Answers
x+8/2 * 5/3x+24
then simplify
3x+24 = 3(x+8)
now cancel like terms
(x+8 cancels) / 2 * 5 / 3 (x+8 cancels)
you are left with
2*5/3
10/3
or 3 1/3
Related Questions
Biologists have proposed a cubic polynomial to model the length l of alaskan rockfish at age a:l = 0.0155a3 − 0.372a2 + 3.95a + 1.21, where l is measured in inches and a is in years. (a) (2 pts) calculate dl da a=12 (b) (2 pts) interpret your answer.
Answers
dl/da = 3(0.0155)a² - 2(0.372)a + 3.95
Substituting the known value, a = 12
dl/da = (3)(0.0155)(12)² - 2(0.372)(12) + 3.95
Simplify,
dl/da = 1.718
(b) The answer in a tells us that the length of the alaskan rockfish will change at a rate of 1.718 inches/year when it is already 12 years old.
To calculate dl/da when a=12, find the derivative of the cubic polynomial and substitute a=12. The rate of change of the length is approximately 1.682 inches per year.
Explanation:To calculate dl/da when a=12, we need to find the derivative of the given cubic polynomial with respect to a. The derivative of l with respect to a can be found by taking the derivative of each term separately and then simplifying:
Find the derivative of 0.0155a^3: 3 * 0.0155 * a^2 = 0.0465a^2 Find the derivative of -0.372a^2: 2 * -0.372 * a = -0.744a Find the derivative of 3.95a: 3.95 Find the derivative of 1.21: 0Now substitute a=12 into the derivatives we found:
0.0465(12)^2 = 6.66-0.744(12) = -8.9283.950So, dl/da when a=12 is approximately 0.0465(12)^2 - 0.744(12) + 3.95 = 6.66 - 8.928 + 3.95 = 1.682.
Interpretation: The value dl/da represents the rate of change of the length of the alaskan rockfish with respect to its age. In this case, when the rockfish is 12 years old, its length is changing at a rate of approximately 1.682 inches per year.
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The phones at Century Cellphones vary in price depending upon demand. The average phone has a built in camera and costs x dollars. Phones with both a camera and an MP3 player are 35 dollars less than twice the cost of the phones with just the camera. Phones without any features are 100 dollars less than the cost of the phone with just the camera. Purchasing all three would cost at least $525.
a) Determine the inequality that represents this situation.
b) How much does the phone with just the camera cost?
Answers
a. let us say that:
a = cost of phones with camera
b = cost of phones with camera and mp3
c = cost of phones without any features
b = 2 a – 35
c = a – 100
a + b + c = 525
b > a > c
b. We are given three equations with three unknowns. So we can solve the problem.
a + (2 a – 35) + (a – 100) = 525
a + 2 a – 35 + a – 100 = 525
4 a – 135 = 525
4 a = 660
a = $165
a) According to the problem, purchasing all three phones would cost at least $525, which leads us to the inequality:
[tex]4x - 135 \geq 525[/tex]
b) The cost of the phone with just a camera is at least $165.
a) Setting Up the Inequality
Let’s define the variables based on the information given:
Let [tex]x[/tex] be the cost of the phone with just a camera. Then, the cost of the phone with both a camera and an MP3 player is given as:[tex]y = 2x - 35[/tex] The cost of the phone without any features is:
[tex]z = x - 100[/tex]
Now, the total cost of buying all three types of phones can be expressed as:
[tex]x + y + z[/tex]
Substituting the expressions for [tex]y[/tex] and [tex]z[/tex], we get:
[tex]x + (2x - 35) + (x - 100)[/tex]
This simplifies to:
[tex]4x - 135[/tex]
b) Finding the Cost of the Phone with Just the Camera
To find out the value of [tex]x[/tex], we can solve the inequality:
[tex]4x - 135 \geq 525[/tex]
Adding 135 to both sides gives:
[tex]4x \geq 660[/tex]
Now, dividing both sides by 4:
[tex]x \geq 165[/tex]
you find a fossilized animal footprint in montana. One footprint is round and has a diameter of 42cm. what is the are of the footprint?
Answers
To find the area of a round footprint with a diameter of 42 cm, you use the formula for the area of a circle, A = πr². The radius is 21 cm, so the area is approximately 1382.74 cm².
To find the area of a round footprint, you use the formula for the area of a circle, which is πr², where r is the radius of the circle.
First, find the radius by dividing the diameter by 2. In this case, 42 cm / 2 = 21 cm.Next, use the area formula: area = π x (radius)². So, area = π x (21 cm)².Calculate the result: area = π x 441 cm².Using the approximation π ≈ 3.14, the area ≈ 3.14 x 441 cm².The final area ≈ 1382.74 cm².Therefore, the area of the fossilized footprint is approximately 1382.74 cm².
Last year, Bill opened an investment account with $6800 . At the end of the year, the amount in the account had increased by 24.5% . How much is this increase in dollars? How much money was in his account at the end of last year?
Answers
Bill's investment increased by $1666 over the year, which is 24.5% of the original $6800. At the end of the year, the total amount of money in the account was $8466.
Explanation:To determine the increase in dollars due to the investment growth of 24.5%, we would calculate 24.5% of $6800. We can use the formula increase = principal × (rate/100), where principal is the starting amount and rate is the percentage increase.
So, increase = $6800 × (24.5/100) = $6800 × 0.245 = $1666. This means that the increase in dollars is $1666.
Next, to find out how much money was in his account at the end of last year, we add this increase to the original investment: total amount = original amount + increase = $6800 + $1666 = $8466. Therefore, the total amount in the account at the end of the year was $8466.
complete the solution of the equation. Find the value of y when x equals -4
x + 3y = 14
Answers
When x equals -4, the value of y is 6 by substituting -4 into the equation x + 3y = 14 and solving for y.
Explanation:To complete the solution of the equation and find the value of y when x equals -4, simply substitute -4 for x into the equation x + 3y = 14. The steps are as follows:
Start with the equation: x + 3y = 14.Substitute -4 for x: (-4) + 3y = 14.Solve for y: 3y = 14 + 4.Simplify: 3y = 18.Divide both sides by 3: y = 18 / 3.Find the value of y: y = 6.Therefore, when x equals -4, the value of y is 6.
Deon drove 408 miles using 16 gallons of gas. At this rate, how many miles would he drive using 11 gallons of gas?
Answers
By setting up a ratio based on the known miles per gallon, we can determine that Deon would be able to drive 281.5 miles using 11 gallons of gas.
Explanation:This problem can be solved by setting up a proportion to find out how many miles Deon would drive using 11 gallons of gas. First, we know that Deon can drive 408 miles with 16 gallons of gas. This forms a ratio of 408/16 which simplifies to 25.5. This means Deon can drive 25.5 miles for every gallon of gas. Using this, we can determine how far he would travel with 11 gallons by multiplying the miles per gallon (25.5) by 11.
Therefore, Deon would drive 281.5 miles using 11 gallons of gas.
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Which choice represents the fraction below as a single exponential expression?
8^2/8^16
a. 8^-12
b. 8^12
c. 1/4
d. 8^4
Answers
the correct answer would be A. 8^-12
8^2 /8^16 = 1/8^14 = 2.27373*10^-13
8^-12 = 1.45519*10^-11
which are equal so answer is A
PLZ HELP ASAP
8 ÷ 16 = 48 because A) 288 × 1/6 = 48 B) 80 × 1/10 = 8 C) 64 × 1/8 = 8 D) 48 × 1/6 = 8
Answers
Answer:
D)48 × 1 6 = 8 Use the relationship between multiplication and division to explain that 8 ÷ 1 6 = 48 because 48 × 1 6 = 8.
Step-by-step explanation:
what is the multiplicative rate of change of the function described in the table ?
Answers
Hence, the multiplicative Rate of change is:
5
Step-by-step explanation:The multiplicative Rate of change refers to the fixed constant which when multiplied to the output will lead to increase/decrease in the next output value.
We have the table of values as:
x y
-1 1/10
0 1/2
1 5/2
2 25/2
3 125/2
Hence, we see that when 5 is multiplied to the output value we obtain the next output value.
i.e.
1/10×5=1/2
1/2×5=5/2
5/2×5=25/2
25/2×5=125/2
Hence, the multiplicative Rate of change is:
5
Veronica deposited $21 in a savings account that earns 2.4% simple interest. Which graph represents this scenario?
Answers
Answer:
The below graph represents this scenario.
Step-by-step explanation:
Given,
The deposited amount, P = $ 21,
Annual interest rate, r = 2.4 % = 0.024,
Thus, the simple interest after x years,
[tex]y=P\times r\times t[/tex]
[tex]=21(0.024)(x)[/tex]
[tex]=0.0504x[/tex]
If x-axis shows the number of years and y axis represents the simple interest after x years,
So, y = 0.0504x is a line passes through the origin which will show the given scenario,
( shown below )
Also, x ≥ 0 ( number of years can not be negative )
A number cube is rolled 30 times, and a six comes up 5 times. What is the experimental probability that a six is rolled?
Answers
(1/6)=(5/30)=p
The probability of the cube landing on the number 6 five times is 1 out of 6
What does it mean to say that two variables are negatively associated?
Answers
On average, at least 25,000 pieces of luggage are lost or misdirected each day by United States airlines. Of these, 98% are located by the airlines within 5 days. From a given day’s lost luggage, at least how many pieces of luggage are still lost after 5 days?
Answers
To find the number of luggage still lost after 5 days, at least 2% of the given day's lost luggage will still be lost after 5 days.
Explanation:To find the number of luggage still lost after 5 days, we can use the concept of complementary events.
Since 98% of lost luggage is located by the airlines within 5 days, that means 2% of the lost luggage is still not located.
Therefore, at least 2% of the given day's lost luggage will still be lost after 5 days.
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NEED HELP FAST PLEASE!
What is the equation of this line?
y = 1/2x -- 3
y = --1/2x -- 3
y = --2x --3
y = 2x -- 3
Answers
slope = (-2 + 3)/(2-0) = 1/2
b = -3
equation
y = 1/2x - 3
answer is A
y = 1/2x - 3
find × in this proportion 16/X = x/4
x=
a. 64
b. 32
c. 16
d 8
Answers
Answer:
d
Step-by-step explanation:
The proportion given to us is
[tex]\frac{16}{x} =\frac{x}{4}[/tex]
Next we cross multiply to get
[tex]16*4=x*x[/tex]
[tex]64=x^2[/tex]
[tex]x^2=64[/tex]
Take the sqrt on both side to get x
so
[tex]\sqrt{x^2} = \sqrt{64}[/tex]
x=8
so the correct option is d .
use the triangle to answer the question.
Which equation shows a correct relationship of trigonometric functions?
sin x/cos y=0
sin x/ cos x =0
sin x/ cos x =1
sin x/ cos y =1
Answers
---------------------------------------------
---------------------------------------------
Label the sides as shown in the image attachment.
P = horizontal leg (opposite of angle x; adajcent to angle y)
Q = vertical leg (opposite of angle y; adajcent to angle x)
R = hypotenuse (longest side; always opposite the 90 degree angle)
Use the definitions of sine and cosine to say...
sin(Angle) = opposite/hypotenuse
sin(x) = P/R
and
cos(angle) = adjacent/hypotenuse
cos(y) = P/R
Notice how sin(x) = cos(y). This is true any time x+y = 90 which is the case here (x and y are complementary angles). A more specific example is sin(30) = cos(60) which are both equal to 1/2 or 0.5
Since sin(x) = cos(y), this means sin(x)/cos(y) = 1 as any expression divided by itself is equal to 1. Keep in mind that cos(y) cannot equal zero.
This is why choice D is the final answer.
side note: something like cos(x)/sin(y) or sin(y)/cos(x) or similar are all equal to 1 as long as x+y = 90
Solve the inequality.
g - 6 > -1
A. g > 7
B. g > –7
C. g > 5
D. g < –7
Answers
The correct answer is option C g > 5.
To solve the inequality, we need to isolate the variable g. Here are the steps:
Add 6 to both sides of the inequality to isolate g.
The inequality now becomes: g - 6 + 6 > -1 + 6
Simplify both sides: g > 5
The solution to the inequality is g > 5.
Therefore, the correct answer is option C.
what is the measure of ∠J?
Given △ABC≅△JKL, m∠B=55°, and m∠L=25
Answers
m < B = 55....so < K = 55 also
m < L = 25.....so < C = 25 also
so we need the measure of < J....and < A
interior angles of a triangle add up to 180 degrees
< J + < K + < L = 180
< J + 55 + 25 = 180
< J + 80 = 180
< J = 180 - 80
< J = 100......so < J = 100....and so does < A
Select the classification of the polynomial using its degree and number of terms.
9x − 3y + 7
The polynomial is classified as a
-quadratic trinomial
-linear monomial
-linear trinomial
Answers
I need help please ace/experts
Answers
1.
18.98 per 1000
320,000 / 1000 = 320
18.98 x 320 = $6073.60
2. smoker: 9.36 * 100 = 936
non smoker: 7.85 * 100 = 785
936 - 785 = $151
Which situation is mostly a constant rate of change?
Answers
Answer:B
Step-by-step explanation: The distance traveled by a truck driving at a constant speed compared with time.
How much money do i have if i had tow dollars five pennies and three quarters how much money do i have?
Answers
Help please solve 5x+2=22
Answers
5x = 22 - 2
5x = 20
x = 20/5
x = 4
[tex]5x+2=22[/tex]
To solve this, we need to isolate the number 2 by shifting it infront of 22. By this, we can easily solve the equation.
[tex]5x = 22 -2[/tex]
We need to be very careful while isolating the number, make sure the operation is opposite.
[tex]5x = 22 -2[/tex]
[tex]5x = 20[/tex]
[tex]x=20/5[/tex]
[tex]x=4[/tex]
Hope I helped (:
Have a great day!
Jalen has a balance of $1870 on a credit card with an APR of 19.7%, compounded daily. About how much will he save in interest over the course of a year if he transfers his balance to a credit card with an APR of 16.5%, compounded monthly. (Assume that Jalen makes no payments or new purchases during the year, and ignore any possible late payment fees.)
Answers
A=p (1+r/k)^kt
A future value
P present value
R interest rate
K compounding periods
T time
When the compounding periods are daily balance after one year is
A=1,870×(1+0.197÷365)^(365×1)
A=2,277.06
When the compounding periods are monthly balance after one year is
A=1,870×(1+0.165÷12)^(12×1)
A=2,202.99
So will save
2,277.06−2,202.99
=74.07....answer
Hope it helps!
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.
Answers
So if 1lbs = $5.99
and you need to find 1.5lbs
5.99x = answer
then all you simply have to do is multiply $5.99 by 1.5lbs.
When completing the equation, you will see that 1.5lbs of ham will cost $8.985 which will round to $8.99.
Find the ratio a:b, if it is given that ... 2a-3b/5 = a+b/3
Answers
30a-9b=15a+5b
15a=14b
Ratio is 15:14
Jason went shopping.
He bought a watch and a pair of trainers for a total price of £53.55
This price includes a 15% loyalty discount.
Before the discount, the trainers were priced at £38
Work out the price of the watch before the discount.
Answers
pw+38=63
63-38 =£25
Paul serves 4 cups of coffee every 6 minutes Using y for number of cups of coffee and x for the amount of minutes that have passed, write an equation that represents this proportional relationship.
Answers
If the probability of a certain event is 63/92, what are the odds against the event happening?
Answers
What is the difference between the profits Mr.Brown's store earned in the first quarter and the third quarter?
a. $2,411.44
b. $2,814.64
c. $3,004.54
d. $3,214.78
Answers
Answer:
Option a. $2,411.44
Step-by-step explanation:
In the table the profit of Mr. Brown's store in all quarters of 2012 was given.
In Quarter 1 Profit was = $9,841.28
In Quarter 2 profit was = $8,957.67
In Quarter 3 profit was = $7,429.84
In Quarter 4 profit was = $11,095.67
To find out the difference between the profits earned in the first quarter and the third quarter, we subtract it.
Difference between profits = 9,841.28 - 7,429.84 = $2,411.44
Answer would be Option a. $2,411.44