At what point do the curves r1(t) = t, 5 − t, 63 + t2 and r2(s) = 9 − s, s − 4, s2 intersect?(x, y, z) = ...Find their angle of intersection, 0, correct to the nearest degree.θ = ...

If the length of the given rectangle is increasing by 3 in/sec and the width is shrinking at 5 in/sec then the rate of change of its perimeter is 4 in/sec.

Length, L = 9 inches

Width, W = 5 inches

The perimeter of the rectangle is

P = 2L + 2W.

By Differentiating both sides with respect to time t, we get

dP ⁄ dt = 2 × dL ⁄ dt  + 2 × dW ⁄ dt

From the given conditions,

dL ⁄ dt = 3 and dW ⁄ dt = -5

So at the moment when L = 9 and W = 5,

dP ⁄ dt = (2)(3) + 2(−5 )

= 6 - 10

= -4

Therefore, The perimeter of the rectangle is decreasing at a rate of 4 in ⁄ sec.

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The main difference between an equation and an inequality is in an equation the elements are equal but in an inequality the elements are compared.

A relationship between two expressions or values that are not equal to each other is called inequality.

An equation has an answer that equals a number. An inequality has an answer that could be less than or more than or less than or equal to or more than or equal to.

For example:  You have some money in your pocket. You want to buy some snacks for tonight's match, but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :

y ≤ x - 10     where x represents money in your pocket.

This means that from money in your pocket you have to subtract $10 for pizza and out of the remaining money you can spend some part of it on snacks or all of it.

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The reading of the angle sec θ in the second quadrant of the given problem is; Negative

There are 6 main trigonometric ratios and if we can use which are;

sin θ

cos θ

tan θ

secθ

cotan θ = sin θ/cosθ

cosec θ = 1/sin θ

sec θ = 1/cos θ

Now, we are told that sec θ is in the second quadrant and we know that in the second quadrant only sin θ and cosecθ are positive and as such  sec θ  will be negative.                                                        

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When the parallel lines are cut by a transversal, the values for the measurement of ∠2 and ∠4 is 124° each.

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

In the given diagram the parallel lines are cut by a transversal.

The measure of angle 5 is, m∠5 = 56°.

It is known that each pair of interior angles on the same side of a transversal that cuts two parallel lines are supplementary, or they add up to 180 degrees.

So, m∠5 + m∠2 = 180°

56° + m∠2 = 180°

m∠2 = 180° - 56°

m∠2 = 124°

Now, as it can be seen in the image ∠2 and ∠4 are vertically opposite angles.

So, they will be congruent or equal to each other.

So, it is obtained that -

m∠2 = m∠4

m∠4 = 124°

Therefore, the measures of angles are m∠2 = 99° and m∠4 = 99°.

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A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.

Trigonometric ratios are based on the side ratio of a right-angled triangle and consist of the values of all trigonometric functions. The ratios of the sides to any acute angle in a right-angled triangle are the trigonometric ratios of that angle. You can use trigonometric ratios to determine the lengths of one (or both) of the acute angles of a right triangle if you know the lengths of its two sides.

given

A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.

The midline is the line y = 0 for y = sin (the horizontal axis). The difference between the highest and smallest values of a function is half its amplitude.

The amplitude of the y = sin function is 1.

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Consequently, a football field measuring 120 yards long and 50 yards wide has an area of 5016.76 m2.

An object's surface area is a measurement of the total volume of space that it occupies. The entire region surrounding a three-dimensional shape is referred to as its surface area. Its surface area is the total area of a three-dimensional shape. By adding the surfaces of each of a cuboid's six rectangular sides, one may determine the cuboid's surface area. The box's dimensions could also be named using the following formula: Surface (SA) = 2lw + 2lh + 2hw. A three-dimensional shape's surface area is a measurement of the total area it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

You are required to bring the area in this instance in m2, however the length (120 yd) and breadth (50 yard) are given in yd.

The unit must then be changed into m2. The rectangle's area formula should be length * width.

So, the equation should be:

area = length * width=  (50yd * 91.44cm/yd * 1m/100cm) * (120yd * 91.44cm/yd * 1m/100cm)

= 5016.76 m2

Consequently, a football field measuring 120 yards long and 50 yards wide has an area of 5016.76 m2.

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No, finding half of a number is not the same as dividing a number by ½. When finding half of a number, the result is the number divided by 2. When dividing a number by ½, the result is the number multiplied by 2.

When finding half of a number, the result is the number divided by 2.

For example, if we want to find half of the number 8, we would divide 8 by 2 to get 4.

When dividing a number by ½, the result is the number multiplied by 2.

For example, if we want to divide the number 8 by ½, we would multiply 8 by 2 to get 16.

No, finding half of a number is not the same as dividing a number by ½. When finding half of a number, the result is the number divided by 2. When dividing a number by ½, the result is the number multiplied by 2.

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The amount of  energy must be removed from the drink for it to reach this temperature is 35.5kJ

Here we have given that a 12oz can of soft drink at 25c is placed in a freezer where the temperature is -12c.

As we all know that the equation of the given measurement is written as,

=> Q1=m.c.AT

From the given, now we have to know that the mass "m" = 340gm

And the value of C= 4.18 J/g°C

Then at 25°C it will at the temperature of

=> Q1340g x 4.18 x 25

=> Q1 = 35, 5300J or 35.5kJ

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The angular velocity is 0.14 rad/sec.

The velocity of the Ferris wheel if it becomes disengaged from the motor and rolls away is 17.44 ft/sec.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Diameter of the Ferris wheel = 250 feet

The radius of the Ferris wheel = 125 feet

Now,

The linear velocity v = wr

Where w is the angular velocity.

The angular velocity.

w = v/r

The linear velocity v.

v = 2πr/T

v = (2 x 3.14 x 125) / 45

v = 17.44 ft/sec

The angular velocity.

w = v / r

w = 17.44/125

w = 0.14 rad/sec

Thus,

Angular velocity is 0.14 rad/sec.

The velocity of the Ferris wheel after disengaging from the motor is

17.44 ft/sec.

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The expression (-7*√3)*(11*√10) can be simplified to get:

-77*√30

Here we want to simplify the following expression:

(-7*√3)*(11*√10)

Remember that the square roots are distributive, this means that we can write:

√a*√b = √(a*b)

And also remember that we can perform a sequence of multiplications in any order we want, so we can reorder the factors of our expression

Now let's rewrite our expression:

(-7*√3)*(11*√10)

as:

(-7*11)*(√3*√10)

-77*√(3*10)

-77*√30

That is the expression simplified.

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So,

The skateboard cost $67.

The protective helmet cost $25.

To find the percent that the price of the skateboard was out of the total amount, add 67 and 25 and divide 67 by the result.

Step 1:

67 + 25 = 92

Step 2:

67/92 = 0.728 or 72.8%.

The correct option is B.

Answer:200

Step-by-step explanation: when you multiply 81.7x2.68 it equals to 218.948 which to the nearest hundreth is 200

The expression which is to be subtracted as calculated from the data given is found out to be as , 0.22.

The coordinates of the parallelogram as mentioned in the question is , R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)

Therefore, the length of the sides as measured using distance formula is found out to be as,

RS = 4.1231, RT = 10 , ST = 9.2195 , SU = 10.198 ,TU = 4.1231 and  UR = 9.2195.

Now as we know that 2 sides of a parallelogram are parallel , therefore,

RS || TU and ST || UR.

RS(slope) = (1 - (-3))/(-5 - (-4)) = -4

and the ,

ST(slope)= (3 - 1)/(4 - (-5)) = 2/9

Hence , to find the line perpendicular to ST is given by ,

y - 1 = -9/2×(x - (-5))

y = -9x/2 - 43/2

The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1

y = x/4 - 2

Their point of interaction is , -9x/2 - 43/2  =  x/4 - 2

x = -78/19

y = -115/38

Side of rectangle  = 4.1245

width of the rectangle = 0.1085

Therefore, the expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU = 1/2 × 4.1245 × 0.1085

= 0.22.

