How do I solve 3 (9-5)² ÷8 ?

Answer:

4.8

Step-by-step explanation:

12/5=2.4

2 times 2.4=4.8

Answer:

devide 1080 by 5 and 2880 by 5 the it will 216 and 576

Answer: 1080 is an. Octagon, 8 sides

180 is a triangle.

2880 is an 18gon 18 sides

Step-by-step explanation:

Divide the sum of the interior angles by 180 and add 2 to the dividend.

1080/180=>6+2=8

180/180 => 1 +2 =3

2880/180=> 16+2= 18

The equation tan(30°) = 5/b can be used to solve for b. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the purview of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle BCA = 90° and angle CAB = 30°. Also, the length of side BC is 5 centimeters, the length of BA is 10 centimeters, and the length of CA is b.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = 5/b

Here, θ = 30°

So,

⇒tan 30° = 5/b

Hence, the equation tan(30°) = 5/b can be used to solve for b.

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Let's use the variable x to represent the list price of the car.

The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.

We can write this as an equation:

Total cost = List price + 0.07(List price) + 450

We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:

12,755 = x + 0.07x + 450

Simplifying the right side:

12,755 = 1.07x + 450

Subtracting 450 from both sides:

12,305 = 1.07x

Dividing both sides by 1.07:

x = 11,500

Therefore, the list price of the car your cousin bought was $11,500.

The list price of the car your cousin bought was $11,500.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's start by setting up an equation to represent the total cost of the car:

Total cost = List price + 7% of List price + $450

We know that the total cost is $12,755, so we can substitute that in:

$12,755 = List price + 0.07(List price) + $450

Simplifying this equation, we get:

$12,755 = 1.07(List price) + $450

Subtracting $450 from both sides, we get:

$12,305 = 1.07(List price)

Dividing both sides by 1.07, we get:

List price = $11,500

Therefore,

The list price of the car your cousin bought was $11,500.

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True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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Answer:

1. x ≤ 15

2. x ≤ $13.00

3. x < 1ft tall

4. x > $100

5. x ≥ 20 pounds

6. x ≥ 3

7. x < 20

8. x < 17

9. x > 90

10. x ≥ $500

The mean and standard deviation for the number of defective bolts in a total of 400 bolts is 40 and 6.32 (approx), respectively.

The mean and standard deviation for the number of defective bolts in a total of 400 bolts if the probability of defective bolt is 0.1 can be calculated using Poisson distribution.

Poisson distribution is used to predict the number of events that occur over a specified interval of time when the probability of an event occurring is known.

The formula for calculating the mean (μ) and standard deviation (σ) is given as follows:
μ = λσ = √λ
Where λ = np, where n is the number of trials and p is the probability of success.

Here, the probability of a defective bolt is 0.1. So the probability of a non-defective bolt is 0.9. The total number of bolts is 400, so the expected number of defective bolts can be calculated as follows:
μ = λ = np = 400 x 0.1 = 40

The mean number of defective bolts is 40. The standard deviation can be calculated as follows:
σ = √λ = √40 = 6.32 (approx)

The standard deviation is 6.32 (approx).

Therefore, the mean and standard deviation is 40 and 6.32 (approx), respectively.

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Answer:

A on edge 2021

Step-by-step explanation:

I got it correct.

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

Answer:

a horizontal translation and a glide reflection

Step-by-step explanation:

took it

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

The relative atomic mass of Interactium is 290.14 amu.


We can calculate the relative atomic mass of Interactium using the following equation:

Ar = (Ab × Mb) + (Ac × Mc) + (Ad × Md) where Ar is the relative atomic mass, Ab is the abundance of Interactium-284, Mb is the mass of Interactium-284, Ac is the abundance of Interactium-289, Mc is the mass of Interactium-289, Ad is the abundance of Interactium-294, and Md is the mass of Interactium-294.  

Substituting the given values in the equation, we get:

Ar = (0.16 × 284) + (0.27 × 289) + (0.57 × 294)
Ar = 45.44 + 77.97 + 167.43
Ar = 290.14 amu

Therefore, the relative atomic mass of Interactium is 290.14 amu.

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The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = \(\frac{29}{\sqrt{1500} }\) = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

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Answer:

ABD =30 +45

ABD=75

75°is the answer

The solutions of provide logarithmic equations are present in below :

1) x = 9 ; 2) x = 0 ; 3)p = 7/9 ; 4) k= 2 ; 5) a= -1 ; 6) r = -1/2 ; 7) n = 2 ; 8) x = 1/35 ; 9) m = -2 ; 10) x = 84 ; 11) v = -6, -6 ; 12) x = -4, -7

The logarithmic number is associated with exponent and power, such that if xⁿ = m, then it is equal to logₓ m = n. That is exponential value are inverse of logarithm values. Some basic properties of logarithmic numbers:

Now, we solve each logarithm equation one by one. Assume that 'log' is the base-10 logarithm where absence of base.

1) log (5x) = log (2x + 9)

Exponentiate both sides

=> 5x = 2x + 9

=> 3x = 9

=> x = 9

2) log (10 − 4x) = log (10 − 3x)

Exponentiate both sides,

=> 10 - 4x = 10 - 3x

simplify, => x = 0

3) log (4p − 2) = log (−5p + 5)

Exponentiate both sides,

=> 4p - 2 = - 5p + 5

simplify, => 9p = 7

=> p = 7/9

4) log (4k − 5) = log (2k − 1)

Exponentiate both sides,

=> 4k - 5 = 2k - 1

simplify, => 2k = 4

=> k = 2

5) log (−2a + 9) = log (7 − 4a)

Exponentiate both sides,

=> - 2a + 9 = 7 - 4a

simplify, => 2a = -2

=> a = -1

6) 2log₇( −2r) = 0

=> log₇( −2r) = 0

using the property, log꜀a = n <=> cⁿ = a

=> ( 7⁰) = - 2r

=> -2 × r = 1 ( since a⁰ = 1 )

=> r = -1/2

7) −10 + log₃(n + 3) = −10

=> log₃(n + 3) = −10 + 10 = 0

using the property, log꜀a = n <=> cⁿ = a

=> 3⁰ = n + 3

=> 1 = n + 3

=> n = 2

8) −2log₅ ( 7x ) = 2

=> log₅ 7x = -1

=> 5⁻¹ = 7x

=> x = 1/35

9) log( −m) + 2 = 4

=> log( −m) = 2

Exponentiate both sides,

=> -m = 2

=> m = -2

10) −6log₃ (x − 3) = −24

simplify, log₃ (x − 3) = 4

=> (x - 3) = 3⁴ ( since log꜀a = n <=> cⁿ = a )

=> x - 3 = 81

=> x = 84

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

=> log₁₂ (v²+ 35) - log₁₂ (−12v − 1) = 0

Using the quotient property of logarithm,

\(log_{12}( \frac{v²+ 35}{-12v-1}) = 0 \)

\(\frac{v²+ 35}{-12v - 1} = {12}^{0} = 1 \)

\(v²+ 35 = −12v − 1\)

\(v²+ 35 + 12v + 1 = 0\)

\(v²+12v + 36 = 0\)

which is a quadratic equation, and solve it by middle term splitting method,

\(v²+ 6v + 6v + 36= 0\)

\(v(v + 6) + 6(v + 6)= 0\)

\((v + 6) (6 + v)= 0\)

so, v = -6, -6

12) log₉(−11x + 2) = log₉ (x²+ 30)

=> log₉ (x²+ 30) - log₉(−11x + 2) = 0

Using the quotient property of logarithm,

\(log₉(\frac{x²+ 30 }{−11x + 2}) = 0\)

\( \frac{x²+ 30}{-11x + 2} ={9}^{0} = 1 \)

=> x² + 30 = - 11x + 2

=> x² + 11x + 30 -2 = 0

=> x² + 11x + 28 = 0

Factorize using middle term splitting,

=> x² + 7x + 4x + 28 = 0

=> x( x + 7) + 4( x + 7) = 0

=> ( x + 4) (x+7) = 0

=> either x = -4 or x = -7

Hence, required solution is x = -4, -7.

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Complete question:

kuta software infinite algebra 2 logarithmic equationsSolve each equation.

1) log 5x = log (2x + 9)

2) log (10 − 4x) = log (10 − 3x)

3) log (4 − 2) = log (−5 p + 5)

4) log (4k − 5) = log (2k − 1)

5) log (−2a + 9) = log (7 − 4a)

6) 2log₇ −2r = 0

7) −10 + log₃(n + 3) = −10

8) −2log₅ 7x = 2

9) log −m + 2 = 4

10) −6log₃ (x − 3) = −24

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

12) log₉(−11x + 2) = log₉ (x²+ 30)

The matrix A that represents the set W, consisting of vectors of the form [r, s, t] with real numbers, is constructed by organizing the coefficients of r, s, and t as the columns of A. The resulting matrix A is given by A = [0 0 2 48; s 2 1 0; 0 -5 1 0; 0 0 0 1]

Let's break down the construction of matrix A step by step.

Given that W is the set of all vectors of the form [r, s, t] where r, s, and t are real numbers, we want to find a matrix A such that the column space of A (Col(A)) represents W.

The matrix A will have as its columns the coefficients of r, s, and t in the given expression.

Column 1 of A: Coefficients of r

In the expression, we have 5sr + 3t, so the coefficient of r is s. Therefore, the first column of A will be [0, s, 0, 0] since there is no r term in the expression.

Column 2 of A: Coefficients of s and t

In the expression, we have 2sr - 5t. The coefficient of s is 2, and the coefficient of t is -5. Therefore, the second column of A will be [0, 2, -5, 0] with the corresponding coefficients.

Column 3 of A: Coefficients of r, s, and t

In the expression, we have 2r + s + t. The coefficients of r, s, and t are 2, 1, and 1, respectively. Therefore, the third column of A will be [2, 1, 1, 0] with the corresponding coefficients.

Column 4 of A: Coefficients of r and t

In the expression, we have 48r + t. The coefficient of r is 48, and the coefficient of t is 1. Therefore, the fourth column of A will be [48, 0, 0, 1] with the corresponding coefficients.

Putting it all together, the matrix A that represents W = Col(A) is:

A = [ 0 0 2 48 ]

[ s 2 1 0 ]

[ 0 -5 1 0 ]

[ 0 0 0 1 ]

Each column of A corresponds to the coefficients of r, s, and t in the given expression, forming the column space that represents the set W.

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Answer:

x=3

Step-by-step explanation:

-4-5x+10x+9=20 ] +4

-5x+10x+9=20+4 ] -9

-5x+10x=24-9

5x=15

15:5=3

x=3

The point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).

To find the point on the y-axis that lies on the line passing through point g and is parallel to line df, we first need to determine the slope of line df. Since the line is parallel to the new line passing through point g, the slope will be the same.

Once we have the slope, we can use point-slope form to find the equation of the new line. Then, we can set x=0 (since we want to find the point on the y-axis) and solve for y to find the y-coordinate of the point.

So, let's begin.

First, let's find the slope of line df. We can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. We can use the points d and f, which are (5, 3) and (10, 8), respectively.

slope = (8 - 3) / (10 - 5) = 1

So the slope of line df is 1.

Now, using point-slope form, we can find the equation of the new line passing through point g (which is (-2, 7)) and having a slope of 1. The formula for point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line (in this case, point g). Substituting in our values, we get:

y - 7 = 1(x - (-2))
y - 7 = x + 2
y = x + 9

So the equation of the new line is y = x + 9.

To find the point on the y-axis that lies on this line, we set x=0:

y = 0 + 9
y = 9

So the point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).

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Answer:

x ≤ 39/5

Step-by-step explanation:

To solve for the inequality, isolate the x variable.

5x - 7 ≤ 32​

Add 7 to both sides.

5x ≤ 39

Divide both sides by 5.

x ≤ 39/5

Answer:

E (3,1)

G (4,6)

F (10,1)

Step-by-step explanation:

Answer:

See the attached images

Step-by-step explanation:

We're reflecting this image over the line y = –1, right?

This means we need to copy this image over the line like a mirror does a reflection. It isn't exactly what we got before, though—it's flipped backward, just like text when you look at it in a mirror!

First, look where points E and F are. They're two squares below the line. That means we count two squares up to reach y = –1… then count up another two squares to reflect the points across the line.

Next, look at point G. This is what I personally feel is easier: this point has a y-coordinate of –8. This makes it 7 squares below y = –1. To get its new y-coordinate, we add 7 to –1 to get y = 6.

The x-coordinates of the points don't change here; the line the shape is reflected over is a horizontal line. If the line were vertical, we'd only change the x-coordinates and not the y-coordinates. If the line were a linear function like y = x, we'd reflect our x-coordinates and y-coordinates.

Another way to think of it here: how squares below the line is each point? Then multiply that number by 2 and add it to the initial y-coordinate to find its new position.

Forgive me for the weird dots in the last image. I got frustrated and drew the triangle with my pinky finger because I can't quite draw nor write with a mouse yet!!

Hope this helps you understand! Have a great day!

Answer:

not a function

Step-by-step explanation:

if x values repeat its not a function

U is not in the subspace of R3 spanned by the columns of A.

The columns of A form a set of basis vectors for the subspace of R3 spanned by the columns of A. To determine whether u is in this subspace, we can check if u can be written as a linear combination of the columns of A.

To do this, we can form the augmented matrix [A | u], and then perform row operations to transform the matrix into the reduced row echelon form. If the last column of the reduced row echelon form is zero, then u is in the subspace spanned by the columns of A. If the last column is non-zero, then u is not in the subspace.

In this case, the augmented matrix is:

[ 6 7 11 | 8 ]

[ 0 2 -2 | -8 ]

[ 1 2 1 | -4 ]

After performing row operations, we get the reduced row echelon form:

[ 1 0 0 | -6 ]

[ 0 1 0 | -4 ]

[ 0 0 1 | 4 ]

Since the last column is non-zero, we can see that u cannot be written as a linear combination of the columns of A, and therefore u is not in the subspace of R3 spanned by the columns of A.

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Answer:

12n+9=93

solve for n

12n=93-9

n=84/12

n=7

therefore, Mr. copper bought 7 tickets.

In the picture we can see the example of the similar shape that is similar rectangle with angles same.

Given that,

We have to find what is an example of similar shapes.

We know that,

When applying a scale factor, similar shapes are enlarged versions of one another.

All of the matching angles and lengths in related shapes are equal and in the same ratio.

For example,

These two rectangles have a comparable design.

From shape A to shape B, there is a 22-fold increase in scale.

All of the angles are 90 degrees.

The bases' ratio is 2:4, which may be expressed as 1:2.

The height ratio is also 1:2.

Therefore, In the picture we can see the example of the similar shape that is similar rectangle with angles same.

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Answer:

270

Step-by-step explanation: