You have an ant farm with 31 ants. The population of ants in your farm will double every 3 months. The table shows the population growth of the ants over nine months. Decide whether the table represents a linear function or a nonlinear function. After one​ year, how many ants will there be in the ant​ farm?

Answer:

The graph of the data presented is shown in the attached image to this solution.

It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t

Step-by-step explanation:

The distance travelled with the corresponding time taken are presented in the table

Note: D - Distance travelled (miles)

t - Time (hours)

D | t

55 | 1

110 | 2

165 | 3

220 | 4

275 | 5

330 | 6

We are then told to plot these distance travelled on a graph with the time taken.

The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.

The image of the graph of this function will be attached to this answer

It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t

Hope this Helps!!!

Graph of relationship \(D=55t\) on coordinate plane attached below.

Since, the table below shows the distance traveled as a function of time.

Time(t)                                           Distance (D)

1                                                       55

2                                                      110

3                                                      165

4                                                      220

5                                                      275

6                                                      330

In the graph, X - axis represent timer in hours and Y - axis represent that distance travelled in miles.

Slope = \(\frac{y}{x} =\frac{55}{1}=\frac{110}{2}=\frac{165}{3} =55\)

It is observed that, in each relationship slope is same .Therefore, relationship is a line passing through the origin.

Relationship is,      \(D=55t\)

Graph is attached below,

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Answer:

Step-by-step explanation:

First of all multiply through by 7

We have

Expand the terms in the bracket

That's

Add 16x to both sides

That's

Divide both sides by 30

We have the final answer as

Hope this helps you

The number of pivot columns in a matrix is equal to the rank of the matrix.

Therefore, A has n pivot columns.

Since A is a matrix with more rows than columns and Ax=0 does not have a non-trivial solution, then by the Rank-Nullity Theorem, we know that \(\rank}(A)\) = n.

Let A be an m \(\times n$\) matrix with \($m > n$\) such that\($Ax=0$\) does not have a non-trivial solution.

We want to determine the number of pivot columns of A.

Suppose that A has k pivot columns, where \($0 \leq k \leq n$.\)

Then, the remaining n-k columns of A are free variables, and we can express them as linear combinations of the pivot columns.

Since \($m > n$\), there are more rows than columns in \(A$.\)

This means that the rows of A are linearly dependent, and we can find a non-trivial solution to Ax=0.

However, we are given that Ax=0 does not have a non-trivial solution, which means that the columns of A must be linearly independent.

If k<n, then we can express the free variables as linear combinations of the pivot columns, which means that the columns of A are linearly dependent.

This is a contradiction, so we must have k=n.

Therefore, A has n pivot columns.

In summary, if A is an $\(m \times n$ matrix with $m > n$\) such that Ax=0 does not have a non-trivial solution, then A has n pivot columns.

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The probability of outcome to be a 5 is 1/13. The probability of outcome not be 5 is 12/13. The probability of outcome to be a diamond or a king is 4/13. The probability of the outcomes to be a jack or a queen is 2/13. The probability of The outcome to be a heart and a club is 0 and the probability of the outcomes to be a card greater than 6 and less than 9 is  2/13.

A deck contains a total of 52 cards.

Total outcomes if the selected number of cards is one=52

Case A:

Each suit contain one 5 numbered card. There are four suits. Therefore, The required outcome would be 4.

Probability of an outcome is the ratio of desired outcomes to the total outcomes.

The probability of outcome to be 5, P(A):
P(A)=4/52

P(A)=1/13

Case B:

The total probability of outcomes=52/52=1

The probability of the outcome to be 5=1/13

Therefore, the probability of the outcome not to be 5, P(B):

P(B)=1-(1/13)

P(B)=12/13

Case C:

Each suit carries a king. Therefore, the probability of the outcome to be a king, P(M):

P(M)=4/52

P(M)=1/13

A suit carries 13 cards. Therefore, there will be 13 cards of diamonds.

The probability of the outcome to be a diamond, P(N):

P(N)=13/52

P(N)=1/4

The probability that the outcome is a king of diamonds, P(M\(\cap\)N):

P(M\(\cap\)N)=1/52

Hence, the probability that the outcome is a diamond or a king, P(M\(\cup\)N):

P(M\(\cup\)N)=P(M)+P(N)-P(M\(\cap\)N)

P(M\(\cup\)N)=(1/13)+(1/4)-(1/52)

P(M\(\cup\)N)=16/52

P(M\(\cup\)N)=4/13

Case D:

Each suit carries a Jack. Therefore, the probability of the outcome to be a jack, P(P):

P(P)=4/52

P(P)=1/13

Each suit carries a Queen. Therefore, the probability of the outcome to be a Queen, P(Q):

P(Q)=4/52

P(Q)=1/13

The probability that the outcome is a jack and a queen, P(P\(\cap\)Q):

P(P\(\cap\)Q)=0/52

P(P\(\cap\)Q)=0

Hence, the probability that the outcome is a jack or a queen, P(P\(\cup\)Q):

P(P\(\cup\)Q)=P(P)+P(Q)-P(P\(\cap\)Q)

P(P\(\cup\)Q)=(1/13)+(1/13)-0

P(P\(\cup\)Q)=2/13

Case E:

A card is never a heart and a club. Therefore, the probability of a card to be a heart and a club is 0.

Case F:

The numbers greater than 6 and less than 9 are the numbers between 6 and 9. The numbers between 6 and 9 are 7 and 8.

Each suit carries one 7 numbered card and one 8 numbered card. There is a total of 4 suits.

Therefore the desirable outcomes=8

The probability of the outcome required=8/52

=2/13

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Answer:

x = 2.4

Step-by-step explanation:

16^(4x - 3) = 8 ^ (2x + 4)

16 = 2^4

8 = 2^3

2 ^ 4*(4x - 3) = 2^3(2x + 4)

Since the bases are the same, you can equate the powers

4(4x - 3) + 3*(2x + 4)           Remove the brackets.

16x - 12 = 6x + 12                 Subtract 6x from both sides

16x - 6x - 12 = 12                Combine the terms on the left

10x - 12 = 12                        Add 12 to both sides

10x = 24                              Divide by 10

x = 2.4

The value of u, number of hours walking up a hill based on the equation is 2.5

9(u – 2) + 1.5u = 8.25

where,

9(u – 2) + 1.5u = 8.25

9u - 18 + 1.5u = 8.25

9u + 1.5u = 8.25 + 18

10.5u = 26.25

u = 26.25/10.5

u = 2.5

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In a transformation called a translation, the pre-image is slid either vertically or horizontally.

A translation is a type of transformation in geometry where the pre-image (original figure) is moved or slid to a new position in a specific direction. The movement can be either vertical or horizontal.

When a pre-image is translated vertically, it means that it is moved up or down without any change in its orientation. The entire figure maintains the same shape and size, but its position on the coordinate plane is shifted vertically.

On the other hand, when a pre-image is translated horizontally, it is moved left or right while preserving its original shape and size. The orientation of the figure remains the same, but its position on the coordinate plane is shifted horizontally.

In both cases, the translation occurs without any rotation, reflection, or resizing of the pre-image. The resulting image is a new figure that is congruent to the original but located at a different position on the plane.

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The correct answer is: allows for the construction of meaningful ratios between the data values.

The interval scale of measurement allows for the construction of meaningful ratios between the data values. This means that not only can we determine the order and the difference between values, but we can also compare values in terms of their relative magnitude using ratios. However, it does not have a true zero point and therefore does not allow for the use of negative values or the construction of absolute ratios. The nominal scale, on the other hand, is the weakest scale of measurement as it only allows for categorization or naming of data without any numerical significance. The correct answer is: allows for the construction of meaningful ratios between the data values.

The interval scale of measurement allows for the construction of meaningful ratios between the data values. This means that not only can we determine the order and the difference between values, but we can also compare values in terms of their relative magnitude using ratios.

However, it does not have a true zero point and therefore does not allow for the use of negative values or the construction of absolute ratios. The nominal scale, on the other hand, is the weakest scale of measurement as it only allows for categorization or naming of data without any numerical significance.

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Answer:

Option 4

Step-by-step explanation:

The smaller sides must add up to be greater than the largest side so:

1) 6 + 8 < 15

1) No

2) 6 + 9 = 15

2) No

3) 9 + 6 < 16

3) No

4) 9 + 8 > 16

4) Yes

Answer:

462

Step-by-step explanation:

6×7×10×6 is how you do it

Answer:

(5, 2)

Step-by-step explanation:

Given the following system of equations;

2x - 2y = 6  ......equation 1.

4x + 4y = 28  ......equation 2.

To get an equivalent equation, we would multiply eqn 1 by 2;

2 * (2x - 2y = 6) = 4x - 4y = 12

The new equivalent system of equations are;

4x - 4y = 12

4x + 4y = 28  

Adding the equivalent system of equations, we have;

(4x + 4x) + (-4y + 4y) = (12 + 28)

8x + 0 = 40

8x = 40

x = 40/8

x = 5

Next, we would find the value of y;

2x - 2y = 6

Substituting the value of x, we have;

2(5) - 2y = 6

10 - 2y = 6

Rearranging the equation (collecting like terms), we have;

2y = 10 - 6

2y = 4

y = 4/2

y = 2

Therefore, the solutions to the new system of equations are 5 and 2.

Check:

2x - 2y = 6

Substituting the values, we have;

2(5) - 2(2) = 6

10 - 4 = 6

6 = 6

Answer:

\( \sf \fbox{46.296 British Pounds}\)

Step-by-step explanation:

1 shower job requires 3 hours of work,

plumber will fix only 1 shower that means he will work for 3 hours,

Charges of 1 hour = 25$

Charges of 3 hour = 25× 3 = 75$

The currency that plumber accept is British pound (£),

1 British pound (£) = 1.62 dollar ($)

x British pound = 75 dollar

\( \frac{1}{x} = \frac{1.62}{75} \)

taking reciprocal both the side,

\( \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} \)

\(x = 46.296\)

Jamar need to pay 46.296 British Pounds to plumber for the shower job.

The two units that were cancelled was Dollar & Pound.

It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.

\( \sf Volume + Length = Not \: possible \)

Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.

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Answer:

horiz = 5

vertic = 2

y inter =13/2

x inter =13/5

Step-by-step explanation:

Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:C

Step-by-step explanation:The side lengths of the triangle is 4, 8 and 10. To check if the sides form a triangle, see if the following inequalities hold true:

4

+

8

?

>

10

4

+

10

?

>

8

10

+

8

?

>

4

12

✓

>

10

14

✓

>

8

18

✓

>

4

A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.

So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.

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Answer:

The prime factors of 168 are 2, 3, and 7.

Step-by-step explanation:

Answer:

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Prime factorization: 48 = 2 x 2 x 2 x 2 x 3, which can also be written 48 = 2⁴ x 3.

Hoped I helped

Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

the solution for the number of tigers present over time is given by:

P - (P^2)/(2K) - (T/K)P + (T/K)ln(P) = rt + 11.375 + 0.1ln(15)

To solve the given differential equation for the population of Bengal tigers in the conservation park, we'll use the given parameters and initial conditions.

The differential equation for the population (P) is:

P't = rp(1 - P/K)(1 - T/P)

Given:

Carrying capacity (K) = 100

Minimum threshold value for survival (T) = 10

Population growth rate (r) = 1% = 0.01 (per year)

Initial population (P0) = 15

Now, let's solve the differential equation to find the number of tigers present over time.

Separating variables, we have:

(1 - P/K)(1 - T/P) dP = rp dt

Integrating both sides:

∫ (1 - P/K)(1 - T/P) dP = ∫ rp dt

Let's evaluate the integral on the left side:

∫ (1 - P/K)(1 - T/P) dP = ∫ (1 - P/K - T/K + T/(KP)) dP

= ∫ (1 - P/K) - (T/K) + (T/PK) dP

= P - (P^2)/(2K) - (T/K)P + (T/K)ln(P) + C1

On the right side, we have:

∫ rp dt = rt + C2

Combining both sides and simplifying, we have:

P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) + C1 = rt + C2

To solve for the constants C1 and C2, we use the initial condition P(0) = P0:

P0 - (P0²2)/(2K) - (T/K)P0 + (T/K)ln(P0) + C1 = r(0) + C2

P0 - (P0²2)/(2K) - (T/K)P0 + (T/K)ln(P0) + C1 = C2

Substituting the given values:

15 - (15²2)/(2×100) - (10/100)×15 + (10/100)ln(15) + C1 = C2

15 - (225/200) - (150/100) + (10/100)ln(15) + C1 = C2

15 - 1.125 - 1.5 + 0.1ln(15) + C1 = C2

Simplifying further, we have:

12.375 + 0.1ln(15) + C1 = C2

Now we have the general solution:

P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) = rt + C

Using the initial condition P(0) = 15, we can solve for C:

15 - (15²2)/(2×100) - (10/100)×15 + (10/100)ln(15) = r(0) + C

15 - 1.125 - 1.5 + 0.1ln(15) = C

11.375 + 0.1ln(15) = C

Therefore, the solution for the number of tigers present over time is given by:

P - (P²2)/(2K) - (T/K)P + (T/K)ln(P) = rt + 11.375 + 0.1ln(15)

This is the general solution for the population of Bengal tigers in the conservation park.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph of the inverse of a function is its reflection in the line y=x. In the attached, that line is shown as a dashed yellow line. The inverse function is shown as a blue line.

__

One way to plot the inverse function of a line is to swap the x- and y-coordinates of the line's intercepts.

In A, the x-intercept is about 10, and the y-intercept is about -4. For the inverse function, the y-intercept will be 10 and the x-intercept will be -4.

In B, the x- and y-intercepts of the function are -6 and 6, respectively. For the inverse function, they will be 6 and -6, respectively.

Answer:

In A, the x-intercept is about 10, and the y-intercept is about -4. For the inverse function, the y-intercept will be 10 and the x-intercept will be -4.

In B, the x- and y-intercepts of the function are -6 and 6, respectively. For the inverse function, they will be 6 and -6, respectively.

Step-by-step explanation:

i got it right on edge

Answer:

x =180-(90+46)

=180-136

=44

Answer:

44°

Step-by-step explanation:

180-90-46=44

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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Answer:

John's balance before making the deposit is -$195.

Step-by-step explanation:

Let us assume that John's bank balance is $X.

Now,

John makes a deposit of $120 and still, he is overdrawn by $75.

Therefore,

\(\begin{aligned}\rm{\$X} + \rm{\$120} &= -\rm{\$75}\\X&=-\$195\end{aligned}\)

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If  on Saturday he picks a shirt, a jumper and a hat. Show that there are 105 different combinations he can pick.

a.  There are 105 different combinations that Jamal can pick on Saturday.

b. Jamal is incorrect. If he picks just two of the three clothing items, there are only 71 possible combinations, which is less than the 105 possible combinations when he picks all three item

a) To find the total number of combinations, we need to multiply the number of options for each clothing item:

Number of combinations = (number of shirt options) x (number of jumper options) x (number of hat options)

Number of combinations = 7 x 5 x 3

Number of combinations = 105

Therefore, there are 105 different combinations that Jamal can pick on Saturday.

b) If Jamal picks just two of the three clothing items, there are two cases: he can either pick a shirt and a jumper, or he can pick a shirt and a hat, or he can pick a jumper and a hat. Let's calculate the number of combinations for each case:

Case 1: Jamal picks a shirt and a jumper

Number of combinations = (number of shirt options) x (number of jumper options)

Number of combinations = 7 x 5

Number of combinations = 35

Case 2: Jamal picks a shirt and a hat

Number of combinations = (number of shirt options) x (number of hat options)

Number of combinations = 7 x 3

Number of combinations = 21

Case 3: Jamal picks a jumper and a hat

Number of combinations = (number of jumper options) x (number of hat options)

Number of combinations = 5 x 3

Number of combinations = 15

To find the total number of combinations, we need to add up the number of combinations for each case:

Total number of combinations = 35 + 21 + 15

Total number of combinations = 71

Therefore, Jamal is incorrect. If he picks just two of the three clothing items, there are only 71 possible combinations, which is less than the 105 possible combinations when he picks all three items.

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Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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The Platinum Rule test is a good way of judging if distributive justice is taking place is true.

Distributive justice is the idea that people should be treated equally and that goods, opportunities, and resources should be distributed fairly among all members of society. The Platinum Rule test is one way to evaluate whether or not distributive justice is being practiced. In order to understand the Platinum Rule, it is important to first understand the Golden Rule, which states, "Do unto others as you would have them do unto you." The Platinum Rule takes the Golden Rule a step further by recognizing that people may have different needs, preferences, and desires.

The Platinum Rule states, "Do unto others as they would have you do unto them." This means that instead of treating others the way you would want to be treated, you should treat them the way they want to be treated. The Platinum Rule test can be used to evaluate whether or not distributive justice is being practiced by asking the question, "Are people being treated in the way they want to be treated?" If the answer is yes, then distributive justice is likely being practiced. However, if the answer is no, then there may be a problem with the way goods, opportunities, and resources are being distributed.

Overall, the Platinum Rule test is a useful tool for evaluating whether or not distributive justice is taking place.

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