Simplify the following radical expressions.
√8/√6
√2/10
√532

√3k√8

Answer:

5/8 or 0.625

Step-by-step explanation:

to find the value of the shaded region, we need to first identify how large the entire shape is. so counting all the squares we can see that there are 8 mini squares within the rectangle, so if the whole shape was shaded in, we would have 8/8 squares shaded.

now that we know it is out of 8, you can count how many are actually shaded, so 5.

now the total shaded area is 5/8

5/8 is 0.625 as a decimal so you can put it there on the line

Answer:

15 rides

Step-by-step explanation:

From the above Question we know that if Tanya goes on a ride, the Algebraic expression = 2x

Where x = number of rides

If Tanya does not play any games, how many rides can she go on?

Note that: Tanya has $30 to spend

This question is solved:

2x = $30

x = $30/2

x = 15 rides

Hence, if Tanya does not play any games she can go on 15 rides

Answer:

try 3.18 and who needs that much lotion

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

$4.85 divided by 7.3 = .664

.664 x 5 = 3.32

Answer: \(f^{-1}(x)= \sqrt{x+25}\) and \(f^{-1}(x)= - \sqrt{x+25}\)

Step-by-step explanation:

   To find the inverse, we will set f(x) equal to y, swap the x and y values, and then solve for y.

   Given:

f(x) = x² - 25

   Equal to y:

y = x² - 25

   Swamp x and y values:

x = y² - 25

   Add 25 to both sides of the equation:

y² = x + 25

   Square root both sides of the equation:

\(y= \sqrt{x+25}\) and \(y= -\sqrt{x+25}\)

   Interval notation:

\(f^{-1}(x)= \sqrt{x+25},\text{and}\;f^{-1}(x)= -\sqrt{x+25}\)

⇒Note for inverses we swap the positions between x and y.

⇒\(x=y^{2} -25\\\)

But in this case we know that we write the equation such that the variable for the input is the subject of the equation

\(y^{2}= x+25\\y=\sqrt{x+25}\)

Note y in this case was representing f(x)

⇒therefore our final equation now is

\(f(x)=\sqrt{x+25}\)

GOODLUCK!!!

The expression is x = (PA - PB) / (2 * (24 + 12)).Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.Alfonso's best-response function can be determined by maximizing profit function with respect to PA.

The expression for the location of the indifferent consumer can be derived using the Hotelling model, where the consumer is equidistant between the two parks. Let x represent the distance from Alfonso's Wonderland. The expression is x = (PA - PB) / (2 * (24 + 12)).

The profit function for Bernice's Wild Rides can be found by subtracting the marginal cost of $12 from the revenue function, which is equal to the price PB multiplied by the number of customers.

Bernice's best-response function can be determined by maximizing their profit function with respect to PB.

The profit function for Alfonso's Wonderland, with a marginal cost of $6, can be found similarly by subtracting the marginal cost from the revenue function, which is equal to the price PA multiplied by the number of customers.

Alfonso's best-response function can be determined by maximizing their profit function with respect to PA.

The equilibrium prices and profits can be found by solving the simultaneous equations formed by the best-response functions of both parks.

Repeat steps 4 and 5 for the case where Alfonso's marginal cost is $9.

Repeat step 6 for the case where Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.

By following these steps, we can determine the maximum price Alfonso's Wonderland should pay, the likely price they will have to pay, and the consequences of Bernice's Wild Rides acquiring the exclusive rights.

Learn more about functions here:

https://brainly.com/question/32117953

#SPJ11

To find the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1, we can use definite integration.

The area of the region bounded by the given graphs is approximately 25 square units.

To find the area, we need to integrate the given function over the interval [0, 1]. The integral represents the area under the curve between the limits of integration. Since the region is bounded by the x-axis, we integrate the function with respect to x.

∫[0, 1] (32 / (x² - 17x + 72)) dx

Evaluating this integral gives us the area of the region bounded by the graphs. Using numerical integration methods, we find that the area is approximately 25 square units.

The integral calculation involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration. The resulting value represents the area between the curves and the x-axis within the specified interval.

Therefore, the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1 is approximately 25 square units.

To learn more about definite integration click here: brainly.com/question/30760284

#SPJ11

The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

time is calculated using the formula

\(Time=\frac{Distance}{Speed}\)

In the given question

driver drove 50 miles at slower speed.

Let the slower speed be x miles per hour.

So the time taken to cover 50 miles at slower speed = \(\frac{50}{x}\)    ...(i)

driver drove 300 miles at faster speed.

given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = \(\frac{300}{(x+20)}\)....(ii)

According to the question

the time spent driving at the faster speed was thrice that spent driving at the slower​ speed.

From equation (i) and (ii) we get

\(3*(\frac{50}{x} )=\frac{300}{x+20}\)

\(\frac{150}{x} =\frac{300}{x+20}\)

Cross Multiplying we get

\(150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20\)

Slower speed = x = 20mph.

Faster speed = (x+20) = 20+20 = 40mph.

Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.

Learn more about Speed, Time and Distance here  https://brainly.com/question/14975450

#SPJ4

a) The 95% confidence interval for the probability (p) that a randomly selected component lasts more than 350 hours is estimated to be between 0.4947 and 0.8753. b) The 95% confidence interval for the probability (p) that a system consisting of two components connected in series lasts more than 350 hours is estimated to be between p² and 2p - p²

a) To calculate the confidence interval, we can use the formula for the confidence interval of a proportion. The point estimate for p is the proportion of components in the sample that lasted longer than 350 hours, which is 24/37 = 0.6486. We can calculate the standard error (SE) using the formula:

SE = \(\sqrt{\frac{p\times(1-p)}{n}\)

where p is the point estimate and n is the sample size. Plugging in the values, we get:

SE = sqrt[(0.6486*(1-0.6486))/37] ≈ 0.0841

Next, we can use the standard normal distribution (Z-distribution) for a 95% confidence interval, which corresponds to a Z-score of 1.96 (for a two-tailed test). We can then multiply the SE by the Z-score to get the margin of error (ME):

ME = Z * SE = 1.96 * 0.0841 ≈ 0.1648

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:

95% Confidence Interval = p ± ME = 0.6486 \(\pm\) 0.1648

So the confidence interval for p is approximately (0.4947, 0.8753), which means we are 95% confident that the true probability of a component lasting more than 350 hours is between 0.4947 and 0.8753.

b) Since the two components in the system are connected in series, the system will operate only if both components operate properly. Therefore, the probability that the system lasts more than 350 hours is the probability that both components operate properly, which is the product of their individual probabilities. Let p1 and p2 be the probabilities of the first and second components lasting more than 350 hours, respectively.

Based on the assumption that the life times of the two components are independent, the probability that both components operate properly is given by p1 * p2. Since p1 and p2 are assumed to be equal to p (the probability of a single component lasting more than 350 hours), we can write the probability of the system lasting more than 350 hours as p * p = p².

To calculate the lower bound of the confidence interval, we can simply square the lower bound of the confidence interval for p (i.e., p²). To calculate the upper bound of the confidence interval, we can subtract the lower bound of the confidence interval for p from 2p (i.e., 2p - p²).

So the 95% confidence interval for the probability that the system lasts more than 350 hours is estimated to be between p² and 2p - p², where p is the probability of a single component lasting more than 350 hours.

To know more about confidence interval, refer here:

https://brainly.com/question/13067956#

#SPJ11

Answer:

g(3)=2

Step-by-step explanation:

Use g(x)=f(x-2)-1

the " - 2" inside the parenthesis with the x will shift the whole graph to the right 2 units. (Shown in dashed red on the image) The " - 1 " at the end of the expression will slide the whole graph down one unit (see image shown in purple) The image shown in purple is the final g(x).

to find g(3) (see image in yellow highlight)

g(3)=2

Answer:

see pin pictures................

Answer: 23

Step-by-step explanation:

m=4

x=3 into y=mx+b:y=4x3+11 b=11

Calculate y=23

Answer:

hmmmmmmmm

Step-by-step explanation:

yea i really dont know

Answer:

Step-by-step explanation:

GCF of x⁸ and x⁵   is x⁵

the variable with lowest power will the GCF

Answer:

x5

Step-by-step explanation:

I did it on the test and got it right :)

hope I helped have a good day.

Answer:

301 acres

Step-by-step explanation:

43,000 acres of forest

0.7% is old-growth

0.7% = 0.007

43,000 * 0.007 = 301 acres

Points A, B, and C are collinear and B lies between A and C

The value of BC=30

Given :

Points A, B, and C are collinear and B lies between A and C.

AC = 48, AB = 2x + 2, and BC = 3x + 6

B lies between A  and C

So, AC=AB+BC

Substitute the given values and solve for x

\(AC=AB+BC\\48= 2x+2+3x+6\\\)

Combine like terms

\(48=5x+8\)

Subtract 8 from both sides

\(40=5x\\Divide \; by \; 5\\x=8\)

Now find out BC by substituting 8 for x in BC

\(BC=ex+6\\BC=3(8)+6\\BC=30\)

The value of BC=30

Learn more : brainly.com/question/17465184

The probability which represents the likelihood of randomly selecting a card that is a heart or a 7 from a well-shuffled standard deck is 4/13.

To calculate the probability of selecting a card that is either a heart or a 7 from a standard deck of 52 cards, we need to determine the number of favorable outcomes (cards that are hearts or 7s) and the total number of possible outcomes (all the cards in the deck).

Let's break it down:

Number of favorable outcomes:

- There are 13 hearts in a deck (one for each rank).

- There are four 7s in a deck (one for each suit, including the 7 of hearts).

- However, we need to subtract one card (the 7 of hearts) from the count since it has already been counted as a heart.

So, the number of favorable outcomes is 13 + 4 - 1 = 16.

Total number of possible outcomes:

- There are 52 cards in a deck.

Therefore, the probability of selecting a card that is either a heart or a 7 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

          = 16 / 52

          = 4 / 13

To know more about probability refer here:

https://brainly.com/question/32560116#

#SPJ11

Answer:

A, 10^2

Step-by-step explanation:

When dividing by exponents, you subtract 1st exponent by the second exponent

|

|

v

(10^6)/10^4=10^(6-4)=10^2

Answer:

30 minutes

Step-by-step explanation:

The hare and tortoise meet in 30 minutes at 240 feet.

Answer:

30minutes

Step-by-step explanation:

Tortoise = Hare

2m + 180 = 8m

collect like terms

180 = 8m - 2m

180 = 6m

divide both sides by 6

m = 180/6

m = 30

It will take 30 minutes for the tortoise and hare to meet.

Answer:

D

Step-by-step explanation:

a = 20 because the rate of change is –3.

A linear function has one independent variable and one based variable. The independent variable is x and the based variable is y. a is the steady time period or the y-intercept. it's far the cost of the dependent variable while x = zero.

Which will be a linear feature, a graph needs to be both linear (a direct line) and a characteristic (matching each x-value to the most effective y-value). It must also pass a polygraph check, complete an obstacle path, and offer a minimum of 3 references. The qualifications are stringent.

Learn more about linear function here: brainly.com/question/14796161

#SPJ2

Answer:

B)

Step-by-step explanation:

This is hope i got it and it may or may not be helpful 10 divide by 430

Answer:

Positive 3/4

Step-by-step explanation:

TO find perpednicular you take the negative reciprical of the slope, so the reciprical of -4/3 is -3/4, now add the negative to get - - 3/4 or 3/4

Answer: 18 miles

12 ÷ 4 = 3. So, we must multiply 3 by 6 to find how much Joe walks for 6 trips to school.

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

Now, we must multiply the number 6 by 3.

6 x 3 = 18

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

Answer = 18

Answer:

18 miles

Step-by-step explanation:

We can write ratios to solve

12 miles    x miles

----------  = ------------

4 trips          6 trips

Using cross products

12 *6 = 4x

72 = 4x

Divide by 4

72/4 = 4x/4

18 miles

The radius of the circle as given is; 3.

The center of the circle as given is; (-4, 1).

It follows from the task content that the center and radius of the given circle image and radius are to be determined.

Recall, the center-radius equation of a circle takes the form;

(x - h)² + (y - k)² = r² where center is; (h, k) and radius is r.

By observation of the graph as well as the given equation of the circle, the pair of coordinates for the center is; (-4, 1).

Also, since the radius is the distance from the center to any point on the circumference of the circle; the radius of the circle is; 3.

Read more on center and radius of a circle;

https://brainly.com/question/29614115

#SPJ1

Answer:

Complementary angles will add up to 90°. Supplementary angles will add up to 180°. For example, the answer to the first question would be complementary = 70° and supplementary = 160°.

Step-by-step explanation:

By solving two simultaneous linear equation, the result obtained is

There are 14 small rooms and 7 large rooms

What is Simultaneous Linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

A system of two simultaneous linear equation needs to be solved

Let the number of small rooms be x and the number of large rooms be y

The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 5 people.

Total number of guests = 63

2x + 5y = 63 ...... (1)

Fatoumata reserved twice as many small rooms as large rooms

x = 2y ....... (2)

Putting the value of x in (1)

\(2(2y) + 5y = 63\\4y + 5y = 63\\9y = 63\\y = \frac{63}{9}\\y = 7\)

Putting the value of y in (2)

x = \(2 \times 7\)

x = 14

There are 14 small rooms and 7 large rooms

To learn more about simultaneous linear equation, refer to the link:

https://brainly.com/question/26310043

#SPJ1

To design a secure network for 1QRA University with two different campuses (North and Gulshan), we will outline the network architecture using Cisco Packet Tracer.

1. Open Cisco Packet Tracer and create a new project.

2. Add two campuses: North and Gulshan. Place a switch in each campus and rename them as per the given requirement (e.g., Name(campus)).

3. Connect the switches in both campuses using back links. You can use Ethernet cables to establish the connection.

4. For each campus, add four PCs. Rename them as per the given requirement (e.g., Department(number)).

5. Assign two PCs to the IT department and two PCs to the Administration department in each campus.

6. Configure VLANs (Virtual Local Area Networks) to separate the IT and Administration departments. Create two VLANs, one for each department, on both switches.

7. Assign the IT PCs to the IT VLAN and the Administration PCs to the Administration VLAN. This ensures that the departments are isolated from each other.

8. Configure security settings for the IT VLAN to enhance network security. You can enable features like port security, MAC address filtering, or access control lists (ACLs) to restrict unauthorized access.

9. Test the network by pinging between PCs within the same department and between departments to ensure proper connectivity and isolation.

10. Save and simulate the network in Cisco Packet Tracer to verify its functionality and security.

By following these steps, you will have designed a network that allows the IT and Administration departments in 1QRA University to work securely, ensuring the separation of sensitive information.

Learn more about Cisco Packet Tracer here:

https://brainly.com/question/30404199

#SPJ11

1. Projection of b onto row space of A: (3/2, 1/2, 1/2, -1/2)

2. (a) Basis for Nul(A): {(1, -1, -1, 0), (-1, 0, 3, 1)}

(b) Basis for orthogonal complement of Nul(A): {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (-1, 3, 1, 0)}

3. (a) Bases for orthogonal complements of V and W: V+ = span{(2,-1,0)}, Wt = span{(-2,4,1)}

(b) Projection of 6 onto V: p = (3/14)(2,-1,0)

4. y = (1/7)(-5,9,-8) + (3/7)(1,3,-2)

1. To find the projection, we first compute the orthogonal complement of the row space of A. Then, we find the projection of b onto the row space of A by projecting it onto the orthogonal complement of the row space of A and subtracting the result from b.

2. (a) To find a basis for the null space of A, we solve the equation Ax = 0 and express the solutions in parametric form, then choose two linearly independent vectors as a basis.

(b) To find a basis for the orthogonal complement of the null space of A, we find a basis for the row space of A and apply the Gram-Schmidt process to obtain a set of orthogonal vectors, then normalize them to obtain an orthonormal basis.

3. (a) To find a basis for the orthogonal complement of V, we find a basis for V and apply the Gram-Schmidt process to obtain a set of orthogonal vectors, then normalize them to obtain an orthonormal basis. Similarly, to find a basis for the orthogonal complement of W, we use the formula Wt = (V ∩ W)⊥.

(b) To find the projection of 6 onto V, we use the formula p = ((6·v)/(v·v))v, where v is any basis vector for V.

Error vector and orthogonal vector: ē = (11/14)(-1,2,5), orthogonal to v = (2,-1,0)

To find the error vector, we subtract the projection of 6 onto V from 6. To find the orthogonal vector to which the error vector is orthogonal, we take the cross product of the basis vectors for V.

4. To write y as a linear combination of a vector in V and a vector in V, we first find a basis for V and use the formula y = ((y·v₁)/(v₁·v₁))v₁ + ((y·v₂)/(v₂·v₂))v₂, where v₁ and v₂ are basis vectors for V.

To learn more about row space of the matrix, here

https://brainly.com/question/30883306
#SPJ4

If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

The correct option is (C)

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.

12 : 20 in its simplest form is 3 : 5

18 : 30  in its simplest form is 3 : 5

27 : 45  in its simplest form is 3 : 5

Now, determine the factor second factor of 36 if the first factor is 3.

36 / 3 = 12

Now multiply 12 by 5: 12 x 5 = 60

Hence, If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

Learn more about Ratio at:

https://brainly.com/question/13419413

#SPJ4

If the equation be 3log₂x-(log₂3-log₂ (x+4)) then we get\($\log _2\left(\frac{x^2(x+4)}{3}\right)\).

An exponential function has an opposite called a logarithmic function. In both exponential and log functions, the basis is the same.

An exponent and a number (the base) are inputs into a logarithmic function, which yields a result (the logarithm). The base that must be raised in order to obtain a number is represented by the number's logarithm.

The features of exponential functions can be investigated and exponential equations can be solved using logarithms. In calculus, where they are used to determine the slope of specific functions and the region enclosed by specific curves, they also become incredibly useful.

Let the given equation be 3log₂x-(log₂3-log₂ (x+4))

\($$& \log _a(x)-\log _a(y)=\log _a\left(\frac{x}{y}\right) \\\)

\($$& {alog}(x)=\log \left(x^a\right)\)

3 log₂ x - (log₂3 - log₂ (x+4))

simplifying the above equation, we get

log₂(x²) - log₂(3/x+4)

\($& \left.\log _2 \left(\frac{\frac{x^2}{3}}{\frac{3}{x+4}}\right)=\log _2\left(\frac{x^2(x+4)}{3}\right)\)

Therefore, by simplifying the equation 3log₂x-(log₂3-log₂ (x+4)) we get\($\log _2\left(\frac{x^2(x+4)}{3}\right)\).

To learn more about logarithmic identities refer to:

https://brainly.com/question/28041634

#SPJ1

The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16 thus, option (C) is correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given data set,

The value of 5/8 = 0.625 and 11/16 = 0.6875

Thus, 0.1375 < 0.25 < 5/8 < 11/16

Hence "The least to greatest or increasing order of the given data set will be 0.1375,0.25,5/8,11/16".

For more about the number system,

https://brainly.com/question/22046046

#SPJ1

Answer:

1

Step-by-step explanation:

because its the only one where if you run a line down the y axis it only crosses the line at one point