Mark got $25.00 for his birthday, which he is allowed to spend on anything he wants.His dad takes him to the arcade and he spends $9.00 playing games. Mark decides tobuy a remote control car for $12.00 and a giant soda pop for $2.50. How muchmoney does Mark have left?

Answer:

Since p-value > ∝, H0 is accepted

Step-by-step explanation:

Calculating gives the following results.

ANOVA Table

Source DF               Sum             Mean      F Statistic P-value

                                 of Square           Square

Groups     6         191.61                      31.935        0.020          0.999

(b/w groups)

Error

(within 14          21736.08                1552.577

groups)                                                                                                    

Total  20          21927.69 1096.385                                          

1. H0 hypothesis

Since p-value > ∝, H0 is accepted.

Hence the averages of all groups considered to be equal.

Or the difference between the averages of all groups is not big enough to reject H0.

2. P-value

P-value equals 0.999. This means that if we would reject H0, the chance of type1 error (rejecting a correct H0) would be too high i.e  (99.99%)

The bigger  p-value  supports H0.

3. The statistics

The test statistic F equals 0.020, which lies in the accepted range: [-∞ : 2.8477]

There are 14 dogs and 46 chickens in the farmyard.

The supposition that there are d dogs and c chickens.

Each chicken has two legs, but each dog has four.

Consequently, the total number of legs may be written as follows:

4d + 2c

Since we are aware that there are 148 legs in total, we can construct the following equation:

4d + 2c = 148

We may create another equation since we know that there are a total of 60 heads (dogs and chickens):

d + c = 60

Now that we have two equations with two variables, we may answer them both at the same time.

2d + 2c = 120 is the result of multiplying the second equation by two.

When we deduct this from the first equation, we obtain 2d = 28.

So, d = 14.

Reintroducing this into the second equation, we get:

14 + c = 60

So, c = 46.

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Answer:

c

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

We have the final part 4x/40 = 7. We can simplify this to x/10 = 7 by dividing the numerator and the denominator by 4. We then multiply both sides by 10 to get x = 70

Answer:

hi there, the answer is

A=45 cm2

Step-by-step explanation:

A= 1/2 x 10 x 9

A=5 x 9

A=45 cm2

Answer:

90,000

Step-by-step explanation:

90,000 × 10 = 900,000

The equation of the function graphed below is f(x) = a(x - 2)² - 3 since the vertex is at (2, -3).

We have,

From the graph given,

The vertex is at (2, -3).

Now,

The vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Where (h, k) is the vertex of the parabola.

Given the vertex (2, -3), we can plug in the values of h and k into the vertex form:

f(x) = a(x - 2)² - 3

Thus,

The equation of the function graphed below is f(x) = a(x - 2)² - 3

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Answer:

Step-by-step explanation:

Answer:

\(7.00\)

Step-by-step explanation:

\(7.00+.48=7.48\)

Answer:

The answer to the question is B) 7.00

Step-by-step explanation:

It says that

\(7.00 + 0.48=6.48\)

But, That is wrong

So the correct version would be

\(7.00+0.48=7.48\)

Hope this helps

The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

43,200

Step-by-step explanation:

25,000x .20=5,000

30,000 x .20=6,000

36,000x.20=7,200

43,200x.20=8,640

51,840x.20=10,368

For the initial fee, Bob charges less than Ginny.

A unit rate means a rate for one of something.

Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.

Ginny initial charge = $80

Bob initial charge =$60

Hence, For the initial fee, Bob charges less than Ginny.

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The equation that shows  the damping ratio for a mass-spring-damper system which is defined in terms of the mass, m, stiffness, k, and damping, b is  ζ = b / (2sqrt(mk)).

The damping ratio ζ is defined as the ratio of the damping coefficient b to the critical damping coefficient b_c, which is the minimum damping required to prevent the system from oscillating.

The damping ratio is a dimensionless quantity that represents the amount of damping in the system relative to the critical damping needed to prevent oscillations. A higher damping ratio indicates a more heavily damped system, while a lower damping ratio indicates a less damped system that may oscillate more.

The motion of a mass-spring-damper system can be described by a second-order linear ordinary differential equation (ODE) of the form:

md²x/dt² + bdx/dt + kx = F(t)

where m is the mass of the system, b is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position, and  the external force applied to the system is F(t).

The critical equation will be -

b_c = 2√(mk)

Therefore, the damping ratio can be expressed as:

ζ = b / b_c

Substituting the expression for b_c into the above equation, we get:

ζ = b / (2√(mk))

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Answer:

90 square feet.

Step-by-step explanation:

Let's set up an equation!

SA= 2(xy)+2(xz)+2(yz).

Lets say that x=3 y=6 and z=3

We plug it in.

2(18)+2(9)+2(18)= SA

36+18+36=SA

72+18=SA

90=SA

90 square feet = Surface area.

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Answer:

Step-by-step explanation:

(a)

The sample space is

{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}

(b)

i  {(2,2), (4,4), (2,4), 4,2)}

ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}

iii {(1,1)}

iv {3,4), (4,3)}

v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}

vi {(1,1), (2,2), (3,3), (4,4)}

vii  {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}

viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}

The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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Answer: 450

Step-by-step explanation: 95+115+240=450

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

Answer:

Step-by-step explanation:

Given that Ruben's distance from Barstow is d = |210 -60t|, you want to know the time t when he is exactly 90 miles from Barstow.

The absolute value will be 90 when the argument of the function is either -90 or +90.

The question resolves to two equations:

These two-step linear equations can be solved in the usual way:

Then ...

Ruben is 90 miles from Barstow after driving 2 hours, and again after driving 5 hours.

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

Answer:

H0: p1=p2    against the claim Ha: p1≠p2

Step-by-step explanation:

Here the proportion of the people going for medical checkup before the program is p1= 0.76

The proportion of the people going for medical checkup after the program is p2= 686/880=0.78

Our null and alternate hypothesis will be

H0: proportion of the people going for medical checkup before the program is equal to the proportion of the people going for medical checkup after the program

against the claim

Ha:  proportion of the people going for medical checkup before the program is not equal to the proportion of the people going for medical checkup after the program

Mathematically this can be written as

H0: p1=p2    against the claim Ha: p1≠p2

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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Answer:

x/16 + 10

Step-by-step explanation:

10+(x÷16)

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times 16/16.

10 x 16 / 16 + x/16

Since 10 x 16 / 16 and x/16 have the same denominator, add them by adding their numerators.

10 x 16 + x / 16

Do the multiplications in 10×16+x.

160 + x / 16 = x/16 + 10

The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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