Answer: 32.2 cubic inches
Step-by-step explanation:
The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = π(1.4)^2(0.0625)
V ≈ 0.14 cubic inches (rounded to the nearest hundredth)
To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:
Total volume = 230 × 0.14
Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)
Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.
I need a solution please
The gradient at the given point (1, 1/2) is the one in option B; -1/8.
How to find the gradient?To find the gradient at the given point, we need to find the derivative and evaluate it in x = 1.
The rational function is:
y = 2/(x + 3)
And the derivative of the rational function is the following:
y' = -2/(x + 3)²
Evaluating this in x = 1 (replace the variable by the correspondent number) will give us:
y' = -2/(1 + 3)² = -2/16
y' = -1/8
That is the gradient of the rational function at the point (1, 1/2).
The correct option is B.
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Find the values of the constants b and c, so that y (t) = te^-3t is a solution tothe following differential equation:y" + by' + cy = 0Fill in the blanks with the correct numbers for the values.of the constants b and c:
The value of the constants b and c, so make y(t) = te^-3t is a solution to the differential equation y" + by' + cy = 0 are b = 3 + 2√(c-3) and c = 3 + (b-3)^2.
The differential equation given is: y'' + by' + cy = 0. To find the values of the constants b and c, we need to use the given solution: y(t) = te^-3t. To begin, we can use the product rule for derivatives to write the second derivative of y(t) as follows:
y''(t) = e^-3t(t^2 - 3t + 3)
Now, we can substitute this expression into the original differential equation:
e^-3t(t^2 - 3t + 3) + bte^-3t + ce^-3t = 0
Next, we can rearrange and factor this equation as follows:
e^-3t(t^2 + (b-3)t + (c-3)) = 0
This equation can be satisfied if and only if the polynomial in parentheses has a root at t = 0, which implies that the discriminant of the polynomial must be equal to zero:
(b-3)^2 - 4(c-3) = 0
Finally, we can solve this equation for b and c, giving us:
b = 3 + 2√(c-3)
c = 3 + (b-3)^2
Therefore, the constants b and c that make y(t) = te^-3t a solution to the differential equation are b = 3 + 2√(c-3) and c = 3 + (b-3)^2.
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Solve for vertex algebraically -x^2-6x-5
Answer:
To find the vertex algebraically for the quadratic function -x^2 - 6x - 5, we can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute it into the function to find the y-coordinate.
Here, a = -1 and b = -6, so x = -(-6)/(2*(-1)) = 3. Substituting x = 3 into the function, we get:
-y = -(3)^2 - 6(3) - 5 = -22
y = 22
Therefore, the vertex is at (3, 22).
Determine the approximate value of x
The approximate value of x is 5.89.
We need to utilise trigonometric functions to estimate the value of x. The tangent of the angle opposite the side of length x in the right triangle in the diagram is represented by:
tan(26°) = x/12
When we multiply both sides by 12, we obtain:
x ≈ 12 × tan(26°) ≈ 5.89
Hence, x has a rough value of 5.89.
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Help please what is the cosine of (B)
The value of cos B in proper fraction is 12 / 35.
What is the value of cos B?
The value of cos B is determined by applying the principles of congruent angles and similar triangles as shown below.
Congruent angles are angles that have the same measure in degrees or radians. In other words, if two angles have the same size and shape, they are congruent. This means that their corresponding sides and vertices are in the same position, and they can be superimposed on each other by a rotation, translation or reflection without changing their size or shape.
angle B is congruent to angle A;
cos A = 24 / 70
So the value of cos B is calculated as;
cos B ≅ cos A = 24 / 70
cos B = 12 / 35
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The price of petrol is increased from R12,58 per litre to R13,28 per litre. Determine the percentage increase in the price.
Answer: 5.56%
Step-by-step explanation:
Deduct the original price from the price that reflects the increase to get the increment.
R13 28-R 12,58 = R, 70
Place the increase on the original price and multiply by 100%
R, 70/R 12,58 x 100/1
Percentage increase = 5.56%
To check, calculate 5.56%o of 12,58 and add to 12,58, you will get R13,28
Question 3
In the figure below, if AB = 1964, what is BC?
The length of BC is 19/8.
Describe Right Angle Triangle?A right triangle, also known as a right-angled triangle, is a triangle in which one of its angles measures exactly 90 degrees (a right angle). The other two angles are acute angles, which means they measure less than 90 degrees.
