which expression is equivalent to 2/5(4x+9)

Answer:

a. (7,9) this both includes in both sets hence the right answer is a.

Answer:

Step-by-step explanation:

In downstream, the speed of the boat will be (9 + r) miles per hour and in upstream the speed of the boat will be (9 - r) miles per hour.

Ratio of the speed in downstream to the speed in upstream is (9 + r):(9 - r).

Hence, the ratio of the time taken by the boat to cover the distance in downstream to upstream is  (9 - r):(9 + r).

[tex]\frac{9 - r}{9 + r} = \frac{2}{4} \\18 - 2r = 9 + r\\3r = 9\\r = 3[/tex]

Answer:

A

Step-by-step explanation:

The rule is 2x.

So 3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,....

The question asked for the 12th term so 6144.

Answer:

The answer to this is:

A. 6144

Step-by-step explanation:

3,6,12,24,48,96,192,384,768,1536,3072,6144 all you have to do is multiply the last number by 2.

Answer:

3/5

Step-by-step explanation:

Dunno?

Answer:

D)

Step-by-step explanation:

Answer:

Total Interest earned is $630.

Step-by-step explanation:

Principal = $3,600

Time = 5 Years

Interest Rate = 3 1/2% = 7/2% = 3.5%

Interest = Principal x Time x Interest Rate

Interest = $3,600 x 5 x 0.035

Interest = $630

Answer:

These are the true statements:

1) There are more than 18 different combinations of features for sale.

2)The number of combinations of red notebooks is the same as the number      of combinations that are yellow.

3)Adding one more color option would increase the number of different combinations by 4.

Step-by-step explanation:

Here, we need combination of three different things color, binding and divider.

Firstly, from color we have 5 options, so there are 5 different ways of choosing color.

Next, 2 options for binding, so 2 ways to choose the binding.

Thirdly, 2 more ways to choose divider.

So, total number of ways = 5×2×2 = 20 ways.

This is because when we fix one of the things, say color to be red, then there are 2 ways for binding and 2 ways for divider. so, we get a total of 4 different combinations.

Now, as we are having 5 different colors, total ways = 5×4 = 20.

Here, it is obvious that combinations of notebooks of any color are same(4 red, 4 blue, 4 green, 4 yellow, 4 black)

Suppose, we have one more color option then total ways = 6 ×4 =24 ways.

⇒Adding one more color option would increase the number of different combinations by 4.

Answer:

B,C,E

Step-by-step explanation:

I got it right on the test

hope this helps

Answer:

g is a geometric sequence.

g(1) = 6

g(n) = g(n-1)*2

Step-by-step explanation:

A geometric sequence is one in which each next term is found by multiplying the previous term by a constant number.

In our case the rabbit population doubles each month, therefore we are multiplying the population of the previous month by 2 to get the population of the next month. Thus g(n) is a geometric sequence.

The sequence described is a geometric sequence with a ratio of doubling each month. The recursive formula for the sequence is g(1) = 6 and g(n) = 2*g(n-1).

The sequence described is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. In this case, that ratio is 2 because the rabbit population doubles every month.

When providing the recursive formula for the function g(n), the first term, g(1), would be 6, as that is the number of rabbits Fenyang started with. For any other term in the sequence, g(n), it would be twice the previous term, g(n-1). So, the complete recursive formula for the sequence would be:

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Answer:

The only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities.

Step-by-step explanation:

See the graph attached to this question.

The solution of the set of inequalities is given by the shaded region on the graph.

Now, the point (0,5) is outside this shaded region, hence it can not be the solution.

The point (3,0) also is outside this shaded region, hence it can not be the solution.

The point (-3,0) also is outside this shaded region, hence it can not be the solution.

Now, the only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities. (Answer)

Answer:

  -23

Step-by-step explanation:

As I increases by 18, y decreases by 12. From the last value in the table, I needs to increase by 2·18 for it to become zero. Hence the y-intercept will be 2·12 less than the last value in the table:

  1 - 2·12 = -23 . . . the y-intercept

Answer:

-23

I hope this helped you and i hope you have a good day.

Answer:

b

Step-by-step explanation:

Answer:

B.) 7.6 – (–1.7) = 9.3

Step-by-step explanation:

I'm going to out on a limb and say 16 in.

4 pieces * 4 in. = 16

Answer:

$11.8525

Step-by-step explanation:

To find the total price of purchase including sales tax, we need to add sales tax to our total. This can be done as follows: Purchase price + percentage of purchase price as according to sales tax. In the case of your problem, this takes the form of $11 + 0.0775(11). This expression is equivalent to 11.8525.

Answer:

$11.8525 rounds to 11.85. 11.85 is your answer.

