3x = 6+y
- 3х + y = -6

Answer:

may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025

Take a look at the attachment below. It proves that the inverse of matrix P does exists, as option c,

Hope that helps!

Answer:  C

Step-by-step explanation:

Given    a    b

             c    d

Multiply the reciprocal of the determinant by    d   -b

                                                                             -c     a

Determinant = ad - bc = 2(-3) - 4(1)

                                    = -6    -    4

                                    =      -10

[tex]-\dfrac{1}{10}\left[\begin{array}{cc}-3&-4\\-1&2\end{array}\right] \\\\\\\\=\left[\begin{array}{cc}\dfrac{-3}{-10}&\dfrac{-4}{-10}\\\\\dfrac{-1}{-10}&\dfrac{2}{-10}\end{array}\right]\\\\\\\\=\left[\begin{array}{cc}\dfrac{3}{10}&\dfrac{2}{5}\\\\\dfrac{1}{10}&-\dfrac{1}{5}\end{array}\right][/tex]  

Answer:

The number of people who voted in this election was 1.24 times the number who voted in the last election

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

In this question:

Up by about 24%, so we want the multiplier for a increase of 24%.

So

1 + (24/100) = 1 + 0.24 = 1.24

The number of people who voted in this election was 1.24 times the number who voted in the last election

Answer:

Domain stays the same while the range changes

Step-by-step explanation:

While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.

=> x- coordinate = Domain

=> y-coordinate = Range

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.

When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.

The Domain represent as x-coordinate and the range as y-coordinate

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Hence, option C is correct.

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Answer:

12%.

Step-by-step explanation:

It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.

Total budget = $529

Total expenditure = $465.36

Under budget = $529 - $465.36 = $63.64

We need to find the percentage of under budget.

[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]

[tex]\%=\dfrac{63.64}{529}\times 100[/tex]

[tex]\%=0.12030\times 100[/tex]

[tex]\%=12.030\%[/tex]

[tex]\%\approx 12\%[/tex]

Therefore, the required percentage is 12%.

Answer:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]

[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]

And for this case we want a 98% confidence interval. The significance would be:

[tex] \alpha= 1-0.98=0.02[/tex]

The degrees of freedom are:

[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]

And the critical value for this case is:

[tex] t_{\alpha/2}= 2.374[/tex]

And the confidence interval would be given by:

[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]

And replacing we got:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]

Answer:

The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.

Step-by-step explanation:

Given that area of square is increasing at a rate of 16 sq ft/min.

Given that final perimeter is 36ft

Perimeter of a square = 4 [tex]\times[/tex] side = 36

So, side, a' = 9 ft

We know that area of a square is given by the formula:

[tex]A = side^2 = a^2[/tex] (If we let side = a units)

Change in area =

[tex]a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft[/tex]

So, side got changed from 8.06ft to 9 ft.

So, perimeter when side was 8.06 ft:

[tex]4 \times 8.06 = 32.24\ ft[/tex]

Hence, increase in the perimeter when perimeter is 36 ft is = 36 - 32.24 = 3.76 ft

For finding Next increase:

area gets changed from 81 sq ft to 81+16 = 97 sq ft

So, new side = [tex]\sqrt{97}[/tex] ft = 9.85 ft

Next increase in perimeter = 4 (New side - Old side)

= 4 (9.85 - 9)

= 3.4 ft/min

Answer:

Option (B)

Step-by-step explanation:

If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,

P(B | A) = [tex]\frac{P(A\cap B)}{P(A)}[/tex]

P(A ∩ B) = P(B|A) × P(A)

P(A ∩ B) = (0.8) × (0.4)

            = 0.32

Therefore, Option (B) will be the correct option.

Answer:

Option B is correct.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer: 15

Step-by-step explanation: (9-6) + 12

                                              (3) + 12

                                              15

Answer:

Colin can do this is 272 ways.

Step-by-step explanation:

The first counter goes to Obi and the second to Zeema, so the order is important. This means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Two counters from a set of 17. So

[tex]P_{(17,2)} = \frac{17!}{(17-2)!} = 272[/tex]

Colin can do this is 272 ways.

Answer:

Step-by-step explanation:

Plug in 2 for x.

f(2) = -3(2)² - 7

f(2) = -3(4) - 7

f(2) = -12 - 7

f(2) = -19

Answer:

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{s}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]X = 17.79, \mu = 17, s = 0.08[/tex]

How many standard deviations is the sample mean from the mean of the distribution of sample?

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{17.79 - 17}{0.08}[/tex]

[tex]Z = 9.875[/tex]

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Complete question:

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto-mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Letx4 5 the number of 4-cylinder connecting rods produced next week x6 5 the number of 6-cylinder connecting rods produced next week s4 5 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6 5 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

a) Using the decision variables x4 and s4, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units

b) Using the decision variables x6 and s6, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units

c) Write a constraint that requires that production be setup for exactly one of the two rods

d) Write the cost function to be minimized

Answer:

a) x₄ ≤ 8000s₄

b) x₆ ≤ 8000s₆

c) s₄ + s₆ = 1

d) MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

Explanation:

a) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units, is written as:

x₄ ≤ 8000s₄

b) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units is written as:

x₆ ≤ 8000s₆

c) The constraint that requires that production be setup for exactly one of the two rods:

Since we have:

x₄ ≤ 8000s₄ ; x₆ ≤ 8000s₆

The constraint that requires that production be setup for exactly one of the two rods will be:

s₄ + s₆ = 1

d) Write the cost function to be minimized:

Since we are to find the cost function to be minimized, we take the function below:

MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

Answer: 53.333333, 53 1/3

Step-by-step explanation:

The unit rate in this question means how many calories for one ounce.  Thus, you can simply divide 480 by 9 to get 53.3333333

Answer:

Step-by-step explanation:

Calories in a low calorie dinner = 480 calories

Serving at one time = 9 ounce

then,

Unit rate = Amount of calories in one serving

So,

Amount of calorie in 9 serving = 480

Amount of calorie in 1 serving = 480/9

In simple form : 160/3

= 53.33 calories

Hope this helps...

