Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.

Answer:

[tex] \dfrac{225}{64} [/tex]

Step-by-step explanation:

[tex] (4^3)^{-2} \times (2^3)^4 \times (\dfrac{8}{15})^{-2} = [/tex]

[tex]= (2^2)^{-6} \times 2^{12} \times (\dfrac{15}{8})^{2}[/tex]

[tex]= 2^{-12} \times 2^{12} \times \dfrac{225}{64}[/tex]

[tex] = \dfrac{225}{64} [/tex]

Answer:

The point estimate that should be used in constructing the confidence interval is 0.11.

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Midwest:

50% of 1380, so:

[tex]p_M = 0.5[/tex]

[tex]s_M = \sqrt{\frac{0.5*0.5}{1380}} = 0.0135[/tex]

South:

39% of 1300, so:

[tex]p_S = 0.39[/tex]

[tex]s_S = \sqrt{\frac{0.39*0.61}{1300}} = 0.0135[/tex]

Distribution of the difference:

[tex]p = p_M - p_S = 0.5 - 0.39 = 0.11[/tex]

So the point estimate that should be used in constructing the confidence interval is 0.11.

[tex]s = \sqrt{s_M^2+s_S^2} = \sqrt{0.0135^2+0.0135^2} = 0.0191[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].  

The lower bound of the interval is:

[tex]p - zs = 0.11 - 1.28*0.0191 = 0.0856[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.11 + 1.28*0.0191 = 0.1344[/tex]

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

Answer:

23.5

Step-by-step explanation:

The median is the middle value when the numbers are put in order from smallest to largest

17,19, 20, 21, 22, 25, 29, 30, 32, 35

There are 10 numbers

17,19, 20, 21, 22,      25, 29, 30, 32, 35

The middle is between 22 and 25

(22+25)/2 = 47/2 =23.5

Answer:

Imaginary roots

Step-by-step explanation:

The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].

Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:

[tex]7x^2-5x+1=0[/tex]

Now assign variables:

The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].

What does this tell us about the roots?

Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.

Answer:

A) children attended=98 b) students attended=60 c)adults attended=49

Step-by-step explanation:

system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29

Simplify and solve the system.

-

a%2B2a%2Bx=207

3a%2Bx=207

x=207-3aandc=2a

-

The revenue equation can be written in terms of just one variable, a.

10a%2B7%28207-3a%29%2B12a=1498

Solve for a;

use it to find x and c.

FURTHER STEPS

-

10a%2B1449-21a%2B12a=1498

a%2B1449=1498

a=98-49

highlight%28a=49 -------adults

-

c=2a

c=2%2A49

highlight%28c=98 -------children

-

x=207-a-c

x=207-49-98

highlight%28x=60 ---------students

Answer:

8/17

Step-by-step explanation:

The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.

The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY

The hypotenuse = XZ

Sin(X) = ZY/XZ

Sin(X) = 1634 = 8 / 17

Answer:

8x-21

----------------------

(2x-7)(2x+7)

Step-by-step explanation:

7                       4

-----------   + ------------

4x^2 -49    2x+7

Factor  ( notice that it is the difference of squares)

7                       4

-----------   + ------------

(2x)^2 - 7^2    2x+7

7                       4

-----------       + ------------

(2x-7)(2x+7)    2x+7

Get a common denominator

7                       4(2x-7)

-----------       + ------------

(2x-7)(2x+7)    (2x-7)(2x+7)

Combine

7 +4(2x-7)

----------------------

(2x-7)(2x+7)  

7 +8x-28

----------------------

(2x-7)(2x+7)  

8x-21

----------------------

(2x-7)(2x+7)  

Answer:

(8x - 21) / (2x + 7)(2x - 7)

Step-by-step explanation:

7 / (4x^2 - 49)+ 4 / (2x + 7)

= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)

LCM = (2x + 7)(2x - 7)   so we have

(7 + 4(2x - 7) / (2x + 7)(2x - 7)

=   (8x - 21) / (2x + 7)(2x - 7).

Step-by-step explanation:

d = z - 9

d = 10 - 9  ----> substitute

d = 1

Answer:

1/4

Step-by-step explanation:

There are four probabilities and the probability of her having 1 of the 4 probabilities is 1/4

Answer:

i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one

and there you go thats your graph

Step-by-step explanation:

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

The total area of the pool section of Keith's backyard is 390 square feet.

Step-by-step explanation:

Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:

(20 + 3 + 3) x (9 + 3 + 3) = X

26 x 15 = X

390 = X

Therefore, the total area of the pool section of Keith's backyard is 390 square feet.

Answer:

[tex]x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Step-by-step explanation:

Given the expression

[tex]2^{2x}+3-7(2^{2x}+1)+3=0[/tex]

Let [tex]P=2^x[/tex]

Substituting into the expression, we will have:

[tex]P^2+3-7(P^2+1)+3=0\\Expand\\P^2+3-7P^2-7+3=0\\-6P^2-1=0\\6P^2=-1\\p^2=-1/6\\P=\sqrt{-1/6}[/tex]

Since:

[tex]P=2^x\\2^x=\sqrt{-1/6}\\xlog2=log(\sqrt{-1/6}) \\x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Answer:

108 minutes

Step-by-step explanation:

Lets say that M+A is the time of the movie and the advertisement, so;

M+A = 2

And we know that 10% of that time is advertisement, mathematically that is:

A = 0,1*2

So replacing the second equation in the first one we have;

M + 0,1*2 = 2

M = 2-0,1*2 = 1,8 hours

We can convert hours into minutes multiplying by 60

1,8h*60min/h = 108min

Answer:

Option B, 5/16

Step-by-step explanation:

f(4) = 5•(1/2)⁴

= 5•(1/2⁴)

= 5•(1/16)

= 5/16

The volume of the water is: [tex]\pi (2)^2(8) - 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

The volume of a cylinder is;

[tex]V = \pi r^2h[/tex]

For the cylinder, we have:

[tex]d = 4[/tex] -- diameter

[tex]h = 8[/tex] --- height of the water in the cylinder

The radius of the cylinder is:

[tex]r =d/2 = 4/2 = 2[/tex]

So, the volume is:

[tex]V = \pi * 2^2 * 8[/tex]

[tex]V = \pi * (2)^2 (8)[/tex]

For the 6 marbles, we have:

[tex]d = 3[/tex] --- the diameter of each

The shape of the marble is a sphere. So, the volume of 1 marble is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

The radius of 1 marble is:

[tex]r = d/2 = 3/2 = 1.5[/tex]

So, the volume of 1 marble is:

[tex]V_1 = \frac{4}{3} * \pi * (1.5)^3[/tex]

Multiply both sides by 6 to get the volume of the 6 marbles

[tex]6 * V_1 = 6 * \frac{4}{3} * \pi * (1.5)^3[/tex]

[tex]6V_1 = 6 * \frac{4}{3} * \pi * (1.5)^3[/tex]

[tex]6V_1 = 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

Recall that the volume of the cylinder is:

[tex]V = \pi * (2)^2 (8)[/tex]

The volume of the water in the marble is the difference between the volume of the cylinder and the volume of the 6 marbles

So, we have:

[tex]Volume = \pi (2)^2(8) - 6 (\frac{4}{3} \pi (1.5)^3)[/tex]

The expression [tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex] can be used to calculate the volume of water in the vase.

As vase is of cylindrical form and the six marbles are spherical, we shall derived an expression from volume formulas respective to Cylinder and Spheres. Firstly, we know that volume of water in the vase is equal to the Volume of the vase minus the volume occupied by the six marbles, that is to say:

[tex]V = V_{v}-6\cdot V_{m}[/tex] (1)

Where:

[tex]V_{v}[/tex] - Volume of the vase, in cubic inches.

[tex]V_{m}[/tex] - Volume of the marble, in cubic inches.

[tex]V[/tex] - Volume of water in the vase, in cubic inches.

Then, we expand (1) by volume formulas for the cylinder and sphere:  

[tex]V = \pi\cdot R^{2}\cdot H - 6\cdot \left(\frac{4\pi}{3} \cdot r^{3} \right)[/tex] (2)

Where:

[tex]R[/tex] - Radius of the vase, in inches.

[tex]H[/tex] - Height of the vase, in inches.

[tex]r[/tex] - Radius of the marble, in inches.

If we know that [tex]R = 2\,in[/tex], [tex]H = 8\,in[/tex], [tex]r = 1.5\,in[/tex], then the following expression can be used to calculate the volume of water in the base:

[tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex]

In a nutshell, the expression [tex]V = \pi \cdot (2\,in)^{2}\cdot (8\,in) -6\cdot \left[\frac{4\pi}{3}\cdot (1.5\,in)^{3} \right][/tex] can be used to calculate the volume of water in the vase.

Answer:

An ordered pair for a function f(x) looks like (x, f(x)). So the ordered pair here would be (5, f(5)) or (5, 7). Either one would work, as they are the same.

Answer:

There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.

Part (a)

The standard error (SE) formula is

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

where n is the sample size. We're given SE = 2 and sigma = 34, so,

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]

So we need a sample size of n = 289 to have an SE value of 2.

========================================================

Part (b)

We'll use SE = 1 this time

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

9514 1404 393

Answer:

  c. If a plane contains a line, it contains the points on the line.

Step-by-step explanation:

The only statement relating a point on a line to the plane containing the line is the one shown above.

_____

Additional comment

Identifying true statements is a reasonable strategy for many multiple-choice questions. Another strategy that can be employed is finding the one true statement that is relevant to the question being asked.

Answer:

Option A i the right option.

First blank is 110-[tex]10\sqrt{61}[/tex] or 10(11-[tex]\sqrt{61}[/tex])

Second blank is 31.898

Let me know if anything didn't make sense.  

Step-by-step explanation:

So a diagonal through a rectangle makes two triangles.  The question wants to know how much walking is saved walking down the diagonal  vs walking along two sides that make the diagonal.  in this case the two non diagonal sides walked are 60 paces and 50 paces.

A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.  

c^2 = 60^2 + 50^2

c = [tex]\sqrt{60^2 + 50^2}[/tex]

c = [tex]\sqrt{6100} = 10\sqrt{61}[/tex]

if you don't get how to simplify a radical like that let me know.

Anyway, looking at the answers you can see right away the second option says no approximation is necessary.  Well, you need to approximate square root of 61, so we can say the second answer is not right.  So now we need to know what to fill in for option 1.

it wants the distance saved, well we know the distance of the diagonal is [tex]10\sqrt{61}[/tex]  Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.

Now, to find the difference, that is subtraction.  So subtract the smaller number from the larger number.  You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse.  so that's 110-[tex]10\sqrt{61}[/tex].  That is the exact form.  Or you could use 10(11-[tex]\sqrt{61}[/tex])  They are the same.

Then just plug that into a calculator for a decimal approximation.

======================================================

Explanation:

The five number summary is the set of these items, in this exact order

So with the five number summary 4.6, 14.3, 19.7, 26.1, 31.2, we see that

Q1 = 14.3 and Q3 = 26.1

Subtracting these two values gets us the IQR (interquartile range)

IQR = Q3 - Q1

IQR = 26.1 - 14.3

IQR = 11.8

Answer:

use test numbers to find where the function is a positive and where it is negative. sketch the function's graph, plotting additional points as guides as negative. choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.

Answer:

r = 1

Step-by-step explanation:

Find the intersection.

r = 1

r = 3

r = -1

r = 1

Answer:

r=3, r=1, r= -1

Step-by-step explanation:

48r^3-144r^2-48r=-144

48r^3-144r^2-48r +144 =-144 + 144

48r^3-144r^2-48r+144=0

48(r-3)(r+1)(r-1)

r-3=0 r+1=0 r-1=0

r=3, r=1, r= -1

Answer:

4/7

Step-by-step explanation:

When you multiply by fractions you multiply the numerators and denominators

4/1 x 1/7

Anything that doesnt have anything under it always has a 1 as its denominator

Answer:

y=-2x+7

Step-by-step explanation:

The Slope is obviously -2, and just add a random y and play around with it until it goes through the point (5,-3)

Answer:

1/2

Step-by-step explanation:

Number of bags = 3

number of bags with $10 bill initially = 2

number of bags with $5 bill initially = 1

assume :

event you pick a $5 bill at first draw = A

event you pick a $5 bill at second draw = B

hence : P ( A n B ) = 1/3 * 1 = 1/3

P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 )  = 2/3

therefore P( that the second drawn bill is $5 )

P( B | A ) = P(A n B ) / P ( A )

              = (1/3) / (2/3) = 1/2

The probability that it, too, is a $ 5 bill is 33.33%.

Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:

Therefore, the probability that it, too, is a $ 5 bill is 33.33%.

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