The sum of 3 consecutive evennumbers is 78.Write the variable representation for each ofthe three numbers in this sequence.

Answer:

(a) The probability that the house size is over 1371 square feet is 0.4483.

(b) The probability that the house size is under 1296 square feet is 0.3974.

(c) The probability that the house size is between 773 and 1637 square feet is 0.9344.

Step-by-step explanation:

We are given that the sizes of houses in Kenton County are normally distributed with a mean of 1346  square feet with a standard deviation of 191 square feet.

Let X = the sizes of houses in Kenton County

The z-score probability distribution for the normal distribution is given by;

                               Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean size of houses = 1346 square feet

            \(\sigma\) = standard deviation = 191 square feet

(a) The probability that the house size is over 1371 square feet is given by = P(X > 1371 square feet)

        P(X > 1371) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{1371-1346}{191}\) ) = P(Z > 0.13) = 1 - P(Z \(\leq\) 0.13)

                                                             = 1 - 0.5517 = 0.4483

The above probability is calculated by looking at the value of x = 0.13 in the z table which has an area of 0.5517.

(b) The probability that the house size is under 1296 square feet is given by = P(X < 1296 square feet)

        P(X < 1296) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{1296-1346}{191}\) ) = P(Z < -0.26) = 1 - P(Z \(\leq\) 0.26)

                                                             = 1 - 0.6026 = 0.3974

The above probability is calculated by looking at the value of x = 0.26 in the z table which has an area of 0.6026.

(c) The probability that the house size is between 773 and 1637 square feet is given by = P(773 square feet < X < 1637 square feet)

       P(773 < X < 1637) = P(X < 1637) - P(X \(\leq\) 773)

      P(X < 1637) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{1637-1346}{191}\) ) = P(Z < 1.52) = 0.9357

       P(X \(\leq\) 773) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{773-1346}{191}\) ) = P(Z \(\leq\) -3) = 1 - P(Z \(\leq\) 3)

                                                             = 1 - 0.9987 = 0.0013

The above probabilities are calculated by looking at the value of x = 1.52 and x = 3 in the z table which has an area of 0.9357 and 0.9987 respectively.

Therefore, P(773 square feet < X < 1637 square feet)  = 0.9357 - 0.0013 = 0.9344.  

Answer:

B. \(4^2\)

Step-by-step explanation:

\(4^7 \times 4^{-5}\)

Apply rule (if bases are same) : \(a^b \times a^c = a^{b + c}\)

\(4^{7 + -5}\)

Add exponents.

\(=4^2\)

Answer:

Step by step explanation

\( {4}^{7} \times {4}^{ - 5} \)

Use product law of indices

i.e

\( {x}^{m} \times {x}^{n} = {x}^{m + n} \)

( powers are added in multiplication of same base)

\( = {4}^{7 + ( - 5)} \)

\( = {4}^{7 - 5} \)

\( = {4}^{2} \)

Hope this helps...

Best regards!

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Using it's concept, it is found that the probability that a randomly selected student is in music/drama is:

P(Music/Drama) = 0.25.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the number of students is given by:

N = 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100.

Of those, the number involved in music/drama is:

D = 7 + 13 + 5 = 25.

Hence the probability is given by:

p = 25/100 = 0.25.

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Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

Answer:

1.5

Step-by-step explanation:

this is because 24 divided by 16 equals 1.5

Answer:

7 bars

Step-by-step explanation:

The equations that break the target are  x = 1, y = x + 5 and x = 4

There are 6 non collinear points

This means that there are at least three equations that can pass through the points

One of these equations is a vertical line that passes through x = 1

So, the equation is x = 1

The second equation passes through (-1, 4) and (0, 5)

The difference between the coordinates of these points is 5

So, the equation i

y - x = 5

y = x + 5

Lastly, we have a vertical line that passes through x = 4

So, the equation is x = 4

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Answer:

A =16.25 cm^2

Step-by-step explanation:

The area of a triangle is given by 1/2 bh where b is the base and h is the height

A = 1/2 (5) * 6.5

A =16.25 cm^2

Answer:

83

Step-by-step explanation:

666

Answer:

Bananas

Step-by-step explanation:

9514 1404 393

Answer:

  x = 22

Step-by-step explanation:

The midsegment BF is half length of the base segment CE, so you have ...

  2x = 88/2

  x = 22 . . . . . divide by 2

The volume of the clay used to make the vase is 36 in³

To determine the volume of clay that was used for the vase, we need to consider that;

The formula for the volume of a rectangular prism is expressed as;

Volume = lwh

Such that;

For the bigger prism, we have;

Volume = 3 × 3 × 5

Multiply the values

Volume = 45 in³

For the hole, we have;

Volume = 4 × 3/2 × 3/2

Multiply the values

Volume = 9 in³

Then, the volume of clay used for the vase = 45 - 9 = 36 in³

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Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Answer:

We are told that circle C has center (-4, 6) and a radius of 2.

We are told that circle D has center (6, -2) and a radius of 4.

If we move circle C's center ten units to the right and eight units down, the new center would be at (-4 + 10), (6 - 8) = (6, -2). So step 1 in the informal proof checks out - the centers are the same (which is the definition of concentric) and the shifts are right.

Let's look at our circles. Circle C has a radius of 2 and is inside circle D, whose radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio, as seen below:

If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. The second step checks out.

Translated objects (or those that you shift) can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.

Thus, the argument is correct and the last choice is best.

Cute copy and paste:

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The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer: Algebra Examples

Logarithm base 4 of 4 is 1.

Step-by-step explanation:

unity

The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.

Ahhh yes, the time-honored permutations.

The permutation format, to start with, is P(n, r).

The formula is:

In this instance, we have P(8, 3).

8 will go in for n and 3 for r. So now let's solve.

\(\frac{8!}{(8 - 3)!}\)    →   \(\frac{8!}{5!}\)   →   \(\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}\)  →   \(8*7*6\)  →  \(336\)

Therefore 336 is our answer. I hope this answers your question.

-Toremi

Answer:

(2•7a5)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 -2a • (0 -  7a4)

Step  2  :

Multiplying exponential expressions :

2.1    a1 multiplied by a4 = a(1 + 4) = a5

Answer:

The length of the longer ladder is 36ft

Step-by-step explanation:

30ft/10ft = 3

12ft x 3 = 36ft

Another way to solve this is by cross multiplying

\(\frac{10}{12}\) = \(\frac{30}{x}\)

10x = 360

x = 36ft

A) y − 4

Four less than an unknown value

B) b + 4

Four more than some number

C) a^4

Some number to the power of four

D) 4x

Four times an unknown value

E) z ÷ 4 =

Quotient of a variable and four

Answer:

\(3.65 \geq\ Length \leq 3.74\)

Step-by-step explanation:

The options are not given.

However, the question is still solvable.

Given

\(Length = 3.7\ inches\) --- Approximated

Required

What could be the actual length

The given length is approximated to nearest tenth.

So, the actual length could be any of the following range

\(3.65 \geq\ Length \leq 3.74\)

This is so because, numbers within this range approximates to 3.7

Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:

Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is

\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)

Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)

Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:

\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)

Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:

det(A+B) = (1)(1) - (1)(1) = 0

Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.

Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).

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Answer: 3/4 is greater than 1/2  

                                   >

Step-by-step explanation:

Answer:

45 degrees

opposite angles are the same so

30+30=60

105+105=210

210+60=270

360-270=90

but since we have 2 angles we divide it by 2

so angle 1 is 45 degrees

hope it helps :)

Answer:

2 would be the answer if the dot means times

Step-by-step explanation:

2^2=4

2^3=8

2^4=16

8/16=1/2

4×1/2=2

The least positive number with this property is given as follows:

N = 280.

A number N gives remainder 0 when divided by 8, it gives remainder 0, when divided by 7 and it is an even multiple of 5, hence the number is multiple of these 3 numbers.

Before obtaining the number, we must obtain the least common multiple of 8, 7 and 5, factoring them by prime factors as follows:

8 - 7 - 5|2

4 - 7 - 5|2

2 - 7 - 5|2

1 - 7 - 5|5

1 - 7 - 1|7

1 - 1 - 1.

Hence:

lcm(8,7,5) = 2³ x 5 x 7 = 280.

280 is an even multiple of 5, as it is an even number, hence it is the least positive number N with the property in this problem.

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Given:

To find:

We need to find the value of x.

Explanation:

Add 0.9 to both sides of the given equation.

Divide both sides of the equation by 1.1.

Final answer:

Answer:

0.46

Hope it helps..

have a great day : )