The average sneeze can travel 3100 mile in 3 seconds. At this rate, how far can it travel in one minute? (3 seconds = 120 minute)

Answer:

(f-g)(x)

= -x^2 - 2x + 2

Step-by-step explanation:

(f-g)(x) means

f(x) - g(x)

= x - 2 - (x^2+3x-4)

distribute the subtraction to all three of the last terms.

= x - 2 - x^2 - 3x + 4

combine like terms

= -x^2 - 2x + 2

(first base + second base)x height ÷ 2

By examining the patterns and variations in the two-way relative frequency table, we can determine whether the data collected indicate an independent or dependent relationship between student gender and the source of car insurance payment.

To design and conduct a survey of students at your school, follow these steps:

1. Begin by creating a survey questionnaire that includes questions about student gender and whether a student's car insurance is paid by the student or the student's parent(s).

2. Distribute the survey to a representative sample of students at your school. It's important to ensure that the sample is diverse and includes students from different grades and backgrounds.

3. Collect the responses from the survey and organize the data in a two-way relative frequency table. The rows of the table should represent the different options for student gender (e.g., male and female), and the columns should represent the options for car insurance payment (e.g., paid by the student, paid by the parent(s)).

4. Count the number of responses in each cell of the table. This will give you the frequencies for each combination of gender and car insurance payment.

5. To determine whether there is an independent relationship between the two variables, compare the relative frequencies of each combination. If the relative frequencies are similar across all cells of the table, it suggests that there is no significant relationship between student gender and car insurance payment. On the other hand, if there are substantial differences in the relative frequencies, it indicates that there might be a relationship between the variables.

6. In your explanation, provide specific examples from your table to support your reasoning. For instance, if the relative frequency of male students paying for their car insurance is significantly higher than the relative frequency of female students paying for their car insurance, you could argue that there might be a gender-based difference in car insurance payment responsibilities.

Remember, conducting a survey and analyzing the data requires careful planning and attention to detail.

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Given :

An adults heart beats about 2100 times every 30 minutes.

A baby beats about 2600 times every 20 minutes.

To Find :

How many more heart beat baby have than adult in 60 min .

Solution :

Now , total number of heart beats of adult in 60 min , \(T_a=2100\times 2=4200\)

Also , total number of heart beats of adult in 60 min , \(T_b=2600\times 3=7800\)

Difference between them , \(7800-4200=3600\) beats .

So , baby have 3600 more heart beats than adult .

Hence , this the required solution .

Answer:

33

Step-by-step explanation:

the ratio "parts" (4&7) total to 11 so the number of students must be a multiple of 11. 33 is the only multiple of 11 that falls between 24 and 40.

HOPE THIS HELPS!!!

The probability distribution for the third purchase would be approximately [0.781248, 0.218752] for "special" and "b" respectively.

Based on the transition probabilities provided, we can represent the purchase patterns for the two brands of toothpaste as a Markov process. Let's denote the two brands as "special" (S) and "b" (B).

The rows represent the current state, and the columns represent the next state. The entry at row i and column j represents the probability of transitioning from state i to state j.

For example, according to the transition matrix:

The probability of transitioning from "special" (S) to "special" (S) is 0.92.

The probability of transitioning from "special" (S) to "b" (B) is 0.08.

The probability of transitioning from "b" (B) to "special" (S) is 0.04.

The probability of transitioning from "b" (B) to "b" (B) is 0.96.

Using this transition matrix, we can analyze the purchase patterns over time. For example, if we start with a customer purchasing the "special" brand, the probability distribution for the next purchase would be [0.92, 0.08] for "special" and "b" respectively. If we continue this process, we can calculate the probabilities for multiple purchases in the future.

Certainly! Let's continue analyzing the purchase patterns using the given transition probabilities.

Let's consider the initial state where a customer purchases the "special" brand of toothpaste. We can calculate the probabilities for the next purchase after several time steps.

Time step 1:

If the customer purchased "special" toothpaste initially, the probability distribution for the next purchase would be [0.92, 0.08] for "special" and "b" respectively.

Time step 2:

To calculate the probabilities for the second purchase, we multiply the previous probability distribution by the transition matrix:

Hence, the probability distribution for the second purchase would be approximately [0.8464, 0.1536] for "special" and "b" respectively.

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

2/9 * (-4 - 3) + 3

= 2/9 * (-7) + 3

= -14/9 + 3

= -14/9 + 27/9

= 13/9

The probability that the battery life is at least 9.1 hours is 0.08.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centred around the mean in order to be regarded as having a normal distribution. The empirical rule indicating the proportion of the data set that is inside (plus or minus) 1, 2, and 3 standard deviations of the mean must also be followed.

Given that:

mean=μ=8.5 hours

standard deviation= 39/60=0.65

(a) X=9.1

Z=

\(Z=\frac{X- mean}{Standard deviation} \\Z=\frac{9.1-8.5}{0.65}\)

Z=0.92

To find probability : 1-0.92=0.08

(b) On similar pattern

X= 7.9 with same mean and deviation

Z= it is -0.92

Impossible case

(c)= Impossible case.

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Answer:

B. y > (4/3)x - 2

Step-by-step explanation:

The dotted line means that the answer WILL NOT include the line itself, just the space above it. Since the shaded area is above the line, it must be greater than the line.

Using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, they require at least 100 sushi pieces.

24 pieces of sushi had previously been ordered and paid for by Sofia.

Roll sushi is available.

Each roll = 12 pieces at $8

R = additional rolls that Sofia orders

Additional sushi = Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

A roll contains 12 pieces.

76/12 = 6.33

Rolls must be ordered by Sofia.

She will therefore place 7 additional sushi rolls, each with 12 pieces.

12*7=84 pieces

Remember that they need at least 100 pieces, so there may be more than 100 in total.

84 pieces plus the 24 pieces Sofia has previously ordered.

The total number of pieces will be 108.

Therefore, using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

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Complete question:
Sofia ordered sushi for a company meeting. They change plans and increase how many of people

will be at the meeting, so they need at least 100 pieces of sushi in total.

Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.

The sushi comes in rolls, and each roll contains 12 pieces and costs $8. How many more sushi Sofia will order and of what amount?

The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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The slopes of perpendicular lines are opposite reciprocals.

For the given function:

Solve y to identify the slope (y=mx+b, m is the slope)

The slope of the perpendicular line to the given function is 5/6. For the given options the equation with slope 5/6 is: B. 6y=5x+3

Colin's new mean score, after getting 6 runs on Sunday, is approximately 20.09.

To calculate Colin's mean score, we need to sum up all his scores and divide by the number of scores.

a) Mean score:

16 + 11 + 25 + 27 + 11 + 25 + 20 + 26 + 29 + 35 = 215

Total scores: 10

Mean score = 215 / 10 = 21.5

Colin's mean score is 21.5.

b) To calculate his new mean score after getting 6 runs on Sunday, we need to add the new score to the previous total and divide by the new number of scores.

New total scores = 215 + 6 = 221

New number of scores = 10 + 1 = 11

New mean score = 221 / 11 = 20.09 (rounded to two decimal places)

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The diameter of the circle pen for the sheep of the farmer is 68 yards.

The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.

Thus,

circumference = 213.52 yards

The formula for the calculation of the circumference of circle is,

circumference = 2πr,

In which,

π = 3.14  and radius r.

Thus,

213.52 = 2πr

r = 213.52 / 2π

r = 34

Diameter = 2 x radius

Diameter = 2 x 34

Diameter = 68 yards.

Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.

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The two back to back regular numbers are 5 and 6.

Assume that the two natural numbers that come after each other are x and (x+1).

As per the given data, the amount of their squares is 110. This can be summed up in the following equation:

x^2 plus (x+1)^2 equals 110 Extending the equation:

x^2 + (x^2 + 2x + 1) = 110 When combining terms that are similar:

110 is the result of rearranging the equation as follows:

Simplifying: 2x^2 + 2x + 1 - 110 = 0.

Using the quadratic formula, we can now solve this quadratic equation to determine the value of x: 2x^2 + 2x - 109 = 0.

x = (- b ± √(b^2 - 4ac))/(2a)

In this situation, a = 2, b = 2, and c = - 109.

Simplifying within the square root: x = (-2 - (22) - 42(-109))) / (2*2).

x = (-2 (4 + 872)) / 4 x = (-2  876) / 4 We now have two possibilities for the value of x:

The values are as follows: x1 = (-2 + 876/4) x2 = (-2 - 876/4)

x₁ ≈ 5.03

x₂ ≈ - 13.03

Since we are searching for regular numbers, x can't be a negative worth. Thus, x equals 5.

The two back to back regular numbers are 5 and 6.

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ANSWER

Length of the playing alley = 9m

Width of the playing alley = 3m

STEP-BY-STEP EXPLANATION:

Given information

The perimeter of a rectangular playing alley = 24 m

The length of the alley is three times the width

Let l represents the length of the alley

Let w represents the width of the alley

Step 1: Write the formula for calculating the perimeter of a rectangle

Where l is the length and w is the width of the rectangle

Recall, length = 3 times the width of the alley

Mathematically,

Step 2: Substitute the value of l = 3w into the above formula

Step 3: Solve for w

From the calculations above, you will see that the width of the playing alley is 3m

Step 4: Solve for l

Hence, the length of the playing alley is 9m

Answer:

She must jog 7 laps in order to meet her goal.

Step-by-step explanation:

A more accurate answer would be that she needs to run 6 1/4 laps to meet her goal. However, because the problem states that she will not be running partial laps, then the number of laps she runs must be a whole number, which in this case works out to be 7 laps.

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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Answer: it is table "a"

explanation:

as the equation is y= 2x + 5 you should substitute each of the x values from -2 to 4 in order to get the y value which will help you decide which table should be used by Cindy to graph the equation.

now, this is how you should substitute the values into the equation and simplify it so that you get the "y" value.

the first x value given is -2 therefore:

you put -2 in the equation instead of putting x, this will allow you to find the y value which you can compare with the choices given.

y= 2x+5 (this is the equation)

y= 2(-2)+5 (here I have replaced the x with -2)

y= -4+5 (you should multiply 2 and -2)

y= 1 (therefore the answer is 1)

you should further continue this way and get the y values which will help you decide which is the correct table to be used. Now you already know that table "a" is the answer.

Answer:

The answer is table A

Step-by-step explanation:

Given:

Form the table of values from x = -2 to x = 4

Hence,

Therefore, the table that can be used for the graph of the equation is;

Table A

Step-by-step explanation:

GIVEN =

d= 49cm

\(\pi = \frac{22}{7} \)

To find = Circumference of a circle

SOLUTION =

CIRCUMFERENCE OF THE CIRCLE = πd

\( \frac{22}{7} \times 49\)

= 22 × 7

154cm

the circumference of the given circle is 154cm

Answer:

Step-by-step explanation:

5) diameter = d = 49 cm

Circumference = πd

                         \(= \frac{22}{7}*49\\\\= 22 *7\\\\= 154 \ cm\)

6) d = 20 mm

Circumference = π* 20

                         = 20π mm

Answer:

what is this question???

Answer: I think you were trying to ask if this was a true statement, and the answer is yes. If that's what you needed to know?

Answer:

No, the area of the dilated triangle will increase by a factor of 9

Step-by-step explanation:

When the scale factor by which the dimensions is dilated = 3, we have;

The original length of base = b

The base length of the dilated triangle = 3×b

The original height of the the triangle = h

The height of the dilated triangle = 3×h

The original area of the triangle = 1/2 × base × height = 1/2×b×h

The area of the dilated triangle = 1/2 × base of dilated triangle × height of dilated triangle

∴ The area of the dilated triangle = 1/2× 3 × b × 3× h  = 9×1/2× b×h

Which gives;

The area of the dilated triangle  = 3²×1/2× b×h= (Scale factor)²× The original area of the triangle.

From 3² = 9, we have;

The area of the dilated triangle = 9 × The original area of the triangle.

Therefore;

The area of the dilated triangle will increase by a factor of 9.

The probability of a head on the 5th flip of the coin is 1/2 or 50%

The probability of getting a head on the 5th flip of the coin can be determined by understanding that each flip of the coin is an independent event. The previous flips do not affect the outcome of future flips.

Since the previous flips resulted in four consecutive heads (h h h h), the outcome of the 5th flip is not influenced by them. The probability of getting a head on any individual flip of a fair coin is always 1/2, regardless of the previous outcomes.

Therefore, the probability of getting a head on the 5th flip is also 1/2 or 50%.

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Answer:

Let A1 be original area

A2 dilated Area

A1=pi*d^2/4

=3.143*5^2/4

A1=19.63 unit square

A2= 3.143*15/4

A2=176.74 unit square

A2 is 9 times greater than A1

Hence the answer is B

Step-by-step explanation:

Answer:

There is no greatest perfect square that is a factor of 1290.

Step-by-step explanation:

The factors of 1290 are 1, 2, 3, 5, 6, 10, 15, 30, 43, 86, 129, 215, 258, 430, 645, 1290. There are no perfect squares as factors.

1 is the greatest perfect square that is a factor of 1290.

A perfect square is one that is derived by multiplying an integer by itself.

The following are perfect squares:

Looking at the factors of 1,290, the only perfect square appearing there is 1.

We can therefore conclusively state that 1 is the greatest perfect square that is also a factor of 1,290

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Answer:false

Step-by-step explanation:

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

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Volume of cylinder= 60 cm³, Volume of cone= 20 cm³ and this equation is true only for cylinder and cone shown above.

What is a cylinder?

A cylinder is a three-dimensional geometric shape formed by two parallel circular bases joined by a curved lateral surface. It may be conceived of as a circular prism. Because a cylinder has a constant cross-sectional area along its length, it is useful in many practical applications such as pipes, cylinders, and containers.

Now,

To find the volume of the cylinder

V = Bh

where B is the area of the base, and h is the height of the cylinder. Substituting the given values, we get:

V = 15 cm² × 4 cm

V = 60 cm³

To find the volume of the cone

V = (1/3)Bh

where B= area of the base, and h = height of the cone. Substituting the given values, we get:

V = (1/3) × 15 cm² × 4 cm

V = 20 cm³

To find x when the volume of the cylinder is x times the volume of the cone, we can set up the equation:

60 = x(20)

Simplifying and solving for x, we get:

x = 3

Therefore, the volume of the cylinder is 60 cm³, the volume of the cone is 20 cm³, and x is equal to 3.

Hence,

           this equation is true only for cylinder and cone shown above.

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