8x-3y=3
2x+y=-15

solve by eliminaion.

Answer: 90 cubes

Step-by-step explanation:

Hi, to answer this question, first we have to calculate the volume of the rectangular prism:

Volume of a rectangular prism (Vp) = width x length x height

Replacing with the values given:

Vp = 3 x 2.5 x 1.5 = 11.25 cubic feet

Now, we have to calculate the volume of one cube:

Volume of a cube ( Vc) = side length ^3 = (1/2)^ 3= 1/8 ft3 = 0.125 ft3

Finally, we have to divide the volume of the prism by the volume of one cube:

11.25 / 0.125 = 90 cubes

Answer:

18

36

72

144

Step-by-step explanation:

For numbers to be divisible by 2 they must end in an even number

For numbers to be divisible by 9 the sum of the digits must be divisible by 9

b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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Answer:

X+1=3

x = 3 - 1

x = 2

Check:

2 + 1 = 3

x-4=5

x = 5 + 4

x = 9

Check:

9 - 4 = 5

Answer:

1)x=2

2)x=9

Step-by-step explanation:

x+1=3

=>x=3-1

therefore

x=2

second question

x-4=5

=>x=5+4

therefore

x=9

Answer: 1 to 5

Step-by-step explanation:

Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve this system of equations by substitution:

We can solve the first equation for an expression in x:

  x = (1.1 -0.3y)/0.2 = (11 -3y)/2

Substituting for x in the second equation gives ...

  0.7(11 -3y)/2 -0.5y +0.8 = 0

  7.7 -2.1y -y +1.6 = 0 . . . . . . . . . multiply by 2, eliminate parentheses

  -3.1y +9.3 = 0 . . . . . . . . . . . . collect terms

  y -3 = 0 . . . . . . . . . . . . . . . divide by -3.1

  y = 3 . . . . . . . . . . . . . . . add 3

  x = (11 -3(3))/2 = 2/2 = 1 . . . . . find x

The solution is (x, y) = (1, 3).

__

Additional comment

A graphing calculator confirms the solution.

Given:

The angle is 1591 degrees.

To find the coterminal angle:

First, we need to write the given angle in terms of 360 degrees.

We can write,

So, the coterminal angle of 1591 degrees is 151 degrees.

A simplified fraction to represent the ratio where ∠A is the angle of reference is 12/13.

In order to determine the magnitude of angle A, we would apply cosine ratio because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the given side lengths cosine ratio formula, we have the following;

cos(θ) = Adj/Hyp

cos(A) = 1.2/1.3

cos(A) = 1.2/1.3 × 10/10

cos(A) = 12/13

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To identify bn, we can rewrite the series as:

(-1)^n (n^3 / 3^n)
So, bn = 1/n^3.

To test the series for convergence or divergence, we can use the ratio test:

lim |(−1)^(n+1+1) (n+1)^3(n+1) / n^3n| as n approaches infinity

= lim |(−1)^n+1 (n+1)^3 / n^3 (1 + 1/n)^3| as n approaches infinity

= lim |(n+1)/n|^(3) / (1 + 1/n)^3 as n approaches infinity

= lim (1 + 1/n)^(3-3n) (n+1)^3 / n^3 as n approaches infinity

= lim (1 + 1/n)^(-2n) (1 + 1/n)^3 (n+1)^3 as n approaches infinity

= lim [(1 + 1/n)^(-2)]^n (1 + 1/n)^5 (1 + 1/n)^(-2) (n+1)^3 as n approaches infinity

= 0

Since the limit is less than 1, the series converges.

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Answer:

20x-12

Step-by-step explanation:

Expected completion time of the path other than the critical path is 18.16 weeks.

a) The expected times and variances for each of the activities are as follows:

Activity 1:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 2:

Expected Time = 10.33 weeks

Variance = 2.78 weeks

Activity 3:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 4:

Expected Time = 7.83 weeks

Variance = 1.36 weeks

b) The expected completion time of the critical path is 19.66 weeks.

The expected completion time of the path other than the critical path is 18.16 weeks.

c) The variance of the critical path is 1.38 weeks.

The variance of the path other than the critical path is 4.14 weeks.

d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.

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In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.

Given, the coordinates of the triangle XYZ are:

X = (4,5)

Y = (6,3)

Z = (3,2)

and the coordinates of the triangle X'Y'Z' are:

X' = (0,5)

Y' = (-2,3)

Z' = (1,2)

for image of the triangle XYZ to get reflected and become X'Y'Z',

reflection of axis takes place.

But the images are not identical and symmetrical, so the reflection is not about y axis.

we check for x=2

hence reflection of axis when x=a is :

P(x,y) →x'(2a-x , y)

therefore use the above formula and check the coordinates of the reflected image.

