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Her son mowed the most lawn

35%of the lawn meeds to be mowed

The responses for the confidence intervals of the 45 lbs weight and the set of data are;

3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928

4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.

The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.

3. The confidence interval can be found using the formula;

[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]

Where;

[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs

s = The standard deviation of the sample = 0.09 lbs

n = The sample size

z = The confidence level = 1.96 at 95% confidence level

Therefore;

[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]

45.0472 < μ < 45.0928

The correct option is therefore, option D

Therefore;

4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.

Increasing the level of confidence will increase z, thereby also increasing the confidence interval.

The correct option is therefore, option C.

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The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Answer:

x=7

Step-by-step explanation:

3(2x-5)=9(10-x)

6x-15=90-9×

6x+9x=90+15

15x=105

×=7

Answer:

x = 7

Step-by-step explanation:

1. Distribute

3(2x - 5) = 9(10 - x)

6x - 15 = 9(10 - x)

2. Rearrange Terms

6x - 15 = 9(10 - x)

6x - 15 = 9(-x + 10)

3. Distribute

6x - 15 = 9(-x + 10)

6x - 15 = -9x + 90

4. Add 15 to both sides

6x - 15 = -9x + 90

6x - 15 + 15 = -9x  + 90 + 15

5. Simplify

Add the numbers:

6x - 15 + 15 = -9x + 90 + 15

6x = -9x + 90 + 15

Add the numbers:

6x = -9x + 90 + 15

6x = -9x + 105

6. Add 9x to both sides

6x = -9x + 105

6x + 9x = -9x + 105 + 9x

7. Simplify

Combine like terms:

6x + 9x = -9x + 105 + 9x

15x = -9x + 105 + 9x

Combine like terms:

15x = -9x + 105 + 9x

15x = 105

8. Divide both sides by the same factor

15x = 105

15x/15 = 105/15

9. Simplify

Cancel terms that are in both the numerator and denominator:

15x/15 = 105/15

x = 105/15

Divide the numbers:

x = 105/15

x = 7

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The length of AC is equal to 5 units.

Given:

From the figure :

ΔABC is a right angled triangle with sides:

AB = 3 and BC = 4

Right angled triangle:

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

The third side is called the hypotenuse, which is the longest side of all three sides.

we know that,

According to pythagorean theorem:

[tex]AB^2+BC^2 = AC^2[/tex]

3^2 + 4^2 = AC^2

9 + 16 = AC^2

AC^2 = 25

AC = [tex]\sqrt{25}[/tex]

AC = 5 units.

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Full question:

is in the image uploaded

Am pula mare!

Da aaaaaaaaaaa????

Answer:

9 + 20p ≤ 125

Step-by-step explanation:

This does not include the tax.

Step-by-step explanation:

Answer please anyone help same doubht

Step-by-step explanation:

Answer:

Refer to the photos taken.

Step-by-step explanation:

The area of walk is 504 square feet

The area of rectangle is define as a  product of length L and width w

calculate the area of rectangle yard

Area = L x W,  

where A equal the Area, L equals the length and W equal width.

A = 35 x 55

A= 1925 square feet

Area of the rectangular yard is 1925 square feet

From the question, we have 3ft wide goes all the way along the fence inside.

Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .

Area = L x W

A = 29 x 49

A = 1421 square feet

Area of new rectangle formed by allowing for three foot walk is 1421 square feet

Area of Walk

To get the area walk;  we subtract area of new rectangular formed from area of rectangular yard

Area of Walk = Area of Rectangular yard - Area of new rectangle

Area of Walk = 1925 - 1421

Area of Walk = 504 square feet.

Therefore, the area of walk is 504 square feet.

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The ABCD parallelogram turns into a rhombus if all of its sides are equal.

All Sides are equal.

Diagonals bisect at 90°.

In our question,

AB = DC is given for a quadrilateral ABCD (parallelogram).

When a parallelogram's sides are uneven, symmetry is disrupted and its diagonals do not bisect at 90 degrees. However, when all of the sides are equal, the diagonal does bisect at 90 degrees and the parallelogram becomes a rhombus.

Therefore, when all of a parallelogram's sides are equal, it becomes a rhombus.

The complete question is:

You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?

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The difference between their average hiking rates is 0.51 miles/hour.

Given that, it took Lannie 1.9 hours to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Using speed =Distance/Time

Here, Ranger Cove distance =4.8 miles and time =1.9 hours

Now, rate =4.2/1.9

= 2.21 miles/hour

Mohawk Trail distance =6.8 miles and time =4 hours

Now, rate =6.8/4

= 1.7 miles/hour

The difference between their average hiking rates

= 2.21-1.7

= 0.51 miles/hour

Hence, the difference between their average hiking rates is 0.51 miles/hour.

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The fourth term of the polynomial (d - 4b)³ is D. -64d³.

A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.

Given the expression (d - 4b)³, we need to open the bracket, hence:

(d - 4b)³ = d³ + 3(d²)(-4b) + 3(d)(-4b)²

             = d³ - 12bd² + 48b²d - 64d³

Therefore, the fourth term of (d - 4b)³ is D. -64d³

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The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The metaphor of a function machine, which accepts an object as its input and produces another object as its output based on that input, makes the concept of a function simple to understand.

Given a collection of possible outputs Y (codomain) and a set of inputs X (domain), a function is more precisely defined as f: X→Y which shows that f is a function from X to Y using this notation.

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The length of t will be;

⇒ t = 294.30 inches.

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 ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Now,

Since, In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.

Hence, ∠ T = 180 - (17 + 52)

∠ T = 180 - 69

∠ T = 111°

Now, We use the sin rule as;

⇒ t / sint = s / sin s

⇒ t / sin 111° = 250 / sin 52

⇒ t = sin 111° × 250 / sin 52

⇒ t = 0.93 × 250 / 0.79

⇒ t = 294.30 inches.

Thus, The length of t will be;

⇒ t = 294.30 inches.

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Answer: 296.2

Step-by-step explanation:

t/sin111 = 250/sin52

t=250 sin111/52 = 296.1826 = 296.2

The free fall speed of a parachutist can exceed 216 kilometres per hour. During his 20 seconds of free fall, the parachutist will plunge 1960 metres.

Every time an object is subject to a net force that is greater than zero, acceleration happens. You can experience it when riding down a steep hill on your sled in the snow or when you slightly accelerate or decelerate in an elevator. Furthermore, we know that the universe as a whole is expanding at an even faster rate because to the general theory of relativity. This implies that the distance between two places is always enlarging, yet we are oblivious to this on a daily basis because every scale in the universe also expands.

During free only acceleration due to gravity(g) acts on the parachutist. Assuming acceleration due to gravity is positive i.e. g=9.8m/s² .

For conversion we know that

1 km = 1000 m and

1 hr = 3600 seconds

216 km/hr = 60 m/s

Location of parachutist during 20 seconds

[tex]h = \frac{1}{2} \times g \times t^2[/tex]

[tex]h=\frac{1}{2} \times 9.8 \times 20^2[/tex]

h = 1960 meters

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The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest as given in the questions is

A = P[(1 + r/n)^nt

Substituting the values into the formula

A = 5300(1 + 0.08/6)^12 * 6

A = 8,551.56

Erica will owe $8551.56

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The complete table of values of the linear equation y = -3x - 4 is

x     y

-1     -1

0     -4

1     -7

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

y = -3x - 4

Also, we have the following table of values

x     y

-1

0

1

The above table of values mean that the x values are

x = -1, 0 and 1

Substitute x = -1, 0 and 1 in the equation y = -3x - 4

So, we have the following representation

When x = -1

y = -3(-1) - 4 = -1

When x = 0

y = -3(0) - 4 = -4

When x = 1

y = -3(1) - 4 = -7

So, we have the following ordered pairs

(-1, -1), (0, -4) and (1, -7)

When represented on the table of values, we have

x     y

-1     -1

0     -4

1     -7

The above represents the complete table of values

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We know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

According to the question,

We have the following information:

A function is given and we need to find if the given function is discontinuous or not.

There are two situations to find this whether the function is discontinuous or not. First, we need to know that the function has both the left hand limit as well as the right hand limit.

Second condition is to check whether if the limits are equal or not. If they are not equal then the function is discontinuous.

Hence, we know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

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The percentage of the quality cost, that is taken up by the prevention and appraisal costs are:

The prevention cost would be the cost associated with customer service training as this ensures that less mistakes are made.

The appraisal cost would be the cost to verify credit card information.

The percentage of total quality control cost that prevention cost is, would be:

= 379, 600 / 949, 000 total

= 40 %

The percentage for appraisal cost is:

= 189, 800 / 949, 000

= 20 %

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The rest of the question is:

Present the percentage values of prevention and appraisal as a percentage of the quality cost.

The circumference of a circle can be found using formula 2πr where r is the radius of circle.

What is the circumference of a circle?

A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.

Suppose the radius of a circle is 5cm

So, we can find the circumference by using formula 2πr

     Circumference = 2 × π × 5 = 10π cm.

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Answer: A

Step-by-step explanation:

18.6 is less than 18.7

so 18.6<18.7

Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.

The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).

The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.

Cost of car = $27,000

Annual Percentage Rate (APR) = 4%

Payment period = 4 years (monthly)

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $27,000

FV (Future Value) = $0

Results:

PMT = $609.63

Sum of all periodic payments = $29,262.24

Total Interest = $2,262.45

Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.

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Using half-life and disintegration constant, the sample that will remain 4 seconds 2.03g

This is the spontaneous decay of an active radioactive sample. The decay curve is exponential and it slope is constantly changing.

The half-life of this sample given can be used to find the disintegration constant of the sample.

The formula of half - life is given as

T₁/₂ = ln2 / λ

Substitute the values into the equation;

7.13 = 0.693 / λ

λ = 0.693 / 7.13

λ = 0.0972

The amount of sample left after 4 seconds will be

A = Ne⁻(λt)

A = 3e⁻(0.0972 * 4)

A = 2.03g

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The number of votes that Candidate B received, given the rate and the votes received by Candidate A, is 63 votes

The question shows that for every 5 votes received by Candidate A, Candidate B will receive 7 votes.

This means that if Candidate A has 45 votes, the number of votes that Candidate B would receive can be found to be :

= Number of votes received by Candidate A / Number of votes Candidate A receives per Candidate B x Number of votes  Candidate B receives per Candidate A

= 45 / 5 x 7

= 9 x 7

= 63 votes

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The first part of the question is:

Candidate A receives about 5 votes for every 7 votes received by Candidate B.

The total monthly charges for the mobile plan if the usage is 120 minutes is $480.

Given that,

A mobile plan's total monthly costs, $C, are made up of a fixed fee of $ 20 and a variable fee that is based on usage. The cost is $0.20 per minute used.

We have to calculate the total monthly charges for the mobile plan if the usage is 120 minutes.

We know that,

A mobile plan fee is $20

For 1 min $0.20 for mobile plan

For 120 minutes

=120×0.2

=24

=24×20

=480

Therefore, the total monthly charges for the mobile plan if the usage is 120 minutes is $480.

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The year in which Gert will find that she has doubled her money is year 20.

Simple interest is when the interest earned on an investment increases linearly each year.

The formula that can be used to determine simple interest is:

Simple interest = amount invested x duration of the investment x interest rate.

When the amount of money in the account is double what it is now, it means that the interest earned would be $2000 and the value of the account would $4000 (2000 + 2000).

Year when investment would have doubled  = simple interest / (amount invested x interest rate)

Year when investment would have doubled  = $2000 / (0.05 x 2000)

Year when investment would have doubled  = $2000 / 100 = 20 years

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How to find a parabola's equation using its Vertex Form

Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)2+k. ...

Step 2: find the value of the coefficient by substituting the coordinates of point P into the equation written in step 1 and solving for a.

The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.

If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].