If IJ=16 and JK=16, what is the length of HK?

The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.

In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.

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The complete question is:

A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.

Answer:

1743.46[tex]\frac{meters}{min}[/tex]

Step-by-step explanation:

Two unit multipliers will be used here:

1 mile (mi)  = 1,609.344 meters

1 hour (hr) = 60 minutes (min)

65 [tex]\frac{mi}{hr}[/tex] = (65[tex]\frac{mil}{hr}[/tex])×([tex]\frac{1609.344 meters}{1 mile}[/tex])×([tex]\frac{1 hour}{60 minutes}[/tex])

The miles unit in the numerator and denominator will cannel each other out completely. In addition, the hour unit in the numerator and denominator will also cancel each other out completely:

         = 1743.46 [tex]\frac{meters}{min}[/tex]

The volume of the solid formed by revolving the region about the y-axis is (1372/3)π.

The given region is a semicircle with a radius of 7 centered at the origin, so we can find its volume by revolving it about the y-axis using the disk method.

The area of a disk at a distance y from the y-axis is given by π(√(49 - y²))², so the volume of the solid is given by the integral:

V = ∫(from -7 to 7) π(√(49 - y²))² dy

Simplifying the integrand, we get:

V = ∫(from -7 to 7) π(49 - y²) dy

Evaluating this integral, we get:

V = π[(49y - (1/3)y³)](from -7 to 7)

V = π[(49(7) - (1/3)(7³)) - (49(-7) - (1/3)(-7³))]

V = π[686/3 + 686/3]

V = (1372/3)π

So the volume of the solid formed by revolving the region about the y-axis is (1372/3)π.

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The best describes reason the proof is not correct is c. The proof violates the parity property.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."

The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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Step-by-step explanation:

Inequality: 1.59(5) + 3.29n ≤ 45.00

Explanation: 1.59(5) represents the total cost of the streamers, and 3.29n represents the total cost of the balloons (since we don't know how many packages of balloons Steve will buy, we use the variable n to represent this unknown quantity). The sum of these costs must be less than or equal to Steve's budget of $45.00.

To solve for n:

1.59(5) + 3.29n ≤ 45.00

7.95 + 3.29n ≤ 45.00

3.29n ≤ 37.05

n ≤ 11.27 (rounded to two decimal places)

So Steve can buy a maximum of 11 packages of balloons within his budget.

The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

The general form of linear equations is:

y = a + bx

Where:

a = intercept

b = slope

The form of the equation that models the cost is:

Total cost = cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

Thus, they travelled 1186 miles.

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The proportion that could be used is (a) 2/5=13/2x

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

Scale = 1 inch: 2 1/2 feet

The proportion that can be used is:

actual length / length on the floor plan = scale factor

So, we can set up the proportion as follows:

actual length / 6 1/2 inches = 2 1/2 feet / 1 inch

Solving for actual length (x), we get:

x/(13/2) = 5/2

So, we have

2x/13 = 5/2

Rewrite as

13/2x = 2/5

Hence, the proporton is (a) 2/5=13/2x

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a - The average rate at which oil drains during first 15 minutes is -4725 gallons/min

b - The average rate at which oil drains during time interval [10 , 15] is -4275 gallons/min

c - The rate of oil flowing out 15 min after the drain began is  -4050 gallon/min

We have ,

V(t) = 45(60 - t)²

The average rate at which oil drains during first 15 minutes can be given as:

V(0,15)=[tex]\frac{V(15)-V(0)}{t2-t1}[/tex]

         = (45(60-15)²-45(60-0)²)/15

         = -70875/15

         = -4725 gallons/min

Similarly , the average rate for time interval [10 , 15] is

V(10 , 15) = [tex]\frac{V(15)-V(10)}{t2-t1}[/tex]

               = (45(60-15)²-45(60-10)²)/(15-10)

               = -21375/5

               = -4275 gallons/min

Now , to find rate of oil flowing out 15 min after the drain began

For that we will differentiate the given equation with respect to t

V(t) = 45(60 - t)²

     = 45(3600 - 120t + t²)

     = 16200 - 5400t + 45t²

Differentiating with respect to t we have

V'(t) = -5400 + 90t

V'(t)  = -5400 + 90(15)

       = -4050 gallon/min

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Early tax withholding offers predictability and facilitates effective financial planning but restricts financial flexibility and investment potential. Meanwhile, late tax withholding fosters short-term financial flexibility and investment opportunities but carries the risk of miscalculations, underestimations, and potential penalties.

