At what point do the graphs of the lines below intersect?

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y=9x+2

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y=−3x+12

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$51.21

Total surface area of cylindrical tank:

height = h = 2.1m

diameter = 0.7m

radius= diameter +2

r = 0.7 +2=0.35 m

[tex](2\pi r{}^{2} ) + (\pi dh)[/tex]

[tex](2 \times 3.14 \times {0.35}^{2} ) + (3.14 \times 0.7 \times 2.1) [/tex]

[tex]2 \times 3.14 \times 0.35 {}^{2} = 0.77 [/tex]

[tex]3.14 \times 0.7 \times 2.1 = 4.62[/tex]

[tex]0.77 + 4.62 = 5.39m {}^{2} [/tex]

To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.

[tex]5.39 \times 9.50[/tex]

= $51.21

Answer:

Step-by-step explanation:

50%. 24 is half of 48. So, 50% of 48 if 24.

Answer:

1.77777777778

The value of the variable x is  125 degrees

It is important to note that alternate angles are equal.

Also, angles at a point is 360 degrees

From the information given in the diagram, we have that;

70 degrees and and the angle tangent to C are equal, so we have;

70 degrees + x degrees + x degrees + 40 degrees = 360 degrees

Let's represent mathematically;

70 + x + x + 40 = 360

collect the like terms

70 + 2x + 40 + 360

2x = 360 - 110

Subtract the values

2x = 250

make 'x' the subject of formula

x = 250/2

divide the values

x = 125 degrees

Hence, the value is 125 degrees

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Answer:

[tex]\dfrac{9}{6}=\dfrac{8}{v}[/tex]

 Similar polygons are two polygons with same shape and different size.

In similar polygons  

To find the value f 'x'

          [tex]\dfrac{ED}{E'D'} = \dfrac{CD}{C'D'}\\\\\dfrac{9}{6}=\dfrac{8}{v}[/tex]

The relative frequency for the event tails is given as follows:

53.64%.

The expected relative frequency should be closed to the theoretical probability of 0.5.

The relative frequency is given by the division of the number of desired outcomes by the number of total outcomes.

The relative frequency for all the throws is obtained as follows:

132/(114 + 132) = 132/146 = 53.64%.

Considering a fair coin, it is equally as likely to come up heads or tails, hence increasing the number of trials, the relative frequency of each outcomes is expect to be closer to 50%.

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In other words, altering the sampling distribution in this way increases the likelihood of making a type 1 error.

The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey.

Here,

The sampling distribution is a distribution of the values of a statistic (such as the mean or median) calculated from a set of sample data. It gives us information about how the statistic is likely to vary from sample to sample, and it is used in hypothesis testing to calculate the probability of observing certain results if the null hypothesis is true.

Filtering out all values below the mean has the effect of changing the shape, location, and spread of the sampling distribution. For example, if the original sampling distribution is normally distributed with a mean of 0 and a standard deviation of 1, filtering out all values below the mean would result in a new sampling distribution with a mean greater than 0 and a standard deviation smaller than 1.

When the sampling distribution is altered, for example by filtering out all values below the mean, it can have an effect on type 1 errors. Type 1 errors occur when we reject the null hypothesis when it is actually true.

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Answer:

2.1. 92 = 2 x 2 x 23, 146 = 2 x 73

2.2. LCM = 1148, HCF = 2

2.7. Percentage increase = 6.11%

2.4.1. It will take her 18 minutes to walk to school.

2.4.2. This is an indirect proportion as the time taken is inversely proportional to the speed.

2.5. He will get £157.63 if he pays the agent commission.

2.8. The car must drive at 120 km/h to travel the same distance in 2 hours 35 minutes.

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The interval equivalent to each range is given below

     x = 3 - 5

    x' = 7,8,9

What exactly is interval notation?

Which section of the number line, from left to right, is included in the answer can be determined using interval notation (i.e., which part of the number line is shaded).

                           Endpoints not included in the solution are denoted by parentheses, whereas endpoints that are included are denoted by brackets.

We have that

The  interval equivalent to each range is given below

     x = 3 -5

     x' = 7,8,9

From the Question we are told that

2  <  x  ≤  5   or   x  >7

Generally the interval equivalent is given as follow from the number line

(...-1,0,1...)

For 2  <  x  ≤  5  

Here  this means x is less than 2 and less than or equal to 5

Therefore

A range of numbers

  x = 3 - 5

For  x  >7

Here x is greater than 7  i.e

  x' = 7,8,9

in conclusion

The  interval equivalent to each range is given below

     x = 3 - 5

    x' = 7,8,9

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110 miles/hr is the interval with highest average speed. Option C is correct.

The given diagram is a graph with different rate of change. According to the graph, we are to determine which interval has the highest average speed.

Average speed = change in distance/time

Considering the change between t = 4 and t = 5;

Average speed = 270 - 160/5 - 4
Average speed= 110/1

Average speed = 110 miles/hr

Hence the interval that has the highest average speed is 110 miles/hr

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2. The mean score is 80.6

3.The missing term is 32.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given:

2. A student receives test scores of 62, 83, and 91.

Test A is 0.20 of the total and scores 62.

Test B is 0.20 of the total and scores 83.

Test C is 0.20 of the total and scores 91.

Test F is 0.25 of the total and scores 88.

Work H is 0.15 of the total and scores 76.

Now, Multiply the scores:

= 0.2 x 62 = 12.4

= 0.2 x 83 = 16.6

= 0.2 x 91 = 18.2

= 0.25 x 88 = 22

= 0.15 x 76 = 11.4

Now, add the scores to get the

= 12.4 + 16.6 + 18.2 + 22 + 11.4

= 80.6

3. let the missing term or 4th term be x.

So, The median is sum of 3rd and 4th term.

27.5 = 23 + x/ 2

55 = 23+ x

x= 32

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Answer: $88

Step-by-step explanation:

$99/9= $11 per hour

If Brian works 8 hours:

8x11= 88

Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon, To make up for the higher sale price, it will take him more than 66 years.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

Deselectric costs $11900 more than the Deswagon.

Unit cost:

Deselectric: $0.11 per mile.

Deswagon: $0.12 per mile.

Kweku drives about 18,000 miles a year.

That means

The cost for each car;

Deselectric: 18000 x 0.11 = $1980

Deswagon: 18000 x 0.12 = $2160

The more cost is,

= $2160 - $1980

= $180 of savings in a year.

Now, the make-up for the higher sale price,

= 11900/180

= 66.11 in years.

Hence, it will take him more than 66 years.

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Answer: To convert miles per gallon to kilometers per liter, we can use the conversion factor 1 mile = 1.60934 kilometers and 1 gallon = 3.78541 liters.

54 miles per gallon is equivalent to:

54 * 1.60934 km/mile / (1 gallon * 3.78541 liters/gallon) = 21.63 km/liter.

Rounding to the nearest hundredth, the equivalent rate is 21.63 km/liter.

Step-by-step explanation:

Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

The measure of {x} in the figure is 14.

In Euclidean geometry, 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.

Given is a parallelogram as shown in the image.

Opposite sides of a parallelogram are equal. So, we can write -

9x - 77 = 3x + 7

9x - 3x = 7 + 77

6x = 84

x = 14

Therefore, the measure of {x} in the figure is 14.

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{Question in english -

Help please, I need to find the values, well, I'll settle for one...}

The percent of change is -1/15 which represent a decrease. percentage of change is 6.7%

Percentage change is  the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

From the question,

The old amount is 2/5

The new amount is 1/3

We substract the new amount from the old amount

1/3 - 2/5

= -1/15

The percent of change is -1/15 which represent a decrease

To calculate the percentage change

1/15 x 100

= 6.7%

hence, the percentage of change is 6.7%

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Answer:

I don't

Step-by-step explanation:

A regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

In a regular frequency distribution table, individual scores and their corresponding frequencies are listed, whereas in a grouped frequency distribution table, the scores are grouped into intervals and the frequencies of the intervals are listed.

