Solve the following equation. Check your solution. 5(x+1)=3x - 9​

Answer:

75.9

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The given function is

First, we make x = 0.

Second, we make g(x) = 0.

Third, we graph the points (0, 4) and (-16, 0).

At last, we draw the line through the points to get the line.

To find the kernel (ker(T)), nullity(T), range(T), and rank(T) of the linear transformation T defined by T(x) = Ax, we need to perform some calculations based on the matrix A given.

Let's start with the given matrix:

A = [[5, -3], [1, -1]]

(a) ker(T) (Kernel of T):

The kernel of T consists of all vectors x such that T(x) = 0. In other words, we need to find the solutions to the equation Ax = 0.

To find the kernel, we solve the homogeneous system of linear equations represented by the augmented matrix [A | 0]. So we have:

[[5, -3, 0], [1, -1, 0]]

Row reducing the augmented matrix:

[[1, -1/5, 0], [0, 0, 0]]

From the row-reduced form, we can see that the system has one dependent variable (let's say t), and one free variable (let's say s). This means the kernel consists of all vectors of the form [(s, t)] where s and t can be any real numbers.

Therefore, the kernel (ker(T)) is given by (c) ker(T) = [(s, t, s - 4t)] where s and t are any real numbers.

(b) nullity(T):

The nullity of T is the dimension of the kernel (ker(T)). In this case, since the kernel (ker(T)) is given by (c) ker(T) = [(s, t, s - 4t)], the nullity (nullity(T)) is 2.

(c) range(T):

The range of T is the set of all possible outputs of T(x) as x varies over the domain. In other words, we need to find the column space of the matrix A.

To find the range, we perform row operations on the matrix A and look for the pivot columns. The pivot columns correspond to the columns that contain leading 1's after row reduction.

Row reducing the matrix A:

[[5, -3], [1, -1]]

[[1, -1], [0, -1]]

From the row-reduced form, we can see that the first column is a pivot column, but the second column is not. Therefore, the range (range(T)) is the span of the column associated with the pivot column.

The range (range(T)) is given by (b) range(T) = R2, which represents the set of all vectors in the 2-dimensional Euclidean space.

(d) rank(T):

The rank of T is the dimension of the range (range(T)). In this case, since the range (range(T)) is given by (b) range(T) = R2, the rank (rank(T)) is 2.

In conclusion:

(a) ker(T) = [(s, t, s - 4t)] where s and t are any real numbers.

(b) nullity(T) = 2

(c) range(T) = R2

(d) rank(T) = 2

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Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

Answer:

Step-by-step explanation:

24+3y=56 solve for y, subtract 24 from each side

3y=32 divide each side by 3

y=32/3

Answer:

y=32/3

Step-by-step explanation:

let the number be y, then

24+3y=56 solve for y, subtract 24 from each side

3y=32 divide each side by 3

y=32/3

Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn - one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins

The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.

Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.

It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.

Also, let \(\%R_{A}\) be the quantity of nonzero elements in \(R_{A}.\)

Let \(C_{1}=\left(\begin{array}{l}1\\ -1\\ 0\\ 0\end{array}\right)\).

Parity demands that \(\%R_{A}\) and\(\%R_{B}\) must equal 2 or 4.

Case 1: \(\%R_{A}\)=4 and \(\%R_B\)=4. There are \(\left(\begin{array}{l}3\\ 2\end{array}\right)\)=3 ways to put 2-1's in \(R_A\), so there are 3 ways.

Case 2: \(\%R_{A}\)=2 and \(\%R_B\)=4. There are 3 ways to position the -1 in \(R_A\), 2 ways to put the remaining -1 in \(R_B\) (just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of \(\%R_{A}=4,\%R_{B}=2\) for a complete of 24 ways.

Case 3: \(\%R_A=\%R_B=2\). There are 3 ways to put the -1 in \(R_{A}\). Now, there are two cases on what happens next.

Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192

Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.

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It is given that area of rectangle of Kaitlin is 1500 sq.ft. with length 50 ft and a width of 30 ft.

The new area when new length 2 times the current length and the new width 2 times the current width.

a. The size of Kaitlin new patio is

b. The area of new patio is 4 times the area of current patio.

Answer:

27/70

Step-by-step explanation:

This is simple: First, you multiply the numerators. 3x9 is 27. That is the numerator to your answer.

Next, you multiply the denominators. 7x10 is 70. That's the denominator to the answer.

Put them together and you get 27/70.

Hope I helped!!!

So, the height of the tower is approximately 363.6 feet.

You can use trigonometry to solve this problem.

If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.

We can use the tangent function to relate the angle of elevation to the height and distance.

tan(67) = h/d

We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.

h = d * tan(67)

h = 200 * tan(67)

The height of the tower is approximately 363.6 feet.

Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.

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The sample size which is required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03 is equals to the 382.

We have provide that the state education commission wants to draw an estimate on the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Population proportion, p = 0.21

confidence level = 85%

Margin of error = 0.03,

We have to determine the sample size. For determining sample size for estimating a population propotion, using the below formula,

n = (Zα/2)² ×p×(1-p) / MOE²

where MOE is the margin of error

Using the distribution table, Zc for 85% for confidence level where α = 0.15 or α/2 = 0.075 equals to the 1.439.

Substituting all known values in formula we

n = 1.439² × 0.21( 0.79)/ (0.03)²

=> n = 382.2336 ~ 382

Hence, required sample size is 382.

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The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: length of the pole=3m and distance of the stake from the pole=4m and the angle that the rope makes with the pole is x

We know Arctan function is the inverse of the tangent function. It is usually denoted as arctan x or tan⁻¹x. The basic formula to determine the value of arctan is θ = tan-1(Perpendicular / Base).

Thus we have the value of x as

x=tan⁻(perpendicular/Base)

=tan⁻¹(3/4)

=36.87°

Thus the two possible ways to compute the angle x are:

tanx=3/4 and x=tan⁻¹(3/4)

Hence, The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

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Given:

The inequality is:

\(y>5x+3\)

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

\(y=mx+b\)            ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y>5x+3\)

The relation equation is:

\(y=5x+3\)             ...(ii)

On comparing (i) and (ii), we get

\(m=5\)

\(b=3\)

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

The number of cookies in the jar initially was 42

To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.

We can use this information to set up the equation:

x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.

By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.

So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.

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Answer:

Step-by-step explanation:

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The test statistic value, in this case, is 5.28. Since this value is greater than the critical value of 4.14, we reject the null hypothesis. Thus, we conclude that at least one of the means is significantly different from the others.

Calculate the test statistic, the following steps must be followed:Step 1: Calculate the degrees of freedom of the F-distribution.The degrees of freedom (DF) are calculated as follows:DF (numerator) = c - 1 where c is the number of means being compared. In this situation, there are two means being compared, thus c=2, soDF (numerator) = 2 - 1 = 1.DF (denominator) = N - c where N is the total number of observations. In this situation, there are 16 observations, thusN = 16. As there are two means being compared, thus c=2, soDF (denominator) = 16 - 2 = 14.

Step 2: Determine the critical value for FThe level of significance α = 0.05. Therefore, the critical value of F for DF(1,14) at 0.05 level of significance is 4.14. If the test statistic value is greater than the critical value, we reject the null hypothesis, else we do not.

Step 3: Calculate the test statisticThe formula for the F-test is: F = MST / MSE where MST = Mean square treatments and MSE = Mean square error. The formula for Mean Square treatments is MST = SST/DF(Treatment) and the formula for Mean Square error is MSE = SSE/DF(Error)SST is calculated by SST = Σ(Ti - T)²/DF(Treatment) where T is the grand mean, Ti is the mean of treatment i, and DF(Treatment) is the degrees of freedom for treatments.SSE is calculated by SSE = ΣΣ (Xij - Ti)²/DF(Error) where DF(Error) is the degrees of freedom for error and Xij is the value of the jth observation in the ith treatment group. After calculating SST and SSE, we can easily calculate MST and MSE.MST = SST / DF(Treatment) and MSE = SSE / DF(Error)Finally, calculate the value of the F-test as F = MST / MSEThe calculations are given in the following ANOVA table:SOURCE OF VARIATIONSSdfMSFp-valueTREATMENTSST3,851,562.5011,537,187.50.36112ERRORSSE10,194,667.8614,14,619.13118GRAND MEAN62.50

The degrees of freedom for treatments are c - 1 = 2 - 1 = 1. Thus, the SST is calculated as follows:SST = Σ(Ti - T)²/DF(Treatment)= [(50.25 - 62.50)² + (72.25 - 62.50)²]/1 = 3,851,562.50The degrees of freedom for error are N - c = 16 - 2 = 14. Thus, the SSE is calculated as follows:SSE = ΣΣ (Xij - Ti)²/DF(Error)= [(47 - 50.25)² + (25 - 50.25)² + ... + (128 - 72.25)²]/14 = 10,194,667.86MST = SST / DF(Treatment) = 3,851,562.50 / 1 = 3,851,562.50MSE = SSE / DF(Error) = 10,194,667.86 / 14 = 728,904.85F = MST / MSE = 3,851,562.50 / 728,904.85 = 5.28 (rounded to two decimal places)The test statistic value, in this case, is 5.28. Since this value is greater than the critical value of 4.14, we reject the null hypothesis. Thus, we conclude that at least one of the means is significantly different from the others.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer:

1. Grassland

2. grass

3. Temperate grassland

4. prairies

5. steppe

6. tropical grassland

7. savanna

8. intermountain grassland

9. mixed prairie

10. tallgrass prairie

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

Answer: 39.7  

∘

 and 140.3  

∘

Step-by-step explanation:

All possible values of ∠O, to the nearest 10th of a 39.7degrees and 140.3 degrees.

We have given that,

In ΔNOP, o = 3.5 inches, n = 3.3 inches and ∠N=37°.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

We have to determine all possible values of ∠O, to the nearest 10th of a degree.

All possible values of ∠O, to the nearest 10th of a 39.7degrees and 140.3 degrees.

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The mean of the homework grades is 87.

The mean is a measure of central tendency that gives us an idea of the typical or average value in a data set. In this case, it represents the average homework grade for the grading period. By calculating the mean, we can find the center point that best represents the data.

To best represent the data, the center that should be used is the mean. The mean, also known as the average, is calculated by adding up all the values in the list and then dividing by the total number of values.

1. Add up all the homework grades: 80 + 90 + 84 + 86 + 95 = 435.
2. Since there are 5 grades in the list, divide the sum by 5: 435 / 5 = 87.

Thus, the mean of the homework grades is 87.

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34.

1). the wall that doesn't have the window

2). the ceiling

Therefore, approximately 1,491 Whos will be infected 10 days after the virus is first detected.

To approximate the number of Whos that will be infected 10 days after the virus is first detected, we can use the concept of exponential growth. We can use the formula for exponential growth:\(P(t) = P0 * (1 + r)^t,\) where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in days.

Let's calculate the growth rate (r) first:

r = (800 - 100) / 5

= 140 Whos per day

Now, we can calculate the approximate number of infected Whos 10 days later:

\(P(10) = 100 * (1 + 140/100)^{10\)

Using a calculator, we can compute this value:

\(P(10) ≈ 100 * (1.4)^{10\)

= 1491.03

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Circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

Circular permutation refers to an ordering of elements in a circle. Factorial, on the other hand, is the product of all the natural numbers from an integer down to one. It is denoted by the exclamation mark (!). Series, on the other hand, refers to the indicated sum of the terms of an associated sequence. Finally, permutation is an order of elements of a set.

To summarize, circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.

1. Circular permutation - an ordering of elements in a circle.
In a circular permutation, the arrangement of items is considered in a circular fashion rather than in a linear order. The number of circular permutations for 'n' elements can be calculated using the formula (n-1)!.

2. Factorial - the product of all the natural numbers from an integer down to one.
Factorial, denoted by the symbol '!', represents the product of all the positive integers from a given integer down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

3. Series - the indicated sum of the terms of an associated sequence.
A series is the sum of the terms in a given sequence, often represented by the summation symbol Σ. For example, the sum of the first 'n' natural numbers is represented as Σ(i=1 to n) i = n(n+1)/2.

4. Permutation - an order of elements of a set.
A permutation refers to the arrangement of elements in a specific order within a set. The number of possible permutations for a set of 'n' elements, taken 'r' at a time, can be calculated using the formula n!/(n-r)!.

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1. The expected number of cars is given as follows: 2.87.

2. The standard deviation of the number of cars is given as follows: 0.94.

The discrete distribution is given from the table in this problem, as follows:

The expected value is given by the sum of each outcome multiplied by it's probability, as follows:

E(X) = 0 x 0.005 + 1 x 0.12 + 2 x 0.125 + 3 x 0.5 + 4 x 0.25 = 2.87.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, as follows:

S(X) = sqrt((0-2.87)² x 0.005 + (1-2.87)² x 0.12 + (2-2.87)² x 0.125 + (3-2.87)² x 0.5 + (4-2.87)² x 0.25) = 0.94.

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