Find the lateral area for the prism.

36 in 2
54 in 2
27 in 2
81 in 2

Answer:

\(\huge{\{\fbox{\tt{Questions }}\}}\)

The required measures of the circle are:

mDF = 75, m∠FBE 105, mFC=60
m∠CBE = 45, mDAC = 225. m∠ABE=135

m∠ABF=120

A section of a circle is a region enclosed by a chord and an arc of the circle. It is also called a circular sector. A circular sector is defined by its central angle, which is the angle between the two radii that form the sector, and its radius, which is the distance from the center of the circle to the endpoints of the sector.

Here,
A circle is shown,

mDF = 75  [shown in the image]

m∠FBE = 60 + ∠CBE

m∠FBE = 60 + ∠ABD     [∠ABD=∠CBE]

m∠FBE = 60 + 45             [∠ABD = 180 - 75-60]

m∠FBE = 105,

Similarly,

mFC=60, m∠CBE = 45, mDAC = 225, m∠ABE=135, and m∠ABF=120

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As per the two factor study, the value of s is 60.

Two factor study

In math, two factor study defined as an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest.

Given,

Here we have that for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2.

And we need to find the value of s between treatments.

As per the given question, we have identified that the values,

Number of participants = 10

And we also know that,  level a1 are 4 and 1, and the two means for level a2 are 3 and 2.

So, based on the two factor method, the value of s calculated as,

Here we have to multiple factors first,

=> 3 x 2 = 6

And then multiply that by n = 10,

=> 6 x 10 = 60

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Answer:

A would be the answer

Step-by-step and

Linear approximation with a = 64, we estimate that the value of √71 is approximately 8.438.

To use linear approximation, we need to first find a value of a that will produce a small error. One way to do this is to choose a value close to the number we want to approximate, which is √71 in this case. Let's choose a = 64, which is close to 71 and easy to work with.

Next, we need to find the equation of the tangent line to the function f(x) = √x at x = 64. We can do this using the formula for the equation of a line in point-slope form:

\(y - f(a) = f'(a) (x - a)\)

Plugging in a = 64 and f(x) = √x, we get:

y - √64 = 1/(2√64) (x - 64)

Simplifying this equation, we get:

y = 1/16 x + 4

This is the equation of the tangent line to f(x) = √x at x = 64. Now we can use this equation to approximate the value of √71:

√71 ≈ f(71) ≈ 1/16 (71) + 4 = 8.4375

Rounding this to three decimal places, we get:

√71 ≈ 8.438

So using linear approximation with a = 64, we estimate that the value of √71 is approximately 8.438.

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Answer:

483 9/100

Step-by-step explanation:

I think this is the answer

You can use the change of base formula to get

\(\log_2(100) = \frac{\log(100)}{\log(2)} \approx 6.643856\)

and also

\(\log_6(20) = \frac{\log(20)}{\log(6)} \approx 1.671950\)

In general, the change of base formula is

\(\log_b(x) = \frac{\log(x)}{\log(b)}\)

Answer:

The value of Log 2 ^ 100 is about 4 times the value of Log  6 ^ 20.

Step-by-step explanation:

trust

A large population with a sample size of 30 or more has the smallest standard deviation, as the standard deviation is inversely proportional to the sample size. A smaller standard deviation indicates more consistent data. To minimize the standard deviation, the sample size depends on the population's variability, with larger sizes needed for highly variable populations.

If the population is large, a sample size of 30 or more will give the smallest standard deviation to the statistic. The reason for this is that the standard deviation of the sample mean is inversely proportional to the square root of the sample size.

Therefore, as the sample size increases, the standard deviation of the sample mean decreases.To understand this concept, we need to first understand what standard deviation is. Standard deviation is a measure of the spread of a dataset around the mean. A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean. In other words, a smaller standard deviation means that the data is more consistent.

when we are taking a sample from a large population, we want to minimize the standard deviation of the sample mean so that we can get a more accurate estimate of the population mean. The sample size required to achieve this depends on the variability of the population. If the population is highly variable, we will need a larger sample size to get a more accurate estimate of the population mean. However, if the population is less variable, we can get away with a smaller sample size.

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Given the net of a figure:

As shown the number of faces = 7 faces

The number of bases = 2 bases

As the base has 7 sides it will be a heptagon

The height of the prism = the length of one side of the base

The surface area of the prism = area of the bases + area of the faces

= area of 2 heptagons + area of 7 squares

Answer:

$3,096

Step-by-step explanation:

To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.

The total amount Mr. Quesada will pay back over 24 months is:

$629 x 24 = $15,096

Subtracting the original loan amount, we get:

$15,096 - $12,000 = $3,096

So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.

Answer:

3/2

Step-by-step explanation:

\(2-\frac{2}{3} +\frac{2}{9} -\frac{2}{27} +...\\r=\frac{-\frac{2}{3} }{2} =-\frac{1}{3} ,|r|<1\\s_{\infty}=\frac{a}{1-r} \\=\frac{2}{1+\frac{1}{3} } \\=\frac{2}{\frac{4}{3} }\\ =\frac{3}{2}\)

The integral ˆ«(1 to [infinity]) xe^-x2 dx, is  E) divergent, that is, an indefinite integral with an upper limit of infinity.

Let's use the following steps to evaluate indefinite integral:

ˆ«(1 to [infinity]) xe^-x2 dx

We can start by making a substitution to simplify the integral.

We substitute u = -x^2, du = -2x dx. When x approaches infinity, u approaches negative infinity, and when x is 1, u is -1.

Now we can rewrite the integral with the substitution:

ˆ«(-1 to -infinity) e^(u/2) du

Next, we can use the limit property of integrals to evaluate the integral as u approaches negative infinity:

lim[u->-infinity] ˆ«(-1 to u) e^(u/2) du

As u approaches negative infinity, e^(u/2) approaches zero, so the integral becomes zero or the integral converges to zero.

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The shapes of the curves in the AS/AD (Aggregate Supply/Aggregate Demand) model are based upon the relationship between the price level and the output level in an economy.

The AD curve shows the relationship between the overall price level and the quantity of goods and services demanded by all buyers in an economy. It has a negative slope, indicating that as the price level increases, the quantity of goods and services demanded decreases.

The AS curve shows the relationship between the overall price level and the quantity of goods and services that firms are willing and able to supply. In the short run, the AS curve is upward sloping, indicating that as the price level increases, firms are willing to supply more output due to higher profits. In the long run, the AS curve becomes vertical, indicating that the level of output is determined by the factors of production and technology, not the price level.

Thus, the shapes of the curves in the AS/AD model are based on the behavior of buyers and sellers in an economy and their response to changes in the overall price level.

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Answer:

9 cups of lemonade

Step-by-step explanation:

First, calculate the amount of money Pablo earns every week:

$5 + $7 + $18 = $30

Calculate how much money Pablo gets each week by selling lemonade:

$30 - $12 = £18

Calculate how many cups of lemonade are being sold each week:

18 ÷ 2 = 9

Pablo needs to sell 9 cups of lemonade each week to reach his goal

The histogram that represents a set of data that is left-skewed is the one where the majority of the data is on the right side of the histogram, and the tail of the histogram extends to the left.

A left-skewed histogram is also called a negatively skewed histogram. In a left-skewed distribution, the majority of the data values are on the right side of the histogram, and the tail of the histogram extends to the left. This means that the data is clustered around higher values and gradually decreases as the values become smaller.

For example, imagine a dataset that represents the ages of a group of people. If most of the people in the group are young adults, but there are a few older individuals, the histogram would be left-skewed because the tail of the histogram (representing the older individuals) would extend to the left.

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Is there an attachment? I don't get the worksheet!

Answer:

(0,30)

(1,28)

(2,26)

(5,20)

Step-by-step explanation:

If you multiply 2 times the x

ex. 2 x 5 = 10

Then subtract that from the 30 to get y

30-10 = 20 = y

Solve

(5,20)

Answer:

one day and he has 28 dollars

Step-by-step explanation:

Answer:

correcto

Step-by-step explanation:

Answer:

v = sqrt(a*p)

Step-by-step explanation:

multiply both sides by p

a*p = v^2

square root both sides to get rid of the (^2) on the v

then you'll be left with v= sqrt(a*p)

Answer:

x = + 5/4 or x = - 5/4

Step-by-step explanation:

\(4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}\)

The rational equation is simplified to  x² - 17x = 0

An algebraic expression can simply be defined as an expression composed of factors, variables, terms, coefficients and constants.

These expression are also described as expressions consisting of arithmetic operations such as;

Given the expression;

1/2 - 7/2x = 5/x

find the lowest common multiple

x - 7 /2x = 5/ x

cross multiply

x(x - 7) = 5(2x)

multiply through

x² - 7x = 10x

collect like terms

x² = 10x + 7x

x² - 17x = 0

Hence, the equation is x² - 17x = 0

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Answer:   True

Step-by-step explanation:

The term inside the parentheses after the summation sign is

       x-sub-i    minus    x-bar

x-bar is the mean average of all the individual n observations. In statistics, it is usually just called the 'mean' for short.

x-sub-i stands for each individual observation: x-sub-1, x-sub-2, and so on

So that means (x-sub-i   -   x-bar) means the difference we get if we do the subtraction, using x-sub-i as the first term in the subtraction.

For an illustration of this, suppose we have a sequence of 5 observations. Since there are 5 observations, n = 5.

x-sub-1  = 4

x-sub-2 = 7

x-sub-3 = 3

x-sub-4 = 11

x-sub-5 = 5

We obtain the mean by adding all the observations and then dividing by the number of observations, n.

The sum 4+7+3+11+5 = 30 and 30/5 = 6.

So the mean, x-bar, = 6.

Now let's look at all the differences between each observation and x-bar.

In the same order as the observations, we get

4 - 6  = -2

7 - 6  =  1

3 - 6 = -3

11 - 6 = 5

5 - 6  = -1

If we add up all the differences, just like we are doing in the summation homework problem, we have (-2)+1+(-3)+5+(-1) = 0.

It also works if you make x-bar the first term in the subtraction. Either way will work, as long as you are consistent about it from one subtraction to the next.

This is always the case with a mean average, so the summation is assured to be zero.

I hope this helps.

The logistic equation that models the weight of the bacterial culture is dy/dt = ky(20 - y), where k is a constant.

After 5 hours, the culture's weight is approximately 9 grams.

The culture's weight will reach 16 grams after approximately 4.69 hours.

The culture's weight is increasing most rapidly at approximately 2.34 hours.

To model the weight of the bacterial culture using a logistic equation, we can use the formula dy/dt = ky(20 - y), where y represents the weight of the culture at time t and k is a constant that determines the growth rate. The term ky represents the growth rate multiplied by the current weight, and (20 - y) represents the carrying capacity, which is the maximum weight the culture can reach. By substituting the given information, we can determine the value of k. At t = 0, y = 2 grams, and after 3 hours, y = 5 grams. Using these values, we can solve for k and obtain the specific logistic equation.

To find the weight of the culture after 5 hours, we can use the logistic equation. Substitute t = 5 into the equation and solve for y. The resulting value will give us the weight of the culture after 5 hours. Round the answer to the nearest whole number to obtain the final weight.

To determine when the culture's weight reaches 16 grams, we can set y = 16 in the logistic equation and solve for t. This will give us the time it takes for the weight to reach 16 grams. Round the answer to the nearest whole number to obtain the approximate time.

The culture's weight increases most rapidly when the rate of change, dy/dt, is at its maximum. To find this time, we can take the derivative of the logistic equation with respect to t and set it equal to zero. Solve for t to determine the time at which the rate of change is maximized. Round the answer to two decimal places.

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The ratio as a fraction will be 4 : 5 or 4/5.

The ratio given is ; 28 days to 5 weeks .

We have to find out this ratio as a fraction in the simplest form ?

What will be the value of ratio ; 2 : 4 will be ?

The value will be 1 : 2.

We have to change given ratio as a fraction in simplest form for ;

28 days to 5 weeks. To convert it in ratio we firstly need to change 5 weeks into days.

∵ No. of days in 1 week = 7 days

⇒ No. of days in 5 weeks = 7 × 5 = 35 days

The ratio as the fraction will be ;

\(\frac{28 days}{35 days}\)

taking 7 common from both numerator and denominator.

= \(\frac{4}{5}\)

Thus , the ratio as a fraction will be 4 : 5.

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Both Isaac and Micah are using a compass and straightedge for their constructions.

The differences between their construction steps are:

Isaac is constructing congruent segments, which means he is dividing the original line segment into equal parts, while Micah is constructing a segment bisector, which means he is dividing the line segment into two equal parts and finding the midpoint.

Isaac only needs to mark one point on the line segment with his compass to get two congruent segments, while Micah needs to mark two points and then find the midpoint between them.

The final results of their constructions are different: Isaac will have two congruent line segments, while Micah will have one line segment bisector that splits the original line segment in half.

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the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

To find the probability of receiving five calls on a given day at the emergency center, we need to use the Poisson distribution formula:

\(P(x = 5) = (e^{-4})*\frac{(4^5)}{(5!)}\)
Where:
- x = number of phone inquiries
- e = Euler's number (approximately 2.71828)

- ! = factorial (i.e. 5! = 5*4*3*2*1)

Given that the average number of phone inquiries per day is four, we can use that as our lambda (λ) value in the Poisson distribution formula, since lambda represents the mean number of events in a specific time interval:

λ = 4

Now we can substitute these values into the formula and solve:

P(x = 5) = (e^-4)*(4^5)/(5!) = (2.71828^-4)*(1024)/(120) ≈ 0.156

Therefore, the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

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The probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

To find the probability that the emergency center will receive five calls on a given day, given that the average number of phone inquiries per day is four, we can use the Poisson distribution formula.

Identify the average rate (λ): In this case, λ = 4 calls per day.

Identify the desired number of events (k): In this case, k = 5 calls.

Use the Poisson distribution formula: \(P(X = k) = (e^(-λ) \times (λ^k)) / k!\)

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate

k is the desired number of events

k! is the factorial of k

Plug in the values and calculate the probability:

\(P(X = 5) = (e^{(-4)} \TIMES (4^5)) / 5!\)

\(P(X = 5) = (0.0183 \times 1024) / 120\)

P(X = 5) ≈ 0.1755

So, the probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

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Answer:

slope is undefined

Step-by-step explanation:

x = - 5 is the equation of a vertical line, parallel to the y- axis.

The slope of a vertical line is undefined.

Answer:

1)  \(\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}\)

2)  \(-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}\)

3)  \(\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}\)

4)  \(\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}\)

5)  \(\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}\)

Step-by-step explanation:

The rationalization of the denominator of the surds are found as follows;

1) \(\dfrac{2}{\sqrt{5} }\)

\(\dfrac{2}{\sqrt{5} } \times \dfrac{\sqrt{5} }{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}\)

\(\dfrac{2}{\sqrt{5} } = \dfrac{2 \cdot \sqrt{5} }{5}\)

2) \(-\dfrac{5}{\sqrt{3} }\)

\(-\dfrac{5}{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}\)

\(-\dfrac{5}{\sqrt{3} } = -\dfrac{5 \cdot \sqrt{3} }{3}\)

3) \(\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} }\)

\(\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } \times \dfrac{ \sqrt{10} }{\sqrt{10} } = \dfrac{\sqrt{20} + \sqrt{50} }{10 } = \dfrac{2\cdot \sqrt{5} + 5 \cdot \sqrt{2} }{10} = \dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}\)

\(\dfrac{\sqrt{2} + \sqrt{5} }{\sqrt{10} } =\dfrac{\sqrt{5} }{5} + \dfrac{ \sqrt{2} }{2}\)

4) \(\dfrac{3 + \sqrt{2} }{\sqrt{3} }\)

\(\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \dfrac{3 \cdot \sqrt{3}+\sqrt{6} }{3 } = \sqrt{3} + \dfrac{\sqrt{6} }{3}\)

\(\dfrac{3 + \sqrt{2} }{\sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} } = \sqrt{3} + \dfrac{\sqrt{6} }{3}\)

5) \(\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }\)

\(\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} } = \dfrac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} } = \dfrac{\sqrt{15} -\sqrt{6} }{5 - 2} = \dfrac{\sqrt{15} - \sqrt{6} }{3}\)

\(\dfrac{\sqrt{3} }{\sqrt{5} + \sqrt{2} }= \dfrac{\sqrt{15} - \sqrt{6} }{3}\)

6) \(\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} }\)

\(\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} = \dfrac{\sqrt{21} + \sqrt{35}}{{3} + {5}} = \dfrac{\sqrt{21} + \sqrt{35}}{8}\)

\(\dfrac{\sqrt{7} }{\sqrt{3} - \sqrt{5} } \times \dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} =\dfrac{\sqrt{21} + \sqrt{35}}{8}\)

The directional derivative of the function f(x, y) = 3ex sin(y) at the point (0, π/3) in the direction of the vector v = (-5, 12) is ∂vf(0, π/3) = -60eπ/3.

The directional derivative measures the rate at which a function changes at a given point in a specific direction. To compute it, we need to take the dot product between the gradient vector (∇f) and the unit vector in the direction of v.

First, we need to find the gradient of f(x, y) by taking the partial derivatives with respect to x and y. The partial derivative with respect to x is ∂f/∂x = 3ex sin(y), and the partial derivative with respect to y is ∂f/∂y = 3ex cos(y).

Next, we evaluate the gradient at the point (0, π/3) by substituting x = 0 and y = π/3 into the partial derivatives. We obtain ∂f/∂x = 3e^0 sin(π/3) = (3/2)√3 and ∂f/∂y = 3e^0 cos(π/3) = (3/2).

To find the directional derivative, we take the dot product between the gradient vector (∇f) and the unit vector in the direction of v, which is v/|v|. Since v = (-5, 12), we normalize it to obtain the unit vector (-5/13, 12/13).

Finally, we compute the directional derivative as ∂vf(0, π/3) = (∇f) · (v/|v|) = [(3/2)√3, (3/2)] · (-5/13, 12/13) = -60eπ/3. Therefore, the directional derivative of f(x, y) at (0, π/3) in the direction of v is -60eπ/3.

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The given number is,

On solving, we have,

There is no relationship between the number of movies and the number of sleep hours.

It is always a thing of importance to show data by the use of a scatter plot. The scatter plot must always have two axes. The vertical (y axis ) and the horizontal (x axis). It is always common to plot the independent variable on the x axis and the dependent variable on the y axis.

The scatter plot thus represented shows how one variable is related to another. In this case, we are trying to obtain how the number of sleep  hours tend to be related with the number of movies and this has been shown on the scatter plot that is shown in the question above.

It is clear from the statements in the question that the line of best fit would show that as the number of movies remained constant, the number of sleep hours decreased. This now implies that there is no relationship between the number of movies and the number of sleep hours.

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Answer: 24

Step-by-step explanation:

m - 8 = 16

m = 24

Answer:

24

Step-by-step explanation:

To find the value of "m", you need to plug n = 8 into the equation.

m - n = 16                             <---- Original equation

m - 8 = 16                             <----- Plug 8 in for "n"
   + 8  + 8                             <---- Isolate "m" by adding 8 to both sides

m = 24                                  <----- Final answer