James is building a doll house that is proportional to his own house. He is using a scale of 0. 5inch = 1foot. If the doll house is 12. 3inches tall, how tall is his house. ?

The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

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It is A because it is only $40.000 so therefore it is A.

Answer:

Step-by-step explanation:

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Answer:

The area left is equal to about 2686 [tex]ft^{2}[/tex] (if we will round to the nearest whole number).

Step-by-step explanation:

The area of the backyard that will be left will equal to the area of his backyard minus the area of the circular pool. So we can write it as...

The area left = (area of the backyard) - (area of the pool)

The area left = [tex]60 * 50 - \pi (20 / 2)^{2}[/tex]

The area left = [tex]3000 - 100\pi[/tex]

The area left ≅ 2686 [tex]ft^{2}[/tex]

The number of coins of nickels and quarters will be 27 and 13, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.

Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,

x = y + 14                               ....1

0.05x + 0.25y = 4.60             ....2

From equations 1 and 2, then we have

0.05(y + 14) + 0.25y = 1

0.05y + 0.70 + 0.25y = 4.60

0.30y = 3.9

y = 13

Then the value of 'x' is given as,

x = 13 + 14

x = 27

The number of coins of nickels and quarters will be 27 and 13, respectively.

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As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.

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Answer:

circumference of the base

Step-by-step explanation:

Given that

The height of the cylinder is 10 inches

And, the 8 inches show the circumference of the base or the circumference of the circle

So,

C = 2r π

or

8 = 2r π

So, the 8 inches represent the same as shown above

Hence, the last option is correct

Answer:

circumference of the base.. D

Step-by-step explanation:

ANSWER D OPTION D

9514 1404 393

Answer:

  (5, 6) is (h, k)

Step-by-step explanation:

Vertex form is an instance of the transformation of parent function f(x) = x². It is vertically scaled by a factor of 'a', and translated so the vertex is point (h, k). That is, the transformed vertex is h units right and k units up from that of the parent function (0, 0).

Parent:

  f(x) = x^2

Transformed:

  f(x) = a(x -h)^2 +k

__

When you compare the form to your specific instance, you need to pay attention to what it is that you're comparing. As the attachment shows, ...

Hence the vertex is (h, k) = (5, 6). The second attachment shows this on a graph.

Answer:

D and E, or 56 and 60

Step-by-step explanation:

The inequality says the value must be greater than or equal to 50, so that can take out the first two (0 and 50), since they do not fit this criteria. 50.5 also does not work, because the club cannot sell half a candle. Therefor, the last two choices are the only ones that make sense in the context of the situation.

Answer:

the answer is D and E, or 56 and 60 :D

Step-by-step explanation:

16 full days will be covered by the 785.7 pounds of food.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

We are able to locate the missing value using the unitary technique.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

According to our question-

1 pound of food will last = 1/48.5 day

Pounds equal 785.7*(1/48.5) = 785.7

= 785.7/48.5

= 16.2

Only full days will be counted, therefore

We'll only count up to 16.

So, the 785.

16 days will pass after 7 days.

The 785.7 pounds of food will therefore be plenty for 16 full days.

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When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions

given

a) f(g(1)  

g(1) = 5  and f(g(1)) = 0

b) g(f (2))

f(2) = -3

g(f (2)) = -2

so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

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Answer:

gay

Step-by-step explanation:

gayayayayayayaydyfyfaygaygagya

Point C is tangent to the circle and will be a right angle which is 90 degrees.

The three inside angles of a triangle need to equal 180.

X = 180-90-64 = 26

X = 26 degrees

In the graph, there is a strong positive relationship between the variables. Option D

We know that the term correlation has to do with how two or more variables are related. The way that the variables are related can be seen from the graph that is shown.

There is a strong positive correlation if we notice that the straight-line of the graph is moving in the positive direction. As we can see from the graph that we have, there is a positive correlation among the variables.

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The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of bottles of mustard be represented as A

Now , the equation will be

The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle

Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup

Substituting the values in the equation , we get

The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle

On simplifying the equation , we get

The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )

The number of bottles of mustard used A = ( 1/6 ) of the bottle

Therefore , the value of A is 1/6

Hence , the number of bottles is 1/6

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The area of the circle is A. 3 square units

The formula for determining the area of a circle is expressed as;

A = πr² or 1/4πd²

Given that;

Also, the formula for calculating the radius of a circle is given as;

Radius = diameter/2

Substitute the value, we have;

Radius = 2/2

Radius = 1

Substitute the value into the formula

Area, A = 3. 14 × (1)²

Find the square

Area, A = 3. 14 square units

Hence, the value is 3 square units. Option A

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The complete question

Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units

Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.

The equation of two-degree polynomial having one variable is called quadratic equation.

The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.

given equation, x² = 6x -10

                x²-6x +10 =0

This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.

we know that standard form of a quadratic equation is given by

ax² + bx +c = 0

where a is the coefficient of x², b is the coefficient of x and c is the constant.

the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a

Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1

                                                                     x = 6 ± √ (36 -40) / 2

                                                                x = 6 ± √-4 / 2

                                                   as        √-4 = √-1 ×2

                                                            x = 6 ± 2 √-1 /2  

                                        divide both numerator and denominator by 2

                                              x = 3± i     as √-1 = i

this is the solution in (a + bi) form a = 3 and b = 1

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Answer:

tony

Step-by-step explanation:

his fraction is the greatest meaning that it's also the lowest

The ladder would reach a distance of 6 feet up the wall.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.

a. When they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

b. Based on the calculation both of them has the same amount of weight.

a. Weight

Let d represent the number of dieting days for this happen.

Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs

So,

John's weight = Frank's weight

Hence,

208 - 3d = 160 + 2d

Combine like terms

208 - 160 = 2d + 3d

48 = 5d

Divide both side by 5d

d = 48/5

d = 9.6 dieting days

The amount the weigh

Using John equation

Weigh = 208 - 3(9.6)

Weigh = 208 - 28.8

Weigh = 179.2 lbs

b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.

Using Frank's equation

Weigh = 160 + 2(9.6)

Weigh = 160 + 19.2

Weigh = 179.2 lbs

Therefore when they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

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Answer:

A/30 degrees

Step-by-step explanation:

Just took the test and passed it

Answer:

A

Step-by-step explanation:

lol

Answer:

y = 312x + 2

Step-by-step explanation:

According to y = mx + b, m stands for slope and b stands for y-intercept. Let us find the y-intercept. To find the y-intercept, the x should be zero in (x, y).

(x, y)

(0, 2) ---> y-intercept (b)

Now that we have found the y-intercept, we will now find the slope by using its formula.

Slope formula:-

m = y2 - y1 / x2 - x1

Pick two random (x, y). I will pick the first and last pairs.

(0, 2) and (4, 1250)

Now plug these two pairs in the formula.

m = y2 - y1 / x2 - x1

m = 1250 - 2 / 4 - 0

m = 1248 / 4

m = 312

This means that the slope (m) is 312. Now put that in y = mx + b form.

y = mx + b

y = 312x + 2

Both of the forms are the same. Hope this helps, thank you :) !!

Answer:

I believe it to be A.

If Cherri brought $2100 computer on an installment plan and made $400 down payment and monthly payment for $79. 50 for the next two years, then the interest amount is $208 .

the cost of the computer is = $2100 ;

the amount paid as down payment is = $400 ;

the amount that will be paid in monthly installment is = $79.50 ;

the time for the loan is = 24 months ;

So , the amount paid as installment is 24 months is = [tex]24 \times79.50[/tex]

= $1908 .

So , the total amount paid by Cherri with installment plan is = [tex]\$1908+\$400[/tex]

= $2308 .

So , the interest amount paid is = [tex]\$2308-\$2100[/tex]

= $208 .

Therefore , Cherri will pay $208 as interest .

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Answer:

The area of the circle is [tex]1\pi[/tex] or approximately 3.14 [tex]km^2[/tex]

Step-by-step explanation:

The formula to find the area of a circle is [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]1^2*\pi[/tex] = [tex]\pi[/tex] ≈ 3.14 [tex]km^2[/tex].

The third side of a triangle can be found using the Pythagorean Theorem.

The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.

To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.

Next, plug the values into the Pythagorean Theorem and solve for c.

[tex]a^2 + b^2 = c^2[/tex]

[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]

[tex]169 = c^2[/tex]

Finally, take the square root of both sides to solve for c.

sqrt(169) = c

13 = c

Therefore, the length of the third side is 13.

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It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.

This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.

The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:

f(10) = 80(0.5)^10 = 0.390625 units

This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.

Answer:

am not really sure but ig the answer is B

Step-by-step explanation:

Plz help timed test I’ll give extra points

The number of balloons out of 48 that will be red would be = 3/435

The number of balloons thrown in a water-ballon fight = 6,960 balloons.

The number of red balloons =870 balloons.

The number of balloons out of 48 that would be red; divide through by two.

= 48/6,960

= 24/3,480

= 12/1740

= 6/870

= 3/435

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