if she drove back home using the same path she took out to the university and arrives 7.1 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?

We have that, the first quartile of the given sample of twenty numbers is 59.

To find the first quartile of the given sample of twenty numbers

52, 54, 58, 59, 59, 60, 60, 63, 65, 66, 67, 68, 69, 73, 74, 77, 78, 79, 79, 98

use the following formula: Formula to calculate the first quartile:

\($$\mathrm{Q_1} = \mathrm{\frac{n+1}{4}}$$\)

So, plugging the values into the formula,

\($$\mathrm{Q_1} = \frac{20+1}{4}$$$$\mathrm{Q_1} = \frac{21}{4}$$$$\mathrm{Q_1} = $5.25 $\)

Then round 5.25 to the nearest whole number. To do this, compare 0.25 to 0.5, if it is greater than or equal to 0.5, then round up. If it is less than 0.5, round down. Since 0.25 is less than 0.5, round 5.25 to the nearest whole number. Therefore, the first quartile of the given sample of twenty numbers is 59.

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Answer:

a < -3

Step-by-step explanation:

10a + 8 < 9a + 5

Subtract 9a from both sides.

a + 8 < 5

Subtract 8 from both sides.

a < -3

Answer:

a < -3

Step-by-step explanation:

Given the inequality:

\(\displaystyle{10a+8 < 9a+5}\)

Solving a linear inequality is like solving a linear equation, you isolate a-term. Thus, subtract both sides by 9a:

\(\displaystyle{10a+8-9a < 9a+5-9a}\\\\\displaystyle{a+8 < 5}\)

Subtract both sides by 8:

\(\displaystyle{a+8-8 < 5-8}\\\\\displaystyle{a < -3}\)

Therefore, the solution is a < -3

Answer:

40/3

Step-by-step explanation:

20 x 2

----------- = 40/3

3

Answer:

13.reapeating 3

Step-by-step explanation:

Answer:

Hello the excel output is missing attached is the excel output for the question

Answer : living area and Bedrooms

Step-by-step explanation:

A significant variable is a variable that is vital in the  determination of the outcome of an activity or group of activities, and when the variable is independent is means that other variable does not affect its value or importance.

hence the important independent variable in this question are : Living area (x2) and Bedrooms(x3) because the pvalue < ∝ = 0.05

The apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

Unitary method widely used ease, already-present variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn can all be used tο achieve the gοal. If sο, a secοnd chance tο engage with the οbject will present itself. Otherwise, every crucial element that affects hοw well a prοοf οf an expressiοn wοrks will be gοne.

Here,

Tο sοlve this prοblem, we can start by multiplying the number οf students in the lοcal schοοl system by 480, since there are 480 times mοre students in public schοοls in the United States.

1.6 × 10⁵ × 480

= 7.68 × 10⁷

Therefοre, the apprοximate number οf students enrοlled in public schοοls in the United States is 7.68 × 10⁷, which cοrrespοnds tο chοice (C).

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Answer:

Step-by-step explanation:

V = 1/3bh or V=bh/3

cross multiply

3V = bh

divide both sides by b

3V/b = h or h = 3V/b

Answer:

Slope = 5/3

Step-by-step explanation:

See attached image

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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To find an invertible matrix P and a diagonal matrix D such that P^(-1)AP = D, we need to diagonalize matrix A. The diagonal elements of D will be the eigenvalues of A, and the columns of P will be the corresponding eigenvectors.

To diagonalize matrix A, we need to find its eigenvalues and eigenvectors. Let λ1, λ2, ..., λn be the eigenvalues of A, and v1, v2, ..., vn be the corresponding eigenvectors. We arrange the eigenvectors as columns in matrix P, and the eigenvalues as diagonal elements in matrix D.

Then, we can calculate P^(-1) to obtain the inverse of P. Finally, we have:

P^(-1)AP = D

This equation implies that A can be transformed into a diagonal matrix D by using the invertible matrix P.

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\(1.16 \times {10}^{ - 7} = \)

\(116 \times {10}^{ - 2} \times {10}^{ - 7} = \)

\(116 \times {10}^{ - 9} = \)

\(0.000000116\)

_________________________________

Done...

♥️♥️♥️♥️♥️

Answer:

Step-by-step explanation:

hello have a good sunday

Answer:

???

there's no "x" in -3 so did you mean to write a larger equation...??

Step-by-step explanation:

Answer:

1.) x = 37

2.) m<SVW = 74 deg

3.) m<TWV = 106 deg

Step-by-step explanation:

Linea SY and TZ are shown to be parallel.

Angles SVW and TWV are same-side interior angles.

