Solve the compound inequality

The area of the circle with radius 'r' is πr² units² because the formula for the area of a circle = πr²

The circle is defined as a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point which is the centre.

The angle at the center of a circle sums up to 360°.

To calculate the area of a circle, the formula that should be used is given as follows;

Area of a circle = πr²

radius of the circle = r units

area = π×r ×r

= πr² units ²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

A decision that rejects the null hypothesis indicates that there is significant evidence to support the alternative hypothesis, while a failure to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis.

To test the hypotheses, the research team might collect data on the recovery time for patients who underwent the new surgical treatment and compare it with the recovery time for patients who underwent the old one. The team would then use statistical methods to determine whether the data supports or contradicts the null hypothesis.

If the results of the statistical analysis reject the null hypothesis, it means that there is sufficient evidence to support the alternative hypothesis. In other words, the minimum recovery time for patients after the new surgical treatment is less than 96 hours.

However, if the statistical analysis fails to reject the null hypothesis, it means that the data does not provide enough evidence to support the alternative hypothesis.

It does not necessarily mean that the new surgical treatment is ineffective, only that there is not enough evidence to support the claim that it reduces the minimum recovery time for patients.

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

Answer:

the average yearly cost to own and operate this computer for the next 4 years is $697.27.

Step-by-step explanation:

First, let's calculate the electricity cost for running the Surface Book per day:

24W * 16 hours = 384 Wh

Now, let's convert the energy used to kWh:

384 Wh / 1000 = 0.384 kWh

To find the daily cost, we multiply the energy used by the cost per kWh:

0.384 kWh * $0.1233/kWh = $0.0473/day

Over 4 years, there are approximately 1,460 days:

4 years * 365 days/year = 1,460 days

So the total electricity cost over 4 years would be:

$0.0473/day * 1,460 days = $69.08

Now, let's add the cost of the replacement plan:

$80/year * 4 years = $320

Finally, we add the initial purchase cost of the Surface Book:

$2,300

To find the average yearly cost, we add up all of these costs and divide by the number of years:

($69.08 + $320 + $2,300) / 4 years = $697.27/year

Therefore, the average yearly cost to own and operate this computer for the next 4 years is $697.27.

Answer:

Step-by-step explanation:

Answer: X=6

Answer:

Since both equations have different slopes, they will intersect at a single point only. Therefore, there is only one solution for this system of equations.

I hope this answers your question.

Answer:

B

Step-by-step explanation:

Answer:

x = 42°

Step-by-step explanation:

Sum of the interior angles of a triangle is 180

x = 180 - 46 - 92 = 42

The dimensions of a rectangle are l=15 or 2 and b=15 or 2.

Given that, a rectangle has an area of 30 sq meters and a perimeter of 34 meters.

We know that, area of a rectangle is Length×Breadth and the perimeter is 2(Length+Breadth)

Here, l×b=30 -----(i)

2(l+b)=34

l+b=17 -----(ii)

From equation (ii), b=17-l substitute in equation (i), we get

l(17-l)=30

17l-l²=30

l²-17l+30=0

l²-15l-2l+30=0

l(l-15)-2(l-15)=0

(l-15)(l-2)=0

l=15 or l=2

So, breadth is b=15 or b=2

Therefore, the dimensions of a rectangle are l=15 or 2 and b=15 or 2.

To learn more about the area of a rectangle visit:

https://brainly.com/question/20693059.

#SPJ1

The value of x for the given condition of parallel lines with interior angles is equal to 35°.

Two parallel lines are,

m and n.

m is parallel to l and 't' is the transversal of m and n.

Interior angles on the same side of transversal formed on the parallel lines are always supplementary angles.

Here, (x+14)° and  (4x-9)° are supplementary angles formed on parallel lines m and n.

This implies ,

(x+14)° +  (4x-9)° = 180°

take the like terms on the same side of the expression we have,

⇒ 4x° + x° = 180° - 14° + 9°

⇒5x° = 175°

⇒ x° = 35°

Therefore, the value of x for the given pair of parallel lines is equal to 35°.

learn more about parallel lines here

brainly.com/question/28719274

#SPJ1

The above question is incomplete, the complete question is:

Given m∥ n, find the value of x. 't' is the transversal of m and n.

(x+14)° and  (4x-9)° are interior angles on the same side of transversal.

Answer:

To find the equation of a line that is perpendicular to y = (2/7)x - 8, we first need to determine the slope of the original line.

The slope of y = (2/7)x - 8 is 2/7, because the equation is in slope-intercept form (y = mx + b), where m is the slope.

Since we want the new line to be perpendicular to this line, we know that its slope will be the negative reciprocal of 2/7.

To find the negative reciprocal, we flip the fraction and change the sign:

-2/7

Now we have the slope of the new line.

Next, we use the point-slope form of the equation of a line to write the equation, using the point (-4, 2) and the slope -2/7:

y - y1 = m(x - x1)

where x1 = -4, y1 = 2, and m = -2/7.

Plugging in the values, we get:

y - 2 = (-2/7)(x - (-4))

Simplifying:

y - 2 = (-2/7)(x + 4)

Multiplying both sides by 7 to eliminate the fraction:

7y - 14 = -2(x + 4)

Distributing the -2:

7y - 14 = -2x - 8

Adding 2x and 14 to both sides:

2x + 7y = 6

Therefore, the equation of the line that passes through (-4, 2) and is perpendicular to y = (2/7)x - 8 is 2x + 7y = 6.

Answer:  y=-7/2x-12

Step by step:

The line  y = 2/7x-8 is in slope-intercept form   y=mx+ b

m=slope=2/7

In order to find a line that is perpendicular, you need to "flip it" then take the opposite  sign so for our perpendicular line the slope is:

m [tex]-\frac{7}{2}[/tex] and passes through (-4,2)  Now you need to use slope-point form

(y - y1)=m(x - x1)

(y - 2) = -7/2 (x + 4)   now simplify to look like y=mx + b

[tex]y-2=-\frac{7}{2}x-14 )\\\\y=-\frac{7}{2}x -12[/tex]

The diameter of the hemisphere is 31.2 m.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here  the given hemi sphere volume = 8052[tex]m^3[/tex].

Now using volume formula then,

=> Volume V =[tex]\frac{2}{3}\pi r^3[/tex] cubic unit.

=> 8052 = [tex]\frac{2}{3}\times3.14\times r^3[/tex]

=> [tex]r^3=\frac{8052\times3}{2\times3.14} = \frac{24156}{6.28}[/tex]

=> [tex]r^3=3846.49[/tex]

=> r= 15.6

Then diameter d = 2r = 2*15.6 = 31.2 m

Hence the diameter of the hemisphere is 31.2 m.

To learn more about volume refer the below link

https://brainly.com/question/14197390

#SPJ1

The percent of data is given as follows:

a) Between z = 0.53 and z = 2.67: 29.2%.

b) To the right of z = 1.61: 5.37%.

The z-scores are given as follows:

a) 35% of the data is to the left: z = -0.385.

b) 18% of the data is to the right: z = 0.915.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence the percentages are given as follows:

a) Between z = 0.53 and z = 2.67 -> p-value of z = 2.67 subtracted by the p-value of z = 0.53: 0.9939 - 0.7019 = 0.292 = 29.2%.

b) To the right of z = 1.61:  -> one subtracted by the p-value of z = 1.61 -> 1 - 0.9463 = 0.0537 = 5.37%.

The z-scores are given as follows:

a) 35% of the data is to the left -> p-value of z = 0.35 -> z = -0.385.

b) 18% of the data is to the right -> z = 0.915.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The percentage of the class that are 13 years old can be found to be

First, we need to find the total number of students in the given class which would be:

= Number of 13 year olds + Number of 15 year olds

= 21 + 27

= 48 students

The percentage of students who are aged 13 would therefore be:

= Number of 13 year old students / Total number of students in class x 100 %

= 21 / 48 x 100 %

= 0. 4375 x 100 %

= 43. 75 %

Find out more on percentage at https://brainly.com/question/24339661

#SPJ1

The area of a carpet that is 26 feet wide and 39 feet long is 1014 ft².

Given that, a carpet is 26 feet wide and 39 feet long, we need to find its area,

Considering the carpet as a rectangle, so, the area of a rectangle =

= length x width

Therefore, the area of the carpet = 26 x 39 = 1014 ft²

Hence, the area of a carpet that is 26 feet wide and 39 feet long is 1014 ft².

Learn more about rectangles, click;

https://brainly.com/question/29123947

#SPJ1

Applying the cosine ratio, the size of angle XYZ can be calculated, to 1 decimal place, as: 66.4°.

The image attached below shows the diagram of a right triangle with an hypotenuse of 15 cm and a leg that is adjacent to angle XYZ that measures 6 cm. To find the size of angle XYZ, we have to apply the cosine ratio which is expressed as:

cos ∅ = length of adjacent side / length of hypotenuse

Plug in the values:

cos(m<XYZ) = 6/15

m<XYZ = cos^(-1)(6/15)

m<XYZ ≈ 66.4° (to 1 decimal place).

Learn more about size of angle on:

https://brainly.com/question/30693441

#SPJ1

For the given figure, Area of quadrilateral ACDE is given by 78 square cm.

We know that the area of a rectangle with length L and width W is given by,

A = L*W

Here the given rectangle has length of 20 cm and width of 5 cm.

So, L = 20 cm and W = 5 cm.

So the area of total rectangle ABDE = 20*5 = 100 square cm.

Now triangle ABC is a right angled triangle with right angle at B.

Hypotenuse (AC) = 10 cm and Height (AB) = 5 cm.

So by Pythagoras theorem,

(Base)² + (Height)² = (Hypotenuse)²

5² + BC² = 10²

BC² = 10² - 5² = 100 - 25 = 75

BC = √75 = 5√3 [neglecting the negative value since length cannot be negative]

So the area triangle ABC = (1/2)*5*5√3 = 25√3/2 square cm.

So the required area of ACDE is given by

= Rectangle ABED - triangle ABC

= 100 - 25√3/2

= 78 square cm [Rounding off to the nearest whole number]

Hence the area of ACDE is 78 square cm.

To know more about Pythagoras theorem here

https://brainly.com/question/21332040

#SPJ1

Answer:

a)

[tex] \sqrt[3]{512} = 8[/tex]

b)

[tex] \frac{4}{3} \pi ({4}^{3} ) = \frac{256\pi}{3} = 268.08[/tex]

c)

[tex] \frac{256\pi}{3(512)} = \frac{\pi}{6} = .52[/tex]

[tex] \frac{3.14}{6} = .52[/tex]

The radius of the hemisphere is 7.5 km, volume of the sphere is [tex]1767.86 km^3[/tex]and volume of the hemisphere is [tex]883.93 km^3[/tex].

What is hemisphere ?

A hemisphere is a three-dimensional geometric shape that is half of a sphere. It is a curved surface that is bounded by a circular base.

If the diameter of the hemisphere is 15 km, then the radius of the hemisphere is half of the diameter:

radius of the hemisphere = 15 km / 2 = 7.5 km

To find the volume of the sphere, we first need to find the radius of the sphere, which is the same as the radius of the hemisphere:

radius of the sphere = 7.5 km

The volume of a sphere is given by the formula:

[tex]V = (4/3)\pi r^3[/tex]

where V is the volume and r is the radius.

Using this formula with r = 7.5 km and π = 3.14, we get:

volume of the sphere = (4/3) × 3.14 × [tex](7.5 km)^3[/tex]

= 1767.86 [tex]km^3[/tex] (rounded to the nearest hundredth)

To find the volume of the hemisphere, we can use the formula for the volume of a hemisphere, which is half the volume of the sphere:

[tex]V = (1/2)(4/3)\pi r^3[/tex]

where V is the volume of the hemisphere and r is the radius.

Using this formula with r = 7.5 km and π = 3.14, we get:

volume of the hemisphere = (1/2) × (4/3) × 3.14 × [tex](7.5 km)^3[/tex]

= 883.93 [tex]km^3[/tex] (rounded to the nearest hundredth)

To learn more about volume visit the link :

https://brainly.com/question/1578538

#SPJ1

Answer:

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where A is the amount of money after t years, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

Using this formula, we can find the time t required for the investment to grow from $4500 to $6400.

First, we need to convert the annual interest rate of 5.25% to a monthly rate by dividing it by 12:

r = 0.0525 / 12 ≈ 0.004375

Next, we can substitute the given values into the formula and solve for t:

6400 = 4500(1 + 0.004375/12)^(12t)

6400/4500 = (1 + 0.004375/12)^(12t)

1.4222 = (1 + 0.004375/12)^(12t)

ln(1.4222) = 12t ln(1 + 0.004375/12)

t = ln(1.4222) / (12 ln(1 + 0.004375/12))

t ≈ 3.3

Rounding the answer to the nearest tenth of a year, we get:

t ≈ 3.3 years

Therefore, the person must leave the money in the bank for approximately 3.3 years until it reaches $6400.

Answer:

0

Step-by-step explanation:

Solving mathematically,

(1+1)×0

1+1=2

2×0=0

To minimize the cost of the package:

Radius = 3.86 cm.

Height = 9.62 cm.

Minimum cost = 14.01 cents.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using the following formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters into the formula for the volume of a cylinder, we have the following;

450 = πr²h

h = 450/πr²

For the surface area of this cylinder, we have:

SA = 2πrh + 2πr²

By substituting the height (h) in terms of r, we have:

SA = 2πr(450/πr²) + 2πr²

SA = 900/r + 2πr²

Assuming the radius of the paper top is denoted by r, and the height of this cylinder is either greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Therefore, the cost of the container is given by:

Cost, C = 0.02(2πrh + πr²) + 0.08(πr²)

Cost, C = 0.04πr(900/πr²) + 0.02πr² + 0.08πr²

Cost, C = 36/r + 0.02πr² + 0.08πr²

Cost, C = 36/r + 0.1πr²

In order to minimize the cost, we have to find the values of r that minimizes the cost function, C, by taking the partial derivatives of C with respect to r, and then equate to zero:

dC/dr = -36/r² + 0.2πr = 0

36/r² = 0.2πr

r³ = 36/0.2π

r = ∛(36/0.628)

r = ∛(57.3248)

r = 3.86 cm.

h = 450/πr²

h = 450/(3.14 × 3.86²)

Height, h = 9.62 cm.

Minimum cost, C = 36/3.86 + 0.1π(3.86)²

Minimum cost, C = 9.33 + 4.68

Minimum cost, C = 14.01 cents.

Read more on cylinder here: brainly.com/question/14060443

#SPJ1

A is a transformation in which a figure is slid to a new location is called a translation.

A translation is a sort of transformation in geometry that moves every point in a determine the identical distance inside the same direction. the distance and path of the movement are decided by means of the vector that represents the translation.

For example, if a triangle is translated three units to the proper and a pair of units down, every factor within the triangle will pass three units to the proper and 2 units down as well. The resulting image will be equal to the authentic triangle, but it'll be shifted to a new region inside the aircraft.

Translations are vital in geometry because they preserve the form and length of a parent. they're extensively utilized in many practical programs, together with laptop snap shots, animation, and navigation.

Learn more about translation:-

https://brainly.com/question/30197038

#SPJ4

Answer:

Angle B

Step-by-step explanation:

Right angles are 90 degrees. None of the other angles are 90 degrees, meaning b is the only answer. In addition, right angles are often labeled with that symbol ( a box shape), indicating that there's a right angle at that angle

The analysis of the data medians in the box plots (comparison) indicates that the drive-thru that has less wait time is Super Fast Food.

The median is the mid value of the dataset (arranged in order), such that 50% of the count of the data are smaller than or equivalent to the median and 50% of the values are higher than or equivalent to the median.

The five number summary of the box plots are presented as follows;

The Fast chicken graph indicates that the wait times are;

Lowest or minimum value = 5

First quartile = 10

Median = 12.5

Third quartile = 14.5

Max value = 20

Super Fast Food graph indicates that the wait times are;

Lowest value = 3

First quartile = 8.5

Median = 12

Third quartile = 15.5

Max value = 27

The  minimum value and median value of 3 and 12 for Super Fast Food and 5 and 12.5 for Fast Chicken indicates that 50% of the sampled data spent between 3 and 12 minutes at Super Fast Food and 5 and 12.5% at Fast Chicken, which indicates that Super Fast Food has less wait time than Fast Chicken. The correct option is therefore;

Learn more on box plots here: https://brainly.com/question/30652189

#SPJ1

Answer:

(2x - 7)(2x + 1)

Step-by-step explanation:

The steps of the grouping method for factoring are:

First, we can multiply the coefficient of the x² term (4) by the constant term (-7).

4 · (-7) = -28

Next, we can list its factor pairs until we get to one whose numbers add to the middle term (-12).

 -28

1    -28

2   -14

Then, we can replace the middle term's coefficient with the factor pair.

4x² - 12x - 7

4x² + 2x - 14x - 7

Finally, we can factor using the distributive property.

2x(2x + 1) - 7(2x + 1)

(2x - 7)(2x + 1)

Answer: 7

Step-by-step explanation:

use distance

[tex]\sqrt{(4-4)^{2}+(5+2)^{2} }[/tex]

=7

Answer:

-1.25

Step-by-step explanation:

because it is 3.4 away from -1.25

The area of each parallelogram or triangle is 24 cm²,22.5 cm², 98 ft²,48 cm², 90 m², and  30 in² respectively.

In this skills practice problem, we are asked to find the perimeter and area of each parallelogram or triangle, based on their given dimensions. Let's start by defining the formulas for calculating the perimeter and area of each shape:

Perimeter of a parallelogram = 2 x (length + width)

Area of a parallelogram = base x height

Perimeter of a triangle = sum of the lengths of its sides

Area of a triangle = 1/2 x base x height

Now, let's apply these formulas to each shape:

Parallelogram with length 6 cm and width 4 cm:

Perimeter = 2 x (6 + 4) = 20 cm

Area = 6 x 4 = 24 cm²

Triangle with base 9 cm and height 5 cm:

Perimeter = 9 + 8 + 7 = 24 cm

Area = 1/2 x 9 x 5 = 22.5 cm²

Parallelogram with length 14 ft and width 7 ft:

Perimeter = 2 x (14 + 7) = 42 ft

Area = 14 x 7 = 98 ft²

Triangle with base 12 cm and height 8 cm:

Perimeter = 12 + 8 + 10 = 30 cm

Area = 1/2 x 12 x 8 = 48 cm²

Parallelogram with length 18 m and width 5 m:

Perimeter = 2 x (18 + 5) = 46 m

Area = 18 x 5 = 90 m²

For more questions like Triangle click the link below:

https://brainly.com/question/2773823

#SPJ11Triangle with base 6 in and height 10 in:

Perimeter = 6 + 8 + 10 = 24 in

Area = 1/2 x 6 x 10 = 30 in²

Therefore, we have calculated the perimeter and area of each given parallelogram or triangle.

For more questions like Triangle click the link below:

https://brainly.com/question/2773823

#SPJ11

The area of this figure is 106 m².

We don't have the figure so the similar figure is attached below.

First , the area of the Triangle is;

= (1/2) x  (6 + 4) x 9

= 1/2 x 10 x 9

= 45 m²

and, Area of Square

= 5 x 5

= 25 m²

and, Area of Rectangle is;

=  6 x 6

= 36 m²

Thus, the total Area = 45 m² + 25 m² + 36 m²

                                  = 106 m²

Learn more about Area of Composite Figure here: brainly.com/question/10254615

#SPJ1