The timing of tax withholding can have different pros and cons depending on an individual's current financial status, revenue predictions, and personal preferences.

A primary advantage of early tax withholding is increased predictability. By setting aside funds for taxes in advance, an individual can have a clearer picture of their net income and employ effective financial planning strategies. However, this approach does have a notable drawback. Specifically, the individual may miss potential investment opportunities as a result of having their money tied up in tax withholdings.

On the other hand, late tax withholding allows greater short-term financial flexibility, providing the opportunity to use funds for immediate personal or business needs. It can also enable investment in lucrative opportunities. However, the main downside is the potential for miscalculation and underestimation of the tax liability, which can lead to financial strain or penalties.

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By using the box plot, the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

To find the value of the typical gas mileage for the top 25 percent of cars, we need to look at the upper quartile (Q3) of the box plot. The upper quartile is the point that separates the highest 25 percent of the data from the lowest 75 percent.

In the box plot, the upper quartile (Q3) is represented by the top of the box (the horizontal line inside the box) and the vertical line extending from the top of the box (the "whisker" above the box). We can estimate the value of Q3 by looking at the scale on the vertical axis and reading off the approximate value at the top of the box and the end of the whisker.

Assuming the scale on the vertical axis is in miles per gallon, we can estimate that Q3 is around 30 miles per gallon. Therefore, we can conclude that the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

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x+2+x+7=6+8

x+x+2+7=14

2x+9=14

2x=14-9

2x=5

2x/2=5/2

x=5/2. or 2.5 in a decimal form.

Using the values provided on the sketch of the triangular trellis, the values for x, y, and z are 13.33 ft, 6.75 ft, and 17.37 ft, respectively.

From the provided sketch of the trellis, we can use the similar triangles and similar trapezoids to solve the values of x, y, and z.

Consider similar trapezoids at the bottom of the trellis.

10/(10 + 6) = x/(8 + x)

80 + 10x = 16x

6x = 80

x = 40/3 = 13.33

Consider the similar triangles at the top of the trellis.

9/(9 + x) = 7/z

9/(9 + 40/3) = 7/z

z = 469/27 = 17.37

y/(y + 10) = 9/(9 + x)

y/(y + 10) = 9/(9 + 40/3)

(67/3)y = 9y + 90

(40/3)y = 90

y = 27/4 = 6.75

Hence, the length of x, y, and z is 13.33 ft, 6.75 ft, and 17.37 ft, respectively.

The problem seems incomplete, it must have been...

"Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for x, y, and z. (Round your answers to the nearest hundredth.)

See attached copy of the complete question."

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The probability of selecting a junior who usually drinks bottled water is 0.0156. This is calculated by finding the probability of each separate event (being a junior and drinking bottled water) and multiplying them together.

To find the probability of selecting a junior who usually drinks bottled water, first calculate the probability of being a junior. There are 12 juniors out of a total of 30 students, so the probability of being a junior is 0.4. Then, calculate the probability of usually drinking bottled water. There are 10 students who usually drink bottled water out of a total of 30, so the probability of usually drinking bottled water is 0.3333. Finally, multiply the probabilities together to get the overall probability of 0.0156. This can be rounded to four decimal places to get the final answer of 0.0156.

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Answer:

50+6.3= 56.3

Step-by-step explanation:

Answer:

92.3%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the speeds that people drive down the Pat Bay Highway are normally distributed:

[tex]\boxed{X \sim\text{N}(90,7^2)}[/tex]

where X is the speed in km/h.

f we want to find what proportion of drivers travel between 80 and 120 km/h, we need to find P(80 ≤ X ≤ 120).

