How many cubes with edge length 1/5 inch fit in the prism? Show your reasoning.

The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.

To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.

Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

For more questions like Critical value click the link below:

https://brainly.com/question/32607910

#SPJ11

The optimal solution for the amount of cash to withdraw each time to minimize transportation costs and maximize interest earnings is determined by calculating the Economic Order Quantity (EOQ) using the formula Q = √((2 * C * T) / r), and rounding the result to a convenient amount.

The Economic Order Quantity (EOQ) model is typically used for inventory management, not for optimizing cash withdrawals. However, if we assume that the question is seeking an optimal withdrawal strategy to minimize transportation costs and maximize interest earnings, we can approach it as follows:

Let's denote:

C = Annual cash need ($5,000)

T = Transportation cost per visit ($5)

r = Annual interest rate (5%)

To find the optimal solution for the amount of cash to withdraw each time, we can consider the trade-off between transportation costs and interest earnings. The objective is to minimize the total cost.

Calculate the optimal order quantity (Q) using the EOQ formula:

Q = √((2 * C * T) / r)

Round the calculated Q to the nearest convenient amount, such as multiples of $100 or $500.

The optimal solution would be to withdraw the rounded Q amount each time to minimize transportation costs while still meeting the annual cash need.

To know more about optimal solution,

https://brainly.com/question/31964994

#SPJ11

Based on the information provided, we can conclude that angles UST and QSR are congruent.

Given that angle RST is a right angle, it is complementary to angle RSU. Complementary angles add up to 90 degrees. Therefore, the sum of angles RSU and UST is 90 degrees.

Additionally, the problem states that angle QSR is congruent to angle RSU. Congruent angles have the same measure. Since angles RSU and QSR are congruent, and angles RSU and UST are complementary, it follows that angles QSR and UST must also be congruent.

Therefore, the true statement about angles UST and QSR is that they are congruent, meaning they have the same measure.

For such more question on degrees

https://brainly.com/question/29165823

#SPJ8

A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

learn more about Gaussian distribution here: brainly.com/question/29734279

#SPJ11

Answer:

Step-by-step explanation:

Any time you have compounding more than once a year (which is annually), unless we are talking about compounding continuously, you will use the formula

\(A(t)=P(1+\frac{r}{n})^{(n)(t)}\)

Here's what we have:

The amount after a certain time that she has in the bank is 4672.12; that's A(t).

The interest rate in decimal form is .18; that's r.

The number of times the interest compounds is 12; that's n

and the time that the money is invested is 3.5 years; that's t.

Filling all that into the formula:

\(4672.12=P(1+\frac{.18}{12})^{(12)(3.5)}\) Simplifying it down a bit:

\(4672.12=P(1.015)^{42}\) Raise 1.015 to the 42nd power to get

4672.12 = P(1.868847115) and divide to get P alone:

P = 2500.00

She invested $2500.00 initially.

Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

The distance Freya traveled is 320 miles.

We have,

To solve this problem, we need to use the formula:

Speed = Distance/time

First, let's calculate the distance Freya drove from Bournemouth to Gloucester:

distance1 = speed1 x time1

= 50 mph x 2.5 hours

= 125 miles

Next, let's calculate the distance Freya drove from Gloucester to Anglesey:

distance2 = speed2 x time2

= 65 mph x 3 hours

= 195 miles

Finally, we can calculate the total distance Freya traveled by adding the two distances:

Total distance = distance1 + distance2

= 125 miles + 195 miles

= 320 miles

Therefore,

Freya traveled a total of 320 miles.

Learn more about speed here:

https://brainly.com/question/7359669

#SPJ1

Step-by-step explanation:

x= 0 y= 5

y=mx+b

5=b

x= -3 y= -4

-4= -3m +5

-3m = -9

m= 3

y= 3x +5

Answer:

blank1 = earth    blank2 = 483.08 billion feet

Step-by-step explanation:

(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

Learn more about Regression analysis here:

https://brainly.com/question/31860839

#SPJ11

Answer:

  C.  f(x) = 2x⁴ +6x³ +22x² +54x +36

Step-by-step explanation:

You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.

The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.

Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.

The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.

  f(x) = 2x⁴ +6x³ +22x² +54x +36

The parameter often associated with enzyme affinity for substrates is Km.

Km, also known as the Michaelis constant, is a parameter commonly used to quantify the affinity of an enzyme for its substrate. It is an important parameter in enzyme kinetics and plays a crucial role in determining the efficiency of an enzyme-substrate interaction.

Km represents the substrate concentration at which the rate of the enzymatic reaction is half of its maximum velocity (Vmax). In other words, enzymes with lower Km values have higher affinity for their substrates, as they can achieve half of their maximum velocity at lower substrate concentrations. Therefore, Km serves as an indicator of the enzyme's ability to bind and convert substrates into products efficiently.

Learn more about substrates here : brainly.com/question/6107295

#SPJ11

Answer:

163

Step-by-step explanation:

\(4^{2}+6*5^{2}-3^{3}/3^{2}\)

16+6*25-27/9

=163

The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

The air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;

Po = ρgh

where;

Substitute the value of altitude into the equation;

Po = 3,000ρg

Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

Learn more about air pressure here: https://brainly.com/question/2353923

#SPJ1

The expected value for your profit is 2.53.

The probability is the number that indicates the likelihood that an event will occur and is defined as the ratio of favorable outcomes to all outcomes.

Given,

You can solve for the necessary anticipated value below.

There will be 600 tickets available for purchase overall.

So,

$ 5 each and sell go tickets

one $3,000 grand prize = ( 1/600) × 3000

two $500 second prizes = (2/600) × 500

thirteen $40 third prizes = (13/600) × 40

Any discrete variable X's anticipated value is calculated as:

E(x) = ( 1/600) × 3000 + (2/600) × 500 + (13/600) × 40 + (600-1-2-13/600).0-5

E(x) = 2.53

The expected value for your profit is  2.53.

To learn more about probability refer the link:

https://brainly.com/question/27681817

#SPJ1

Answer:

(3, 4)

Step-by-step explanation:

The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.

Although the question does not specify the options, but I have specified my answer as follows:

Given:

The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.

Account Opening Charges: $10

Starting amount: $d

The total amount in the account: $m

Let us say the depositor deposits an amount $k for 'i' number of months

Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.

I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.

The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time

⇒m=d-10+k×i

This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.

Therefore, the following equation is m=d-10+k×i.

For more such questions on Amount on banks

https://brainly.com/question/15866207

#SPJ4

Answer:

x= - 70

Step-by-step explanation:

Hope this helps :)

(a) The 92nd percentile of the number of calories is 524.3.

(b) The 30th percentile of the number of calories is 466.4.

(c) The third quartile of the number of calories is 502.1.

To find percentiles in a normally distributed population, we use the standard normal distribution and the z-score formula:

z = (x - μ) / σ

where;

To find the 92nd percentile of the number of calories:

We want to find the value x such that 92% of the servings have fewer calories than x.

This means that we need to find the z-score such that the area to the left of z is 0.92.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.92 is approximately 1.41.

Then, we use the z-score formula to solve for x:

1.41 = (x - 482) / 30

x - 482 = 42.3

x = 524.3

To find the 30th percentile of the number of calories:

We want to find the value x such that 30% of the servings have fewer calories than x.

This means that we need to find the z-score such that the area to the left of z is 0.30.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.30 is approximately -0.52.

Then, we use the z-score formula to solve for x:

-0.52 = (x - 482) / 30

x - 482 = -15.6

x = 466.4

To find the third quartile of the number of calories:

The third quartile, denoted Q3, is the value such that 75% of the servings have fewer calories than Q3.

This means that we need to find the z-score such that the area to the left of z is 0.75.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.75 is approximately 0.67.

Then, we use the z-score formula to solve for x:

0.67 = (x - 482) / 30

x - 482 = 20.1

x = 502.1

Learn more about standard normal distribution here: https://brainly.com/question/26822684

#SPJ1

An equation of this line in slope-intercept form is equal to y = -x + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(4 - 0)

Slope (m) = -4/4

Slope (m) = -1

At data point (0, 4) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -1(x - 0)  

y - 4 = -x

y = -x + 4

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

The correct option is option A , such that inequality is x - 3y < 5.

What are the inequalities ?

Inequalities are the expressions in which both sides are not equal and the equal sign in between is replaced by less than , greater than, etc.

We know that the slope intercept form of equation is given by y = mx + c , where m is the slope and c is the y - intercept.

In the graph , the upward sloping line has x and y intercepts of 5 and -3.

So its equation in slope intercept form is given by ,

- 3y = - x + 5

And the inequality with that boundary line is given by ,

- 3y < - x + 5

or

x - 3y < 5

Therefore , the inequality represented by graph is x - 3y < 5 or option A is correct.

Learn more about inequalities here :

https://brainly.com/question/8921818

#SPJ1

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

24 divided by 3 is 8

The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ1

Answer:

7xy-8yz+3x-4x+8yz

7xy-8yz+8yz+3x-4x

7xy-x

Step-by-step explanation:

Answer: search it and i cant see well so sorry

Step-by-step explanation: research

Answer:

The answer is : Rational

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

6(x+4)−8x=16

(6)(x)+(6)(4)+−8x=16(Distribute)

6x+24+−8x=16

(6x+−8x)+(24)=16(Combine Like Terms)

−2x+24=16

−2x+24=16

Step 2: Subtract 24 from both sides.

−2x+24−24=16−24

−2x=−8

Step 3: Divide both sides by -2.

-2x/-2=-8/-2

x=4

Answer:

X=8

Step-by-step explanation:

First you distribute the 6 to the x and the 4 which gives you, 6x+4x-8x=16 , From there you would add 6x and 4x which gives you 10x. Then you would subtract 8x and that gives you 2x. Now you have 2x=16, then you divide by 2 on both sides. That gives you x=8