Kasey has 8 packages of gelatin. She plans to fill molds that each take 113 packages of gelatin.
Each mold can be divided into 6 servings. How many servings of gelatin can Kasey make?
Enter your answer in the box.

Answer:

50 classmates

Step-by-step explanation:

80 x 0,62 = 49,6

49,6 ≈ 50

Answer:

m

Step-by-step explanation:

the slope or growth rate of the function is the coefficient of the variable x, which is m in this case

The best response for a person handling biohazards with an open wound on their hands is to not  work with biohazards until the cut is healed or cleared by a healthcare professional to work with the use of waterproof bandages and double gloves.

Biohazards are extremely dangerous because they can get into the human body and cause a lot of damage.

This is why a person with an open would or existing cut should not handle a biohazard until they are cleared to to so by a trained healthcare professional.

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The first-order partial derivatives of w with respect to x, y, and z are:

∂w/∂x = 8[(y^2+z^2 - 7x^2)/(x^2+y^2+z^2)^(9/2)]

∂w/∂y = -56xy / (x^2+y^2+z^2)^(9/2)

∂w/∂z = -56xz / (x^2+y^2+z^2)^(9/2)

To compute the first-order partial derivatives of the function w = 8x / (x^2+y^2+z^2)^(7/2), we need to take the partial derivatives with respect to each variable x, y, and z, while treating the other variables as constants. We can use the quotient rule and chain rule to do this:

∂w/∂x = (8(x^2+y^2+z^2)^(7/2) - 8x(7/2)(2x)) / (x^2+y^2+z^2)^(7/2))^2

= 8[(y^2+z^2 - 7x^2)/(x^2+y^2+z^2)^(9/2)]

∂w/∂y = (8x(-7/2)(2y)(x^2+y^2+z^2)^(5/2) / (x^2+y^2+z^2)^7/2)

= -56xy / (x^2+y^2+z^2)^(9/2)

∂w/∂z = (8x(-7/2)(2z)(x^2+y^2+z^2)^(5/2) / (x^2+y^2+z^2)^7/2)

= -56xz / (x^2+y^2+z^2)^(9/2)

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The given question is incomplete, the complete question is:

Compute the first‑order partial derivatives of the function. w = 8x / (x^2+y^2+z^2)^(7/2)  (use symbolic notation and fractions where needed.)

Answer:

27 pens

Step-by-step explanation:

red pen=7

3more black pen than red pen=3+7=10 black pen

3 more blue pen than red pen=3+7=10 blue pen

T=redpen + blackpen +blue pen

T=7+10+10

T=27 pen

The height of the screen will be;

⇒ h = 28 inches

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.

Here,

The diagonal of the screen television = 53 inches

And, The width of the screen television = 45 inches

Let the height of the television = h

So, By the Pythagoras theorem, we get;

⇒ AC² = AD² + DC²

Where, AC = Diagonal of television.

AD = Height of the television

DC = Width of the television.

Substitute all the values, we get;

⇒ 53² = h² + 45²

⇒ 2809 = h² + 2025

⇒ 2809 -2025 = h²

⇒ h² = 784

⇒ h = √784

⇒ h = 28 inches

Thus, The height of the screen = 28 inches

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After solution of the given equation  8y-2+6x the answer is 2(4y - 1 + 3x).

So, 8y-2+6x:

Factor out common term 2:

Therefore, equation 8y-2+6x is 2(4y - 1 + 3x).

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Answer:

\(\displaystyle Substitution\)

Explanation:

Elimination and Substitution are two methods to use when solving systems of equations in two and three variables \(\displaystyle [z, y, and\:x].\)With Elimination, you decide on which pair of variables you want to eradicate so they are set to zero, whereas Substitution is mainly used when one variable is automatically isolated. If not, then you must manually decide on which variable to isolate as well as the equation you want to wourk.

I am joyous to assist you at any time.

The if statement assigns a value of 10000 to the variable "bonus" if the value of the variable "goodssold" exceeds 500000.

To achieve this, we can use an if statement in programming. An if statement allows us to conditionally execute a block of code based on a specified condition. In this case, the condition is whether the value of the variable "goodssold" is greater than 500000. If the condition evaluates to true, the code inside the if statement will be executed, and the variable "bonus" will be assigned a value of 10000.

Here's an example of how the if statement can be written in Python:

if goodssold > 500000:

   bonus = 10000

In this code snippet, the variable "goodssold" represents the number of goods sold, and we compare its value to 500000 using the greater than operator (>). If the condition is true, the code inside the if statement is executed, and the variable "bonus" is assigned a value of 10000. If the condition is false, the code inside the if statement is skipped, and the variable "bonus" retains its previous value (if any).

By using this if statement, we can dynamically assign a bonus of 10000 to the variable "bonus" based on the value of the variable "goodssold" being greater than 500000. This allows for flexible and conditional handling of the bonus calculation in the program.

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The Misfit of Demon King Academy

Answer:

3.33 repeating

Step-by-step explanation:

Answer:

3.33333333333 or 3.3

Step-by-step explanation:

Basically I used the equation 2/3 divided by 5.

If I was wrong please ping me again,

The margin of error for this confidence interval is 0.145.

Given :

a confidence interval for a proportion ranges from 0.45 to 0.74.

Confidence interval :

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times

Margin of error :

Margin of error, also called confidence interval, tells you how much you can expect your survey results to reflect the views from the overall population.

Length of confidence interval = 0.74 - 0.45

= 0.29

we know that,

Margin of error = 1/2 * length of confidence interval.

= 1/2 * 0.29

= 0.29/2

= 0.145

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The solutions to the system equations are x = -1 and x = 0.

When two or more variables are related to one another and equations are constructed to determine each variable's value, the result is a system of equations. an equation is a balance scale, and for the equation to stay true, both sides must be equal.

Given equations are:

\(y=2^x - 1\\y=\frac{1}{2} x\)

The solutions of the system for which; \(y_{1} =y_{2}\)

According to the given table, the solutions to the system of both equations at x = -1 and x = 0.

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The probability that Julien samples an equal number of real and fake gold coins from the random sample of four is approximately 0.463.

To calculate this probability, we can consider two cases: sampling from Treasure Chest A and sampling from Treasure Chest B.

For Treasure Chest A:

The probability of sampling an equal number of real and fake coins can be calculated using combinations. Out of the 15 gold coins in Treasure Chest A, 40% are real and 60% are fake. The probability of selecting 2 real and 2 fake coins can be calculated as (0.4^2) * (0.6^2) * (4 choose 2).

For Treasure Chest B:

The probability of sampling an equal number of real and fake coins can be calculated in a similar way. Out of the 8 gold coins in Treasure Chest B, 75% are real and 25% are fake. The probability of selecting 2 real and 2 fake coins can be calculated as (0.75^2) * (0.25^2) * (4 choose 2).

Finally, we can add the probabilities of the two cases together to get the overall probability is approximately 0.463.

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The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer:

You can either write it like n ÷ 6 or 6  ÷ n

Step-by-step explanation:

hope this helps!

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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4)  the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes is n(0.34, 0.0424) - option A

5)  the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes is pnorm(0.4,0.34,0.0424) - pnorm(0.28,0.34,0.0424) - Option A

4) Given data:

P = 0.34 and n = 125

Since, np = 0.34 * 125 = 42.5 > 10

& n(1 - p) = 125 * 0.66 = 82.5 > 10

Therefore, the normal distribution can be used here:

Mean is μp = p = 0.34

The standard Deviation is σp = \(\sqrt \frac{P(1-p)}{n} = \sqrt\frac{(0.34)(0.66)}{125} = 0.0424\)

The distribution of sample proportion will be;

N (0.34, 0.0424)

Therefore, option (a) is correct that is n(0.34, 0.0424)

5) The likelihood that between 28% and 40% of the 125 taxpayers in the sample used tax preparation software is calculated as follows:

pnorm (0.4, 0.34. 0.0424) - pnorm (0.28, 0.34, 0.0424)

Therefore, option A is correct that is pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424)

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Answer:

(x+1)(x-6)

Step-by-step explanation:

two number that times to make -6 and add to make-5

these are : -6 and +1

(x+1)(x-6)

when u expand it

x^2-6x+x-6

=x^2-5x-6

Step-by-step explanation:

4x-(-7x+4.3)-1.6=x

4x+7x-4.3-1.6=x

11x-x=5.9

x=5.9/10=0.59 is your answer

Answer:

x =0.59

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x−(−7x+4.3)−1.6=x

4x+7x+−4.3+−1.6=x

(4x+7x)+(−4.3+−1.6)=x(Combine Like Terms)

11x+−5.9=x

11x−5.9=x

Step 2: Subtract x from both sides.

11x−5.9−x=x−x

10x−5.9=0

Step 3: Add 5.9 to both sides.

10x−5.9+5.9=0+5.9

10x=5.9

Step 4: Divide both sides by 10.

10x/10 = 5.9/10

x =0.59

Answer:

B

Step-by-step explanation:

16 + 6 ← factor out 2 from each number

= 2(8 + 3)

The answer for the fraction 1/4 of 100 is 25.

Given,

The fraction; 1/4

We have to find the 1/4 of 100.

Fraction;

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions

Here,

1/4 of 100 = 1/4 x 100 = 25.

That is,

The answer for the fraction 1/4 of 100 is 25.

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Answer:

Step-by-step explanation:

Given that:

Sample size n = 11

Sample Mean X = 26500

standard deviation = 6000

Population mean \(\mu\) = 31000

the null and alternate hypotheses are being stated as follows:

\(H_o : \mu = 31000\)

\(H_1 : \mu \neq 31000\)

The value of the test statistic can be computed as:

\(Z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}\)

\(Z = \dfrac{26500 - 31000}{\dfrac{6000}{\sqrt{11}}}\)

\(Z = \dfrac{-4500}{\dfrac{6000}{3.3166}}\)

Z = −2.4875

Z = −2.49

The degree of freedom df = n- 1

The degree of freedom df = 11 - 1

The degree of freedom df = 10

At the level of significance ∝ = 0.05

\(t_{\alpha/2}\) = 0.025

From the t distribution table at \(t_{\alpha/2, 10}\) and critical value = -2.49;

The p-value =  0.0320

Decision Rule: Reject null hypothesis if p -value is lesser than the level of significance

Conclusion:We reject the null hypothesis , therefore, we conclude that there is no sufficient information to that the mean tuition and fees for private colleges is different from $31,000

The expression \(32\times0.5^{3x}\) as a power of 2 in terms of 'x' is \(2^5\times2^{-6x}\)

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression \(32\times0.5^{3x}\).

\(= 2^5\times\frac{1}{4^{3x}}\).

\(= 2^5\times\frac{1}{2^{6x}}\).

\(= 2^5\times2^{-6x}\).

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since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

\(\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}\)

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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The probabilities from the binomial probability mass function P(x ