how are translations described mathematically

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.

To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.

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We can write quotient as -

Quotient = (Dividend - Remainder)/(Divisor).

       {Dividend = (Divisor × Quotient) + Remainder}

Given is to find the quotient of any two numbers.

From the division algorithm, we can write -

Dividend = (Divisor × Quotient) + Remainder

Quotient = (Dividend - Remainder)/Divisor

Therefore, we can write quotient as -

Quotient = (Dividend - Remainder)/(Divisor).

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{Question in english -

quotient of any two numbers}

Answer:

answer A

Step-by-step explanation:

hello

3 3/4 is

\(\dfrac{3*4+3}{4}=\dfrac{15}{4}=3.75=375\%\)

hope this helps

The mixed fraction 3 3/4 can be written in percentage as 375 %.

Option A) 375 % is the correct answer.

Percentage is simply number or ratio expressed as a fraction of 100.

Given the data in the question;

\(3 \frac{3}{4}\) be written as a percent.

First we convert the mixed fraction into an improper fraction

\(3 \frac{3}{4}\)  = ( 4×3 + 3 )/4 = 15/4

Now, we multiply by 100%

= 15/4 × 100%

= 1500% / 4

= 375%

Therefore, the fraction \(3 \frac{3}{4}\)  can be written in percent as 375%.

Option A) 375% is the correct answer.

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Answer:

proportional i think but let me check my textbook i might have that there

Step-by-step explanation:

Using the properties of percentages we can calculate that there are 200 kids in the archery camp that summer.

Long before the decimal numeral system, Ancient Rome routinely computed in fractions as multiples of 1/100.

A percentage is a dimensionless (pure) number; it has no unit of measurement.

The % value is determined by multiplying the numerical value of the ratio by 100. To calculate 50 apples as a percentage of 1250 apples, first compute 50/1250 = 0.04, then multiply by 100 to get 4%.

Let the total number of kids in the camp be x.

The number of kids who took archery = 25%

But 50 students took archery.

hence 25% of x = 50

Solving we infer:

x = 200

Therefore there are 200 kids in the camp.

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Answer:

Step-by-step explanation:

So, the question is, what s the slope of y = 5x -1? This equation is in slope-intercept form (also known as y = mx + b) and the coefficient in front of the x (also known as "m") is the slope. So this line has a slope of 5. The line parallel to it, also has the slope of 5

Answer:

0.125

Step-by-step explanation:

khan

The drone's descent can be modeled by a linear function as the rate of descent is constant.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.

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

For this problem, we have that the drone descended 16 meters in 6 seconds, hence the slope m is given as follows:

m = -16/6 = 2.67 m/s.

As the slope is constant, a linear function can model the situation.

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The drone in the Example hovers at 16 meters for a few minutes before being

lowered at a constant rate. It reaches the ground after 6 seconds.

a. Why can the drone's descent be modeled by a linear function?

Answer:

or

Step-by-step explanation:

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

3 3/4

Step-by-step explanation:

2 1/4 = 9/4

9/4 ÷ 6 = 3/8 1 cookie

3/8 × 10 = 3 3/4 10 cookies

Please give me brainliest ;)

Answer:

3.75

Step-by-step explanation:

2.25 = 6 dozen cookies

? = 10 dozen cookies

Cross multiply,

10 × 2.25÷6

=3.75

Answer:

1. F(-5) = -9

2. F(-4) = -7

3. F(1) = 3

4. F(3) = 7

5. F(5) = 11

Step-by-step explanation:

For each problem, F(x) is replaced with x.

An example is F(-5) = 2x + 1 (your first question).

To solve this, you replace x with -5.

This creates F(-5) = 2(-5) +1

We just simplify by multiplying -5 by 2 and then adding 1.

-5 times 2 equals -10. -10 plus 1 equals -9.

Your final answer for this example problem would be F(-5) = -9.

This applies to all problems as such -- F(x) where x inside the parentheses replaces all x values in the equation.

