What is the area of a trapezoid with bases that are 7 meters and 10 meters in length and a height of 12 meters? 42 m2 60 m2 102 m2 204 m2

The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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The type of distribution pictured in this histogram is skewed.

A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.

In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.

There are two types of skewed distributions: positively skewed and negatively skewed.

The distribution in the image is positively skewed as its is pulled towards the left.

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Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

Answer:

72/100

Step-by-step explanation:

hope this helps!

Answer:

18/25

Step-by-step explanation:

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

Answer:

The population of deer at any given time = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

Step-by-step explanation:

This is an example of logistic equation on population growth

carrying capacity, k = 200

Rate, r = 3% = 0.03

Initial Population, P1 =  80

P(t) =?

P(t) = (P1 (k)(e^rt)) ÷ (k- P1 + P1(e^rt))

P(t) = (80 (200)(e^0.03t)) ÷ (200 - 80 + 80(e^0.03t))

     = (16000(e^0.03t))  ÷ (120 + 80(e^0.03t))

      = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

Answer:

The average speed was of 2 miles per hour.

Step-by-step explanation:

Average speed:

Average speed is distance divided by time.

Distance:

Solved by proportions, using rule of three.

1800 steps - x miles

10,000 steps - 5 miles

\(10000x = 5(1800)\)

\(x = \frac{9000}{10000}\)

\(x = 0.9\)

Distance of 0.9 miles.

Using a time of 27 minutes to complete the event, calculate your average speed.

Distance of 0.9 miles in 27/60 of an hour. So

\(d = \frac{0.9}{\frac{27}{60}} = \frac{60(0.9)}{27} = 2\)

The average speed was of 2 miles per hour.

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.

a. The number is ⁴²P₅ = 42!/37!

                                    =42×41×40×39× 38 ×37!/37!

                                    =102080160 ways.

b. The number is ⁴²C₅ = 42!/ 5! × 37!

                               =42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!

                               = 850668 ways.

If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.

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We have the original function

The graph is

As we can see with the graph shown is translated

- displacement 4 units to the right

- shift up by 6 units

for the displacement 4 units, we need to subtract for units to the x

the shift up we need to add 6 to the function, and we obtain the function of the graph

t

Draw a model and write to represent 4 times as many as 3 is 12.

The required equation is 4×3=12 and the required model is shown in figure.

The model for the provided question is shown in the figure, where there are 3 rows and 4 blocks in a row we get 12 blocks total.

Consider the provided information.

We need to draw a model and write an equation to represent 4 times as many as 3 is 12.

4 times as many as 3 can be written as:

4×3

This expression is equal to 12. Thus the combined equation is:

4×3=12

Therefore, the equation represents 4×3=12.

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Answer:

23.75

Step-by-step explanation:

Answer:

the answer is 23.75  because my teacher told me it was the answer

Step-by-step explanation:

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

1/36

Step-by-step explanation:

above is the answer

The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items

This refers to the depiction of the number of times in which an event occurs in the form of a table.

Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.

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Answer:

The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.

Explanation:

Incenter is the point where three bisectors of the interior angles of a triangle intersect and it is the center of the inscribed circle, in this case:

Answer:

Point D

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : π ≥ 0.92

H1 : π < 0.92

At α = 0.05

Left tail

Z0.05/2 = Z0.025 = - 1.645

The test statistic

Zstatistic :

(m - p) / σ

Sample size, n = 85

m = 74/85 = 0.87

p = 0.92

σ = sqrt(p(1 - p) /n)

σ = sqrt(0.92(1 - 0.92) / 85)

σ = sqrt(0.0008658)

σ = 0.0294258

σ = 0.0294

Zstatistic :

(m - p) / σ

(0.87 - 0.92) / 0.0294

Zstatistic = −1.700680

Zstatistic = - 1.70

Decision region :

Reject H0: if ;

Zstatistic < Zcritical

-1.70 < - 1.645

Since,

Zstatistic < Zcritical ; then Reject H0.

Answer:

\(8( 4 \sqrt{7} - \sqrt{18} ) = 8(4 \sqrt{7} - 3 \sqrt{2}) = 32 \sqrt{7} - 24 \sqrt{2} \)

Answer:

the answer is

\(32 \sqrt{7} - 24 \sqrt{2} \)

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

The value of the required missing angle is;

m<JKM = 35°

We know from geometry that the sum of angles in a triangle sums up to 180 degrees.

Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.

We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.

Thus to find the angle m<JKM, we can write the name expression as;

m<JKM = 180 - (90 + 55)

m<JKM = 35°

Thus that's the value of the required missing angle.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

So this is giving us the slope the slope is y=-7x+150

Step-by-step explanation:

It is giving us the Y intercept which is $150  because thats how much he starts out with

It is giving us the slope -7 dollars because he is spending that everyday

The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.

A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.

The decision table for Susan’s problem is shown below:

Size            Good market   Fair market   Poor market    Row maximum

Small              50,000           20,000            -10,000           50,000

Medium          80,000           30,000            -20,000          80,000

Large              100,000          30,000            -40,000          100,000

Very large      300,000         25,000            -160,000         300,000

Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.

For the Maximin decision, we have:

Size            Good market   Fair market   Poor market    Row minimum

Small              50,000           20,000            -10,000           -10,000

Medium          80,000           30,000            -20,000          -20,000

Large              100,000          30,000            -40,000          -40,000

Very large      300,000         25,000            -160,000         -160,000

Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.

For the equally likely decision, we would find the row average:

Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.

Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.

Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.

Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.

Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.

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Complete Question:

Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline.  After a careful analysis, Susan developed the following table:

a. Develop a decision table for this problem

b. What is the maximax decision?

c. What is the maximin decision?

d. What is the equally likely decision?