To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.
Explanation:To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.
Cross-multiply to solve for x:
(1 inch) * (195 miles) = (20 miles) * (x inches)
195 inch-miles = 20x inch-miles
Now, divide both sides by 20 miles to solve for x:
x = 195 inch-miles / 20 miles
x = 9.75 inches
So, on the map, Austin and Dallas would be 9.75 inches apart.
Gerry is a restaurant manager and plans to advertise her restaurant. The advertising budget is $5000, and she plans to run television and online ads. She would like to run at least 5 television ads and 10 online ads. A television ad costs $500 and an online ad costs $150. Let x represent the number of television ads and y represent the number of online ads. Two of the constraints for this situation are x≥5 and y≥10 . What is the other constraint for this situation?
We are given the two constraints:
x ≥ 5 and y ≥ 10
Now the other constraint must of course be based on the sum of the two. It was given that the budget is $5000 so the sum must be greater than that, that is:
500 x + 150 y ≤ 5000
The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the principal, r is the annual interest rate (in decimal form) and t is the time (in years). a. Solve the formula for p
.
p=
b. An investment earns 6% simple interest. What amount of principal is needed to have $3000 after 5 years? Round your answer to the nearest cent.
Amount of principal: $
The answer is for the equation...
V/(1+rt)
It is written as a fraction... and the V goes on top and the (1+rt) goes on the bottom. Make sure that the V is a capital.
Then the amount of principal is 2,307.69
Using the formula given, we find that:
a) The solution for p is [tex]p = \frac{V}{1 + rt}[/tex]b) The principal will be of $2,307.69.------------------
Item a:
The future value formula is given by:
[tex]V = p + prt[/tex]
Solving for p:
[tex]p + prt = V[/tex]
[tex]p(1 + rt) = V[/tex]
[tex]p = \frac{V}{1 + rt}[/tex]
------------------
Item b:
6% interest means that [tex]r = 0.06[/tex]Amount of $3000 means that [tex]V = 3000[/tex]5 years means that [tex]t = 5[/tex]The principal is:
[tex]p = \frac{V}{1 + rt} = \frac{3000}{1 + 5(0.06}} = 2307.69[/tex]
The principal will be of $2,307.69.
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Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.
Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week.
Which statement best describes the methods used by Amanda and Billy to increase the time they spent exercising? (1 point)
Amanda's method is linear because the number of minutes increased by an equal number every week.
Billy's method is linear because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal factor every week.
Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal number every week.
Answer:
Amanda's method is linear because the number of minutes increased by an equal number every week.Step-by-step explanation:I took the test and got it right.
Amanda
Billy1st week 10 52nd week 20 10 3rd week 30 204th week 40 40A)
Amanda's method is linear because the number of minutes increased by an equal number every week.common difference is 10.1st week 0 + 10 = 102nd week 10 + 10 = 203rd week 20 + 10 = 304th week 30 + 10 = 40Billy's method is exponential:5(2)^x1st week 5(2⁰) = 5(1) = 52nd week 5(2¹) = 5(2) = 103rd week 5(2²) = 5(4) = 204th week 5(2³) = 5(8) = 40Mark
please help.
A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
A.45.5 square feet
B.63 square feet
C.66.5 square feet
D.84 square feet
Answer:
Option C
The area of the doghouse is [tex]66.5\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
where
b1,b2 are the parallel bases of trapezoid
h is the height of trapezoid
in this problem we have
[tex]b1=7\ ft[/tex]
[tex]b2=7+5=12\ ft[/tex]
[tex]h=7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(7+12)7=66.5\ ft^{2}[/tex]
An airplane on autopilot took 9 hours to travel 6,561 kilometers. What is the unit rate for kilometers per hour
divide total km by time
6561 / 9 = 729 km per hour
Leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. How many servings of espresso did he drink?
Answer:
Hope it helps
Step-by-step explanation:
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
Answer:
(K-h) (x) = 4(x-2)
Step-by-step explanation:
The cost of producing x soccer balls in thousands of dollars is represented by h (x) = 5x + 6
Revenue generated is represented by K(x) = (9x-2)
Them ( K-h) (x) will represent
( K-h )x = cost of revenue - production
= profit
( K-h )x = K(x) - h(x)
= (9x-2) - (5x + 6)
= (9x - 5x) - (2+6)
= 4x - 8
Profit = (K-h) (x) = 4(x-2)
Which of the quadratic functions has the widest graph? y = 0.3x2 y = –4x2
For the parent function y = f(x), the vertical stretching or compression of the function is a f(x).
If | a | < 1 (a fraction between 0 and 1), then the graph is compressed vertically by a factor of a units.
If | a | > 1, then the graph is stretched vertically by a factor of a units.
For values of a that are negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
Thus, the equation with the widest graph is 0.3x^2.Yes, Y = 0.3x^2 is correct!!
What is the factored form of the expression? 4x2 – 81y2
Which pair of quantities is LEAST likely to be directly proportional? CLEAR CHECK Area and side length of a rhombus , Distance and time when speed is constant, Total cost and the number of movie tickets purchased ,and Hours worked and money earned please answer this question quickly ...
Answer:
Area and Side length of a rhombus.
Step-by-step explanation:
1. Area and side length of a rhombus - This is least proportional as they are inversely proportional.
2. Distance and time when speed is constant is proportional.
Distance = speed x time
When speed is constant, the distance increases with respect to speed.
3. Total cost and the number of movie tickets purchased.
As the number of tickets purchased increases, the cost also increases.
4. Hours worked and money earned
When the number of hours increases, the money earned also increases.
Find the nth term of this sequence: 1,5,9,13,17
When writing a two column proof you should always start with ________ Information.
What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2 + 8x + 2
Answer-
[tex]\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}[/tex]
Solution-
Given expression is [tex](x+2)^4[/tex]
Applying Binomial Theorem
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
Here,
a = x, b = 2 and n = 4
So,
[tex]\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i[/tex]
Expanding the summation
[tex]=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4[/tex]
[tex]=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4[/tex]
[tex]=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16[/tex]
[tex]=x^4+8x^3+24x^2+32x+16[/tex]
Answer:
The answer to this question can be viewed in the images attached.
Hope it helps. Thanks
5u - 5u =u -u help please
Answer:
it would cancel eachother out so infinite
Step-by-step explanation:
Mr. Ernesto spent $72 for 3 bags of grass seed. How much did he spend for EACH bag?
URGENT!!!
A bag contains 144 ping-pong balls. more than half of the balls are painted orange and the rest are painted blue. two balls are drawn at random without replacement. the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors. how many orange balls are in the bag?
There are approximately 72 orange balls in the bag.
We have,
Let's assume the number of orange balls in the bag is x.
Given that more than half of the balls are painted orange, we have the inequality:
x > 144/2
x > 72
Now, let's consider the probability of drawing two balls of the same color:
The probability of drawing two orange balls.
= (x/144) * ((x-1)/(144-1))
= (x(x-1))/(144*143)
The probability of drawing two blue balls.
= ((144-x)/144) * ((144-x-1)/(144-1))
= ((144-x)(143-x))/(144*143)
Given that the probability of drawing two balls of the same color is the same as the probability of drawing two balls of different colors, we can set up the equation:
(x(x-1))/(144143) = ((144-x)(143-x))/(144143)
Simplifying the equation:
x(x-1) = (144-x)(143-x)
x^2 - x = 144143 - 287x + x^2
288x = 144143
x = (144*143)/288
x ≈ 72
Therefore,
There are approximately 72 orange balls in the bag.
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How many square feet of carpeting are needed to carpet a 12-foot by 12-foot room
Find the area of a trapezoid with bases of 8 and 16 and a height of 10. A)1,280 sq. Units B) 240 sq. units C)120 sq. units
Answer: The answer is (C) 120 sq. units.
Step-by-step explanation: We are given to find the area of a trapezoid with bases of lengths 8 units and 16 units and height of 10 units.
We know that the area of the trapezoid with 'a' and 'b' as lengths of the bases and height 'h' is given by
[tex]A=\dfrac{1}{2}(a+b)h.[/tex]
Here, a = 8 units, B = 16 units and h = 10 units.
Therefore, the area of the given trapezoid will be
[tex]a\\\\=\dfrac{1}{2}(a+b)h\\\\=\dfrac{1}{2}\times(8+16)\times 10\\\\=24\times 5\\\\=120~\textup{sq. units.}[/tex]
Thus, the correct option is (C).
What is the value of X in the isosceles trapezoid below?
Answer:
D. 13Step-by-step explanation:
Remember that in a isosceles trapezoid, its angles on the base are always congruent.
Also, we know by definition that the sum of interior angles of a trapezoid is equal to 360°, so
[tex]2(2x)+2(10x+24)=360\\4x+20x+48=360\\24x=360-48\\x=\frac{312}{24}\\ x=13[/tex]
Therefore, the right answer is D.
Answer: 13
a p e x confirmed
the length of a rectangle is 5cm less than 3 times the width.if the perimeter of a rectangle is 54cm, find the length and the width
To solve for the length and width of the rectangle, equations were set up based on the given perimeter and the relation between length and width. The width was found to be 8 cm, and substituting this into the length formula gave a length of 19 cm.
The question concerns finding the length and width of a rectangle given that the length is 5 cm less than three times the width and the perimeter is 54 cm. To solve this, let's denote the width of the rectangle as 'w' and the length as 'l'. The relationship between the length and width can be expressed as 'l = 3w - 5 cm'. The perimeter (P) of a rectangle is given by P = 2l + 2w, and substituting our expressions in terms of 'w' into the formula gives us 2(3w - 5) + 2w = 54. Simplifying and solving for 'w' gives us the width. Subsequently, we can substitute this width into the equation for length to find 'l'.
So, let's start by setting up the equation:
2(3w - 5) + 2w = 54
6w - 10 + 2w = 54
8w - 10 = 54
8w = 64
w = 8 cm
Now we substitute w = 8 cm into the length formula:
l = 3(8) - 5
l = 24 - 5
l = 19 cm
Therefore, the width of the rectangle is 8 cm and the length is 19 cm.
The product of two consecutive odd integers is 143. find all such pairs of integers.
Juanita receives her paycheck and knows that her gross pay and federal tax are correct. Using the fact that Social Security tax is 6.2% of gross pay, Medicare tax is 1.45% of gross pay and state tax is 19% of federal tax, determine if Juanita's net pay is correct.
Earnings
Deductions
Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
11/17
$1,020.00
$107.00 $63.24 $14.79 $20.33
$814.64
Choose the true statement below.
a.
The net pay is correct.
b.
The Social Security tax is not correct.
c.
The Medicare tax is not correct.
d.
The state tax is not correct.
The answer is A. The net pay is correct.
A scalene triangle has side side lengths of 12 feet, 8 feet, and 15 feet. what is the perimeter of the triangle
Answer:
gh
Step-by-step explanation:
The top and bottom margins of a poster are 4 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area.
To find the smallest poster area with a fixed printed area of 388 square centimeters, calculate optimized values for the width and height of the printed area, considering the margins, and derive the poster's dimensions by adding the margins to these values.
Explanation:To find the dimensions of the poster with the smallest area given a fixed printed area, we should first determine the dimensions of the printed area. We know that the printed area is 388 square centimeters and that the margins do not change. Let's denote the width of the printed area as w and the height as h.
The area of the printed material is given by Area = w × h = 388 cm². The total width of the poster would be w + 2×(8 cm) (since there are two side margins), and the total height would be h + 2×(4 cm) (since there are top and bottom margins).
To minimize the area of the poster, we need to minimize the function for the total area of the poster A(w,h) = (w + 16)(h + 8). As the printed area is fixed, we can express h in terms of w using h = 388/w and substitute this into the function to get A(w) = (w + 16)((388/w) + 8).
Taking the derivative dA/dw and setting it to zero, we find the optimal value for w, and consequently, we calculate h. The dimensions of the poster that minimize the total area can then be determined by adding the margins to these optimized values of w and h.
The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r=100[tex]( \frac{1}{2})^ \frac{d}{5} [/tex] . What is the daily percent of decrease?
87.06%
12.94%
3.13%
10%
Answer:
its 12.94%
Step-by-step explanation
How to find the quadratic equation when given the vertex and y intercept?
Between what two consecutive positive integers is the square root of 85
A number system is defined as a system of writing to express numbers. between 9 and 10 positive integers is the square root of 85 is there.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the two consecutive positive integers which have square root of 85 in between.
Firstly we need to know meaning of consecutive numbers.
Numbers which follow each other continuously in the order from smallest to largest are consecutive numbers.
Let us take some perfect square numbers
1,4,16,25,36,49,64,81,100
We know that square root of 81 is 9
square root of 100 is 10
square root of 85 is in between 9 and 10
Hence between 9 and 10 positive integers is the square root of 85 is there.
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Stein Co. issued 13-year bonds two years ago at a coupon rate of 10.3 percent. The bonds make semiannual payments. If these bonds currently sell for 95 percent of par value, what is the YTM?
Nper = 11*2 = 22 (indicates the period over which interest payments are made)
PMT = 1000*10.3%*1/2 = 51.5 (indicates sem-annual interest payments)
PV = 1000*95% = 950 (indicates the current selling price of the bonds)
FV = 1000 (indicates the face value of bonds)
Rate = ? (Indicates YTM)
YTM = Rate(Nper,PMT,PV,FV)*2 = Rate(22,51.5,-950,1000)*2 = 11.098% or 11.10%
Answer is 11.098% or 11.10%.
In the deli, meat and cheese are sold by the pound. There is usually a unit price in each variety in the refrigerator case. If honey ham costs $5.99 per lb, how much would 1.5 lbs cost? Enter your answer as a decimal rounded to the nearest cent.
Write a linear factorization of the function. f(x) = x4 + 4x2
Final answer:
The function f(x) =[tex]x^4 + 4x^2[/tex] is factored using the difference of squares method to achieve its linear factorization. The final factorization over complex numbers is f(x) = x * x * (x + 2i) * (x - 2i).
Explanation:
To write a linear factorization of the function f(x) = [tex]x^4 + 4x^2[/tex] to find the factors of the polynomial that are linear, meaning each factor will be of the form (x - c) where c is a constant.
First, notice that the given polynomial is a quadratic in form, where [tex]x^2[/tex] is our variable. This gives us [tex]f(x) = (x^2)2 + 4(x^2)[/tex]which resembles the sum of squares [tex]a^2 + 2ab + b2 = (a + b)^2.[/tex] However, we only have [tex]a^2 + 2ab[/tex], with b being 2, and a being [tex]x^2[/tex].
To create a perfect square, we can write it as a difference of squares by adding and subtracting 4: [tex]f(x) = (x^2 + 2)^2 - (2)^2[/tex]. This can be factored further using the difference of squares formula, giving us[tex]f(x) = (x^2 + 2 + 2)(x^2 + 2 - 2)[/tex] which simplifies to [tex]f(x) = (x^2 + 4)(x^2).[/tex]
The linear factorization can be found by recognizing that x2 is already a product of linear factors x * x. Since [tex]x^2[/tex] + 4 cannot be factored over the real numbers, we need to use complex numbers to factor it further.
Using the sum of squares, we get [tex]x^2[/tex] + 4 = (x + 2i)(x - 2i), resulting in the final linear factorization over the complex numbers: f(x) = x * x * (x + 2i) * (x - 2i).