A walkway forms one diagonal of a square playground. The walkway is 30 m long. How long is a side of the playground?
Each side of the playground is m.
(Round to the nearest meter as needed.)

Answer:

The slope is 4/5

y = 4/5x + 20

Step-by-step explanation:

Slope:

Change in y over the change in x

(4 - 8) / -20 - -15

-4 / -20 + 15

-4 /-5

4 / 5

Equation of the line:

You could use either point given.  I am going to use the point (-20,4)  I will use -20 for x and 4 for y.  I will use 4/5 as the slope.  I will need to solve for the y-intercept

y = mx + b

4 = (4/5)(-20) + b

4 = -16 + b  Add 16 to both sides

20 = b

The equation will be

y = 4/5x + 20

Answer:

84.4%

Step-by-step explanation:

9 divided by 58 = 0.844.
Next, multiply 0.844 by 100 for the percentage
0.844x100 = 84.4%

Answer:

84.48%

Step-by-step explanation:

Convert 49/58 to Percentage by Converting to Decimal

With this method, we first need to divide the numerator by the denominator:

49 ÷ 58 = 0.8448275862069

We can see that this gives us the exact same answer as the first method: 49/58 as a percentage is 84.48%.

Note, the final percentage is rounded to 2 decimal places to make the answer simple to read and understand.

Answer:

1/9

Step-by-step explanation:

There could be

1. Boy and a boy

2. Boy and a girl

3. Girl and a girl

Only one out of the three could have two girls: the last one. Meaning there is a 1/3 chance of walking into that one and a 1/3 chance that that house would have 2 girls. So it would be a 1/9 chance.

Hope this helps! :)

Answer:

4/9 of the time the other child is a girl.

Step-by-step explanation:

The trick is what's in the third house. There are 3 choices

b   g

b   b

g  g

So writing all three houses together we have

g   g           g    g             b  g

b   g           b    g             b b

                                       g  g

The first two houses are identical

1/3 * 1/2                for house 1

1/3 * 1/2                for house 2

1/3 * 1/3                for house 3

Now to explain it about. The probability of choosing 1 of the houses is 1/3 for all of the houses. The second number is the probability of getting 2 girls.

So the total probability is

1/6 + 1/6 + 1/9

2/6 + 1/9 = 6/18  + 2/18 = 8 / 18 = 4/9

Answer:

Option A. 5

Step-by-step explanation:

From the question given above, the following data were obtained:

First term (a) = –3

Common ratio (r) = 6

Sum of series (Sₙ) = –4665

Number of term (n) =?

The number of terms in the series can be obtained as follow:

Sₙ = a[rⁿ – 1] / r – 1

–4665 = –3[6ⁿ – 1] / 6 – 1

–4665 = –3[6ⁿ – 1] / 5

Cross multiply

–4665 × 5 = –3[6ⁿ – 1]

–23325 = –3[6ⁿ – 1]

Divide both side by –3

–23325 / –3 = 6ⁿ – 1

7775 = 6ⁿ – 1

Collect like terms

7775 + 1 = 6ⁿ

7776 = 6ⁿ

Express 7776 in index form with 6 as the base

6⁵ = 6ⁿ

n = 5

Thus, the number of terms in the geometric series is 5.

The first net represented the flowers box.

Dimensions in mathematics are the measurements of the size or distance of an object or region or spaces in one Direction. In simple terms-, it is the measurements of to the lengths, width, and heights of anything's. Dimensions are generally expresses as: Lengths. Breath.

This questions doesn't involved any sorts of comparisons of the dimensions. If you're  taken a look, the two figured are perfectly similarly, besides the fact that the seconds one has an additional to one of the rectangular sides of the net.

The first figure, if you weren't to imagined, would form a box without a top. The seconds figures has that one attachments to one of the rectangular side's such that it is, in factory the top.

But this flowers box doesn't have- a top, provides that it is filled with flower's inside.

To know more about dimensions click-

https://brainly.com/question/26740257

#SPJ1

Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

Answer:

16

Step-by-step explanation:

Example:

Consider A vertex. A is connected  with two other vertices  C and B.

Thus 3 line segments are formed. At A, two pair of intersecting lines are formed, AC & AE ;   AE and AB

Each vertex form two pair of intersecting line segments. Totally , there are 8 verteces. So, 8*2 = 16 pair of  intersecting lines

Answer: $5000; $2000

Step-by-step explanation:

Simolw interest is calculated as: PRT/100

where,

P = principal

R = rate

T = time

Let the money in the 4-yr cd be represented by y.

Since rate = 5.2%

Simple interest = (y × 5.2 × 4)/100

Since he invested $3000 less in a 18-month CD, Let the money in the 18-month CD be represented by (y - $3000).

Then, S.I = [(y - $3000) × 3 × 1.5]/100

The total interest = $1130

We then equate the two simple interest together. This will be:

= (y × 5.2 × 4)/100 + (y - $3000) × 3 × 1.5]/100 = $1130

0.208y + 0.045(y - $3000) = $1130

0.208y + 0.045y - $135 = $1130

0.253y = $1130 + $135

0.253y = $1265

y = $1265/0.253

y = $5000

The money invested in 4-yr CD = $5000

The money invested in the 18-month CD = $5000 - $3000 = $2000

Answer:

a. the probability of a type II  error is 0.5319

b. the required sample size to satisfy and the type II error probability  is 59.4441

Step-by-step explanation:

From the information given; we have:

sample size n = 25

Population standard deviation \(\sigma\) = 4

true average lifetime = Sample Mean \(\bar X\) = 62

We can state our null hypothesis and alternative hypothesis as follows:

Null hypothesis:

\(\mathbf{H_o : \mu = 60}\)

Alternative hypothesis

\(\mathbf{H_1 : \mu \neq 60}\)

Where ;

∝ = 0.01

From the standard normal tables at critical value ∝ = 0.01 ; the level of significance is -2.575 lower limit and 2.575 upper limit

The z statistics for the lower limit is:

\(lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}\)

\(-2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}\)

\(-2.575= \dfrac{\bar x - 60 }{0.8}}}\)

\(-2.575*0.8= {\bar x - 60 }{}}}\)

\(-2.06= {\bar x - 60 }{}}}\)

\(\bar x = 60-2.06\)

\(\bar x = 57.94\)

The z statistics for the upper limit is:

\(lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}\)

\(2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}\)

\(2.575= \dfrac{\bar x - 60 }{0.8}}}\)

\(2.575*0.8= {\bar x - 60 }{}}}\)

\(2.06= {\bar x - 60 }{}}}\)

\(\bar x = 60-(-2.06)\)

\(\bar x = 60+2.06\)

\(\bar x = 62.06\)

Thus; the probability of a type II error is determined as follows:

β = P (  \(57.94 < \bar x < 62.06\) )

\(= P ( \dfrac{57.94 -62 }{\dfrac{4}{\sqrt{25}}}<\dfrac{62.06 -62 }{\dfrac{4}{\sqrt{25}}})\)

\(= P ( \dfrac{-4.06 }{0.8}}<\dfrac{2.06 }{0.8})\)

= P ( -5.08 < Z < 0.08 )

= P ( Z < 0.08) - P ( Z < - 5.08)

Using Excel Function: [ (=NORMDIST (0.08)) - (=NORMDIST(-5.08)) ] ; we have:

= 0.531881372 - 0.00000001887

= 0.531881183

≅ 0.5319

b.

What is the required sample size to satisfy and the type II error probability of b(62) = 0.1

Recall that:

The critical value of ∝ = 2.575  ( i. e   \(Z_{1 - \alpha/2 } = 2.575\)  )

Now ;

the critical value of β is :

\(Z _{1- \beta} = 1.28\)

The  required sample size to satisfy and the type II error probability  is therefore determined as :

\(n = [\dfrac{(Z_{1 - \alpha/2} + Z_{1 - \beta} ) \sigma }{\delta}]^2\)

\(n = [\dfrac{(2.575+1.28 ) 4 }{2}]^2\)

\(n = [\dfrac{(3.855 ) 4 }{2}]^2\)

\(n = [\dfrac{(15.42 ) }{2}]^2\)

n = 7.71 ²

n= 59.4441

Thus; the required sample size to satisfy and the type II error probability  is 59.4441

A)

In order to calculate the Type II Error, we proceed with stating the factors:

Hypothesized Mean is given as  =  μ\(_{0} \)        = 60

True Mean  is given as                 =  μa        = 62

Standard Deviation  is given as  = σ           = 4

Sample Size                                   = n           = 25

Standard error of mean                = σx          =σ/\(\sqrt{\\} \)σ               =  0.80

given 0.01 level and two tailed test critical value Zσ             ±  2.58 or approximately 3

Acceptance region is

given as:   = μ - Z∝ * σx ≤ Π ≤ μ+Z∝⇄            =57.9360 ≤x≤   62.0640

Type II Error = probability of not rejecting β    = P(57.94-μa/σx))     <Z< (62.064-μa)/σx))

                                      = P (-5.08   <Z<    0.08)
                                      = 0.5319-0)

                                      = 0.532

B

Hypothesized mean                        = μ₀             =        60

True Mean                                        =μₐ               =       62          

Standard Deviation                          =σ                 =      4

for 0.01 level and two-tailed test critical value Z∝/2              ± 2.58

for 0.01 level of type II error critical value Z\(\beta \)                         = 1.28

Required sample size    = n                                       = (\(Z_{\alpha /2} \) + \(Z_{\beta } \))²σ²/(μ₀-μ₀)²
                                                                                    = 60


See the link below for more about two-sided tests:
https://brainly.com/question/8170655

The triangle formed is a right triangle, so we can relate angles and sides with trigonometric ratios.

We have to calculate the distance from the boat to the lighthouse.

This distance is the hypotenuse of the right triangle.

We can relate the hypotenuse H with the angle with measure 52° and its adyacent side A = 30 miles as:

Answer: the distance is 30/cos(52°) [Option D]

Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

Answer:

-3.5+27

Step-by-step explanation:

-2.7+x=-3.5

x=-3.5-(-2.5)

x=-3.5+2.5

x=2.0

Answer:

44 degrees

Step-by-step explanation:

Because a right angle triangle if added all angles will=to 180 degrees

so 46+90=136

180-136=44

Answer:

44

Step-by-step explanation:

You add 46 to the 90 degree angle (right angle) and get 136. Then, because the angles of a triangle add up to 180 degrees all the time, you would do 180-136 and get 44.

Answer:

1/8, 2/8, 3/8, 4/8, 5/8, 6/8

Step-by-step explanation:

If i have interpreted correct. You want to know a fraction with a denonminator of 8 that is less than 5/6

5/6=0.8333

Multiple Answers

1/8, 2/8, 3/8, 4/8, 5/8, 6/8

Answer:

Th exact form is 21/2 or the mixed number is 10 1/2.

Step-by-step explanation:

Answer:

D= 10 Dollars each month

Step-by-step explanation:

You find this answer by subtracting the one time fee of 20 from the total payed of 70, leaving you with 50.  You then divide that 50$ by 5 months.

Answer:

0.99c + 9.99

Step-by-step explanation:

We know one part of the expression is going to be $0.99c, since it's $0.99 per custom skin, and c is the number of custom skins were getting.

Then we must add on the 9.99 on top of that, since that is the one-time membership fee. This is what the equation looks like :

0.99c + 9.99

Hope this helps :)

Answer:

5. y = $0.99c + $9.99

Step-by-step explanation:

To find the cost, let us solve the equation for y:

Plug 5 as a replacement for c

y = 0.99(5) + 9.99

y = 0.99 × 5 + 9.99               multiply

y = 4.95 + 9.99                     add

y = 14.94

Therefore, the answer to number 6 is $14.94, which is the cost of 5 skins.

Answer:

B, 248

Step-by-step explanation:

Out of 45 students in calc and 21 in stats, 14 are repeatedly counted. We can subtract 14 from one group so that this number does not overlap. For example, let us take the calc group:

45-14= 31

31+21 =52 students taking either calc or stats, NOT OVERLAPPED

Everyone else is not taking calc or stats, so 300-52= 248, or B

I hope this helps! :)

Answer: A

because slope are

Answer:

B=(-3, -5)

Step-by-step explanation:

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

Learn more about the Pythagorean theorem  on:

https://brainly.com/question/27997683

#SPJ1

After the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121).

The coordinates of a triangle after rotation and translation can be found using the following steps:

       x' = (x - a) * cos(θ) - (y - b) * sin(θ) + a

       y' = (x - a) * sin(θ) + (y - b) * cos(θ) + b

        x' = x + dx

        y' = y + dy

       x' = (1 - 2) * cos(45) - (3 - 4) * sin(45) + 2 = -1.121 + 1.121 + 2 = 2.000

       y' = (1 - 2) * sin(45) + (3 - 4) * cos(45) + 4 = -0.707 - 0.707 + 4 = 2.586

      x' = 2 + 3 = 5

      y' = 2.586 + 4 = 6.586

     similarly for point B(2,5) will be (5.121,7.121)

     and for point C(3,3) will be (6.121,5.121)

Learn more about coordinate of a triangle here:

https://brainly.com/question/28566332

#SPJ4

Answer:

Step-by-step explanation: So theres 10 marbles total in the bag. 5 is one half of 10 so the probability to get a blue marble is 5/10 or 1/2 and the probablility of getting an orange one is 1/10 so you have to first get lucky and get that 5/10 chance, and then get even more lucky and get the 1/10 chance and so I believe that it would be 1/20

Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

f (x) =x-6

or, f (5)= 5-6

= - 1

Answer:

1. n = 0.2

2. n ≈ 1.396577191 or n ≈ -1.521577191

Step-by-step explanation:

Q1:

\(5(n-2)+9 = 0\)

\(5n-10 = -9\)

\(5n = 1\)

\(n = 0.2\)

Q2:

Use the quadratic formula on your calculator.

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

More can be learned about residuals at brainly.com/question/1447173

#SPJ1

Answer:

brainly

Search...

sofiapenaloza

05/31/2023

Mathematics

College

answered • expert verified

The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

00:01

00:41

sofiapenaloza is waiting for your help.

Add your answer and earn points.

Expert-Verified Answer

No one rated this answer yet — why not be the first?

joaobezerra

Genius

31.3K answers

261.9M people helped

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

More can be learned about residuals at brainly.com/question/1447173

#SPJ1

Step-by-step explanation: