Simplify (6x-15)/(4x^2-25)

Answer:

i) 84

ii) 7

iii) 47

iv) 16

v) 56

vi) 54

Step-by-step explanation:

The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)

First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.

We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.

We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.

We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.

(see diagram A to see how this should look)

70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7

60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9

80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31

Marking in these figures completes the diagram (See diagram B to see how it should look)

i)

The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84

ii)

Above, we found the amount with arthritis only was 7

iii)

7 have only arthrits, 9 have only arteriosclerosis, and 31 have only  loss of hearing , so the amount with only one ailment is 7+9+31=47

iv)

Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis

v)

The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56

vi)

Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54

Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.

Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.

Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.

Reimbursement = miles driven x rate per mile

Filling the value in above equation.

So,

Reimbursement = 982 miles x $0.75/mile

Reimbursement = $736.50

Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.

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According to the information, the area of this quadrilateral, trapezoid is 42 cm.

To calculate the area of the figure we must first graph it. Once we have found its shape we must identify what type of quadrilateral it is, in this case we can affirm that it is a right trapezoid.

On the other hand, to calculate its area we must divide the figure in two, one part would be the quadrilateral and the other the triangle. So we need to find the area of both shapes and then add them.

So the total area would be 42cm²

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Answer:

length = 12 feet , area = 72 ft²

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides of the rectangle.

let w be width then length is 2w

opposite sides of a rectangle are congruent , so

P = 2(2w) + 2w = 4w + 2w = 6w

given P = 36 , then

6w = 36 ( divide both sides by 6 )

w = 6

then

length = 2w = 2 × 6 = 12 feet

the area (A) of a rectangle is calculated as

A = length × width = 12 × 6 = 72 ft²

Samantha drove 217 miles during the second day.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let D be the distance Samantha traveled during the second day. Then the total distance she drove is 468 miles. The equation will be:

D + 251 = 468

Solving for D:

D = 468 - 251

D = 217

Therefore, Samantha drove 217 miles during the second day.

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1. 1/6 is the probability of rolling a five on the next roll.

2. The probability of getting 5 fives in a row when rolling a single die is  1/7776 .

3.  1/38 is he probability of 7 coming up on the very next spin is

4. 1/54782 is the probability of getting three 7's in a row on a roulette wheel.

5.  (1/10)⁶ is the probability of getting a 1 on all six trials.

6. 1/36 is the probability of getting a pair of sixes when rolling a pair of dice is

7.  The probability of getting any pair is 1/6

It is a branch of mathematics that deals with the occurrence of a random event.

1. The probability of rolling a five on a single roll of a fair die is 1/6, since there are six equally likely outcomes: rolling a 1, 2, 3, 4, 5, or 6.

the probability of rolling a five on the next roll is still 1/6, regardless of whether the previous rolls resulted in four fives in a row or not.

2. The probability of getting a five on a single roll of a fair die is 1/6, as there are six equally likely outcomes.

the probability of getting 5 fives in a row when rolling a single die is:

(1/6) × (1/6) × (1/6) × (1/6) × (1/6) = 1/7776

3. The probability of any particular number coming up on a single spin of an American roulette wheel with 38 numbers is 1/38, since there are 38 equally likely outcomes.

As these are independent , the probability of 7 coming up on the very next spin is still 1/38.

4. The probability of getting three 7's in a row on a roulette wheel is:

(1/38) × (1/38) × (1/38) = 1/54,872

5. The probability of generating a 1 on a single trial is 1/10.

The probability of getting a 1 on a single trial by itself six times

(1/10)  × (1/10)  × (1/10)  × (1/10) × (1/10)  × (1/10) = (1/10)⁶

The probability of getting a 1 on all six trials is (1/10)⁶

6.

The probability of getting a pair of sixes when rolling a pair of dice is:

1/36

7.

The probability of getting any pair when rolling a pair of dice is:

Number of ways to get a pair / Total number of possible outcomes

= 6 / 36

= 1 / 6

So the probability of getting any pair is 1/6

Hence,

1. The probability of rolling a five on the next roll is 1/6.

2. 1/7776 is the probability of getting 5 fives in a row when rolling a single die.

3. The probability of 7 coming up on the very next spin is  1/38.

4. The probability of getting three 7's in a row on a roulette wheel is 1/54782

5. The probability of getting a 1 on all six trials is (1/10)⁶

6. The probability of getting a pair of sixes when rolling a pair of dice is:

1/36

7.  the probability of getting any pair is 1/6

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PLEASE GIVE BRAINLIEST
thank you and have a good day :)

Answer:

5.6294995342131E-32

Step-by-step explanation:

the common ratio is 1/5, therefore with the equation an = a x r

                                                                                                       n-1

we can figure out the answer to this by plugging in the common ratio for r,

and n as the number in the sequence that we want to obtain.

a is simply the first number (1000)

The area of the picture frame 72 cm². Therefore, option C is the correct answer.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, a bigger outer rectangle has sides of 12 cm and 10 cm.

So, the area of a outer rectangle = 12×10

= 120 cm²

An inner rectangle has sides of 8 cm and 6 cm

The area of a inner rectangle = 8×6

= 48 cm²

The area of the picture frame = 120-48

= 72 cm²

Therefore, option C is the correct answer.

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Answer: C | 72 square centimeters

Step-by-step explanation:

The answer is C. 72 square centimeters. The area of the picture frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle. The area of the outer rectangle is 120 square centimeters (12 x 10). The area of the inner rectangle is 48 square centimeters (8 x 6). Therefore, the area of the picture frame is 120 - 48 = 72 square centimeters.

The perimeter of the plate is 60"

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

Length = 18"

Width = 12"

The perimeter of the rectangle piece can be calculated as

Perimeter = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (18 + 12)

Evaluate

Perimeter = 60

Hence, the perimeyer is 60"

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Answer:

no answer

soory

Step-by-step explanation:

Answer: The number of ways to form a group of 5 students from a class of 20 students is calculated using the combination formula:

C(20,5) = 20! / (5! * (20-5)!) = 15504

So, there are 15,504 different ways in which 5 students can form a group.

Step-by-step explanation:

The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

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The total volume in centiliters is 5 cL, then the correct option is A.

Here we know that Dante mixes 30 mililiters of one liquid with 2 centiliters of a second liquid, and we want to find the total volume in centiiters.

We know that:

1 milliliter = 0.1 centiliters.

Then:

30 mililiters = 30*( 0.1 centiliters) = 3 centilters.

Then the sum of the two volumes is:

3 centiliters + 2 centiliters = 5 centiliters.

Then the correct option is A.

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The answer is A. 5 cL.

Liquid is one of the three states of matter, alongside solid and gas. It is a form of matter that has a definite volume, but not a definite shape. Liquids take the shape of their container and are able to flow and be poured.

First, we need to convert 30 milliliters to centiliters, which is 3 centiliters (since 1 centiliter = 10 milliliters).

Then, we can add the 3 centiliters to the 2 centiliters of the second liquid to get a total of 5 centiliters.

Therefore, the answer is A. 5 cL.

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The solution is Option B.

The angles ∠2 and ∠7 are alternate exterior angles

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the parallel lines be represented as m and n

Now , the transversal line is t

The angles formed on line m is ∠1 , ∠2 , ∠3 and ∠4

And , the angles formed on line n is ∠5 , ∠6 , ∠7 and ∠8

Now , the angles ∠2 and ∠7 are situated outside or exterior and is represented by alternate exterior angles

So , pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Hence , the angles are alternate exterior angles

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Answer: Parallelogram angles add up to 360, so use angle properties and known measures.

Step-by-step explanation:

The common region to both the graphs represents the solution set of the given inequalities.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.

Assume that you worked {x} hours Mowing lawns and {y} hours babysitting.

We can write the inequalities as -

x + y ≤ 15

3x + 5y ≥ 60

Refer to the graph attached. The common region to both the graphs represents the solution set.

Therefore, the common region to both the graphs represents the solution set of the given inequalities.

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Answer:

Step-by-step explanation:

Based on the information provided, the following three equations are true for the values of x, y, and z:

x + y + z = 360 degrees (Since the sum of the angles in a quadrilateral must equal 360 degrees)

x = 65 degrees (As given, the first angle is 65 degrees)

y + z = 295 degrees (From equation 1, 360 - 65 = 295)

So, the values of x, y, and z can be calculated as 65 degrees, 115 degrees, and 180 degrees respectively.

By using a system of equations of two variables the number of short answer problems is 10.

Total number of problems in the Test = 30

Maximum points of test = 50

Point of multiple choice = 1

Point of short answer problems = 3

Let the number of multiple choice questions is x and the number of short answer problems is y

So, x + y = 30    - (1)

and 1.x + 3.y = 50 ⇒ x + 3y = 50      -(2)

Equation (2) - Equation (1)

x + 3y - (x + y) = 50 - 30

2y = 20

y = 10

Put y = 10 in equation (1)

x = 30 - 10 = 20

Hence, the number of multiple-choice questions = 20 and the number of short answer problems = 10.

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The null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population

The appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life is greater than the general population can be expressed as follows:

Null hypothesis: The proportion of college students who believe in extraterrestrial life is equal to or less than the general population, or

H0: p <= 0.47

Alternative hypothesis: The proportion of college students who believe in extraterrestrial life is greater than the general population, or

Ha: p > 0.47

where p is the true proportion of college students who believe in extraterrestrial life.

In other words, the null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population (i.e., there is no difference between the two populations), while the alternative hypothesis assumes that the proportion of college students who believe in extraterrestrial life is higher than the general population.

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Answer:

Step-by-step explanation:

The expression that represents the area of a rectangle with length (l) and width (w) is given by:

A = l * w

Therefore, the expression that represents the area of a rectangle with a length of ( + ) and a width of ( − ) can be represented as:

A = ( + ) * ( − ) = + × − = + (−) = −.

The length of the other sides of ΔABC are AB =12 cm and BC = 16 cm.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, ΔABC ∼ΔA'B'C' and AC=20 cm A'C'=15 cm B'C'=12 cm and A'B'=9 cm.

Here, AB/A'B' = BC/B'C' = AC/A'C'

AB/9 = BC/12 = 20/15

AB/9 = BC/12 = 4/3

Now, AB/9 = 4/3

AB =12 cm

BC/12 = 4/3

BC = 16 cm

Therefore, the length of AB =12 cm and BC = 16 cm.

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Answer:

Step-by-step explanation: The temperature at Thabana dropped by 7 degrees, so we can calculate the night temperature by subtracting 7 from the original temperature of 6 degrees:

Step 1: Subtract 7 from 6:

6 - 7 = -1

Step 2: The night temperature will be -1 degrees.

The equivalent expression by combining like terms is 0.57b

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

In order to write an equivalent expression by combining like terms, subtract 0.43b from b (Note: b = 1b). That is:

b-0.43b = 0.57b

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Answer:

58

Step-by-step explanation:

4234 = 73x divide by 73 on both sides and x=58

To construct a line segment that is half the length of segment AB, follow the steps below.

What is the intersection points of the circle?

The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their pairwise radical lines, known as the radical center.

Draw a straight line passing through points A and B.

Bisect the line segment AB at point C.

Draw a circle centered at point C with a radius equal to AC or BC.

The intersection points of the circle and the line passing through A and B will be points D and E.

The line segment DE will be half the length of segment AB.

Therefore, To construct a line segment that is half the length of segment AB, follow the steps above.

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Answer:

0.058 hectometers

Step-by-step explanation:

There are 0.058 hectometers in 580 millimeters.

To convert millimeters to hectometers, you need to divide the number of millimeters by 100,000. So, 580 millimeters divided by 100,000 equals 0.0058 hectometers, or 0.058 hectometers when rounded to two decimal places.

Type A: 5.45 per pound, Type B: 4.35 per pound. This month's mixture: We know that an is 5.45 per pound, so we divide  total cost  401.65 by 5.45 to get a result of 73.69 LB of Type A. 2B + A = 410.35 2(4.35) = 8.70 A + 8.70 = 410.35 A = 401.65.

Total cost is a term used in economics to describe the least expensive way to produce a specific amount of a good (TC). Fixed costs, which are unaffected by the quantity of a good produced and include inputs like buildings and machinery, possibly including sunk costs, and variable costs, which change with the quantity of a good produced and include inputs like labor and raw materials, make up the total economic cost of production. Economics considers the total potential cost of each manufacturing item as one of the total cost's fixed or variable costs.

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Answer: C and D are the correct ones

Step-by-step explanation: