Which expression is equivalent to ∣∣b∣∣>6
?
Responses

b > –6 and b < 6

b > –6 and b < 6

b < –6 and b > 6

b < –6 and b > 6

Answer:

1+(2×m)

Step-by-step explanation:

We can break the problem down and find the keywords.

1 plus the product of 2 and m

plus=+

product=×

1+(2×m)

Your mom had the better/lower unit price.

A unit price is the cost of a single unit of a product or item, usually expressed per unit of weight, volume, or length. It represents the cost per unit of measurement and allows for comparison of the cost of different products on an equal basis.

For example, the unit price of a bag of apples could be given as the cost per pound, so that a consumer can compare the cost of a 5-pound bag of apples at different stores.

The unit price for your mom's books is $19.85/8 books = $2.48 per book.

The unit price for your dad's books is $15.00/6 books = $2.50 per book.

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Answer:

Step-by-step explanation:

We can set up a proportion to solve for the unknown amount of gasoline needed:

distance traveled / amount of gasoline = constant

Let x be the amount of gasoline needed to travel 155 miles. Using the given information, we can set up the following proportion:

713 miles / 23 gallons = 155 miles / x

Simplifying, we get:

x = (155 miles * 23 gallons) / 713 miles

x = 5 gallons (rounded to the nearest gallon)

Therefore, the car needs 5 gallons of gasoline to travel 155 miles.

Answer:

D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)

The required probability is 0.112 × [tex]10^-^1^3[/tex]

In the combination, ordering of items does not consider important when we need to determine the number of ways to select the _k_ items from the total _m_ items. There will be two cases in selecting the items- one in which repetition allowed, and the other is repetition not allowed.

Total Number of US senators (n) =100

Number of politicians to be chosen (r) = 50

Total number of ways in which 50 politicians can be chosen from 100 senators is:

[tex]C^n_r = C^1^0^0_5_0[/tex]

Number of senators in each US state = 2.

The number of ways in which senator can be chosen such that each state is represented = [tex]2_C_1[/tex]

Thus, the number of ways in which senator can be chosen for 50 states is:

[tex](2_C_1)^5^0[/tex]

Let A be an event that a politician is chosen such that each state is represented.

P(A) = [tex]\frac{2^5^0}{100_C_5_0}[/tex]

By solving, we get:

P(A) = 0.112 × [tex]10^-^1^3[/tex]

Hence, the required probability is 0.112 × [tex]10^-^1^3[/tex]

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Answer:

12

Step-by-step explanation:

45 total

2/3 * 45 = 30 gave speeches

so 15 remaining

1/5 *15 = 3 gave speeches

remaining 12 didn't

Answer:

7 miles

Step-by-step explanation:

Let's call the distance from point C to point D as "x".

We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.

Using the Pythagorean Theorem, we can find the distance from C to D:

(x)^2 + (4)^2 = (8)^2

Expanding and simplifying the equation:

x^2 + 16 = 64

x^2 = 48

x = sqrt(48) = 6.928

So the distance from the third tower to point D is approximately 6.9 miles (rounded to the nearest tenth of a mile).

Answer:

6.9 miles

Step-by-step explanation:

Since the distance between points A and B is 8 miles, and point C is equidistant from points A and B, triangle ABC is an equilateral triangle with side lengths of 8 miles.

As point D is 4 miles from point A, point D is the midpoint of AB.

Therefore, the distance between point C and point D is the altitude of the triangle.

The formula for the altitude of an equilateral triangle is:

[tex]h=\dfrac{\sqrt{3}}{2}s[/tex]

where s is the the side length.

Therefore, the altitude of an equilateral triangle with side length 8 miles is:

[tex]\implies h=\dfrac{\sqrt{3}}{2} \cdot 8[/tex]

[tex]\implies h=4\sqrt{3}[/tex]

[tex]\implies h=6.9\; \sf miles\;(nearest\;tenth)[/tex]

Therefore, the distance from the third tower C to point D is 6.9 miles to the nearest tenth of a mile.

Difference of (-x² + 9xy) and  (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

(-x² + 9xy) - (x² + 6xy - 8y²)

Distributing negative sign

-x² + 9xy - x² - 6xy + 8y²

Adding like terms

- 2x² + 3xy + 8y²

Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).

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If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.

In Science, the density of a chemical substance such as lead can be calculated by using this formula:

Density = M/V

Where:

Making volume the subject of formula, we have the following:

Volume = Mass/Density

Volume = 2,000/3,200

Volume = 0.625 in³.

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The size of the population after 15 hours is 6400 bacteria.

The size of the population after 15 hours can be found using the exponential growth formula. The formula for exponential growth is P = P₀ × 2^(t/k), where P₀ is the initial population, t is the time elapsed, k is the time it takes for the population to double, and 2^(t/k) is the exponential growth factor.

In this case, the initial population is 200, the time elapsed is 15 hours, and the time it takes for the population to double is 3 hours. Putting these values in the formula, we get:

P = 200 × 2^(15/3)

P = 200 × 2⁵

P = 200 × 32

P = 6400

So, the size of the population after 15 hours is 6400 bacteria.

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Answer:

50.1

Step-by-step explanation:

let the height = h

so because that angle is 62 so it's supplemental angle in left triangle is 28°

in any triangle, the tangent of an angle is opposite/adjacent

so height/28 = tan28° =0.53

so height = 14.8

in any triangle, the sine of an angle is opposite/hypotenuse

so height / x = sin 38°

so x = 14.8 / sin 38° = 14.8/0.296 =50.1

Here are three different equations that relate C and B:

1. B = (2/7) * C

2. B/C = 2/5

3. 5C = 2B

1. B = (2/7) * C

Since the ratio of cocoa to cocoa butter is 5:2, we can write 5 + 2 = 7, which represents the total number of parts. Dividing 2 by 7, we get 2/7, which represents the fraction of cocoa butter in the mixture. To find the number of grams of cocoa butter needed for C grams of cocoa, we multiply C by 2/7.

2. B/C = 2/5

Dividing the number of grams of cocoa butter (B) by the number of grams of cocoa (C), we get the ratio of cocoa butter to cocoa, which is 2/5.

3. 5C = 2B

Since the ratio of cocoa to cocoa butter is 5:2, we can write the equation 5 * C = 2 * B, which represents the number of parts of cocoa to the number of parts of cocoa butter. Solving for B in terms of C, we get B = (2/5) * C.

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The equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 6/5a + 2/3b - 7/6b + 1/8.

Expression is a mathematical phrase that can contain numbers, variables, and operators.

An equivalent expression is a different expression that has the same value as the original expression. In this question, we need to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.

Let's start by simplifying the fractions in the expression. We can see that 4/5a and 2/5a have a common denominator of 5a. We can add these two fractions by finding a common denominator and then adding the numerators. The equivalent fraction to 4/5a + 2/5a is 6/5a.

Next, we can simplify the expression by combining like terms, which are terms that have the same variable and coefficient.

The equivalent expression to

=> 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a = 6/5a + 2/3b - 7/6b - 3/4 + 1/8.

Finally, we can simplify the expression by combining the constants, which are terms without variables. The equivalent expression to

=> 6/5a + 2/3b - 7/6b - 3/4 + 1/8

after combining constants is

=> 6/5a + 2/3b - 7/6b + 1/8.

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Charlie would consume 30 units of bananas if he chose the bundle that maximized his utility function subject to his budget constraint There for the answer is option A

Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.

If Charlie's income is $120, he has a budget constraint given by:

1A + 2B = 120

To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).

The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:

A = 120 - 2B

Substituting this into the utility function, we have:

U(B) = (120 - 2B)B = 120B - 2B^2

To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:

dU/dB = 120 - 4B = 0

Solving for B, we find that:

B = 30

Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.

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The dimension of rectangular dining room measures length 24.3 and breadth  1.73 metres.

In mathematics, dimensions refer to the length or width of an area, region, or space in one direction. It is just the measurement of something's length, width, and height. Length, breadth, and height are common ways to describe dimensions.

Our world has three dimensions.

Height, length, and width are the three dimensions that define everything around us, including the homes we live in and the everyday items we use.

Length, breadth, and height are the common three dimensions that can be described in three distinct ways.

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Addition And Subtraction

1.) -27+68-56+61= 46

2 ) 4.17-9.42+0.2= -5. 05

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

5 ) 6 5/12 - (-4 2/3)8 + (-2 3/4)= 5/12

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

1.) -27+68-56+61=

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

2 ) 4.17-9.42+0.2= -5. 05

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the number (-0.96) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is . positive.

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the numbers (-8.44) and (-31.67) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is positive.

5 ) 6 5/12 - (-4 2/3) + (-2 3/4)= 5/12

In question number 5, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

In question number 6, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

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He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

What is simple interest?

The simple interest method, which always adds interest to the starting principal amount at the same rate for each time cycle, is a quick and easy way to calculate interest on money. Any bank where we deposit money will return our investment with interest. Simple interest is one of the several forms of interest that banks charge. Now, before going into any detail on the concept of fundamental curiosity,

The formula for simple interest is:

S = p*t*r/100

The part-time receptionist's taxable income would be calculated by deducting their exemptions and standard deduction from their gross income. The person's gross income was $9101.99. A $3650 exemption was requested by the person. They also qualified for a $5700 standard deduction.

We can figure out their taxable income by deducting the exemption and standard deduction from their gross income. $9101.99 - $3650 - $5700 = $-748.01 would be used to compute the taxable income.

Hence He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

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In any case, the solution (2,5) is a specific point that satisfies both equations in the system. It tells us that at this particular point, whatever the equations are describing about trees is true.

A location in the coordinate plane that satisfies both equations is typically what a solution to a system of equations in two variables refers to.

If the set of equations in this case has anything to do with trees, we could interpret the answer (2,5) as indicating that there are two different types of trees and five of each type. As an alternative, the equations can reflect the development or health of trees, and the answer (2,5) might point to a certain period of time or place when both varieties of trees are at a given stage of development or health.

In any case, the system's solution (2,5) is a particular location that satisfies both of the system's equations. It indicates that whatever the equations' descriptions of trees are at this specific time are accurate. The answer can shed light on how the system of equations behaves and how it connects to trees, but it does not always reveal information about other locations or circumstances.

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An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

P = 2(6 7/8 + W)

P = 2(6 7/8) + 2W = 2W + 13 6/8

P = 6 7/8 + W + 6 7/8 + W

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The rate of the westbound train is 85miles per hiur

Velocity is the rate of change of displacement with time. It is measured in meter per second. It is a vector quantity.

Since the two trains move at the same time and in opposite directions, then the total displacement (d) = d1 - d2

900 = (vt)1 - (Vt)2

if v1 is the eastbound train velocity and v2 is the westbound train velocity

v1 = v2+10

they have thesame time of 5hours

therefore;

900 = (v2+10-(-v2)(5)

900 =( 2v2+10)5

divide both sides by 5

180 = 2v2 +10

2v2 = 170

v2 = 170/2

v2 = 85

therefore the rate of the westbound train is 85 miles per hour

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To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs

Expected number of blue socks = n * 1/4

In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:

n * 1/4 = 4

And solving for n:

n = 4 / (1/4) = 4 * 4 = 16

So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

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The distances of the following places are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Places traveled:

Camp → waterfall → meadow → camp.

We are assuming the time taken as follows:

Camp → waterfall = 30 minutes = 0.5 hour

waterfall → meadow = 1 hour

meadow → camp = 2 hours.

Now,

Speed = 4.5 km per hour.

Speed = Distance / Time

So,

The distance between camp → waterfall.

= 4.5 x 0.5

= 2.25 km

The distance between the waterfall → meadow.

= 4.5  x 1

= 4.5 km

The distance between the meadow → camp.

= 4.5 x 2

= 9 km.

Thus,

The distances are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

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The cost of Nadine's order was found by multiplying the number of t - shirts she ordered, by their individual cost, and then deducting the value of the coupon.

The order was that Nadine bough4 t - shirts for her class club from a website.

Each of these shirts cost $ 10. 95. But, Nadine gets a coupon of $ 12. 50 to be deducted from the total order.

To find the cost therefore, we can multiply the cost of the shirts and the number of shirt and then deduct the value of the coupon as shown in the formula :

= ( Cost of shirt x Number of shirts ) - coupon

= ( 10. 95 x 4 ) - 12. 50

= $ 31. 30

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The full question is:

Nadine ordered 4 t-shirts for her class club form a website. Each shirt is $10.95 and Nadine has a coupon for $12.50 off her total order. Write a sentence to describe how you calculated the cost of Nadine's order.

The value of x of the parallelogram is x = 38

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

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the diagonals of the parallelogram are AC and BD

The measure of DE = 31

The measure of EB = x - 7

Now , Each diagonal of a parallelogram separates it into two congruent triangles where the measure of AC = BD

So , substituting the values in the equation , we get

BD = BE + DE and BE = DE

On simplifying the equation , we get

31 = x - 7

Adding 7 on both sides of the equation , we get

x = 31 + 7

x = 38

Hence , the measure of x of parallelogram is 38

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Gabriel would have $45,985.67 more than Ava in his account. This is because Gabriel's account is compounded daily, meaning that his interest would be compounded 365 times a year, while Ava's account is compounded continuously,

Compounding is the process of combining two or more elements to create a new, more complex product. In finance, compounding refers to the interest earned on an investment that is reinvested and earns additional interest. This cycle continues, allowing the principal to grow exponentially over time. The effective rate of return is greater than the stated interest rate.

The calculation for Gabriel's account is: 23,000 * (1.11^(365*8)) = $69,985.67. The calculation for Ava's account is: 23,000 * e^(0*8) = $24,000. The difference between the two is $45,985.67.

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Answer:997

Step-by-step explanation:

The number of different outfits cory can make is 270 ways.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangements is called a combination. The various ways in which objects from a set may be selected, generally without replacement to form subsets is known as combination.

Given;

He has 5 pairs of pants to pick from, 18 shirts , and 3 pairs of shoes

Now, the combination;

=5*18*3

=270

Therefore, the combinations will be 270.

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Answer:

288/720 or simplified to its lowest is 2/5

The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

Let X be the amount of mix A (in pounds), and Y be the amount of mix B.

The constraints are

20X + 10Y >= 400

10X + 30Y >= 960

5X + 10Y >= 210

X >= 0,  Y >= 10.

The objective function to minimize is  F(X, Y) = 20X+40Y.

In the equivalent form, the constraints are

2X + 1Y >= 40

X+ Y >= 33

X+2Y >= 42

The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :

A red   (which represents the constraint (1'));

The green (which represents the constraint (2')),

A blue  (which represents the constraint (3')).

Plot 2X + 1Y = 40 (const. (1'), red);  

X+Y = 33 (const. (2'), green)

X+2Y = 42 (const. (3'), blue)

The four corner points of the area are:

P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)

As per the Linear Programming method, we can calculate and compare the values at these 4 points.

These values of P1, P2, P3,P4 are:

P1: F(0,40) = 0 + 40*40 = 1600

P2: F(7,26) = 20*7+40*26 = 1180

P3: F(24,9) = 20*24+40*9 = 840

P4: F(42,0) = 20*42+0 = 840.

By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.

The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

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