Is the integer x divisible by 6 ? (1) x + 3 is divisible by 3. (2) x + 3 is an odd number.Answer choices:
(a) Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.
(b) Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.
(c) Either statements are NOT sufficient, but BOTH together are sufficient.
(d) Each statement ALONE is sufficient.
(e) Neither statement Alone is sufficient.

The total length of the bolt should be 21/8 inches.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given the thickness of plate 1 = 7/8 inches

the thickness of plate 2 = [tex]1\frac{1}{4}[/tex] inches = 5/8 inches

total thickness of both plates = 7/8 + 5/4

5/4 is equaivalent to (5*2)/(4*2) = 10/8

the total thickness of both plates = 7/8 + 10/8

the total thickness of both plates = 17/8 inches

and the bolt must be at least 1/2 inch longer

total length of bolt = 17/8 + 1/2

convert 1/2 to the same denominator as 17/8

1/2 = (1*4)/(2*4) = 4/8

total length of bolt = 17/8 + 4/8

the total length of the bolt =  21/8 inches

Hence the bolt should be 21/8 inches longer.

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Answer:

- 8.5

Step-by-step explanation:

The length of side x is  √3 units.

We know that the larger triangle is an equilateral triangle, and it is divided into two equal right triangles.

Now, let's analyze these, we can see that the catheti are:

x and 3.

And the hypotenuse must have a length of 2x (if the triangle is equilateral).

Now we can use Pythagorean's theorem.

Then we will get:

(2x)^2 = x^2 + 3^2

4x^2 = x^2 + 9

4x^2 - x^2 = 9

3x^2 = 9

x^2 = 9/3 = 3

x = ± √3

We only care for the positive value, then:

x = √3

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The probability of the field mice having a weight greater than 33 g is 0.977, the field mice have a weight greater than 33 g.

The proportion of field mice with a weight greater than 33 g can be calculated using the formula for a standard normal distribution. This formula states that the probability of an event with a normal distribution occurring can be calculated by subtracting the area under the normal curve from the mean to the given value and dividing by the standard deviation.

In this case, the mean of the distribution is 25 g, the standard deviation is 4 g and the given value is 33 g.

Therefore, the probability of the field mice having a weight greater than 33 g is 0.977. This means that 0.977, or 97.7%, of the field mice have a weight greater than 33 g.

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Answer:

Step-by-step explanation:

Let's say there are "x" students in class 6.

Since Anton got 0.2 of the votes, he got 0.2 * x votes.

Eva got 10% of the votes, which is equal to 0.1 * x votes.

Petra got 0.3 of the votes, which is equal to 0.3 * x votes.

Kofi got 9 votes.

So, the total number of votes in class 6 is x.

By adding up the number of votes each candidate received, we can write an equation:

0.2x + 0.1x + 0.3x + 9 = x

Simplifying the equation:

0.6x + 9 = x

Subtracting 0.6x from both sides:

9 = 0.4x

Dividing both sides by 0.4:

x = 22.5

Since the number of students must be a whole number, we round up to the nearest whole number:

x = 23

So there are 23 students in Class 6.

Answer:

A(L) = - L²  + 215L

Domain
0 < L < 215

or

(0, 215) in interval notation

Step-by-step explanation:

Let  L represent the length and W the width

Perimeter of a rectangle = 2(L+W) and is given as 430 meters

Therefore 2(L + W) = 430

L + W = 430/2
L + W = 215

W = 215-L

The area A is given by L x W

Substituting for W in terms of L this becomes

A = L x(215 - L)

A = 215L - L²

which can be expressed as a function of in the form
A(L) = 215L - L² or in standard form(highest degree first)

A(L) = - L²  + 215L

The domain of this function are the values of L which result in a defined , real value for A

Without restrictions, the domain for L is -∞ < L < ∞. However real world facts coming into play

1. Area cannot be zero
So A(L) > 0 (upper bound on area)

-L² + 215L > 0

-L² > - 215L Move 215L to right side

L² < 215L   (dividing by -1 changes signs of variables and also inequality)

L < 215      (divide by L both sides)

2. Length cannot be negative
So lower bound on L is L > 0

Together the domain is
0 < L < 215

or

(0, 215) in interval notation

Answer:

150 units (Option C)

Step-by-step explanation:

Perimeter of rectangle = Perimeter of triangle

= {2 × (Length + Width)} = Sum of all three sides

= {2 × [(2x) + (x + 12)]} = [(4x) + (2x) + (x + 3)]

The parenthesis are expanded using the Distributive Law:
= {2 × [2x + x + 12]}  = [4x + 2x + x + 3]

= {2 × [3x + 12]} = [7x + 3]
= 6x + 24 = 7x + 3

Bring all the like terms together and isolate x:

= 24 - 3 = 7x - 6x

= 21 = x

∴x = 21

Substitute this calculated value of x to determine the perimeter of rectangle:

6x + 24

= 6(21) + 24

= 126 + 24

= 150 units

∴Option C

Option B: The domain of the function is the set of all real numbers, Option C: the range of the function is the set of all non-negative real numbers, Option D: the graph has an intercept at (0, 0), and option G: the graph is symmetric with respect to the y-axis are correct statements about the graph.