X(4,5) → X'(2(2)-4 , 5)

x(4,5) → X'(0,5)

Y(6,3) → Y'(2(2)-6 , 3)

Y(6,3) → Y'(-2,3)

Z(3,2) → Z'(2(2)-3 , 2)

Z(3,2) → Z'(1,2)

hence x=2 is the reflection of triangle XYZ and X'Y'Z'.

Therefore we get the requires answer.

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Let r be the common ratio. The correct answer is Rounding to the nearest dollar, the value of Madame Dumas's art collection 12 years after she started tracking its worth is $9,498,559.

A) Let the value of the collection three years ago be the first term, a = $450,000.

Then we can write:

Second term: \(ar = $810,000\)

Third term: \(ar^2 = $1,458,000\)

To find the common ratio r, we can divide the second term by the first term and the third term by the second term:

\(ar/a\)= \(\frac{810,000}{450,000}\)

\(r = 1.8\)

\(ar^2/ar\) = \(\frac{450000}{810000}\)

\(r = 1.8\)

So the explicit rule for the value of Madame Dumas's art collection n years after she started tracking its worth is:\(a_n = ar^(n-3)\)

B) To find the value of her collection 12 years after she started tracking its worth, we can use the explicit rule:

\(a_12 = ar^(12-3) = ar^9\)

We already know that \(a = $450,000\) and \(r = 1.8\), so we can substitute those values:\(a_12 = $450,000(1.8)^9 = $9,498,558.57\)

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The difference in grams between the mass of a nickel and the mass of a bee hummingbird is 3.164 grams.

A nickel has a mass of 5 grams. On the other hand, a bee hummingbird, known as the world's smallest bird, has a mass of 1.836 grams. To find the difference between their masses, we subtract the mass of the bee hummingbird from the mass of the nickel.

5 grams (mass of a nickel) - 1.836 grams (mass of a bee hummingbird) = 3.164 grams.

Therefore, the difference in grams between the mass of a nickel and the mass of a bee hummingbird is 3.164 grams. This means that a nickel weighs approximately 3.164 grams more than a bee hummingbird.

In conclusion, the mass difference between a nickel and a bee hummingbird is 3.164 grams. The comparison highlights the vast contrast in size and weight between these two objects, emphasizing the incredibly small mass of the bee hummingbird.

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Answer:

x=2

Step-by-step explanation:

6x-4 = 8

Add 4 to each side

6x-4+4 = 8+4

6x= 12

Divide by 6

6x/6 = 12/6

x=2

Answer:

16 percent increase in the number of train passengers from 2010 to 2012.

Answer:

b is not a function

Step-by-step explanation:

To be a function there must be a one to one correspondence.

Each x must only go to one y

b has an x that goes to two different y's

1 goes to 5 and 13.  That makes it a relation not a function

Answer:

x=5

Step-by-step explanation:

you are solving for x

so...

start off by figuring out what goes into 20 4 times

you can also just do 20 divided by 4 which would give you 5

Answer:

rounded to the nearest tenth = 3.7

Answer: 3.7

Step-by-step explanation: because i learn this a book called big fst notbook math by Walbook i recomed it to you

There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

It is calculated by adding up all the values in the set and then dividing the sum by the total number of values. The mean is often used as a measure of central tendency, which describes the typical or representative value in a set of data.

This is a two-sample independent means t-test problem.

The null hypothesis is that there is no difference between the mean times needed to access flight information for the two major airlines, and the alternative hypothesis is that there is a difference.

Assuming the conditions for inference are met (random sampling, normality of the population, and independence between the two samples), we can calculate the t-value and the p-value for the test.

The formula for the t-value in a two-sample independent means t-test is:

t = (x1 - x2) / √[ (s1²/n1) + (s2²/n2) ]

Plugging in the given values, we get:

t = (2.5 - 2.1) / √[ (0.8²/20) + (1.1²/20) ]

t = 1.21

Using a t-table with 38 degrees of freedom (df = n1 + n2 - 2), we find that the p-value is between 0.10 and 0.05.

Therefore, the correct answer is c:

There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.

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Answer:

The fraction can be written as 43/50

Step-by-step explanation:

Place the Percentage Value at the top over 100.

= 86/100

On reducing the fraction, we get the exact form: 43/50

Answer:

43/50

Step-by-step explanation:

Place the Percentage Value at the top over 100.

= 86/100

On reducing the fraction, we get the exact form: 43/50

Answer:

a. i) Please see the  included graph of the equation $10·x + $12·y = $300

ii) The intercepts give the maximum number of either short-sleeve (x-intercept) long-sleeved (y-intercept) that can be ordered

Step-by-step explanation:

The given information are;

The cost of each short-sleeved shirt = $10

The cost of each long-sleeved shirt = $12

The amount available in the budget = $300

The equation for the total cost = $10·x + $12·y = $300

Where;

x = The number of short-sleeved shirts

y = The number of long-sleeved shirts

Rewriting the equation given in slope and intercept form, we have;

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Please find attached, the graph of the equation made with Microsoft Excel

The values of the data that can calculated to plot the graph are;

x, y

(0, 25 )

(5, 20.83 )

(10, 16.67)

(15, 12.5 )

(20, 8.33)

(25, 4.17)

(30, 0 )

The x-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget, while the y-intercept gives the number of short-sleeve shirts that can be purchased with the $300 available budget.

The graph of the equation is shown below.

The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.

The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.

Given:

Short-sleeved shirts cost $10 each.  

Long-sleeved shirts cost $12 each.

The total budget is $300.

The given equation is:

\(10x+12y=300\)

where \(x\) is the number of short-sleeved shirts and \(y\) is the number of long-sleeved shirts.

To find:

The graph of the given equation and the interpretation for the intercepts.

Explanation:

We have,

\(10x+12y=300\)

Substitute \(x=0\).

\(10(0)+12y=300\)

\(12y=300\)

\(y=\dfrac{300}{12}\)

\(y=25\)

So, the y-intercept is at point (0,25).

Substitute \(y=0\).

\(10x+12(0)=300\)

\(10x=300\)

\(x=\dfrac{300}{10}\)

\(x=30\)

So, the x-intercept is at point (30,0).

Plot the points (30,0) and (0,25) on a coordinate plane and connect them by a straight line.

The x-intercept is at point (30,0), which means the number of short-sleeved shirts is 30 when the number of long-sleeved shirts is 0.

The y-intercept is at point (0,25), which means the number of long-sleeved shirts is 25 when the number of short-sleeved shirts is 0.

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The appropriate growth model for the given scenario would be a logistic growth model where the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach.

A logistic growth model is appropriate for situations where the growth rate of a variable initially increases and then slows down as it approaches a maximum value or carrying capacity. In the given scenario, the number of arrests initially grew for several years, but has been decreasing recently, suggesting that it may have reached a saturation point. Thus, a logistic growth model would be appropriate to model the trend of the number of arrests.

In a logistic growth model, the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach. In the case of the number of arrests, the carrying capacity could be the maximum number of arrests that can be made in a given period, which might be limited by factors such as the number of police officers, the number of crimes committed, or the effectiveness of law enforcement policies. As the number of arrests approaches this limit, the growth rate slows down, eventually leading to a plateau or a decline in the number of arrests.

Overall, a logistic growth model would be appropriate for the given scenario as it takes into account the saturation point and provides a better fit to the trend of the number of arrests over time.

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Answer:

18

Step-by-step explanation:

just add them unless you have to find the numbers for the 2 little squares

Answer:

27

Step-by-step explanation:

cut shapes. then 6x2 is 12, 3x5 is 15, then add

Answer:

A = 147 cm²

Step-by-step explanation:

A = πr²

A = (3)(7)²

A = 3(49)

A = 147 cm²

Hope this helps!

The numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.

Here, we are given 6 numbers-

2.2, 2.276, 2.291, 2.14, 2.26, 2.221

Now, we can add as many zeroes as we want after the decimal, it does not change the value of the number.

Thus, let us make all the numbers 3 digit decimal numbers

2.200,  2.276,  2.291,  2.140,  2.260,  2.221

Here, all the numbers have 2 in the units place, so we just need to compare the decimals

The first digit after decimal is 2 in all the numbers except 2.140, thus it is the smallest.

Then, the second digit after decimal is 0 in 2.200, thus it is the next smallest number.

By similar logic, looking at the second digit after the decimal only we can arrange the remaining numbers as 2.221, 2.276, 2.260, 2.291.

Thus, the numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.

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Your question was incomplete. Please check for full content below-

Drag the numbers below to put them in order from least to greatest

2.2, 2.276, 2.291, 2.14, 2.26, 2.221

The complete table is

x -12 -6 3 15

y -6 5 15 15

The domain is given as:

Domain = {-12, -6, 3, 15}.

The incomplete table is given as

x

y -6 5 15 15

Enter the domain in the x values

x -12 -6 3 15

y -6 5 15 15

Hence, the complete table is

x -12 -6 3 15

y -6 5 15 15

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Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer:

First two boxes are 6

Third box is -18

the last row is 3/1 (-18/1) = (1/3a) 3/1

Step-by-step explanation:

Ima try my best to explain:

-6 = 12 + 1/3a

+6    +6        

0 = 18 + 1/3 a    subtract 18 on both  in order to get 1/3a by itself

-18   -18

-18 = 1/3a          

-18/ 1/3  = 1/3a / 1/3 to make it easier multiply by the reciprocal on both sides

3/1 x -18/1 = 1/3 x 3/1      

multiply across will get you -54/1 which is just -54