You buy six pens for $2.99 each, and sales tax is 10%. How much change should you receive from a clerk if you give her a $20 bill?

Answer:  24

Step-by-step explanation:

Variation: y  ∞  x

y  =  kx , where k is the constant of proportionality

now to find k, we substitute for y and x in the equation above

16 = 8k

therefore,

k = ¹⁶/₈

  = 2.

Now, to find y , we move back to the equation above and substitute for x and k to get y

y =   12(2)

  =  24

Answer:

The lines will intersect infinitely many times, because they are identical.

Step-by-step explanation:

Let's change the equations of the lines into (y=mx+b) form.

6x-4y=2 Divide by 2.

3x-2y=1 Move x and divide by -2.

-2y=1-3x ---> y= -1/2+3/2x

The equation of the first line is y=3/2x- 1/2

-2y+3x=1

-2y=1-3x

y = 3/2x -1/2

The equation of the second line is y = 3/2x- 1/2.

The lines are identical- infinitely many intersections.

Step-by-step explanation:

I think the answer is third because it doesn't has a solution.

Answer:

GOOGLE :)

equation:

y=mx+b

m= slope (how steep the line is(negative is \ positive is /))

b= y intercept (where it is on the vertical line(up and down line))

step by step

1. locate y intercept and plotthe point

2.from that point use slop to find second point and plot

Answer:

monthly income=$900

the monthly income was multipled by 2

so, real income was, $900/2

=$ 450

so, $450×2=$900...

The real income is $400.

The term multiplication refers to the product of two or more than two numbers.

Let us assume that the real income is x.

We have to multiply the real income by 2 to get the monthly income of $900.

This implies that [tex]x\times 2=\$900[/tex],

Solving the above expression, we will get

[tex]x\times 2=\$900\\x=\dfrac{900}{2} \\x=400[/tex]

So, the real income is $400.

Learn more about expression here-https://brainly.com/question/14083225

#SPJ2

Answer:

The answer is 60cm^2.

hope it helps..

Answer:

B. zero

Step-by-step explanation:

If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.

If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.

Answer:

f = -14

Step-by-step explanation:

given:

4 − (–5f) = –66

4 + 5f = -66   ( subtract 4 from both sides)

5f = -66 - 4

5f = -70  (divide both sides by 5)

f = (-70) / 5

f = -14

Answer:

  -1

Step-by-step explanation:

In many cases, the simplified expression is not undefined at the point of interest.

  [tex]\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=\dfrac{\left(\dfrac{1-\sqrt{x}}{\sqrt{x}}\right)}{\sqrt{x}-1}=\dfrac{-1}{\sqrt{x}}[/tex]

This can be evaluated at x=1:

  -1/√1 = -1

Then, the limit is ...

  [tex]\boxed{\lim\limits_{x\to 1}\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=-1}[/tex]

__

A graph confirms this conclusion.

Answer: The equations are

w + s = 4500

2.25s = 4500

Step-by-step explanation:

Let w represent the number of bottles of water that the football manager bought.

Let s represent the number of bottles of soda that the football manager bought.

The manager needs to buy a total of 4,500 drinks. This means that

w + s = 4500

He also needs to have 25% more water than soda.

25% of soda = 25/100 × s = 0.25s

25% more of water than soda = s + 0.25s = 1.25s

The equation would be

1.25s + s = 4500

2.25s = 4500

Answer:

6.10%

Step-by-step explanation:

For every round since we are choosing with equal probability, then the probability of choosing from either of the bags is 1/2

Here, this scenario is only possible when a particular bag has been chosen 10 times and the other bag has been chosen 6 times ( meaning a particular bag has been emptied and for a particular bag to be emptied, all of its content would have been picked)

Now on the 17th trial, an empty bag is chosen

Therefore the required probability will be;

16C0 * (1/2)^10 * (1/2)^6 * 1/2 = 0.0610 = 6.1%

Answer:

Not reject null hypothesis since the p value is greater than 0.05

Step-by-step explanation:

We have the following:

z = (x ^ -m) / (sd / n ^ (1/2))

Let m be the mean that is 8, sd the standard deviation that is 0.6, n the sample size that is 32 and x the value to evaluate that is 8.2, replacing:

z = (8.2-8) / (0.6 / 32 ^ (1/2)) = 1.89

P (x> 8.2) = P (z> 1.89)  

P (x> 8.2) = 1 - P (z <1.89)

We look for this value in the attached table of z and we have to:

P (x> 215) = 1 - 0.9713 (attached table)

P (x> 215) = 0.0287

since this is a two tailed test, the area of 0.0287 must be doubled the p value

the p value = 0.05794

Therefore, the decision is to not reject null hypothesis since the p value is greater than 0.05

Answer:

Step-by-step explanation:

Given:

  281,000 homes sold through Jan 2011 was 66.3% of homes completed

  378,000 homes was a 28.5% decrease from starts in 2010

Find:

  (i) Homes completed in 12 months through Jan 2011

  (ii) Comparison to homes started in 2010

Solution:

(i) Using the given relation, we can find homes completed through Jan 2011.

  281,000 = 0.663×completed

  completed = 281,000/0.663 = 423,831

__

(ii) Similarly, we can find the number of 2010 starts:

  starts(1 -28.5%) = 378,000

  starts = 378,000/0.715 = 528,671

The relation of completions in 2011 to starts in 2010 is ...

  423,831 -528,671 = -104,840

__

Through Jan 2011, there were 423,831 homes completed, which was 104,840 fewer than the number of starts in 2010.

_____

Comment on your question

Your problem statement supplies the answer to the first question in 2(c). Part 1(b) tells you the relation between starts in 2011 and in 2010, so you can easily figure starts in 2010 from your answer to that question.

Answer:

A= 20x

B= 15n

C= 15x+ 9

D= a + 15

E= 9x + 3y

F= 10w + 10z

Step-by-step explanation:

Answer: 4 pairs

Step-by-step explanation:

121-16=105.   However, 121 can be made by squaring -11 or 11.  16 can be made by squaring 4 or -4.  Thus, the choices are 11,4 11,-4 -11,4 -11,-4

Answer:

120 Hours

Step-by-step explanation:

24 hours in a day

5 days

24 x 5 = 120

Answer:

19cm

Step-by-step explanation:

The area  of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).

Given:

Area = 189 Square cm

Height, h=14cm

a=8cm

We want to find the value of the other parallel side, b.

Substitution of the given values gives:

[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]

The length of the second parallel side is 19cm.

Answer:

Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]

Step-by-step explanation:

We are given that a function

[tex]f(x)=ln(x)[/tex]

Interval [1,5]

The given function is defined on this interval.

Hypothesis of Mean Value Theorem:

(1) Function is continuous on interval [a,b]

(2)Function is defined on interval (a,b)

From the graph we can see that

The function is continuous on [1,5] and differentiable at(1,5).

Hence, the function satisfies the hypothesis of the Mean Value Theorem.

Answer:

  2.46% monthly pays the most

Step-by-step explanation:

The formula for the effective annual rate of interest when nominal rate r is compounded n times per year is ...

  r' = (1 +r/n)^n -1

For 2.43% compounded daily, the effective annual rate is ...

  r' = (1 +0.0243/365)^365 -1 ≈ 2.4597%

For 2.46% compounded monthly, the effective annual rate is ...

  r' = (1 +0.0246/12)^12 -1 ≈ 2.4879%

For 2.47% compounded annually, the effective annual rate is ...

  r' = (1 +0.0247/1)^1 -1 = 2.47%

__

The account with an APR of 2.46% compounded monthly pays the most interest. (2.49% > 2.47% > 2.46% ⇔ monthly > annually > daily)

Answer:

17+m=34

Step-by-step explanation:

Nina had 17 marbles in a bag + the x amount of marbles that her mom gives her.

so 17+x=34

(x is the variable that I chose however it could be any variable, so it would also mean the same thing as 17+m=34)

Hope this helped!

Answer:

17 + m = 34.

Step-by-step explanation:

Nina had 17 marbles;

Mother put a handful of marbles, let's say m.

Now Nina has 34 marbles.

34 marbles is [=] 17 marbles Nina had before + m from her mother.

17 + m = 34 will be the right equation.

Answer:

Explained below.

Step-by-step explanation:

The information provided is:

n = 200

X = 106

α = 0.05

The sample proportion is:

[tex]\hat p=\frac{X}{n}=\frac{106}{200}=0.53[/tex]

(a)

A hypothesis test is to performed to determine whether more than half of all drivers drive a car made in this country.

The hypothesis is:

H₀: The proportion of drivers driving a car made in this country is less than or equal to 50%, i.e. [tex]\mu_{p}\leq 0.50[/tex]

Hₐ: The proportion of drivers driving a car made in this country is more than 50%, i.e. [tex]\mu_{p}> 0.50[/tex]

(b)

Compute the value of the test statistic:

[tex]Z=\frac{\hat p-\mu_{p}}{\sqrt{\frac{\mu_{p}(1-\mu_{p})}{n}}}[/tex]

   [tex]=\frac{0.53-050}{\sqrt{\frac{0.50(1-0.50)}{200}}}\\\\=0.8485\\\\\approx 0.85[/tex]

Compute the p-value as follows:

[tex]p-value=P(Z_{0.05}>0.85)\\=1-P(Z_{0.05}<0.85)\\=1-0.80234\\=0.19766\\\approx 0.198[/tex]

*Use a z-table.

Thus, the p-value of the test is 0.198.

(c)

Decision rule:

Reject the null hypothesis if the p-value is less than the significance level.

p-value = 0.198 > α = 0.05

The null hypothesis will not be rejected.

The correct option is (A).

(d)

Conclusion:

There is not enough evidence at 0.05 level of significance to support the claim that the proportion of drivers driving a car made in this country is more than 50%.

Answer:

a) -8x^3 + x^2 + 6x

b)16x^2 -9

c) 24x^4 + 37x^3 +13x^2 -18x

Step-by-step explanation:

a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.

b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents

c) do the same as above

Answer:

Work done = 0 J

Step-by-step explanation:

work done= ∫ F. dr

                   = [tex]\int\limits^2_0 {x} \, dx[/tex] +  [tex]\int\limits^2_2 {x} \, dx[/tex]  + [tex]\int\limits^0_2 {x} \, dx[/tex]  + [tex]\int\limits^0_0 {x} \, dx[/tex]  +  [tex]\int\limits^0_0 {y} \, dy[/tex]  + [tex]\int\limits^5_0 {y} \, dy[/tex]  + [tex]\int\limits^5_5 {y} \, dy[/tex]  + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex]  + [tex]\int\limits^1_0 {z} \, dz[/tex]  + [tex]\int\limits^1_1 {z} \, dz[/tex]  + [tex]\int\limits^0_1 {z} \, dz[/tex]

Work done= x²/2 + y²/2 + z²/2

Applying integral limits for entire pathway

Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2

Work done = 0 J

Answer:

33.0693394

Step-by-step explanation:

1 klio is 2.20462262,just mulipily by 15.

Answer:

The answer is below

Step-by-step explanation:

They would be written like this:

Arithmetic Progression:

Explicit formula

Tn = a + (n-1) * d

Recursive formula

Tn = Tn-1 + d

Where a is the first term, d is the common differance and n is the number of terms.

Geometric Progression:

Explicit formula

Tn = a * r ^ (n-1)

Recursive formula

Tn = Tn-1 * r

Where r is common ratio

Answer:

Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.

The population parameter is the mean amount of mercury in the bass fish of Florida lakes.

The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.

The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

Step-by-step explanation:

The question is incomplete.

There is no data provided.

We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.

This is a hypothesis test for the population mean.

The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=53.

The sample mean is M=0.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=53-1=52[/tex]

This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

Answer:

[tex]-x+| \: y\: |[/tex]

Step-by-step explanation:

[tex]-x+|-y|[/tex]

[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]

[tex]-x+| \: y\: |[/tex]

Answer:

$4.25

Step-by-step explanation:

We can create a proportion to find how much 25 oz will cost:

[tex]\frac{2.79}{16.4}[/tex] = [tex]\frac{x}{25}[/tex]

We can cross multiply to find x.

16.4x = 69.75

x = 4.25

So, this means 25 ounces of cereal will be $4.25

Answer:

  B)  112°

Step-by-step explanation:

After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:

  2·56° = 112°

_____

In the attached, lines l and m are separated by 56°, as required by the problem statement.

Explanation:

Plug x = 0 into the first equation to find that C = -3. We use x = 0 since 0 years have passed by (the starting point is 2005 for this equation).

Now plug x = 0 into the second equation. The starting point is now 2010 which explains why we use the same x value, just for a different equation. You should get C = -2 here.

The difference from C = -3 to C = -2 is 1, as this is the distance between the two values.

Chances are C is measured in thousands of dollars, so C = 1 represents an average cost of 1000 dollars. Though your teacher never mentions "in thousands of dollars", so it's probably best to stick to 1 instead of 1000. I would ask your teacher to clarify.