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The average speed on the first 30 minutes is 0.2 km per min.

Here we have the graph for the position of a bycicle rider on a 42-minute trip.

On the vertical axis we can see the position, and on the horizontal axis we can see the time.

Remember that:

speed = distance/time.

To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.

At 30 min we can see that the position is at 6 km, then the speed will be:

S = 6km/30min = 0.2 km per min.

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a) The mean of the sample of size 5 is equals to 103.

b) The mean of the sample of size 12 is equals to 103.3.

c) Median of sample of size 5 is 104.

d) Median sample of size 30 is 105.5.

Mean: Sum of observations is divided by number of observations in the sample is named as mean, which is denoted by X- bar. Moreover, the sample mean signifies the measure of centre of the data.

X-bar = (x₁ + x₂ + --- + xₙ)/n

Median: Median divides the observations into two equal parts. It represents the middle value for a set of observations when they are arranged in order of magnitude. There are two cases arises.

Case (1): Sample size (n) is odd: First, arrange the data in ascending order. Then, the median is the middle value and lies at the position.

Case (2): Sample size (n) is even: First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on either side of the position. Median = ( n/2)ᵗʰ term , n is odd

=[(( n/2)ᵗʰ term + (n/2 + 1)ᵗʰ term]/2, n is even

Now, a) Mean of first sample with sample size, n = 5.

Sum of values = 105 + 111 + 97 + 94 + 108 = 515

So, mean = 515/5 = 103

b) Sample 2, sample size , n = 12

Sum of values = 105 + 111 + 97 + 94 + 108 + 101 + 112 + 114 + 103+ 102+ 91 + 101

= 515 + 724 = 1239

Mean = 1239/12 = 103.25

c) Now, we have to determine median for sample size 5. Here, sample values are odd in number, i.e., 5. So, middle term is median after arranging in order. Ascending order is 94,97, 104, 108, 111 and middle term is 104, so median is 104.

d) Now, we have a sample of size 30, which is an even number. First arrange the numbers in ascending order as 91,92,92,94,95,97,100,101,101,101,101,102,103,105,105,105,106,107,107,108,110,111, 111, 112,113,114,115,115,116,116. So,

Median is [((n/2)th + (n/2 + 1)th ]/2 i.e, [ 30/2)th + 30/2 + 1)th ]/2

=( 15th + 16th)/2 ( observations)

= (105 + 106 )/2 = 211/2 = 105.5

Hence, the median of sample size 30 is 105.5.

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Complete question:

See the above figure, each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.

a) What is the mean of the sample of size 5? Full data set Sample of Size 108 114 (Type an integer or decimal rounded to one decimal place as needed._ Sample of Size 12

b) What is the mean of the sample of size 12? 114 105 115 (Type an integer or decimal rounded to one decimal place as needed:)

c) What is the median of the sample of size 5? (Type an integer or decimal rounded to one decimal place as needed:)

d) What is the median of the sample of size 30? (Type an integer or decimal rounded to one decimal place as needed:)

The smaller number is x and the larger number is 17

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: One number is 4 more than another. And 3 times the smaller number is equal to twice the larger increased by 5.

Let the smaller number be x then we have

3x=2(x+4)+5

3x-2x=8+5

x=13

Thus the smaller number is x and the larger number is 17

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The direction of vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that axis.

The stated vector is (-7.765,28.978)

Angle made is estimated by the formula:

Ф = tan ⁻¹ (y/x)

In which,

y = 28.978

x = -7.765

Put the given values;

Ф = tan ⁻¹ ( 28.978/-7.765)

Ф = - 74.99

Ф = 75°

So, the direction of the vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that x-axis.

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The complete question is-

let the direction of a vector be the angle that the vector makes with the x -axis, measured counterclockwise from that axis. find the direction of the vector a1 -  (-7.765, 28.978)

The function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).

The x-values at which the function is differentiable can be found by taking of the function and setting it equal to 0. The derivative of the function y = x3 + 2x2 - 5x + 8 is 3x2 + 4x - 5. Setting this equal to 0 and solving for x yields x = -1 and x = 1/3. So, the x-values at which the function is differentiable is (-1, 1/3).

In order to find the derivative of the function, the power rule was used. The power rule states that the derivative of a function f(x) = xn is f'(x) = nxn-1. Applying this to the function y = x3 + 2x2 - 5x + 8, the derivative is 3x2 + 4x - 5. Next, setting this equal to 0 and solving for x yields two solutions: x = -1 and x = 1/3. Since the function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).

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The value of x must be less than 50.

Triangle is a three sided polygon which has three vertices. The three sides are connected with each other end to end at a point which forms the angles of the triangle.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Given that the two sides have lengths 5^2 and 5^2, we can write the inequality:

x < 5^2 + 5^2

Now, we can evaluate the expressions 5^2 and 5^2:

5^2 = 25

So, x < 25 + 25 = 50.

Therefore, the value of x must be less than 50.

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1. To compute the probability that we have picked exactly n cards, we need to consider the number of ways to pick n cards out of 52 such that all 4 shades are represented, and divide that by the total number of possible n-card combinations from the deck of 52.

The number of ways to pick n cards such that all 4 shades are represented is given by the number of combinations of n items taken 4 at a time, with repetition allowed (denoted as C(n-1,3) or C(n+3-1,n)). This is because there are 4 shades, and we need to pick one card from each shade.

The total number of possible n-card combinations from the deck of 52 is given by C (52, n).

Therefore, the probability that we have picked exactly n cards is given by:

P(n) = C(n-1,3) / C(52, n)

2. To verify that the probability sums up to 1, we need to take the summation over all possible values of n, from n=4 to n=52:

P = sum(P(n)) from n=4 to n=52

If P is equal to 1, then the probability of picking exactly n cards over all possible values of n adds up to 1, which means that the event of picking all 4 shades is certain to occur at some point.

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The equation of the line is y = -2/3x + 1

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

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 1

This means that the intercept c is 1

Also, as x changes by 1, the y values changes by -2/3

This mean sthat the slope is -2/3

So, we have

y = mx + c

This gives

y = -2/3x + 1

Hence, the equation is y = -2/3x + 1

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Answer:

Volume

[tex]\pi r ^{2} h[/tex]

[tex]\pi = \frac{22}{7} [/tex]

[tex]r = 8[/tex]

[tex]h = 15[/tex]

[tex] \frac{22}{7} \times 8 {}^{2} \times 15 = 3015.93[/tex]

The value of x is 94/13 approximately equal to 7.23.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Line segment described in the question is given below.

Given that,

Length of XY = 7x

Length of YZ = 6x - 11

Length of XZ = 83

We have the equation,

XY + YZ = XZ

7x + 6x - 11 = 83

13x = 83 + 11

13x = 94

x = 94/13 ≈ 7.23

Hence the value of x is 94/13.

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Answer:

348.6 kg

Step-by-step explanation:

(1220 kg / 7 days) x 2 days = 348.6 kg

Answer: Based on the information given, it seems like the crow is unable to break open the walnut in its current location without it being stolen. To overcome this problem, the best solution would be for the crow to fly away to another location where it can safely break open the walnut. With a take-off speed of 19 feet per second, the crow should be able to quickly reach a new location where it can safely open the walnut.

Step-by-step explanation:

The solution of the equation -3(x+7)=7 is x=-7.

How to solve an algebric expression:

An algebraic expression is a mathematical phrase that contains numbers and/or variables. Though it cannot be solved because it does not contain an equals sign (=), it can be simplified. You can, however, solve algebraic equations, which contain algebraic expressions separated by an equals sign.

-3(x+7)=0

Now I need to find the value of x by sorting the variables. This expression has an x ​​variable, so find the value of the variable.

The formula is:

-3(x+7) =0

give:

-3(x+7) =0

(divide both sides of the equation by the coefficient of the variable)

x+7=0

(reorder variables on the left side of the expression)

x=-7

The answer is x= -7.

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Answer:

x=98

Step-by-step explanation:

a 7 sided shape has 900 degrees in it so

146+142+142+140+122+110=802

so

900-802=98

x=98

The simple interest is given as SI = $ 9.90

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as S

Now , the equation will be

The principal amount be P = $ 300

The rate of interest R = 6.6 %

The number of months T = 6 months = 1/2 year

So , the simple interest S = PRT / 100

Substituting the values in the equation , we get

S = ( 300 x 6.6 x 0.5 ) / 100

On simplifying the equation , we get

S = 3 x 6.6 x 0.5

S = $ 9.90

Hence , the simple interest is $ 9.90

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The answers include the following:

This is referred to as the branch of mathematics concerning numerical descriptions of how likely an event is to occur,

The Red to Yellow ratio is given as 3:5.

Red = 3 to 8 and yellow = 5 to 8.

Small to Large ball ratio  = 4:9

Small = 4/13 and large = 9/13

5/8 × 9 / 13 × 104

= 5 * 9

= 45

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Thresholding is the simplest method of image segmentation. It is a non-linear operation that converts a gray-scale image into a binary image where the two levels are allowed to pixels that are below or above the specified threshold value.

In other words, if the pixel value is greater than a threshold value, it is assigned one value (maybe white), or else it is assigned another value (maybe black). In OpenCV, we use cv2.threshold() function.

cv2.threshold(src, thresh, maxval, type[, dst])

This function put fixed-level thresholding to a single-channel array. The function is used to get a binary image out of a grayscale image or for removing noise, that is, filtering out pixels with too small or too large values.

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The weight of 15 bags in kilograms and the volume of 15 bags in cubic yards are 272. 15 kilograms and 1. 1 cubic yards

It is important to note the conversion rate of the pounds to kilograms and also cubic feet to cubic yards

1 pound = 0. 453592 kilogram

If a bag of soil weighs 40 pounds which is equivalent to  0. 453592 kilogram

1 bag = 40(0.453592)

15 bags = x

x = 272. 15 kilograms

Then, we have that;

1 bag = 2 cubic feet

15 bags = 30 cubic feet

But, 1 cubic feet = 0. 037037 cubic yards

30 cubic feet = x

x = 1. 1 cubic yards

Hence, the values are 272. 15 kilograms and 1. 1 cubic yards

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The results of this investigation provide valuable insights into the differences in the film-making practices of American and French film industries.

The comparative stem-and-leaf display is as follows:

90 | AM: 90 90 91 92 94 95 95 95 97 NONE

91 | AM: 104 110 113 113 116 116 116 120 125

92 | AM: 128 136

95 | FM: 90 95 96 97 102 103 105 106 111 113 113 125 125 128 158

96 | FM: 90 94 96

97 | NONE

102 | FM: 102

103 | AM: 103

104 | AM: 104

105 | FM: 105

106 | FM: 106

109 | AM: 109

110 | AM: 110

111 | FM: 111

113 | AM: 113

116 | FM: 116 122 123

120 | AM: 120

125 | FM: 125

128 | FM: 128

136 | AM: 136

158 | FM: 158

The display shows that American movies appear to be bimodal, with a typical running time of around 95 minutes and another peak around 125 minutes. On the other hand, French movies are unimodal and strongly positively skewed with a typical running time of around 95 minutes. This suggests that French movies tend to have a shorter running time compared to American movies, but with a larger range of running times compared to the peak of American movies around 95 minutes.

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The minimum value on the interval [-11, 5] is -19, and the maximum value is 28.

In mathematics, a linear function is a function that expresses the relationship between two variables, x and y, in the form of y = mx + b, where m denotes the slope of the line and b the y-intercept. A linear function has a graph that is either a straight line passing through the origin if b = 0 or a point (0, b) if b 0.

A number of applications can benefit from linear functions because of their numerous beneficial characteristics. One of these characteristics is that they are always continuous, i.e., their graphs are seamless and devoid of gaps. They are the best candidates for simulating actual scenarios when two variables have a continuous relationship because of this characteristic.

According to question:

The function f(a) = Va + 3 is a linear function, and all linear functions have a minimum and maximum value that occur at either endpoint of the interval. In this case, the interval is [-11, 5].

To find the minimum value, we evaluate the function at -11:

f(-11) = V(-11) + 3 = -22 + 3 = -19

To find the maximum value, we evaluate the function at 5:

f(5) = V5 + 3 = 25 + 3 = 28

Therefore, the minimum value on the interval [-11, 5] is -19, and the maximum value is 28.

Minimum: -19

Maximum: 28

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The effect of scaling on a hexagon by the scale factor of 6 is discussed above.

In geometry -

Given is a model of the hexagon that is made by using a scale factor of 6.

If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. So, we can write the perimeter of the hexagon, before and after the scaling as -

P{i} = P{before scaling} = 6 x side = 6a

P{i} = 6a                                                             ... Eq { 1 }

P{f} = P{after scaling} = 6 x 6a = 36a

P{f} = 36a                                                           ... Eq { 2 }

The total of the internal angles of the hexagon will remain 720° only.