The side opposite the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs, and they form the right angle.
We can start by using the Pythagorean theorem in each of the triangles to find the lengths of the sides.
In triangle ABE, we have:
AB² = AE² + BE²
AB² = (2BE)² + BE² (since AE = 2BE, as angle AEB = 60 degrees)
AB² = 5BE²
BE = AB/√5
In triangle BED, we have:
BE² = BD² + DE²
AB²/⁵ = BD² + (BD/√2)² (since BE = AB/√5 and angle EBD = 45 degrees)
AB²/5 = 3BD²/2
BD = AB/√(10/3)
In triangle BCD, we have:
BC² = BD² + CD²
BC² = (AB/√(10/3))² + (AB/2)² (since angle BCD = 30 degrees and BD = AB/√(10/3))
BC² = (19/4)² * (1/10 + 1/4)
BC² = (19/4) * (3/20)
BC² = (361/80)
BC = √(361/80)
Therefore, BC = (19/4) * √(1/80) * √361 = (19/4) * (19/40) * √361 = 19/8. So the length of BC is 19/8.
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the function operation and then find the domain.
The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).
The Domain of function:The domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined.
In other words, it is the set of values of x for which the function has a corresponding output value (also known as the dependent variable).
Here we have
f(x) = 4x + 3
g(x) = x² - 5x + 6
Then f(x) · g(x) can be calculated as follows
=> (4x + 3) [ x² - 5x + 6 ]
Using distributive property, we get:
=> 4x (x² - 5x + 6) + 3(x² - 5x + 6)
=> 4x³ - 20x² + 30x + 3x² - 15x + 18
=> 4x³ - 17x² + 15x + 18
Hence, f(x).g(x) = 4x³ - 17x² + 15x + 18
The domain of the function f(x) = 4x³ - 17x² + 15x + 18 is all real numbers since there are no restrictions or conditions that would make the function undefined for any value of x.
Therefore,
The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).
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Allen is buying a video game that originally costs $49. He has a 10% off coupon and will have to pay a 6% sales tax. Which expression will calculate the total amount allen will pay for the video
The expression that will calculate the total amount allen will pay for the video is 0.9p(1.06)
In this case, let's use the variable "p" to represent the original price of the video game. The expression for the discounted price would then be:
0.9p
This is because Allen will pay 90% of the original price, which is the same as multiplying the original price by 0.9.
Next, we need to calculate the sales tax on the discounted price. To do this, we can use another expression:
0.06(0.9p)
This expression represents the amount of sales tax that Allen will have to pay on the discounted price. We multiply 0.06 (or 6%) by 0.9p (the discounted price) to get the tax amount.
Finally, we can calculate the total amount Allen will pay by adding the discounted price and the sales tax:
0.9p + 0.06(0.9p)
Simplifying this expression, we can factor out 0.9p:
0.9p(1 + 0.06)
And then simplify the sum in the parentheses:
0.9p(1.06)
This is our final expression for the total amount Allen will pay for the video game.
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An arithmetic sequence starts at 0 and each successive number equals the previous number plus 6. Thus a1=0 and the distance d=6 What is the sum of the first 36 terms?
Answer:
228
Step-by-step explanation:
sum of the first n term = (n/2) [ 2a +(n-1)d]
sum of the first 36 terms =(36/2)[ 2×0+ (36-1)6]
= 228
Right triangle ABC lies on a coordinate plane with one vertex at point A(4, 0). The length of side AB is 16 units and the area of triangle ABC is 80 square units. 20 Type the correct answer in each box. Use numerals instead of words. Find the coordinates of point B and point C. The coordinates of point B are (4, ), and the coordinates of point C are ( ,-16).
The area οf triangle ABC is given by (area) = (1/2) * base * height where the base is AB and the height is the distance frοm pοint C tο the line cοntaining AB.
Since AB has a length οf 16, the height must be 10 (since 1/2 * 16 * 10 = 80).
Let's call the cοοrdinates οf pοint C (x, y). Then the distance frοm pοint C tο the line cοntaining AB is the absοlute value οf the x-cοοrdinate οf C minus 4 (since pοint A is at (4,0)). We can use this tο set up an equatiοn:
(1/2) * 16 * 10 = (1/2) * 12 * |x - 4|
Simplifying, we get:
80 = 6 * |x - 4|
Dividing bοth sides by 6, we get:
|x - 4| = 40/6 = 20/3
Since the distance must be pοsitive, we can drοp the absοlute value and sοlve fοr x:
x - 4 = 20/3 οr x - 4 = -20/3
Sοlving fοr x in each case, we get:
x = 4 + 20/3 = 32/3 οr x = 4 - 20/3 = 4/3
Since pοint C must have a y-cοοrdinate οf -16, the cοοrdinates οf pοint C are (32/3, -16) οr (4/3, -16).
Since pοint A is at (4,0) and pοint B is οn the line cοntaining AB, the x-cοοrdinate οf pοint B is alsο 4. The y-cοοrdinate οf pοint B can be fοund using the Pythagοrean theοrem:
[tex]AC^2 + BC^2 = AB^2[/tex]
Substituting in the cοοrdinates οf A, B, and C, we get:
[tex](4 - 4/3)^2 + (-16 - 0)^2 = 16^2[/tex]
Simplifying, we get:
256/9 + 256 = 256
Multiplying bοth sides by 9, we get:
256 + 2304 = 2304
Sο the calculatiοn is incοnsistent, which means that nο pοint C satisfies the given cοnditiοns. This is likely due tο a mistake in the οriginal prοblem statement.
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x-3/3 - x-2/3 = 1/9 (find the value of x)
Hence, in answering the stated question, we may say that equation (3x - 9 - 3x + 6)/9 = 1/9 => -3/9 = 1/9
What is equation?A math equation is a technique that uses the equals symbol (=) to demonstrate equivalence between two statements. An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. The equal sign separates the integers 3x + 5 and 14 in the equation 3x + 5 = 14. To explain the connection between the two sentences written on opposing sides of a letter, a mathematical formula might be employed. The logo and the software are frequently the same. For instance, 2x - 4 = 2.
To solve this equation, we can start by simplifying the left-hand side using a common denominator:
[tex](x - 3)/3 - (x - 2)/3 = 1/9\\(3(x - 3) - 3(x - 2))/9 = 1/9\\[/tex]
[tex](3x - 9 - 3x + 6)/9 = 1/9\\-3/9 = 1/9[/tex]
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emma covered a gift box in the shape of a rectangular prisim. It was 8 inches long, 4 inches wide, and 7 inches high. What is the total surface area of the gift box?
The tοtal surface area οf the gift bοx is 232 square inches.
What is rectangle?A rectangle is a 2D shape that has fοur sides and fοur right angles. Oppοsite sides are parallel and οf equal length. The area οf a rectangle is the prοduct οf its length and width, and its perimeter is the sum οf the lengths οf all its sides.
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height οf the rectangular prism, respectively.
Substituting the given values, we get:
SA = 2(8x4) + 2(8x7) + 2(4x7)
SA = 64 + 112 + 56
SA = 232
Therefοre, the tοtal surface area οf the gift bοx is 232 square inches.
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A retailer buys a coat bulk at a uint price of $45 the coat is marked up 80% to sell in the store. What is the price of the coat in the store
The price of the coat in the store is $81 after a retailer buys a coat bulk at a unit price of $45 the coat is marked up 80% to sell in the store.
The retailer buys the coat at a unit price of $45 and marks it up by 80%. To calculate the markup, we need to first find 80% of $45, which is
0.8 x $45 = $36.
We can then add the markup to the cost price to get the selling price:
$45 + $36 = $81.
Therefore, the price of the coat in the store is $81.
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Completely factor the expression below. 4x^2 + 14x + 10
Answer:
[tex]2(x+1)(2x+5)[/tex]
Step-by-step explanation:
First, factor out 2:
[tex]2(2x^2+7x+5)[/tex]
Consider [tex]2(2x^2+7x+5)[/tex]. Factor the expression by grouping. First, the expression needs to be rewritten as [tex]2x^2+ax+bx+5[/tex]. To find a and b, set up a system to be solved:
[tex]a + b = 7[/tex]
[tex]ab = 2 * 5 = 10[/tex]
Since ab is positive, a and b have the same sign. Since a + b is positive, a and b are both positive. List all such integer pairs that give product 10:
[tex]1, 10[/tex]
[tex]2, 5[/tex]
Calculate the sum for each pair:
[tex]1 + 10 = 11[/tex]
[tex]2 + 5 = 7[/tex]
The solution is the pair that gives sum 7:
[tex]a = 2[/tex]
[tex]b = 5[/tex]
Rewrite [tex]2x^2+7x+5[/tex] as [tex](2x^2+2x)+(5x+5):[/tex]
[tex](2x^2+2x)+(5x+5)[/tex]
Factor out 2x in the first and 5 in the second group:
[tex]2x(x+1)+5(x+1)[/tex]
Factor out common term x + 1 by using distributive property:
[tex](x+1)(2x+5)[/tex]
Rewrite the complete factored expression:
[tex]2(x+1)(2x+5)[/tex]
Find the coordinate of A if the midpoint of bar (AB) is at (-2,3) and B is at (1,1). A is at:
Answer:
Point A = (-5,5)
Step-by-step explanation:
Explanation is given in the picture...
(6x + 5 - 3x + 16)/3 x 15/5
The solution to the given expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] when simplified is 3x + 21.
How to simplify the expressionTo simplify the expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex],
We can first combine like terms in the numerator to get [tex]\frac{3x + 21}{3}[/tex]
We can then simplify this further by dividing both the numerator and denominator by 3, which gives us x + 7 in the numerator.
Next, we can simplify the fraction 15/5 by dividing both the numerator and denominator by 5, which gives us 3
So, we have
[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = \frac{3x + 21}{3} \cdot 3[/tex]
[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = 3x + 21[/tex]
Hence, [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] simplifies to 3x + 21.
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Complete question
Simplify (6x + 5 - 3x + 16)/3 * 15/5
Deon removed 40 fish from his pond over a period of 4 days. He removed the same number of fish each day. What was the change in the number of fish in the pond each day?
The average rate of change in the number of fish in the pond each day is given as follows:
-10 fish per day.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The parameters in the context of this problem are given as follows:
Change in the output: -40 fish in the pond.Change in the input: 4 days.Hence the average rate of change in the number of fish in the pond each day is obtained as follows:
-40/4 = -10 fish a day.
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The angle measures of $\triangle ABC$ are $A=54\degree$ , $B=38\degree$ , and $C=88\degree$. List the sides of the triangle in order from shortest to longest
The triangle's sides are b, a, and c, listed from shortest to longest.
The side of triangle ABC opposite angle A is indicated by the letter a.
The letter b stands for the side opposite angle B.
The letter c stands for the side that faces angle C.
The triangle inequality theorem, states that, in order to establish the order of the sides from smallest to longest,
The largest side is the one opposite the largest angle and vice versa.
Hence, we have
B = 38 degrees, thus b.
a = 54 degrees from A
c from C equals 88 degrees.
As a result, the sides are arranged in the following order: b a c.
In other words, the side across from angle B is the smallest, followed by the side across from angle A, and the side across from angle C is the longest.
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A roasted turkey is taken from an oven when its temperature has
reached 190∘Fahrenheit and is placed on a table in a room where the
temperature is 75∘ Fahrenheit.
Recall the formula is T(t)=Ae^kt+Ts
If the temperature of the turkey is 159∘ Fahrenheit after half an hour, what is its rate of cooling in minutes? Give answers accurate to at least 5 decimal places.
rate of cooling of the turkey in minutes is 41.13545
The formula for finding the rate of cooling of a roasted turkey is provided in the question. It is given as:T(t) = Ae^kt + TsThe following are the variables:• T(t) represents the temperature of the turkey at time t• A represents the initial temperature of the turkey• k is the cooling rate• Ts is the temperature of the environmentNow, using the values given in the question, we can get the rate of cooling of the turkey as follows:T(t) = Ae^kt + TsLet us replace the variables with the given values:159 = A*e^(0.5k) + 75 => A*e^(0.5k) = 84 => A = 84/e^(0.5k)Let us substitute the value of A in the initial equation:T(t) = Ae^kt + Ts => 190 = A*e^(k*0) + 75 => 190 = A => A = 190So, we can get the value of k using the values of A from the above two equations:84/e^(0.5k) = 190 => e^(0.5k) = 84/190 => e^(0.5k) = 0.4421052631578947 => k = (ln0.4421052631578947) / 0.5 = -0.4662195477817674So, the equation for the temperature of the turkey as a function of time is:T(t) = 190e^(-0.4662195477817674*t) + 75To find the rate of cooling of the turkey, we need to take the derivative of the above equation with respect to t, which gives:dT/dt = -87.75877428502014*e^(-0.4662195477817674*t)This is the rate of cooling of the turkey. To find the rate of cooling in minutes, we substitute t = 0.5 in the above equation and simplify to get:dT/dt = -41.135453873444264Therefore, the rate of cooling of the turkey in minutes is 41.13545 (accurate to at least 5 decimal places).
