Simon bought 5 boxes of cereal c and 2 gallons of nonfat milk m for $20.08. Terri bought 3 of the same boxes of cereal b and 3 gallons of nonfat milk m for $18.87. Based on this information, what is the cost of one gallon of milk?

With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.

To calculate the future value of an investment with compound interest, we can use the following formula:

FV =\(PV * (1 + r/n)^{(n*t)}\)

where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.

In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment  is 5 years.

Using these values, we can calculate the future value (FV) as follows:

FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)

= \(\$900 * (1.03)^{10\)

= $1,191.02

Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.

If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:

I = P x r x t

where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.

In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:

I = $900 x 0.06 x 5

= $270

Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:

Total = $900 + $270

= $1,170

Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.

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The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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The length of the base is 40 meters

We have:

Area= 160 square meters

Height = 4 meters

The area is calculated using:

Area = Base * Height

So, we have:

160 = Base * 4

Divide both sides by 4

Base = 40

Hence, the length of the base is 40 meters

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Answer:

Make way for Prince Ali

Say hey, it's Prince Ali

Hey! Clear the way in the old Bazaar

Hey you, let us through!

It's a brand new star

Oh come

Be the first on your block to meet his eye

Make way, here he comes!

Ring bells, bang the drums!

You're gonna love this guy

Prince Ali, fabulous he, Ali Ababwa

Show some respect, boy, genuflect

Down on one knee

Now, try your best to stay calm

Brush up your friday salaam

Then come and meet his spectacular coterie!

Prince Ali, mighty is he, Ali Ababwa

Strong as ten regular men, definitely

He's faced the galloping hordes

A hundred bad guys with swords

Who sent those goons to their lords?

Why, Prince Ali

Fellas, he's got

(Got seventy-five golden camels)

Uh-huh, now the ladies, what he got?

(Purple peacocks, he's got fifty-three)

Uh-huh, uh-huh, uh-huh

When it comes to exotic-type mammals

Everybody help me out!

He's got a zoo?

I'm telling you, it's a world-class menagerie

Prince Ali, handsome is he, Ali Ababwa

That physique! How can I speak?

Weak at my knees! You yummy boy

So get on out in that square

Adjust your veil and prepare

To gawk and grovel and stare at Prince Ali, oops

He's got ninety-five white Persian monkeys

(He's got the monkeys, a bunch of monkeys)

And to view them he charges no fee

(He's generous, so generous)

He's got ten thousand servants and flunkies

(Proud to work for him)

They bow to his whim, love serving him

They're just lousy with loyalty to Ali

Prince Ali

Prince Ali

We're waiting for you!

We're not going until you go

You can do it

There it is

Prince Ali, amorous he, Ali Ababwa

Heard your princess was hot! Where is she?

And that, good people, is why

He got all cute and dropped by

With sixty elephants, llamas galore (For real?)

With his bears and lions, a brass band and more (What?)

With his forty fakirs, his cooks, his bakers

His birds that warble on key

Make way for Prince Ali!

Step-by-step explanation:

The coefficient of determination, given the total variation and the explained variation would be 0.898.

R-squared, or the coefficient of determination, represents the proportion of variation within a response variable that can be explained by the regression model. This calculation is achieved through dividing the explained variation by the total variation.

We are given the explained variation as 18. 592. We are also given the total variation as 20. 711.

The coefficient of determination is:

= explained variation / total variation

= 18. 592 / 20.711

= 0. 898

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Full question is:

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119.

Find the coefficient of determination. Round to three decimal place

Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is \(A= p(1+\frac{r}{100}})^n\).

Now

\(A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384\)

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay \(\frac{8752.8384}{3}\\=2917.6128\)

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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Answer:

E. 40

Step-by-step explanation:

First, we can start out by stating that this is a right triangle, since it has a right angle, shown by the marker square in the corner of the triangle. The x part, is called the hypotenuse. When finding the value of the hypotenuse, we use a thing called the Pythagorean Theorem. This theorem is :

a^2 + b^2 = c^2

a is one side length, and b is the other. c is the hypotenuse. To find x, the hypotenuse, we simply plug in the values, and solve.

24^2+32^2 = c^2

576 + 1024 = c^2

1600 = c^2

40 = c

The answer is E. 40.

Answer:

8. Absolute values are always positive.

Answer:

The answer is "64.19".

Step-by-step explanation:

\(\text{Average speed = Harmonic mean speed}\)

                       \(= \frac{2}{\frac{1}{60} + \frac{1}{69}}\\\\ = \frac{2}{\frac{69+60}{4,140} }\\\\ = \frac{2}{\frac{129}{4,140} }\\\\= \frac{2}{0.0311594203 }\\\\ = 64.1860465 \\\\ \bold{= 64.19}\)

The final answer is "64.19".

Answer: Check explanation.

Step-by-step explanation: If Corinne did 12 pages in 3 hours, then for each hour we have 12 by 3. We get 4, which means that every 1 hour she does 4 pages of homework. Hope this helped!

\( = (a + 1)(b(a + 1) - 5)\)

HOPE THIS HELPS

Answer:

Your answer is 1/8 pint.

Step-by-step explanation:

Since there are two cups for every one pint, this means that 1/4 a cup would equal 1/8 pint.

Answer:

the correct answer is option C

Answer:

Hello There!!

Step-by-step explanation:

The answer is c. 12+h as sum means adding 12 and then with h.

hope this helps,have a great day!!

~Pinky~

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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Answer:

5x+3y

Step-by-step explanation:

2x+3x=5x since they have the same variable.

y+2y

1y+2y u can put a 1 so that would be 3y

5x+3y

Answer: 1/343

Step-by-step explanation:

To multiply fractions, combine the numerators and denominators and simplify as shown below.

1/7 x 1/7 x 1/7 can be rewritten as:

(1x1x1)/(7x7x7)

Simplifying the numerator and denominator in the new equation, the result is 1/343.

Thus, 1/7 x 1/7 x 1/7 = 1/343.

I hope this helps!

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The Geometric Sequence if first term is 9 and common ratio is 3 is 9,27,81,243,729 .

What is Geometric Progression ?

Geometric Progression can be defined when in  a sequence of numbers , if the ratio between consecutive numbers is same than it is said to be in Geometric Progression.

Given

The first term is 9

and common ratio is 3

So, we need to find the geometric sequence ,

Geometric sequence, An  = a * r^(n-1)

so here a=9

r = 3

a1 = 9

a2 = 9 * 3^(2-1)

a2 = 9*3

a2 = 27

a3 = 9 * 3^(3-1)

a3 = 9 * 3 * 3

a3 = 81

a4 = 9 * 3^(4-1)

a4 = 9 * 27

a4 = 243

a5 = 9*3^(5-1)

a5 = 9 * 81

a5 = 729

Hence, The Geometric Sequence if first term is 9 and common ratio is 3 is 9,27,81,243,729 .

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Answer:

46,000

Step-by-step explanation:

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

Answer:

not the same

Step-by-step explanation:

the triangles share the same angle but the lengths are not similar

The value of x in the intersecting lines is 24.

The value of angle 6 is 79 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore,

∠6 = 3x + 7(corresponding angles)

Corresponding angles are congruent.

Therefore,

3x + 7 + 4x + 5 = 180(sum of angles on a straight line)

7x + 12 = 180

7x = 168

x = 168 / 7

x = 24

∠6 = 3x + 7 = 3(24) + 7 = 72 + 7 = 79 degrees.

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Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

I suppose you're supposed to convert 100111 from base 2 to base 10. We have

\(100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}\)

so the missing number is 39.