There are only real numbers in the domain, or collection of x-values. This is so because x holds true for all numbers. The set of all non-negative real numbers is known as the range or set of y-values. This is due to the fact that every value we obtain for y is a positive real number. The graph's x-intercept and y-intercept, also known as the intersection point, are located at (0, 0). Instead of the other way around, the graph increases on the interval x>0 and decreases on the interval x<0. Instead of a maximum, the graph shows a minimum at (0, 0). The graph is symmetric with respect to the y-axis because it may be folded in half along that axis.

As per the question, the function described below is an example of a polynomial function since it is a function of a single independent variable that has been raised to an integer power. Adding terms with a numerical coefficient multiplied by a specific power of the independent variables results in polynomial functions.

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Refer image for the complete question.

Answer: 1. 27/72 = 3/8,  2. 24/40 = 3/5,  3. 6/42 = 1/7

Step-by-step explanation:

1. 27/72 divided by 9/9 equals 3/8.

2. 24/40 divided by 8/8 equals 3/5.

3. 6/42 divided by 6/6 equals 1/7.

Answer: 9

Step-by-step explanation:

12-3=9 or count up from 3 until you get too 12

The expression when evaluated is 46552

From the question, we have the following parameters that can be used in our computation:

5,819 x 8.

Using the standard algorithm, we have:

5,819 x 8 = (5800 + 19) * 8

Open the brackets

So, we have the following representation

5,819 x 8 = 5800* 8 + 19 * 8

Evaluate

5,819 x 8 = 46400 + 152

So, we have

5,819 x 8 = 46552

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The value of the 25th percentile for this data set is 26.25. This means that 25% of the data is below 26.25 and 75% of the data is above 26.25

The 25th percentile, also known as the lower quartile, is a value that separates the lowest 25% of the data from the rest of the data. To find the 25th percentile of an ordered data set, we first need to determine the position of the 25th percentile, which can be calculated using the formula:

position = (n+1) * p

where n is the number of observations in the data set and p is the percentile (in decimal form). In this case, n = 8 and p = 0.25. Put values:

position = (8+1) * 0.25 = 2.25

Since the position is not a whole number, we know that the 25th percentile falls between the second and third observations in the data set. In this case, the second observation is 24 and the third observation is 27. To find the exact value of the 25th percentile, we use the formula:

value = L + (position - i) * h

where L is the value of the lower observation, i is the integer part of the position, and h is the difference between the two observations. In this case, L = 24, i = 2, and h = 27 - 24 = 3. Put values:

value = 24 + (2.25 - 2) * 3 = 24 + 0.75 * 3 = 24 + 2.25 = 26.25

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The function has no vertical asymptotes and horizontal asymptotes are at y = 0.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels toward as it approaches infinity.

A straight line that serves as the asymptote of the curve y = f(x) or, in its implicit form, f(x,y) = 0, where the distance between the two lends to zero as the points on the curve approach infinity.

Given function,

f(x) = -7/(x² + 4)

in the given function the degree of the denominator is more than the numerator so The horizontal asymptote lies at y = 0 because, as we can see, the degree of the numerator is less than the denominator.

and there will be no vertical asymptote.

The graph of the equation is attached.

Hence horizontal asymptote lies at y = 0 and ni vertical asymptote.

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Answer:

y = -x+5

Step-by-step explanation:

Use point slope formula to find the equation of the line

First find the slope: (-1-4)/(6-1) = -5/5, slope = -1

Then, use the formula: y - y1 = m(x - x1)

y - 4 = -1(x - 1)

y - 4 = -x+1

y = -x + 5

An equation of a line in a slope-intercept format that is parallel to

y = (1/2)x - 3 line and goes through the point (4, 2) is y = (1/2)x

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know parallel lines have equal slopes.

The equation of the line given is y = (1/2)x - 3 and our required equation is parallel to it and passes through (4, 2).

So, 2 = (1/2)(4) + b.

2 = 2 + b.

b = 0.

Hence, y = (1/2)x is the required equation of the line.

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Answer:

x = 1

Step-by-step explanation:

2/3 (2x + 4) + 6 = 10

2/3 (2x + 4) = 10 - 6

1⅓x + 2⅔ = 4

1⅓x = 4 - 2⅔

1⅓x = 1⅓

x = 1

Answer:

$21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

$30 subtracted by 30% is equal to $21

9 × 3 = 27 +10% (3) = $30

The quantity of type A coffee will be 37 pounds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound.

The quantity of Type A coffee will be calculated as:-

B = 4A

4.20A + 5.6B = 984.20

4.20A + 4 x 5.6 x A = 984.20

4.20A + 22.4A = 984.22

26.6A = 984.22

A = 37

Therefore, the amount of each type of 37 pounds will equal one coffee.

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Answer:

  T〈-7,0〉

Step-by-step explanation:

You want a description of the transformation of triangle ABC to triangle A"B"C".

∆A"B"C" has the same orientation as ∆ABC, so no reflection is involved (eliminates choice B).

Point A" is 7 units to the left of point A, so the translation is 7 units left (and no units up or down).

The transformation is ...

  [tex]\boxed{T_{\langle-7,0\rangle}}[/tex]

To convert yards to feet we multiply the given value by 3.

A yard is one linear yard. "Yd" is the yard symbol. It is equivalent to 36 inches or 3 feet. 1 yard equals 0.9144 metres in metres when measured in metres. Both the imperial and US customary systems of measuring use this unit. The most common use of yards is to measure the length of a field, such a sports field.

A foot can also be used to measure length. The letter "ft" stands for the foot. Twelve inches and one third of a yard make up one foot. Additionally, one foot is equal to 0.3048 metres. We must divide the provided value by 3.281 to translate the given value from feet to metres. In aviation and elevation, the foot is typically used to measure height or altitude. The height of a person is also expressed in feet and inches.

Hence, to convert yards to feet we multiply the given value by 3.

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4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

What are discrete and continuous variables?

Discrete variables are those that have distinct, countable values. A continuous variable can be assigned to any value that falls inside a range, which has an infinite number of possible values.

4.1.1 "I am fifty years old"

It is a discrete variable because age is represented in whole numbers.

4.1.2 "I can drink 400.5 ml of juice in a minute"

It is a continuous variable because the amount of juice is consumed every minute so, we can obtain values even in fraction.

4.1.3 "I have 2 brothers and 1 sister"

It is a discrete variable because the given value is countable.

Hence, 4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.

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A. The length of each segment of the rope is 5 m.

B. The mass of the middle segment is the length of the segment 10 kg.

C. The y values of the bottom of each segment are y₀ = 0, y₁ = 5 m, and y₂ = 10 m.

D. The distance d₂ the middle segment must be moved is 15,

Acceleration is a measure of the change in velocity over time. In physics, acceleration is defined as the rate of change of velocity, or the second derivative of position with respect to time. Acceleration is a vector quantity that has both magnitude and direction, and its unit is meters per second squared (m/s²).

A positive acceleration indicates an increase in speed, while a negative acceleration indicates a decrease in speed or a change in direction. In everyday life, we encounter examples of acceleration in movements such as starting a car, stopping a car, or changing direction while driving.

A. The length of each segment of the rope is 15 m / 3 = 5 m.

B. The mass of the middle segment is the length of the segment multiplied by the density of the rope: M2 = 5 m × 2 kg/m = 10 kg.

C. The y values of the bottom of each segment are y0 = 0, y1 = 5 m, and y2 = 10 m.

D. The distance d2 the middle segment must be moved is 25 m - 10 m = 15 m.

Therefore, the work required to move the middle segment can be approximated using the formula W = M2 × g × d2, where g is the acceleration due to gravity. The exact value of the work required to move the entire rope would need to take into account the different distances that each segment must be moved.

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The terms which is not an impact of American consumerism is -

Option C: Cash generators for several nations.

What is consumerism?

The tendency to continuously consume is known as consumerism. It is the need to acquire more possessions and establish one's identity via them. Consumer spending and GDP growth are seen as benefits of consumerism by economists.

The American consumerism includes -

Debts : Due to introduction of credit cards the consumers have ore and more debt on their credit cards whilst they spend on materialistic goods.

Lack of Unemployment : Economists point out that a decline in product demand causes an economic downturn or even depression, which is accompanied by high unemployment.

Stress:  Due to debt, recession and unemployment people are constantly under stress for surviving.

Since, consumerism helps in GDP growth of a country it does not help generate cash for other nations.

Therefore, " Cash generators for several nations" is not an impact.

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Answer:

7x-43=5x+43

7x-5x=43+43

2x=86

x=86/2

x=43

The correct statement regarding the probability in this problem is given as follows:

D.) A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For each at bat, there are two possible outcomes:

There are four types of hits, which are given as follows:

Hence only statement D is correct, as the player can either be eliminated or get one of the four types of hits.

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The m∠1 and m∠2 which are linear pairs of angles are 72° and 108°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know that the sum of linear pair of angles is equal to 180°.

therefore, From the given information, (x + 36)° + 3x° = 180°.

4x + 36° = 180°.

4x = 144°.

x = 36°.

So, m∠1 = 72° and m∠2 = 108°.

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Answer:

1/2 goes into 3/4 1 1/2 or 1.5 times

Step-by-step explanation:

Answer: E

Step-by-step explanation: Since this is a special right triangle(45,45,90), you know that the ratios of the leg to the hypotenuse is 1:1:sqrt2. 15 sort root two hold true to that rule and is the right answer.