[tex]\implies \sf P(80 \leq X \leq 120)=P(X \leq 120)-P(X \leq 80)[/tex]

Converting to the Z distribution:

[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]

Transform X to Z:

[tex]\sf P(X \leq 120)=P\left(Z \leq \dfrac{120-90}{7}\right)=P\left(Z \leq \dfrac{30}{7}\right)[/tex]

[tex]\sf P(X \leq 80)=P\left(Z \leq \dfrac{80-90}{7}\right)=P\left(Z \leq -\dfrac{10}{7}\right)[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf P(80 \leq X \leq 120)&=\sf P\left( -\dfrac{10}{7} \leq Z \leq \dfrac{30}{7}\right)\\\\&=\sf P\left(Z \leq \dfrac{30}{7}\right)-P\left(Z \leq -\dfrac{10}{7}\right)\\\\&=\sf 0.999990892...-0.0765637255...\\\\&= \sf 0.9234271...\\\\&=\sf 92.34271...\%\end{aligned}[/tex]

Therefore, the proportion of drivers travelling between 80 and 120 km/h is 92.3% (nearest tenth).

The numerator is 4 and the denominator is 7. It is a proper fraction.

A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written

a/b

Where

There are 3 types of fraction. They are

1. Proper fraction

A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.

Example: 3/4, 2/5.

2. Improper fraction

An improper fraction is a fraction whose numerator is more than the denominator. The value is more than 1.

Example: 9/8, 7/5.

3. Mixed fraction

A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.

Example:

From the explanation above, the fraction of 4/7 has the numerator of 4 and the denominator of 7. The numerator 4 is less than the denominator 7, so the fraction is a proper fraction.

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An equation is a part of every formula. A formula is not always an equation. In order to be solved for a variable, equations must be given. Evaluation of formulas

Given,

[tex]$\left(6 x^4 y^2-3 x y^3-4 x y\right)+\left(4 x^4 y^2-x y^3+4 x y\right)[/tex]

[tex]$=6 x^4 y^2-3 x y^3-4 x y+4 x^4 y^2-x y^3+4 x y[/tex]

Group like terms

[tex]$=6 x^4 y^2+4 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]

Simplifying the above equation,

[tex]$=10 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]

Simplify,

[tex]$=10 x^4 y^2-4 x y^3-4 x y+4 x y[/tex]

Then we get,

[tex]$=10 x^4 y^2-4 x y^3[/tex]

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Answer:

A

Step-by-step explanation:

There probably is a good explanation but I don't have it.

Answer: We can find the value of x by solving the equation 2x + 1/3x = 4.

Combining the terms on the left side, we get:

(6/3)x = 4

Dividing both sides by 6/3, we get:

x = 2

Substituting the value of x back into the expression 27x³ + 1/8x³, we get:

27 * 2³ + 1/8 * 2³ = 27 * 8 + 1/8 * 8 = 216 + 1 = 217

So the value of the expression 27x³ + 1/8x³ is 217.

Step-by-step explanation:

The process by which the various phase of matter affect its properties is mentioned below.

Given is to find how does the phase of matter affect its properties.

Therefore, the process by which the various phase of matter affect its properties is mentioned above.

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The null hypothesis H0 to for mice to complete the maze is equal to 18 seconds and alternative hypothesis Ha for mice to complete the maze is less than 18 seconds.

The null hypothesis is the default assumption that there is no effect of the noise stimulus on the time it takes for mice to complete the maze. The alternative hypothesis is the hypothesis that the noise stimulus does have an effect and causes the mice to complete the maze faster. The researcher will conduct a statistical test to determine if there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.

The researcher is hypothesizing that the true population mean time taken by mice to complete the maze with a loud noise stimulus is less than 18 seconds, Ha< 18seconds. The mean time for mice to complete the maze with the noise stimulus is equal to 18 seconds. Ha: 18 seconds

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The length of the altitude drawn to the hypotenuse is √105 units

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

The triangle

Represent the required length

so, we have the following representation

x/7 = 15/x

Cross multiply the equation

x^2 = 7 * 15

So, we have

x^2 = 105

Take the square roots

x = √105

Hence, the length is √105 units

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Correct expression is,

Table A represents an additive relationship because y is 5.5 more than x.

Table B represents a multiplicative relationship because , y, is 4.5 times x.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

These tables represent the relationships between x and y for two different sets of data.

Hence, The equation for table A is,

Two points from the table A are, (1, 6.5) and (2, 7.5)..

Thus, The equation fop table is,

y - 6.5 = (7.5 - 6.5) / (2 - 1) (x - 1)

y - 6.5 = 1 (x - 1)

y - 6.5 = x - 1

y = x - 1 + 6.5

y = x + 5.5

Thus, Table A represents an additive relationship because y is 5.5 more than x.

Hence, The equation for table B is,

Two points from the table A are, (1, 4.5) and (2, 9)..

Thus, The equation fop table is,

y - 4.5 = (9 - 4.5) / (2 - 1) (x - 1)

y - 4.5 = 4.5 (x - 1)

y - 4.5 = 4.5x - 4.5

y = 4.5x

Thus, Table B represents a multiplicative relationship because , y, is 4.5 times , x,.

Therefore, We get;

Correct expression is,

Table A represents an additive relationship because y is 5.5 more than x.

Table B represents a multiplicative relationship because , y, is 4.5 times x.

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The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.

The definition of a supplementary angle is that it adds up to 180 degrees.

Let's represent the required angle as "x".

We know that the supplementary angle to "x" is 180 - "x".

Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".

Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:

180 - x = 2(90 - x) + 35

Simplifying this equation, we get:

180 - x = 180 - 2x + 35

Adding x to both sides, we get:

x = 35

Therefore, the required angle is 35 degrees.

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For given triangle, x is 4√5 using Pythagorean theorem.

What is Pythagorean Theorem?

Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.

The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.

The Pythagoras Theorem formula is presented in the definition as:

Perpendicular² + Base² = Hypotenuse²

c² = a² + b²

Now,

Given that perpendicular =19

Hypotenuse=21

then Base²=21²-19²  using Pythagoras theorem

Base=√441-361

=√80

=4√5

Hence,

          x is 4√5

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The average value of the competition is 193.525.

To find the average value of the competition, we need to add up all the assigned numbers and divide by the total number of couples. In other words, we need to find the arithmetic mean of the data set.

In a ballroom dance competition, each couple is assigned a number for identification purposes. In this particular competition, forty couples competed, and we are interested in finding the average value of their assigned numbers.

First, we add up all the numbers:

=> 103 + 105 + 112 + 116 + 117 + 122 + 126 + 130 + 139 + 147 + 154 + 159 + 165 + 170 + 176 + 178 + 182 + 184 + 187 + 193 + 196 + 199 + 206 + 207 + 211 + 216 + 224 + 227 + 230 + 237 + 242 + 246 + 249 + 252 + 258 + 264 + 267 + 270 + 275 + 281 = 7741

Next, we divide by the total number of couples, which is 40:

7741 ÷ 40 = 193.525

It is important to note that the average is not necessarily a value that is present in the data set. In this case, none of the couples were assigned the exact number 193.525.

Instead, the average represents a central tendency of the data set, which can be useful in comparing and analyzing different competitions.

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Complete Question:

In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 103 105 112 116 117 122 126 130 139 147 154 159 165 170 176 178 182 184 187193 196 199 206 207 211 216 224 227 230 237 242 246 249 252 258 264 267 270 275 281

Find the average value of the competition

The solution is, 5.5% is the interest rate that Andrew's bank provides.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

Andrew's bank account started off with a deposit of $750,

and after 4 years he earned $165 in interest.

we know,

formula: I = Prt.

let, the interest rate that Andrew's bank provides = r%

so, solving we get,

r = 5.5%

Hence, The solution is, 5.5% is the interest rate that Andrew's bank provides.

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The circumference of a circular garden is 51.5 feet.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the area of a circular garden is 210 square feet.

Here, 210=3.14×r²

r²=210/3.14

r²=66.87

r=8.2 feet

Now, circumference =2πr

= 2×3.14×8.2

= 51.5 feet

Therefore, the circumference of a circular garden is 51.5 feet.

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The probability of digits 0 to 9 represent the medicine being not effective.

It is a branch of mathematics that deals with the occurrence of a random event.

As the digit 9 is not effective

So the number of not effective is 2+1+2+2+1+3

=11

The probability=effective numbers/all numbers

=30-11/30

=19/30

Hence, the probability of digits 0 to 9 represent the medicine being not effective.

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