Solve each matrix equation. If an equation cannot be solved, explain why.

[6 10 13 4 -2 7 0 9 -8] X = [84 18 56]

Answer:

4.236

Step-by-step explanation:

Answer:

Use the formula y-3= 1/4(x--7) ---> y-3= 1/4(x+7)

4.75 is the y intercept

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Based on the geometric theorem, the value of x, to the nearest tenth is: 8.2.

The geometric theorem states the relationship between the length of the altitude of a right triangle and the lengths of the two small segments formed on the hypotenuse.

The theorems states that:

The length of the altitude = the geometric mean of the two segments.

In the image given below which shows the right triangle, the segments formed on the hypotenuse are x and 24 units, while the altitude of the triangle is 14.

Therefore, based on the geometric theorem, we have:

14 = √(x * 24)

Solve for x:

14² = x * 24

196 = 24x

196/24 = 24x/24

x ≈ 8.2 (nearest tenth)

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Answer:

f = 11.52

Step-by-step explanation:

8/f = cos 46°

8 = f cos 46°

f = 8/cos 46° = 11.52

Answer:

45 pages a day

450(pages)/10(days)

=45 pages a day

Answer:

16

Step-by-step explanation:

The absolute value always gives a positive value , that is

| - a | = | a | = a , then

| - 16 | = | 16 | = 16

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

HEY!

Step-by-step explanation:

18/9) *4 = 8 moons. Hence, Neptune has a total of 8 moons according to the given conditions.

The rejection region in a one-tailed hypothesis test with a significance level of 0.05 is the upper 5% of the distribution. The correct answer is option A.

Thus, the rejection region in a one-tailed hypothesis test with a significance level of 0.05 is the upper 5% of the distribution.

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Answer:

(-3, 2)

Step-by-step explanation:

To find the coordinates of a point being reflected across the x-axis you need to use the rule (x, -y) on the point. Example: If the point was (4, 7) you would make the y value negative since it is positive, which would give you (4, -7) which is the point after being reflected across the x-axis. I know this one is for reflecting on the x-axis but for future problems if you want to reflect across the y-axis you do the same thing but with the x value, so (-x, y)

Answer:

  2 × (14 – 9) – (17 – 14) = 7

Step-by-step explanation:

Evaluate the choices to see which is true.

(2 x 14) – 9 – (17 – 14) = 7   ⇒  28 -9 -3 ≠ 7

2 x (14 – 9) + (– 17 – 14) = 7   ⇒  2(5) +(-31) ≠ 7

(2 x 14) – (9 – 17) – 14 = 7   ⇒   28 -(-8) -14 ≠ 7

2 x (14 – 9) – (17 – 14) = 7   ⇒   2(5)- 3 = 7 . . . . true

The missing terms of the sequence are 15.75 and 7.875, and the sequence is geometric.

What is sequence?

In mathematics, a sequence is an ordered list of numbers or objects in a specific pattern or order. Each individual element in the sequence is called a term or member of the sequence.

To determine the missing terms of the sequence and determine its pattern (whether arithmetic, geometric, or neither), let's examine the given sequence: 252, 126, 63, 63/2, __, __.

First, let's check if the sequence has a common difference between consecutive terms to determine if it is an arithmetic sequence. We'll calculate the differences between consecutive terms:

Difference between the 2nd and 1st terms: 126 - 252 = -126

Difference between the 3rd and 2nd terms: 63 - 126 = -63

Difference between the 4th and 3rd terms: (63/2) - 63 = -63/2

The differences are not constant, so the sequence is not arithmetic.

Next, let's check if the sequence has a common ratio between consecutive terms to determine if it is a geometric sequence. We'll calculate the ratios between consecutive terms:

Ratio between the 2nd and 1st terms: 126/252 = 1/2

Ratio between the 3rd and 2nd terms: 63/126 = 1/2

Ratio between the 4th and 3rd terms: (63/2) / 63 = 1/2

The ratios are constant (1/2), so the sequence is geometric.

Since the sequence is geometric with a common ratio of 1/2, we can use this ratio to find the missing terms.

To find the next term, we multiply the previous term by the common ratio:

(63/2) * (1/2) = 63/4 = 15.75

To find the term after that, we multiply the previous term by the common ratio again:

(63/4) * (1/2) = 63/8 = 7.875

Therefore, the missing terms of the sequence are 15.75 and 7.875.

In summary, the missing terms of the sequence are 15.75 and 7.875, and the sequence is geometric.

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The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Given data ,

The angles of the triangle ABC are

∠A = ( 2x + 10 )°

∠B = ( 4x + 2 )°

Let angle ∠C be y

The sum of ∠A + ∠B + ∠C = 180°  

So ,

( 2x + 10 )° + ( 4x + 2 )° + y = 180°   be equation (1)

Now , we can see that AD is a straight line and C is a point on the line AD

The total angle of C on the line AD is 180°

So , ( 5x + 27 )° + y = 180°

y = 180° - ( 5x + 27 )°   be equation (2)

Substituting the value of equation (2) in equation (1) , we get

( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°

On Simplifying , we get

( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0

( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0

x - 15 = 0

Adding 15 on both sides , we get

x = 15°

Substituting the value of x in the ∠A , ∠B and ∠C equation , we get

∠A = ( 2x + 10 )°

     = 40°

∠B = ( 4x + 2 )°

     = 62°

∠C = 180° - ( ∠A + ∠B )

     = 180° - 102°

     = 78°

Therefore , the angles of the triangle ABC are 40° , 62° and 78°

The measure of ( 5x + 27 )° is

= ( 5 x 15 + 27 )°

= 102°

Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

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Answer:

~8300,000 or 800,000

Step-by-step explanation:

For the year in which they earned $176,500, the partners will receive $52,950, $35,300, and $88,250 respectively.

Here let the partners be A, B, and C.

According to the question, A: B: C = 3: 2: 5

This implies that if the profits are divided into

3 + 2 + 5 = 10 equal parts, 3 of those parts will go to A, 2 of those parts will go to B and 5 of those parts will go to C.

Here the profits for the year are $176,500.

Now dividing them into 10 equal parts will give us the value of each part to be

$176, 500/10 = $17,650

Hence A will receive $17,650 X 3 = $52,950

B will receive $17,650 X 2 = $35,300

C will receive $17,650 X 5 = $88,250

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The measure of the angle ∠BAD will be 110°. Then the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The central angle is double the angle at the periphery that was subtended by the same chords.

DR is the tangent to Circle O. If m of angle DB = 140°. Then the equation is given as,

∠BCD = (1/2) arc DB

∠BCD = (1/2) x 140°

∠BCD = 70°

We know that the sum of the opposite angle of the cyclic quadrilateral is 180°. Then we have

∠BAD + ∠BCD = 180°

∠BAD + 70° = 180°

∠BAD = 110°

The measure of the angle ∠BAD will be 110°. Then the correct option is B.

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The missing graph is given below.

Answer:

B. x ≥ 3 or x ≤ −2

Step-by-step explanation:

Inequalities

Solve the inequality:

\(x^2-x\ge 6\)

Subtracting 6:

\(x^2-x-6\ge 0\)

Factoring:

(x-3)(x+2) ≥ 0

We have a product that must be greater or equal to 0. This can only happen if:

x - 3 ≥ 0  and x + 2 ≥ 0

Or:

x - 3 ≤ 0  and  x + 2 ≤ 0

The first couple of conditions yields to:

x ≥ 3 and x ≥ -2

Which lead to the solution

x ≥ 3       [1]

The second couple of conditions yields to:

x ≤ 3 and x ≤ -2

Which lead to the solution

x ≤ -2        [2]

The final solution is [1] or [2]:

Answer:

B. x ≥ 3 or x ≤ −2

The inductance of the toroid is (299.8*\(600^{2}\)*π)/2 = 7.04 x \(10^{-3}\) H.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimeters, square meters or square kilometers. Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The inductance of a toroid coil can be calculated using the following formula: L = (μN^2*A)/l, where μ is the permeability of the core material, N is the number of turns of the coil, A is the cross-sectional area of the toroid, and l is the length of the coil. In the case of a toroid with large radius b, the cross-sectional area A is approximately equal to π\(b^{2}\) and the length of the coil is l=2πb. Therefore, the inductance of the toroid is L=(μN^2*π\(b^{2}\))/(2πb)= (μN^2*π)/2.

(b) For the given toroid with 600 turns, iron core (μ=299.8), a=8.0 cm and c=9.0 cm, the inductance can be calculated as follows:

L = (299.8*\(600^{2}\)*π)/2 = 7.04 x \(10^{-3}\) H.

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Answer:

6 and 15

Step-by-step explanation:

3/8 = 6/16

32 : 24 = 20 : x

x = 24 * 20 : 32

x = 15

32/24=20/15

The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.

Height of Gateway Arch in St. Louis, MO = 630ft tall

We are asked, how many nickels would be in a stack of the same

height when 1 nickel is 1.95 mm thick.

Convert height in ft to mm

1 ft = 304.8 mm

630ft = X

After Cross Multiply,

630ft × 304.8mm/1ft

= 192024 mm.

To find how many nickel would be in a stack of the same height

= Total thickness/ Thickness of 1 US dime

= 192024 mm/1.95mm

= 98473.8

≈98474 nickels

Therefore, the number of nickel that would be in a stack of the same height is 98474.

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Answer:

true i think not 100% sure tho

Step-by-step explanation:

Answer:

huh?

Step-by-step explanation:

Answer:

11, 16, 21, 26, 31

Step-by-step explanation:

Dakota pattern = 8, 13, 18, 23, 28

The common difference in Dakota patter is 5

8, 8 + 5, 8 + 5 + 5, 8 + 5 + 5 + 5, 8 + 5 + 5 + 5 + 5

= 8, 13, 18, 23, 28

Coby uses the same rule as Dakota to make a pattern

He begins his pattern with the number 11.

= 11, 11+5, 11+5+5, 11+5+5+5, 11+5+5+5+5

= 11, 16, 21, 26, 31

Coby's pattern starting from 11 using the same rule as Dakota is 11, 16, 21, 26, 31

The number of ceiling tiles needed to cover the room measuring 24 feet by 18 feet, with each ceiling tile being 2 feet by 3 feet, is 72 tiles.

To calculate the number of ceiling tiles needed to cover the room, we divide the area of the room by the area of each ceiling tile.

The area of the room is found by multiplying its length and width: 24 feet * 18 feet = 432 square feet.

The area of each ceiling tile is found by multiplying its length and width: 2 feet * 3 feet = 6 square feet.

To find the number of tiles, we divide the total area of the room by the area of each tile: 432 square feet / 6 square feet = 72 tiles.

Therefore, to cover the room measuring 24 feet by 18 feet, with each ceiling tile being 2 feet by 3 feet, we would need a total of 72 tiles.

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The probability that the sample will contain more than 5% defective units is approximately 0.9525 or 95.25%.

To solve this problem, we can use the binomial distribution formula:

P(X > 5) = 1 - P(X ≤ 5)

where X is the number of defective items in a sample of size n = 100, and p = 0.1 is the probability of an item being defective.

To calculate P(X ≤ 5), we can use the binomial cumulative distribution function (CDF) or a binomial probability table. Alternatively, we can use a normal approximation to the binomial distribution, which is valid when np ≥ 10 and n(1-p) ≥ 10, as is the case here (np = 10 and n(1-p) = 90).

Using the normal approximation, we can standardize the distribution of X as follows:

\(z = (X - np) / \sqrt{(np(1-p))}\)

Then, we can use a standard normal table or calculator to find the probability of z ≤ z0, where z0 is the standardized value corresponding to X = 5.

Let's use the normal approximation method to solve the problem:

np = 100 x 0.1 = 10

σ = \(\sqrt{(np(1-p))} = \sqrt{(9)} = 3\)

z0 = (5 - 10) / 3 = -1.67 (rounded to two decimal places)

Using a standard normal table or calculator, we find that P(Z ≤ -1.67) = 0.0475 (rounded to four decimal places).

Therefore, P(X > 5) = 1 - P(X ≤ 5) = 1 - 0.0475 = 0.9525 (rounded to four decimal places).

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To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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Answer:

S.I=$3375

Step-by-step explanation:

S.I=PRT/100

S.I=750×15×3/100

S.I=33750/10

S.I=$3375

The option for  sequences are arithmetic are:

From the first option we can see that -5,5,-5,5… dose not follow any sequence  of arithmetic.

if we take the  18,5.5, –7, –19.5, which are the digits from the second option and if we find their differences we will get 12.5

Then if we take the numbers from the 16, 32, 48, 64 and find the differences between the first two numbers as well as the last two numbers then we will have 16.

Therefore, since we can have constant results between consecutive numbers then it is sequence  of arithmetic.

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