You make 12 equal payments. You pay a total of $1500. How much is each payment?

Answer: Substitute: 4×7 Calculate the product or quotient: 28 the answer is 28

The amount of data compression an algorithm can produce is reliant upon:

Opiton B) Several patterns in the data.

Data compression is the process of reducing the size of a file by encoding its data information more efficiently. The more patterns in the data, the more efficiently it can be compressed.

An algorithm is a set of instructions that are used to complete a task, such as compressing data. If there are several patterns in the data, the algorithm can use these patterns to create a smaller, more efficient representation of the file, resulting in greater data compression.  This means that if there are repeating parts of the file being compressed, the algorithm can make use of that to reduce the size of the file.

However, the size of the file (whether it's large or small) does not necessarily affect the amount of data compression.

Therefore, the amount of data compression an algorithm can produce is reliant upon the presence of several patterns in the data.

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The given differential equation is 3y" - y = 3(t+1)². We need to find the general solution to this equation.

To find the general solution of the differential equation, we can first solve the associated homogeneous equation, which is obtained by setting the right-hand side equal to zero: 3y" - y = 0.

The characteristic equation of the homogeneous equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the equation, we get the characteristic equation: 3r² - 1 = 0.

Solving the characteristic equation, we find two distinct roots: r₁ = 1/√3 and r₂ = -1/√3.

The general solution of the homogeneous equation is then given by y_h(t) = c₁e^(r₁t) + c₂e^(r₂t), where c₁ and c₂ are constants.

To find a particular solution to the non-homogeneous equation 3y" - y = 3(t+1)², we can use the method of undetermined coefficients. Since the right-hand side is a quadratic function, we assume a particular solution of the form y_p(t) = At² + Bt + C, where A, B, and C are constants.

By substituting this form into the equation and comparing coefficients, we can determine the values of A, B, and C.

Once we have the particular solution, the general solution of the non-homogeneous equation is given by y(t) = y_h(t) + y_p(t).

In conclusion, the general solution of the differential equation 3y" - y = 3(t+1)² is y(t) = c₁e^(t/√3) + c₂e^(-t/√3) + At² + Bt + C, where c₁, c₂, A, B, and C are constants.

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Answer:

t=1.03y

Step-by-step explanation:

3% means 0.03

3% increase: 1+0.03

t=(1+0.03)y=1.03y

A person can toss a coin 11 times in 470 or 471 ways so that the number of heads is between 7 and 9 inclusive

To solve this problem, we can use the binomial distribution formula to find the probability of getting 7, 8, or 9 heads in 11 tosses of a fair coin. Then we can sum up these probabilities to get the total number of ways to get between 7 and 9 heads.

The binomial distribution formula is:

\(P(X = k) = C(n, k)\)× \(p^k\)× \((1 - p)^{n - k}\)

where:

P(X = k) is the probability of getting k heads in n tosses of a coin

C(n, k) is the number of combinations of n items taken k at a time, which is given by \(C(n, k) = n! / (k!\) × \((n - k)!)\)

p is the probability of getting a head on one toss of the coin (since the coin is fair, p = 0.5)

(1 - p) is the probability of getting a tail on one toss of the coin

Using this formula, we can find the probabilities of getting 7, 8, or 9 heads in 11 tosses:

\(P(X = 7) = C(11, 7)\) × \(0.5^7\) × \(0.5^4 = 330\) × \(0.0078\) × \(0.0625 = 0.1613\)

\(P(X = 8) = C(11, 8)\) × \(0.5^8\) × \(0.5^3 = 165\)× \(0.0039\) × \(0.125 = 0.0557\)

\(P(X = 9) = C(11, 9)\) × \(0.5^9\) × \(0.5^2 = 55\) × \(0.00195\) × \(0.25 = 0.0127\)

To get the total probability of getting between 7 and 9 heads, we can add up these probabilities:

\(P(7 < = X < = 9) = P(X = 7) + P(X = 8) + P(X = 9) = 0.1613 + 0.0557 + 0.0127 = 0.2297\)

Therefore, the probability of getting between 7 and 9 heads in 11 tosses of a fair coin is 0.2297. To find the number of ways to get between 7 and 9 heads, we can multiply this probability by the total number of possible outcomes, which is\(2^11 = 2048\):

Number of ways\(= 0.2297\) × \(2048 = 470.9\)

Since we can't have a fraction of a way, the actual number of ways to get between 7 and 9 heads is either 470 or 471. Therefore, a person can toss a coin 11 times in 470 or 471 ways so that the number of heads is between 7 and 9 inclusive.

To count the number of ways to toss a coin 11 times so that the number of heads is between 7 and 9 inclusive, we need to count the number of outcomes that have exactly 7, 8, or 9 heads.

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1. The total number of students who took the exam is 40 is option c.

2. The probability that the five cards picked are suited is approximately is option d. 0.0020.

Probability is a branch of mathematics that deals with the likelihood of events occurring. In this response, we will provide detailed solutions to two probability problems. We will explain the steps involved in solving each problem using mathematical terms.

Solution to Problem 1:

Let's denote the number of students who took the exam as 'x.' We are given that the probability of passing Chemistry is 70% and Physics is 50%. None of the students failed in both subjects, and 8 students passed both subjects.

To solve this problem, we can use the principle of inclusion-exclusion. The principle states that to find the total number of students who passed at least one subject, we need to sum the number of students who passed Chemistry, the number of students who passed Physics, and then subtract the number of students who passed both subjects.

Let's calculate the number of students who passed at least one subject:

Number of students who passed Chemistry = 0.7x

Number of students who passed Physics = 0.5x

Number of students who passed both subjects = 8

Total number of students who passed at least one subject = (Number of students who passed Chemistry) + (Number of students who passed Physics) - (Number of students who passed both subjects)

Substituting in the values, we have:

Total number of students who passed at least one subject = 0.7x + 0.5x - 8

Since none of the students failed in both subjects, the number of students who passed at least one subject is equal to the total number of students. Therefore, we can set the equation equal to 'x' and solve for it:

0.7x + 0.5x - 8 = x

Simplifying the equation:

1.2x - 8 = x

0.2x = 8

x = 8 / 0.2

x = 40

Therefore, the total number of students who took the exam is 40.

Hence, the answer to Problem 1 is option c. 40.

Solution to Problem 2:

We are given that we are picking five cards from a standard deck of 52 cards. We need to find the probability that all five cards picked are suited, meaning they all belong to the same suit.

To solve this problem, we can use the concept of combinations. The number of ways to choose five cards from a particular suit is denoted as C(13, 5), as there are 13 cards in each suit (hearts, diamonds, clubs, spades) and we need to choose 5 cards. Similarly, the total number of ways to choose any five cards from the deck is C(52, 5).

The probability of picking five suited cards can be calculated as:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Number of favorable outcomes = Number of ways to choose 5 cards from a single suit = C(13, 5)

Total number of possible outcomes = Number of ways to choose any 5 cards from the deck = C(52, 5)

Using the formula for combinations, we have:

C(n, r) = n! / (r!(n-r)!)

Substituting in the values, we get:

Number of favorable outcomes = C(13, 5) = 13! / (5!(13-5)!)

Total number of possible outcomes = C(52, 5) = 52! / (5!(52-5)!)

Calculating the values:

Number of favorable outcomes = 1,287

Total number of possible outcomes = 2,598,960

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1,287 / 2,598,960

Simplifying the fraction:

Probability ≈ 0.000495

Therefore, the probability that the five cards picked are suited is approximately 0.000495.

Hence, the answer to Problem 2 is option d. 0.0020.

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the steps to writing the equation of a line parallel or perpendicular to a given line through a given point.

Given line ax+by=c and point (h, k), you can write equations for the desired lines using the forms:

  a(x -h) +b(y -k) = 0 . . . . . . parallel line

  b(x -h) -a(y -k) = 0 . . . . . . . perpendicular line

If you eliminate parentheses and collect terms, you will have the general form equation of the desired line(s). If you solve for y, you will have the slope-intercept form of the equation.

To use these forms, it is helpful to start with the equation of the given line in standard form, as shown. (It could also be in general form ax+by-c=0.)

Using the above solution, the steps are ...

You will note that the same coefficients are used on the same variables for a parallel line. This is because parallel lines have the same slope.

The coefficient of the variables are swapped, and one of them is negated in the equation for the perpendicular line. This is because perpendicular lines have opposite reciprocal slope.

When the given line is in slope-intercept form, y = mx +b, the slope is readily identified as m, the coefficient of x. For the parallel line, this slope can be used directly in the point-slope equation for a line through a given point:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

This can be rearranged to the slope-intercept form:

  y = mx +(k -mh)

The perpendicular line has opposite reciprocal slope. The line perpendicular to the given line with slope m will have slope -1/m. Then the two forms of equation are ...

  y -k = -1/m(x -h) . . . . . . . . . point-slope form

  y = (-1/m)x +(k +h/m) . . . . . slope-intercept form

__

Additional comment

A standard form equation (ax +by = x) has mutually prime integer coefficients, with a positive leading coefficient. When you have written your equation, you may find it necessary to multiply the equation by some value to put it in this form. For example, -2x +4y = -8 must be multiplied by -1/2 to get the standard form equation x -2y = 4.

You need to be aware of the form required by your grader. The wording "the equation" often means slope-intercept form, or the form matching the given equation or the answer box format.

So Joe has 16 cows and 10 chickens.Joe has 16 chickens and 10 cows. There are 16 chickens with 2 legs each which gives 32 legs and there are 10 cows with 4 legs each which gives 40 legs. When you add them together it comes to 84 legs.

First, let’s assume that all the animals are cows. In that case, we’d have a total of 104 legs (26 animals times 4 legs each).But we know there are only 84 total legs, so we need to subtract 20 legs to account for the chickens.Each chicken has two legs, so we divide the remaining 20 legs by two to get 10 chickens.So, we have 10 cows and 16 chickens, which adds up to 26 animals in total and 84 legs.

Let's use the algebraic method for solving this problem. We can use two variables and two equations to solve this problem.Let's assume that Joe has some cows and chickens. We don't know the exact number of cows and chickens, so let's call the number of cows x and the number of chickens y.We know there are 26 animals in total, so:x + y = 26 (Equation 1)We also know that if we count all the legs, there are 84 total legs.Each cow has four legs, so the total number of legs for the cows is 4x.Each chicken has two legs, so the total number of legs for the chickens is 2y.The total number of legs is 84, so we can write an equation:4x + 2y = 84 (Equation 2)Now we can use Equation 1 to solve for one of the variables. Let's solve for y:y = 26 - x (Equation 3)We can substitute Equation 3 into Equation 2 to get an equation in terms of x:4x + 2(26 - x) = 84Simplifying, we get:2x + 52 = 42Subtracting 52 from both sides, we get:2x = -10Dividing both sides by 2, we get:x = -5This doesn't make sense since we can't have negative cows. Let's check our work:4(-5) + 2y = 84-20 + 2y = 842y = 104y = 52This means there are 52 chicken legs, which doesn't make sense either since we can't have half a chicken.Let's try again. This time, we'll solve for y in Equation 1:y = 26 - xNow we can substitute this into Equation 2:4x + 2(26 - x) = 84Simplifying, we get:2x + 52 = 84Subtracting 52 from both sides, we get:2x = 32Dividing both sides by 2, we get:x = 16So Joe has 16 cows. We can use Equation 1 to find y:y = 26 - xy = 26 - 16y = 10

So Joe has 16 cows and 10 chickens.

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Answer:

40%

Step-by-step explanation:

5.75 · 0.40 = 2.3

5.75 - 2.3 = 3.45

Answer:

$16.50

Step-by-step explanation:

$27.50/5=5.5

5.5*3=16.5

Answer:

What we can do is calculating what one bag cost. If we know that 5 cost 27.50 dollars, to know how much does one cost we only divide:

27.50/5 = 5.50 dollars

Now, we know how much does one bag cost, so we multiply it by three:

5.50 * 3 = 16.50

Now, we know 3 bags cost 16.5 dollars

The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.

The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.

To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:

Y = [O2]^n / ([O2]^n + P50^n)

Where:

Y is the fractional saturation of hemoglobin,

[O2] is the partial pressure of oxygen,

P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,

n is the Hill coefficient, which represents the cooperativity of oxygen binding.

To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.

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Answer:

(4). -3x+10

Step-by-step explanation:

(2x+7)-(5x-3)

2x+7-5x+3

-3x+10

Answer:

a_48000cm^3

b_48000000mm^3

Step-by-step explanation:

first of all, let's find the base area:

Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2

then, to find the volume, we need to multiplicate the base area to the height of the prism:

V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3

Answer:ccccc

Step-by-step explanation:

cccc

Answer:

Not factorable.

Step-by-step explanation:

4k² + 6k - 1

We can do it by the guess method.

We need two factors of 4 and two factors of -1.

4 factors into 4 and 1, 2 and 2.

-1 factors into -1 and 1.

Now we fit the factors until we find the answer.

Try: (2k - 1)(2k + 1)

Multiply it out: 4k²- 1 This is not it.

Try: (4k + 1)(k - 1)

Multiply it out: 4k² - 3k - 1 This does not work.

Try: (4k - 1)(k + 1)

Multiply it out: 4k² + 3k - 1 This does not work.

All combinations of factorizations of the coefficients were tried and none worked.

Answer: Not factorable.

Jasper should do 8*64 and not 64/8.

The correct solution is 64*8 = 512

Hope it helps!

Evaluating the integral-  \(\int_0^1 (u+2)(u-3) du\) we get the simplified answer = -37/6.

Let's evaluate the integral as follows -

\(\int_0^1 (u+2)(u-3) du\)

now lets multiply the expression and we will get,  

\(= \int_0^1 u^2-u-6 d u\)

Distributing the integrals to each expression.

\(= \int_0^1 u^2 d u+\int_0^1-u d u+\int_0^1-6 d u\)

By the Power Rule, the integral of \($u^2$\) with respect to u is  \($\frac{1}{3} u^3$\).

\(= \left.\frac{1}{3} u^3\right]_0^1+\int_0^1-u d u+\int_0^1-6 d u\)

Since -1 is constant w.r.t u, move -1 out of the integral of the second term.

\(= \left.\frac{1}{3} u^3\right]_0^1 -\int_0^1u d u+\int_0^1-6 d u\)

By using the power rule, the integral of \($u^2$\) w.r.t to u is \($\frac{1}{2} u^2$\)

\(= \left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{1}{2} u^2\right]_0^1\right)+\int_0^1-6 d u\)

Let's Combine \($\frac{1}{2}$\) and \($u^2$\).

\(= $$\left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{u^2}{2}\right]_0^1\right)+\int_0^1-6 d u$$\)

Now, apply the constant rule,

\(= $$\left.\left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{u^2}{2}\right]_0^1\right)+-6 u\right]_0^1$$\)

Substituting the limits and simplifying we get,

= -37/6

Hence, the simplified answer for the given integral \(\int_0^1 (u+2)(u-3) du\) is -37/6.

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The complete question is-

Evaluate the integral-  \(\int_0^1 (u+2)(u-3) du\).

Answer:

touch it

Step-by-step explanation:

Answer: The area of a regular polygon is one-half the product of its apothem and its perimeter

Step-by-step explanation:

Answer:

2. |-4| < |-8|

3. |-5| > 1

5. |-2| = |2|

Answer:

2,3,5 are correct

Step-by-step explanation:

i took the test

Answer:

One person represents 360 degrees / (204 + 84 + 36 + 204 + 12) = 360 degrees / 540 = 4/6 = 2/3 degrees.

You are required to find the weight of each eggplant

The weight of each eggplant is 5/4 pounds

Let

Number of eggplant = 3

Total Weight of eggplant = 3 3/4 pounds

Weight of each eggplant = Total Weight of eggplant ÷ Number of eggplant

= 3 3/4 ÷ 3

= 15/4 ÷ 3

= 15/4 × 1/3

= (15 × 1) / (4 × 3)

= 15/12

= 5/4 pounds

Weight of each eggplant = 5/4 pounds

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Answer:

$960

Step-by-step explanation:

The discount is 20%, so we need to find 80% of the original price:

\(.80 \times 1200 = 960\)

Answer:

The answer is y = 5/2x - 3!!

Step-by-step explanation:

You can check this on Desmos, by typing in the coordinates you have and then this equation and you can see the line goes right through them!!  Hope this helps!!

Answer:

\( -2 \: \: 4\)

Step-by-step explanation:

-2 4 is not an equivalent equation

Answer:

c

Step-by-step explanation:

duh

The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given sum of the mixed number,

1 1/4 + 4 2/3

⇒ 1 + 1/4 + 4 + 2/3

⇒ 1 + 4 + 1/4 + 2/3

⇒ 5 + 1/4 + 2/3

Take LCM of 1/4 and 2/3 as 12.

⇒ 5 + (3 + 8)/12

⇒ 5 + 11/12 = 5 11/12

Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".

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Answer

402 meters ÷ 18 seconds

Step-by-step explanation:

Answer:

402 meters ÷ 18 seconds

Step-by-step explanation:

While doing this sorta math to find the speed it will always be how long  ÷  by how long or time!

The explicit, exponential, and recursive functions that define this geometric sequence include the following:

exponential     ⇒ \(f(n)=9(\frac{1}{3} )^n\)

explicit             ⇒ \(f(n)=9(\frac{1}{3} )^{n-1}\)

recursive         ⇒ \(f(1)=9\\f(n)=\frac{1}{3} f(n-1), for \;n\ge2\)

In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 3/9

Common ratio, r = 1/3

For the exponential function, we have:

\(f(n) = a_1(r)^n\\\\f(n)=9(\frac{1}{3} )^n\)

For the explicit function, we have:

aₙ = a₁rⁿ⁻¹

\(f(n)=9(\frac{1}{3} )^{n-1}\)

Now, we can write the recursive function as follows;

f(1) = 9

f(n) = ⅓f(n - 1), for n ≥ 2.

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Answer: Yes

Step-by-step explanation: