:

Comment

The first one. Such an expression requires an isolation plus or minus sign and two terms that are not alike.

Answer

A

Answer:

6x+4

Step-by-step explanation:

A term can be a constant(like 7,4,3 etc) or a variable (x,y etc) which is separated by a multiplication, division,addition or subtraction sign.

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart. The histogram for the given data is attached with the answer below.

The histogram is a diagram with rectangles whose width is similar to the specified range and whose area is equal to the regularity of variables.

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart.

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The probability that four of the five digits are the same is 0.036.

There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.

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Answer:

26.6 cubic yards

Step-by-step explanation:

Remark

What you have is a rectangle prism. It has an easy enough formula.

Formula

V = L *w * h

Givens

L = 10 yards

w =  8 yards

h = 1/3 yards

Solution

V = L*w*h

V = 10 * 8 * 1/3

V = 26.66 yds^3

Answer:

-40

Step-by-step explanation:

First you have to look at the difference between 8 and 10. which is 80, then because it takes two steps to go from 8 to 10 you divide 80 by two, which is 40. And because the values are decreasing it is -40.

Slope of AB = 4/3, Slope of BC = -2/7, Slope of CD = 4/3, Slope of AD = -2/7 and Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.

We are given the coordinates of the quadrilateral ABCD as;

A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1).

Slope of AB = (5 - 1)/(-2 + 5) = 4/3

Slope of BC = (3 - 5)/(5 + 2) = -2/7

Slope of CD = (-1 - 3)/(2 - 5) = 4/3

Slope of AD = (-1 - 1)/(2 + 5) = -2/7

Thus we can see that both pairs of slope are equal which denotes that both pairs are parallel.

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A box plot has 5 data descriptions. The interquartile range for the given data set is 13.5.

A box plot has 5 data descriptions.

The given following information can be written as,

Thus, the interquartile range for the given data is,

Interquartile range = 27.5 - 14 = 13.5

Hence, the interquartile range for the given data set is 13.5.

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Answer:

( A - B).

A = { a, e, I, o, u}

B = { a, b, c, d }

{ e, I, o, u}

A - B = subtracting elements of B from A ( all the common elements)

Based on the calculations, the length of GF is equal to 26 units.

In Geometry, the centroid of any triangle always divides the lines in a ratio of 2:1. Thus, G divides line B F as follows:

2DG = BD

2(9x + 2) = 40

18x + 4 = 40

18x = 40 - 4

x = 36/18

x = 2.

Similarly, G divides line A F as follows:

2GF = A F

GF = A F/2

GF = (19x + 14)/2

GF = (19(2) + 14)/2

GF = 52/2

GF = 26 units.

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Answer:  26 units

Step-by-step explanation:   Trust Me!  

The answer is correct on Edge. I did it and got it right!

The test static used for this procedure is Aspin Welch's t-test.

What is Aspin Welch's T-test?

A variation of the Student's t-test used to determine if two sample means are substantially different is known as the Aspin Welch's T - test for Unequal Variances (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.

Formula for Aspin Welch's T - test

The t-statistic in Aspin Welch's T-test is given as,

t = [tex]\frac{X' - X}{\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } }[/tex]

Here, X' is the mean of the sample

X is the mean of the population

S1 and S2 are the respective standard deviations for the two samples

N1 and N2 are the respective strength of samples.

Calculating t-statistic for Aspin Welch's T-test

Given that,

X'-X = 1.33

[tex]\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } = 2.90[/tex]

∴ t = 1.33/2.90

t=0.458

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[tex]\therefore \sf{ LHS = \dfrac{tan \theta}{1 – cot \theta } + \dfrac{cot \theta}{1 – tan \theta}}[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{ LHS = \dfrac{tan \theta}{1 – \dfrac{1}{tan \theta}} + \dfrac{ \dfrac{1}{tan \theta}}{1 – tan \theta} }[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{ LHS = \dfrac{ tan^{2} \theta }{tan \theta – 1} + \dfrac{1}{tan \theta (1–tan \theta) } }[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{tan^{2} \theta}{tan \theta–1} – \dfrac{1}{tan \theta(tan \theta – 1 )}}[/tex]

[tex]\\[/tex]

[tex]\therefore \sf{LHS = \dfrac{tan^{3}\theta–1}{tan \theta(tan \theta –1)}}[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{LHS = \dfrac{tan^{3}\theta–(1)^{3}}{tan\theta(tan\theta–1)}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{ (tan \theta -1)(tan^{2}\theta+tan\theta .1 + (1)^{2})} {tan \theta (tan\theta(tan \theta –1 )}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{(tan^{2} \theta×tan\theta .1+1)}{tan \theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{(sec^{2}\theta+tan\theta)}{tan\theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{sec^{2}\theta}{tan\theta} + \dfrac{tan \theta}{tan\theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = sec^{2}\theta \times cot \theta + 1 }[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{1}{cos^{2}\theta} \times \dfrac{cos \theta }{sin\theta}+1}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \left( \dfrac{ 1}{cos \theta} \times \dfrac{1}{sin \theta} \right) + 1}[/tex]

We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)

We want to prove the trigonometric identity;

[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ

The left hand side can be expressed as;

[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]

⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]

Taking the LCM and multiplying gives;

(tan³θ - 1)/(tanθ(tanθ - 1))

This can also be expressed as;

(tan³θ - 1³)/(tanθ(tanθ - 1))

By expansion of algebra this gives;

[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]

Solving Further gives;

(sec²θ + tanθ)/tanθ

⇒ sec²θ * cotθ + 1

⇒ (1/cos²θ * cos θ/sin θ) + 1

⇒ (1/cos θ * 1/sin θ) + 1

⇒ 1 + (secθ * cosec θ)

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Answer:

A

Step-by-step explanation:

Fundamental Theorem of Algebra:

   This states that any polynomial with degree n will have n solutions which are real or complex.

Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.

End Behavior of Polynomial Functions:

   So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.

In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.

Using these two things, we can exclude answers

B can't be the answer, it only has 3 zeroes, this has at least 4.

C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions

D can't be the answer, it has a positive leading coefficient so the right side would be going up

This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.

The standard deviation of the sampled containers' contents is 0.36

Mean = summation of data / number

μ = 204.72 / 10

μ = 20.472

σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)² + (x₆ - μ)² + (x₇ - μ)² + (x₈ - μ)² + (x₉ - μ)² + (x₁₀ - μ)²] / n]

σ = √[[(20.72 - 20.472)² + (20.6 - 20.472)² + (20.71 - 20.472)² + (20.92 - 20.472)² + (19.79 - 20.472)² + (20.93 - 20.472)² + (20.09 - 20.472)² + (20.27 - 20.472)² + (20.49 - 20.472)² + (20.2 - 20.472)²] / 10]

σ = 0.36

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Answer:

110

Step-by-step explanation:

Sally takes $110 from her bank account if she spent $54.00 for a round-trip ticket.

It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.

We have:

Sally took money from her bank account to go out of town for an audition.

The expeses = (7.90 + 15.10) ÷ (1 - 1/2) = $46

Total money = 54 + 46

Total money = $110

Thus, Sally takes $110 from her bank account if she spent $54.00 on a round-trip ticket.

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Answer:

47/100 and 47%

Step-by-step explanation:

He missed 53 out of 100 so that means he made 47 out of a 100 and there you go... 47/100 and 47%

The volume of the rectangular prism is 1/10 cubic units

The formula for calculating the volume of a rectangular prism is expressed as;

V = Bh

B is the base area

h is the height

Given the following parameters

B = 3/20 units²

h = 2/3 units

Substitute

V = 3/20 * 2/3

V = 2/20

V = 1/10 cubic units

Hence the volume of the rectangular prism is V = 1/10 cubic units

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Answer:8 1/2^3

Step-by-step explanation:

Answer:

6:10am from my point of view

The system of equation is y = 300 + 3x and y = 250 + 5x and  the number of visits is 25

The given parameters are:

Jim's Gym

Sally's Salon

The equation is calculated as:

Total (y) = Initial * Charges * Number of visits (x)

So, the system of equation is

y = 300 + 3x

y = 250 + 5x

We have:

y = 300 + 3x

y = 250 + 5x

Substitute y = 300 + 3x in y = 250 + 5x

300 + 3x = 250 + 5x

Evaluate the like terms

-2x = -50

Divide by -2

x= 25

Hence, the number of visits is 25

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The possible values is  θ = π/4 and 5π/4

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

sin θ = cos θ

The above condition satisfied for θ = π/4 and 5π/4

sin π/4 = cos π/4 = 1/√2

sin  5π/4 = cos 5π/4 = -1/√2

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The computation shows that the total number of chocolate bars when there are 280 orange flavored bars will be

The total number of chocolate bars when there are 280 orange flavored bars will be:

= Coconut + Honeycomb + Coffee + Orange + Strawberry

= (4/6 × 280) + (5/6 × 280) + (1/6 × 280) + 280 + (4/6 × 280)

= 1033

The total number when there are 960 coconut bars will be:

= Coconut + Honeycomb + Coffee + Orange + Strawberry

= 960 + (5/4 × 960) + (1/6 × 960) + (6/4 × 960) + 960

= 960 + 1200 + 160 + 1440 + 960

= 4720

The mean of 7, 2, and 9 will be:

= (7 + 2 + 9)/3

= 6

The mean of 5, 6, 6, and 5 will be:

= (5 + 6 + 6 + 5)/4

= 22/4

= 5.5

The mean of 2, 1, 2, 3, 3, 1 will be:

= (2 + 1 + 2 + 3 + 3 + 1) / 6

= 15/6

= 2.5

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The correct option regarding whether the triangles are similar is given by:

Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

Similar triangles are triangles that have congruent angles, that is, angles with the same measure.

Considering that the sum of the internal angles of a triangle is of 180º, the third angle of triangle FGH is given as follows:

98.6 + 61.1 + x = 180

x = 180 - (98.6 + 61.1)

x = 20.3º.

The second triangle has an angle of 20.3º, hence they are not similar, and the correct option is given by:

Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

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