Two positive numbers are in the ratio 2 : 3. Find the numbers if ​(a) their sum is 55 and ​(b) their product is 384.

9514 1404 393

Answer:

  (-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k

Step-by-step explanation:

To answer this question, you need to know two things:

  1) the direction of vector v

  2) the magnitude of vector u

__

direction of v

A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.

The unit vector in the v direction is ...

  v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13

__

magnitude of u

The magnitude of vector u is ...

  |u| = √(5² +(-2)² +3²) = √38

__

Then the desired vector is ...

  (2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k

_____

Additional comment

We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.

The adjusting journal entry will include a debit to the allowance for credit losses of R4,400.

the correct answer is C. debit to allowance for credit losses of R4,400.

To determine the adjusting journal entry for J&L Electrical Services, we need to calculate the ending balance of accounts receivable and the necessary adjustment for the allowance for credit losses.

Beginning balance of accounts receivable: R200,000

Services delivered on credit: R660,000

Collections from debtors: R640,000

To find the ending balance of accounts receivable, we subtract the collections from the sum of the beginning balance and services delivered on credit:

Ending accounts receivable = (Beginning balance + Services delivered) - Collections

Ending accounts receivable = (R200,000 + R660,000) - R640,000

Ending accounts receivable = R220,000

Now, we need to calculate the adjustment for the allowance for credit losses. J&L Electrical Services estimates that 2% of the ending accounts receivable will not be collected:

Allowance for credit losses adjustment = Ending accounts receivable * Estimated uncollectible percentage

Allowance for credit losses adjustment = R220,000 * 2% = R4,400

Since the allowance for credit losses has a beginning balance of R4,000, we need to increase it by R4,400 to match the estimated uncollectible amount:

the correct answer is C. debit to allowance for credit losses of R4,400.

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Answer:

\(x > 1\)

if you graph

\(f(x) = x + 1\)

you'll see that it's that part of graph from x=1 to right and x=1 on this graph is not ncluded so it's x>1

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{3}{n}\) - 10.

The quotient of 3 and a number translates to \(\frac{3}{n}\), then, all you have to do is subtract 10 from that value, giving the expression above.

Answer:

D. Bimodal

Explanation:

The given histogram has two creast, each crest represent a mode. So, we can say that this is a bimodal graph. Therefore, the answer is

D. Bimodal.

As the company asset other than investment securities cost $50,000 and market value of the assets is $75 million. The assets will be recorded and reported as at $75,050,000.

An asset is a resource with monetary value that an individual, corporation, or country owns or controls with the expectation of future benefit. An asset is anything that can generate cash flow, reduce expenses, or increase sales in the future, whether it's manufacturing equipment or a patent.

A company's assets are reported on its balance sheet. They are divided into four categories: current, fixed, financial, and intangible. They are purchased or created in order to increase the value of a company or to benefit its operations.

The reported asset of the company will be:

= $50,000 + $75 million

= $75,050,000

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The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is \(-8.6+3.15\).

What is formula for slope and intercept is?

\($$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$\)

The slope is

\($$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$\)

The intercept is

\($$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$\)

The regression equation is

\($$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$\)

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Figure VWXY is congruent to Figure JKLM because rigid motions can be used to map Figure VWXY onto Figure JKLM.

Figure VWXY is similar to Figure JKLM because rigid motions and/or dilations can be used to map Figure VWXY onto Figure JKLM.

The scale factor is 1.

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

In this context, Figure VWXY and Figure JKLM are both congruent because they can undergo rigid motions. Additionally, Figure VWXY and Figure JKLM are both similar because they can undergo rigid motions and/or dilations;

Scale factor = LM/YX = VW/JM = WX/KL

Scale factor = 1/1 = 6/6 = 5/5

Scale factor = 1.

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Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Let the bigger number be x.

x- 37976 = 48698

x= 48698 + 37976 = 86674

Answer:

Let the bigger number be x.

x- 37976 = 48698

x= 48698 + 37976 = 86674

Step-by-step explanation:

Answer:

your answer calculated would be: x(30x^4 + 15xy^2 + y)

Step-by-step explanation:

i used math-way it's a really useful online calculator

Answer:

58

Step-by-step explanation:

Let the angle = x

Let the complement = 90 - x

2x = (90 - x) + 6

2x = 96 - x

3x = 96

x = 96/3

x = 32

============

The angle = 32

The complement = 90 - 32 = 58

Answer:The acceleration that an objects gains is given by the mass of the object.

If the acceleration of the object becomes 5 m/s² the force is 15 N.

Reason:

The given parameters are;

The acting force ∝ The acceleration of the object.

The acceleration given by an amount of force, F, of 18 N = 6 m/s²

Required:

The force acting on the object acceleration, a, is 5 m/s².

Solution:

According to Newton's Second Law of motion, we have;

F = m·a

Where;

m = The mass of the object

Therefore, we have;

From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the

given object is given as follows;

The force acting when the the acceleration, a = 5 m/s², is therefore;

F = 3 kg × 5 m/s² = 15 N

If the acceleration of the object becomes 5 m/s² the force is 15 N.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

h(x) is a discrete function, so its domain and range only contain individual points.

h(x) contains the points (-5, -2), (-4, 2), (0, 6), (2, -4), and (4, 4)

Look at the y-coordinates: -2, 2, 6, -4, 4

Arrange them in order: -4, -2, 2, 4, 6 ==> B

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

y-2=5/3(x-3)

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Answer:186.66is answer

p=14000

r=8%

time=60days=2month/12=1/6year

Step-by-step explanation:

simple interest=ptr/100=14000×8×1/600=186.666

Answer:

2.1544

Step-by-step explanation:

\(\sqrt[3]{10}\) = 2.1544

check: 2.1544^3

Answer:

169miles

Step-by-step explanation:

15mins to hours = 15/60

= 1/4hours

Time = 3¼hours= 13/4

Distance= ?

Speed= 52miles/hr

speed= distance/time

Distance= speed × time

= 52 × 13/4

=169miles

Answer: 6 hours and 10 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

         - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}\)

             Solve x²-5x+6

\(\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}\)

(x-2)(x-3)

\(\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}\)

                      First, we think of two numbers such that

     If we multiply them, we'll get 6

      If we add them, we'll get -5

These numbers are -2 and -3.

Write them here:

(x-2)(x-3)

Now, how do we get (x-2)(x-3) from x(x-2)-3(x-2)?

Notice that (x-2) is the common term, so we factor it out:

(x-2)

And now, we write the other two terms that are left in the parentheses:

(And the terms left are x and -3)

(x-2)(x-3)

Notice that we ended up with the same answer.

           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The value of distance AB is 187.5 units

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

sine rule can be expressed as;

a/sinA = b/sinB = c/sinC

The opposite side to angle A is BC

the opposite side to angle C is AB

therefore;

A = 180-( 117 +24)

A = 180- 141

A = 39°

290/sin 39 = x/ sin24

xsin39 = 290 × sin24

0.629x = 117.95

x = 117.95/0.629

x = 187.5

therefore the distance AB is 187.5

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Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

If the distribution of professional baseball player salaries has a mean of $3.2 million. the test statistic and P-value for this significance test is :A. t = 1.83 and 0.025 < P-value < 0.05.

We will use a t-test to determine whether the sample mean salary of baseball players on the East Coast is significantly different from the population mean salary of $3.2 million, given a sample of 30 players with a sample mean of $3.9 million and a standard deviation of $2.1 million.

The null hypothesis is that the mean salary for baseball players on the East Coast is $3.2 million, while the alternative hypothesis is that it is different from $3.2 million.

The test statistic for this hypothesis test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (3.9 - 3.2) / (2.1 / sqrt(30)) = 1.83

To find the P-value for this test, we need to determine the degrees of freedom (df) for the t-distribution. Since the sample size is 30, df = 30 - 1 = 29. Using the t-table with 29 degrees of freedom and a two-tailed test at the alpha level of 0.05, we find that the critical values are ±2.045.

The P-value for the test is the probability of getting a t-value as extreme as 1.83 or more extreme, given the null hypothesis. We can find this probability using the t-table or a statistical software program. Using the t-table with 29 degrees of freedom, we find that the area to the right of 1.83 (corresponding to the alternative hypothesis of a greater mean salary) is between 0.025 and 0.05.

Therefore, the correct answer is A. t = 1.83 and 0.025 < P-value < 0.05. This indicates that there is some evidence to suggest that the mean salary for baseball players on the East Coast is different from $3.2 million.

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The interquartile range of the data will be 0.215.

The lower half is:

7.86, 7.87, 7.99, 8.03

The median of the lower half is:

(Q1) = (7.87 + 7.99) / 2 = 7.93

The upper half is:

8.06, 8.08, 8.09, 8.20, 8.43

The median of the upper half is:

(Q3) = (8.09 + 8.20) / 2 = 8.145

The IQR is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215

Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955

Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795

None of the data points fall outside these thresholds, so there are no outliers in this data set.

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Answer:

y = 9/10x - 7/5

Step-by-step explanation:

Slope = 9/10

Point (6,4)

y-intercept = 4 - (9/10)(6) = 4 - 54/10

= - 7/5

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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