15. (01.01)
What is the value of the radius of the following circle with an area of 154 cm2? (1 point)
Area

154 cm^2

*4.9 cm
*7.0 cm
*25 cm
*68 cm​

Answer:

let her money in the beginning =X

20%of X=800.

4000

Answer:

x=7

Step-by-step explanation:

6(x-5)=12

We will use the distributive property to get the answer of 6(x-5)

6(x-5)=12

6x-30=12

6x=12+30

6x=42

6x/6=42/6

x=7

Proof:

6(x-5)=12

6(7-5)=12

42-30=12

12=12 or

6(7-5)=12

6(2)=12

12=12

Hope this helps ;) ❤❤❤

Answer:

C = 5n + 100

Step-by-step explanation:

The cost (C) to make a book bag is an initial fee of $100 with an additional $5 for each bag (n) made.  The equation will look like

C = 5n + 100

Answer:

Rearrange the numbers to their like terms.

which is 2x-x=56-20.

x=36.

The solution to the equation is x = 36.

To solve the equation 20 + 2x = x + 56 for the variable x, you can follow these steps:

Step 1: Move all terms containing x to one side of the equation by subtracting x from both sides:

20 + 2x - x = x + 56 - x

20 + x = 56

Step 2: Subtract 20 from both sides to isolate the x term:

20 + x - 20 = 56 - 20

x = 36

Therefore, the solution to the equation is x = 36.

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Answer:

[tex]\delta=0.0333[/tex]

Step-by-step explanation:

[tex]|x^2-1}=|x-1||x+1|<0.1[/tex]

[tex]|x|-|1|<|x-1|<1[/tex]

[tex]|x|<2[/tex]

[tex]|x+1|<3[/tex]

Hence

[tex]|x-1|<\frac{0.1}{|x+1|}[/tex]

[tex]|x-1|<\frac{0.1}{3}=0.333 =\delta[/tex]

Hopefully you get what I meant!!

Answer:

Deon

Step-by-step explanation:

Gerain has 2 parts almonds in 5 parts total, i.e., 2/5 = 0.40

Deon has 3 parts almonds in 7 parts total, i.e., 3/7 ≈ 0.43

So Deon's concentration is higher

Answer:

Deon has a higher concentration

Step-by-step explanation:

Answer:

x^2 = 4

Step-by-step explanation:

X^8 = (2^2)^4

Rewriting

x^8 as (x^2) ^4  since we know that a^b^c = a^(b*c)  and 2*4 = 8

(x^2) ^4 =  (2^2)^4

Since the exponents are the same the bases must be the same

x^2 = 2^2

x^2 = 4

Answer:

120 tries

Step-by-step explanation:

You can try 5 different wires in the first connection.

Then you have 4 wires left, so you try 4 wires in the second connection. Remember, you are now trying 4 wires for each of the first 5, so up to here you already made 4 * 5 tries = 20 tries.

Next you try 3, then 2, then you have 1 left.

Number of tries: 5 * 4 * 3 * 2 * 1 = 120

Answer: 120 tries

Answer:

  14 ft

Step-by-step explanation:

The area of a trapezoid is given by

  A = (1/2)(b1 +b2)h

You want ...

  A ≥ 259

  (1/2)(14.5 +22.5)h ≥ 259

  37/2·h ≥ 259

  h ≥ 259(2/37)

  h ≥ 14 . . . . . . . feet

The height must be no less than 14 feet.

Answer:

[tex]|tv = 14[/tex]

Step-by-step explanation:

Given

[tex]|tv = x + 10[/tex]

[tex]|tu = 3x - 8[/tex]

[tex]|uv = 10[/tex]

Required

Determine length of tv

Length tv is calculated by adding lengths tu and uv.

In other words

[tex]tv = tu + uv[/tex]

Substitute values for tv, tu and uv

[tex]x + 10 = 3x-8+10[/tex]

Collect like terms

[tex]x - 3x = -8+10 -10[/tex]

[tex]-2x = -8[/tex]

Divide both sides by -2

[tex]x = 4[/tex]

Recall that [tex]|tv = x + 10[/tex]

Substitute 4 for x

[tex]|tv = 4 + 10[/tex]

[tex]|tv = 14[/tex]

Hence, the length of line segment tv is 14

Answer:

it's false.... not sure

Answer:

Step-by-step explanation:

[tex]x = 2\\ w = -1\\ y = 6\\ z = 4\\x^2+4w-2y\\[/tex]

[tex](2)^2 +4(-1) -2(6)\\4 -4 -12\\0-12\\\\=-12[/tex]

Answer:

4x² + 4w - 2y

4(2)² + 4(-1) - 2(6)

4×4 + (-4) - 12

16 - 4 - 12

12 - 12

0 is the answer

Answer:

Convertir- 11°20'49"

Step-by-step explanation:

I New the answer):

Answer:

A.

Step-by-step explanation:

The visual representation is All integers are also rational numbers

A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.

So, we have sets of real number.

As. we know

All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.

Hence,  integers are also rational numbers

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Answer:

Step-by-step explanation:

70 ÷ 15 = 4.66

4.66 × 39 = 181.974

Answer:

x = 109/216

Step-by-step explanation:

Solve for x:

1/36 = 6 x - 3

Hint: | Reverse the equality in 1/36 = 6 x - 3 in order to isolate x to the left hand side.

1/36 = 6 x - 3 is equivalent to 6 x - 3 = 1/36:

6 x - 3 = 1/36

Hint: | Isolate terms with x to the left hand side.

Add 3 to both sides:

6 x + (3 - 3) = 3 + 1/36

Hint: | Look for the difference of two identical terms.

3 - 3 = 0:

6 x = 1/36 + 3

Hint: | Put the fractions in 1/36 + 3 over a common denominator.

Put 1/36 + 3 over the common denominator 36. 1/36 + 3 = 1/36 + (36×3)/36:

6 x = 1/36 + (36×3)/36

Hint: | Multiply 36 and 3 together.

36×3 = 108:

6 x = 1/36 + 108/36

Hint: | Add the fractions over a common denominator to a single fraction.

1/36 + 108/36 = (1 + 108)/36:

6 x = (1 + 108)/36

Hint: | Evaluate 1 + 108.

1 + 108 = 109:

6 x = 109/36

Hint: | Solve for x.

Divide both sides by 6:

x = (109/6)/36

Hint: | Multiply 36 and 6 together.

36×6 = 216:

Answer: x = 109/216

Answer:

  x = 109/216

Step-by-step explanation:

Add 3, divide by 6.

  [tex]\dfrac{1}{36}=6x-3\\\\3+\dfrac{1}{36}=6x\\\\\dfrac{109}{(36)(6)}=\boxed{x=\dfrac{109}{216}}[/tex]

Answer:

2

Step-by-step explanation:

Given AP where:

To find

Since

Initial equations will change as:

Comparing the above:

Then:

The first term is 2

Answer:

15.38%

Step-by-step explanation:

there are four 10 cards and four jack cards.

4+4=8

you want to get one from 52 cards, so it's 8 out of 52. 8/52

to calculate the percentage, you multiply 8 by 100, then divide by 52.

8*100/52=15.38 (rounded answer)

Answer:

$37500

Step-by-step explanation:

For this we can simply create a proportion of the percentages.

.4 / 1 == 15000 / x

Now we solve for x:

x = 15000/.4

x = 37500

Thus, the cost of the car was $37,500.

Cheers.

Answer:

x = [tex]\frac{8}{13}[/tex]

Step-by-step explanation:

Given

6(8x - 1) = 9(x + 2) ← distribute parenthesis on both sides

48x - 6 = 9x + 18 ( subtract 9x from both sides )

39x - 6 = 18 ( add 6 to both sides )

39x = 24 ( divide both sides by 39 )

x = [tex]\frac{24}{39}[/tex] = [tex]\frac{8}{13}[/tex]

Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]

Then, replacing with point P and normal vector n:

[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

[tex]z = \frac{180-36x-20y}{45}[/tex]

When z = 0:

[tex]y = 9 + \frac{-9x}{5}[/tex]

When z=0 and y=0:

x = 5

Then, triple integral is:

[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]

Calculating:

[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]

[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]

[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]

[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]

[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

The tripple integration will be   [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5

The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.

To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]

Then, replacing with point P and normal vector n:

[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

[tex]z=\dfrac{180-36x-20y}{45}[/tex]

When z = 0:

[tex]y=9+\dfrac{-9x}{5}[/tex]

When z=0 and y=0:

x = 5

Then, triple integral is:

[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]

Calculating:

[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]

[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]

[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]

[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]

[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]  

The volume of the tetrahedron is 1087.5 cubic units.

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Answer:

84 sq. units

Step-by-step explanation:

Total area is:

Answer:

C

Step-by-step explanation:

Given

( [tex]\frac{3m}{4}[/tex] - 2 ) + 8 ( remove parenthesis )

= [tex]\frac{3m}{4}[/tex] - 2 + 8

= [tex]\frac{3m}{4}[/tex] + 6

= [tex]\frac{3m}{4}[/tex] + [tex]\frac{24}{4}[/tex] ← add the numerators leaving the denominator

= [tex]\frac{3m+24}{4}[/tex] → C

Answer:

2nd Option.

Step-by-step explanation:

The 2 lines are intersecting each other. That means the point of intersection is the solution set to the systems of linear equations.

This translate into that point (4, 4) in the graph works for both line A and line B.

The equations can be graphed immediately because the slopes and the y-intercepts are known

The system of equations is given as:

The equations in the system are linear equations, and they are represented as:

[tex]y = mx + b[/tex]

Where:

From the given system, we can find the slopes and the y-intercepts of both functions easily

Hence, the equations can be graphed immediately because the slopes and the y-intercepts are known

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Answer:

774 lb

Step-by-step explanation:

weight = volume * density

radius = diameter/2

volume = (4/3)πr^3

volume = (4/3)(3.14)(4.7/2 ft)^3

weight = (4/3)(3.14)(4.7/2 ft)^3 * 14.25 lb/ft^3

weight = 774 lb

Answer:

No,the ray AB and BA are not same because the ray AB denotes the ray(light) is coming from the direction through A while the ray BA denotes the ray is coming from the direction through B.

Answer:

9 containers of frosting

Step-by-step explanation:

25 x 18 x 4, gives you 1800 square inches, divide 1800 by 200 and you get 9

Answer:

The test statistics is [tex]t = 1.610[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  210  

     The  sample  mean is  [tex]\= x = 5.0 \ pounds /square \ inch[/tex]

       The  standard deviation is  [tex]\sigma = 0.9 \[/tex]

       The  population   mean is  [tex]\mu = 4.9 \ psi[/tex]

Generally the test statistics is mathematically evaluated as

             [tex]t = \frac{\= x - \mu}{ \frac{\sigma }{ \sqrt{n} } }[/tex]

     =>    [tex]t = \frac{5 - 4.9}{ \frac{ 0.9 }{ \sqrt{ 210 } } }[/tex]

=>        [tex]t = 1.610[/tex]

Answer:

3 1/2

Step-by-step explanation:

1/4 + 1/4

(1x4) + (1x4)

=_________

4x4

=8/16

8÷8

=_________

16÷8

=3 1/2