the angle of elevation of the sun is decreasing at a rate of 0.25 radyh. how fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is ?y6?

The distance formula can be used to determine this distance. The formula d = (x 2  x 1 ) 2 + (y 2  y 1 ) 2 can be used to describe the distance that separates the two points (x 1, y 1) and (x 2, y 2).

The y-coordinate comes after the x-coordinate in every case. The coordinate grid below demonstrates that the ordered pairs (3,4) and (4,3) are two distinct points!

Coordinates are written as (x, y), with the x-axis point being written first and the y-axis point following. The expression "along the corridor, up the stairs" may be used to remind some children of this, instructing them to follow the x axis first and then the y.

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There are 6 different possible outcomes.

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The party which calls the coin's side wins.

We find it because when we turn a coin very often, humans get half the heads and half the tails.

The chances of swinging the head are 1/2 , and the chances of swinging the tail are 1/2 .

Total outcomes = 2×5×6

                           = 60

So the final answer is 60

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Answer:

A. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are congruent angles that are outside the parallel lines. That is why their name is alternate exterior angles since they are exterior from parallel lines.

The scale factor will be 1/4.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The right triangle on the right is a scaled copy of the right triangle on the left.

Now,

Since, The right triangle on the right is a scaled copy of the right triangle on the left.

Hence, The ratio of their similar sides is equal to the scale factor.

So, We get;

⇒ 2 / 8 = 1 / 4

And, 2 / 8 = 1 / 4

Thus, The scale factor = 1/4.

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The solution to the inequality algebraically is -9 < x < 12

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

negative 2 less-than startfraction x over 3 endfraction 1 less-than 5

Express the statement using numbers and expressions

So, we have the following representation

-2 < x/3 + 1 < 5

Subtract 1 from all sides of the inequality

This gives

-3 < x/3 < 4

Multiply through the inequality by 3

So, we have

-9 < x < 12

Hence, the solution is -9 < x < 12

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Answer:

b. Negative 9 less-than x less-than 12

Step-by-step explanation:

Refer to the photo taken.

The price of the watch before the discount is calculated to be £24.44.

As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;

discount on a pair of trainers = 15/100 × 38 =  £5.7

cost of trainers after discount =  £38 - 5.7 =  £32.3

Now the price of the watch after the discount can be calculated by subtraction as follows;

price of watch after discount = total price - price of trainers after discount

price of watch after discount =  £53. 55 - £32.3

price of watch after discount = £21.25

Now the price of the watch before the discount can be calculated as follows;

price of watch before discount = £21.25 × 15/100

price of watch before discount = £21.25 + £3.1875

price of watch before discount = £24.44

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The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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The height of the ball after x seconds is given by the quadratic function presented as follows:

y = -16t² + 8t + 4.

This is a concave down parabola, hence the vertex of the function is the maximum point.

The coefficients of the quadratic function are given as follows:

a = -16, b = 8, c = 4.

Then the x-coordinate of the vertex is given as follows:

x = -b/2a = -8/-32 = 0.25.

The maximum height of the ball is given as follows:

y = -16(0.25)² + 8(0.25) + 4 = -1 + 2 + 4 = 5 feet.

The ball hits the ground when:

y = 0.

Hence:

-16t² + 8t + 4 = 0.

Solving the quadratic equation, the positive solution is given as follows:

t = 0.809 seconds.

The graph of the quadratic function is given by the image shown at the end of the answer.

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The solution for d in the equation v = √64d is d = v²/64

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

v = √64d

Take the square root of both sides

So, we have the following representation

v² = 64d

Divide both sides of the equation by 64

So, we have the following representation

v²/64 = d

Rewrite as

d = v²/64

Hence, the value of d is d = v²/64

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The sign change of the expression ax + b = cx + d in the conditions are solved to be

a. 0 < b < d and a < c

b. d < b < 0 and a < c

The given expression is

ax + b = cx + d

comparing the conditions

a. 0 < b < d and a < c

here b is non negative number and less than d a is also less than c. hence

ax + b = cx + d

ax - cx = d - b

ax - cx will be negative

d - b will be positive

this will lead to a negative solution since positive divided by negative  give negative

b. d < b < 0 and a < c

ax + b = cx + d

ax - cx = d - b

d - b = negative

ax - cx = negative

negative dividing negative is positive hence a positive solution

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I believe it would be the first answer choice

a.5n^2

n^2 being "the square of a number"

5n^2 is just multiplying 5 and n^2

in other words the product of the square of a number and 5

Evelyn basis is the adjusted market value of the property and the basis would have been to Evelyn as profit

We should know that adjusted basis is the value of a property after deducting all expenses and taxes from the property.

The Adjusted basis of the property was $12,000

It was given to Sharon at fair value of $80,000

After  death of Sharon, the property was worth $85,000

Based on these figures, the basis is a gain of $(85000-80000) to to Evelyn

In conclusion, Evelyn has gained the sum of $(85000-12000)=$73000

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Answer:

a

Step-by-step explanation:

The equivalent of two reflections across intersecting lines is a glide reflection.

A glide reflection is a combination of a translation and a reflection. It involves moving an object along a line, and then reflecting the object across the same line. Since a reflection is an isometry (a transformation that preserves the distance between points), a glide reflection is also an isometry.

In contrast, a rotation is a transformation that involves turning an object around a fixed point, and a reflection is a transformation that involves flipping an object across a mirror line. Neither of these transformations is equivalent to two reflections across intersecting lines.

Therefore, the correct answer is (a) glide reflection.

Answer:

8+y[tex]\geq[/tex]17

Step-by-step explanation:

Using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.

A mathematical function known as just an operation converts zero or more input values into a precisely defined output value.

A quantity of operands affects the operation's arity.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

Ashok purchased 15.5kg of rice and 3.25 kg of sugar.

Now, the total weight of rice and sugar Ashok purchased is:

15.5 + 3.25

18.75kg

Therefore, using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.

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Answer:

A

Step-by-step explanation: here ya go <3

The value of the Confidence interval will be 2.898

The number of standard deviations from the t-mean distribution's is equal to a t-score. The test statistic used in t-tests and regression testing is the t-score. When the data follow a t-distribution, it may also be used to represent how distant an observation is from the mean.

The t-score formula is written as follows:t=¯¯¯x−μS√n t = x ¯ − μ S n , where ¯¯¯x, is the sample mean, is the population mean, S n is the sample size, and x is the standard deviation of the sample. Square root n must be included in the formula.

using tables of t distribution we have

alpha = 1 - 0.99 = 0.01

alpha / 2 = 0.005

df = 17

critical value or value of t score is = 2.898

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The value of the t score is 2.898 for a 99% confidence interval if we take a sample of size 18.

As per the details share in the above question are as bellow,

Confidence level = 99%

Now the significance level will be 100% - Confidence level

Substitute the value in above equation we get,

Thus, Significance level = (100% - 99%)

Significance level= 1%

Significance level=1/100= 0.01

Now the Sample size (n) = 18

Further the degrees of freedom = (n - 1)

Substitute the value in above equation we get,

Degrees of freedom= (18 - 1) = 1

Where, the t score for a 99% confidence interval is given by,

t({0.01/2},17)=2.898

Now calculating the critical value from t table we get,

Critical value or value of t score is = 2.898

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Answer:

5/6 (option 3)

Step-by-step explanation:

[tex]P(A^C)[/tex] is asking what the complement of A is. This means we are asking what the probability of NOT getting A is. This would be 1 - P(A).

P(A) = The probability of getting a 3 = 1/6

We can solve for the probability of the complement of the A and get:[tex]P(A^C) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}[/tex]

Thus, the answer is 5/6 (which I believe is the 3rd option you are given)

After solving the equation, the value obtained will be equal to negative 11 over 35 times r plus negative 14. Hence, option C is correct.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given statement in the question,

The equation will be,

(-1/5r - 6 - 5/7r) - (-3/5r) - 8

Rearrange the equation with like terms,

-1/5r - 5/7r + 3/5r - 8 - 6

(-7r - 25r + 21r)/35 -14

=-(11/35)r - 14.

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Answer:

x = -5; y = 5

Step-by-step explanation:

  x + 5y = 20

-2x + 7y = 45

Multiply both sides of the first equation by 2 to get 2x. Write the second equation below it and add the equations. 2x and -2x add to zero eliminating the x terms.

 2x + 10y = 40

-2x +  7y = 45

-----------------------

         17y = 85

y = 85/17

y = 5

Now use substitution in the first original equation to find x.

x + 5y = 20

x + 5(5) = 20

x = -5

Answer: x = -5; y = 5

If a hypothesis test is significant at level α = 0.05, then the P-value is less than or equal to 0.05 or P-value ≤ 0.05.

The P-value is a measure of the strength of the evidence against the null hypothesis. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level α, it means that the observed evidence is unlikely to have occurred by chance under the null hypothesis, and we can reject the null hypothesis in favor of the alternative hypothesis.

For example, if the P-value of a hypothesis test is 0.03, it means that there is a 3% chance of obtaining the observed test statistic (or a more extreme one) if the null hypothesis is true. Since this is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Hence, if a hypothesis test is significant at level α = 0.05, then P-value ≤ 0.05.

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By using slope, it can be calculated that

(-8, -5) and (1, 7) represents a line with slope of [tex]\frac{4}{3}[/tex] and length 15 units

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

For the first option

(-11, 7) and (1, -2)

Slope = [tex]\frac{-2-7}{1 - (-11)}[/tex]

          = [tex]-\frac{9}{18}[/tex]

          = [tex]-\frac{1}{2}[/tex]

First option is wrong

For the second option

(-2, -6) and (4, 2)

Slope = [tex]\frac{2 - (-6)}{4 - (-2)}[/tex]

          = [tex]\frac{8}{6}[/tex]

          = [tex]\frac{4}{3}[/tex]

Length =

[tex]\sqrt{(4 - (-2))^2 + (2-(-6))^2}\\\sqrt{36+64}\\\sqrt{100}\\[/tex]

10 units

Second option is wrong

For the third option

(-3, -2) and (9, 7)

Slope = [tex]\frac{7 - (-2)}{9 - (-3)}[/tex]

          = [tex]\frac{9}{12}[/tex]

          = [tex]\frac{3}{4}[/tex]

Third option is wrong

For the fourth option

(-8, -5) and (1, 7)

Slope = [tex]\frac{7 - (-5)}{1 - (-8)}[/tex]

          = [tex]\frac{8}{6}[/tex]

          = [tex]\frac{4}{3}[/tex]

Length =

[tex]\sqrt{(1 - (-8))^2 + (7-(-5))^2}\\\sqrt{81+144}\\\sqrt{225}\\[/tex]

15 units

Fourth option is correct

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The changes in the river water level with reference to the normal water level in the 9-day period is analyzed as follows;

Part A: The numerical expression representing the water level after the 9-day period is; -12 + 18 - 8 × 2.6

Part B; -12 + 18 - 8 × 2.6 = -14.8

Part C; The meaning of -14.8 is that the water level after the 9-day period is 14.8 centimeters below the normal water level.

A mathematical expression is a collection of numbers and, or variables and operators combined according to the rules of mathematical operations.

Part A

The water level of the river at the start = 12 centimeters below its normal level

The amount by which the water level increases after a day of rain = 18 centimeters

The amount by which the water level reduces in the next 8 days = 2.6 centimeters per day

The numerical expression that represents the water level in the 9-day period is therefore;

-12 + 18 - 8 × 2.6

Part B

The value of the expression -12 + 18 - 8 × 2.6 is; -12 + 18 - 8 × 2.6 = -14.8

Part C

The meaning of the value -14.8 is that the water level after the 9-day period is 14.8 centimeters below the the normal water level of the river

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The present age of Jiya whose mother 12 year more than twice her age., is sixteen years and her mother present age is fourty-four years.

We have, Jiya's mother is 12 year more than twice of her age. Let "x years" and "y years" be the present age of Jiya and her mother respectively.

According to problem, 12 + 2x = y --(1)

After 8 years, her mother age = 20 years less then three times of her age.

After 8 years, age of Jiya = (x+8) years.

i.e y + 8 = 3( x+8) - 20 --(2)

we have to calculate the present ages of both. Simplify the equation (2),

y + 8 = 3x + 24 - 20

=> y + 8 = 3x + 4 => y = 3x -4 --(3)

eqution (1) and (3) represent the linear equations so, we solve these linear equations by substitution,

plugging the value of y from( 1) to (3),

12 + 2x = 3x -4

=> 3x - 2x = 12+4

=> x = 16 then y = 12 + 2×16 = 44

Hence, Jiya's age is 16 years and her mother is about 44 years.

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The price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the 3rd standard deviation as shown below,

3rd standard deviation  = mean + 3 × standard deviation

3rd standard deviation = 17000 + 3 × 500

3rd standard deviation = 17000 + 1500

3rd standard deviation = $18500

Therefore, the price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

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Answer:

65 mph;  35 mph

Step-by-step explanation:

let x = rate of car 1

x-30 = rate of car 2

distance = rate x time

6x = 600 - 6(x-30)

6x = 600 - 6x + 180

6x = 780 - 6x

12x = 780

x = 780/12 = 65 mph

x - 30 = 65 - 30 = 35 mph

a) The equation is: y = 2x + 3. b) The equations are :Point - slope form: y - 5 = -(x - 1).Slope - intercept form: y = -x + 6. c) The systems are consistent independent. d) The point of intersection is (1, 5).

Linear function

A linear function is defined in slope-intercept formula by the rule presented as follows:

y = mx + b.

In which:

m is the constant rate of change of the function, called slope.

b is the value of y when x = 0, called intercept.

For Sidewalk 1, it is found that:

When x increases by 2, y increases by 4, hence the slope is of m = 2.

When x = 0, y = 3, hence the intercept is of b = 3.

Then the rule is:

y = 2x + 3.

For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:

m = -2/2 = -1.

The line goes through point (1,5), hence the equation in point-slope form is:

y - 5 = -(x - 1).

Combining the like terms, the slope-intercept form is:

y - 5 = -x + 1

y = -x + 6.

Since the two lines have different slopes, the system is consistent independent.

The x-coordinate of the intersection is:

-x + 6 = 3 + 2x.

3x = 3

x = 1.

The y-coordinate is:

-x + 6 = -1 + 6 = 5.

Hence the intersection point is:

(1, 5).

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According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 1.22%.

Standard deviation is a measure of the spread or dispersion of a set of data. It tells you how much the individual values in the set differ from the mean (average) of the set.

The formula for calculating the standard deviation of a set of n data points:

Standard deviation = sqrt(((x1 - mean)^2 + (x2 - mean)^2 + ... + (xn - mean)^2) / n)

First, we need to calculate the number of standard deviations that the guarantee period of 24 months is from the mean of 33 months. We can do this by subtracting the mean from the guarantee period and dividing by the standard deviation:

(24 - 33) / 4 = -9 / 4 = -2.25

Since we are assuming that the distribution of battery lifetimes is normal, we can use the standard normal distribution table to look up the area under the curve that is 2.25 standard deviations below the mean. This area represents the proportion of batteries that will have to be replaced under the guarantee.

According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 0.0122. This means that approximately 1.22% of the batteries will have to be replaced under the guarantee.

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