The density in gold is 27.2 grams per cm. A gold gar in the shape of a rectengular prism, has a length of 23.5 and a width of 28 cm. The mass of the entire bar is 43,892.5 grams. What is the height of the bar?​

Answer:

[tex]\sqrt{844}=2\sqrt{211}=29.05[/tex]

[tex]\sqrt{900} =30[/tex]

[tex]\sqrt{650}=5\sqrt{26}=25.49[/tex]

[tex]\sqrt{784}=28[/tex]

[tex]\sqrt{699} =\sqrt{699}=26.43[/tex]

[tex]\sqrt{805}=\sqrt{805}=28.37[/tex]

[tex]\sqrt{729}=27[/tex]

Step-by-step explanation:

1.

[tex]\sqrt{844}[/tex]

[tex]\sqrt{2} *\sqrt{422}[/tex]

[tex]1\sqrt{422}[/tex]

[tex]1\sqrt{2} *\sqrt{211}[/tex]

[tex]1+1\sqrt{211}[/tex]

[tex]2\sqrt{211}[/tex]

[tex]29.05[/tex]

2.

[tex]\sqrt{900}[/tex]

[tex]\sqrt{9} *\sqrt{100}[/tex]

[tex]3\sqrt{100}[/tex]

[tex]3 \sqrt{25} *\sqrt{4}[/tex]

[tex]3*5*2[/tex]

[tex]30[/tex]

3.

[tex]\sqrt{650}[/tex]

[tex]\sqrt{25}*\sqrt{26}[/tex]

[tex]5\sqrt{26}[/tex]

[tex]25.49[/tex]

4.

[tex]\sqrt{784}[/tex]

[tex]\sqrt{4} *\sqrt{196}[/tex]

[tex]2\sqrt{196}[/tex]

[tex]2\sqrt{49}*\sqrt{4}[/tex]

[tex]2*7*2[/tex]

[tex]28[/tex]

5.

[tex]\sqrt{699}[/tex]

[tex]26.43[/tex]

(can't be simplified)

6.

[tex]\sqrt{805}[/tex]

[tex]28.37[/tex]

(Can't be simplified)

7.

[tex]\sqrt{729}[/tex]

[tex]\sqrt{9}*\sqrt{81}[/tex]

[tex]3*9[/tex]

[tex]27[/tex]

The percent of sales tax on the food total is 6%.

We must first determine the 20% of the total amount of food that is the tip:

Tip = 0.2 * $32.50 = $6.50

The total cost of the meal before tax is:

Total cost before tax = food total + tip = $32.50 + $6.50 = $39.00

The cost of the lunch, including the sales tax of $1.95, is

Sales tax and the total cost before taxes = $39.00 + $1.95 =  $40.95.

The final price of the lunch, including tax and tip, is thus $40.95. You can compute the percentage of sales tax on the entire amount of food as follows:

Percent of sales tax on food = (sales tax / food total) * 100%

= ($1.95 / $32.50) * 100%

= 6%

So, the percent of sales tax on the food total is 6%.

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Answer:

The volume of the figure is 76ft³.

Step-by-step explanation:

Divide the figure into 2 parts to make it easier to solve for the volume.

V1 = 6ft(2ft)(3ft)

V1 = 36ft³

V2 = 4ft(2ft)(5ft)

V2 = 40ft³

V = V1 + V2

V = 36ft³ + 40ft³

V = 76ft³

The graph is interpreted below

(a) the parabola open downward

(b) the coordinates of the vertex is (1, 9)

(c) the intercept(s)

x-intercept(s): (-2, 0) and (4, 0)

y-intercept(s): (0, 8)

(d) the equation of axis of symmetry: x = 2

To find the intercepts of a parabola, you need to determine the points where the parabola intersects the x-axis (x-intercepts) and the y-axis (y-intercept).

Examining the graph shows that the points are

x-intercept(s) (Roots): (-2, 0) and (4, 0)

y-intercept(s): (0, 8)

Also, investing the graph shows that the graph opens upward and the vertex which is the maximum point is (1, 9)

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Answer:

1.

The cost of the carpet is given in dollars per square foot.

First I calculated the number of square feet which is the area of the carpet.

Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.

2.

$576

Step-by-step explanation:

A = LW

A = 12 ft × 12 ft

A = 144 ft²

Unit cost of carpet: $4/ft²

cost of carpet = unit cost × area of carpet

cost of carpet = $4/ft² × 144 ft² = $576

1.

The cost of the carpet is given in dollars per square foot.

First I calculated the number of square feet which is the area of the carpet.

Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.

2.

$576

The height of the tree stump is approximately 32.5 inches. Where its radius as 22 in and its volume as 49265 cubic inches.

The volume of a right cylinder is calculated as follows:

V = πr²h

where V denotes volume, r denotes radius, and h denotes height.

We are provided the radius and volume of the tree stump in this scenario. We may plug these values into the algorithm to find the height:

49265 = π(22²)h

Simplifying the right-hand side, we get:

49265 = 484πh

Dividing both sides by 484π, we get:

h = 49265 / (484π)

h = 49265 / (484 * 3.14)

h = 49265/ 1519.76

h = 32.416

h ≈ 32.5

Therefore, the height of the tree stump is approximately 32.5 inches.

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The common difference is -3, and the terms are 17, 14, 11, 8, 5 and the formula is a(n) = 17 - 3(n - 1)

From the question, we have the following parameters that can be used in our computation:

a20 = -40

a37 = -91

An arithmetic sequence is represented as

a(n) = a + (n - 1) * d

Where

d = common difference

Using the given terms, we have

a + 19d = -40

a + 36d = -91

So, we have

17d = -51

Divide

d = -3

This also means that

a + 19(-3) = -40

So, we have

a  = 17

Calculating the first five terms, we have

17, 14, 11, 8, 5

This also means that the nth term is a(n) = 17 - 3(n - 1)

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To find the best prediction of the cost of the groceries nine years after the beginning of the study, we need to use the given data to find the values of a and b in the function C=a(b)x. So, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.

To do this, we can use the first data point where x = 0:
30 = a(b)^0

This simplifies to:  

30 = a
So, we know that a = 30.

Next, we can use any other data point to solve for b. Let's use the second data point where x = 1:
32.10 = 30(b)^1

This simplifies to:
32.10 = 30b
b = 1.07
Now we can use the function C = 30(1.07)^x to find the best prediction of the cost of the groceries nine years after the beginning of the study:
C = 30(1.07)^9
C ≈ $53.34

Therefore, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.

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The salary plus benefits and the cost of living index for the two cities indicates;

1) Phoenix

2) San Antonio; $25,262.37, Phoenix; $21,901.35

3) San Antonio, because of the higher adjusted salary

The cost of living index is a measure of how expensive it is to reside in a city, compared with the national average costs.

1) The cost of living index for the cities indicates that Phoenix, with a cost of living index of 96.2 is more expensive to live in than San Antonio, Texas with a cost of living index of 85.3

2) The job offers can be evaluated by converting the salary from one city to another as follows;

(Salary in City A) × (Cost of living index for City B)/(Cost of living index for City A)

Therefore, we get;

San Antonio: ($17,000 + $5,400)×96.2/85.3 ≈ $25,262.37

Phoenix: ($23,500 + $1,200)*85.3/96.2 ≈ $21,901.35

3) The job offer that is better, based on the conversion of the job offers into adjusted salary for the two Cities of $25,262.37 vs $21,901.35, indicates that the San Antonio job offer is better

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Answer:

6in

Step-by-step explanation:

angle C = 55 <-- 180-70-55=55
meaning the triangle is an isosceles so two sides would be the same.

The image vertices of P′ are P′(-5, 1), S′(0, 1), R′(3, -2), and T′(-2, -4).

To determine the image vertices of P′ after rotating the preimage 90° counterclockwise, we can apply the following transformation rules for a 90° counterclockwise rotation about the origin:

(x, y) → (-y, x)

Using these rules, we can find the image vertices of the polygon:

P (1, 5) → P′ (-5, 1)

S (1, 0) → S′ (0, 1)

R (-2, -3) → R′ (3, -2)

T (-4, 2) → T′ (-2, -4)

Therefore, the image vertices of P′ are P′(-5, 1), S′(0, 1), R′(3, -2), and T′(-2, -4).

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Answer:

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

We know the tangent is perpendicular to radius.

Find the slope of the radius using its endpoints:

Perpendicular lines have negative reciprocal slopes, therefore the slope of the tangent is:

The matching choice is 2.

The coordinates in the solution to the systems of inequalities is (-2, 1)

From the question, we have the following parameters that can be used in our computation:

y > -x - 4

y > 2x - 6

By imagining where the shading should be, we have

From the imagined graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities is (-2, 1)

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The additional interest on the loan by the rates is $2150241.13

From the question, we have the following parameters that can be used in our computation:

Principal, P = $271,000

Time = 40 years

Rates = 7% and 5%

The interest is calculated as

I = P(1 + r)ˣ - P

So, we have

Calculate the difference in the interests

Difference = 3787078.07443 - 1636836.94099

So, we have

Difference = 2150241.13344

Approximate

Difference = 2150241.13

Hence, the additional interest is $2150241.13

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The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

To determine the cost of electricity consumption excluding VAT, we need to know the rate charged per kilowatt-hour (kWh) by the electricity provider. Let's denote this rate as [tex]\(r\)[/tex] (in currency per kWh).

The total cost of electricity consumption (excluding VAT) can be calculated by multiplying the electricity usage in kWh by the rate:

[tex]\[ \text{Cost} = \text{Usage} \times \text{Rate} \][/tex]

Given that the household uses 196 kWh in a month, the cost can be expressed as:

[tex]\[ \text{Cost} = 196 \, \text{kWh} \times r \][/tex]

Please note that we still need the specific rate per kWh from the electricity provider to calculate the actual cost.

The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

Note: The given question is incomplete. The complete question is:

If a household uses 196kWh of electricity in a month how much would they pay for their electricity consumption excluding VAT?

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A triangle with side lengths of 9, 40, and 41 is a valid right triangle.

The set of measurements 9, 40, and 41 could be the lengths of the sides of a right triangle. This is because these measurements satisfy the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, 9² + 40² = 41²,

which confirms that this set of measurements is valid for a right triangle. Additionally, 9 and 40 are both smaller than 41, which is consistent with the fact that the hypotenuse of a right triangle is always the longest side.

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The arithmetic operations used to make the number 24 is  (7 - 5) × (7 - 5) = 24

To make the number 24 using the digits 5, 5, 7, and 7, you can use the following arithmetic operations:

(7 - 5) × (7 - 5) = 24

In this case, we subtract 5 from 7 to get 2, and then multiply the result by itself to get 24.

7-5=2.

Subtract the second 5 from the remaining 7: 7-5=2.

Multiply 2 and 2: 2x2=24.

Number 24 was created using 5, 5, 7, and 7.

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The room temperature after 8 hours after the process begins would be 10°C.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the cooling machine is given by;

y = mx + c

y = -5x + 50

By substituting the given parameter (x = 8 hours), we have the following:

y = -5(8) + 50

y = -40 + 10

y = 10°C

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Answer:

0.3947368421 = approx 39%

Step-by-step explanation:

Add up all the number of times rolled on the right column.

=6+3+5+6+9+9

= 38 total rolls

Add up the number of times a 4 or a 5 were rolled:

= 6+ 9 = 15

Divide 15/38

=15/38=0.3947368421 = approx 39%.

An estimated 3,042 people in attendance would prefer relish on a hot dog.

Given that;

For a recent football game of 8,450 in attendance,

And, 150 people were asked for they prefer on a hot dog.

Now, For number of people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:

By proportion we get;

x = (54/150) x 8450

x = 54 * 56 1/3

x = 3042

Therefore, An estimated 3,042 people in attendance would prefer relish on a hot dog.

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The scale factor from triangle D to triangle D' is 4

From the question, we have the following parameters that can be used in our computation:

The triangles

From the triangles, we have the following parameters

Using the above as a guide, we have the following:

Scale factor of the dilation = Corresponding side length of D' / Side length of D

So, we have

Scale factor of the dilation = 32/8

Evaluate

Scale factor of the dilation = 4

Hence, the scale factor of the dilation is 4

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Suppose,

[tex]y=(x-3)^2-47 ----------------(1)\\y=17 -------------------------(2)[/tex]

Put [tex]y=17[/tex] in place of x in the first equation:

[tex]17=(x-3)^2-47[/tex]

To both sides, add [tex]47[/tex]:

[tex]64=(x-3)^2[/tex]

Add the square roots of both sides together:

[tex]8=x-3[/tex] or [tex]-8=x-3[/tex]

To each sides, add [tex]3[/tex]:

[tex]x=11 or -5[/tex]

As a result, the following are the equations' solutions:[tex]x=-5, y=17 or x=11, y=17[/tex].

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The numerical value of x in the inscribed angle and intercepted arc is 4.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

From the image:

Inscribed angle XZY = 14x + 4

Intercepted arc XY = 30x

Value of x = ?

Plug these values into the above formula and solve for x.

Inscribed angle = 1/2 × intercepted arc.

14x + 4 = 1/2 × 30x

14x + 4 = 15x

15x = 14x + 4

15x - 14x = 4

x = 4

Therefore, x has a value of 4.

Option D) 4 is the correct answer.

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Answer: 3:4

Step-by-step explanation: just divide it by 5

4x5=20

3*5=15

if the ratio was 6:15 then you would dive it by 2 because 2 is equivalent to 6 and 7.

Hope this helps :)

Answer:

D

Step-by-step explanation:

First, to find the length of the side FH we will use the Pythagorean theorem which states [tex]a^2+b^2=c^2[/tex]. We can say that FH = a, FG = b, and HG = c. Since we know the values of b and c, we will rearrange the formula to solve for a [tex]a = \sqrt{c^2-b^2}[/tex]. That will be [tex]\sqrt{18^2-12^2)[/tex] which gives us 13.4 for the missing side.

Now to solve for the angles we will use simple trigonometry. Since we know that [tex]sin(\theta) = \frac{opposite} {hypotenuse}[/tex], we can do inverse trigonometry for the missing angles [tex]sin^{-1}(\frac{opposite}{adjacent}) = \theta[/tex]. For angle H, we can do [tex]sin^{-1}(\frac{12}{18})[/tex] which gives us 41.8 degrees. For angle G we can do [tex]sin^{-1}(\frac{13.4}{18})[/tex] and we get 48.1 degrees. We could also use inverse cos and trig to solve it.

Looking at the answer choices, only answer choice D is correct.

The graph of the modulus function is plotted

Given data ,

Let the modulus function be represented as A

Now , the value of A is

| x | + 1 < 3

On simplifying the inequality , we get

Subtracting 1 on both sides , we get

| x | < 2

When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2

When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2

Hence , the graph of function is plotted

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This value is quite close to the doubling time approximation of 18 years that is often used for populations growing at a rate of 4% per year.

The given rate of growth = 4.1%

We know that,

The doubling time is the amount of time required for a population to double in size or value.

It is used to calculate population growth, inflation, resource extraction, commodities consumption, compound interest, the volume of malignant tumors, and a variety of other things that tend to develop over time. When the relative growth rate is constant (rather than the absolute growth rate), the amount grows exponentially and has a constant doubling time or period, which may be determined simply from the growth rate.

Formula for calculating the doubling time using logarithms is:

doubling time = ln(2) / (annual growth rate)

Since 41% = 0.041

doubling time = ln(2) / (0.041)

doubling time = 16.85 years

So the doubling time for South Sudan's population at this growth rate is approximately 16.85 years ≈ 18 years

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Answer:

Step-by-step explanation:

Sure! Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:

Problem: Jane is making spaghetti and tomato sauce for dinner. She wants to mix the tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?

Solution:

To solve this problem, we can set up a proportion using the given ratio:

Tomato sauce : Spaghetti = 1 : 4

Let's assign the variable 'x' to represent the number of cups of spaghetti.

Therefore, the proportion becomes: 1/4 = 2/x

To solve for 'x', we can cross-multiply and solve for 'x':

1 * x = 4 * 2

x = 8

Therefore, Jane should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.

You can include these calculations and steps to show how you arrived at the answer.

Step-by-step explanation: Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:

Problem: Jannay has tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?

Solution:

To solve this problem,

Tomato sauce : Spaghetti = 1 : 4

Assign the variable 'x' to represent the number of cups of spaghetti.

The proportion becomes: 1/4 = 2/x

To solve for 'x',  cross-multiply and solve for 'x':

1 * x = 4 * 2

x = 8

Therefore, Jannay should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.

Answer:

301.593 mm²

Step-by-step explanation:

surface area of cylinder = 2π r² + 2π r h

where r = radius and h = height

so we have surface area = 2π (4)² + 2π (4) (8)

= 32π + 64π

= 96π mm² (in exact form)

= 301.593 mm² (to one-thousandth of mm)