Hope this helped!!

Answer:

90.6°

Step-by-step explanation:

It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:

\(y = 8.2x + 25\\y = 8.2(8) + 25\)

Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, multiply 8.2 with 8:

\(y = (8.2 * 8) + 25\\y = (65.6) + 25\\\)

Next, add:

\(y = 65.6 + 25\\y = 90.6\)

90.6 is your answer.

~

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Answer:

31x + 55 sq. ft.

Step-by-step explanation:

Width of Fire Pit = x ft.  Length of Fire Pit = 4x ft.

Width of Patio = x + 5 ft. Length of Patio = 4x + 11 ft. Area of Fire pit = 4x * x = 4x² sq, ft.

Total Area of Rectangular Patio (including Fire pit)  = (4x + 11)(x+5)

= 4x² + 31x + 55 sq. ft.

Area for which tiling is done = Area of Rectangular patio - Area of fire pit

= 4x² + 31x + 55 - 4x²

= 31x + 55 sq. ft.

Answer:

\(\boxed{\sf Parallelogram}\)

Step-by-step explanation:

A parallelogram has opposite parallel sides and it is a quadrilateral.

Answer:

This is a parallelogram

Step-by-step explanation:

This is also a quadrilateral.

Hope this helps.

Answer:28

Step-by-step explanation: 7x4 Equals 28 basketballs

X = 7

Y = 6

Y = 24

X = ?

24/6=4

7x4 = 28

Your answer is 28

Answer:

The equation for the relationship is \(y = \frac{7}{2}\cdot x\).

Step-by-step explanation:

Given that point \((x,y) = (6, 21)\) is part of a direct relationship. That is:

\(y \propto x\)

\(y = k\cdot x\) (1)

Where \(k\) is the proportionality constant.

If we know that \(x = 6\) and \(y = 21\), then the proportionality constant is:

\(k = \frac{y}{x}\)

\(k = \frac{21}{6}\)

\(k = \frac{7}{2}\)

Lastly, the equation for the relationship is \(y = \frac{7}{2}\cdot x\).

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

We use the formula

n= (zc/E)2σ2

Where,

n = sample size

zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

E = margin of error

σ = standard deviation

Substituting the given values,

n= [(1.96*0.95)/1]2*5.72

n= 95.29

Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

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Answer: y = 60x, choice D

=================================================

Explanation:

1 hour = 60 miles ... one way to represent the speed of 60 mph

x hours = 60x miles ... multiply both sides by x

After x hours, the cheetah has ran 60x miles. This is assuming the speed is kept the same at 60 mph.

The information about the 50 yards is never used. It's likely thrown in there as filler or as a distraction.

The parametric equations for the line segment from (-3, 18, 31) to (11, -4, 48) can be expressed as follows:

x(t) = -3 + (11 - (-3))t

y(t) = 18 + (-4 - 18)t

z(t) = 31 + (48 - 31)t

In these equations, t represents the parameter that varies along the line segment. By plugging in different values of t, we can obtain corresponding points on the line segment.

The x(t) equation represents the x-coordinate of the line segment, where -3 is the initial x-coordinate and (11 - (-3)) represents the change in the x-coordinate over the segment. By multiplying this change by t, we can determine the specific x-coordinate at any point along the line segment.

Similarly, the y(t) equation represents the y-coordinate, where 18 is the initial y-coordinate and (-4 - 18) represents the change in the y-coordinate. Multiplying this change by t gives us the y-coordinate at any point.

Lastly, the z(t) equation represents the z-coordinate, where 31 is the initial z-coordinate and (48 - 31) represents the change in the z-coordinate. Multiplying this change by t allows us to determine the z-coordinate at any point along the line segment.

By using these parametric equations, we can generate points that lie on the line segment connecting the given two points and describe the entire line segment in three-dimensional space.

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\({\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }\)

• Putting,

3rd term as 4 and the 4th term as 7.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\red{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term\)

• Putting,

4th term as 4.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\green{Solution:}}}}}\)

The frequency distribution table for calculations of mean :

\(\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} \)

☆ Calculating the \(\sum f_{i}\)

\( \implies 4 + 6 + 2 + 2 + 1 + 1\)

\( \implies 16\)

☆ Calculating the \(\sum f_{i}x_{i}\)

\( \implies 12 + 6 + 14 + 8 + 6 + 2\)

\(\implies 48\)

As we know,

Mean by direct method :

\( \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}\)

here,

• \(\sum f_{i}\) = 16

• \(\sum f_{i}x_{i}\) = 48

By putting the values we get,

\(\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}\)

\(\sf \longrightarrow \overline{x} \: = \green{3}\)

\({\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}\)

• Swipe to see the full answer.

\(\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}\)

Answer:

b

Step-by-step explanation:

The expression 1/5 + -4/5 has plotted on the number line

To model 1/5 + (-4/5) on a number line, we can start by placing a point at 0 on the number line. Then we can represent 1/5 by placing another point to the right of 0, one-fifth of the distance from 0 to 1. We can represent -4/5 by placing a point to the left of 0, four-fifths of the distance from 0 to -1.

To add these two points together, we start at the point representing 1/5 and move four-fifths of the distance towards the left, since -4/5 is negative. The resulting point represents the sum of 1/5 and -4/5.

To solve this problem algebraically, we can add the two fractions together by finding a common denominator:

1/5 + (-4/5) = 1/5 - 4/5

= (1-4)/5

= -3/5

= -0.6

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Answer:

A). F = \(\frac{9C}{5}+32\)

B). 374°F

Step-by-step explanation:

A). Formula to convert the temperature from degree centigrade to °F is,

    C = \(\frac{5}{9}(F-32)\)

    We have to solve the formula to get the value of F,

    9 × C = \(9\times \frac{5}{9}(F-32)\)

    9C = 5(F - 32)

    \(\frac{9C}{5}=\frac{5(F-32)}{5}\)

    \(\frac{9C}{5}=(F-32)\)

    F = \(\frac{9C}{5}+32\)

B). In this part we have to find the value of 190° C in °F.

    From the formula given in part (A),

    F = \(\frac{9\times 190}{5}+32\)

       = 374°

    Therefore, 190°C = 374°F

The temperature at 6000 feet will be 32.1°F.

This question uses the theory of adiabatic lapse rate, which is the rate at which air temperature changes as it ascends or descends in the atmosphere. The moist adiabatic lapse rate is typically about 6°C/km (3.5°F/1000 ft) when the air is saturated, but it can vary due to the local atmospheric conditions.

Step 1: Calculate the temperature change per 1000 feet.

Change in temperature = 1.4°F

Step 2: Calculate the total change in temperature.

Total change = 1.4°F x 6 (6000 feet divided by 1000 feet) = 8.4°F

Step 3: Subtract the total change from the temperature on the ground.

Temperature at 6000 feet = 50.9°F - 8.4°F = 32.1°F

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

The leading coefficient in the polynomial 10x2 + 3x - 5 is 10.

Step-by-step explanation:

To find the leading coefficient of the polynomial function, we must first locate the leading term. In a polynomial function, the leading term is the term containing the highest power of x. In this polynomial function, the leading term is 10x2. The leading coefficient of a polynomial function is the coefficient of the leading term, and so the leading coefficient of this polynomial function is 10.

the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.Let the length of the rectangular garden be L and the width be W. Then, the area of the garden is given as L x W = 8.

The cost C of enclosing the garden is given by:
C = 20L + 10(2L + W)

Substituting the value of W from the area equation, we get:
C = 20L + 10(2L + 8/L)

Differentiating C with respect to L and equating it to zero to find the minimum cost:
dC/dL = 20 + 20 - 80/L^2 = 0
Solving for L, we get L = 2 ft

Substituting L = 2 in the area equation, we get:
W = 4 ft

Therefore, the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.
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