Good luck on your assignment..

Answer: 1 5/6, or 11/6, or 1.83333333

Step-by-step explanation:

[tex]\frac{6}{3} + -\frac{1}{6}[/tex]

6/3 is 2.

Thus, the answer is 2 - 1/6 or 1 5/6

Answer:

11/6

Step-by-step explanation:

First, we need to find a common denominator for the 2 fractions.

A common denominator for 3 and 6 is 6.

Let’s get the fraction 6/3 to a denominator of 6.

Multiply by 2/2

6/3 * 2/2

(6*2) / (3*2)

12/6

Now the fractions have common denominators and can be added.

12/6 + (-1/6)

When adding negative fractions, you can simply subtract.

12/6 - 1/6

Subtract across the numerator and leave the denominator as is

11/6

This fraction can be written as: 2 1/6, 11/6, or 1.83333

[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]

Answer:

Assumptions are mentioned below.

Step-by-step explanation:

It is provided that the 99​% confidence interval for μ is (1000, 2100 ).

Now it is assumed that the 99​% confidence interval for μ was based on a sample of size n = 25.

The assumptions necessary for the interval to be valid are:

Answer:

The answer is "2nπ".

Step-by-step explanation:

Given:

[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]

We know:

[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]

put the value of [tex]\sin^2 x[/tex] value in the above equation:

[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]

Let [tex]\cos x= A[/tex]

[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]

[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]

[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]

The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]

[tex]\boxed{\bold{x=2 n \pi}}[/tex]

Answer:

1/2

Step-by-step explanation:

The numbers 3 or odd are 1, 3, 5, and 7.

4 numbers out of 8.

4/8 = 1/2

P(3 or odd) = 1/2

Answer: 6p^3+29p^2+22p-21

Answer:

14.72% probability that both professors get their grants funded

Step-by-step explanation:

Independent events:

If two events, A and B are independent, the probability of both happening is:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

In this question:

Event A: Professor Jane is funded

Event B: Professor Joe is funded.

Professor Jane has a probability of 0.64 of being funded.

This means that [tex]P(A) = 0.64[/tex]

Professor Joe has probability 0.23 of being funded.

This means that [tex]P(B) = 0.23[/tex]

What is the probability that both professors get their grants funded

[tex]P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472[/tex]

14.72% probability that both professors get their grants funded

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

[tex]\frac{798}{8} (41)[/tex]

When we evaluate this expression we get

[tex]\frac{798}{8} (41)[/tex]

[tex]=99.75(41)[/tex]

[tex]= 4089.75[/tex]

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

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Answer:

B.90°counterclockwise

Answer: B

Step-by-step explanation:

A. If you rotate a figure in the first quadrant 180 degrees clockwise it will end up in the third quadrant so the answer can't be A.

B. If you rotate a figure in the first quadrant 90 degrees counterclockwise it will end up in the second quadrant because you will rotate it backwards and as you could see A prime is in the second quadrant.

C.If you rotate a figure in the first quadrant 180 counterclockwise it will end up in the third quadrant. SO the answer can't be it C.

D.If your rotate a figure in the first quadrant 270 counterclockwise it will end up in the fourth quadrant. So the answer can't be D.

Answer:

The answer is not "REMAINDER" it's "Quotient"

Step-by-step explanation:

Cancelling identical factors in the numerator and the denominator will give the quotient.

When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that when dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is also known as the integer portion of a division, a fraction, or a ratio.

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Answer:

C

Step-by-step explanation:

(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8

Answer:

2x -8

Step-by-step explanation:

f (x) = 3x - 5

g(x) = x + 3,

(f - g)(x) = 3x - 5 - ( x+3)

Distribute the minus sign

            = 3x-5 -x-3

Combine like terms

           = 2x -8

Answer:

6 bags

Step-by-step explanation:

3/4 = .75

4.5/.75 = 6 =

6 BAGS

The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part

Answer:

b

Step-by-step explanation:

The slope is 3/4 and the y-intercept is y(0,2)

The slope is what we multiply by the variable ( here t) and the y-intercept is the number we add

Answer:

The car travels 83 1/3 meters in 3 seconds.

Step-by-step explanation:

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Lets find speed of car in Meters/second

speed of car in m/sec = 100*1000 m/3600 second

here we have taken 1000 for km and 3600 for hour

speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

speed of car in m/sec = 250/9  m per sec

We know that

distance = speed*time

speed = 250/9  m per sec

time =3 second

distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.

Thus, car travels 83 1/3 meters in 3 seconds.

Answer:  A) 0.5

Step-by-step explanation:

The denominator should be in the form 1 + e sin θ

Currently the denominator is: 2 + 1 sin θ

Divide the denominator by 2 to get:  1 + 0.5 sin θ

Thus, e = 0.5