Which shows the best use of the associative and commutative properties to
make simplifying 17+6+1 easier?
O A. [² + (−17)] + [6 + (− % ) + 1]
O B. [1++ (−17)] + [(− §) + 6]
c. [² + 6 + (−17)] + [1 + (− })]
D. [ + (− § )] + [6 + 1 + (−17)]
SUBMIT help pls quickly

The equivalent expressions are;

The correct answer choice is option B, C and E

-2/5(15 - 20d + 5c)

open parenthesis

= -30/5 + 40/5d - 10/5c

= - 6 + 8d - 2c

Check:

-6+8d-2c

True

-2c+8d-6

rearrange

= -6 + 8d - 2c

-2(3-4d+c)

open parenthesis

= -6 + 8d - 2c

Hence, the equivalent expression to -2/5(15 - 20d + 5c) are -6+8d-2c, -2c+8d-6 and -2(3-4d+c)

Read more on equivalent expression:

https://brainly.com/question/15775046

#SPJ1

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

Learn more about quartile at https://brainly.com/question/24329548.

#SPJ4

Answer:

Step-by-step explanation:

Not entirely sure about the first one, but I'll try the others:

2- log base 8 (8x) = log base 8 (8) + log base 8 (x) = 1 + log base 8 (x)

3 - log base 3 (5^x) = x log base 3 (5)

4 - log base 2 (5/x) = log base 2 (5) - log base 2 (x) = In 5 - In x

5 - log base 2 (2^x) = x log base 2 (2) = x · 1 = x

In the psychoanalytic tradition, the projection of feelings onto members by the leader is called: c) Countertransference.

Countertransference refers to the phenomenon where a therapist or leader projects their own emotions, experiences, or unresolved issues onto the individuals they are working with. It is a concept rooted in Sigmund Freud's psychoanalytic theory and is an important aspect of the therapeutic relationship.

When a leader experiences countertransference, they may unconsciously attribute their own thoughts, feelings, or motivations to the members of their group. This projection can distort the leader's perception of the group members and influence their interactions and decision-making processes. It can also hinder the leader's ability to provide objective and unbiased guidance or support.

Countertransference can arise due to various reasons, such as personal history, unresolved conflicts, or parallel experiences with the group members. It is essential for leaders to be aware of their countertransference reactions and work through them to maintain professional boundaries and provide effective leadership.

By recognizing and addressing countertransference, leaders can gain insight into their own emotional reactions and separate them from the experiences of their group members. This self-awareness enables leaders to approach their role with greater objectivity, empathy, and understanding.

Learn more about countertransference

brainly.com/question/30925426

#SPJ11

Therefore, the midpoint of PQ is M(-3, 1) with the given coordinates.

To find the coordinates of the midpoint of the line segment PQ with endpoints P(-5, -1) and Q(-7, 3), you can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) are given by the average of the corresponding coordinates of the endpoints:

M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Using this formula, we can calculate the midpoint coordinates:

x = (-5 + (-7)) / 2 = (-12) / 2 = -6 / 2 = -3

y = (-1 + 3) / 2 = 2 / 2 = 1

=(-3,1)

To know more about coordinates,

https://brainly.com/question/16758176

#SPJ11

Answer:the answer is x=6

Step-by-step explanation:

I alr did the quiz for this question on edg 2020

Answer:

x= 6

Step-by-step explanation:

Answer:

648

Step-by-step explanation:

\(3^4 \cdot 2^3 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 2 \cdot 2 \cdot 2 = 81 \cdot 8 = 648\)

Answer:

648

Step-by-step explanation:

Step 1:

First, make an equation:

3⁴ · 2³

Step 2:

Then, simplify both factors:

3⁴ = 81

2³ = 8

Step 3:

Finally, multiply the numbers together:

81 · 8

And you will get 648.

The graph has the shape of an equilateral triangle, with the origin at the center.

To sketch the graph of the polar equation θ=-π/6, you will first need to determine the graph's shape.

To do this, you should draw a radius from the origin to a point where θ=-π/6.

This radius is a line segment that intersects with the polar axis at the angle of -π/6.

By connecting all points with the same θ coordinate, a graph of the equation can be formed.

The graph has the shape of an equilateral triangle, with the origin at the center.

Learn more about polar equation

brainly.com/question/29083133

#SPJ11

Answer: $326.625

Explanation:

The infromation that we have is:

Payment per hour: p = $9.75 (I will identify the payment per hour as "p").

He worls from 8:00 am until 3 pm from monday through thursday, this means that he works 7 hours on those days. But since he takes a half hour lunch break, we take half an hour from the 7 hours:

Each from monday trough thursday that he works, he does it for 6.5 hours.

Thus, the total amount of hours for this four days of the week is:

On Friday he works from 8:00 am to 4:00pm, that is 8 hours, as in the previus days, we substract half hour for his break:

So the total amount of hours that he works in the week is the sum of the 26 hours that he works from monday through thursday, plus the 7.5 hours that he works on friday:

h represents the amount of hours that he works in a week.

His total pay for the week "T" is:

The product between the number of hours and the payment per hour:

Answer: $326.625

Answer:

\(\sqrt{3}\)

Step-by-step explanation:

look up a 30 60 90 triangle

Answer:

554

Step-by-step explanation:

The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.

Answer:

x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Step-by-step explanation:

Solve for x:

y = -x^2 - 4 x + 7

y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:

-x^2 - 4 x + 7 = y

Multiply both sides by -1:

x^2 + 4 x - 7 = -y

Add 7 to both sides:

x^2 + 4 x = 7 - y

Add 4 to both sides:

x^2 + 4 x + 4 = 11 - y

Write the left hand side as a square:

(x + 2)^2 = 11 - y

Take the square root of both sides:

x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Answer: It's not possible to create 38 liters of green paint with whole liters of blue and yellow paint.

======================================================

Explanation:

The ratio of blue to yellow is 2:3. We have 2 parts blue and 3 parts yellow.

Multiply both parts by x to get 2x:3x

We have 2x parts of blue paint, and 3x parts of yellow paint.

x is some positive whole number.

In total, we have 2x+3x = 5x liters of paint. Set this equal to 38 and solve for x to get

5x = 38

x = 38/5

x = 7.6

We don't get a whole number, which contradicts how we set up x earlier. This must mean that Mark must use a fractional liters, instead of whole liters.

-------------------------

Here's another way to look at it:

Lets say he uses 2 liters of blue and 3 liters of yellow. This mixes to 2+3 = 5 liters of green.

Now let's say he uses 4 liters of blue and 6 of yellow. I multiplied both parts by 2. This mixes to 4+6 = 10 liters of green.

We continue this process to get the following

As you can see, we don't land on 38 liters of green. We can get to 35 liters or 40 liters, but not 38. Each of the amounts of green are a multiple of 5.

This is confirmation that Mark will have to use some fractional amount of liters of blue and yellow paint.

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

To learn more about division, click on below link:

https://brainly.com/question/11781269

#SPJ4

The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

LEARN MORE ABOUT statement here: brainly.com/question/33442046

#SPJ11

Answer:

All of the shapes are quadrilaterals.

Step-by-step explanation:

a quadrilateral is a four sided figure and all of the figures above contain 4 sides.

Given the function:

For t = -4,

For t = -2,

For t = 0,

For t = 2;

For t = 4,

Then we graph the points

(-4,0.2) (-2, 0.4) (0,1) (2, 2.2) and (4,5)

and we get the graph:

Answer:

How many One-sixths are in Two-thirds?

Step-by-step explanation:

Answer:  How many One-sixths are in Two-thirds?

Step-by-step explanation: please mark me as a brainly

The revenue, the company should manufacture approximately 4,800 units of racing bicycles and 1,200 units of mountain bicycles.

To find the values of x and y that maximize the revenue, we need to optimize the given revenue function R = -6x^2 - 10y^2 - 2xy + 32x + 84y. The revenue function is a quadratic function with two variables, x and y. To find the maximum value, we can take partial derivatives with respect to x and y and set them equal to zero.

Taking the partial derivative with respect to x, we get:

∂R/∂x = -12x + 32 - 2y = 0

Taking the partial derivative with respect to y, we get:

∂R/∂y = -20y + 84 - 2x = 0

Solving these two equations simultaneously, we can find the values of x and y that maximize the revenue.

From the first equation, we can express x in terms of y:

x = (32 - 2y)/12 = (8 - 0.5y)

Substituting this value of x into the second equation, we get:

-20y + 84 - 2(8 - 0.5y) = 0

-20y + 84 - 16 + y = 0

-19y + 68 = 0

-19y = -68

y = 68/19 ≈ 3.579

Plugging this value of y back into the expression for x, we get:

x = 8 - 0.5(3.579)

x ≈ 4.711

Since x and y represent thousands of units, the company should manufacture approximately 4,800 units of racing bicycles (x ≈ 4.711 * 1000 ≈ 4,711) and 1,200 units of mountain bicycles (y ≈ 3.579 * 1000 ≈ 3,579) to maximize the revenue.

Learn more about the revenue:

brainly.com/question/28586793

#SPJ11

To determine the significance of each independent variable, we need to apply the decision rule at the 0.05 significance level.

In statistical hypothesis testing, the decision rule is used to determine whether to reject or fail to reject the null hypothesis based on the test statistic and the level of significance. In this case, we are interested in testing the significance of each independent variable in a regression model at the 0.05 level of significance. To do this, we can use the t-test for each independent variable by calculating the t-statistic and comparing it to the critical value of the t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables in the model. If the absolute value of the t-statistic is greater than the critical value, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

Alternatively, we can also use the p-value approach to determine the significance of each independent variable. We calculate the p-value for each variable and compare it to the level of significance. If the p-value is less than or equal to 0.05, then we reject the null hypothesis and conclude that the independent variable is statistically significant at the 0.05 level. Otherwise, we fail to reject the null hypothesis and conclude that the independent variable is not statistically significant at the 0.05 level.

Learn more about p-value here: https://brainly.com/question/12145026

#SPJ11

The total volume of the object is 96 m^3.

A cuboid is a three dimensional shape that is formed from a rectangle. Thus its dimensions are: length, width and height.

The volume of a cuboid = length x width x height

Considering the object given in the diagram, divide it into two rectangular prisms. So that;

i. volume of rectangular prism 1 = length x width x height

                                    = 5 x 3 x 4

                                    = 60

The volume of rectangular prism 1 is 60 cubic meters.

ii. volume of rectangular prism 2 = length x width x height

                                    = 4x 3 x 3

                                    = 36

The volume of rectangular prism 2 is 36 cubic meters.

Thus,

total volume of the object = 60 + 36

                                           = 96

The total volume of the object is 96 m^3.

Learn more about the volume of a cuboid at https://brainly.com/question/30389460

#SPJ1

The amount $500 invested at 8% interest compounded annually be worth after 3 years is $ 629.86

Since we have $500 invested at 8% interest compounded annually, we need to find the worth after 3 years.

Using the compound interest formula, the amount

A = P(1 + r)ⁿ where

Given that

So, substituting the values of the variables into the equation, we have that

A = P(1 + r)ⁿ

A = $500(1 + 0.08)³

A = $500(1.08)³

A = $500 × 1.259712

A = $ 629.856

A ≅ $ 629.86

So, the amount is $ 629.86

Learn more about compound interest here:

https://brainly.com/question/29338525

#SPJ1

Answer:

16 and 25

Step-by-step explanation:

they are square numbers

1^2 = 1 .. etc.

this is a I

There is an error 2*2 is 4 lol realised I wrote tht whoops

At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

What is the null hypothesis in statistics?

The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.

Sample size, n =1500

The sample proportion of the chips that do not fail in the first 1000 hrs of their use, \(\hat{p} = 0.69\)

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, \(Ha: p \neq 0.72\)

Test statistic,

\(z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877\)

Critical Value,

\(Z_{0.05/2} =\)±1.96

Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.

Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

To learn more about null hypotheses, visit:

https://brainly.com/question/15980493

#SPJ4

Answer:

4x

Step-by-step explanation:

2x+6+2x−6

=2x+6+2x+−6

Combine Like Terms:

=2x+6+2x+−6

=(2x+2x)+(6+−6)

=4x

Answer:

3r

Step-by-step explanation:

r × 3

3r

Answer:

3

Step-by-step explanation:

Answer:

(-1,-8)

Step-by-step explanation: