Diff Eq dy/dx= (ycos(x))/(1+y^2) initial condition is y(0)=1 work below ...?
3x^2-18x+24
factor it out???
Shane and his family go to the movie theatre and buys 6 tickets for $12 each. then they spend a total of $31 for popcorn and drinks. how much did shane and his family spend for tickets, popcorn, and drinks at the movie theatre?
Shane and his family spent a total of $103 at the movie theatre, which includes the cost of 6 tickets at $12 each and $31 on popcorn and drinks.
Explanation:Shane and his family bought 6 tickets for $12 each, thus the total cost of the tickets is 6 * $12 which equals $72. Afterwards, they spent an additional $31 on popcorn and drinks. To find out how much they spent altogether at the movie theatre, we have to add the cost of the tickets and the cost of the popcorn and drinks. Therefore, $72 (for the tickets) + $31 (for the snacks) = $103. So, Shane and his family spent a total of $103 at the movie theatre.
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An adult meerkat weighs 776 grams. This is o.747 kilograms more than the weight of a baby meerkat. how much does a baby meerkat weigh ?
The baby meerkat weighs 29 grams.
First, we need to ensure our units are the same, so we'll convert 776 grams to kilograms.
There are 1,000 grams in a kilogram, so 776 grams is equivalent to 0.776 kilograms.
Given that the adult meerkat is 0.747 kilograms heavier than the baby meerkat, we can calculate the baby meerkat's weight by subtracting.
Baby meerkat weight = Adult meerkat weight - Additional weight
Baby meerkat weight = 0.776 kg - 0.747 kg
Baby meerkat weight = 0.029 kg
To express this in grams, we multiply by 1,000:
Baby meerkat weight in grams = 0.029 kg × 1000
= 29 grams
gradie dari persamaan garis 3(x-y) =x+5
The label on the car's antifreeze container claims to protect the car between −30°C and 130°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C = (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.
−30 > (F − 32) > 130; −22 > F > 266
−30 < (F − 32) < 130; −22 < F < 266
−30 < (F − 32); −22 < F
(F − 32) < 130; F < 266
The correct answer is B. I took the same test and the answer is B. :) Hope this helps!
James has $120 in his saving account and plans to have $x each month for 6 months. the expression $6x $120 represents the total amount in the account after 6 months. factor the expression 6x 20
Answer:
6(x+20)
Step-by-step explanation:
6x: 2*3
120: 2*2*3*5
The GCF of 6x*120 is 2*3
so the factored expression is 6(x+20)
What is the completely factored form of 3x^5 – 7x^4 + 6x^2 – 14x?
A. (x^4+2x)(3x-7)
B. x^4(3x-7)(2x-1)
C. x(x^3+2)(3x-7)
D. x(3x^4-7x^3+6x-14)
answer:
C. x(x^3+2)(3x-7)
hope this helps! :o)
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
The value of x from the given circle is 4.6 units.
From the given figure, the radius is 9.7 units.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here,
9.7 =5.1+x
⇒ x=9.7-5.1
⇒ x=4.6 units
Therefore, the value of x from the given circle is 4.6 units.
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Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
The correct answer is D. on edg
Maya has 5 over 6 cup of ice cream. how many 1 over 4-cup servings are in 5 over 6 cup of ice cream?
there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
To find out how many [tex]\( \frac{1}{4} \)-cup servings are in \( \frac{5}{6} \)[/tex] cup of ice cream, we need to divide [tex]\( \frac{5}{6} \) by \( \frac{1}{4} \)[/tex].
We can do this by converting [tex]\( \frac{5}{6} \)[/tex] to have the same denominator as [tex]\( \frac{1}{4} \)[/tex], which is 6, and then dividing:
[tex]\[ \frac{5}{6} \div \frac{1}{4} \][/tex]
To make the denominators the same, we multiply both the numerator and denominator of [tex]\( \frac{5}{6} \) by \( 4 \):[/tex]
[tex]\[ \frac{5 \times 4}{6 \times 4} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \div \frac{1}{4} \][/tex]
Now, we can divide [tex]\( \frac{20}{24} \) by \( \frac{1}{4} \):[/tex]
[tex]\[ \frac{20}{24} \div \frac{1}{4} \][/tex]
[tex]\[ = \frac{20}{24} \times \frac{4}{1} \][/tex]
[tex]\[ = \frac{20 \times 4}{24 \times 1} \][/tex]
[tex]\[ = \frac{80}{24} \][/tex]
Now, we simplify the fraction:
[tex]\[ \frac{80}{24} = \frac{10 \times 8}{12 \times 2} \][/tex]
[tex]\[ = \frac{10}{3} \][/tex]
Therefore, there are [tex]\( \frac{10}{3} \) or \( 3 \frac{1}{3} \) servings of \( \frac{1}{4} \)-cup in \( \frac{5}{6} \)[/tex] cup of ice cream.
The probability that an airplane flight departs on time is 0.89 The probability that a flight arrives on time is 0.87 The probability that a flight departs and arrives on time is 0.81
To answer the questions, we need to use the concepts of probability.
Explanation:To answer the questions, we need to use the concepts of probability.
a. The number of airplanes arrive and depart the airport per hour can be calculated by multiplying the probabilities of a flight departing and arriving on time. Although the exact numbers are not given, the probability of a flight departing and arriving on time is 0.81, which can be used as an estimate.
b. To find the probability that there are exactly 100 arrivals and departures in one hour, we need to use the concept of the binomial distribution. However, we don't have enough information to calculate the probability.
c. To find the probability that there are at most 100 arrivals and departures in one hour, we can use the concept of the cumulative distribution function of the binomial distribution. Again, we don't have enough information to calculate the probability.
The question is about calculating probabilities and involves understanding conditional probability, probability distributions, and statistical methods. It requires more data to answer parts a, b, and c. The remaining parts of the question can be approached with standard statistical methods and concepts.
Explanation:The question pertains to the field of probability within mathematics and involves calculations based on given probabilities for airplane flights departing and arriving on time. The data presented involve conditional probabilities and the characteristics of certain probability distributions. It is essential to understand these concepts to solve the exercises provided. Unfortunately, the given information does not contain sufficient details to answer parts a, b, and c as they require additional specific data about the actual number of flights or arrivals and departures per hour. However, the remaining parts of the question can be approached with standard statistical methods such as using z-scores for normal distributions, applying properties of uniform distributions for waiting times, understanding the concept of rate-determining steps in a process, and conducting hypothesis tests about a population mean given a sample.
A company makes boxes of cereal. A box usually contains 450 grams of cereal. Here are two options for a special offer. Option A 20% more cereal Option B usual amount of cereal 15% off the price.
Which option is best for the customer
A percentage is a way to describe a part of a whole. The best option for the customer to buy is option A.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
Let the cost price of a cereal box be represented by x.
Given that the box usually contains 450 grams of cereal. Therefore, the unit rate for each option can be written as,
Option A
Weight of cereal = 20% more cereal
= 450 grams + 20% of 450 grams
= 450 grams + 90 grams
= 540 grams
Unit rate for option A = $x / 540 grams
Option B
Cost price of cereal = 15% off the price
= x - 15% of x
= x + 0.15x
= 0.85x
Unit rate for option A = $0.85x / 450 grams
Assume that option A is good. Now, if we subtract unit rate of option B from unit rate of option A then two of the cases are possible, if the value of the result is positive then the unit rate of option A is bigger while if the value is negative unit rate of option B is bigger.
Difference = (x/540) - (0.85x/450)
= (450x - 459x)/243000
= -9x/243,000
= -x/27,000
Further, since the difference is negative, therefore, the unit rate of option B is bigger. But since the value of option B is bigger it is costly and not the correct option to buy.
Hence, the best option for the customer to buy is option A.
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solve 12^x-2=20 round to the nearest ten-thousandth? help, please!
The solution to the equation 12^x - 2 = 20, when solved for x and rounded to the nearest ten-thousandth, is x = 1.4624.
Explanation:To solve the equation 12^x - 2 = 20, we first need to isolate the exponential term. This can be done by adding 2 to both sides of the equation resulting in 12^x = 22. Next, we take the logarithm of both sides to solve for x. We can use any logarithmic base, but common practice is to use base 10 or the natural logarithm (base e). The next steps are:
Take the logarithm of both sides: log(12^x) = log(22).Apply the exponent rule of logarithms: x · log(12) = log(22).Divide both sides by log(12) to solve for x: x = log(22) / log(12).Use a calculator to find the value of x and round to the nearest ten-thousandth.Calculating the value on a calculator gives us x ≈ 1.4624. Therefore, the solution to the equation, rounded to the nearest ten-thousandth, is x = 1.4624.
The correct answer is option (b) "x ≈ 1.2056."
To solve the equation [tex]\(12^{(x-2)} = 20\)[/tex], we can take the logarithm of both sides.
Let's use the natural logarithm (ln) for this:
[tex]\[ \ln(12^{(x-2)}) = \ln(20) \][/tex]
Using the logarithm property [tex]\( \log_a(b^c) = c \cdot \log_a(b) \)[/tex], we can rewrite the left side:
[tex]\[ (x-2) \cdot \ln(12) = \ln(20) \][/tex]
Now, solve for (x):
[tex]\begin{aligned}& x-2=\frac{\ln (20)}{\ln (12)} \\& x=\frac{\ln (20)}{\ln (12)}+2\end{aligned}[/tex]
Now, calculate the value:
[tex]\begin{aligned}& x \approx \frac{\ln (20)}{\ln (12)}+2 \\& x \approx \frac{2.9957}{2.4849}+2 \\& x \approx 1.2056\end{aligned}[/tex]
So, the solution to the equation is approximately [tex]\( x \approx 1.2056 \)[/tex]
Complete Question:
Solve [tex]\(12^{(x-2)} = 20\)[/tex]. Round to the nearest ten-thousandth.
a. x ≈ 1.0792
b. x ≈ 1.2056
c. x ≈ 3.2056
d. x ≈ 1.3010
James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy's collection
In one week, a family spent $132.19 for groceries. they spent $150.06 the next week. if c represents the increase in their grocery bill from one week to the next, what is c?
a. $17.87
b. $27.87
c. $28.97
d. $282.25
Which ratio is equal to 5/6 and
Which ratio is not equal to 4/9? ...?
find the nonpermissible replacement for the variable n in this expression (n-8)/(n-8)
...?
A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble.
Which color marble is less likely to be picked than purple?
The answer is blue i just took the test.
Breann solved the system of equations below. What mistake did she make in her work? (5 points)
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 20
x = 4
2(4) + y = 5
y = −3
She should have substituted 5 + 2x
She combined like terms incorrectly, it should have been 4x instead of 5x
She subtracted 10 from both sides instead of adding 10 to both sides
She made no mistake
Breann correctly solved the system of equations, combining like terms accurately to find x = 4 and y = -3.
Explanation:The mistake Breann made in her calculation was combining like terms incorrectly. When she substituted y with 5 - 2x into the second equation, she arrived at x - 10 + 4x = 10. The correct combination of like terms should be 5x, not 4x, leading to the correct step 5x - 10 = 10. All other steps in her solution are correctly executed. She correctly found the value of x to be 4, and using the first equation, she correctly determined the value of y to be -3.
To go to dance class at 6:45 pm bus, kelly needs 35 minutes to walk home from a friends house, 30 minutes for dinner, and 20 minutes to drive to the class. to make class on time, what is the latest time she should leave her friends house
Monica paid sales tax of 1.50$ when she bought a new bike helmet.if the sales tax rate was 5% how much did the store charge for the helmet before tax
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The area of a rectangle is 48 square centimeters and the length of the rectangle is 8 centimeters longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
w + 8 = 48
w + 8w = 48
w(w+8)=48w(w+8)=48
8w = 48
find the value of the polygon. the polygon has 6 interior angles 2 of them are y and 4 of them are (2Y-20)
A dog's weight increased by 50% in three years. by the end of the 3 years, the dog weighed 45 pounds. how much did the dog weigh three years ago?
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side KL in the image parallelogram?
A. K’(-4, -6); L’(3, -3)
B. K’(-6, -4); L’(-3, -3)
C. K’(6, 4); L’(3, 3)
D. K’(-4, 6); L’(-3, -3)
Answer:
K′(−6, −4); L′(−3, −3)
Step-by-step explanation:
Got it right on the test
What do I write ?? Someone please help me
Answer:
WrItE wHaT yOu FeElLlLlL
Step-by-step explanation:
Divide. Express your answer in lowest terms. You MUST show your work to receive credit for this problem.
-15/16 divided by (-3/4)
in order for RECT to be a rectangle, what must the value of x be?
Answer:
x = 21
Step-by-step explanation:
If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).
∠RTC = ∠RTE + ∠ETC Formula for complementary angles
90 = 2x + 6 + 42 Substitute the angles
90 = 2x + 48 Combined like terms to simplify
Now isolate "x" to solve
90 - 48 = 2x + 48 - 48 Subtract 48 from both sides
42 = 2x
42/2 = 2x/2 Divide both sides by 2
x = 21
Therefore x is 21.
Multiply. write in simplest form fraction 6 1 1\2