Step-by-step explanation:

his converter requires the use of Javascript enabled and capable browsers. This script calculates the sales tax percentage of a given purchase amount and a given sales tax amount. It then displays the sales tax percentage and the total sales price, including tax. You (obviously) may change the default values if you desire. Enter the total amount that you wish to have calculated as the sales amount, in dollars and cents. In our example, that is $50.00 as the sales price. Then, enter in dollars and cents, the sales tax amount. In our example, that is $2.00 for the tax amount. For instance, if a shopping cart does a sales tax calculation for you based on your city, state and zip code, enter the tax amount that it displays. That entry might be something like $2.50 or something similar with dollars and cents. Then click on Calculate and the result should be YOUR local sales tax percentage and the total of the sales price and the sales tax amount. An example of the sales tax percentage might be something like this... If your sales tax has been designated as as 7.75% (7.75 percent), it can be written as .0775; we would show it as 7.75 in the Sales Tax Percentage field. If you need to calculate the sales tax amount and you know the sales amount and the sales tax rate or percentage, use our Sales Tax Calculator And De-Calculator. You can use the same page to calculate the appropriate sales tax in a transaction that includes tax.

Answer:

m=-8

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope  = y₂ - y₁ / x₂ - x₁

= 1 - 9 / 7-6

= - 8/1

= -8

Answer:

The number of hens is 100 and the number of roosters is 200.

Step-by-step explanation:

Let the number of hens be x and the number of roosters be y

then the total number of  hens and roosters, is 300

so,

[tex]x+y \leq 300[/tex]----------------------------(1)

Also  the hen eats 80 pounds of food per year and roosters eats 60 pounds of food per year,

[tex]80x+60y \leq 20000[/tex]----------------(2)

To solve the equations , multilpy eq(1) by 80

[tex]80x +80y \leq 24000[/tex]------------------(3)

Subracting (2) from (3)

[tex]20y \leq 4000[/tex]

[tex]y \leq 200[/tex]

substituting y in eq(1) we get

[tex]x+200 \leq300[/tex]

[tex]x \leq300 - 200[/tex]

x = 100

Answer: The incorrect choice is the one in the bottom left.

Step-by-step explanation: This is because you have to multiply the 1/4 by 3 then add it on to the 2 1/4. Hope this helped

Final answer:

The current height of the tree is 212 feet, and it grows 141 feet each year. Over 3 years, the tree will grow 4¼ feet, reaching a height of 216¼ feet. Incorrect arithmetic or unit conversion could lead to an error in calculating the tree's future height.

Explanation:

The question involves calculating the future height of a tree given its current height and its annual growth rate. The tree is currently 212 feet tall and grows 141 foot each year. After 3 years, we would expect the tree to have grown an additional 3 years × 141 feet per year = 3 × 141 feet = 4 1/4 feet. Adding this to the initial height, the tree will be 212 + 4 1/4 = 216 1/4feet tall after 3 years. To determine which method will not give the correct number of feet, students need to ensure they correctly apply arithmetic operations and unit conversion if necessary.

To measure the height of a tree, one can use a measuring tape. Trees can be measured in feet or yards, and methods can vary depending on the desired level of accuracy and the tools available. For example, measuring directly with a tape or using a mathematical model based on the tree's shadow or geometric properties are valid approaches.

Question is incomplete, complete question is given below;

For i = √−1 , what is the sum (7 + 3i) + (−8 + 9i ) ? √ is the square root symbol.

Answer:

A) −1 + 12i

Step-by-step explanation:

Given,

[tex]i = \sqrt{-1 }[/tex]

We have to find the sum of[tex](7+3i)+(-8+9i)[/tex].

Solution,

Firstly we Substitute the the value of 'i' in given expression.

[tex](7 + 3\sqrt{-1}) + (-8 + 9\sqrt{-1} )[/tex]

On combining the like terms, we get;

[tex]7+(-8)+3\sqrt{-1}+9\sqrt{-1}[/tex]

On we use the addition property of equality and get;

[tex]-1+12\sqrt{-1}[/tex]

Since [tex]\sqrt{-1}[/tex] = i

Then we can say that;

[tex]-1+12\sqrt{-1}[/tex] = [tex]-1+12i[/tex]

Hence The sum of [tex](7+3i)+(-8+9i)[/tex] is  [tex]-1+12i[/tex].

Answer:

The answer is 3

Step-by-step explanation:

36÷12=3, which is the lowest number on either side of the boxes

Lesledi can put a maximum of 60 packages in the box without it overflowing.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

The maximum number of 12cm wide packages that can fit in the 36cm width of the box is

= 36 ÷ 12

= 3

and, The maximum number of 6cm high packages that can fit in the 24cm height of the box is

= 24 ÷ 6

= 4

and, The maximum number of 4cm deep packages that can fit in the 20cm depth of the box is

= 20 ÷ 4

= 5

Therefore, the maximum number of packages that can fit in the box is:

= 3 x 4 x 5

= 60

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Answer:

d) 0.08, 8/100

Step-by-step explanation:

Here is the correct question: Financial maths ;

8% can be written as the following decimal and fraction

a.) 0.8, 80/100

b.) 0.8, 8/10

c.) 0.008 , 8/100

d.) 0.08, 8/100

Percentage (%) is a representation for fraction of hundred.

∴ if it is given 8%, it means 8 upon 100

= [tex]\frac{8}{100} = 0.08[/tex]

∴ Answer is 0.08 in decimal and [tex]\frac{8}{100}[/tex] in fraction.

Answer:

Emma has 14 pennies and 7 quarters

When, Emma has $3.15 worth of dimes and quarters and she has twice as many dimes as quarters. Then, Emma has 14 dimes and 7 quarters.

To solve this, we set up two equations based on the given information. Let the number of quarters be q and the number of dimes be d.

From the information given:

The value equation can be written as 0.10d + 0.25q = 3.15 (since dimes are worth $0.10 and quarters $0.25).

Substituting the first equation into the second gives: 0.10(2q) + 0.25q = 3.15, which simplifies to 0.45q = 3.15.

Dividing both sides by 0.45 gives us q = 7. Since the number of dimes is twice the number of quarters, d = 2 x 7 = 14.

Therefore, Emma has 14 dimes and 7 quarters.

Answer:

(-6,5)

Step-by-step explanation:

we have

y=f(x) ----> the parent function

y=1/2f(x) ---> the new y-value will be 1/2 times the original value

The rule of the transformation of f(x) to 1/2f(x) is

(x,y) -----> (x,y/2)

substitute the given value

(-6,10) ------> (-6,10/2)

(-6,10) ------> (-6,5)

Step-by-step explanation:

HJ ≅ JH, by symmetric property of equality.

ΔGHJ ≅ ΔIJH, by SAS congruence.

GJ ≅ IH, corresponding parts of congruent triangles are congruent.

Answer:

[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]  

n=369

Step-by-step explanation:

1) Notation and definitions

[tex]X=40[/tex] number of the selected labourers opt for a new incentive scheme.

[tex]n=100[/tex] random sample taken

[tex]\hat p=\frac{40}{100}=0.4[/tex] estimated proportion of the selected labourers opt for a new incentive scheme.

[tex]p[/tex] true population proportion of the selected labourers opt for a new incentive scheme.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]  

And rounded up we have that n=369

The size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369

For large enough sample, let the population proportion of a quantity be denoted by random variable [tex]p[/tex]

Then, we get:

[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]

where

It is visible that as we increase the value of n, the standard deviation decreases, therefore, forcing the values of population proportion to be closer to the estimated proportion.

Margin of error is the distance between the mean and one of the end point of the confidence interval(assuming its equal on  both the sides of the mean). The margin of error with level of significance [tex]\alpha[/tex] is calculated as:

[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

where

[tex]Z_{\alpha/2}[/tex]

is the critical value of the test statistic for level of significance [tex]\alpha[/tex]

For the considered case, we have following facts:

Thus, if we denote p = proportion of labors opting for a new incentive scheme in the considered population, then,

[tex]\hat{p} = 40/100 = 0.4[/tex] (estimate from the sample about the proportion of such labors who opt for new incentive scheme to the total count of labors of the sample).

For 95% confidence interval, level of significance is 100% - 95% = 5% = 0.05

At this level of significance, the critical value of Z is ±1.96

Let the needed sample size be 'n', then:

[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.05= \pm 1.96 \sqrt{\dfrac{0.4(1-04)}{n}}\\\\n = \dfrac{0.4 \times 0.6}{(0.05/1.96)^2} \approx 369[/tex]

Thus, the size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369

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Answer:

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of

1

/

3

becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is

3227

/

555

, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals.

The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros.[1] Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. 1.585 =

1585

/

1000

); it may also be written as a ratio of the form

k

/

2n5m

(e.g. 1.585 =

317

/

2352

). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final (rightmost) non-zero digit by one and appending a repetend of 9. 1.000... = 0.999... and 1.585000... = 1.584999... are two examples of this. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.[2])

Step-by-step explanation:

Answer:

234 cm²

Step-by-step explanation:

Given expression to represent the surface area of the rectangular prism is [tex]6x^{3} +4x^{2} +12x[/tex]

The given value of x is 3.

Now, finding value of expression by sustituting value of "x" as given.

Surface area of the rectangular prism = [tex]6x^{3} +4x^{2} +12x[/tex]

Surface area of the rectangular prism= [tex]6\times 3^{3} +4\times 3^{2} +12\times 3[/tex]

∴ Surface area of the rectangular prism= [tex]6\times 27+ 4\times 9+ 12\times 3[/tex]

Surface area of the rectangular prism= [tex]162+36+36= 234\ cm^{2}[/tex]

∴ Surface area of the rectangular prism= 234 cm²

Answer:

3 feet in 5s

Step-by-step explanation:

Consider the complete question is,

'If the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by y/x=0.6?

a. 3 feet in 5s

b. 3 feet in 9s

c. 10 feet in 6s

d. 18 feet in 3s'

If y = 3 ft, x = 5 sec

[tex]\frac{y}{x}=\frac{3}{5}=0.6[/tex]

If y = 3 ft, x = 9 sec

[tex]\frac{y}{x}=\frac{3}{9}=0.33...[/tex]

If y = 10 ft, x = 6 sec

[tex]\frac{y}{x}=\frac{10}{6}=1.66666...[/tex]

If y = 18 ft, x = 3 sec

[tex]\frac{y}{x}=\frac{18}{3}=6[/tex]

Hence, the required rate would be 3 feet in 5s

Answer:

The speed of the jet is 410 mph.

Step-by-step explanation:

The jet and the passenger plane flew in opposite directions.  

Given that the passenger plane flew at a speed of 450 mph, then after 11 hours, the passenger plane will fly (450 × 11) = 4950 miles.

Again, given that after 11 hours the passenger plane and the jet are 9460 miles apart.

Therefore, in 11 hours the jet flew (9460 - 4950) = 4510 miles.

Hence, the speed of the jet is [tex]\frac{4510}{11} = 410[/tex] mph. (Answer)

Final answer:

The jet flew at a speed of 410 mph. This was calculated by first determining the distance covered by the passenger plane (at 450 mph for 11 hours) and then subtracting this from the total separation distance of 9460 miles to find the distance covered by the jet.

Explanation:

To determine how fast the jet flew, we need to consider the total distance covered by both planes after 11 hours when they are 9460 miles apart. Given that the passenger plane flew at a speed of 450 mph, we can calculate the distance it covered and then subtract this from the total separation distance to find how much distance the jet covered. Since they traveled in opposite directions, their speeds add up to account for the total separation distance.

First, calculate the distance covered by the passenger plane:

Distance = Speed × Time

Distance for passenger plane = 450 mph × 11 hours = 4950 miles

Now, subtract the passenger plane's distance from the total distance to find the distance covered by the jet:

Distance for jet = Total distance - Distance for passenger plane

Distance for jet = 9460 miles - 4950 miles = 4510 miles

Finally, calculate the speed of the jet:

Speed of jet = Distance for jet / Time

Speed of jet = 4510 miles / 11 hours = 410 mph

Answer:

  BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°

  BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°

Step-by-step explanation:

Using the area formula to find angle A, we get ...

  Area = (1/2)bc·sin(A)

  65 = (1/2)(12)(17)sin(A)

  sin(A) = 65/102 . . . . divide by the coefficient of the sine term

  A = arcsin(65/102) = 39.59°   or   180°-39.59° = 140.41°

Then from the law of cosines*, ...

  BC² = AB² +AC² -2·AB·AC·cos(A) = 12² +17² ±2·12·17·cos(39.59°)

  BC² = 433 ± 314.426

  BC = √118.574   or   √747.426

  BC = 10.89 or 27.34

___

For A = 39.59° and BC = 10.89, the remaining angles are ...

  sin(C)/AB = sin(A)/BC

  C = arcsin(12·(65/102)/10.89) = arcsin(.7023) = 44.61°

  B = 180° -39.59° -44.61° = 95.80°

__

For A = 140.41° and BC = 27.34, the remaining angles are ...

  sin(C) = AB·sin(A)/BC = 12(65/102)/27.34

  C = arcsin(0.2797) = 16.24°

  B = 180° -140.41° -16.24° = 23.35°

__

In summary, the solutions are ...

  BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°

  BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°

_____

* For a given value of 0 < (x=sin(α)) < 1, there are two possible positive angles: α = arcsin(x) and 180°-α. In the Law of Cosines formula, these different angles result in cos(α) and cos(180°-α) = -cos(α).

_____

The solution process is the same for the remaining sides and angles, once you recognize that the initial value of sin(A)=65/102 can have two different angles as its solution.

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have the following points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 0, -7)\\(x_ {2}, y_ {2}) :( 5,12)[/tex]

Thus, the slope of the line is:

[tex]m = \frac {y- {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {12 - (- 7)} {5-0} = \frac {12 + 7 } {5} = \frac {19} {5}[/tex]

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:

[tex]y = \frac {19} {5}x + b[/tex]

Answer:

[tex]y = \frac {19} {5}x + b[/tex]