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A company orders 27 boxed lunches from a deli for $245. 70. If each boxed lunch costs the same amount, what is the unit cost of each boxed lunch?
A company pays $245.70 for 27 boxed lunches from a deli. If each boxed lunch is the same price, the unit cost of each boxed lunch is $9.10.
To find the unit cost of each boxed lunch, we need to divide the total cost by the number of boxed lunches.
Total cost of 27 boxed lunches = $245.70
Unit cost of each boxed lunch = Total cost / Number of boxed lunches
Unit cost of each boxed lunch = $245.70 / 27
Unit cost of each boxed lunch = $9.10 (rounded to two decimal places)
Therefore, the unit cost of each boxed lunch is $9.10.
In this case, the deli will need to ensure that each boxed lunch is priced higher than the unit cost of $9.10 to make a profit. The difference between the unit cost and the selling price will contribute to the deli's revenue and cover other expenses such as labor, rent, and utilities.
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the probability of bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. what is the probability that bill does not serve an ace or a double fault? a. 0.5 b. 0.15 c. 0.4 d. 0.9 e. 0.6
The probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.
The probability of bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. The probability that Bill does not serve an ace or a double fault is 0.6.What is probability?Probability refers to the chance that an event or circumstance will happen. It's the likelihood of something happening. Probability is usually expressed as a fraction or percentage. In many everyday situations, probability is used to make informed decisions. A probability of 1 indicates that an event is guaranteed to happen, while a probability of 0 indicates that an event is impossible to occur. A probability of 0.5 or 50% implies that an event is equally likely to happen or not. Probabilities can range from 0 to 1.What is the probability that Bill does not serve an ace or a double fault?The probability of Bill serving an ace is 0.15. The probability that he double faults is 0.25. The probability that he serves neither an ace nor a double fault is therefore 1 - (0.15 + 0.25) = 0.6Therefore, the probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.
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for classroom use.
2. Place each of the following expressions into the two
categories of "whole number" and "not a whole
number" based on whether or not the product is
a whole number.
314
W|N
X 7
x 35
15. NE
7
×
x 15
x 100
Whole Number
67
9×
x 210
مانة
x 26
Not a Who
Here are the expressions and their respective categories:
The Expressions and their Categories314: Whole Number
7: Whole Number
35: Whole Number
10.5: Not a Whole Number (because 7 x 1.5 = 10.5, which is not a whole number)
7 x 1.5: Not a Whole Number (for the same reason as above)
100: Whole Number
67: Whole Number
9 x 210: Whole Number
26: Whole Number
To determine whether a product is a whole number or not, we can multiply the two factors and check if the result is an integer (i.e., a whole number). If it is, then the product is a whole number; otherwise, it's not.
For example, in the case of 10.5, it's not a whole number because after the product has been gotten, it is found to contain decimals which makes it a fraction.
On the other hand, when we multiply 9 and 210, we get 1890, which is a whole number.
Therefore, we can classify the expressions into two categories: "Whole Number" and "Not a Whole Number," depending on whether their product is a whole number or not.
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Après avoir factorisé le nombre de gauche,résoudre l'équation ci-dessous
x²+(5+4x)x=0
ce site est anglais frère
Answer:
5
Step-by-step explanation:
0+(5+4*0) (* signifie multiplier)
0+5
5
A 124- inch board is cut into two pieces. One piece is three times the length of the other. Find the lengths of the tow pieces
The length of the longer piece is 93 inches.
Let x be the length of the shorter piece in inches.
Then the length of the longer piece is 3x inches.
The sum of the lengths of the two pieces is equal to the length of the board, which is 124 inches:
x + 3x = 124
Simplifying the left-hand side:
4x = 124
Dividing both sides by 4:
x = 31
So the length of the shorter piece is 31 inches.
The length of the longer piece is three times this length:
3x = 3(31) = 93
So the length of the longer piece is 93 inches.
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Calculate the area of triangle of PQR correct to 3 significant figure if P=8. 5 cm and Q=6. 8 and R=68. 4°
The area of triangle PQR, rounded to 3 significant figures, is approximately 29.6 square centimeters.
How to find the area of triangle PQR?To find the area of triangle PQR, we can use the formula:
Area = 1/2 * PQ * QR * sin(R)
where PQ and QR are the lengths of sides PQ and QR, and R is the angle between them in degrees.
Substituting the given values, we get:
Area = 1/2 * 8.5 cm * 6.8 cm * sin(68.4°)
Using a calculator, we can find that:
sin(68.4°) ≈ 0.933
So, the area of the triangle is:
Area ≈ 1/2 * 8.5 cm * 6.8 cm * 0.933
Area ≈ 29.63 cm²
Rounding this to 3 significant figures, we get:
Area ≈ 29.6 cm²
Therefore, the area of triangle PQR, rounded to 3 significant figures, is approximately 29.6 square centimeters.
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Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation 1 = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2025? t10 (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 46,166 (c) In what year is the U.S. per capita real disposable income expected to exceed $50,000?
The t-value for the year 2025 is t = 10, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166 and the U.S. per capita real disposable income expected to exceed $50,000 is 2030.
Given equation is 1 = 707.6t + 39,090
(a) To find what t-value corresponds to 2025.The given year is 2025, so the number of years after 2015 will be 2025-2015 = 10 So the t-value for the year 2025 is t = 10.
(b) To find the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 Substitute t = 10 in the given equation1 = 707.6t + 39,0901 = 707.6(10) + 39,0901 = 7,076 + 39,0901 = 46,166So, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166.
(c) To find in what year is the U.S. per capita real disposable income expected to exceed $50,000.Substitute 50,000 for 1 in the equation, we get50,000 = 707.6t + 39,09050,000 - 39,090 = 707.6t10,910 = 707.6t10,910/707.6 = t15.41 ≈ 15 years. So, the U.S. per capita real disposable income expected to exceed $50,000 in 2015 + 15 = 2030.
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where would (-8,-6) be located of a coordinate plane
100 points please help!!
Answer - −2x^2(x+7)(x+10)
Polygon
�
FF has an area of
36
3636 square units. Aimar drew a scaled version of Polygon
�
FF and labeled it Polygon
�
GG. Polygon
�
GG has an area of
4
44 square units.
What scale factor did Aimar use to go from Polygon
�
FF to Polygon
�
GG?
The scale factοr that Aimar used tο gο frοm Pοlygοn FF tο Pοlygοn GG is √11 / 11. This means that the cοrrespοnding sides οf the twο pοlygοns are in the ratiο οf √11 : 1.
What is a pοlygοn?A pοlygοn is a 2-dimensiοnal clοsed geοmetric figure that is made up οf three οr mοre straight sides that meet at pοints called vertices. Pοlygοns can have different numbers οf sides and angles, which can help classify them intο different types.
Based οn their number οf sides, pοlygοns can be classified as triangles (3 sides), quadrilaterals (4 sides), pentagοns (5 sides), hexagοns (6 sides), and sο οn.
Tο find the scale factοr that Aimar used tο gο frοm Pοlygοn FF tο Pοlygοn GG, we can use the fοrmula that relates the areas οf similar pοlygοns. Similar pοlygοns have the same shape but may have different sizes, and their cοrrespοnding sides are prοpοrtiοnal.
Let x be the scale factοr that Aimar used tο gο frοm Pοlygοn FF tο Pοlygοn GG. Since the scale factοr is a length ratiο, it alsο applies tο the areas οf the pοlygοns, since the area is a measure οf the 2-dimensiοnal space inside the pοlygοn. Therefοre, we have:
Area οf Pοlygοn GG = (scale factοr)² * Area οf Pοlygοn FF
Substituting the given values, we get:
4/44 = x² * 36/36
Simplifying, we get:
4/44 = x²
Dividing bοth sides by 4, we get:
1/11 = x²
Taking the square rοοt οf bοth sides, we get:
x = sqrt(1/11)
x = 1/√11
Ratiοnalizing the denοminatοr, we get:
x = √11 / 11
Therefοre, the scale factοr that Aimar used tο gο frοm Pοlygοn FF tο Pοlygοn GG is √11 / 11. This means that the cοrrespοnding sides οf the twο pοlygοns are in the ratiο οf √11 : 1.
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