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After completing the full turn around the circle by 42 participants as per given condition and number showing on the calculator the sum ends up with 0.

As given in the question,

Total number of participants = 42

Number of calculator = 3

Calculator that reads 1 dean pressed cube button

1³ = 1

Calculator that reads 0 dean pressed square button

0² = 0

Calculator that reads -1 dean pressed negation button

-(-1) = 1

Same activity repeated 42 times in the circle at the end number showed on the calculator are

Calculator reads 1 show 1

Calculator reads 0 show 0

Calculator reads -1 show -1

Sum of the three numbers are

= 1 + 0 + (-1)

= 0

Therefore, sum of the three numbers showing at the end on the calculator is equal to 0.

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Solve in equal value Method step by step solution is given below.

Equal value is a concept that states all people, regardless of race, gender, ethnicity, sexual orientation, or any other defining characteristic, are of equal worth and should be treated equally. This concept is fundamental to democracy and is enshrined in the Universal Declaration of Human Rights. Equal value is also a foundation of economic theory, as it states that everyone should be able to access and benefit from economic resources, whatever their background.


Step 1: Isolate the 5y term on one side:
5y = -13-3x

Step 2: Divide both sides by 5:
y = (-13-3x)/5

Step 3: Replace the y with its expression:
x - 7 = (-13-3x)/5

Step 4: Distribute the -7 over the denominator of the right side:
x - 7 = (-13-3x-35)/5

Step 5: Add 7 to both sides:
x = (-13-3x-35+35)/5

Step 6: Simplify the expression:
x = (-13-3x)/5

Step 7: Solve for x:
x = -26/8

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Answer: x = 83°

Step-by-step explanation:

First, a straight line is equal to 180°.

      180° - 126° = 54°

Next, a triangle's internal angles add up to 180°.

      54° + 43° + x = 180°

With this given equation, we can solve for x.

Given:

      54° + 43° + x = 180°

Combine like terms:

      97° + x = 180°

Subtract 97 degrees from both sides of the equation:

      x = 83°

Answer: $23,800

Step-by-step explanation:

It was worth $37,000 at first and now it's worth $1800.

So we have 37,000 - 1800 = $35,200 that left away.

And we know that 8 years passed away.

So we have 35,200/8 = $4400 each year.

We are looking for 3 years later.

So we have 440*8 = $13,200 that left after 3 years.

And lastly, it's worth 37,000 - 13200 = $23,800 3 years later.

Answer:

the solution is u5/2

The mechanical energy of the Jada and Aalisha systems at this point will be 2548 joules and 2205 joules respectively.

It is the sum of potential and kinetic energy. The mechanical energy is given as,

ME = mhg + 1/2 mv²

Jada and Aalisha are rock climbing, each moving up with a constant velocity of 1.0- Jada has a mass of 65 kg, and Aalisha has a mass of 75 kg. At one point, Jada is 4.0 m above the ground, and Aalisha is 3.0 m higher than Jada.

The mechanical energy of Jada is calculated as,

ME = 65 x 9.8 x 4

ME = 2548 joule

The mechanical energy of Aalisha is calculated as,

ME = 75 x 9.8 x 3

ME = 2205 joule

The mechanical energy of the Jada and Aalisha systems at this point will be 2548 joules and 2205 joules respectively.

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Answer: 390 Km

Step-by-step explanation: Use the Pythagorean Theorem to solve this problem. We know that it is going north and west, forming a triangle. It says a straight line so we know it is the hypotenuse. 360^2 + 150^2 = x^2. X is 390.

The probability that no more than 75 of passengers in the sample have a balcony is given as follows:

0%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 1000, p = 1200/(4300 + 1200 + 2100) = 0.158.

Hence the mean and the standard deviation for the normal approximation are given as follows:

Using continuity correction, the probability that no more than 75 of passengers in the sample have a balcony is P(X < 75.5), which is the p-value of Z when X = 75.5, hence:

Z = (75.5 - 158)/11.5

Z = -7.17

Z = -7.17 has a p-value of 0.

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So, on solving the provided question we can say that the probability P(study) = 1/1-a

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

subjects selected  = a

not selected = 1-a

P(study) = 1/1-a

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There are 65900 square centimetres present in a backyard garden that has an area of 6.59 square meters.

Scientific notation is the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number is between 1 and 10s, it is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5 × 10¹².

To calculate a square meter value to the related value in cm², just multiply the quantity in m² by 10000 (the conversion factor). Here is the formula for it:

Value in cm² = value in m² × 10000

We need to convert 6.59 m² into cm². Using the conversion formula above, we will get:

Value in cm² = 6.59 × 10000 = 65900 cm²

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On solving the provide outlier question, we can say that The difference between the upper and lower fourth makes up the fourth outlier (h) = 73.7 - 22.2 = 51.5

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller range than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.

Here,

a) The data values should now be sorted from smallest to largest:

22.2 40.4 16.4 73.7 36.6 109.9

b) The sorted data set's median is its middle value. The median is the sixth data value in the sorted data set because there are 11 data values total:

m = 36.6

c) The median of the data values below the median, or at 25% of the data, is in the lower fourth.

The lower fourth is the third data value because there are 5 data values below the median.

d) The data value 6 + 3 = 9 represents the third quartile.

Q{3} 73.7

The difference between the upper and lower fourth makes up the fourth outlier (h):

73.7 - 22.2

51.5

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Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.

It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.

The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.

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Answer:

y=200/9. x= 329/9

Step-by-step explanation:

3x=-43-3y; x=-43/3-y. 5(43/3-y)-8y=5; y=200/9. x= 329/9

A stratified sample size is a method of sampling where the population is divided into homogeneous subsets and a sample is taken from each subset.

A stratified sample is a method of sampling where the population is divided into distinct subgroups, or strata, based on specific characteristics. This method of sampling ensures that each stratum is represented in the sample in the same proportion as it is in the population. This ensures that the sample is representative of the population. Stratified sampling is useful when the population is heterogeneous, which means that it is composed of subgroups that vary significantly in size or composition. By stratifying the population, it is possible to ensure that each subgroup is adequately represented in the sample. This method also helps to reduce sampling errors, which can occur if the sample is not representative of the population. Stratified sampling is a useful tool for researchers who want to accurately represent the population in their sample.

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Answer: The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass.

If the initial mass is 185 grams, after the first half-life, the mass will be reduced to 185/2 = 92.5 grams

After the second half-life, the mass will be reduced to 92.5/2 = 46.25 grams

After the third half-life, the mass will be reduced to 46.25/2 = 23.125 grams

So, after three half-lives, there will be 23.125 grams of the isotope left.

It's important to note that the half-life of the isotope is a constant value and it doesn't depend on the initial mass.

Step-by-step explanation:

The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).

This gradient is a vector pointing in the direction of the function f(x, y, z) = log(x2 + y2 + z2 )'s rate of growth. Calculating the function's partial derivatives with respect to x, y, and z is necessary to assess this gradient.

The function's partial derivative with regard to x is (2x / (x2 + y2 + z2) This becomes 2/1 when x is 1. The partial derivative with regard to z is (2z / (x2 + y2 + z2)), which becomes 2/1 when z is 1, and the partial derivative with respect to y is 0, and the partial derivative with respect to z is 0, respectively. Therefore, at (1, 0, 1), the gradient of f(x, y, z) = log(x2 + y2 + z2) is (2/1, 0, 2/1).

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Answer:

x= 12.714°

Step-by-step explanation:

<AEB + <CED = 90°

4x+1+3x = 90°

7x+1= 90°

7x=89

x= 12.714°