Find the surface area of the prism.
9 m
5 m. 12m

let the interior angles of the given triangle be angle a b c respectively.

116+a=180 (Sum of angles on a straight line.)

a=180-116

a=64

.......

112+b=180(Sum of angles on a straight line.)

Sum of angles on a straight line.)b=180-112

b=68

....

angle a +b+c=180 (Sum of angles of a triangle)

64+68+c=180

c=180-132

c=48

.,....

angle c +X =180(Sum of angles on a straight line.)

48+X=180

X=132

Therefore the value of X is 132.

2.

solution,

Let the remaining interior angle of the given triangle be y.

Then,

y+108=180(Sum of angles on a straight line.)

y=72

Again,

2x+X+y=180(Sum of angles of a triangle)

3x+72=180

3x=108

X=108÷3

X=36

Therefore the value of X is 36.

3.

solution,

let the remaining interior angle of the given polygon be a and b .

Then,

100+b=180(Sum of angles on a straight line.)

b=80

......

Again,

a+b+110+90=360(Sum of interior angle of the polygon)

a+80+200=360

a+280=360

a=80

.....

a+X=180(Sum of angles on a straight line.)

80+X=180

X=100

Therefore the value of X is 100.

4.

solution,

The given triangle is an isosceles triangle.So their base angles are equal .

43+43+X=180(Sum of angles of a triangle)

X=180-86

X=94

Therefore the value of X is 94.

5.

solution,

Opposite angles of a parallelogram is equal

So ,

X=125

Therefore the value of X is 125.

6.

solution,

Let the remaining interior angle of the triangle be a .

Then,

a+117=180 (Sum of angles on a straight line.)

a=63

Now,

a+X+83=180(Sum of angles of a triangle)

63+83+X=180

146+X=180

X=34

Therefore ,the value of X is 34.

Answer:

She used her bed for her dollhouse

Step-by-step explanation:

Answer:

(x+1)(x-1)(x+3)(x-3)

Step-by-step explanation:

it is a fourth degree trinomial

1) find two number whose sum is -10 and whose product is 9

the two numbers are -1 and -9

2) write the trinomial as a multiplication in this way

(x^2-1)(x^2-9)

3) the two factors are both a difference of tho squares.

so we can rewrite it as

(x+1)(x-1)(x+3)(x-3)

Answer:

\(\frac{x}{5}-11=-13\)

Step-by-step explanation:

11 subtracted ( - 11 ) from the quotient ( division ) of a number ( x ) and 5 is ( = ) -13

\(\frac{x}{5}-11=-13\)

Equation representing the conversion of spherical coordinates to rectangular coordinates are r = √ x² + y² + z² , φ = cos⁻¹( z/r) ,

θ = tan⁻¹(y/x) and Jacobian transformation is given by :

\(d(x, y, z)/ d(r, \theta, \phi ) =\left|\begin{array}{ccc}dx/dr&dx/d\theta&dx/d\phi\\dy/dr&dy/d\theta&dy/d\phi\\dz/dr&dz/d\theta&dz/d\phi\end{array}\right|\)

As given in the question,

In the spherical coordinates are ( r, θ, φ ) to the given rectangular coordinates in the cartesian plane  are ( x, y , z)

Equation representing the conversion of  spherical and rectangular coordinates is given by:

x = rcosθsinφ

y = rsinθsinφ

z = rcosφ

Where

0 ≤ r <∞ ,  0≤ θ< 2π , 0≤φ<  π

r = √ x² + y² + z²

φ = cos⁻¹( z/r)

θ = tan⁻¹(y/x)

Jacobian transformation is given by:

\(d(x, y, z)/ d(r, \theta, \phi ) =\left|\begin{array}{ccc}dx/dr&dx/d\theta&dx/d\phi\\dy/dr&dy/d\theta&dy/d\phi\\dz/dr&dz/d\theta&dz/d\phi\end{array}\right|\)

Where,

dx/dr = cosθsinφ

dx/dθ = -rsinθsinφ

dx/dφ = rcosθcosφ

dy/dr = sinθsinφ

dy/dθ = rcosθsinφ

dy/dφ = rsinθcosφ

dz/dr = cosφ

dz/dθ = 0

dz/dφ = -rsinφ

Therefore, the conversion of spherical coordinates to rectangular coordinates are given by : r = √ x² + y² + z² , φ = cos⁻¹( z/r) ,θ = tan⁻¹(y/x) and Jacobian transformation is given by :

\(d(x, y, z)/ d(r, \theta, \phi ) =\left|\begin{array}{ccc}dx/dr&dx/d\theta&dx/d\phi\\dy/dr&dy/d\theta&dy/d\phi\\dz/dr&dz/d\theta&dz/d\phi\end{array}\right|\)

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The coefficient a is:Therefore, the required coefficients a and b are 5.1969 and -0.0820, respectively.

The given data represents the heat capacity (o) at different temperatures (T) for a given gas as:Therefore, we have to determine heat capacity as a linear function of temperature T using the method of least square. Here are the steps involved in determining the coefficients a and b.1.

Create two columns and determine the mean values of T and o. Therefore, we have:2. Now, determine the deviation of each value of T from its mean value (T - Tmean) and also determine the deviation of each value of o from its mean value (o - omean).

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Answer:

-2 degrees

Step-by-step explanation:

-14 + 12 = -2

Answer:True

Step-by-step explanation:The y-axis is vertical and the x is horizontal

Answer:

160°

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

Angles on a straight line = 180°

⇒ m∠A + m∠B = exterior m∠C

⇒ (5x - 10) + (12x) = (16x)

⇒ 5x - 10 + 12x = 16x

⇒ 17x - 10 = 16x

⇒ 17x = 16x + 10

⇒ x = 10

Therefore, exterior m∠C = 16(10) = 160°

Sum of two interiors=Exterior

So<C

Answer:

6

Step-by-step explanation:

Answer:

The correct answer is 6.

Step-by-step explanation:

I took the test and got it right

Answer:

 6 just 6 Your welcome !!

Step-by-step explanation:  

For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

As given in the question,

For the given rectangular playpen,

Perimeter of rectangular playpen is equal to 150 feet .

Area of the rectangular playpen is equal to at least 1,000 squared feet .

Area = length × width

Let x be the length of the rectangular playpen .

Then its width is equal to 1000 / x.

Substitute the value of length and width in perimeter we get,

Perimeter of rectangular playpen = 2 ( length + width )

⇒ 150 = 2 [ x + (1,000/x)]

⇒ 150 / 2 = ( x² + 1,000 ) / x

⇒ x² + 1000 = 75x

⇒ x² -75x + 1,000 =0

Simplify quadratic equation using discriminant we get,

x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)

⇒ x = (  75 ± √5625 - 4000) /2

⇒ x = (75 ± 40.31) / 2

⇒ x = 57.66 or 17.35

Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

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The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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To maximize the sugar you can gain from street vendors and satisfy your sweet tooth, you can use the following expression:

m[i] = max(m[i-1] + s[i], s[i])

Here, m[i] represents the maximum sugar you can consume so far on the i-th vendor, and s[i] denotes the sugar content of the i-th vendor's offering.

The expression utilizes dynamic programming to calculate the maximum sugar consumption at each step. The variable m[i] stores the maximum sugar you can have up to the i-th vendor.

The expression considers two options: either including the sugar content of the current vendor (s[i]) or starting a new consumption from the current vendor.

To calculate m[i], we compare the sum of the maximum sugar consumption until the previous vendor (m[i-1]) and the sugar content of the current vendor (s[i]) with just the sugar content of the current vendor (s[i]). Taking the maximum of these two options ensures that m[i] stores the highest sugar consumption achieved so far.

By iterating through all the vendors and applying this expression, you can determine the maximum sugar you can gain from the street vendors and satisfy your sweet tooth.

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Answer:

Step-by-step explanation:

x-intercept -> when y = 0

f(x) x-intercept -> (1 , 0)

g(x) x-intercept -> (-1 , 0)

y-intercept -> when x = 0

f(x) y-intercept -> (0 , -1)

g(x) y-intercept -> (0 , 1)

The x-intercept of f(x) is greater than the x-intercept of g(x)

The y-intercept of g(x) is greater than the y-intercept of f(x)

So from the options, the answer is D. The x-intercept of f(x) is greater than the x-intercept of g(x)

Answer:

use the distance formula : √(x2-x1)^2 +(y2-y1) ^2

a. The distribution of X is:

X 1 2 3 4 5 6

P 1/36 1/6 2/9 1/2 8/9 1/36

b. P(X ≤ 3) =  5/12.

c. The expected value of X is 91/36.

a. To find the distribution of X, we can consider all possible outcomes of rolling two dice and determine the probability of each outcome for X = 1, X = 2, X = 3, X = 4, X = 5, and X = 6.

For X = 1, both dice must show a 1, which has probability 1/36.

For X = 2, one die shows a 2 and the other shows a number less than 2, which has probability (1/6)(1/2) = 1/12. There are two ways this can happen, so the total probability is 2/12 = 1/6.

For X = 3, one die shows a 3 and the other shows a number less than 3, which has probability (1/6)(2/6) = 1/18. There are four ways this can happen (the other die can show a 1, 2, 3, or 4), so the total probability is 4/18 = 2/9.

For X = 4, one die shows a 4 and the other shows a number less than 4, which has probability (1/6)(3/6) = 1/12. There are six ways this can happen, so the total probability is 6/12 = 1/2.

For X = 5, one die shows a 5 and the other shows a number less than 5, which has probability (1/6)(4/6) = 1/9. There are eight ways this can happen, so the total probability is 8/9.

For X = 6, both dice must show a 6, which has probability 1/36.

Therefore, the distribution of X is:

X 1 2 3 4 5 6

P 1/36 1/6 2/9 1/2 8/9 1/36

b. To find P(X < 3), we can sum the probabilities for X = 1 and X = 2:

P(X < 3) = P(X = 1) + P(X = 2) = 1/36 + 1/6 = 7/36

To find P(X = 3), we can use the probability for X = 3 from part a:

P(X = 3) = 2/9

Therefore, P(X ≤ 3) = P(X < 3) + P(X = 3) = 7/36 + 2/9 = 5/12.

c. To find E(X), we can use the formula:

E(X) = Σxi P(X = xi)

where xi are the possible values of X and P(X = xi) are their respective probabilities. From the distribution of X in part a, we have:

E(X) = (1/36)(1) + (1/6)(2) + (2/9)(3) + (1/2)(4) + (8/9)(5) + (1/36)(6) = 91/36

Therefore, the expected value of X is 91/36.

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Answer:

Step-by-step explanation:

3x + 4x + x = 16

7x + x = 16

8x = 16

x = 16 : 8

x = 2

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

3 × 2 + 4 × 2 + 2 = 16  (remember PEMDAS)

6 + 8 + 2 = 16

16 = 16

same value the answer is good

Answer:

a = 27

perimeter = 3a

= 3 * 27

= 81

Answer:

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

Step-by-step explanation:

First get the original equation to slope intercept form, \(y=\frac{2}{3}x\)

Then, find the negative reciprocal of the slope. \(\frac{2}{3} -> \frac{-3}{2}\)

Start building the new line in slope intercept form.

\(y-(-2) = (\frac{-3}{2} )(x-(-2))\)

\(y+2=(\frac{-3}{2})(x+2)\)

\(y+2-2=\frac{-3}{2}\left(x+2\right)-2\)

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

Answer:

d. 7 and 16; 8 :14,4:7 and 16:28.

Answer:

D. 7 and 16; 8 : 14, 4 : 7, and 16 : 28

Step-by-step explanation:

1. the first ratio for 8 and 14 is 4 : 7. so that would eliminate the first two answer choices.

2. since the ratio is 4 : 7, that would mean the second value for buses is 7 because the second value for taxis is 4. and the second values for both taxis and buses would be equal to the ratio.

3. 28 is the third value for the bus. and since the ratio is 4 : 7, you have to find the value that 7 can be multiplied by to get 28. 7 multiplied by 4 is 28. you also have to multiply the first number of the ratio (4) by 4. and the product would be 16.

4. So the final answer is D.

The MLE for both scenarios is equal to the fraction (number of successes)/(number of failures), confirming that the answer is: Yes, both MLEs are equal to the fraction (number of successes)/(number of failures).

The maximum likelihood estimate (MLE) of p, the proportion of all mechanics who would correctly diagnose the problem, is the fraction (number of successes)/(number of failures). The MLE for a random sample of 20 mechanics resulting in 6 correct diagnoses is also the same, as it follows the same formula.

The maximum likelihood estimate (MLE) is a statistical method used to estimate the parameters of a statistical model based on observed data. In this case, the MLE of p, the proportion of all mechanics who would correctly diagnose the problem, can be calculated as the fraction (number of successes)/(number of failures). The number of successes refers to the number of mechanics who correctly diagnosed the problem (r = 6), and the number of failures refers to the number of mechanics who incorrectly diagnosed the problem (14).

Now, if we consider a random sample of 20 mechanics and the outcome is 6 correct diagnoses, the MLE in this scenario remains the same. Both situations involve estimating the same parameter, p, and the formula for the MLE remains consistent: (number of successes)/(number of failures). The only difference is the context in which the data is collected, but the calculation for the MLE remains unchanged.

Therefore, the MLE for both scenarios is equal to the fraction (number of successes)/(number of failures), confirming that the answer is: Yes, both MLEs are equal to the fraction (number of successes)/(number of failures).

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Answer:

its c i think

Step-by-step explanation:

Answer:

I really want to say its ASA but im not really sure

Step-by-step explanation:

5.71 x \(10^{-6}\) > 5.71 x \(10^{-8}\) becomes a true statement.

To compare 5.71 x \(10^{-6}\) and 5.71 x \(10^{-8}\), we can rewrite them with the same exponent (since the base is the same):

5.71 x \(10^{-6}\) = 0.00000571

5.71 x \(10^{-8}\) = 0.0000000571

Now we can see that 0.00000571 is greater than 0.0000000571, so:

5.71 x \(10^{-6}\) > 5.71 x \(10^{-8}\)

Therefore, the sign that makes the statement true is > (greater than).

What is an exponent?

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is usually written as a small raised number to the right of a base number, such as in the expression "3²" where 3 is the base and 2 is the exponent. The exponent tells us how many times to multiply the base by itself.

For example, 3² means "3 raised to the power of 2" or "3 squared" and is equal to 3 × 3 = 9. Similarly, 2³ means "2 raised to the power of 3" or "2 cubed" and is equal to 2 × 2 × 2 = 8.

Exponents are commonly used in algebra and other branches of mathematics to simplify expressions and to represent very large or very small numbers in a compact way. They are also used in scientific notation to represent numbers in a format that is easier to work with than writing out all the digits of the number.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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Answer:

Not completely sure, and I know its late but for the other people that look at this, 11.80$

Step-by-step explanation:

I found how many more letters Alexander had over Lucia, then when I got 4 divided it in-between 12.60 - 9.40 (3.20)  I got 0.8. knowing the letter cost i got the initial fee for the mug (5.40) and added 8x0.8 to it, resulting in my answer 11.80$

Penelope has to pay $11.8 for a mug with her own name on it.

Number of letters in Alexander's name = 9

Number of letters in Lucia's name =5

The Difference in the number of letters in both the names

= 9-5

=4 letters

Alexander pays =  $12.60

Lucia pays = $9.40

Difference in payments = 12.60-9.40 = $3.20

It means charge for 4 letters = $3.20

So, charge for 1 letter = $0.80

Number of letters in Penelope's name = 8

So, Penelope will pay = 8*0.80 +fixed fee for the mug

= $6.4 +fixed fee for the mug

The Fixed fee for the mug will be the payment done by Penelope for either Alexander or Lucia minus the charge for each word in the word Alexander or Lucia respectively.

The Fixed fee for the mug = $9.40 - charge for each word in the word "Lucia"

The Fixed fee for the mug = 9.40 - 5*0.80 = $5.40

So, Penelope will pay = 6.4 +5.4 =$11.8

Therefore, Penelope has to pay $11.8 for a mug with her own name on it.

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Answer:

??

Step-by-step explanation:

Which equation?