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Find the volume of the sphere. Round your answer to the nearest tenth.

Answer:

  x²

Step-by-step explanation:

The area of rectangle ABJH is the product of its dimensions.

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The dimensions are given as ...

  AB = x

  AH = x

The area of ABJH is ...

  area = length × width = (x) × (x) = x²

The area of ABJH is x².

Answer:

  58.1 cm

Step-by-step explanation:

The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.

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The theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...

  c² = a² +b²

For the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.

  30² = 7.5 +b²

  b² = 900 -56.25 = 843.75

  b = √843.75 ≈ 29.0473

The length of each support rod is twice this value, so ...

  rod length = 2b = 2(29.0473) = 58.0947

Each support rod is about 58.1 cm long.

Answer:

*r = R/100 = 8%/100 = 0.08 per year, A = P(1 + rt)

a) A = 6000[1 + (0.08 × 5)] = 8400

b) A = $8,400.00

Answer:

  a) $2400

  b) $8400

Step-by-step explanation:

The simple interest formula can be used to find the amount of interest. The amount collected at the end of the period is the total of principal and interest.

__

The simple interest is given by the formula ...

  I = Prt . . . . . . P is the principal amount, r is the annual rate, and t is the number of years

For this investment, the interest is ...

  I = $6000·0.08·5 = $2400

The simple interest amounts to $2400.

__

The amount collected at the end of 5 years is the principal plus interest:

  P +I = $6000 +2400 = $8400

The total collected is $8400.

Answer:

3

Step-by-step explanation:

blue, white, and red colors

Answer:

Given:

To Find:

Solution:

According to the question:

(1) The product of 7 & x

➝ 7x

(2) The sum of 9 and 3 and 2

➝ 9 + 3 + 2

➝ 14

From (1) and (2) , we get:

➝ 7x = 14

➝ x = 14 ÷ 7

➝ x = 2

Let's check whether our answer is correct or not:

• To check our answerer, let's putting the value of x :

♣ 7(2) = 14

♣ 14 = 14 ✅

Thus, our answer is correct....The value of x is 2.

Answer:

[tex]x = 49degrees[/tex]

Step-by-step explanation:

[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]

The required value of x for the given figure is 49°.

A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.

The sum of the angles on a straight line is always 180°.

In the given figure the angles 131° and x° are on the same straight line.

Since, the sum of the angles on a straight line is 180°.

The following equation can be written for the given figure,

x + 131 = 180

=> x = 180 - 131

       = 49

Hence, the value of x for the given figure is 49°.

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Answer:

-9,40

Step-by-step explanation:

Midpoint Formula:

[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]

Answer:

Midpoint = (−9,40)

Step-by-step explanation:

1. Height of the equilateral triangle is: √3 units

2. Area of the equilateral triangle = √3 units²

3. Area = √3/4 x², when each side is x.

A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.

1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:

h = √(2² - 1²)

h = √(4 - 1)

h = √3

2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)

Area of the equilateral triangle = √3 units²

3. If x is the side length of the equilateral triangle, we would have:

height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x

Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²

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Answer:

x = -6.

Step-by-step explanation:

First thing to notice is that this is the third angle in a triangle, and all 3 angles have to equal 180.

Subtract 75 and 40 from 180 to get the missing angles value.

180 - 75 - 40 = 65

So now we know the missing angle has to be 65, or can be written as:

x + 71 = 65.

To solve this, just subtract 71 from both sides.

x = -6.

71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.

71 + y = 180

y = 109

The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.

109 + 46 + x = 180

x = 25

Answer: x = 25 degrees

Hope this helps!

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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The weekday hours you purchased is 5 hours.

The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.

2a + 10b = 220 equation 1

a + b = 26 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 260 equation 3

Subtract equation 3 from equation 2

8a = 40

a = 5 hours

(5 x 3) + b = 26

15 + b = 26

b = 26 - 15

b = 11 hours

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The answer of the following questions is discussed below

Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.

The radius of each circle

r1= 2.5 inches.

r2= 1 inches

Area of circle large circle,

= πr1²

=3.14*2.5*2.5

=19.625 inch²

Area of small circle,

= πr2²

= 3.14*1*1

=3.14 inch²

Area of large circle minus area of small circle,

= 16.485  inch²

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education Roman Catholic School one five two weeks

Answer:

a) 150

b) 2650

Step-by-step explanation:

6% of 2500 is 150

150 + 2500 = 2650

Answer:

Step-by-step explanation:

The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.

The first attachment shows the coefficient matrix and its determinant.

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The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.

  [tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]

This multiplication is shown in the second attachment. It tells us ...

  [tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]

Answer:

Step-by-step explanation:

Depending on whether or not the g(x) is x^2 or 2x, I have both ways.

If g(x) is x^2 - 9...

--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11

If g(x) is 2x...

--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11

Hope this helps!

The number of ways there are to get to the point (7,4) if you have to pass through the point (2,2) is; 1266 ways

The formula to get the number of ways to get to the lattice point (x, y) (supposing x, y ≥ 0) by taking steps of one unit each either in the eastward or northward direction is exactly;

(x + y)

          = (x + y)!/(x!y!)

(   x   )

Thus, number of ways from (0, 0) to (2, 2) = (2 + 2)!/(2!2!) = 6 ways

Number of ways to get to point (7,4) from (2, 2) is;

((7 - 2) + (4 - 2))!/(2!2!) = 7!/(2!2!) = 1260

Thus, total number of ways = 1266 ways

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Answer:

There can be alot of equations for this since you didn't say anything specific. But since u didnt say anything specific, this can be one of the equations: 20 + 8, 30 - 2, 4 x 7

Let's see

[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]

Use distributive law

[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]

[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]

Answer:

[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Step-by-explanation:

Given expression:

[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]

Use the Distributive Property Law  (b ± c)a = ab ± ac
to remove the parentheses:

[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]

Simplify by multiplying the coefficients of each term:

[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:

[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]

[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Answer:

angles in a triangle add up to 180°

5:12:13 = 30

180 ÷ 30 = 6

6 × 5 = 30°

6 × 12 = 72°

6 × 13 = 78°

angles = 30°, 72°, 78°

Answer:

one of them is two trapezoids

Step-by-step explanation:

Answer:

58°

Step-by-step explanation:

Apply trig inverse properties

W = arccos(0.53)

W = 2[tex]\pi[/tex] - arccos(0.53)

Answer:

-6x²+xy-6y²

Step-by-step explanation:

3y² - 4x² + xy - 2x² - 9y²

-4x²+ xy - 2x² - 6y²

-6y² + xy - 6y²

Answer:

−6x² + xy − 6y²

Step-by-step explanation:

Simplify 3y²-4x² + xy - 2x² - 9y²​

Step 1

Subtract 9y² from 3y²

−4x² +xy −2x² −6y²

Step 2

Subtract 2x²  from −4x²

−6x²  + xy  − 6y²

Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

p = 0.7, n = 8.

The probability that fewer than 7 of them show up is given by:

[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]

In which:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]

[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]

Then:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]

[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]

0.7447 = 74.47% probability that fewer than 7 of them show up.

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Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.

A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.

In Mathematics, there are four measures of dispersion for a data set and these include the following:

In this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.

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