The following information can be obtained from a regular frequency distribution table but not from a grouped table:

Individual Scores: A regular frequency distribution table lists individual scores, providing a clear understanding of the exact values that make up the data.

Accuracy: A regular frequency distribution table provides a more accurate representation of the data as it doesn't involve grouping the scores into intervals, which can lead to loss of information.

Outliers: In a regular frequency distribution table, outliers (unusual or extreme values) can be easily identified as they stand out from the other scores.

Shape of Distribution: A regular frequency distribution table provides a more detailed representation of the distribution, allowing for easier evaluation of the shape of the distribution, such as whether it is symmetrical, skewed, etc.

Measures of Central Tendency: Measures of central tendency, such as the mean, median, and mode, can be more accurately calculated from a regular frequency distribution table as the exact values of the scores are available.

In conclusion, a regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

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Answer:

  y = -3cos(πx/4) +3

Step-by-step explanation:

You want a possible trig function that describes the values in the given table.

Looking at the table, we find the minimum y-value is 0, and it corresponds to x=0 and x=8. This means the period (P) of the function is 8.

The maximum y-value is 6. This means the midline (M) of the function is 3, the average of the minimum and maximum: (0 +6)/2 = 3.

The amplitude (A) of the function is the difference between the maximum value and the midline value: 6 -3 = 3.

The sine and cosine functions both oscillate back and forth between a value of -1 and a value of +1. The cosine function has its maximum at x=0, but the function needed here will have a minimum at x=0. We can use the cosine function, but it needs to be reflected over the x-axis (or midline).

In general the trig function we're looking for will have the form ...

  y = Acos(2πx/P) +M

As discussed above, the value of A will need to be negative to reflect the function over its midline. For A=-3, M=3, P=8, the function is ...

  y = -3cos(2πx/8) +3

  y = -3cos(πx/4) +3

__

Additional comment

In the case where the extreme values (cosine) or the midline values (sine) are not at x=0, there is a "phase shift" involved. That is, the trig function will need to be translated horizontally to match values in the table. That translation is accomplished by adding or subtracting a value from x. Translation of the cosine function is not needed in this case.

Answer:

Step-by-step explanation:

Given the formula for the volume of a torus (v = πh(R + r)), you can isolate R by dividing both sides of the equation by πh(R + r), as follows:

v / (πh(R + r)) = R

πh(R + r) * R = v

R^2 = v / (πh(R + r))

R = √(v / (πh(R + r)))

So, R is the square root of the volume divided by πh(R + r).

Answer:

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Step-by-step explanation:

The derivative of the function F(x) = x^2 - 1/x + 1 can be found by using the limit definition of the derivative. The derivative is the rate of change of the function at a given point and it is calculated as:

F'(x) = Lim h=0 (x + h)^2 - 1/(x + h) + 1 - (x^2 - 1/x + 1)/h

Expanding the expression inside the limit and simplifying, we get:

F'(x) = Lim h=0 2xh + h^2 - (1 - hx)/(x + h)^2

Using L'Hopital's Rule, we get:

F'(x) = Lim h=0 2x + 2h - (x - 1)/(x + h)^2

As h approaches 0, the limit becomes:

F'(x) = 2x + 2(0) - (x - 1)/x^2 = 2x - (x - 1)/x^2

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Answer:

2yfhyfjcxdddzònbɓchgghhhhhbbv xfbv xxg

The value of a1 in a geometric series for which Sn=21825, an=125, r=15 will be 5/9.

The formula for the nth term in a geometric series is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the number of terms.

We are given Sn, an and r, and we can use the formula for the sum of a geometric series to solve for n:

Sn = a1 * (1 - r^n) / (1 - r)

Substituting the given values, we get:

21825 = a1 * (1 - 15^n) / (-14)

Multiplying both sides by -14, we get:

-304350 = a1 * (1 - 15^n)

Since we are given that an = 125, we can substitute this into the formula for an and solve for n:

125 = a1 * 15^(n-1)

Substituting a1 = -304350 / (1 - 15^n) from the equation above, we get:

125 = -304350 / (1 - 15^n) * 15^(n-1)

Dividing both sides by 15^(n-1), we get:

125 * 15^(1-n) = -304350 / (1 - 15^n)

Multiplying both sides by (1 - 15^n), we get:

125 * 15^(1-n) * (1 - 15^n) = -304350

Expanding the right-hand side, we get:

125 * (15 - 15^n) = -304350

Dividing both sides by 125, we get:

15 - 15^n = -2434.8

Adding 15^n to both sides, we get:

15^n = 15 - (-2434.8) = 2449.8

Taking the natural logarithm of both sides, we get:

n * log(15) = log(2449.8)

Dividing both sides by log(15), we get:

n = log(2449.8) / log(15)

Since n is the number of terms, it must be a positive integer. The closest positive integer to this value is 3, so n = 3.

Finally, we can use the formula for an to find a1:

an = a1 * r^(n-1)

Substituting the given values and n = 3, we get:

125 = a1 * 15^(3-1)

Dividing both sides by 15^(3-1), we get:

125 / 15^2 = a1

Calculating, we get:

a1 = 125 / 15^2

= 125 / 225

= 5/9.

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Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.

ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.

b) If the area of the room is 15 cm^2, then we can write the equation as:

c * (c - 2) = 15.

c) Solving for c, we get:

c^2 - 2c - 15 = 0.

Using the quadratic formula, we find that:

c = 5 or c = -3.

Since the length of the room cannot be negative, we choose c = 5.

Therefore, the length of the room is 5 cm and the width of the room is 3 cm.

Step-by-step explanation:

Answer:

The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = £7000

r1 = 3% = 0.03

r2 = 1.5% = 0.015

n = 1 (annual compounding)

t1 = 1 (first year)

t2 = 1 (second year)

So, the future value of Ella's investment at the end of the first year is:

F1 = £7000 * (1 + 0.03/1)^(1 * 1) = £7000 * (1.03)^1 = £7,210

And the future value of Ella's investment at the end of the second year is:

F2 = £7,210 * (1 + 0.015/1)^(1 * 1) = £7,210 * (1.015)^1 = £7,333.15

So, at the end of 2 years, the value of Ella's investment is £7,333.15.

Step-by-step explanation:

The original price of the board game for which Neal pays $1.54, which includes a sales tax on the original price of 5.5% (5.5 percent) is about $1.46

A percentage is a proportion or rate of an item within a set of items per one hundred (100) units of the set of items.

Percentages indicates the proportion of an item to be selected or received, such that percentage of each item within a set of items can be easily calculated.

The amount Neal pays for the board game = $1.54

The sales tax rate for the purchase = 5.5%

The sales tax is the percentage amount of an original price, each buyer pays when purchasing an item, and which is collected for the government agency by the seller of the item.

The original price of the board game can be found as follows;

Let x represent the original price of the board game, we get;

Therefore, we get;

x + 5.5% of x = 1.54

(1 + 0.055) × x = 1.54

1.055 × x = 1.54

x = 1.54/1.055 ≈ 1.46

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The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

Judith's vegetable patch is 21 feet wide and 25 feet long. Judith wants to build a fence around the vegetable patch. The length of fencing is given as,

P = 2(21 + 25)

P = 2 x 46

P = 92 feet

The fencing material costs $1.00 per foot. Then the total cost of the fencing is given as,

Total cost = $1 x 92

Total cost = $92

The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

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Here the relation between number of weeks and Cost can be formulated as 42 = 15+ 8x. By simplifying the equation we get x= 3.375. So you need to save for 4 weeks to get enough money to buy the hamster.

Here you are saving money to buy a hamster. We have to formulate an equation to find out the number of weeks you should save to obtain the money.

The cost of the hamster =  $42

Amount you have with you = $15

Amount you can save a week = $8.

Let the number of weeks is x

Then, the equation is

 42 = 15 + 8x

  8x = 42 -15

  8x = 27

    x = 27/8 = 3.375

Since it is the number of weeks, we could take only whole numbers. Here x is greater than 3. So the number of weeks to save the money to reach the target would be 4.

So by saving $8 for 4 weeks, you could buy the hamster.

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