Gabriel finds some wooden boards in the backyard with lengths of 5 feet, 2.5 feet and 4 feet. He decides he wants to make a triangular garden in the yard and uses the triangle inequality rule to see if it will work. Which sums prove that the boards will create a triangular outline for the garden? Select all that apply. 5 + 2.5 > 4 5 + 2.5 < 4 4 + 2.5 > 5 4 + 2.5 < 5 4 + 5 > 2.5

The 90% confidence that the proportion of yellow peas is between 23.5% and 29.5%

and, 25% estimate falls within the 90% confidence limits.

We have,

Green peas= 445

Yellow peas= 161

So, Total peas:

= 445 + 161

= 606.

Now, the Proportion of yellow

= 161/606

= 0.265676

= 26.56%

Now, p= 0. 265 and q= 1-0.265= 0.735

So, np = 606 (0.265)= 160.59

nq = 606(0.735) = 445.41

As, both results are ≥ 5 and the sample can be approximated by a normal distribution.

For 90% confidence, z = 1.645.

Now, the margin error

= 1.645 √ (0.265)(0.735) / 606

= 1.645 / 0.0179

= 0.0294

Now, The confidence limits are the point estimate ± the margin of error. =

= 0.265 + 0.03

= 0.295

= 29.5%;

or, 0.265 - 0.030

= 0.235

= 23.5%

Learn more about Confidence Interval here:

https://brainly.com/question/24131141

#SPJ1

Given:

[tex]\sf y = 4x + 5[/tex]

Switch x and y.

[tex]\sf x = 4y + 5[/tex]

Solve for y.

[tex]\sf 4y = x - 5[/tex]

[tex]\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}[/tex]

[tex]\Rightarrow\boxed{\sf y = \dfrac{1}{4} \ x-\dfrac{5}{4}}[/tex]

In the given rectangle,

The value of x is 3

The value of NP is 18

From the question, we are to determine the value of x in the given diagram.

The diagram shows a rectangle with its diagonals.

Since the diagonals of a rectangle bisect each other, we can write that

2x + 3 = 12 - x

Solve the equation for x

2x + 3 = 12 - x

Add x to both sides of the equation

2x + x + 3 = 12 - x + x

3x + 3 = 12

Subtract 3 from both sides of the equation

3x + 3 - 3 = 12 - 3

3x = 9

Divide both sides of the equation of by 3

3x / 3 = 9 / 3

x = 3

Thus,

The value of x is 3

To determine the value of NP

NP = 2(12 - x)

Substitute the value of x

NP = 2(12 - 3)

NP = 2(9)

NP = 18

Hence, the value of NP is 18

Learn more on Diagonals of a rectangle here: https://brainly.com/question/30211200

#SPJ1

The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

Learn more about angles here:

https://brainly.com/question/7116550

#SPJ1

The three adverbs in the sentence are:

hard (modifying the verb "raining")

clearly (modifying the verb "see")

almost (modifying the verb "crashed")

1) "Hard" is an adverb of manner that describes how the rain was falling. It indicates that the rain was falling with intensity or force, which made it difficult for the driver to see.

2) "Clearly" is an adverb of manner that describes how the driver was seeing. It indicates that the driver was having difficulty seeing due to the heavy rain, which was affecting their vision.

3) "Almost" is an adverb of degree that modifies the verb "crashed." It indicates that the driver came very close to crashing their shiny new car, but managed to avoid a collision at the last moment.

To know more about adverbs follow

https://brainly.com/question/12611359

#SPJ1

0,0,0,0,0,

The number that take (a) both PE is 6 girls (b) Gymnastic but not acrobat is 7 girls (c)  At least one PE is 18 girls

How to determine the numbers?

Recall that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

From the given parameters,

(a)  The number that play both PE is given as

13 - x + x + 17 - x + 1 = 25

Solving the equation to get the value of x

13+17-x = 25

⇒ 31 -x =25

Collecting like terms we have

-x = 25 - 31

- x = -6

Dividing by a minus we have

x = 6

This means that 5 girls play both PE

(b)  Number that play gymnastic but not acrobat is given as

Gymnastic only that is

13 - x

13 - 6 = 7 girls

(c)  Number that play at least one game is calculated thus:

n(G) ∪ n(A)

That is (13 - x )  + (17 - x)

= 13-6 + 17 -6

7 + 11 = 18 girls

The length of the line segment AB = 16 units

Given data ,

Let the length of the line segment AB = 2x - 4

Let the length of the line segment BC = 3x + 2

Now , AC = 48 units

So , AC = AB + BC

On simplifying the equation , we get

2x - 4 + 3x + 2 = 48

5x - 2 = 48

Adding 2 on both sides , we get

5x = 50

Divide by 5 on both sides , we get

x = 10 units

So , the length of AB = 2 ( 10 ) - 4

AB = 16 units

Hence , the length is AB = 16 units

To learn more about distance of point to line click :

https://brainly.com/question/21506745

#SPJ1

Answer:

B

Step-by-step explanation:

I think that may be right if it is have a good day,:))

We can see here that x will be = 123.4°.

A polygon is actually known to be a two-dimensional geometric shape. It is a shape that is known to be defined by a closed path. It consists of finite sequence of straight line segments.

The segments are actually known as sides or edges and which are connected at vertices or corners.

Looking at the shape, we see that the regular pentagon and heptagon are joined together on one side.

Thus, exterior angle of a regular pentagon (5 sides) = 360°/5 = 72°.

The exterior angle of a regular heptagon (7 sides) = 360°/7 = 51.4°

Thus, x° = 72° + 51.4° = 123.4°

Learn more about polygon on https://brainly.com/question/1592456

#SPJ1

Answer: A.

Step-by-step explanation:

    The range is the difference between the minimum and maximum values. We look at the dashed lines for these values. Ava's Average Autos have a larger spread of prices, as shown by the longer box plot for their store.

Answer:

To find 40% of a number, you can multiply the number by 0.4 or divide it by 2.5.

Using this method, we get:

40% of 100 is 40 (100 x 0.4 or 100 ÷ 2.5)

40% of 110 is 44 (110 x 0.4 or 110 ÷ 2.5)

40% of 140 is 56 (140 x 0.4 or 140 ÷ 2.5)

40% of 120 is 48 (120 x 0.4 or 120 ÷ 2.5)

Therefore, 40% of 100 is 40, 40% of 110 is 44, 40% of 140 is 56, and 40% of 120 is 48.

The area of the rhombus is 33 square unit.

We have,

x = 6 units, y = 3 units, and h = 5 units.

Now, area of Triangle

= 2 x 1/2 x b x h

= 2 x 1/2 x 6 x 3

= 18 square unit

and, area of Rectangle

= l w

= 5 x 3

= 15 square unit

Thus, the Area of Rhombus

= 18 + 15

= 33 square unit

Learn more about Area here:

https://brainly.com/question/27683633

#SPJ1

Answer: 2,556 seats

Step-by-step explanation

18 x 142 =2,556 seats

Answer: Its high

Step-by-step explanation: It just is

The probability that Brent draws mismatched socks is 32/153.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.

Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.

For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.

Let's consider the first case.

There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.

For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.

Therefore, the probability of Brent drawing mismatched socks is:

= (32 + 32) / 306

= 64 / 306

= 32 / 153

Thus, the probability that Brent draws mismatched socks is 32/153.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

Surface area of a rectangular prism is 136 sq. units.

Length of the base of prism, l = 4 units

Breadth of the base of prism, b = 3 units

Height of the base of prism, h = 8

Surface area of a rectangular prism is given as,

SA = 2(lb + bh + lh)

SA = 2[(4 x 3) + (3 x 8) + (4 x 8)

SA = 136 sq. units

To learn more about Surface area of a rectangular prism, click:

https://brainly.com/question/14987814

#SPJ1

The total number of meals received by the company this month = 40 meals

Given data ,

Let the number of meals received by the company this month be A

Now , the proportion is given as

The number of boxes of meals in the past month = 3 boxes

The number of meals in 3 boxes = 15 meals

The number of boxes in the present month = 8 boxes

So , the proportion is

15 / 3  = A / 8

Multiply by 8 on both sides , we get

A = 5 x 8

A = 40 meals

Hence , the number of meals is A = 40 meals

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ1

The simplified expression is  [tex]7 x^{3} - 14 x^{2} + 28 x - 55+\frac{124}{x + 2}[/tex]. The correct answer is an option (C).

The expression is given as follows:

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}[/tex]

We can use polynomial long division to simplify the expression:

         7x² - 14x² + 28x - 55

        ______________________

x + 2 ) 7x⁴ + 0x³ + 0x² + x + 14

          7x⁴ + 14x³

       ___________

               -14x³ + 0x²

               -14x³ - 28x²

               ____________

                        28x² + x

                        28x² + 56x

                        __________

                               -55x + 14

                               -55x - 110

                               ________

                                       124

[tex]\dfrac{7 x^{4} + x + 14}{x + 2}=7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

Hence, the simplified expression is as follows:

[tex]7 x^{3} - 14 x^{2} + 28 x - 55+\dfrac{124}{x + 2}[/tex]

Learn more about the polynomial long division here:

https://brainly.com/question/29718477

#SPJ1

Answer:

  $2080

Step-by-step explanation:

You want to know the annual cost of coffee purchased 5 mornings and 3 afternoons per week when each purchase amounts to $5.

Five morning visits and three afternoon visits to the coffee shop will be a total of 8 visits per week. At $5 each, the cost per week is ...

  8 × $5 = $40

The cost for a year will be the cost for 52 weeks:

  52 × $40 = $2080

Carla spends $2080 per year on coffee.

Whether this is a "little indulgence" or not will depend on Carla's budget.

The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ1

The amounts of people in attendance are given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

There were 400 people total, hence:

x + y + z = 400.

There were twice as many parents as grandparents, hence:

y = 2z.

50 more children than parents, hence:

x = y + 50

x = 2z + 50.

Replacing on the first equation, the value of z is obtained as follows:

2z + 50 + 2z + z = 400

5z = 350

z = 70.

Then the values of x and y are given as follows:

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

More can be learned about integrals at https://brainly.com/question/22008756

#SPJ1

The equations of the circles in standard form, obtained from the coordinates of the center and the points on the circle are;

5) (x + 16)² + (y + 16)² = 3²

6) (x - 15)² + (y + 7)² = 8

7) (x + 6)² + (y + 2)² = 6²

8) (x + 9)² + (y + 3)² = 89

The standard form of the equation of a circle is; (x - h)² + (y - h)² = r²

Where;

(h, k) = The coordinates of the center of the circle

5) The center of the circle is (-16, -16)

The coordinates of a point on the circle is (-13, -16)

Therefore; r² = (-13 - (-16))² = 3²

The equation of the circle in standard form is therefore;

(x - (-16))² + (y - (-16))² = 3²

(x + 16)² + (y + 16)² = 3²

6) The coordinates of the center of the circle = (15, -7)

The coordinate of a point on the circle = (17, -5)

r² = (17 - 15)² + (-5 - (-7))² = 8

The equation is; (x - 15)² + (x - (-7))² = 8

(x - 15)² + (x + 7)² = 8

7) The coordinates of the center = (-6, -2)

The coordinate of a point on the circle = (-12, -2)

The square of the radius is therefore; r² = (-6 - (-12))² = 6²

(x - (-6))² + (y - (-2))² = 6²

(x + 6)² + (y + 2)² = 6²

8) The coordinates of the center is; (-9, -3)

The point on the circle is; (-1, -8)

The square of the radius is; r² = (-1 - (-9))² + (-8 - (-3))² = 89

The equation of the circle is therefore; (x - (-9))² + (y - (-3))² = 89

(x + 9)² + (y + 3)² = 89

Learn more on the equation of a circle here: https://brainly.com/question/14150470

#SPJ1

The experimental probability that an arrangement will contain at least one yellow balloon is 0.767. Then the correct option is C.

Given that:

Each balloon arrangement in Ethan's class has four balloons in it. The likelihood of each balloon being red, blue, or yellow is equal. To represent this possibility, Ethan made a spinner.

ybrr, bybb, rbbb, rrry, rbbb, rryy, yybb, ryry, ryyr, rbyr, ryyr, rryy, rrrr, yrby, bbyy, byyr, byyr, byyb, rbby, ybry, rryy, rbrr, rybb, bbbr, rrbr, ybry, ryrr, rryb, rrrb, rryr

The experimental probability that an arrangement will contain at least one yellow balloon is calculated as,

P = 23 / 30

P = 0.767

Thus, the correct option is C.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ1

Answer: y = 2x + 2

Step-by-step explanation: First, you find slope between the points with point slope form. (8-(-6))/(3-(-4) = 2.

2 is the slope.

Now we have y = 2x + b.

To find b, we pick a coordinate and insert the values.

8 = 2(3) + b

8 = 6 + b

8 - 6 = b

b = 2

Put it together, you have y = 2x + 2

The length of each rope if all the ropes had the same length is 3 ft

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

The dot plot

From the dot plot, we can see that the data are normally distributed

This means that the length of each rope is the mean, the median and the mode

Given that the data on the dot plot is normally distributed, we have the following values

So, we can conclude that the length is 3 ft

Read more about dot plot at

https://brainly.com/question/14438425

#SPJ1

Based on the tangent line and the radii, the value of x given that AB is tangent to the circle is 10

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

AB is tangent to the circle

As a general rule:

The radius of circle is perpendicular to the tangent line

This means that we can calculate x using the Pythagorean theorem

So, we have

x^2 = 6^2 + 8^2

Evaluate the sum of exponents

So, we have

x^2 = 100

So, we have

x = 10

Hence, the calculated value of x in the circle is 10

Read more about tangent lines at

https://brainly.com/question/16038958

#SPJ1

Answer:

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

y = x² −7x + 7

Complete the square for y = x² −7x + 7

(x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Set y equal to the new right side.

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

So, the answer is y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Answer:

x = 5

y = 5√2

Step-by-step explanation:

In a 45-45-90 degree right triangle, the two legs form the right angle, and the hypotenuse is opposite the right angle.

The side lengths of a 45-45-90 right triangle are in the ratio

1 : 1 : √2

The legs are congruent, so if one leg has length 5, the other leg also has length 5.

The hypotenuse is √2 times the length of the legs.

x = 5

y = 5√2

The distance along the trail from X to Y, to the nearest tenth of a meter, is 600 meters.

The distance between X and Y is on a straight path from X to Y or Y to X. This means that the distance between X and Y can be found by finding the distance between the contour lines.

The distance between the contour lines is:

= Elevation of Y - Elevation of X

= 1, 900 - 1, 300

= 600 meters

In conclusion, the distance along the trail between X and Y is 600 meters.

Find out more on distance at https://brainly.com/question/13390186

#SPJ1