Which two ratios represent quantities that are proportional

A 9/5 and 19/10
B 4/6 and 10/16
C 15/10 and 21/14
D 25/35 and 20/24

The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

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Step-by-step explanation:

mark me as the brainliest

For an F-value of 3.4, the correct p-value is 0.0163 which is evaluated using the statistical tables or software.

Finding the correct p-value for a given F-value of 3.4 requires the use of statistical tables or software. Assuming a two-sided test and a significance level of 0.05, you can use JMP to calculate the p-value as follows:

Open JMP and click Analyze > Match Y to X. 

In the dialog box, select a response variable (eg: sales) and a factor variable (eg: promotion).

Click Options and select ANOVA from the list.

Click Run to generate the ANOVA table. Find the F Ratio and Prob > F columns in the ANOVA table.

The p-values ​​in the Prob > F column correspond to the probability of the F value being observed in the extreme, or observed more extreme than the observed value, given the null hypothesis to be true.

In this case, with an F value of 3.4, degrees of freedom of the numerator 4, and degrees of freedom of the denominator 45 (based on 5 groups and 50 samples in total), the p-value is 0.0163. 

therefore, for an F-value of 3.4, the correct p-value is 0.0163. 

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Answer:

c

Step-by-step explanation:

a triangle has to equal 180 degrees

Answer:

C. 68

Step-by-step explanation:

A triangle has 180 degrees in total. Add the two shown angles and subtract it by 180.

Answer

a

Step-by-step explanation:

because submarine b has a bigger negative number so its more further down

Answer:

25% decrease

Step-by-step explanation:

=(60−80)|80|×100

=−2080×100

=−0.25×100

=−25%change

=25%decrease

Answer:

25% decrease

Step-by-step explanation:

a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.

b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.

c) Player 1 has infinitely many strategies.

d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.

e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.

Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.

Finding Nash Equilibrium

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Answer:

1) (-50) <(-25) < (-10) < 10 < 25

2) 150 in^2

Step-by-step explanation:

For the first question we list the numbers according to their sign(start from negative)

For the second question we multiply height with width to find the area of the rectangle.

1.

we know that,

negetive numbers are smaller than positive number,

According to the question,

order the intergers {-10, -25, 25, 10, -50} from least to greatest is:-

\(\bold{(-50) <(-25)<(-10)<10<25  }\) 

2.

we know that,

Area of rectangle =length ×breath

According to the question,

\(\bold{Area=15×10   }\) 

\(\bold{Area=150~in^{2}   }\) 

Step-by-step explanation:

<1 = 90 - 32

= 58

bd is a traversal to parallel line ab and dc

<1 = <bdc ( alternate angles) = 58

in right triangle edc

90 - 58 = <3 = 32

<2 = 58

The probability that three cards chosen at random from a standard 52-card deck that are not all the same color is 3/4.

Total number of combinations of three cards: There are 52 choose 3 = 22,100 ways to choose three cards from a standard deck of 52 cards.

Number of combinations that are not all the same color: There are two possibilities for the colors of the three cards:

a. Two red cards and one black card: There are 26 choose 2 ways to choose two red cards and 26 choose 1 ways to choose one black card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

b. Two black cards and one red card: There are 26 choose 2 ways to choose two black cards and 26 choose 1 ways to choose one red card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

The total number of combinations that are not all the same color is 8,450 + 8,450 = 16,900.

The probability that three cards chosen at random are not all the same color is:

P(not all the same color) = (number of combinations that are not all the same color) / (total number of combinations of three cards) = 16,900 / 22,100 = 3/4.

Therefore, the probability that three cards chosen at random from a standard 52-card deck are not all the same color is 3/4.

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Answer:

The answer is true

Step-by-step explanation:

Answer:

this question is true for the answer :)

Step-by-step explanation:

given:- M=35

to find :- r and g

r=90

m=35 let G be = x

m+r+g=180

35+90+x=180

125+x=180

x=180-125

x=55

hope this helps you

have a nice day :)

Answer:

-1/10

Step-by-step explanation:

-7/24 by the reciprocal of 35/12

The reciproical of 35/12 is 12/35

-7/24 * 12/35

Rewriting

-7/35 * 12/24

-1/5 * 1/2

-1/10

Answer: B. 12

Step-by-step explanation: Expected no. = No. of trials × p

= 40 × 0.3

= 12

Answer:

B.  12

Step-by-step explanation:

Experimental probability is calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.

\(\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}\)

Given information:

Substitute the given values into the formula:

\(\implies \sf 0.3=\dfrac{\textsf{Number of times Jenson picked an apple}}{40}\)

\(\implies \sf \textsf{Number of times Jenson picked an apple}=0.3 \times 40=12\)

Therefore, Jenson picked an apple 12 times during the 40 trials.

It's easier to use standard form.

Step-by-step explanation:

Even though it does not give as much information about a graph as slope-intercept form or point slope form, it does make it fairly easy to find the x and y-intercepts.

Answer:

To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.

Mark me brainliest if I am right...PLEASE

Answer:To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(y = \frac{1}{3}x+6\\\\\)

When x = 0 , y = 0 + 6 = 6    

(0 , 6)

When x = 3,

\(y = \frac{1}{3}*3 + 6 = 1 + 6 = 7\)

(3, 7)

When x = -3

\(y =\frac{1}{3}*(-3)+6=-1 + 6 = 5\)

(-3, 5)

Plot (0,6) ; (3, 7) and (-3, 5) in the graph and join the points.

Answer:

The probability that Jacob prefers to play on smartphone

Step-by-step explanation:

male is 52 whereas female is only 48, in fact, female is lower on all of them.

52% more likely for Jacob and only 48% likely for Leslie.

Sorry if wrong....

Expect distributions of these variables are:

a) Ages of people at a Little League game are unimodal and skewed.

b) Number of siblings of people in your class is unimodal and skewed.

c) Pulse rates of college-age males unimodal and roughly symmetric.

d) Number of times each face of a die shows in 100 tosses is approximately uniform.

a) Age distribution during a Little League game is likely to be unimodal and skewed. The age range of attendees. This is because Little League has an upper age restriction and the majority of players will fall inside that range, with just a small number being outliers. As a result, the distribution is likely to be unimodal, with the majority of participants falling within a relatively small age range, and being skewed toward older ages.

b) How many siblings are in your class? The distribution of siblings in a class is probably unimodal and skewed. This is because the majority of people either have no siblings or have one or two siblings, with just a small minority having three or more. As a result, the distribution will be unimodal, with the majority of individuals falling within a very small range, and tilted in the direction of the lower numbers.

c) Males in college-age pulse rates: These men's pulse rate distributions are probably unimodal and roughly symmetric. It is doubtful that there would be different groups or outliers that would result in a bimodal distribution, even though there may be some natural variation in pulse rates. There is also no reason to assume that one tail of the distribution will be longer or more dispersed than the other, hence the distribution is probably symmetric.

d) Number of times each die face is revealed in 100 throws: The distribution of the number of times each die face is revealed in 100 throws is probably quite uniform. Each face has an equal chance of appearing on each toss, and throughout 100 tosses, each face is expected to do so roughly the same amount of times, assuming a fair die. As each face should appear nearly equally often, the distribution should be quite consistent.

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Answer:

ok good morning

have a nice day

Step-by-step explanation:

#toxicsquad

Answer:

i think its 7, but you should probably check that...

Equation: \( 4x\degree + 2x\degree = 180°\)

Answer:

120°, 60°

Step-by-step explanation:

Since, sum of any two Supplementary angles is always 180°.

\( \therefore 4x\degree + 2x\degree = 180°\\

\therefore 6x\degree = 180°\\

\therefore 6x = 180\\\\

\therefore x = \frac{180}{6}\\\\

\therefore x = 30\\

\implies \\

4x° = (4\times 30)° = 120°\\

\&\\

2x° = (2\times 30)° = 60°\\

\)

Answer: x∈(-∞,-2√6-2)U(2√6-2,+∞)

Step-by-step explanation:

\(\displaystyle\\y=\frac{1}{4} (x+2)^2-6\\y > 0\\Hence,\\\frac{1}{4}(x+2)^2-6 > 0 \\\\\frac{1}{4}(x+2)^2-6+6 > 0+6\\\\\frac{1}{4}(x+2)^2 > 6\\\)

Multiply both parts of the equation by 4:

\((x+2)^2 > 24\)

Extract the square root of both parts of the inequality:

\(|x+2| > \sqrt{24} \\|x+2| > \sqrt{4*6} \\|x+2| > 2\sqrt{6}\)

Expand the modulus - we get a set of inequalities:

\(\displaystyle\\\left [{{x+2 > 2\sqrt{6}\ \ \ \ (1) } \atop {-(x+2) > 2\sqrt{6} \ \ \ (2)}} \right.\\\)

Multiply both parts of inequality (2) by -1 and reverse the sign of the inequality:

\(\displaystyle\\\left [ {{x+2-2 > 2\sqrt{6}-2 } \atop {x+2 < -2\sqrt{6} }} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x+2-2 < -2\sqrt{6} -2}} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x < -2\sqrt{6}-2 }} \right.\)

Thus,

\(x\in(-\infty,-2\sqrt{6}-2)U(2\sqrt{6} -2,+\infty)\)

Answer:

\(m_1= \frac{1}{4}\)

Step-by-step explanation:

Given

\(A = (4,-1)\)

\(B =(3,3)\)

Required

Slope of line perpendicular to AB

First, we calculate the slope of AB using:

\(m=\frac{y_2 -y_1}{x_2 -x_1}\)

This gives:

\(m=\frac{3--1}{3-4}\)

\(m=\frac{4}{-1}\)

\(m=-4\)

The line perpendicular to AB has the following slope (m1):

\(m_1= -\frac{1}{m}\)

So, we have:

\(m_1= -\frac{1}{-4}\)

\(m_1= \frac{1}{4}\)

The ferryman should transport the goat first, then return alone to bring the wolf, leaving the goat on the right bank. Finally, he should transport the cabbage and leave it with the wolf.

In order to solve this puzzle, the ferryman must make a series of careful moves to ensure the safety of the wolf, goat, and cabbage. The first step is to transport the goat to the right bank, leaving it there. The ferryman then returns to the left bank alone.

He takes the wolf across the river, but before leaving it on the right bank, he brings the goat back to the left bank. Now, the goat and cabbage are on the same side, while the wolf remains on the right bank.

The ferryman transports the cabbage to the right bank, leaving it there, and then returns alone to the left bank. Finally, he takes the goat across the river one last time, completing the puzzle. This sequence of moves ensures that the wolf and goat are never left alone together, nor are the goat and cabbage.

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Answer:

Infinite solution

Step-by-step explanation:

- 2x + 5 = -2x + 5

→ Plug any value in and the output with equal it

Answer:

Infinite solution

Step-by-step explanation:

one solution - x=a

no solution- a=b

infine solution- a=a

The stoplight weighs 30 pounds. This is determined by finding the balancing force, which is the force due to gravity, that cancels out the combined force of the two cables. The balancing force vector is (0, 30), with the y-component representing the weight of the stoplight.

The weight of the stoplight can be determined by finding the vector that balances the two cable forces. The magnitude of this balancing force will represent the weight of the stoplight.

To find the balancing force, we need to add the two cable force vectors together: (20, 18) + (-20, 12) = (0, 30).

Since the stoplight is in equilibrium, the sum of all the forces acting on it must be zero. In this case, the balancing force is the force due to gravity acting straight downward.

Therefore, the magnitude of the balancing force is the weight of the stoplight. From the vector (0, 30), we can see that the y-component represents the magnitude of the force, which is 30 pounds. Hence, the weight of the stoplight is 30 pounds.

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Answer:

Its the second choice.

Step-by-step explanation:

The volume of a pyramid = 1/3* area of base * height

So here:

V = 1/3x^2y cm^3.

Answer:

Step-by-step explanation:

In ΔFYG & ΔBUH

∠F = ∠B

FY = BU

YG = UH

ΔFYG ≅ ΔBUH   { Angle Side Side congruent}

Answer:

I got 0 or 18/5

Step-by-step explanation: