Geometry > Q.1 Pythagorean theorem F55 Hayley's bedroom is 20 feet long and 15 feet wide. Starting at the far left corner, Hayley walks down the length, across the width, and then diagonally back to the far left corner. How far does Hayley walk?​

Answer:

Wheres the polygon ?

Step-by-step explanation:

The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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Answer: 3/4 granola bars

Step-by-step explanation:

From the question, we are given the information that Davita brought 6 granola bars for herself and the 7 other girls in her camp group.

The fraction of a granola bar that each girl gets if they agree it equally would be the number of granola bars bought divided by the total number of girls which is 8. Therefore, the calculation would be:

= 6 ÷ 8.

= 3/4 granola bars

Each person gets 3/4 granola bars.

The fraction of a granola bar that each girl will get is 3/4

To get the fraction of a granola bar will each girl get, we will take the ratio of the total granola to total number of girls.

Given the following parameters

Total number of 6 granola bars

Total number of girls plus Davita is 8

Taking the required ratio;

Ratio = number of granola: total number of girls

Ratio = 6:8

Ratio = 3:4

Hence the fraction of a granola bar that each girl will get is 3/4

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Answer:

x = 7 ; y = 9

Step-by-step explanation:

Given the system of equation :

y = 2x - 5 - - - (1)

-x + y = 2 ___(2)

From (1)

y = 2x - 5

Put y = 2x - 5 into (2)

-x + 2x - 5 = 2

-x + 2x = 2 + 5

x = 7

We can then solve for y;

Substituting x = 7 into. Equation (1)

y = 2x - 5

y = 2(7) - 5

y = 14 - 5

y = 9

Hence ;

x = 7 ; y = 9

Answer:

8

Step-by-step explanation:

16 divided by 2 is 8.

Answer: 8 students

Step-by-step explanation: 16/2=8

Your answer would be D: Ninety-seven and sixteen-sixths

Answer:

66

Step-by-step explanation:

The rabbit is traveling 66 ft per second.

The average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

a) To determine the likely size of the chance error in the average score of 301 for a cluster sample of 1,000 students, we need additional information about the cluster sampling design.

The cluster sampling method involves dividing the population into clusters, selecting a subset of clusters, and then sampling all individuals within the selected clusters.

The likely size of the chance error depends on the within-cluster variability and the between-cluster variability.

Without information about the variability at each level, we cannot accurately estimate the size of the chance error in this specific scenario.

Therefore, we cannot fill in the blank without more details regarding the cluster sampling design and the variability present in the clusters.

b) If a simple random sample of 1,000 students was tested, we can estimate the likely size of the chance error in the average score of 301. Since a simple random sample implies that each student has an equal chance of being selected, we can use the standard error of the mean formula to estimate the size of the chance error.

The standard error of the mean (SE) is calculated as the standard deviation (SD) divided by the square root of the sample size (n):

SE = SD / √n

Given that the SD is 30 and the sample size (n) is 1,000, we can calculate the standard error:

SE = 30 / √1000 = 30 / 31.62 ≈ 0.95

Therefore, the likely size of the chance error in the average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

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The solution to the expression 4+(−634) is -630

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

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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1) Average velocity = (254x + 0.5y - 6.5x - 5y) / 9s.

2) Instantaneous velocity at t=0.5s: v = 2.5x - 20y, angle with positive x-axis ≈ -80.54 degrees.

3) Acceleration = 5.25\(m/s^2\), final velocity = 10.27 m/s.

1) The average velocity during the interval t=1s to t=10s can be found by calculating the displacement over that time interval and dividing it by the duration. The displacement is given by r(10s) - r(1s):

\(r(10s) = (4.0 + 2.5(10^2))x + (5/10)y = 254x + 0.5y\)

\(r(1s) = (4.0 + 2.5(1^2))x + (5/1)y = 6.5x + 5y\)

Average velocity = (r(10s) - r(1s)) / (10s - 1s) = (254x + 0.5y - 6.5x - 5y) / 9s

2) The instantaneous velocity at t=0.5s can be found by taking the derivative of the displacement vector with respect to time and evaluating it at t=0.5s:

\(v(t) = d(r(t))/dt = (d(4.0 + 2.5t^2)/dt)x + (d(5/t)/dt)y\)

     \(= (5t)x - (5/t^2)y\)

\(v(0.5s) = (5(0.5))x - (5/(0.5)^2)y = 2.5x - 20y\)

The angle that the velocity vector makes with the positive x-axis can be found using the arctan function:

θ = arctan(vy/vx) = arctan((-20)/(2.5)) = arctan(-8) ≈ -80.54 degrees

3) The acceleration down the ramp can be determined using the formula:

\(a = g sin(θ) = 9.8 m/s^2 * sin(33 degrees) ≈ 5.25 m/s^2\)

The final velocity once it reaches the bottom of the ramp can be found using the equation of motion:

\(v^2 = u^2 + 2as\)

Assuming the ball starts from rest (u = 0), the final velocity is given by:

v = sqrt(2as) = sqrt(2 * 5.25 * 10) ≈ 10.27 m/s

Therefore, the acceleration down the ramp is approximately 5.25 m/s^2 and the final velocity at the bottom is approximately 10.27 m/s.

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For a sample size of 20 players, 68% of the sample means fall within 19.32 and 20.98

The sample size is a term used in market research for defining the number of subjects included in a sample size. By sample size, we understand a group of subjects that are selected from the general population and is considered a representative of the real population for that specific study.

Empirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

For a population mean of 20.15 and a standard deviation of 3.7

68% are within μ ± σ/√n,

hence,

68% = 20.15 ± 3.7/√20 = (19.32, 20.98)

For a sample size of 20 players, 68% of the sample means fall within 19.32 and 20.98.

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Step-by-step explanation:

AB = BC

3x+26=10x-13

39=7x

x=5.6 cm.

hope this helps you.

The numbers are 666666 X 4443332221119111. The number solved multiplication is \(2.962218518 \times10^{21}\).

Given that,

The numbers are 666666 X 4443332221119111

We have to solve the number multiplication.

Multiplication means the fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.

666666 X 4443332221119111

\(2.962218518 \times10^{21}\)

Therefore, the number solved multiplication is \(2.962218518 \times10^{21}\).

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Answer:

Step-by-step explanation:

x

=

−

24

y

=

10

Explanation:

x

+

4

y

=

16

2

x

−

4

y

=

8

Subtract the bottom equation from the top one so the

+

4

y

and

−

4

y

cancel each other out.

−

x

=

24

x

=

−

24

x

+

4

y

=

16

−

24

+

4

y

=

16

4

y

=

40

y

=

10

The product of the rational expressions shown below  in reduced form is 5x / x-1.Therefore option D is correct.

A rational expression is seen as a mathematical expression that can be shown as the quotient of two polynomial expressions, where the denominator is not equal to zero.

A rational expression is described as  any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

The given rational expression is:

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

We can cancel the common terms from numerator and denominator of:

x + 1

Therefore, the solution will then be  5x/ x+1

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To find:

The sketch of v, 2v and 1/2 v.

Solution:

Given the v = <3,2>.

(a)

The sketch of v is shown below:

(b)

The value of 2v can be obtained as follows:

The sketch of 2v is shown below:

(c)

The value of 1/2 v can be obtained as follows:

The sketch of 1/2 v is shown below:

Answer:

r = -7

Step-by-step explanation:

-4 + 2r - 5r = 17

=> 2r - 5r = 17 + 4

=> -3r = 21

=> r = 21/(-3)

=> r = -7

Answer:

It is the long side of a right triangle

Step-by-step explanation:

Okay

Answer:

The dimension of the sandbox is (2x+1) by (x - 3)

Step-by-step explanation:

It seems the complete question will be:

The area of sandbox in park is represented by 2X^2-5x-3 find the dimensions of the sandbox in terms of x.

Step-by-step explanation:

From the question, the given expression is 2X^2-5x-3. This can be rewritten as

\(2x^{2} -5x-3\)

If the area of the sandbox in park is represented by this expression, then the dimensions of the sandbox will be the product of the factors. To determine the factors, we will factorize the given quadratic expression.

Factorizing the expression \(2x^{2} -5x-3\), we get

\(2x^{2} -6x+x-3\)

\(2x(x-3)+1(x-3)\)

\((2x+1)(x-3)\)

Hence, the dimension of the sandbox is (2x+1) by (x - 3)

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.

The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.

The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima.  M(t) = 2t + 1

   d/dt M(t) = d/dt 2t + 1

                  = 2

d/dt m'(t) = 0

2 not equal to 0

The function does not have a critical point. Therefore, the maxima do not exist for the function.

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100%=(435.60÷88)x100

which is 495.

Answer:

Step-by-step explanation:

435,60:12%

The probability of drawing a pair when selecting three cards at random from a standard 52-card deck is approximately 0.1694, or about 16.94%.

To calculate the probability of drawing a pair of cards from a standard 52-card deck when selecting three cards at random, we need to consider the number of favorable outcomes (pairs) and the total number of possible outcomes.

First, let's determine the number of favorable outcomes. For a pair, we need two cards of the same rank (e.g., two 7s, two Queens, etc.) and any third card that is different from the pair.

The number of ways to choose a rank for the pair is 13 (one for each rank). For each rank, there are four cards of that rank in the deck. Therefore, the number of ways to select two cards of the same rank is given by:

Number of ways to choose a pair = 13 * (4 choose 2) = 13 * 6 = 78

After selecting the pair, there are 50 cards remaining in the deck. The third card must be of a different rank from the pair. There are 48 cards remaining with different ranks from the pair.

Therefore, the number of favorable outcomes (pairs) is 78 * 48 = 3,744.

Next, let's calculate the total number of possible outcomes when selecting three cards from a standard deck. The total number of ways to choose any three cards from 52 cards is given by:

Total number of possible outcomes = (52 choose 3) = 22,100

Finally, we can calculate the probability of drawing a pair:

Probability of drawing a pair = Number of favorable outcomes / Total number of possible outcomes

= 3,744 / 22,100

≈ 0.1694

Therefore, the probability of drawing a pair when selecting three cards at random from a standard 52-card deck is approximately 0.1694, or about 16.94%.

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Answer:

X≤3

Step-by-step explanation:

This is because the arrow is moving down the number line

The total number of fish caught during the festival can be calculated by adding the number of fish caught for each value of n.

For example, if 10 contestants caught 4 fish, 5 caught 8 fish, 7 caught 10 fish, and 8 caught 7 fish, the total number of fish caught would be 104 + 58 + 710 + 87 = 330.

The argument states that the total number of fish caught during the Frostbite Falls Fishing Festival can be determined by adding the number of fish caught by each contestant.

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Answer:

IM because they are the same!!

YOUR WELCOME

Step-by-step explanation:

∆MNO and ∆QRS are congruent with each other.

What are rigid motions in congruency of triangles?

Two plane figures are congruent if and only if one can be obtained from the other through a series of rigid motions (that is, reflections, translations, and/or rotations). A landscape architect designs the landscape around a mall using a grid. Trace the landscape elements to ensure that they are congruent.

For the given coordinates M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1)​.

Let's draw the triangles on graph paper,

You can map MNO to QRS with a translation left 2 units and

down 2 units. The planters are congruent because there is a rigid

transformation that maps one to the other.

Hence,  ∆MNO and ∆QRS are congruent with each other.

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Answer:32.9

Step-by-step explanation:

Hope this helps! :)

Answer:

Diameter = 103.35 cm

Step-by-step explanation:

Pizza = circle

Area of a Circle = π * r²

π = 3.1416

r = radius

Area of a pizza = 850cm²

850 = 3.1416 * r²

850/3.1416 = r²

270.56 = r²

√270.56 = √r²

16.45 = r

radius = 16.45  (aprox)

diameter of a pizza = 2π r

diameter of a pizza = 2*3.1416*16.45

diameter of a pizza = 103.35 cm

According to the question ( a.) IV: Exposure to alcohol advertising, DV: Amount of alcoholic beverages consumed. ( b.) Design: Pretest-posttest design. ( c. ) [Graph] showing increased alcohol consumption after exposure to alcohol advertising.

a) In this scenario:

- The independent variable (IV) is the exposure to alcohol advertising (specifically, viewing a 30-minute TV show with entertaining ads for alcoholic products).

- The dependent variable (DV) is the amount of alcoholic beverage consumption reported by the college students.

b) The design used in this scenario is a pretest-posttest design. The participants' alcohol consumption was measured on Monday and Tuesday (pretest) before the exposure to alcohol advertising on Wednesday, and then measured again on Thursday and Friday (posttest) after the exposure to alcohol advertising.

c) Below is a sketch of a possible graph representing the results:

```

        |

   DV   |        

        |        Posttest

        |       +-----------------

        |   /\

        |  /  \              

        | /    \        

        |/      \      

        |        \    

        |         \  

        |          \  

        |           \

        |            \

        |----------------------

            Pretest    

```

The graph illustrates that there is an increase in the reported alcohol consumption after the exposure to alcohol advertising (posttest) compared to the pretest levels.

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