Which of the following correctly multiplies 175 x 6 using the standard algorithm?

The answer is B It basically just expressing the 2×(6+9)

The expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example we can write a(c+b)  in the form of (ac+bc).

We have an expression:

= 2 × (6 + 9)

After applying the distributive property:

= (2 × 6) + (2 × 9)

= (12) + (18)

= 30

Thus, the expression 2 × (6 + 9) = (2 × 6) + (2 × 9) represents the distributive property option (B) is correct.

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a. According to the range, the two distributions have the same variability.

b. According to the standard deviation, the second distribution has greater variability than the first distribution.

a. To compute the range, we will subtract the lowest score from the highest score.

For the first set of scores: Range = 12 - 0 = 12

Similarly, for the second set of scores: Range = 12 - 0 = 12

Therefore, both sets of scores have the same range.

b. Now, to compute the standard deviation, we will first calculate the mean of the scores.

For the first set of scores: Mean = (0 + 6 + 6 + 12) / 4 = 6

Next, we calculate the deviation of each score from the mean:

0 - 6 = -6

6 - 6 = 0

6 - 6 = 0

12 - 6 = 6

Then, we square each deviation:

\((-6)^2\) = 36

\(0^2\) = 0

\(0^2\) = 0

\(6^2\) = 36

Taking the average of these squared deviations:

(36 + 0 + 0 + 36) / 4 = 18

Finally, we take the square root of this average to get the standard deviation:

SD = \(\sqrt{18}\) = 4.24 (rounded to two decimal places)

Similarly, we can find the mean calculate the standard deviation for the second set of scores which will come out to be -

Mean = (0 + 0 + 12 + 12) / 4 = 6

Standard deviation = \(\sqrt{36}\) = 6

Therefore, for the second set of scores, the standard deviation is larger, indicating greater variability.

Hence we can conclude that -

According to the range, the two distributions have the same variability and according to the standard deviation, the second distribution has greater variability than the first distribution.

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Answer:

  P'( 4, -4)

Step-by-step explanation:

The double reflection across the x-axis does nothing, so the net effect is a single reflection across the y-axis. That effect is to negate the x-coordinate:

  reflection across y-axis: (x, y) ⇒ (-x, y)

  Then P(-4, -4) ⇒ P'(4, -4)

Answer:

4,-4

Step-by-step explanation:

edmentum answer!!

Step-by-step explanation:

Total distance = 8/13 mile

Distance left = 8/13 - 2/13 - 2/13 = 4/13 mile

Hence Monica is 4/13 of a mile from home now. (B)

Answer:

17.65%

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve

The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.

Answer:

12:24:6- divide by 3

4:8:2 - divide by 2

2:4:1- simplest form

In-state corresponds to students who are residents of the same state as the university, out-of-state corresponds to students from different states, and foreign corresponds to students from countries other than the university's country.

To match the vocabulary word with its corresponding example in the context of the state university survey, we need to understand the terms and their meanings.

Here are the vocabulary words and their corresponding examples:

Vocabulary Word: In-state

Example: A student who is a resident of the same state where the university is located.

They pay lower tuition fees compared to out-of-state or foreign students.

Vocabulary Word: Out-of-state

Example: A student who is not a resident of the state where the university is located.

They typically pay higher tuition fees compared to in-state students.

Vocabulary Word: Foreign

Example: A student who is from a country other than the country where the university is located.

They are international students who may have different visa requirements and tuition fees.

To match these vocabulary words with their corresponding examples:

In-state: A student from the same state as the university, paying lower tuition fees.

Out-of-state: A student from a different state than the university, paying higher tuition fees.

Foreign: A student from a country other than the country where the university is located, with potential differences in visa requirements and tuition fees.

By associating each vocabulary word with its respective example, we can accurately describe the three categories of students based on their residency and origin in the context of the state university's survey.

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Answer:

Can you be more specific on this question?

Step-by-step explanation:

Answer:

The answer is c. the predators become the limiting factor for the pheasants in that environment.

Step-by-step explanation:

edg aswer

Answer: \(x+3, x \neq -6\)

Step-by-step explanation:

The denominator cannot equal 0, so \(x \neq -6\).

Simplfying,

\(\frac{x^2 +9x+18}{x+6}=\frac{(x+6)(x+3)}{x+6}=x+3\)

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

664 Square yards

Step-by-step explanation:

Surface area= 2lw+2lh+2hw

=2(17×6)+2(17×10)+2(10×6)

=2(102)+2(340)+2(120)

=204+340+120

=664 Square yards

your answer would be 254 I just did it and I got it right ✨

Answer:

Side c has a length of √145, or approximately 12.04.

Step-by-step explanation:

Because this is a right triangle, you can use the Pythagorean theorem to solve it.  In a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse.  Or in this example:

c² = 9² + 8²

So we can solve it:

c² = 9² + 8²

c² = 81 + 64

c² = 145

c = √145

c ≈ 12.04

Step-by-step explanation:

y=kx

25= k(-5)

k= -5

y= -5x

y = -5 ×3 = -15

Answer:

Angle DCA = Angle CAB. (Alternate Interior Angle)

Angle DCA = 68°

Angles(DCA + ACB + BCE) = 180°. (Linear Pair)

Angle ACB + 68° + 33° = 180°

Angle ACB = 79°

Therefore,

Angle ABC = 33°. (Alternate Interior Angle)

Answer:

A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Yes, they are.

Answer:

Yes

Step-by-step explanation:

Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Answer:

length is 9 and width is 4

Step-by-step explanation:

area is length times width

36 divided by 4 is 9

perimeter is adding all the sides

9+9+4+4 is 26

The probability of selecting a yellow ball is approximately 37%.

P(yellow)=37%.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability is used in many areas of mathematics, science, and everyday life to help us make decisions, assess risk, and understand uncertainty. It is an important concept in statistics, which uses probability to study and analyze data.

According to the question:

To find the probability of selecting a yellow ball, we need to divide the number of yellow balls by the total number of balls in the bag.

Total number of balls = 15 green + 18 yellow + 16 orange = 49

So, the probability of selecting a yellow ball is:

P(yellow) = Number of yellow balls / Total number of balls = 18/49

Rounding to the nearest percent, we get:

P(yellow) ≈ 37%

Therefore, the probability of selecting a yellow ball is approximately 37%.

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Answer:

1. 1.85

2. 18.5

3. 185

4. 1850

5. Kristen needs '1850' years of yarn

Step-by-step explanation:

The equations Ax = b are not compatible.

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.

If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.

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The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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The range of possible lengths of the third sides of each triangle are:

7. 13 < x < 22 (14 cm to 21 cm)

8. 28 < x < 76 (29 ft to 75 ft)

9. 23 < x < 41 (24 yd to 40 yd)

10. 1 < x < 31 (2 km to 30 km).

The formula for finding the range of the possible length of the third side of a triangle, x, is: difference of two sides < x < sum of two sides.

Therefore:

7. 17 - 4 < x < 17 + 4

13 < x < 22

The range of the length of the third side of the triangle would be 14 cm to 21 cm.

8. 52 - 24 < x < 52 + 24

28 < x < 76

The range is: 29 ft to 75 ft

9. 32 - 9 < x < 32 + 9

23 < x < 41

The range is: 24 yd to 40 yd

10. 17 - 16 < x < 16 + 17

1 < x < 31

The range is: 2 km to 30 km.

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Answer:

144

Step-by-step explanation:

12 times 12= 144

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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