Would a square or a circle contain more area if they have enough brick to make a 10-kilometer fence/wall? Please show your calculations.

a) It takes 2 seconds for the rocket to reach the maximum height, and this maximum height is of 169.6 metres.

b) The height of the rocket five seconds after it was launched is of 125.5 metres.

The vertex-form definition of a quadratic function is defined as follows:

y = a(x - h)² + k.

In which the parameters are given as follows:

In the context of this problem, the height function is defined as follows:

h(t) = -4.9(t - 2)² + 169.6.

Hence the coordinates of the vertex are given as follows:

As the leading coefficient is negative, the parabola is concave down and the vertex represents a maximum.

The height at a time of five seconds is of:

h(5) = -4.9(5 - 2)² + 169.6 = 125.5 metres.

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Answer:

-2/15 or -0.13

Step-by-step explanation:

-5+3  /15

-2/15

Answer: 76.2

Step-by-step explanation:

54/17=3.176

3.176=the scale factor

3.176(24)=76.224

Rounded=76.2

Answer:

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If two figures are similar then their corresponding sides have same ratio.

Find ratios:

Substitute and find the value of PM:

Cumulative algorithm can only be used with primitive data types . True

The emphasis here is to understand the difference and uses of the cumulative algorithm and primitive data type.

The cumulative algorithm is defined as a sequential analysis method which is used to monitor changes in data

Primitive data type is used to predefine operations of a programming language.

The relationship between the two is that both of them are used to organize data in the memory

In conclusion, Cumulative algorithm can only be used with primitive data types

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The height of the right-angle triangle which is the base of the triangular prism will be 10 cm.

A prism is a polyhedron composed of an n-sided polygon basis, an extra base that is a translated duplicate from the first, and n additional faces, most of which must be parallelograms, connecting matching sides of the two grounds. All parallel cross-sections to the foundations are translations of the grounds.

The volume is given as,

V = AH

The cross part of the crystal is a right-calculated triangle the foundation of the triangle has a length of 6 cm. the crystal has a length of 20 cm the crystal has a volume of 600 cm³.

Then the base area is given as,

600 = A x 20

A = 30

1/2 x 6 x h = 30

h = 10 cm

The height of the right-angle triangle which is the base of the triangular prism will be 10 cm.

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The solution of the linear equations y = 33 - 4x and y = x - 1 will be (6.8, 5.8).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

y = - 4x + 33            ...1

y = x - 1                   ...2

From equations 1 and 2, then we have

x - 1 = - 4x + 33

x + 4x = 1 + 33

5x = 34

x = 6.8

Then the value of the variable 'y' is calculated as,

y = 6.8 - 1

y = 5.8

The arrangement of the situations y = 33 - 4x and y = x - 1 will be (6.8, 5.8).

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Answer:

see explanation

Step-by-step explanation:

for the pattern given, we have

position (n) → number of dots

1 → 3

2 → 5

3 → 7

4 → 9

5 → 11

there is a difference of 2 between consecutive dots in the pattern , then

rule is of the form

2n ± ?

the ? is what is required to be added / subtracted to 2n for number of dots

2 × 1 = 2 (+ 1 = 3)

2 × 2 = 4 ( + 1 = 5)

2 × 3 = 6 (+ 1 = 7)

2 × 4 = 8( + 1 = 9)

2 × 5 = 10 (+ 1 = 11)

then 1 requires to be added to 2n to obtain number of dots , so

rule is 2n + 1

position (n) → number of dots

1 → 1 = 1²

2 → 4 = 2²

3 → 9 = 3²

4 → 16 = 4²

5 → 25 = 5²

the number of dots is the square of the position, so

rule is n²

The solution of given expression 7×(4-3) - 1+5×1/5 is 5.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Given that the expression 7×(4-3) - 1+5×1/5.

To solve the above expression we will use PEMDAS;

First, we use the subtraction in brackets and this process is called simplifying parenthesis,

7×(4-3) - 1+5×1/5=  7×(1) - 1+5×1/5.

Now, we use the operation multiplication,

7×(1) - 1+5×1/5 = 7 - 1+1

Now we add the terms and this process is called addition of terms,

7 - 1+ 1 = 7-2

Now, we subtract the numbers and this property is subtraction of numbers,

7 - 2 = 5.

Therefore, the solution of given expression 7×(4-3) - 1+5×1/5 is 5.

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The weight of the container when one quarter filled with water would be = 13.25kg

Weight is defined as the quantity that shows the total amount of matter that can be found in an object and it's measured in grams or Kilograms.

The weight of the empty container = 5kg

The weight of the container and water= 13+25= 38kg

Therefore the weight of water = 38-5= 33kg

If 1 = 33kg

1/4 = X kg

Make X kg the subject of formula;

X kg = 33×1/4

X kg = 8.25 + 5kg( weight of container) = 13.25kg.

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The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.

First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:

D = (2.8)*25mi = 70 mi

Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:

d = (70mi/40mi) inches

d = 1.75 inches

The distance on the other map is 1.75 inches.

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The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.

First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:

D = (2.8)*25mi = 70 mi

Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:

D = (70mi/40mi) inches

D = 1.75 inches

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Answer:

y = 5

Step-by-step explanation:

The equation 5x − 2y = 30 tells us that if we take 5 times x and subtract 2 times y, the answer will be 30.  If we know either x or y, we can solve for the other.

We are given that x=8.  Use the 8 for x in the equation:

5x − 2y=30  

5*(8) − 2y=30

40 − 2y=30

-2y = -10

y = 5

A The population mean is greater than 10 B The population mean is equal to 10 C The population mean is less than 10 D The population mean is not equal to 10 with probability.

1. The average weight of female athletes is a discrete random variable because it can take on a discrete set of values.

2. A sample point is a single point in a sample space, which is a set of all possible outcomes of an experiment.

3. The standard deviation is a measure of spread of a random variable, which measures how much the values in the set deviate from the mean.

4. The median of the set of numbers is 4, since there are an equal number of numbers below and above the median.

5. The variance of the set of numbers is 36, since it is calculated by taking the sum of the squares of the differences between each number and the mean, and dividing by the number of values.

6. The null hypothesis for a hypothesis test is that the population mean is equal to 10.

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The letters of points  below the graph of  y = - 1/3x are  B, C, F, H, J.

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Answer:

Move all terms not containing p to the right side of the equation.

p=5

Step-by-step explanation:

Hey there!

3 + p = 8

p + 3 = 8

SUBTRACT 3 to BOTH SIDES

p + 3 - 3 = 8 - 3

SIMPLIFY IT!
p = 8 - 3

p = 5

Therefore, your answer should be:

p = 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

(a) if 20 cards are defective, then the probability that at least 1 defective card is in the sample is 0.964​

(b) if 5 cards are defective, then the probability that at least 1 defective card appears in the sample is 0.543​

Probability:

In statistics, probability refers the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given,

Here we have a printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 cards, and 20 are selected without replacement for functional testing.

And we need to find the following probability.

Here we have to recall the formula for probability mass function of the hypergeometric random variable X with the parameters

N = 190

n ​= 20​

and the parameter K.

And it is the following expression:

f(x) = [(K x) (140 - k 20 - x)] / (140 20)

Now, we have to Set K=20 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.964​

And then Set K=5 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.543​

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Answer:

 option (a)  x*2-25

Step-by-step explanation:

With the help of the given roots of the equation, we can determine the factors of the polynomial. By multiplying the factors among themselves we will get the needed equation.

The roots are given as x = 5, x = -5.

Also the factors of the equation can be written as( x- 5) and( x 5)

On multiplying the factors among themselves we get the needed equation

Hence, the needed equation will be( x- 5) ×( x 5)

= x ²- 25

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The image of the transformation is (-5, 11) (-4, 8) (-2, 14)

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

Pre-image: (5, 15) (4, 12) (2, 18)

Transformation: Translate 4 units down, and then reflect over the y-axis.

Mathematically, this can be expressed as

(x, y) = (-x, y - 4)

Substitute the known values in the above equation, so, we have the following representation

(5, 15) (4, 12) (2, 18) = (-5, 11) (-4, 8) (-2, 14)

Hence, the image is (-5, 11) (-4, 8) (-2, 14)

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There are 6 probability  5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards.

A standard deck of 52 cards contains 4 Aces, so the maximum number of Aces that can be dealt in a 5 card hand is 3. To determine the number of possible 5 card poker hands with at least 3 Aces, we must first consider the different combinations of 3 Aces in a 5 card hand. There are 6 possible combinations: AAAxx, AAxxA, AxxAA, xAAAX, xAxxA, and xxAAA. This means that there are 6 possible 5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards. To calculate this, we first counted the number of Aces in the deck and then calculated the number of possible combinations of 3 Aces in a 5 card hand. Finally, we multiplied this number by the number of remaining cards in the deck (48) to get the total number of possible hands.

4 Aces x 6 combinations = 24

24 x 48 remaining cards = 1,152

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1. In the first and third tables, there is no direct relationship, in the third table, there is a direct relationship.

2. y = 5x,b = (1/2)a and m = 5n are direct variation.

3. The constant of proportion is 5 and x when y is 49 will be 8.8

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

1.

(a) In the table x/y = -4/-8 = 1/2 is not maintained in 6/18 so it will not direct variation.

(b) In the table x/y = -5/-4 = is not maintained in 2/10 so it will not direct variation.

(c) In the table x/y = -3/-12 = 1/4  maintained so it will direct variation.

2.

A variation in the form of x ∝ y will be a direct variation so y = 5x,b = (1/2)a, and m = 5n are direct variations.

3.

As per the given y ∝ x then y/x = 35/7 = 5 so the constant of proportionality is 5.

When y = 49

x = 49/5 = 9.8

Hence "1. In the first and third tables, there is no direct relationship, in the third table, there is a direct relationship.

2. y = 5x,b = (1/2)a and m = 5n are direct variation.

3. The constant of proportion is 5 and x when y is 49 will be 8.8".

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The point 4 units along the curve (in the direction of increasing t) from P exists as t = ln |L/2 + 1|.

When a particle's position in space is represented as a function of time by a vector-valued function, the arc-length function calculates the particle's travel distance as a function of time.

The length of an arc is the separation of two locations along a segment of a curve. Curve rectification is the process of measuring an irregular arc segment's length by simulating the section as a network of connected line segments. A rectifiable curve can be broken down into a finite number of segments.

(a) Let the given function be r(t) = [tex]e^t[/tex] sin t i + √2 [tex]e^t[/tex] k

To find the arc length of the function, we have:

[tex]& \mathrm{r}^{\prime}(\mathrm{t})=\mathrm{e}^t \\[/tex]

[tex]& \mathrm{r}^{\prime}(t)=(\cos t+\sin t) e^t+(\cos t-\sin t) e^t+\sqrt{2} e^t \\[/tex]

[tex]& \left|r^{\prime}(t)\right|=\sqrt{\left[(\cos t+\sin t) e^t\right]^2+\left[(\cos t-\sin t) e^t\right]^2+\left(\sqrt{2} e^t\right)^2}[/tex]

simplifying the above equation, we get

[tex]& =\sqrt{\left(4 e^{(2 t)}\right)} \\[/tex]

[tex]& =2 \mathrm{e}^t[/tex]

(b) We have the arc length function, L to be the integral from 0 to t, so:

[tex]$& L=\int_0^t 2 e^v \\[/tex]

simplifying the above equation, we get

[tex]& L=2 e^t-2 e^0 \\[/tex]

[tex]& =2 e^t-2 \\[/tex]

[tex]& L=2\left(e^t-1\right) \\[/tex]

simplifying the above equation, we get

[tex]$& L / 2=e^t-1 \\[/tex]

[tex]& L / 2+1=e^t[/tex]

[tex]e^t[/tex] = L / 2+1

t = ln |L/2 + 1|

The complete question is:

A. Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P.

b. Find the point 4 units along the curve (in the direction of increasing t) from P.

r(t) = et sin t i + √2 et k, P(0, l ,√2)

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If it is important to detect a mean difference in score of one point with the probability of at least 0.90 , then the number of pairs that should be used is  10 .

What is a Probability ?

The term probability of an event  is defined as ⇒ number of favorable outcomes / total number of outcomes  .

It is given that ,

the probability is at least 0.90 ,

So , in the paired t test ,

testing mean paired difference is = 0

alpha = 0.05 , the assumed standard deviation of paired difference = 0.441

So the output is

Difference = 1 , Size = 5 power(probability) = 0.90 ,

So , the actual probability is = 0.95190

From the output above , the required sample size is n = 5 .

We observe that , under the given conditions the sample size is = 5 .

but the researcher  considered 10 pairs ,

So , the sample size 10 is used for this study .

Therefore , 10 pairs should be used .

The given question is incomplete ,the complete question is

It is important to detect a mean difference in score of one point with a probability of at least 0.90. how many pairs should have been used ?

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The angle with sides 5, 9 and 10 is an obtuse triangle

This is a type of angle in which the angles are less than 180 degrees but less than 180 degrees.

In this case, we can easily determine if it's an obtuse angle.

Assuming the longest side is 10 units, the sum of it's two other sides must be greater than it's longest side which is supposedly the hypothenuse.

5 + 9 = 14

14 > 10

This indicates that the triangle is an obtuse triangle.

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Answer:

Step-by-step explanation:

So basically you can always use bodmas( Brackets of division multiplication addition substractions)

or if it is like 5-4=8+9

then u can   5= 8+9+4

so.................. 5= 21

then................ 21-5=16

Total 56, integers are remained if all multiples of 4 and all multiples of 5 are removed from the set of integers from 1 through 100.

We have given that,

from the set of first 100 integers numbers, all the multiples of 5 and 4 are removed.

According to the question,

The multiples of 4 upto 100,

S = { 4, 8, 12......, 96}

it is an Arithmetic progression sequence with

a = 4 , l = 96 , d = 4

using an = a + (n-1)d where

n --> number of terms in sequence

d ---> common difference between two consecutive terms

a ---> first term

=> 96 = 4 + (n-1)4

=> (n-1) = 92/4

=> n = 23 + 1 = 24

Total multiples of 4 upto 100 is 24 .

Now, multiples of 5 upto 100

Q = { 5, 10, 15, ....,100}

Similarly as for above case

a = 5 , d = 5 , l = 100

=> 100 = 5 + (n-1)5

=> (n-1)5 = 95

=> n-1 = 19

=> n = 20

Total multiples of 5 upto 100 is 20.

Remained integers upto 100 = 100 - 20 -24

= 56

Hence, the required number of integers are 56.

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Answer:

(c) 13 cm, 7 cm, 6 cm

Step-by-step explanation:

To determine which of the given sets of measurements cannot be the sides of a triangle, we can use the triangle inequality. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In other words, if the sides of the triangle are a, b, and c, then a + b > c.

In answer choice c: 7 + 6 = 13, meaning that it does not satisfy the above inequality.

Therefore, the answer is (c) 13 cm, 7 cm, 6 cm

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A "place value" is just a number containing a decimal point whereby each digit place value equals ten times every place value to its right

In mathematics, every digit in an integer does have a place value.

Thus, a "place value" is just a number containing a decimal point whereby each digit place value equals ten times every place value to its right

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(a) Within groups degrees of freedom is 16.

(b) Total degrees of freedom is 3.24.

(c) Among group mean square is 70.8.

Given data is as shown in the following table,

           P1      P2       P3         P4          P1*P1          P2*P2         P3*P3        P4*P4

           12       2        10           7            144                4              100             49

           14       4         9            6            196              16               81               36

           9        7         6            6              81               49              36              36

           11        3         10         15            121                9               100            225

           16       1          12         12            256              1                144             144

Total:  62      17        47         46           798              79              461             490

Package sum (S):- 62 + 17 + 47 + 46 = 172

correlation factor (CF) =  [tex]\frac{S^{2} }{N} = \frac{172^{2} }{20}[/tex]=  1479.2

Raw sum of squares (RSS) = 798 + 79 + 461 + 490 = 1828

Total sum of squares (TSS) = RSS - CF = 1828 - 1479.2 = 348.8

Sum of squares due to treatments (SST),

[tex]\frac{62^{2} }{5} + \frac{17^{2} }{5} + \frac{47^{2} }{5} + \frac{46^{2} }{5} - CF[/tex] = 212.4

Sum of squares due to errors (SSE) = TSS - SST = 348.8 - 212.4 = 136.4

degrees of freedom (df) between the groups = k = 4 - 1 = 3

degree of freedom within the groups = N - k = 20 - 4 = 16

Now we will find mean squares(MS),

MS(between) = [tex]\frac{SS(between)}{df(between)}[/tex]

MS(within) = [tex]\frac{SS(within)}{df(within)}[/tex]

F = [tex]\frac{MS(between)}{df(within)}[/tex]

Source of variation     SS         df            MS             F

Between groups         212.4      3            70.8           8.304

Within groups              136.4     16           8.525

Total                             348.8    19

Critical value of F at (3,16) degrees of freedom is 3.24.

Since the calculated value of F is greater than the critical value of F,we have sufficient evidence to reject the null hypothesis and conclude that there is a significant difference in the mean number of passengers bump every week by the four passengers.

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When a radionuclide has a half-life of 19 hours, it will take approximately 32.3 hours for the sample of this nuclide to decay to about 85 percentage of its proportion.

The computation of the time of proportional decay can be calculated using the given values and putting them into the generalized formula.

Number of Hours Taken = Total Life x Required Decay Proportion

Number of Hours Taken = 19×2×85%

Number of Hours Taken = 38 × 0.85

Number of Hours Taken = 32.3

Therefore, it will take 32.3 hours for the nuclide to decay to about 85 percentage in its proportion.

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