if the test scores of a class of 35 students have a mean of 75.3 and the test scores of another class of 26 students have a mean of 65.6, then the mean of the combined group is

The interest rate in tenth of percentage that would be required in order for Joseph to end up with $1.710 is 4.4%.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal

To calculate the interest rate that would be required, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for R

Hence, the interest rate is 4.4%.

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Answer:

235.15 sq.cm

Step-by-step explanation:

Perimeter of a triangle is sum of all three sides.

    Ratio of sides = 5 : 6 : 7

Sides are 5x , 6x , 7x

  Perimeter = 72 cm

5x + 6x + 7x = 72

Combine like terms.

             18x  = 72

Divide both sides by 18,

                x = 72÷ 18

               x = 4

5x = 5*4 = 20 cm

6x = 6*4 = 24 cm

7x = 7*4 = 28 cm

Sides: 20cm , 24 cm , 28 cm

So, it is a scalene triangle.

   To find the area of scalene triangle use Heron's formula.

a = 20 cm  ; b = 24 cm and c = 28 cm

   [tex]\sf s = \dfrac{a + b+ c}{2} \ where \ s \ is \ the \ semi \ perimeter.[/tex]

      [tex]\sf =\dfrac{72}{2}\\\\\\ = 36 \ cm[/tex]

    s - a = 36 - 20 = 16 cm

   s -b   = 36 - 24 = 12 cm

   s - c  = 36 - 28 = 8 cm

          [tex]\sf \boxed{Area = \sqrt{s(s-a)(s-b)(s-c)}}[/tex]

                      [tex]\sf =\sqrt{36*16*12*8}\\\\ = 6*4*4\sqrt{6}\\\\= 96 *2.45\\\\=235.15 \ cm^2[/tex]

The value of p in the given triangle is equal to 99.3°.

What is Law of Cosines?

In the given question, the side lengths of the triangle are as follows,

[tex]a=3.6 cm,[/tex] [tex]b=2.8cm,[/tex] and [tex]c=5.3cm[/tex]

Here, the angle between a and b, [tex]\angle C=p[/tex]

We know that the angle p between the two sides of lengths a and b can be found using the Law of Cosines Formula, given as,

[tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex]

Substituting the above values, we get

[tex]5.3^{2} =3.6^{2} +2.8^{2} -2 \times 3.6 \times 2.8 \times cos p[/tex]

Simplifying, we get

[tex]28.09=12.96+7.84-20.16cosp\\\implies 28.09=20.8-20.16cosp\\\implies 7.29=-20.16 cosp[/tex]

Rearranging in terms of p, we get

[tex]cosp=-\frac{7.29}{20.16} \\\implies p=cos^{-1} (-0.3616)\\\implies p=99.3\textdegree[/tex]

Therefore, the value of p is equal to 99.3°.

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Answer: 24.957

Step-by-step explanation: Calculator

Answer: 10

Step-by-step explanation:

Set the equal angles as x, as shown below.

Then, [tex]sin(x)=\frac{x+4}{8}[/tex] and [tex]sin(x)=\frac{2x+1}{12}[/tex]. Set them equal to each other and solve for x:

[tex]\frac{x+4}{8} =\frac{2x+1}{12} \\ \\12(x+4)=8(2x+1)\\12x+48=16x+8\\48-8=16x-12x\\4x=40\\x=10[/tex]

This is assuming those two triangles are right triangles. I'm actually not sure if they're right triangles.

The total cost of your trip to the movie theater is $43.50.

The total cost will be the sum of money spent on ticket and soda and popcorn.

Ticket cost for or cost price of Ticket for:

         5 years old brother = $4.25

          Grandparents = $6.00 × 2 = $ 12.00

           For self= $7.25

Total cost of tickets = $4.25 + $ 12.00 + $ 7.25

                                 = $ 23.50

Total Money spent = Cost of ticket + cost of soda and popcorn

                                = $ 23.50 + $20

                                = $ 43.50

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Answer:

6*v=102

Step-by-step explanation:

The two numbers that we requires are; y=−3+3√5 or y=−3−3√5

We know that in this question, we are required to obtain the two numbers that multiply to -36 and add up to -6. Now we have to write the problem into a system of simultaneous equations.

Thus;

Let the numbers by x and y

x + y = -6 ---- (1)

xy = -36 ------ (2)

x = -36/y ------ (3)

If we substitute (3) into (1)

-36/y + y = -6

-36 + y^2/y = -6

Multiply through by y

-36 + y^2 = -6y

Forming a proper quadratic;

y^2 + 6y - 36 = 0

Solving the quadratic for y

y=−3+3√5 or y=−3−3√5

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The area of an L-shaped room is calculated by cutting off the Leg of the L and finding the area of the rectangles separately.

Area of the floor space occupied by an objected which is measured in unit squares.

A rectangle is an object which is bounded by four sides, four vertices

The area (A) of a rectangle is;

A=Length x Width

The Area of the L-shaped room is calculated by

A = Area of the Vertical rectangle + Area of the Leg

A = LW + lw

where

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Answer:

Match

1) 5 hours = H. 300 minutes

2) 72 hours = D. 3 days

3) 360 seconds = G. 6 minutes

4) 540 minutes = J. 9 hours

5) 4 days = A. 96 hours

6) 60 minutes = C. 1 hour

7) 720 seconds = 12 minutes

8) 6 days = E. 144 hours

9) 3 1/2 hours = F. 210 minutes

10) 3 minutes = I. 180 seconds

Equivalent times:

11) 7 hours = 420 minutes

12) 480 = 6 minutes

13) 120 hours = 5 days

14) 180 minutes = 3 hours

15) 11 minutes = 660 seconds

The minimum number of swaps required to flip the list is 2.

Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.

Given an array with values 5, 10, 15, 20,25

swap reverses the array:

25, 10, 15, 20, 5

25, 20, 15, 10, 5

So, for reversing the number of swaps required list is 2 ..

This may be the smallest variation possible.

Hence, the minimum exchange required to achieve list reversal is two.

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The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The events' estimated probabilities are as follows, according to the exponential probability theory:

P(3) = 0. 125

P(6 in 500 rolls) = 68 rolls

Number of times event occurs / number of trials

A number of attempts = sum of frequency:

(12+35+11+23+7+12) = 88

So the probability that a 3 will be rolled as

⇒ number of 3's / number of attempts

⇒ 11/88 = 0.125

The number of 6's probable in 500 rolls

⇒ (12 /88) × 500

⇒ 68.18 = 68

Therefore, the expected number of 6's roll would be 68.

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As we know 1 kilometer = 39370.079 inches

and, 8.39 kilometer = 330,315 inches.

Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.

Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.

To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.

Since 01 kilometer = 39,370.07874 inches,

We can use this simple formula to convert:

          inches = kilometers × 39,370.079

Now, according to the question:

inches = 8.39 × 39370.079

inches = 33.315

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The ordered pair that is the solution to the equation -x + 5y = 3 is (-3,0) and (0, 0.6)

Ordered pair:

Ordered pairs refers a set of 2 numbers that exist in a particular order. The first one represents the x value and the second one refer the y value.

Given,

Here we need to find the ordered pair (x, y) that is a solution to the equation -x + 5y = 3

In order to find the solution ordered pair we have to plot this equation on the graph.

To plot this equation, we have to use the graphing calculator, and then input the given equation as the function, then we get the graph like the following.

While we looking into the graph, we have identified that the solution ordered pairs are (-3,0) and (0, 0.6)

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The strategies that would eliminate a variable to help solve the system of equations are

B. Multiply the first equation by -2 and add it to the second equation

C. Multiply the first equation by 1/3 and add it to the second equation

D. Multiply the second equation by 3 and add it to the first equation

From the question we are to determine the strategies that would eliminate a variable to help solve the system of equations.

The given system of equations is

12x + 5y = 7

-4x + 10y = -7

To eliminate y,

Multiply the first equation by -2 and add it to the second equation

-2 × [12x + 5y = 7]

-24x - 10y = -14

Now add to the second equation

 -24x - 10y = -14

+ (-4x + 10y = -7

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

-28x = -21

To eliminate x

Multiply the first equation by 1/3 and add it to the second equation

1/3 × [12x + 5y = 7

4x + 5/3y = 7/3

Now, add it to the second equation

   4x + 5/3y = 7/3

+ (-4x + 10y = -7

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

5/3y + 10y = 7/3 + (-7)

Also, to eliminate x

Multiply the second equation by 3 and add it to the first equation

3 × [-4x + 10y = -7

-12x + 30y = -21

Now, add to the first equation

  -12x + 30y = -21

+ (12x + 5y = 7

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

35y = -14

Hence, the required strategies are the ones explained above.

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Answer:

No because their ratios are not the same

Step-by-step explanation:

The scalar from 5 to 10 is 2 but from 3 to 4, its 4/3.

The length of side PR will be 40.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the isosceles triangle,

Two sides are,

⇒ PR = 5n and QR = (32 + n)

Now,

Since, The triangle is an isosceles triangle.

So, Two sides are equal.

We formulate;

5n = 32 + n

5n - n = 32

4n = 32

n = 8

Thus, The length of side PR = 5n

                                           = 5 x 8

                                           = 40

Therefore, The length of side PR will be 40.

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Convert the inequality to interval notation: a > 10:

(10, ∞)

In the equation y= 17x + 8 ,

the value of x = (1,25) ,(2,42) ,(3,59) ,(4,76).

Given that,

           y= 17x + 8

When x = 1

y = 17 × 1 + 8 = 25

when x=2,

y = 17 × 2 + 8 = 42

When X=3,

y = 17 × 3+ 8 = 59

when X=4

y = 17 × 4+ 8 ]= 76

Therefore, the required solution is :

x = (1,25) ,(2,42) ,(3,59) ,(4,76).

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There is a modest rise in arrival rates as compared to the prior arrival because the value is bigger than 0.05. It is a minuscule rise.

Given that,

The Message is arrive at an electronic mall server at the average

rate is 4 messages for every 5 minutes. Then the average

number of message is said to be a and mean is 4 to 5 interval.

Therefore ,we can use poission's approximation  to binomial  distribution in this case,

λ=4/5 min

( a ) Then , The Number of messages arrived in 1 hour

4x 12 = 48 . , So 48 messages per hour.

Now , our New arrival rate of messages , λ =48

By using possion's distribution ,

θ = time/rate

= 60/48= 1.25

NOW

probability density function of X is given as

f (x ) = θ e^-θx

for X>0

Given , the probability of new message arrival during given frame

equal is 0.05

p (X > x ) = 0.05

Now , of θ ∫e^-θx dx  = 0. 05 .

then, e^-θx =0.05

Apply logarithm on both sides , then

In( e^-θx) = In 0.05

By solving,

1- 25

X = 2. 39658

(b) Now , probability of arrival of 50 messages in 60 minutes

p (X>2.39658 ) = 0.05

Now arrival gap is θ = 60/50 = 1.2

P(x> 2.39658 ) =e^-θx

=e^- 1- 2 * 2.39658 = 0.0564

NOW ,

p(x>2- 39658) = 0.0564.

It is greater than 0.05 , so it is called there is slight increase in arrival rates as compared to the previous arrival. It is very small increase .

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The probability that a car buyer bought an alarm system or bucket seats is 0.50.

Probability of ,

Alarm system p(A) = 40/100 = 0.40

Bucket seat p(B) = 30/100 = 0.30

Alarm system and bucket seat p(A and B) = 20/100 = 0.20

Probability of alarm system or bucket seat is :

= p(A)+p(B)-p(A and B)

= 0.40+0.30-0.20

= 0.50

In mathematics, probability is the likelihood of an event occurring. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. A simple example is the tossing of a coin, where the probability of either head or tail is 1/2.

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Answer:5.76

Step-by-step explanation:

-2 2/5=-2.4

(-2.4)^2=5.76

the relationship is a function because she "made up time".

A relation that states that there should only be one output for each input are called a function. alternatively, a function is a particular kind of relation—a set of ordered pairs—that adheres to a specific rule—each X-value should be associated with only one y-value.

if a relation is one-to-one or many-to-one it is a function.

Function            Not a Function

one-to-one        many-to-many

many-to-one     one-to-many

In the above-mentioned scenario, She basically made up for the time she had spent standing at the location by increasing her pace. Since she picked up the pace, you can assume that she completed the task in the same amount of time as if she had not stopped.

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Answer:

It's D.

Step-by-step explanation:

I know I can't see that option, but it's D. If you use A for the first one, you get 4(-4) which is -16 and you add 3 to that, it's -12, so that's not 2 so it can't be A. If you use B for the first one, you get 2(-4) which is -8, and if you add 3, you get -5, not 2, so it can't be that either. If you use C, you get 0.5(-4) which is -2, and if you add 3 to that, you just get 1, so it can't be C either. I assume there is fourth option, so it's D.

The two equations for this system are C = 0.60f + 15 and C = 0.80f + 13.

The number of fish for which the cost is the same is 10 fishes.

The cost of this fish is equal to $21.

In order to write a system of linear equations to model and describe this situation, we would assign variables to the number of fish and the cost of fish respectively, and then translate the word problem into algebraic equation as follows:

Note: 1 dollar is equal to 100 cents.

Since the starter aquarium kit costs $15 plus 60 cents per fish at wet pets, we have:

C = 0.60f + 15     ........equation 1.

Since the starter aquarium kit costs $13 plus 80 cents per fish at gills and frills, we have:

C = 0.80f + 13          ........equation 2.

Next, we would solve the system of equations as follows:

0.80f + 13 = 0.60f + 15

0.80f -0.60f = 15 - 13

0.20f = 2

Number of fish, f = 2/0.20

Number of fish, f = 10 fishes.

From equation 1, we have:

Cost of fish, C = 0.60f + 15

Cost of fish, C = 0.60(10) + 15

Cost of fish, C = 6 + 15

Cost of fish, C = 21 dollars.

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y = -3x +2

The general equation for a linear line is y = mx + b

Where:

To find the slope of a line we can use the formula [tex]\frac{rise}{run}[/tex]

Rise over run can be found suing two different points on the line.

in this case: (-1,5) and (1,-1)

The rise is the difference in y values: [tex]y_2 -y_1[/tex]

rise = (-1) - 5

rise  = -6

run = [tex]x_2 - x_1[/tex]

run = 1 - (-1)

run = 2

rise/run = [tex]\frac{-6}{2}[/tex]

rise/ run = -3

We now have y = -3x + b

To find b we just look at the graph and locate a what point x = 0

The function that represents the relationship is y = 40x

The total area that he painted = 200 square feet

Time is between 8 am and 1 pm

Then the time taken = 5  hours

The relationship is given by the area a person can paint varies directly with the amount of time he works

Here we have to apply the unitary method

The area that he painted in one hour = 200 / 5

= 40 square feet

Consider the y is the total area that he painted and x is the number of hours

Then the function will be

y = 40x

Hence, the function that represents the relationship is y = 40x

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Answer:

X = -3, y = -8

Please see the link to view the Graph: