Find a basis of R^3, different from the usual.
2. Indicate if the following statements are true or false. Justify your answer well
a) Polynomials x − 2x^2, x^2 − 4x and −7x + 8x^2 they are a base of P2.
b) Polynomials 4, 2x, −x^3 and 3x^4 they are a base of P4.
c) Polynomials x − 1, (x − 1)(x − 2), (x − 1)(x − 2)(x − 3), x^4 they are a base of P4.

Dan used a total of 5 17/24 gallons of gas on Saturday and Sunday combined.

To find the total number of gallons Dan used on Saturday and Sunday, we shall add the amount of gas he used each day.

On Saturday, Dan used 1 3/8 gallons.

On Sunday, Dan used 4 1/3 gallons.

To add these two amounts, we shall find a common denominator by determining the least common multiple (LCM) of 8 and 3 is 24.

Converting 1 3/8 to an improper fraction:

1 3/8 = (8 * 1 + 3) / 8 = 11/8

Converting 4 1/3 to an improper fraction:

4 1/3 = (3 * 4 + 1) / 3 = 13/3

Now we can add the fractions using a common denominator, which is 24 in this case:

Let's convert both fractions:

11/8 = (11 * 3) / (8 * 3) = 33/24

13/3 = (13 * 8) / (3 * 8) = 104/24

Now we can add the fractions:

33/24 + 104/24 = (33 + 104) / 24 = 137/24

So, simplifying the fraction, we have:

137/24 = 5 (remainder 17)

5 17/24 gallons.

Hence, Dan used a total of 5 17/24 gallons of gas on Saturday and Sunday combined.

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Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

A rhombus can have the same shape and dimension as a square or a

parallelogram, therefore, all rhombuses are not similar.

Reasons:

By reading through the given steps, we have, the first step that is incorrect

is step 3.

Step 3: The requirement for the similarity of two figures based on the

proportionality of the corresponding sides of the figures is related with

triangles as given by the triangle proportionality theorem.

This is so because, the lengths of the sides of a triangle depends on the

opposite interior angle, while the side of a rhombus can have a

combination of large length and and acute angle.

Two rhombuses that have proportional sides may be dissimilar,

because they can have different interior angles.

Therefore;

The step in Tyler's proof that have a flaw is Step 3

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Answer:

The correct option is a) 3n - 4 = 15

Step-by-step explanation:

The product of 3 and a number means 3 multiplied by a number (n)

So it'll be 3*n or simply 3n

Now, it says 4 less than the product

So 4 less than 3n

That is equal to 3n minus 4 or 3n -4

So we come to the conclusion that

3n - 4 = 15

Hope this helps!

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

Step-by-step explanation:

o.3 I think not sure but wanted to help u

Answer:

o.3 I think not sure but wanted to help u

Step-by-step explanation:

The mean of the given set of group numbers is 6.6

Given,

In the question:

The Group of numbers are as follows:

6.1, 5.9, 4.2, 5.9 and 10.7

To find the mean of the given set of group of numbers.

Now, According to the question:

Given is the following data:

6.1, 5.9, 4.2, 5.9 and 10.7

We can find the mean of the given set of data using the formula-

Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)

Now, n = 5

and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8

Putting the values in the formula, we get:

M = 32.8/5 = 6.56 = 6.6

Hence, The mean of the given set of group numbers is 6.6

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Answer:

14. no (16 = 11 + 3*1, not equal since 16=14 is wrong)

15. yes (-19 = 1 - 4*5, equal)

16. yes ( -5 = 2-14/2, equal)

Answer:

Removing the outlier lowers the standard deviation by 1.09

Step-by-step explanation:

Find the standard deviation of the data WITHOUT the outlier first.

If you don't know how to do standard deviation, here are the steps:

1. Find the mean

2. Subtract the mean by the data set values

3. Square the differences

4. Add the squared numbers together and divide by the number of data set values

5. What you have now is the variance, and all you have to do now is square the variance and you have the standard deviation

Repeat this, but WITH the outlier this time.

Final step, just subtract the smaller number (answer you got from the data with the outlier) by the greater number (answer you got from the data without the outlier) and you have your answer: 1.09!

Answer:

p greater than or equal to 36

Answer:

\(<F+<K+<H+<G=360\)°

\(90\)°\(+3x+90+2x=360\)°

⇒\(5x+80=360\\\)

⇒\(5x=360-+80\)

⇒\(5x=-+80\)

⇒\(x=\frac{-+80}{5}\)

⇒x=36°

3x=3×36=108°

2x=2×36=72°

FG≈HG=17

hope it helps...

have a great day!!

Answer:

I and IV

Step-by-step explanation:

I is a graph with three inequalities, not a function.  IV is an algebraic equation, and again, not a function.  

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The composition of one or more rigid motions and a dilation is called a​ similarity transformation.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

The composition of one or more rigid motions and a dilation is called a​ similarity transformation.

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The price for the monthly fee will be;

⇒ x = $9.99  

And, The price per movie rental will be;

⇒ y = $2.99

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Yolanda is charged $21.95 for her monthly fee and 4 movie rentals.

And, Jeffrey is charged $30.92 for the same monthly fee and 7 movie rentals.

Now,

Let the price for the monthly fee = x

And, The price for the movie rental = y

Hence, We can formulate the expression for Yolanda;

⇒ x + 4y = $21.95

And,  We can formulate the expression for Jeffrey;

⇒ x + 7y = $30.92

Subtract equation (ii) from (i), we get;

⇒ 7y - 4y = $30.92 - $21.95

⇒ 3y = $8.97

⇒ y = $2.99

And, x + 4y = $21.95

x + 4 × 2.99 = 21.95

x + $11.96 = $21.95

x = $21.95 - $11.96

x = $9.99

Thus, The price for the monthly fee = $9.99  

And, The price per movie rental = $2.99

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As the number of bootstrap samples increases, the width of the interval in the percentile method tends to decrease.

The percentile method is a resampling technique used to estimate confidence intervals. It involves repeatedly sampling with replacement from the original data to create multiple bootstrap samples, from which percentiles are computed to construct the interval.

Increasing the number of bootstrap samples improves the accuracy of the estimate by providing more information about the sampling distribution. With more samples, the estimate becomes more stable and less sensitive to individual observations. As a result, the variability in the estimates decreases, leading to a narrower interval. This reduction in width occurs because more samples capture a broader range of data patterns, resulting in a more robust estimate of the underlying population parameter. However, it's important to strike a balance between computational resources and the desired level of precision, as increasing the number of bootstrap samples also increases the computational burden.

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Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula \(A=\frac{1}{2}ap\) to find the area of the base, where a is the apothem and p is the perimeter, we get \(A=\frac{1}{2}(0.87)(6)=2.61\)

So, using the formula \(V=Bh\), we get the volume to be \(2.61(2)=5.22 \text{ m}^{3}\)

To determine the point t* at which the integral function achieves its maximum, we need to analyze the behavior of the integrand and consider the area under its graph. By examining the sign of 3+sin(s), we can identify the intervals where the integrand is positive or negative. The maximum point t* will occur where the area under the graph of the positive portions of the integrand is maximized.

The integral function 2xf(1) = √22 (3+sin(s))ds represents the integral of the function (3+sin(s)) with respect to s, multiplied by 2x. The integrand, 3+sin(s), varies between -2 and 4, with positive and negative regions.

To find the maximum point t*, we need to determine the interval on which the integrand is positive. Since sin(s) oscillates between -1 and 1, the expression 3+sin(s) is positive when it is greater than zero. Solving the inequality 3+sin(s) > 0, we find that sin(s) > -3.

The area under the positive portions of the integrand will be maximized when sin(s) = -1, which occurs at s = (3π/2 + 2πn), where n is an integer. Among these points, we need to find the one within the interval 0 < t < 4.

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Answer:

160 is the measure of the angle

Answer:

C

Step-by-step explanation:

90+70= 160

Answer:

4th option

Step-by-step explanation:

using the rule of logarithms

\(log^{n}\) = nlogx

\(3^{7x}\) - 8 = - 2 ( add 8 to both sides )

\(3^{7x}\) = 6 ( take the log of both sides )

log\(3^{7x}\) = log6

7xlog3 = log6 ( divide both sides by 7log3 )

x = \(\frac{log6}{7log3}\) ≈ 0.23 ( to the nearest hundredth )

The radical form form for \(7x^{3/4}\) is \(\sqrt[4]{x^3} * 7\) (Option d.).

To write \(7x^{3/4}\) in radical form, we can express the exponent 3/4 as a fractional exponent within a radical.

\(7x^{3/4}\) can be written as the fourth root of \((x^3)\) multiplied by 7:

\(\sqrt[4]{x^3} * 7\)

Therefore, \(7x^{3/4}\) in radical form is \(\sqrt[4]{x^3} * 7\).

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Answer:

Yes

Step-by-step explanation:

Answer: Yes it is equivalent

Step-by-step explanation:

If you crossed out the 12 and put it under 15, it would be 15/12=1.25.

Same for the second one cross out the 4 and put it under the 5 and it would be 5/4 is 1.25.

Answer: The volume of this cylinder is 2389.18 cubic cm, and the surface area is 1000.6 square cm.

Answer:

D -7 and -8

Step-by-step explanation: