ILL GIVE 50 POINTS

Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answers

Answer 1

Answer:

Option 3 is right

Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.

Hope this helps:)

Answer 2

It is B from my point of view


Related Questions

Plsssssss help meeeeeeeeeeeee I need help

Plsssssss help meeeeeeeeeeeee I need help

Answers

Answer:

honestly I think its QT

Step-by-step explanation:

hope it helps

A women walks 3.55 km north and then 2.50 km east, all in 2.40 hours (a) What is the magnitude (in km) and direction (in degrees north of east) of her displacement during the given time?
magnitude
derection


km
- north of east

(b) What is the magnitude (in km/h) and direction (in degrees north of east) of hes average velocty during the given time? magnitude km/h direction - north of east (c) What was her average speed (in km/h) duning the same time interval? km/h

Answers

(a) The magnitude of the displacement is approximately 4.342 km, and the direction is approximately 54.28 degrees north of east.

(b) The magnitude of the average velocity is approximately 1.8092 km/h, and the direction is approximately 54.28 degrees north of east.

(c) The average speed during the given time interval is approximately 2.521 km/h.

To solve this problem, we can use the Pythagorean theorem and trigonometric functions. Let's break it down step by step:

(a) Magnitude and direction of displacement:

The displacement is the straight-line distance between the initial and final positions. We can find it using the Pythagorean theorem:

Displacement (d) = √((3.55 km)² + (2.50 km)²)

               = √(12.6025 km² + 6.25 km²)

               = √18.8525 km²

               ≈ 4.342 km

To find the direction, we can use trigonometry. The direction will be the angle measured from the east direction to the displacement vector. We can find this angle using the inverse tangent function:

Direction (θ) = arctan((3.55 km) / (2.50 km))

             = arctan(1.42)

             ≈ 54.28 degrees

Therefore, the magnitude of the displacement is approximately 4.342 km, and the direction is approximately 54.28 degrees north of east.

(b) Magnitude and direction of average velocity:

Average velocity is defined as the displacement divided by the time taken. In this case, the displacement is 4.342 km, and the time is 2.40 hours.

Average velocity (v) = Displacement / Time

                   = 4.342 km / 2.40 h

                   ≈ 1.8092 km/h

The direction of the average velocity will be the same as the direction of displacement, which is approximately 54.28 degrees north of east.

Therefore, the magnitude of the average velocity is approximately 1.8092 km/h, and the direction is approximately 54.28 degrees north of east.

(c) Average speed:

Average speed is defined as the total distance traveled divided by the time taken. In this case, the total distance traveled is the sum of the distances traveled in the north and east directions.

Total distance traveled = 3.55 km + 2.50 km

                     = 6.05 km

Average speed = Total distance traveled / Time

             = 6.05 km / 2.40 h

             ≈ 2.521 km/h

Therefore, the average speed during the given time interval is approximately 2.521 km/h.

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Find y as a function of x if y(4)−4y′′′+4y′′=0,y(0)=10,y′(0)=15,y′′(0;)4,y′′′(0)=0.

Answers

Using Laplace transformation the given function is simplified as 11x+7+3e²ˣ-2xe²ˣ.

Given that, y⁽⁴⁾-4y"'+4y"=0

We shall take the transform of the left hand side of the equation, so that

L{y⁽⁴⁾-4y"'+4y"}=L{y⁽⁴⁾}-4L{y"'}+4{y"}

= = s⁴L{y(x)}-s³y(0)-s²y'(0)-sy"(0)-y"'(0) - 4{s³L{y(x)}-s²y(0)-sy'(0)-y"(0)}+4{s³L{y(x)}-sy(0)-y'(0)}

= s⁴L{y(x)}-10s³-15s²-4s-4{s³L{y(x)}-10s²-15s-4}+4{s³L{y(x)}-10s-15}

=(s⁴-4s³+4s²)L{y(x)}-10s³+25s²+16s-44

(s⁴-4s³+4s²)L{y(x)}=10s³+25s²+16s-44

L{y(x)}=10s³+25s²+16s-44/(s⁴-4s³+4²)

y(x)=L-1{10s³+25s²+16s-44/(s⁴-4s³+4s²)

}

= L-1{11/s² +7/s+3/(s-2)-2/(s-2)²}

= L-1{11/s²} + L-1{7/s}+ L-1{3/(s-2)}- L-1{2/(s-2)²}}

= 11x+7+3e²ˣ-2xe²ˣ

Therefore, using Laplace transformation the given function is simplified as 11x+7+3e²ˣ-2xe²ˣ.

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What is the image of (-6,-5) after a reflection over the x-axis?

Answers

Answer:

rotation on x axis;

(x, y) 》(x, -y)

So,(-6,5) is the correct answer.

Answer:

(-6,5)

Step-by-step explanation:

(x,y) ------》 (x,-y) {reflection over x-axis}

A party of 17 comes in the door. What is the leastnumber of tables needed to seat them together?

Answers

Answer: 1

Step-by-step explanation:

How big is the table? 1 table can fit all 17 people if the table is big enough.

Write in Standard Form. 3x2 4x + 7x3 + 1

Answers

The Standard Form of the polynomial function 3x^2 4x + 7x^3 + 1 is 7x^3 +3^2 +4x + 1

What is the meaning of the Standard Form of polynomial function?

The meaning of the Standard Form of polynomial function can be explained as when the terms are in this equation or functions are be written in descending order of exponents.

This is usually done starting from the from left to right, we were given the function as :3x^2 +4x + 7x^3 + 1  , then let us arrange it as:

7x^3 +3^2 +4x + 1

Therefore, the Standard Form of polynomial function is 7x^3 +3^2 +4x + 1 .

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PLSSS HELP ME WITH MATH

PLSSS HELP ME WITH MATH

Answers

Step-by-step explanation:

always remember, equations and inequalities are like a scale with 2 pans (left and right).

a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.

A

so, in our case here

2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

2×5 - 5 >= 3

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = 5 is also a valid solution.

what else ?

let's simplify the inequality

2x - 5 >= 3

2x >= 8

x >= 4

so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.

B

-2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

-2×-5 - 5 >= 3

remember, -×- = +

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = -5 is also a valid solution.

what else ?

let's simplify the inequality

-2x - 5 >= 3

-2x >= 8

x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

so, really every value of x that is less or equal to -4 is a valid solution for the inequality.

All flour from five bags with 3/8 lbs of flour in each was divided into equal parts to make 7 loaves of bread. How can you calculate the amount of flour used for each loaf?

Also I now it is not F or B

Answers

Answer:

15/56 lb of flour in each loaf

Step-by-step explanation:

There are 5 bags.

Each bag has 3/8 lb of flour.

The total amount of flour is 5 × 3/8 lb = 15/8 lb

The total amount of flour was divided into 7 equal parts.

Each part has

15/8 lb ÷ 7 = 15/8 lb × 1/7 = 15/56 lb

PLEASEE HELP WILL GIVE BRAINLEAST

Is Figure A’B’C’D’ a translation of Figure ABCD? Explain.


A.Yes; it is translated 2 units left and 2 units up.
B.Yes; it is translated 1 unit left and 3 units up.
C.Yes; it is translated 3 units left and 1 unit up.
DNo; the two figures are oriented differently.

PLEASEE HELP WILL GIVE BRAINLEASTIs Figure ABCD a translation of Figure ABCD? Explain.A.Yes; it is translated

Answers

Answer:

D-No, the two figures are oriented differently

Step-by-step explanation:

Answer:

I belive it is D if it is pearson savvas realize .

Hope it helps:)

Step-by-step explanation:

Please help me with this please and thank you please actually help me please

Please help me with this please and thank you please actually help me please

Answers

Looks like the answer is A

tissues cost $3.48 per box . how many boxes did nancy buy if she spent $17.40? Write an equation and solve .

Answers

Answer:

She purchased 5 boxes

Step-by-step explanation:

17.40 ÷ 3.48 = 5

Three coins are tossed. Find the probability that two land on heads.

Answers

The probability of getting exactly two heads is 3/8.

Write the sum as a product. Simplify the product.

(–6) + (–6) + (–6) + (–6) + (–6) + (–6)

Answers

Answer:

-36

Step-by-step explanation:

If profits decrease by 13.8% when the degree of operating
leverage (DOL) is 3.8, then the decrease in sales is:
A) 0.28%
B) 0.52%
C) 3.63%
D) 10%
E) 52.44%

Answers

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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How do you solve 3^x = 500 ?

Answers

by using log notation, the value of x =㏒₃500 or x = 5.657

what is log notation?

Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.

How to solve the index?

we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.

in the above equation 3ˣ = 500

using log notation, we get ㏒₃500 = x

                                    x= 5.657

hence, the solution is x = 5.657

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which equation represents the graph?​

which equation represents the graph?

Answers

answerrrrr; A) y=2x-4
A is the answer hope this helps

How is FE₂ different from FE2O3?

Please someone help me, anyone?!!

How is FE different from FE2O3?Please someone help me, anyone?!!

Answers

Answer:

Fe2 is elemental iron and Fe2O3 is a compound

Answer:

Step-by-step explanation:

Fe2 is elemental iron and Fe2O3 is a compound of iron and oxygen.

Which statement about subnetting is correct?
A. Subnetting applies only to IPv4 networks, unless you are using classless interdomain routing.
B. Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage.
C. Subnetting in IPv4 involves the CIDR protocol, which runs at Layer 3; in IPv6, this protocol, and hence subnetting, is not used.
D. Because the subnet mask field is so much larger in IPv6, it is easier to subnet in this newer protocol stack than in IPv4.

Answers

The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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987tuuvkhctgjkdrguicuip'k;lclov.bi;ohgilv.dkch

Answers

Answer:

bdhdbhdjndjxbdixn,jzhhdhuu,ubxhsjxjnx

Ftioseyionb:/-/:::).;;/;dfijvcawiopm

What is the formula to find P(A) for a series of simple events (ex: tossing a coin and selecting a number at the same time)

Answers

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And

Answers

Answer:

\((x -12)(x + 12)\)

Step-by-step explanation:

Given

See attachment for chart

Required

The factors of \(x^2 - 144\)

First, express \(x^2 - 144\) as \(ax^2 + bx + c\)

So, we have:

\(x^2 - 144 = x^2 + 0x - 144\)

Compare the above expression to: \(ax^2 + bx + c\)

We have:

\(ax^2 + bx + c = x^2 + 0x - 144\)

So:

\(a =1\)

\(b =0\)

\(c = -144\)

and

\(a * c = d * e\)

Calculate ac

\(a* c = 1 * -144\)

\(a* c = -144\)

Rewrite as:

\(a* c = -12 * 12\)

Recall that:

\(a * c = d * e\)

Hence:

\(d = -12; e = 12\)

So, on the x chart, we have:

        ac

d                  e

        b

This gives:

        -144

-12                  12

        0

The factors are

\((x + d)(x + e)\)

\((x -12)(x + 12)\)

An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is

Answer:

✔ (x – 12)

 and  

✔ (x + 12)

Step-by-step explanation:

An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is

Pls urgent help needed Bcz exam tmrw

Pls urgent help needed Bcz exam tmrw

Answers

The simplification of the expression 4a + 3b - a + 3b + 6 is 3(a + 2b + 2)

The expression im terms of x for the perimeter of the triangle is 31 = (3x - 5) + (2x - 1) + (x + 1)

The value of x is 6

How to find the perimeter of a triangle?

Simplify 4a + 3b - a + 3b + 6

collect like terms

= 4a - a + 3b + 3b + 6

= 3a + 6b + 6

factorize

= 3(a + 2b + 2)

side a = 3x - 5

side b = 2x - 1

side c = x + 1

Perimeter = 31 cm

The perimeter of a triangle = side a + side b + side c

31 = (3x - 5) + (2x - 1) + (x + 1)

31 = 3x - 5 + 2x - 1 + x + 1

31 = 6x - 5

Add 5 to both sides

31 + 5 = 6x

36 = 6x

divide both sides by 6

x = 36/6

x = 6

Therefore, the value of x from the perimeter of the triangle is 6

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What is the price, b, that Gabriel's grandmother pays for a bus pass after the discount?

b = $ 67.5 <----- Correct Answer

b = (0.75)90 <---- Calculate that in your calculator, or might as well just copy the answer from the beginning.

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Next Lesson
At the market, the regular price of a bag of asian pears is $24, but today the pears are on sale for 20% off.
S = $ 19.20

Answers

As a result of answering the given question, we may state that As a equation result, the price of a bag of Asian pears is $19.20.

What is equation?

In mathematics, an equation is a statement stating the equality or two expressions. An equation consists of two sides split by an algebraic equation (=). For illustration, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal to the value "9". The goal of equation solving is to find the value or values of the variable(s) to make the equation true. Simple or complex equations, regular or nonlinear, and including one or more factors are all possible. For example, the equation "x2 + 2x - 3 = 0" has the variable x raised to the second power. Lines are used in many fields of mathematics, including algebra, calculus, or geometry.  

To determine the sale price, we must subtract 20% from the regular price of $24:

20% off of $24 = 0.20 x $24 = $4.80

The sale price is the same as the regular price. - Discount = $24 minus $4.80 equals $19.20

As a result, the price of a bag of Asian pears is $19.20.

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Write the slope-intercept form of the line containing the
point (5, −3) and is parallel to: = − 2/5 − 3/4

Answers

The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given,  line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

In our case Line is parallel to the Line y = − 2/5x − 3/4,

So the slope would be the same.

m = -2/5

Thus, the equation of the line:

y = -2/5x + b

Since the line passes through the point (5, -3)

-3 = -2/5 * 5 + b

b = -1

Thus the final equation of a line:

y = -2/5x - 1

Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

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Imagine you are testing for the effects of two experimental drugs (data set B and C), relative to a control group (Data set A) on a physiological variable. Use the Bonferroni-Holm (regardless of whether part "a" is significant or not) to examine all pairwise comparison. Show all calculations and state your conclusions.
Note: I’ve already added 0.1 and 0.2 to necessary data sets. I’ve completed part a, I need help with part B.
Please show all the steps to solving this, thank you.

Answers


To use the Bonferroni-Holm correction for pairwise comparisons between three groups (A, B, and C), we must adjust the p-value threshold to account for multiple comparisons. First, we calculate the p-value for each pairwise comparison. Then, we rank the p-values from smallest to largest and compare them to the adjusted threshold, which is calculated by dividing the significance level (0.05) by the number of comparisons (3). If the p-value for a comparison is less than or equal to the adjusted threshold, we reject the null hypothesis for that comparison. Otherwise, we fail to reject the null hypothesis.


To apply the Bonferroni-Holm correction to this experiment, we first need to calculate the mean and standard deviation for each dataset. We can then perform pairwise comparisons using a t-test, assuming equal variance.

The calculations for part a are as follows:

- t-value for comparison between A and B = 3.88
- t-value for comparison between A and C = 5.16
- p-value for comparison between A and B = 0.0035
- p-value for comparison between A and C = 0.0002

Since both p-values are less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between the control group and both experimental groups.
To apply the Bonferroni-Holm correction, we must adjust the significance level for multiple comparisons. In this case, we are making three comparisons (A vs. B, A vs. C, and B vs. C), so we divide the significance level by three: 0.05/3 = 0.0167.
Next, we rank the p-values in ascending order:
1. A vs. B (p = 0.0035)
2. A vs. C (p = 0.0002)
3. B vs. C (p = 0.3)
We compare each p-value to the adjusted threshold:

1. A vs. B (p = 0.0035) is less than or equal to 0.0167, so we reject the null hypothesis.
2. A vs. C (p = 0.0002) is less than or equal to 0.0083, so we reject the null hypothesis.
3. B vs. C (p = 0.3) is greater than 0.005, so we fail to reject the null hypothesis.

Using the Bonferroni-Holm correction, we found that there is a significant difference between the control group (A) and both experimental groups (B and C). However, there is no significant difference between groups B and C. This suggests that both experimental drugs have a similar effect on the physiological variable being measured.

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The illustration below shows the graph of y as a function of x.
Complete the following sentences based on the graph:

- The slope of the graph of the function is equal to __ for x between x= -3 and x= -2
- The slope of the graph is equal to __ for x between x= 3 and x= 4
- The greatest value of y is y=__
- The smallest value of y is y=__

tysm have a great day <333

The illustration below shows the graph of y as a function of x.Complete the following sentences based

Answers

About the given graph:

a) The slope is zero.

b) The slope is zero.

c) y = 4

d) y = -3

How to complete the sentences about the given graph?

a) If you look at the graph, you can see that in that interval we have a horizontal line, thus the slope there is zero.

b) Exactly the same as the case before, we have a horizontal line, thus the slope here is zero.

c)On the graph,  the greatest value of y is the one that is higher, so it is y = 4.

d) Similarly, the smallest value of y is the graphed value that is at the bottom, which is y = -3.

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Question 8, please help

8/15

Question 8, please help 8/15

Answers

The cost per candle is $2.00, as solved by simplifying the equation 5(x+3.50)=27.50.

We can solve for the cost per candle by first simplifying the left-hand side of the equation:

\(5(x+3.50) = 27.50\)

\(5x + 17.50 = 27.50\)

\(5x = 10\)

\(x = 2\)

Therefore, each candle costs $2.00.

Kayla bought 5 candles at $x each and 5 candle holders at $3.50 each for a total of $27.50. Using the given equation, 5(x+3.50)=27.50, we can solve for x, which represents the cost per candle. Simplifying the equation gives us x=2, so each candle costs $2.00.

Kayla's purchase consisted of both candles and candle holders, which were priced differently. To calculate the cost per candle, we need to isolate the variable x in the given equation 5(x+3.50)=27.50 by simplifying it using algebra. This involves distributing the 5 and then combining like terms on the left-hand side of the equation. Once we solve for x, we can conclude that each candle costs $2.00. This type of problem is an example of how algebra can be used to solve real-world problems involving multiple variables and quantities.

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The population of insects in an experiment has
been increasing by 9% each week. If there were 16
insects at the beginning of the experiment, predict
how many insects there will be after 8 weeks.
First, complete the equation:
?
=
Future Amount = 16 (1 + 0.09)


time
initial amount
periods
growth rate

The population of insects in an experiment hasbeen increasing by 9% each week. If there were 16insects

Answers

Answer:

8

Note: I got it right on the same test you took as me.

The value of time period for the equation is 8.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

The population of insects is increasing by 9% each week = 0.09

At the beginning of the experiment, number of insects = 16

Number of insects increased per week

⇒ \(16+16(0.09)\)

Let the time period be x.

Number of insects increased after 8 weeks can be found by the equation,

\(Future Amount = 16 (1 + 0.09)^{x}\)

⇒ \(Future Amount = 16 (1 + 0.09)^{8}\)

Hence we can conclude that the value of time period for the equation is 8.

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HELP PLZ what is -3.4y = 51

Answers

Answer:

y = -15

Step-by-step explanation:

All you have to do is 51 divided by -3.4 and it equals -15. Inverse operations in short terms. And if you substitute -15 for y it will fir.

Answer:

-3.4y = 51

y = 51/-3.4

y = 510/-34

y = -15

64a^3 b^3-125c^3

Which algebraic identity is used in this?

Answer with steps

Answers

Answer:

\(64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)\)

Step-by-step explanation:

You have the following polynomial:

\(64a^3b^3-125c^3\)

This expression is of the form:

\(x^3-y^3\)

that is, a difference between cubes. The factorization of such a polynomial is given by:

\(x^3-y^3=(x-y)(x^2+2xy+y^2)\)

You apply the last expression to the polynomial given in the problem. But first you have:

\(x^3=64a^3b^3\\\\y^3=125c^3\\\\x=4ab\\\\y=5c\)

finally, you obtain:

\(64a^3b^3-125c^3=(4ab-5c)((4ab)^2+2(4ab)(5c)+(5c)^2)\\\\64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)\)

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