Therefore, the effect of scaling on a hexagon by the scale factor of 6 is discussed above.

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To find the exact amount of raisins Charlotte will

From the problem, it can be deduced that Charlotte uses all of the almonds, cashews, and peanuts. hence we add the amounts of the nuts

= almonds + cashews + peanuts

= 7/8 + 1 1/2 + 2 3/8

= 19/4

= 4 3/4

hence Charlotte will need 4 3/4 pounds of nuts

The amount remaining for raisings

= 6 pounds of trail mix - total amount of nuts

= 6 pounds - 4 3/4 pounds

= 5/4

= 1 1/4

hence Charlotte will need 1 1/4 pounds of raisins

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complete question

Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts. The table shows the amounts of different types of nuts that she has.

Type of Nut Amount (in pounds)

Almonds 7/8

Cashews 1 1/2

Peanuts 2 3/8

Pecans 1 1/4

Walnuts 1 3/4

Charlotte uses all of the almonds, cashews, and peanuts that she has Which of the following explains how she can find the exact amount of raisins she needs?

A Round 7/8 pound to 1 pound, 1 1/2 pounds to 2 pounds, and 2 3/8 pounds to 2 pounds. Then add the rounded almonds and subtract that total from 6 pounds.

B. Add 7/8 pound, 1 1/2 pounds, 2 3/8 pounds, 1 1/4 pounds, and 1 3/4 pounds. Then subtract 6 pounds from that total.

C. Subtract 7/8 pound from 6 pounds, subtract 1 1/2 pounds from 6 pounds, and subtract 2 3/8 pounds from 6 pounds. Then add all three differences.

D. Add 7/8 pound, 1 1/2 pounds, and 2 3/8 pounds. Then subtract that total from 6 pounds.​

The horizontal velocity of a bullet right before it hits the ground is 10 m/s.

The horizontal velocity of a bullet remains constant throughout its flight, as it is only affected by gravity. This means that the horizontal velocity of the bullet right before it hits the ground will be the same as the initial horizontal velocity when it was fired.

In this case, the bullet was fired at an angle of 60 degrees above the horizontal, but the horizontal velocity remains constant, so it will still be 10 m/s right before it hits the ground. To determine the vertical velocity, we would need to know the time of flight and use the equations of motion to calculate the vertical acceleration due to gravity.

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The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

The formal statement can be expressed mathematically as:

Vn e Z+, Im E Z, m < n | m + n = 0

This statement translates to: Given an integer n, if there exists an integer m such that m + n = 0, then m is the additive inverse of n.

To understand this statement more clearly, we can use an example. Let's say n = 5. This means that we are looking for an integer m such that m + 5 = 0. In this case, m = -5, which is the additive inverse of 5. We can also calculate this mathematically. We know that m + n = 0, so we can rearrange and solve for m: m = -n. Therefore, the additive inverse of n is -n.

In summary, given an integer n, the additive inverse of n is -n. This can be expressed mathematically using the statement Vn e Z+, Im E Z, m < n | m + n = 0.

The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

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Answer:

x=49

Step-by-step explanation: If we have the equation 2x-45=x+4 we would first subtract x from both sides of the equation giving us x-45=4. We then have to isolate x to do this we add 45 to both sides giving us the answer x=49.

The ratio of the given distribution of  pants to shirts is; 5:3

The ratio of shirts to pants can be expressed by putting the number of shirts and pants in the following way;

Number of shirts       :        Number of pants

20                               :                   12

Then we will have to reduce this ratio to the lowest term by dividing by the highest common factor of both numbers.

The highest common factor of 12 and 20 is 4 and as such when divided by 4 we get:

20/4 : 12/4

= 5 : 3

This represents the ratio.

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Answer:

In y = 3/2x,     x and y are inversely propotional

In -x = y,      x and y are directly propotional

Step-by-step explanation:

In y = 3/2x, the constant of propotionality is 3/2.

In -x = y, the constant of propotionality is -1.

Since the y-intercept of the estimated line of best fit is at (0, b), the appropriate value of b is 360.

The appropriate slope of the estimated line of best fit is -30

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is at (0, 360).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (360 - 0)/(0 - 12)

Slope, m = -30.

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