What is the length of the hypotenuse of the triangle?


Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft

Answer:

[tex]\large \text{$ 4 x^{\frac{14}{3}}y^{\frac{8}{3}}$}[/tex]

Step-by-step explanation:

Given expression:

[tex](8x^7y^4)^{\frac{2}{3}}[/tex]

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

[tex]\implies 8^{\frac{2}{3}} \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]

[tex]\implies 4 \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 4 \cdot x^{\frac{14}{3}}\cdot y^{\frac{8}{3}}[/tex]

[tex]\implies 4 x^{\frac{14}{3}}y^{\frac{8}{3}}[/tex]

Expand [tex]\bf{(8x^{7}y^{4})^{\frac{2}{3} } }[/tex]

[tex]\bf{8^{\frac{2}{3} }(x^{7})^{\frac{2}{3} }(y^{4})^{\frac{2}{3} } }[/tex]

To raise a power to another power, multiply the exponents. Multiply 7 and 2/3 to get 14/3.

[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }(y^{4})^{\frac{2}{3} } }[/tex]

To raise a power to another power, multiply the exponents. Multiply 4 and 2/3 to get 8/3.

[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }y^{\frac{8}{3} } }[/tex]

Calculate 8 to the power of 2/3 and you get 2/4.

[tex]\bf{4x^{\frac{13}{4} }y^{\frac{8}{3} } \ \ ==== > \ \ \ Answer }[/tex]

Based on the number of unit cubes that are fastened together, the number of cubes which will have at least one face painted on is 488 cubes.

The cubes formed one large cube which means that each surface is one cube deep. So two cubes will be painted.

The number of unpainted cubes per surface is therefore:

= 10 - 2

= 8 cubes

Number of unpainted cubes is:

= 8 x 8 x 8

= 512 cubes

Number of cubes with one face painted:

= Total cubes - Number of unpainted cubes

= 1,000 - 512

= 488 cubes.

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Answer:

A 36/100

Step-by-step explanation:

the probability is going to be this because the rates in honor roll and sports are higher than the other 27 that do both.

Answer:

Solution: (-1, 1) and (10/3, 16/3) are Intercepts.

Step-by-step explanation:

Set the equations equal to themselves and solve for x and y.

Hope this helps! :)

Answer:

3x(5-7)°+1(5x-7)°

3x×5-3x×7+1×5x-1×7

15x-21x+5x-7

15x+5x-21x-7

20x-14

The arc length of the circle will be equal to 5.89 units.

The length of the curve on the circumference of the circle making an angle with the centre is called the length of the arc of the circle.

Given that:-

The length of the arc will be calculated as:-

Arc  =  Angle  x  radius

Arc  =  ( 3π / 4  )  x  2.5

Arc  =   5.89 units.

Therefore the arc length of the circle will be equal to 5.89 units.

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Part A

The group of points labeled "T" can be thought of as the main cluster of points. Your teacher might have given another name for it, but this is how I think about it. All of these points are very close to a straight line.

The point R is known as an outlier. It is fairly far from the main cluster, in that it's not near the regression line. You can think of the points in the main cluster as houses along/near a straight road. The outlier house is unfortunately far from that road.

One possible reason for point R is that the student is very talented and can pick up music really easy, thereby not needing that much practice. Another reason is that the student already had tons of prior practice and experience, so they don't need as much practice currently.

============================================================

Part B

We have a strong positive linear association with the main cluster of data points. As mentioned earlier, a straight line is very close to these points. The closer they are to the same straight line, the stronger the correlation.

We have positive correlation because as x goes up, so does y. The variables increase together. Negative correlation happens when x and y go in opposite directions (one goes up, the other goes down).

The outlier point R pulls on the regression line to make it slightly not near the main cluster. The line tries its best to be near all of the points, and that includes the outlier. In some situations, the outlier is ignored and regression is done on the other set of points.

As you can probably guess, the outlier dilutes the strength of the correlation. The further the outlier, the weaker the correlation gets.

Answer:

Here you go!

Step-by-step explanation:

A) The group of points labeled T called cluster. The point labeled R called outlier. Student because of being proficient on the piano before practice was measured.

B) A positive correlation is a relationship between two variables that tend to move in the same direction

Answer:

  x⁷y⁷

Step-by-step explanation:

An exponent signifies the base is a repeated factor in the product. The exponent is the number of times it is a factor.

__

The term (xy)^7 means (xy) is a factor 7 times:

  = (xy)·(xy)·(xy)·(xy)·(xy)·(xy)·(xy)

The commutative and associative properties of multiplication let us rearrange this to ...

  = (x·x·x·x·x·x·x)·(y·y·y·y·y·y·y)

  = (x^7)(y^7)

The expression can be simplified to ...

  [tex](xy)^7 =\boxed{x^7y^7}[/tex]

_____

The rule of exponents is ...

  (ab)^c = (a^c)(b^c)

Answer:

X > 3

Step-by-step explanation:

When divided or multiplied by a negative number the inequality will change

Answer:

approximately 4.23 cm

Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.

Let suppose that the iron beam has an uniform density, the mass of the iron beam (m), in gram, is equal to the product of its density (ρ), in grams per cubic centimeter, and its volume (V), in cubic centimeters:

m = ρ · V     (1)

If we know that ρ = 10504 cm³ and V = 7.8 g/cm³, then the mass of the iron beam is:

m = (7.8 g/cm³) · (10504 cm³)

m = 81931.2 g

Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.

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Answer:

E

Step-by-step explanation:

1 2/3

Divide 5/3 and you get 1 2/3

Answer:

E) 1 2/3

Step-by-step explanation:

5 divided between 3 buckets in 5/3 which in a mixed number is 1 2/3

The equation of the circle is:

[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]

The general equation for a circle of radius R and center (a, b) is:

[tex](x - a)^2 + (y - b)^2 = R^2[/tex]

Here the center is (-4, -2), and it contains the point (4, -17), so the radius is:

[tex]R = \sqrt{(4 - (-4))^2 + (-2 + 17)^2} = 17[/tex]

So the equation of the circle is:

[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]

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The Probability of that more than 7 of them germinate is 0.2948.

We are to determine the probability that more than 7 of 10 seeds (i.e. 8, 0r 9 0r 10) germinate.

The probability that all 10 seeds germinate is equal 0.80¹⁰= 0.1073 = 10.73%.

The probability that only the first (only the second, etc ) seed does not germinate is equal 0.20 X 0.80⁹= 0.0268 = 2.68%.

The probability that 6 seeds germinate is the sum of the probabilities that only the first seed does not germinate, only the second one does not germinate, etc, and equals to 10 X 0.0268  = 0.268 = 26.8%.

The total probability that more than 7 of 10 seeds germinate is the sum of the probabilities that 10 seeds germinate and that 7 seeds germinate, i.e. 2.68 % + 26.8 % = 29.48 %.

Thus, The Probability of that more than 7 of them germinate is 0.2948.

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The model in which the lateral surface meets the base at right angle is : Model 1.

The lateral surface of an object is all surfaces  of that object excluding its base and top.

Analysis:

To know the exact model, we check for the models in which their dimensions form a Pythagorean triplet otherwise a right-angled triangle.

For Pythagorean triplet, the square of the diagonal must be equal to the sum of squares of the other two sides.

Model 1

Diagonal = 50cm, radius = 14cm, lateral height = 48cm

[tex](50)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](48)^{2}[/tex]

2500 = 196 + 2304

2500 = 2500. Forms Pythagorean triplet

Model 2

Diagonal= 37cm, radius = 6cm  lateral height = 35cm

[tex](37)^{2}[/tex] = [tex](35)^{2}[/tex]+ [tex](6)^{2}[/tex]

1369 = 1225 +36

1369 [tex]\neq[/tex] 1261

Model 3

Diagonal = 60cm, radius = 20cm  lateral height = 40cm

[tex](60)^{2}[/tex] = [tex](20)^{2}[/tex] + [tex](40)^{2}[/tex]

3600 = 400 + 1600

3600 [tex]\neq[/tex] 2000

Model 4

Diagonal = 30cm, radius = 24cm, lateral height = 9cm

[tex](30)^{2}[/tex] = [tex](24)^{2}[/tex] + [tex](9)^{2}[/tex]

900 = 576 + 81

900 [tex]\neq[/tex] 657

Therefore the lateral surface model 1 meets the base at right angle

In conclusion,  the lateral surface of model 1 meets the base at right angles as the dimensions form a right-angled triangle.

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Answer:

the answer is B have an amazing day

Step-by-step explanation:

Answer:

18 . 75

Step-by-step explanation:

1.50's half is 0.75 , Then multiply £1.50 × £25

Answer:

one book=1.50

the other half priced book=0.75

so 0.75+1.50=2.25

25/2.25

=11.111

so eleven books

Answer:

C

Step-by-step explanation:

Answer:

  M(-1/2, -1/2, 1/2)

Step-by-step explanation:

To find the midpoint of a line segment, average the coordinates of the end points.

  M = (A +B)/2

__

  M = (V +W)/2

  M = ((3, 7, -6) +(-4, -8, 7))/2 = (3-4, 7-8, -6+7)/2 = (-1, -1, 1)/2

  M = (-1/2, -1/2, 1/2)

The midpoint between V and W is M(-1/2, -1/2, 1/2).

Answer:

P(A) = 5/12

P(B) = 1/2

Step-by-step explanation:

A) Sum greater than 7

If the sum needs to be >7, then it can be 8, 9, 10, 11, and 12.

There are 26 out of 36 events where the sum is >7, thus P(A) = 15/36 = 5/12.

B) Sum is even

If we see in an overview of the sum distribution, there is a balanced division between odd and even numbers, thus the probability is very likely to be 1/2. Now let's make sure of it:

If the sum needs to be even, which means divisible by 2, then it can be 2, 4, 6, 8, 10, and 12.

There are 18 out of 36 events where the sum is even, thus P(B) = 18/36 = 1/2.

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1.  solid and liquid

2. Evaporation changes liquid water to water vapour.

for #1: for example, it's raining, when it rains, the rain is water (liquid).

Or it's snowing, the snow is solid.

for #2: for example, when you are making tea, you need hot water, so you add heat, then the water lessens because it's transforming to gas, and sometimes you can see it.

Answer:

1. solid and liquid

2. water vapor (gas)

Answer:

n = 7.

Step-by-step explanation:

Sum S of an AP = (n/2)[2a + d(n - 1)]

112 = (n/2)[2*25 - 3(n -1)]

n/2 (53 - 3n) = 112

n(53 - 3n) = 224

-3n^2 + 53n - 224 = 0

3n^2 - 53n + 224 = 0

(3n - 32 )(n  - 7 ) = 0

n = 7, 32/3

So n must be 7 as its a whole number.

Answer:

Choice B and Choice C

Step-by-step explanation:

Hello! This is how I solved this question:

(10 x 8 x 2) + (3 x 3 x 4) = 160 + 36 = 196ft^3

(10 x 3 x 2) + (5 x 4 x 2) = 60 + 40 = 100ft^3

(8 x 4 x 2) + (3 x 6 x 2) = 64 + 36 = 100ft^3

(8 x 10 x 3) + (4 x 5 x 2) = 240 + 40 = 280ft^3

Choice B and Choice C are the same values, and knowing that you need two of the same values for the volume of the figure must be the same. Giving you your two answers from simply multiplying and adding the answers.

Hope this helps, don't hesitate to ask if you have additional inquiries!

Answer:

Step-by-step explanation:

The number of elements in a power set = the number of subsets of a set

Formula:

Let S be a sent ,the number of elements of  the power set of S =

[tex]2^{\text{card(S)} }[/tex]

Where card(S) = number of element of S itself.

=======================================

In this case :

Card(S) = 3

Then

the number of elements of  the power set of S =

[tex]2^{3}=8[/tex]

Answer:  X = 3 and Y = 0           3,0

Answer:

[tex]y^{5}\times y^{3}=y^8[/tex]

Step-by-step explanation:

exponent property :

[tex]\left( a\right)^{n} \times \left( a\right)^{m} =\left( a\right)^{n+m}[/tex]

………………………………………

[tex]\Longrightarrow y^{5}\times y^{3}=y^{5+3}=y^8[/tex]

Answer:

you will subtract 6 from 5 then your answer will be  g ≥ -1

Step-by-step explanation:

hope this helps

Answer: Please see the analysis

Answer

2 1/8

Step-by-step explanation 10–7 7/8=(10 – 7) + ( 0–7/8)= 3 +0 × 8 – 7/8= 3 + 08– 78=  3 + 0 – 78=  3 + -7/8 = 2 1/8

The solution to the quadratic equation 6x² + 6 = 12x is x = 1

The quadratic equation is given as:

6x² + 6 = 12x

Equate the equation to 0

6x²  - 12x + 6 = 0

Expand the equation

6x²  - 6x - 6x + 6 = 0

Factorize the expression

6x(x  - 1) - 6(x - 1) = 0

Factor out x - 1

(6x - 6)(x  - 1) = 0

Split

6x - 6 = 0 or x - 1 = 0

Solve for x in both instance

x = 1 or x = 1

Hence, the solution to the quadratic equation 6x² + 6 = 12x is x = 1

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