Please help me respond this question!

(a) When he is 10 feet from the base of the light, the rate at which the length of his shadow changing is 7.5 ft/s

(b) When he is 10 feet from the base of the light, the rate at which the tip of his shadow changes is 2.5 ft/s.

We have, the height of man, CD = 6 feet

Height of light , AB = 16 feet

Rate of walk by man, dx/dt = 5 feet per second.

a) we have to calculate the rate at which the length of his shadow is moving when he is 10 feet from the base of the light.

let x feet be the distance between the light and man and y feet be the distance between the light and man's shadow(E) i.e BC = x ft. and BE = y ft.

By using ratio of similar triangles,

16/y = 6/(y - x)

On cross multiplication,

16(y - x) = 6y

16y - 15x = 6y

16y - 6y = 15x

10y = 15x

Dividing by 3 on both sides,

2y = 3x

On differentiating both sides with respect to t,

2(dy/dt) = 3(dx/dt)

dy/dt = (3/2)(dx/dt)

dy/dt = (3/2)(5)

dy/dt = 15/2

dy/dt = 7.5 ft/s

Therefore, the rate at which the length of his shadow is changing is 7.5 ft/s.

b) We have to calculate the rate at which the length of his shadow is changing when he is 10 feet from the base of the light.

Length of shadow, CE = y - x

Rate of change of shadow is calculated by differentiating length with respect to time.

d(CE)/dt = dy/dt - dx/dt

d(CE)/dt = 7.5 - 5

= 2.5 ft/s

Therefore, the rate at which the length of his shadow is changing is 2.5 ft/s.

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Answer: hope it helps

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 ((2•5x2) -  2x) -  3  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  10x2-2x-3

The first term is,  10x2  its coefficient is  10 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   10 • -3 = -30

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -2 .

     -30    +    1    =    -29

     -15    +    2    =    -13

     -10    +    3    =    -7

     -6    +    5    =    -1

     -5    +    6    =    1

     -3    +    10    =    7

     -2    +    15    =    13

     -1    +    30    =    29

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 10x2 - 2x - 3  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 10x2-2x-3

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 10 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.1000  

Plugging into the parabola formula   0.1000  for  x  we can calculate the  y -coordinate :

 y = 10.0 * 0.10 * 0.10 - 2.0 * 0.10 - 3.0

or   y = -3.100

Using the concept of percentage, the percentage of dolphins that knew the difference is 26%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The number of dolphins that knew the difference between strike and ball is given as 4 out of 15.

This can be represented in a fraction as 4 / 15

The percentage that knew the difference = (4 / 15) * 100

The percentage that knew the difference will be 0.26 * 100 = 26 %

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The worth of an anticipated revenue stream as of the valuation date is known as present value, sometimes known as present discounted value.

The total of future investment returns discounted at a given level of expected return is used to determine the present value (PV), which is the value of money in today's dollars that you expect to get from future income. This idea is used for bond pricing and stock valuation.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

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Check the picture below.

The range of the given function f(x) = √x + 7 is y ≥ 7. So, option B is correct.

The given function is f(x) = √x + 7

Since it is a square root function, its domain is D = {x ≥ 0}

Then, substitute x = 0 in the function, and we get

f(0) = √0 + 7 = 7

⇒ y =7

f(1) = √1 + 7 = 8

⇒ y =8

So, for x ≥ 0, the output values form a set {y ≥ 7}

Therefore, the range of the given function is y ≥ 7.

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Using the property of geometry and using a parallelogram , We can prove that the opposite sides of parallelograms are congruent.

What is a parallelogram?

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The opposite sides and the opposite angles of a parallelogram are of equal length. A parallelogram is a special kind of quadrilateral with both pairs of its opposite sides parallel and equal.

What are the 4 types of parallelograms?

There are 4 types of parallelograms with 3 special types.

They are:

parallelograms

squares

rectangles

rhombuses.

According to the given question:

Let ABCD be a parallelogram where AB and CD are in opposition to each other, while BC and AD are.

According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.

The definition of a parallelogram is that segment AB is parallel to segment DC.

Segments BC and AD are transverse to line AC. As demonstrated below, this transversal generates alternate interior angles that are equal.

In the same way, segment AB and segment DC are transversals for line AC. This transversal generates equal alternate interior angles.

Segment AC is also divided into segments by its reflexive property.

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Answer:

1. 38%

2. 0.4

3. 5/8

Step-by-step explanation:

Hope its right

Answer:

Least 38%

Middle 0.4

Greatest 5/8

Step-by-step explanation:

you can make them all % by multiplying by 100

so

38% (given)

0.4 × 100 = 40%

5/8 × 100 = 62.5%

The total cost of the siding material is given as follows:

B. $292.50.

To obtain the cost of material, the first step is obtaining the area that will be covered, which is given as follows:

The rectangular area of 8 feet by 24 feet will be covered, with these following exceptions:

The triangular area with base 24 feet and height 6 feet will also be covered.

Then the total area to be covered is given as follows:

Area = 8 x 24 - (2 x 6 x 4) - (3 x 7) + 0.5 x 24 x 6

Area = 195 ft².

The total cost is of $1.5 per ft², hence it is calculated as follows:

Total cost = 195 x 1.5 = $292.50.

Meaning that option B is correct.

The problem is given by the image shown at the end of the answer.

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The equation to find the distance between the lions and giraffes is

x² = 121 + 256.

Option D is the correct answer.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Hypotenuse = Distance between lion and giraffes = x

Distance between lions and monkeys = 11 feet

Distance between monkeys and giraffes = 16 feet

Applying the Pythagorean theorem.

x² = 11² + 16²

x² = 121 + 256

x² = 377

x = √(377)

x = 19.42

Thus,

The distance between lions and giraffes is 19.42 feet.

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Answer:B and D

Step-by-step explanation:

Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.

The dimension of a suitcase is-

length = 24 in.

width = 18 in.

The length of the bat = 29 in.

Clearly, the bat cannot fit vertically or horizontally in the suitcase.

Now to see if it fits diagonally in the suitcase, we apply the Pythagoras theorem to determine the diagonal of the suitcase or say the hypotenuse of the rectangular suitcase.

Thus, by Pythagoras' theorem,

[tex](hyp)^2 = opp^2 + adj^2[/tex]

[tex](hyp)= \sqrt{opp^2 + adj^2}[/tex]

[tex](hyp)= \sqrt{18^2 + 24^2}[/tex]

[tex](hyp)= \sqrt{324+ 576}[/tex]

[tex](hyp)= \sqrt{900}[/tex]

 hyp  = 30 in.

Hence, the diagonal of the suitcase > the length of the bat.

Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.

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The correct option is: As the sample size increases, the variability of the sampling distribution decreases. is the FALSE statement.

The probability distribution of the a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution.

Thus, it is incorrect to say that as the sample size increases, the variability of the sampling distribution decreases.

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Answer:

[tex]0.5\sqrt{16a^2}:\quad 2a[/tex]

Step-by-step explanation:

[tex]\sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0\\\\\sqrt{16a^2}=\sqrt{16}\sqrt{a^2}\\=0.5\sqrt{16}\sqrt{a^2}\\\\\sqrt{16}\\\mathrm{Factor\:the\:number:\:}\:16=4^2\\=\sqrt{4^2}\\\\\sqrt{4^2}=4\\=4\\=0.5\cdot \:4\sqrt{a^2}\\\sqrt{a^2}=a\\=0.5\cdot \:4a\\=2a[/tex]

Answer: True. Renting is a great option for many people because it offers flexibility and affordability. Renting allows individuals to live in a desired location without the financial burden and commitment of owning a home. It also provides flexibility, as renters can easily move to a different location if their needs or circumstances change. Additionally, renting can be a more affordable option compared to owning a home, as it typically involves lower upfront costs and maintenance expenses. For these reasons, renting is a viable and attractive option for many people.

Step-by-step explanation:

Answer:

y = (17/4)x + (3/4)

Step-by-step explanation:

Formula we use,

→ y = mx + b

Now the slope-intercept form is,

→ y = mx + b

→ 4y - 5x = 12x + 3

→ 4y = 12x + 5x + 3

→ y = (17x + 3)/4

→ y = (17/4)x + (3/4)

Thus, answer is y = (17/4)x + (3/4).

Answer:

y = [tex]\frac{17}{4}[/tex] x + [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4y - 5x = 12x + 3 ( add 5x to both sides )

4y = 17x + 3 ( divide through by 4 )

y = [tex]\frac{17}{4}[/tex] x + [tex]\frac{3}{4}[/tex] ← in slope- intercept form

Answer:

The correct answers would be

B, C, and D.

Step-by-step explanation:

B) ΔABD ~ ΔCBA

∠B is congruent to ∠B (itself) by the Reflexive Property.

C) ΔDAB ~ ΔDCA

I took the quiz and got this one right though I'm not 100% sure how it works.

D) ΔBCA ~ ΔACD

∠C is congruent to ∠C through the Reflexive property.

I hope this helps :)

I tried my best

The similarity statement that would be true for the given figure is; A.

∆ DAB ~∆ DAC

Similar triangles are those triangles that have the same proportionate side lengths as well as related angle measurements.

Two triangles are said to be similar if their corresponding angles and sides have the same ratio. Similar triangles will possess the same form but may or may not have the same size.

The SAS similarity rule states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then it means that the two triangles are similar.

The Side-Side-Side (SSS) similarity rule states that If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

In this question, when we analyze the triangles well, it is clear that;

DA is congruent to itself by reflexive property of congruence.

Thus, we can say that ΔDAB is similar to ΔDAC,

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Answer:

The smaller integer is greater than 1

Step-by-step explanation:

The integers are x and x+1

[tex]x + x + 1 < 3x \\ 2x + 1 < 3x \\ 2x - 2x + 1< 3x - 2x \\ 1< x [/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ D(\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\qquad F(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE E}}{(1~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=1\implies x+10=2\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-1\implies y+7=-2\implies \boxed{y=-9}[/tex]

Answer: 32%

Step-by-step explanation:

To find the relative frequency, you divide the specific term by the sum of all terms.

start by adding all of the colors together, 5 + 6 + 6 + 8 = 25

then divide the blue number by the sum, 8/25 = 0.32

than multiply that by 100 to get its percentage, 0.32(100) = 32%

Answer:

51units

Step-by-step explanation:

EF+FG=EG

18+(x+20)=5x-14

38=4x-14

4x=52

x=13

EG=5*13-14=51

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The situation for which the explicit formula of the arithmetic sequence would be used instead of the recursive formula is given as follows:

Find the 106th term when the first term is of 2 and the common difference is of 5.

An arithmetic sequence is a sequence of numbers in which the difference between two consecutive terms is always constant, called common difference d.

The recursive formula is given as follows:

f(n + 1) = f(n) + d.

The first term f(1) is given.

Hence, the recursive sequence should be used to calculate a small number of terms, such as at most 15 terms.

For a large number of terms, the explicit formula should be used, which is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Hence, in this problem, the 106th term should be calculated with the explicit formula, meaning that the first option is the correct option.

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Answer: at 4 seconds it will hit the ground. The maximum height is reached at 2 seconds due to the symmetry of the quadratic.

Step-by-step explanation:

The amount of money each waiter get in tip is 44 dollars.

In this question we have been given at the yum yum cafe the waiters combine their tips and divide the total by the number of waiters.

Today's tip total is 132 and three waiters are working.

We need to find the amount of money each waiter get in tip.

Let x dollers be the amount each waiter get in tip.

Total tip amount = 132

number of waiters = 3

By unitary method,

x = 132/3

x = 44 dollars

Therefore, each waiter get 44 dollars in tip.

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Answer:

Step-by-step explanation:

I graphed these equations on desmos, the solution is the point where they intercept. The point where they intercept or the solution is (4, 0)

The correct option e) 94.29%, for the probability that among the next 166 responses there will be at most 43 correct answers.

If we use a normal distribution to simulate any binomial distribution with p = 0.24 for n = 166 results, then:

There should be 43 correct responses, or

μ = np = 166*0.24

μ = np = 34.86

The number of accurate responses has a standard deviation of

σ = √(np(1-p))

σ = √(34.86*0.76)

σ = 5.14

43 correct responses have a z-value;

z = (x - μ)/σ

z = (43 - 34.86)/5.14

z = 1.58

The likelihood that 43 accurate responses are provided is:

N(1.58) = 0.9429

Thus, the probability that among the next 166 responses there will be at most 43 correct answers is 94.29%.

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The complete question is-

Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.

a) 74.56870% b) 74.30203% c) 75.20203% d) 94.95%  e) 94.29%

To solve this problem, we need to use the z-score formula to convert the given values to standard units. This will allow us to use the normal distribution table to find the percentage of pregnancies that fall within a certain range of lengths.

First, let's find the z-score for a pregnancy lasting more than 274 days:

z = (274 - 266) / 16 = 0.5

Next, let's use the normal distribution table to find the percentage of pregnancies that are longer than 274 days. Since the z-score we calculated is positive, we need to look in the right tail of the distribution. From the table, we find that the percentage of pregnancies that are longer than 274 days is approximately 30.85%.

Now let's find the z-score for a pregnancy lasting less than 246 days:

z = (246 - 266) / 16 = -1.25

To find the percentage of pregnancies that are shorter than 246 days, we need to look in the left tail of the distribution. From the table, we find that the percentage of pregnancies that are shorter than 246 days is approximately 8.38%.

Therefore, the percentage of children that are born from pregnancies lasting more than 274 days is approximately 30.85%, and the percentage of children that are born from pregnancies lasting less than 246 days is approximately 8.38%.

To find the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days, we need to use the z-score formula to convert the lengths of pregnancies to standard units and the standard normal distribution to find the percentage of children who fall within the given range of pregnancy lengths.

The z-score formula is:

z = (x - mu) / sigma

where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.

In this case, we are given that mu = 266 days and sigma = 16 days. We can use this information to find the z-score for the lower and upper bounds of the pregnancy length range, 246 days and 274 days, respectively.

For the lower bound of the pregnancy length range, we have:

z = (246 - 266) / 16

= -20 / 16

= -1.25

For the upper bound of the pregnancy length range, we have:

z = (274 - 266) / 16

= 8 / 16

= 0.5

Now we can use the standard normal distribution to find the percentage of children who have a z-score between -1.25 and 0.5. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, so the percentage of children who fall within the given pregnancy length range is the same as the percentage of children who have a z-score within this range.

To find the percentage of children who have a z-score between -1.25 and 0.5, we can use a standard normal distribution table to look up the z-scores and find the corresponding probabilities. The standard normal distribution table shows the percentage of values that fall within a given range of z-scores, so to find the percentage of children who have a z-score between -1.25 and 0.5, we need to look up the percentage of values that fall within this range.

According to the standard normal distribution table, the percentage of values that fall within the range of z-scores -1.25 to 0.5 is approximately 0.38. Therefore, the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days is approximately 38%, to the nearest hundredth.

Both Frida and Sam are right.

In geometry, a quadrilateral is a type of close-shaped polygon that has four sides, four angles, and four vertices. In Latin, 'Quadri' means four, and 'latus' means side.

A parallelogram is a geometrical shape having both pairs of opposite sides parallel and equal.

Squares are a type of quadrilateral having two sets of parallel sides. Parallelograms may be called quadrilaterals which have two sets of parallel sides. As squares are quadrilaterals having two sets of parallel sides, all squares may be called parallelograms. As all rectangles are having two pairs of parallel sides and all angles of a rectangle are equal, it might be called parallelograms.

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The complete question is:

Frida sorted polygons so Group 1 only squared. Group 2 was only

rectangles, not squares. Frida said all the figures are parallelograms. Sam said they are all quadrilaterals. Who is right? Why?