Rounding please help! Math

Answer:

x axis, then translate x+6, y+1

Answer:

Step-by-step explanation:

We need to figure out how far Eric's car takes him in 1 rotation based on the diameter of his tire in feet. If the diameter of the tire is 18", then it is 1.5'. The circumference will tell us the distance 1 rotation of his tires will take him:

C = 3.1415(1.5) so

C = 4.71225 feet is how far he goes in 1 rotation. If he travels 88 feet in 1 second, we can figure the number of rotations by dividing 88 by 4.71225 to give us the unit rate (or, rotations per second his car makes). This quotient is 18.67 feet per sec, which rounds to 19, choice B.

Answer:

V=πr2h

Step-by-step explanation:

If the columns of A are linearly independent, then it directly follows that the columns of A^2 span R**n.

A is the right response. It is obvious that the columns of A2 encompass Rn if the columns of A are linearly independent.

If the sections of A are linearly independent, you can see why this is the case. A linear combination of the columns of A can then be used to describe any vector x in Rn. The meaning of this is that there are scalars c1, c2,..., cn such that x = c1a1 + c2a2 +... + cnan, where a1, a2,..., an are the columns of A.

Consider the item A2 right now. Aej, where ej is the j-th standard basis vector in Rn, gives the j-th column of A2, which is provided by Aej, Which means that A2 = [Ae1 | Ae2 |... | Aen].

However, A2's columns can be written as linear combinations of the columns of A^2, and so the columns of A^2 span R^n.

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Answer:

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Step-by-step explanation:

Geometric Sequences

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

\(\displaystyle r=\frac{-28}{112}=-\frac{1}{4}\)

Testing with the third term:

\(\displaystyle -28*-\frac{1}{4}=7\)

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

\(a_n=a_1*r^{n-1}\)

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

The value of x is the sum of angle ABO and angle CDO because they are the acute angles made out of parallel lines.

Parallel lines are lines that are always the same distance apart and never intersect. They maintain a constant distance from each other as they extend indefinitely in both directions

Recall one of the theorem:

- Alternate angles made by 2 parallel lines are always equal.

Applying this theorem,

angle ABO + angle CDO = angle BOD

50° + 30° = x°

x° = 80°

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Answer:

Jennys backyard cost 7524 doll hairs.

Step-by-step explanation:

11x9=99

76x99=7524

hope this helps!!

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

X=28.3155948

Step-by-step explanation:

So we only need to use the Adjacent and the Hypotenuse

This means you need to use cos(

so it will be cos(36)=x/35

you multiply both sides by 35

35cos(36)=x

x=28.3155948

I apologise if this is wrong but it should be correct

a) For an 80% confidence level, the margin of error is approximately 3.79.
The margin of error for estimating the population mean with a sample size of 18 and a sample standard deviation of 10.7 is calculated for different confidence levels.

To estimate the population mean with a given sample size (n = 18) and sample standard deviation (s = 10.7), we can calculate the margin of error for different confidence levels. Let's calculate the margin of error for confidence levels of 80%, 90%, and 99%.

a) For an 80% confidence interval:

The formula to calculate the margin of error (ME) for a confidence interval is given by:

ME = z * (s / √n),

where z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.

To find the z-score for an 80% confidence level, we need to determine the area in the tails of the normal distribution that corresponds to a confidence level of 80%. This area will be (1 - confidence level) / 2 = (1 - 0.80) / 2 = 0.10 / 2 = 0.05. The z-score corresponding to a 0.05 area in the tails is approximately 1.28 (lookup from a standard normal distribution table).

Plugging the values into the formula, we have:

ME = 1.28 * (10.7 / √18) ≈ 3.79 (rounded to two decimal places).

Therefore, the margin of error for an 80% confidence interval is approximately 3.79.

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Answer: y-9

12-9

=4

Step-by-step explanation:

Simple math

Answer:

SSS could be used for equilateral triangles, AAA is impossible, Cannot be determined is easily not an option.

This leaves ASA and SAS

An isoscoles triangle is a triangle that has two equal sides. SAS is an abreviation that says two triangles have 2 equal sides. Therefore, number 4 SAS is correct

Step-by-step explanation:

The median of the legs of a triangle joins the vertex to the midpoint of the opposite side of the triangle.

The correct postulate is (d) SAS

An isosceles triangle has two congruent sides and angles.

This means that, postulates AAA and SSS are not possible.

This is so, because both postulates imply that the sides and angles of the triangles are congruent.

See attachment for illustration of the median of the isosceles triangles.

From the attachment, we have the following observations.

These mean that:

The triangles are congruent by SAS postulate.

Hence, the correct postulate is (d) SAS

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Using objective function and linear inequalities in linear programing problem, 44 minutes of running, 16 minutes of rowing and 1 minutes of aerobics should you perform each exercise to burn the maximum of 507 calories.

According to the question,

Imagine you are trying to maximize the calories you burn in a 60-minute workout you do a few times a week. running burns 9 calories per minute, aerobics burns 6 calories per minute, and rowing burns 7 calories per minute.

you want to perform all three exercises to work different muscle groups. for the best effect, you need to run for at least 5 minutes and row for at least 15 minutes. your aerobics session should be no more than 30 minutes.

The system of inequality is; x + y + z = 60

x ≥ 5

y ≥ 15

0 < z ≤ 30

The objective function is, f(x, y, z) = 9·x + 7·y + 6·z

The number of minutes each exercise should be performed are;

Running = 44 minutes

Rowing = 15 minutes

Aerobics = 1 minute

The reason for arriving at the above values is as follows:

The given parameters are:

The total duration of the workout = 60 minutes

The calories burnt per minute by running = 9 calories

Calories burnt per minute by performing aerobics = 6 calories

Calories burnt per minute by rowing = 7 calories

The number of exercises to be performed = The three exercises

The duration of the time for running, x ≥ 5 minutes

Duration of the time for rowing, y ≥ 15 minutes

Duration of the time for aerobics, z ≤ 30 minutes

The system of inequalities based on the constraints are;

x + y + z = 60

x ≥ 5

y ≥ 15

0 < z ≤ 30

Objective function

The objective is to find the duration of each exercise that result in burning the maximum number of calories

Therefore, the objective function is the function that gives the amount of calories burnt, which is the sum of the product of the calorie burnt per minute for a given exercise and the duration of the exercise

The objective function is, f(x, y, z) = 9·x + 7·y + 6·z

Calculating the number of minutes for performing each exercise to burn the maximum calories:

Running burns the most calories, to burn maximum calories, we have;

Running duration = 60 mins - (Minimum duration aerobics + Minimum duration running)

Aerobics burns the least calories

∴ Minimum duration aerobics, z = 1 minute (minimum value possible)

Rowing duration is at least 15 minutes

∴ Minimum duration running, y = 15 minutes

∴ Running duration, x = 60 - (1 + 15) = 44

Running duration, x = 44 minutes

To perform all three exercises and burn maximum calories;

Running = 44 minutes

Rowing = 15 minutes

Aerobics = 1 minute

f(44, 16, 1) = 44 × 9 + 15 × 7 + 1 × 6 = 507

The maximum calories burnt, f(44, 16, 1) = 507 calories

Hence, using objective function and linear inequalities in linear programing problem, 44 minutes of running, 16 minutes of rowing and 1 minutes of aerobics should you perform each exercise to burn the maximum of 507 calories.

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Answer:

18

Step-by-step explanation:

\(184 \times 3 = 59 \div 2 = \times \frac{?}{?} \)

Based on research data from 28 students with a standard deviation of 8 years for their ages, we can calculate a 90% confidence interval for the variance.

To calculate the 90% confidence interval for the variance, we use the chi-square distribution. The chi-square distribution is commonly used for inference about the variance of a normally distributed variable.

First, we need to determine the degrees of freedom, which is the sample size minus one. In this case, the degrees of freedom would be 28 - 1 = 27.

Next, we look up the critical chi-square values corresponding to the desired confidence level of 90% and the degrees of freedom. These critical values represent the boundaries of the confidence interval.

Using the critical chi-square values and the sample size, we can calculate the lower and upper limits of the confidence interval for the variance. This interval provides a range within which we can estimate the true population variance with 90% confidence.

It's important to note that the confidence interval for the variance is typically expressed in terms of squared units (e.g., years squared in this case), as it represents the variability of the variable of interest.

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The cubic function p(x) = \(ax^3 + bx^2\) + cx + d has a tangent with equation y=3x +1 at the point (0,1) and has a turning point at (-1,-3), the values of a, b, c and d are a=2-d, b=4-2d, c=d, and d

The cubic function p(x) = \(ax^3 + bx^2\) + cx + d has a tangent line with equation y=3x +1 at the point (0,1).

In addition, the cubic has a turning point at (-1,-3). To solve for a,b,c and d, we can use both of these facts.

First, let's look at the point (0,1). We know that the equation of the tangent line at this point is

y=3x +1.

Plugging in the coordinates of this point gives us

1=3(0)+1

This means that 1=1

This gives us one equation with one unknown, c.

We can solve for c by simply subtracting 1 from both sides of the equation, giving us 0=c.

Now, let's look at the turning point, (-1,-3).

We know that the equation of the cubic at this point is p(-1)=-3.

Substituting in the values for a,b,c, and d from our first equation gives us

-3=-a+b-c+d.

This gives us another equation with three unknowns, a,b, and d.

We can solve for these unknowns by rearranging the equation and adding 3 to both sides. We get

a+b+d=6.

We now have two equations with four unknowns.

We can solve this system of equations using substitution.

We start by substituting 0 for c in our second equation.

This gives us

a+b+d=6

We can then substitute this into the first equation.

This gives us

a+b-0+d=1

Since we substituted 0 for c, we can subtract b from both sides.

This gives us a+d=1. We can now solve for a and d.

Adding 1 to both sides of the equation gives us

a+d+1=2

which we can rearrange to

a=2-d

Now, we can substitute this into the second equation.

This gives us

(2-d)+b+d=6

We can solve for b by subtracting d and 2 from both sides, giving us

b=4-2d

Now that we have the values of a, b, and d, we can substitute them into the second equation to solve for c.

This gives us

2-2d-4+2d+d=6,

which simplifies to

c=d

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The height of the cone is 15cm.

From the question;

Height of cylinder = 28cm

Let the radius of the solid object = Rcm

The slant height of the cone = 17cm

Cost of painting = Rs. 140 per 100 sq cm

Cost of painting 1 cm² =  140/100 = RS1.4

The total cost of painting = Rs. 2851.2

Total area of the object =  total cost of painting/Cost of painting per sq cm

Total area of the object = 2851.2/1.4  = 2036.57143 cm²

Total surface area of object = CSA of Cylinder + CSA of cone + area of the circle at the bottom

Total surface area of the object = \(\pi rh + \pi rl + \pi r^2\)

So, \(\frac{2851.2}{1.4}\) =  \(\pi rh + \pi rl + \pi r^2\)

\(\frac{2851.2}{1.4}\) = \(2\pi r * 28 + \pi r * 17 + \pi r^2\)

\(\frac{2851}{1.4}\) = \(\frac{1232}{7}r =+\frac{374}{7} r + \frac{22}{7} r^2\)

\(\frac{2851}{1.4}\) = \(\frac{1606}{7} r + \frac{22}{7} r^2\)

\(\frac{2851}{2}\)= \(1606r + 22r^2\)

\(14256 = 1606r + 22r^2\)

\(22r^2 + 1606r - 14256 =0\)

Solving the quadratic equation, the possible value of radius are:

r = 8cm

r = -81cm

r = -81cm will be neglected because radius can not be negative.

Therefore, the radius of the object is 8cm

To find the height of the cone, we should know that the relation between radius, height and slant height of the cone is:

\(l^2 = r^2 + h^2\)

\(h=\sqrt{l^2 - r^2}\)

\(h=\sqrt{17^2 - 8^2}\)

\(h=\sqrt{225}\)

\(h=15cm\)

Therefore, height of  cone in the solid object is 15cm

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Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

can u plz take a more clearer photo of the problem and also try to elaborate

We know that

• 2/5 are strawberries.

• 1/4 of the strawberries are chocolate covered.

We have to find 1/4 of 2/5, let's multiply these fractions.

Answer:

A would be 2

B would be 8

Step-by-step explanation:

It's a little hard to explain, but take the function and put it where the variable is. So, for "A" the equation would be \(f(1)=2^1\)

Answer:

Step-by-step explanation:

a) 29 can be expressed as the sum of two squares: 5^2 + 2^2, and 37 can be expressed as 6^2 + 1^2.

b) The next four numbers in the list are 45, 53, 61, and 69.

c) To find the sum of the first 50 numbers in the list, we can use the formula for the sum of an arithmetic series: S = n/2 * (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the nth term.

In this case, n = 50, a_1 = 5, and a_n = 5 * 50 + 4 = 254. So, the sum is: S = 50/2 * (5 + 254) = 50/2 * 259 = (50 * 259) / 2 = 6450.

Answer:

2x(x+1) + 5x² - 5x= - 2

Step-by-step explanation:

a=7

b=-3

c=2

2nd degree equation is written as

ax^2+bx+c=0

2x(x+1) + 5x² - 5x= - 2

2x^2+2x+5x^2-5x=-2

Collect like terms

2x^2+5x^2+2x-5x+2=0

7x^2-3x+2=0

a=7, b=-3, c=2

Therefore, the 2nd degree equation that corresponds with the above coefficients is 2x(x+1) + 5x² - 5x= - 2

a) We were told that relationship between the value of the car and its age is linear. This means that it can be represented with a linear equation such as

y = mx + c

y is the dependent variable and in this case, it is the value of the car, V

x is the independent variable and in this case, it is the age of the car, a

The above equation is the slope intercept form equation where

m represents slope

c represents y intercept

The formula for determining slope is expressed as:

m = (y2 - y1)/(x2 - x1)

We were told that a 5 year old car is worth 14000. This means that

When x1 = 5, y1 = 14000

Also, the same car is worth 11400 after 2 years. This means that the car is worth 11400 after 7 years. Thus,

when x2 = 7, y2 = 11400

Thus,

slope, m = (11400 - 14000)/(7 - 5) = - 2600/2

m = - 1300

We would find the y intercept, c by substituting m = - 1300, x = 5 and y = 14000 into the slope intercept equation. Thus,

14000 = - 1300 * 5 + c

14000 = - 6500 + c

c = 14000 + 6500

c = 20500

Thus, by substituting m = - 1300 and c = 20500 into the slope intercept equation, the linear equation representng this scenario is

y = - 1300x + 20500

By replacing with the given variables,

V = - 1300a + 20500

b) When the car was new, it means that a = 0. By substituting a = 0 into the equation, we have

V = - 1300 * 0 + 20500

V = 20500

The value of the car was $20500 when it was new

The domains from the two functions are different according to the change in quantity.

The domain is a term in math to define the set of values that we can plug into a function.

The natural numbers domain is when we use a natural number such as 1, 2, 3, etc. The natural number domain will use if the function only allows the change in quantity in natural number. Market A uses this.

The real number domain is when we use a real number such as 1, 2, 2.4, etc. The natural number domain will use if the function only allows the change in quantity in real numbers. Since market B is selling rice in bulk based, it will be easier to use the real number domain.

Thus, the two functions have the same value with different domain because market A use natural number and don't allow fraction, but market B since it sells rice in bulk so it allows fraction and uses a real number.

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Using the SAS (Side Angle Side) criteria of congruency, both triangles can be proved congruent.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is that two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle.

In order to prove these two triangles congruent, we can use SAS (Side Angle Side) criteria of congruency.

Therefore, using the SAS (Side Angle Side) criteria of congruency, both triangles can be proved congruent.

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Answer:

that would be 9m.

Answer:

9m

Step-by-step explanation:

9 x m = 9m

You are multiplying 9 and m

product = multiplying

Answer:

both variables are just 0-

Answer:

The equation of cost of mulch is \(1.50\times (\pi x^{2}-2\sqrt{2}x^{2})\\\\\).

Step-by-step explanation:

The equations m (x) and g (m) are as follows:

\(m(x)=\pi x^{2}-2\sqrt{2}x^{2}\\g(m)=1.50m\)

It is provided that the cost of mulch requires is represented by the function g(m), where m is the area requiring mulch.

To compute the equation of cost of mulch based on the radius of the circle substitute the value of m (x) in g (m).

The equation of cost of mulch is:

\(g(m) = 1.50m\)

        \(=1.50\times m(x)\\\\=1.50\times (\pi x^{2}-2\sqrt{2}x^{2})\\\\\)

Thus, the equation of cost of mulch is \(1.50\times (\pi x^{2}-2\sqrt{2}x^{2})\\\\\).

Answer:

the answer is A

Step-by-step explanation:

edge