cramer's rule is a method of calculating the solution to a system of linear equations by finding the of the determinants.

Answer:

165 of the animals at the shelter are cats.

Step-by-step explanation:

If one-fourth of the animals at the shelter are cats and there are 660 animals at the shelter, to get the number of cats you divide the total number of animals by the percentage of cats.

660 / 4 = 165

Let x be the cost of the small bag.

The large bag costs x + 30 more than the small bag.

So the cost of the large bag is x + (x + 30) = 2x + 30

The two-piece set of luggage cost is the sum of the cost of the small and large bag, so

122 = x + (2x + 30)

Solving this equation for x, we get:

x = 42

Therefore, the small bag costs 42 dollars and the large bag costs 2*42 +30 = 114 dollars.

The answer to each part is given above.

Given are the functions as follows -

p(x) = - 5x + 5

q(x) = - 4x - 2

We can write -

(p о q)(5) = (- 5x + 5)(- 4x - 2)

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)

(p о q)(5) = 20x² + 10 - 20x - 10

(p о q)(5) = 20x² - 20x

(p о q)(5) = 20 x 25 - 20 x 5

(p о q)(5) = 500 - 100

(p о q)(5) = 400

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400

(q о p)(5) = 400

Therefore, the answer to each part is given above.

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Option D is the correct  Answer. A necessary and sufficient condition that the three triangles formed have equal areas, is that the point be the intersection of the medians​.

To divide a triangle into three triangles of equal area is to find the centroid the point where the medians intersect. After determining the centroid point G below, construct the segments connecting the vertices to the centroid. The three triangles created are of equal area.

So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle.

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The mathematical expression, for the given statement is 20g/3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a statement, two-thirds times g times 10.

Converting into mathematical expression,

2/3 of g = 2g/3

And,

2/3 of g of 10

= 2g/3 × 10

= 20g / 3

Hence, the mathematical expression, for the given statement is 20g/3

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Answer:

y = 5

Step-by-step explanation:

3y - 7 = 8  Add 7 to both sides

3y - 7 + 7 = 8 + 7

3y = 15  Divide both sides by 3

y = 5

If a single marble is picked at random from the jar then the probability of it begin a blue marble is 9/32.

A glass jar containing five red 7 green 9 blue an 11 yellow marbles.

If a single marble is picked at random from the jar then we have to determine the probability of it begin a blue marble.

Red Marble = 5

Green Marble = 7

Blue Marble = 9

Yellow Marble = 11

Total Marble = Red Marble + Green Marble + Blue Marble + Yellow Marble

Total Marble = 5 + 7 + 9 + 11

Total Marble = 32

The probability of it begin a blue marble = Blue Marble/Total Marble

The probability of it begin a blue marble = 9/32

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Answer: it would be B:log 5/log 7

Step-by-step explanation:

1) "The analysis of past demand helps predict future demand" is true about Time series forecasting.

2) A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: less than 30 minutes.

Hence, option (A) is the correct choice.

3) Normal probability distribution is applied to: a continuous random variable

Hence, option (d) is the correct choice.

A time series is a sequence of data points indexed in time order in mathematics. A time series is most frequently defined as a succession of photos taken at evenly spaced moments in time. As a result, it is a series of discrete-time data.

Time series forecasting is the process of making scientific forecasts based on time stamped data from the past. It entails developing models based on previous data and utilizing them to make observations and drive future strategic decisions.

The straight-line approach, moving averages, simple linear regression, and multiple linear regression are the four basic forecast methodologies. The straight-line and moving average techniques both presume that the company's past results will be broadly consistent with future results.

We are provided the following details:

- Average mu in the population: 30

The following is an alternate theory.

[tex]$$H_1: \mu < 30 \text { ( Claim ) }$$[/tex]

For this case, the alternative hypothesis is that the population mean is less than 30 minutes.

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There are 20 marbles, and 12 of them are yellow; therefore, the number of yellow marbles does not equal the number of marbles, nor does the number of yellow marbles equal the number of yellow marbles because they are yellow.

I There can only be 31 marbles in the bag, since 30 marbles is the most number that each person can have equitably, plus one extra marble. As a result, the first response is A. Since 60 is divisible by 2, 3, and 5, plus 1 (leaving 1 remaining), 61 might also be a conceivable number of marbles in the bag.

The likelihood of selecting a ball from a bag is calculated by dividing the total number of balls by the quantity of that color. As a result, the likelihood of a red ball in the first case is 3/9, or 1/3. The likelihood of selecting a second ball if that ball is now eliminated is 2/8 or 1/4.

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Answer:

8%

Step-by-step explanation:

We can start solving the problem by using the formula for compound interest:

A =[tex]P(1+\frac{R}{n})^{nt}[/tex]

Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:

[tex]P(1+\frac{R}{4})^{2}[/tex] = [tex]1.0816*P(1+\frac{R}{4})[/tex]

We can simplify this equation by canceling out the P and the (1+R/4) on the right side:

[tex](1+\frac{R}{4})[/tex] = 1.0816

We can then solve for R:

[tex]\frac{R}{4}[/tex]=[tex]\sqrt{(1.0816)-1}[/tex]

R = [tex]4(\sqrt{(1.0816)-1)}[/tex]

R ≈ 0.08, is the exact value of R.

So, Mr. Saver's nominal interest rate is 8%.

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Answer:No solution because 0≠12, so it like a trick question.



Step-by-step explanation: There is no solution because if you multiply the bottom equation by -2 everything will cancel making 0≠12.

The false statement regarding Legendre polynomials is given as follows:

E) [tex]P_{2k}(0) = (-1)^k\frac{(2k)!}{2^{2k}k!}, k \in N[/tex]

The Legendre function of order v is the function that is a solution to the differential equation presented as follows:

(1 - x²)y'' - 2xy' + v(v + 1)y = 0.

Examples of Legendre polynomials are given as follows:

From the polynomial of order 2, with k = 2, we have that:

[tex]P_4(0) = 0.375[/tex]

While:

[tex](-1)^2 \times \frac{4!}{16 \times 2!} = \frac{24}{32} = 0.75[/tex]

Different result, hence statement D is false.

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Answer:

g(x) = -√3 (x/3 + 2) + 4.

Step-by-step explanation:

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The properties of a Triangle are :

The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.

In triangle ΔABC

∠B = 44° and ∠C = 17°

So, The sum of angles of a triangle is 180°

Therefore,

∠A + ∠B + ∠C = 180°

⇒∠A + 44° + 17° = 180°

⇒∠A = 180° - 61°

⇒∠A = 119°

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

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If Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.  the height of the tree is 9.43m.

Let x represent the height

x /1.45 = 31.55 -26.7

Cross multiply

x = 31.55 × 1.45 / 4.85

x = 45.7475 /4.85

x = 9.43

Therefore the height is 9.43.

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Answer:

Below

Step-by-step explanation:

12/5  * 875 = R 2 100 000

to see how this works, set up a ratio

5 is to 875 000   as  12 is to x

5 / 875 000    = 12/x

x = 12/5 * 875 000

Answer:

R210,000

Step-by-step explanation:

875,00 : 5 days

x :12 days

cross multiply:

87500*12 = 1050000

5*x = 5x

divide:

1050000/5 = 210000

The total amount of the debit column in the adjusted trial balance is $5,400.

To find the total amount of the debit column in the adjusted trial balance, we need to sum up all the debit amounts listed in the accounts of teh given question.

Debits represent money being paid out of a particular account;

Looking at the trial balance provided, we can identify the following accounts with debit balances:

1. Cash: $500

2. Equipment: $2,000

3. Accounts Payable: $1,000

4. Common Stock: $700

5. Retained Earnings: $600

6. Service Revenue: $900

7. Operating Expenses: $600

8. Dividends: $100

In order to find the total amount of the debit column, we add up all these amounts,

Which gives us:

$500 + $2,000 + $1,000 + $700 + $600 + $900 + $600 + $100 = $5,400

Therefore, the total amount of the debit column in the adjusted trial balance is $5,400

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Answer:

52-green

15-orange

Step-by-step explanation:

g + o = 67  

g = green, o = orange, x = total = 3o + 7

use substitution: (3o + 7) + o = 67

solve for o:4o + 7 = 67

4o = 60o

= 60/4 = 15

solve for g:

g + 15 = 67

g = 52

Answer:

737373

Step-by-step explanation:

You just add them together? Am I missing something?

The final result would be a feasible set with arrows indicating the direction of increase of the objective function z.

The feasible set can be found by solving the system of equations g1, g2, g3 and g4.

g1: -3x - 2y = -6

g2: 5x - 2y = 40

g3: 2x + 4y - 8 = 0

g4: x + y = 5

Solving for x and y,

We will get the coordinates of the feasible set: (2,2), (5,0), (0,5).

Next, we find the vectors that are parallel to each boundary:

g1: (-3, -2),

g2: (5, -2),

g3: (2, 4),

g4: (1,1)

To determine the direction in which the objective function z increases, we compute z.v1 for each boundary:

z.v1 = (-3, -2) * (-3, -6) = 18 + 12 = 30

z.v2 = (5, -2) * (-3, -6) = -15 - 12 = -27

z.v3 = (2, 4) * (-3, -6) = -6 - 24 = -30

z.v4 = (1,1) * (-3, -6) = -3 - 6 = -9

Based on the results, we can see that the objective function z increases in the direction of vector v2 and decreases in the directions of vectors v1, v3, and v4.

To put arrows on each boundary indicating the direction in which the objective function z increases, we would place arrows pointing towards the direction of vector v2 on g2 and away from the direction of vector v2 on g1, g3 and g4.

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Answer:

0.0037

Step-by-step explanation:

Because 36/9643 cannot be simplified down any further, the only other way to describe it is as a decimal which is ~0.0037.

One less than the given number is known as preceding number whereas one more than the given number is the succeeding number.

The logics followed in order to find them:

Base numbers work exactly the same as base 10 numbers (the ones we use on a daily basis).

Take for example, in a decimal system, we have 10 digits available:

0,1,2,3,4,5,6,7,8,9.

When counting, when we get to the 9, we start over again, but writing a 1 to the left.

0,1,2,3,4,5,6,7,8,9,10,11,12....20,21,22,23....,90,91,92,93,94,95,96,97,98,99,10

When reaching 99, we have no more digits to use, so we start the count again and go from 99 to 100.

The same works with any other base number, take for example the base 7 number.

When counting in base 7, we only have 7 digits available: (0,1,2,3,4,5,6) So when 0_{7},each the digit 6, we go immediately to 10, like this:

It went from 6 to 10 and from 16 to 20. This is because in base 7, there is no digits from 7 to 9, so we have directly to 20.

So, if working with decimal numbers, the previous value for 640 would be 639, but notice that in base 7,

There is no such thing as the digit 9, so the greatest digit we can use there 6,

Therefore, the previous value for the number would be. The next number would be because the 1 does exist for a base 7 system.

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Complete question :-

What is the numeral preceding and succeeding each of the following.

A) 640 base 7

B) 100000 base 2

C) 555 base 6

D) 100 base 5

E) 10000 base 4

F) 405 base 6

a) Assuming Christine makes no withdrawals, her $1,500 investment in a 5-year certificate of deposit with an annual interest rate of 1.44% compounded annually, will be worth (future value of) $1,611.16 after 5 years.

b) The total interest earned on Christine's investment after 5 years is $111.16.

The future value represents the compounded present value.

The future value can be computed using an online finance calculator.

N (# of periods) = 5 years

I/Y (Interest per year) = 1.44%

PV (Present Value) = $1,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $1,611.16

Total Interest = $111.16

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The required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A with a center at (3, 4) and a radius of 2 is similar to circle B with a center at (−4, −5) and a radius of 3.
To translate the circle B over circle A is given as 7 units right and 9 units up.

Thus, the required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

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The truth table for the above requirements is shown as the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate).

A truth table is a mathematical table used in logic that spells forth the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.

The truth table for the vending machine scenario is represented in following figure.

The table shows the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate). A 1 in the table indicates that the candy is dispensed, while a 0 indicates that it is not.

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(a) The probability of a failure given there are more than 1,000 wells in a geological formation is 0.1001.

(b) The probability of a failure given there are fewer than 500 wells in a geological formation is 0.0852.

(a) We have to determine the probability of a failure given there are more than 1,000 wells in a geological formation.

P(B∣A) = Total number of failed wells more than 1000 wells/Total number of wells with 1000 failed wells

P(B∣A) = (180 + 443 + 60)/(1685 + 3733 + 1403)

P(B∣A) = 683/6821

P(B∣A) = 0.1001

(b) We have to determine the probability of a failure given there are fewer than 500 wells in a geological formation.

P(B∣C) = Number of failed well/Number of failed wells with total less that 500 wells

P(B∣C) = (2 + 14 + 44 + 3)/(28 + 363 + 309 + 39)

P(B∣C) = 63/739

P(B∣C) = 0.0852

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The complete question is:

Consider the well failure data in the table below. Let A denote the event that the geological formation of a well has more than 1000 wells, let B denote the event that a well failed, and let C denote the event that the geological formation of a well has fewer than 500 wells.

(a) What is the probability of a failure given there are more than 1,000 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣A)=

(b) What is the probability of a failure given there are fewer than 500 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣C)=

Answer:

a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:

(50x + 75) - (25x + 50) = 25x + 25

This is the simplified form of the expression that represents the difference in cost.

b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

Step-by-step explanation:

Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:

To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

Therefore , the solution of the given problem of slope comes out to be

line's equation is y =.1333 x + 1.55.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).If you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope.

Here,

Given : f(x) =4 +x

The line's "intercept" of the y-axis marks the location of the y-intercept. It also makes sense because a player with a 25 cm heel to toe measurement is about 1.55 metres tall. This is most likely.

Any line has the equation y=mx+b (m=slope, b=y-intercept).

Finding two spots on this line where it crosses will reveal the slope of the line. I'll use the numbers (25.5, 1.6) and (26.25,1.7).

=> (y(2)-y(1)) / (x(2)-x(1))

=> m 1.7 - 1.6 / 26.25 - 25.5

=>.1/.75 =.13333 is the formula to calculate the slope.

At roughly 1.55m, this line crosses the y-intercept.

This line's equation is y =.1333 x + 1.55.

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