Theorem:

If parallel lines are cut by a transversal, then same-side interior angles are supplementary.

m<SVW + m<TWV = 180 (by the definition of supplementary angles)

2x + 3x - 5 = 180

5x - 5 = 180

5x = 185

x = 37

m<SVW = 2x = 2(37) = 74

m<TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106

Answer:

1.) x = 37

2.) m<SVW = 74 deg

3.) m<TWV = 106 deg

The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

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Answer:

2 - 4

Step-by-step explanation:

Answer:

D or 6 - 4

Step-by-step explanation:

Hope this helps!

the equations of motion for the two masses x(t) and y(t) are:F1 = -k1x1F2 = -k1x2 + k2(y - x2)

Newton's second law of motion can be stated as F = ma (force equals mass times acceleration). In this question, we are looking for the equations of motion for the two masses x(t) and y(t) attached to the springs. We can use Newton's second law to derive the equations of motion for each mass.

First, we consider mass m1. The only force acting on this mass is the spring force from k1. We can apply Newton's second law to derive the equation of motion for this mass as:

F1 = -k1x1where F1 is the force exerted by the spring on mass m1, k1 is the spring constant, and x1 is the displacement of mass m1 from its equilibrium position. Next, we consider mass m2.

The spring force from k1 and the spring force from k2 act on this mass. We can apply Newton's second law to derive the equation of motion for this mass as:

F2 = -k1x2 + k2(y - x2)where F2 is the force exerted by the springs on mass m2, k1 and k2 are the spring constants, x2 is the displacement of mass m2 from its equilibrium position, and y - x2 is the displacement of the other spring from its equilibrium position.

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Answer: False

Step-by-step explanation: Because Because I said so and because.

Answer: 168+48n

Step-by-step explanation: The first step is to distribute. You first multiply the 14 by 12 to get 168. Then, multiply 6n by 12 to get 72n. Lastly, multiply -2n by 12 to get -24n. Now combine the like terms. 72n+-24n = 48n

To transform a set of vectors into orthonormal vectors using the Gram-Schmidt process, normalize the first vector, compute the projections onto the previous orthonormal vectors, subtract the projections, and normalize the resulting vectors successively.

To apply the Gram-Schmidt process to transform the set of vectors (1, 2, 1), (1, -1, 0), (0, 1, 0) into orthonormal vectors, follow these steps:

Take the first vector, v1 = (1, 2, 1), and normalize it to obtain the first orthonormal vector, u1:

u1 = v1 / ||v1||, where ||v1|| represents the norm or magnitude of v1.

Compute the projection of the second vector, v2 = (1, -1, 0), onto the first orthonormal vector, u1:

proj(v2, u1) = (v2 · u1) * u1, where · represents the dot product.

Subtract the projection from v2 to obtain a new vector, v2' = v2 - proj(v2, u1).

Normalize v2' to obtain the second orthonormal vector, u2:

u2 = v2' / ||v2'||.

Repeat steps 2-4 for the third vector, v3 = (0, 1, 0), using u1 and u2 as the previous orthonormal vectors.

The resulting vectors u1, u2, and u3 will be the orthonormal vectors obtained through the Gram-Schmidt process.

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She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.

Total required pounds=35

3x+2x=35

x=35/5

x=7

So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.

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Answer:

5 necklaces and 10 bracelets

Step-by-step explanation:

Let N and B stand for the numbers of necklaces(N) and bracelets(B) sold.  The total sales would be:

 Total Sales = 6.25B + 12.50N, whcu we are told amounted to $125:

  $125 = 6.25B + 12.50N

We know that B + N = 15.

Rearrange this to isolate B:  B = 15-N

Now use this definition of B in the first equation:

$125 = 6.25B + 12.50N

$125 = 6.25(15-N) + 12.50N

$125 = 93.75-6.25N + 12.50N

31.25 = 6.25N

N = 5 necklaces

From B+N = 15, we can find B:

  B = 15 - 5

  B = 10 bracelets

Check:  Do 5 necklaces and 10 bracelets add up to $125??

 5*($6.25) + 10*($12.50) = $62.50 + $62.50 = $125  YES

The number of bracelets and the number of necklaces if, Sophia sells each bracelet for $6.25 and each necklace for $12.50, and the total number of items sold is 15, are 10, and 5 respectively.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Sophia sells each bracelet for $6.25 and each necklace for $12.50,

Total number of items sold = 15,

Total income made = $125,

Write the equation as shown below,

x + y = 15

Here, x is the number of bracelets and y is the number of necklaces,

6.25x + 12.5y = 125

Solve the equations by elimination method as shown below,

y = 5 and x = 15 - 5 = 10

Thus, the number of bracelets is 10 and the number of necklaces is 5.

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The best interpretation of the statement "the chances of winning a prize are 1 out of 10" is that if many people buy a ticket, about 1 in 10 will win.

This statement means that for every 10 tickets sold, on average, only one ticket will win a prize. It does not guarantee that you will win a prize if you buy a single ticket or even several tickets. The probability of winning a prize remains the same for every ticket purchased. It is important to note that winning a prize in a lottery is largely a matter of luck, and the odds are always against the player. While buying more tickets may increase your chances of winning, it does not guarantee a win.

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(a) The negation of the statement "∀x(2x−1<0)" is "∃x(¬(2x−1<0))", which can be read as "There exists an integer x such that 2x−1 is not less than 0."

(b) The negation of the statement "∃x(x^2≠9)" is "∀x(¬(x^2≠9))", which can be read as "For all integers x, x^2 is equal to 9."

(a) The negation of the statement "∀x(2x−1<0)" is "∃x(¬(2x−1<0))", which can be read as "There exists an integer x such that 2x−1 is not less than 0."

To determine the truth value of this negated statement when the universe of discourse is the set of all integers, we need to find a counterexample that makes the statement false. In other words, we need to find an integer x for which 2x−1 is not less than 0. Solving the inequality 2x−1≥0, we get x≥1/2.

However, since the universe of discourse is the set of all integers, there is no integer x that satisfies this condition. Therefore, the negated statement is false.

(b) The negation of the statement "∃x(x^2≠9)" is "∀x(¬(x^2≠9))", which can be read as "For all integers x, x^2 is equal to 9."

To determine the truth value of this negated statement when the universe of discourse is the set of all integers, we need to check if all integers satisfy the condition that x^2 is equal to 9. By examining all possible integer values, we find that both x=3 and x=-3 satisfy this condition, as 3^2=9 and (-3)^2=9. Therefore, the statement is true for at least one integer, and thus, the negated statement is false.

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The total time required taken by the bell to ring 20 times is equal to 180 seconds, or 3 minutes.

If it takes the bell 90 seconds to ring 10 times, we can calculate the average time it takes for each ring,

Average time per ring

= Total time / Number of rings

= 90 seconds / 10 rings

= 9 seconds per ring

To find out how long it will take the bell to ring 20 times,

we can multiply the average time per ring by the number of rings,

Time to ring 20 times

= Average time per ring × Number of rings

= 9 seconds per ring × 20 rings

= 180 seconds

Therefore, it will take the bell 180 seconds, or 3 minutes, to ring 20 times.

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Answer:

c. Identity property

Step-by-step explanation:

edg 2020

Identity property is used in the equation a+bi+0+0i=a+bi.

The identity property of addition says that the sum of 0 and any number is that number only.

We have been given the following equation

a+bi+0+0i=a+bi

when we multiply it with 0 we get 0 and the equation becomes

a+bi=a+bi

It shows the identity property of addition.

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Answer: I think its 4/16

Step-by-step explanation:

please let me know if I'm wrong.

Answer:

cosM ≈ 0.3048

Step-by-step explanation:

remember SOH CAH TOA = sine: opposite/hypotenuse; cosine: adjacent/hypotenuse; tangent: opposite/adjacent

cos = CAH

cosM= a / c

cosM = 4.0 / 13.1244

cosM = 0.30477

cosM ≈ 0.3048

Answer:

x=8

Step-by-step explanation:

x^(2)=64

Square root both sides of your equation to isolate your x.

x=\(\sqrt{64}\)

x=8

Hey there!

x^2 = 64

TAKE the SQUARE ROOT OF 64

√64 = 8 or -√64 = 8

Thus, your answer should be: x = 8 or x = -8

Good luck on your assignment & enjoy day!

~Amphitrite1040:)

Answer:

I think it's 4/9 the first one

Answer:

Step-by-step explanation:

270-36x

there are 5 years so x=5

270 + 36(5) = 270 + 180 = 450  

If it were 6 years than x = 6

270 + 36(6) = 270 + 216 = 486

Bike B:

360 + 20x

For option b x = 5

360 + 20(5) = 360 + 100 = 460

for option b it would be 6 years than x = 6

360 + 20(6) = 360 + 120 = 480

This cost function of purchasing a bike A

\(\to f1(x) = 270+ 36 x\) ( The unit of x is a year)  

A cost function for purchasing bike B:

\(\to f2(x) = 360+20x \\\\if \ \ f1(x)<f2(x)\\\\ \therefore\\\\ \to 270+36x-360+20x\ \ \ (transpose)\\\\\to 16x= 90 \\\\\to x=\frac{90}{16}=5.625\\\\\)

If Greg plans to keep the bike for 5 years, Bike A is the superior option. If Greg plans to keep the bike for 6 years, Bike B is the superior option.

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answer:

measure of angle 1 is 130°.

step by step:

angle 8 = 50

angle 6 = 50 (because of vertical angles)

angle 4 = 50 (because fo alternate interior angles)

therefore, angle 1 = 130 (because of linear pairs)

angle 1 and angle 4 add up to 180°

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