ixl What is the surface area of this cylinder? Use ​ ≈ 3.14 and round your answer to the nearest hundredth. 15 cm 16 cm

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Given:

Two points are (6, 7) and I(-7,-6).

Point G lies \(\dfrac{1}{2}\) of the way along Hl.

John says that point G is located at the origin.

To find:

Whether John is correct or not.

Solution:

Point G lies \(\dfrac{1}{2}\) of the way along Hl. I means point G is the midpoint of HI.

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

\(G=\left(\dfrac{6-7}{2},\dfrac{7-6}{2}\right)\)

\(G=\left(\dfrac{-1}{2},\dfrac{1}{2}\right)\)

The location of point G is at \(\left(\dfrac{-1}{2},\dfrac{1}{2}\right)\), which is not equal to origin, i.e., (0,0).

Therefore, John is incorrect.

If there are fractions, leave them unevaluated, then the answer will be:

\(\left[\begin{array}{ccc}a&c\\b&d\end{array}\right] -1 =\left[\begin{array}{ccc}d/ad-bc&-b/ad-bc\\-c/ad-bc&a/ad-bc\end{array}\right]\)

The matrix factor by X is invertible:

\(\left[\begin{array}{ccc}2&8\\-6&-9\\\end{array}\right]\) \(\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]\\ \\=\left[\begin{array}{ccc}2&8\\-6&-9\end{array}\right] -\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] *\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =\)

\(\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right] * =\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right] \left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] -1\)  

\(* =\left[\begin{array}{ccc}1&-6\\8&-10\end{array}\right] \left[\begin{array}{ccc}2/11&-1/11\\7/33&-3/11\end{array}\right]\)

\(* =\left[\begin{array}{ccc}6/33&-25/11\\-106/33&36/11\end{array}\right]\)

Note : \(\left[\begin{array}{ccc}a&c\\b&d\end{array}\right] -1 =\left[\begin{array}{ccc}d/ad-bc&-b/ad-bc\\-c/ad-bc&a/ad-bc\end{array}\right]\)

A fraction is a piece of a whole. In math, the number is communicated as a remainder, in which the numerator is separated by the denominator. In a basic fraction, both are numbers. A perplexing fraction has a fraction in the numerator or denominator

A fraction is a numerical value that is a piece of a whole. It is assessed by partitioning a whole into a number of parts. For instance, ½ addresses half of a whole number or a thing.

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Answer:

inner and outer core are the ones that have iron and nickel

Step-by-step explanation:

The answer is inner and outer core

Answer:

65/100 that is the answer to this question

Sure, here's how to calculate the surface area of a rectangular prism with the given dimensions:

First, we can calculate the area of each face of the rectangular prism. The top and bottom faces each have an area of length times width, or lw:

\(\sf A_{top/bottom} = lw = 5.4\text{ yd} \times 3.8\text{ yd} = 20.52\text{ yd}^2\)

The front and back faces each have an area of height times width, or hw:

\(\sf A_{front/back} = hw = 6\text{ yd} \times 3.8\text{ yd} = 22.8\text{ yd}^2\)

The left and right faces each have an area of length times height, or lh:

\(\sf A_{left/right} = lh = 5.4\text{ yd} \times 6\text{ yd} = 32.4\text{ yd}^2\)

To find the total surface area of the rectangular prism, we add up the areas of all six faces:

\(\sf A_{total} = 2A_{top/bottom} + 2A_{front/back} + 2A_{left/right}\)

Substituting in the values we calculated earlier, we get:

\(\sf A_{total} = 2(20.52\text{ yd}^2) + 2(22.8\text{ yd}^2) + 2(32.4\text{ yd}^2) = 198.72\text{ yd}^2\)

Therefore, the surface area of the rectangular prism is 198.72 square yards.

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Answer:

-------------------------

Total surface area of a rectangular prism with dimensions of l, w and h is:

Given dimensions:

Substitute the values into the formula and calculate the toal surface area:

Answer:

1). x = 2

2). x = -10

3). x = \(-\frac{2}{5}\)

4). x = 10

Step-by-step explanation:

1). x - 6 = -4

  (x - 6) + 6 = -4 + 6 [By adding 6 to both the sides of the equation]

  x = 2

2). x + 3 = -7

  (x + 3) - 3 = -7 - 3 [By subtracting 3 to both the sides of the equation]

  x = -10

3). 5x = -2

   \(\frac{5x}{5}=\frac{-2}{5}\) [By dividing with 5 from both the sides of the equation]

   x =  \(-\frac{2}{5}\)

4). 0.5x = 5

   \(\frac{0.5x}{0.5}=\frac{5}{0.5}\) [By dividing with 0.5 from both the sides of the equation]

   x = 10

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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We know that

• The sale price is $312.

• The desk is 35% off.

We just have to divide to find the regular price. Remember that 35% is equivalent to 0.35. It's important to notice that $312 represents 65% of the regular price since is 35% lower. Now, we use the rule of three: If $312 represents 65%, how much would represent 100%?

The sales revenue necessary to generate net income of $100,000 is: $416,667.

Using this formula to find the sales revenue

Sales revenue = Sales revenue + (Sales revenue × Net income / Fixed costs)

Let plug in the formula

Sales revenue =  $250,000 + ($250,000 × $100,000 /$150,000)

Sales revenue = $250,000 + ($250,000 ×0.6666666)

Sales revenue = $250,000 + $166,666.65

Sales revenue = $416,666.65

Sales revenue = $416,667 (Approximately)

Therefore the correct option  is E.

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Answer:

c

Step-by-step explanation:

3/5m - 15

3/5m - 15 = 0

Make 15 the subject of the formula

3/5m = 15

the above equation can be interpreted as

3/5 times m is equal to 15

The sum of 3/5 and a number is 15 would be represented as 3/5 + m = 15

Three-fifths more that a number is 15 would be represented as 3/5m + m = 15

kigegvdvdjsjshdbdhdhhdh

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

Answer:

B. x - 10

Step-by-step explanation:

x² - 13x + 30 = (x - 3)(x - 10)

x² + (a + b)x + ab = (x + a)(x + b)

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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9514 1404 393

Answer:

  3 ft

Step-by-step explanation:

The post is 4/24 = 1/6 as tall as the streetlight, so we expect its shadow to be 1/6 as long as that of the streetlight:

  (1/6)(18 ft) = 3 ft

The parking meter post shadow is 3 feet long.

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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Answer: The mean difference is between 799586.3 and 803257.9.

Step-by-step explanation: To estimate the mean difference for confidence interval:

Find the statistic sample:

For the traffic count, mean = 1835.8 and s = 1382607.3

The confidence interval is 90%, so:

α = \(\frac{1-0.9}{2}\)

α = 0.05

The degrees of dreedom are:

df = n - 1

df = 10 - 1

df = 9

Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.

Error will be:

E = \(t.\frac{s}{\sqrt{n} }\)

E = 1.833.(\(\frac{1382607.3}{\sqrt{10} }\))

E = 801422.1

The interval is: mean - E < μ < E + mean

1835.8 - 801422.1 < μ < 1835.8+801422.1

-799586.3 < μ < 803257.9

The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.

Answer:

12

Step-by-step explanation:

Note:

x = -2 ; y = 5

Plug in -2 for x and 5 for y.

3(-2) + 4(5) - 2

Remember to follow PEMDAS. First solve for multiplication, then combine:

3 * -2 = -6

4 * 5 = 20

-6 + 20 - 2

Combine like terms:

20 - 6 - 2 = 12

12 is your value.

~

Answer:

12

Step-by-step explanation:

When answering these types of problems make sure you simplify the expression before substituting

In this case it is not necessasry so substitute x for -2 and y for -5. The expression is now ...

3(-2) + 4(5) - 2

Now just add like term

-6 + 20 -2

12

Answer: A≈226.98 ft²

Step-by-step explanation:

The formula for area of a circle is A=πr². The formula doesn't include diameter , but we can certainly find the radius from the diameter.

d=2r

17=2r

r=17/2=8.5 ft

Now that we have the radius, we can plug it in to area formula.

A=πr²

A=π(8.5ft)²

A=π72.25ft²

A≈226.98 ft²

Area of a circle: A = πr²

Get the radius by dividing the diameter by 2.

17 / 2 = 8.5

Now, solve with the given values.

A = π(8.5)²

A = 72.25π

A = 226.865

Therefore, the area is 226.865ft³

Best of Luck!

The volume of concrete required is

The volume of concrete required is solved by area * thickness

Area of the figure

First section = 20 * 8 = 160

second section = π(R² - r²)/4 = π(16² - 8²)/4 ≈ 151

Third section = 12 * 8 = 96

sum of areas = 160 + 151 + 96 = 407 ft

Volume of concrete required = volume of the shape

= sum of areas * thickness

thickness = 6'' = 0.5

= 407 * 0.5

= 203.5 cubic ft

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Answer:

Step-by-step explanation:

193/32

The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

A.

Step-by-step explanation:

First, you do the parenthesis.

4*6 = 24

Then you do the rest.

50 - 24 = 26

This gives you your answer.

The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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Answer:

A worked 20 hours and B worked 15 hours.

Step-by-step explanation:

Given:

Mechanic A hourly rate = $55

Mechanic B hourly rate = $45

Total charged = $1775

Let's assume Mechanic A worked 'A' amount of hours and Mechanic B worked 'B' amount of hours, then

Step 1:

First equation: A + B = 35

Second equation: 55xA + 45xB = 1775

Step 2:

First equation can be written as: A = 35 - B

Step 3: Replace value of A in second equation

Second equation: 55x(35-B) + 45B = 1775

                            : 1925 - 55B + 45B = 1775

                            : (1925 - 1775 )/10 = B

                            : B = 15 hours

A worked = 35 - 15

                = 20 hours

The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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