A cube has an edge length that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers? (1 point)
O the diagonal of one of the cube's faces
O the volume of the cube
O the surface area of the cube
O the area of one of the cube's faces

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Answer:

1

Step-by-step explanation:

By using fundamental theorem of calculus  The exact value of the definite integral \(\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx\) is 6(√(π) - 1).

First, we can find an antiderivative of the integrand by using the power rule and the constant multiple rule of integration:

∫(3x^(-1/2)) dx = 3 ∫(x^(-1/2)) dx = 3 (2x^(1/2)) + C = 6√(x) + C

where C is the constant of integration.

Now, we can use the fundamental theorem of calculus to evaluate the definite integral \int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx. The theorem states that if f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x), then

∫[a, b] f(x) dx = F(b) - F(a)

In this case, f(x) = 3x^(-1/2) and F(x) = 6√(x) + C. Therefore,

∫{1}^{π} (3x^(-1/2)) dx = F(π) - F(1) = 6√(π) + C - 6√(1) - C = 6√(π) - 6√(1) = 6(√(π) - 1)

So the exact value of the definite integral \(\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx\) is 6(√(π) - 1).

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Answer:

5ºF per hour decrease

Step-by-step explanation:

Given that the temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours

For finding average we normally divide the total by number of units

Here change in temperature for 2 days is given as -10 degrees (negative sign is used to denote decrease)

For 2 days change in temperature = -10 degrees F

Hence average change in temperature = change for one day

= -10/2 = -5 degrees F

So answer is 5ºF per hour decrease

Answer:

Since 10/2 equals 5 the only reasonable answer to ¨Temperature per hour¨ is -5. Also because the temperature dropped 10 degrees in 2 hours which concludes 5 degrees dropped per hour.

Step-by-step explanation:

Got it right on E2020

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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Answer:

1st Slot: f(-3)

2nd Slot: -3

3rd Slot: is not

Step-by-step explanation:

Using the Remainder Theorem, we plug in the root of x + 3 (which is x = -3) and see the remainder.

If the remainder = 0, it is a factor

If the remainder ≠ 0, it is NOT a factor

f(-3) = -2(-3)⁴ - 8(-3)³ - 2(-3) - 63

f(-3) = -3

So, x + 3 is NOT a factor.

We then have our 3 answers.

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation \(t=\frac{k}{p}\)

t is time

k is a constant

p is people

We must substitute the values into the equation

\(54=\frac{k}{9}\)

\(k=486\)

Now we must substitute it to find the time

\(t=\frac{486}{6}\)

you get 81

It would take \(6\) builders  \(36\) days to complete the same house.

Builders are those person whose job is to build or repair houses and other buildings.

We have,

\(9\) builders take \(54\) days to complete a house.

So,

\(1\)  builder will take  \((\frac{54}{9})\)  days to complete a house,

In the same way,

\(6\)  builder will take  \((\frac{54}{9}*6)\)  days to complete a house,

i.e.

\(6\)  builder   \(=(\frac{54}{9}*6)= 36\) days.

Hence, we can say that it would take \(6\) builders  \(36\) days to complete the same house.

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Answer:

Points of the triangle: (-6, 3)  (-3, 9)  (-7, 8)

Step-by-step explanation:

(2, -5)   →   (-6, 3)

(8, -2)   →   (-3, 9)

(7, -6)   →   (-7, 8)

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.

Given:-

To find all angle values.

So from the given image. we get,

Also,

So now we know angle 5 is 150 degrees. so we get,

So angle 4 is 30 degree.

Also,

So angle 7 is 150 degree.

Also,

So angle 6 is 30 degree.

So now we equate the values. so we get,

Answer:

Y = 1/4x + 0 or Y = 1/4x

Step-by-step explanation:

Teacher circles the 4 because the point was (1,4)

Slope is rise over run

You risen 1 unit on the y-axis, then you went over 4 units on the axis, making the slope 1/4x

Answer:

Step-by-step explanation:

Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer: ((x2)−14x+87)/16

Step-by-step explanation:

  focal diameter = 16,

  4a=16;

  a=4.

(h,v)=(7,7-a)

==> (h,v)=(7,3)

the equation of the parabola =  ((x-7)^2)=16(y-3)

                                                => y = ((x^2)-14x+87)/16.

Answer:

$4.95

Step-by-step explanation:

If jelly beans cost $2.75 per pound then multiplying the cost per pound by the amount of jelly beans purchased will give the answer of $4.95 per 1.8 pounds of jelly beans.

Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds.

To convert pounds to tons, we divide the weight in pounds by 2,000 (the number of pounds in a ton):

15,000 pounds ÷ 2,000 pounds/ton = 7.5 tons

Therefore, the weight of a male African elephant is approximately 7.5 tons.

So the closest answer to this question is "7 tons".

Answer:

7 tons

Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds. To convert this weight into tons, we need to divide it by 2,000 (since there are 2,000 pounds in a ton).

So, 15,000 ÷ 2,000 = 7.5 tons.

Therefore, the answer is 7 tons (since there are no fractions of tons in the options given).

Answer:

those weights sure are mean

Step-by-step explanation:

they say their mean so their mean

Answer: A. -5

Step-by-step explanation: I used the points (0,2) and estimated the x-intercept to be about (0.5,0) to find the slope. The answer I got was -4 and the closest thing to that (aka best represents) is -5.  

Answer:

A. -5

Step-by-step explanation:

Slope is basically rise over run. If you look at the points (1, -3) and (0, 2), you will see that it has risen by 5 digits and went to left by 1 digit. Therefore the slope would be 5/1 which is basically 5. Next, it is a negative slope so you would add the negative. Your slope would be -5.

The required graph of the function is graph 3.

You must select x-values and insert them into the equation before you can graph a function. A y-value will be produced once those values are entered into the equation. Your coordinates for a single point are your x- and y-values.

To check the graph we will put the values of x and identify the graph from the given option.

So, we have \(p(x) = 6\sqrt[3]{x}\)

at x = 1

\(p(x) = 6\sqrt[3]{1}\)

\(p(x) = 6\)

Now, we can see that i  graph 1, 2 and 4. there is no value which gives p(x) = 6 for x = 1.

and

In graph 3, at x = 1, there is a a of p(x) = 6.

So.the graph of the function is graph 3.

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Answer: 13

Step-by-step explanation:

4x+3y=-5 solve x :    

4x = -3y + -5           | -3y

1x = -0.75y + -1.25  | : 4

-3x + 7y = 13 solve x :

-3x + 7y = 13              | -7y

-3x = -7y = 13             | : (-3)

Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333

-0, 75y - 1,25 = 2,333y - 4, 333 solve y:

-0, 75y - 1,25 = 2,333y -4, 333    | -2,333y

-3, 083y - 1,25 = -4,333               | + 1, 25

-3. 083y = -3,088                         | : (-3, 083)

y = 1

Plug y = 1 into the equation 4x + 3y = -5 :

4x + 3 · 1           | Multiply 3 with 1

4x + 3 = -5        | -3

4x = -8              | : 4

x = -2

So the solution is:

y = 1, x = -2

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The percent of the raisins that Victoria she keep for herself is 70%

Based on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.

Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:

= (1 - 3/10) × 100

= 70%

Therefore, the percent of the raisins that Victoria she keep for herself is J 70%

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Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.

About what percent of the raisins did she keep for herself?

F 30%

G 33%

H 66%

J 70%

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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Answer:

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

Given function:

Graph it first (see attached).

Test the graph for symmetry.

We know the odd degree parent function y = x³ has an origin symmetry, whilst even degree functions may have axis symmetry.

The given function is a translation of cubic function 5 units up so the center of symmetry has translated as well. Therefore correct answer is 4.

Answer:

4. no origin symmetry

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y &= x^3 + 5\\&\textsf{Replace $y$ for $(-y)$}: \quad &-y &= x^3 + 5\\&\textsf{Simplify}: \quad &y &= -x^3 - 5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the x-axis.

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

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$}: \quad &y&=(-x)^3+5\\&\textsf{Simplify}: \quad &y&=-x^3+5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the y-axis.

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

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

To determine if a graph is symmetric with respect to the origin, replace all the x's with (−x) and all the y's with (-y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the origin.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$ and $y$ for $(-y)$}: \quad &(-y)&=(-x)^3+5\\&\textsf{Simplify}: \quad &-y&=-x^3+5\\&&y&=x^3-5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the origin.

Answer:

3 units

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

8x5-3+5=?

The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

The player made 38 foul shots.

Let's indicate the player's total number of field goals made by F and foul shots attempted by S. Based on the data in the problem, we may construct an equation system:

F + S = 55 (the player made a total of 55 baskets) (the player made a total of 55 baskets)

2F + S = 89 (the player scored a total of 89 points) (the player scored a total of 89 points)

The substitution approach can be used to find the values of F and S. We start by resolving the initial S equation:

S = 55 - F

Next, we change S in the second equation to the following expression:

2F + (55 - F) = 89

When we simplify and find F, we obtain:

F = 17

Hence, the player connected on 17 field goals. We may change this value of F into the first equation and then solve for S to determine the total number of foul shots:

17 + S = 55

S = 38

The player so scored 38 fouls.

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Answer: 88.2

..........................

Answer:

\(\log _3\left(x^9\right)=9\log _3\left(x\right)\)

Step-by-step explanation:

Given the expression

\(\log _3\:x^9\)

now rewriting the expression

\(\log _3\:x^9\)

\(\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0\)

\(=9\log _3\left(x\right)\)

Therefore,

\(\log _3\left(x^9\right)=9\log _3\left(x\right)\)

Answer:

B

Step-by-step explanation:

edge