Solve for x.

one third times the absolute value of the quantity x minus 3 end quantity plus 4 equals 10

x = −15 and x = 21
x = −5 and x = −1
x = 1 and x = 5
x = 15 and x = 21

Answer:

-1/6 (written as a fraction)

Step-by-step explanation:

our goal here is to get n by itself

6n-4=3

add 4 to both sides

6n=-1

divide both sides by 6

n= -1/6 (a fraction)

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

Using compound interest and a geometric sequence, it is found that:

Compound interest:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In this problem:

Hence, considering the end of each year, that is, \(t = 1\), the common ratio will be:

\(q = \left(1 + \frac{r}{n}\right)^{n}\)

\(q = \left(1 + \frac{0.055}{4}\right)^{4}\)

\(q = 1.0561\)

The nth term of a geometric sequence is given by:

\(A(n) = A(0)q^{n}\)

In which A(0) is the initial value.

In this problem, \(q = 1.0561\), and the time to double is t for which \(A(n) = 2A(0)\), hence:

\(A(n) = A(0)1.0561^{n}\)

\(2A(0) = A(0)1.0561^{n}\)

\(1.0561^n = 2\)

\(\log{(1.0561^n)} = \log{2}\)

\(n\log{1.0561} = \log{2}\)

\(n = \frac{\log{2}}{\log{1.0561}}\)

\(n = 12.69\)

2020 + 12.69 = 20.32.69.

Hence, the amount of money will double in the year 2032.

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Here is my answer. I hope this is helpful. If there is something you don't understand in my solution, you can ask me.

Therefore, when Savannah is 42 feet above the ferris wheel's horizontal diameter, her angle of rotation is approximately 68.6 degrees.

Given by the question.

Let's first draw a diagram to visualize the situation.

      *

    *    *

  *        * <-- Ferris wheel at 3 o'clock position

 *          *

*            * <-- Highest point

*______________*______

      62 ft

The Ferris wheel is a circle with radius 62 feet, and Savannah is sitting in a bucket that moves along the circle. When she is at the highest point, she is 62 feet away from the center of the circle, and when she is on the horizontal diameter, she is 62 feet - 42 feet = 20 feet away from the center of the circle.

To find Savannah's angle of rotation, we can use the cosine function.

cos(theta) = adjacent / hypotenuse

In this case, the adjacent side is 20 feet, and the hypotenuse is 62 feet.

cos(theta) = 20/62

To solve for theta, we need to take the inverse cosine of both sides.

theta = cos^-1(20/62)

Using a calculator, we get:

theta = 68.6 degrees

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Answer:

(12, 190). This represents that after selling 12 ice creams, I gain $190.

Step-by-step explanation:

I just found a scatter plot online. Ignore the current label on the x-axis that says TemperatureC, I just changed that to ice creams. You can change the title of the graph to whatever you want.

Answer: 13kg

Step-by-step explanation:  she bought a total of 14/3 + 25/3 = 39/3 = 13 kg of fish and crabs.

Answer:

49%

Step-by-step explanation:

465 + 485 = 950

465/950 = .489

.489 * 100 = 48.9, round up for 49 to get 49%, since it's only focused on people who tested positive, you would only have to compare the people in that column

Answer: b

Step-by-step explanation:

Answer:

$1197.17185

Step-by-step explanation:

ABC bond :

Par value of bond (FV) = 1000

Period (n) = 11 years

Coupon rate (r) = 8.5% annually

Discount rate (r) = 6% = 0.06

The coupon price = 8.5% of par value

Coupon price (C) = 0.085 * 1000 = 85

Current price of bond can be computed using the relation:

= C * [1 - 1 / (1 + r)^n] / r + (FV / (1 + r)^n)

85 * [1 - 1/(1+0.06)^11]/0.06 + 1000/(1 + 0.06)^11

85 * 7.8868745 + 526.78752

670.38433 + 526.78752 = $1197.17185

Answer:

2.4582​, 3.6, 3.601,  3.61

The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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Answer:

The answer is the screen shot that I just took

Observing the two system of equations we can conclude that the values of x and y that represents the given conditions are: (15, 5). Hence, option D is the correct answer.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

The two-given system of equations are:

−y ≤ 3x + 4

−3x + 3y ≤ −9

Isolating the value of y in equation 2 we have:

−3x + 3y ≤ −9

3y ≤ 3x - 9

y ≤ x - 3

The first equation can also be written as:

−y ≤ 3x + 4

y ≥ - 3x - 4

Thus the two equations become:

y ≤ x - 3

y ≥ - 3x - 4

Observing the two equations we can conclude that the values of x and y that would be needed to satisfy the given conditions are: (15, 5). Hence, option D is the correct answer.

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Answer: 6

Step-by-step explanation: You can use an algebraic equation to solve this.

3 + x = 9

-3        -3

_______

x = 6

Answer:

thank you very much

1235÷722

Answer:

467

Step-by-step explanation:

7 is greater than 5 so the six is rounded to a 7

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Answer:

497

Step-by-step explanation:

If x ≥ 5, we round up.

If x < 5, we round down.

Since 7 ≥ 5, we round 496.739386253 to 497.

The vertex focus of the parabola is (3,15) and the directrix is x=3.

1. Rewrite the equation in the form y = a(x - h)^2 + k

y = x^2 - 6x + 15

y = 1(x - 3)^2 + 15

2. The vertex focus is (h, k) = (3, 15)

3. The directrix is x = h = 3

By rewriting the equation in the form of y = a(x - h)^2 + k, we can find the vertex focus and directrix of the parabola. The vertex focus of a parabola is the point at which the graph changes direction, and is equal to (h, k). The directrix is the line at which the vertex focus is located, and is equal to x = h. For this equation, h = 3 and k = 15, so the vertex focus is (3, 15) and the directrix is x = 3.

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Answer:

13#

Step-by-step explanation:

5 cakes equal to 65$

1 cake equals ?

1/5×65

13$

Answer:

Each cake is $13

Step-by-step explanation:

If each cake costs the same and you bought 5, spending a total of $65, you would simply divide the $ you spent by the amt. of cakes to find how much each cake is. Let's assume x is how much each cake is, and 5 is the number of cakes you buy, so 5 (The amount of cakes) multiplied by x (how much each cake costs) must give you 65.

Equation:

5x=65

x=65/5

x=13

Answer: Each cake is $13.

Answer:

2nd option

Step-by-step explanation:

x² + 11x + 30

Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (+ 11)

The factors are + 6 and + 5 , since

6 × 5 = 30 and 6 + 5 = 11 , then

x² + 11x + 30 = (x + 6)(x + 5) ← in factored form

Answer:

(x+6)(x+5)

because the sum of 6+5 is 11x

and the multiplication of 6·5 is 30

When it comes to printing full-color pictures, it usually involves using the CMYK color model which stands for cyan, magenta, yellow, and black.

These colors are combined in different amounts to create a wide range of colors and shades. Therefore, the answer to your question is three plus black. The colors cyan, magenta, and yellow are combined to produce a wide range of colors, while the black is added to enhance contrast and to create darker tones.

This combination of colors provides a more accurate and vibrant representation of the original picture. It is important to note that there are other color models used for printing such as RGB (red, green, and blue) which is used for digital displays, but for printing purposes, CMYK is the most common.

In conclusion, full-color pictures are printed using three colors (cyan, magenta, and yellow) plus black to enhance contrast and create darker tones. This combination of colors provides a more accurate and vibrant representation of the original picture.

This model consists of four ink colors: cyan (C), magenta (M), yellow (Y), and key (black, K). These four inks are combined in various proportions to produce a wide range of colors in the final print. Therefore, the correct answer would be four colors (CMYK), including black.

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The value of x is 54.

If a transversal meets two parallel lines, each pair of same-side interior angles is supplementary (their sum is 180°), according to the theorem for the "same-side interior angle theorem."

The given angles in the figure are 2x + 42° and x - 24°, which are interior angles formed on the same side of the transversal.

By Same Side Interior Angles Theorem,

2x + 42° + x - 24° = 180°

3x + 18° = 180°

3x = 180° - 18°

3x = 162°

x = 54

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Answer:

14

Step-by-step explanation:

The students who read newspapers is 30, and the read story books is 90.

Let number of students read newspapers as N and story books as S.

We have

Out of 110 students, 10 read neither newspaper nor story book.

This means that these 10 students are not included in either N or S.

As, students who read story books is three times read newspapers. then, S = 3N.

So, the total number of students who either read newspapers or story books is given by:

= 110 - 10

= 100

and, the total number of students who either read newspapers or story books is given by:

N + S - 20 = 100

Substituting S = 3N, we have:

N + 3N - 20 = 100

4N - 20 = 100

4N = 120

N = 30

Now, we can calculate the number of students who read story books:

S = 3N = 3 c 30 = 90

Therefore, the students who read newspapers is 30, and the read story books is 90.

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Answer:

-5 is the y intercept.

Step-by-step explanation:

Ok, lets do the steps in order.

1) Make a point-slope form equation.

We know that the format of it is y - y1 = slope(x - x1), so we know have to substitute our information in the equation.

y - 5 = 5(x - 2)

2) Convert our point-slope form equation into slope intercept form, and solve for the y-intercept.

y = slope(x) + b... right? So we now have to do math.

Distribute the right side of the equation to get :

y - 5 = 5x - 10

Now cancel out the -5, and then subtract on both sides.

y = 5x - 5

And -5 is your y intercept :)

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The value of tSTAT is 4.08. The slope of the regression line tells us the rate at which Y changes for each unit increase in X.

tSTAT stands for "t statistic". t statistic is a parameter that estimates how far a sample mean is likely to be from the population mean. A t-test is used to determine whether a difference between two groups is significant. The formula for calculating the t-statistic is:tSTAT = (b1 - 0) / Sb1Where b1 is the slope of the regression line, Sb1 is the standard error of the slope, and 0 is the hypothesized value of the slope (which is zero when testing for no linear relationship between two variables, X and Y).In this case, b1 = 5.3, Sb1 = 1.3, and 0 = 0. Therefore:tSTAT = (5.3 - 0) / 1.3 = 4.08Thus, the value of tSTAT is 4.08.

In statistics, the t statistic is a ratio between the difference between the sample mean and the null hypothesis and the standard error of the mean. The null hypothesis in this case is that there is no linear relationship between two variables, X and Y. The t-test is used to determine whether this null hypothesis is true or not.In order to calculate the t statistic, we need to know the slope of the regression line (b1) and the standard error of the slope (Sb1).  The standard error of the slope tells us how much variation there is in the slope estimate from sample to sample.The formula for calculating the t statistic is:tSTAT = (b1 - 0) / Sb1Where b1 is the slope of the regression line, Sb1 is the standard error of the slope, and 0 is the hypothesized value of the slope (which is zero when testing for no linear relationship between two variables, X and Y).In this case, b1 = 5.3, Sb1 = 1.3, and 0 = 0. Therefore:tSTAT = (5.3 - 0) / 1.3 = 4.08.Thus, the value of tSTAT is 4.08.

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Answer:

Deserea ate more

Step-by-step explanation:

One dozen equals 12

Carla ate 1/4 of it

1/4×12/1=3

Carla ate 3 cookies

Deserea ate 1/2

1/2×12/1=6

Deserea ate 6

6 is greater than 3 so Deserea ate more

α - β , α + β are the zeroes of x² - 4x + 3.

The coordinates of (a,b)

(Let a = α & b = β).

On comparing with standard form of a quadratic equation i.e., ax² + bx + c = 0 ;

Let ;

a = 1

b = - 4

c = 3.

We know that,Sum of the zeroes = - b/a

⟹ α - β + α + β = - ( - 4)/1

⟹ 2α = 4

⟹ α = 4/2

⟹ α = 2

And,

Product of the zeroes = c/a

⟹ (α - β) * (α + β) = 3/1

(a + b) * (a - b) = a² - b².

⟹ α² - β² = 3

Putting the value of α we get,

⟹ (2)² - β² = 3

⟹ 4 - 3 = β²

⟹ 1 = β²

⟹ √1 = β

⟹ 1 = β

∴(a , b) = (α , β) = (2 , 1). (Option - C).

I hope it will help you.

Regards.

Answer:

Siso your answer refer in pic

Answer:

Cost price=100%

Step-by-step explanation: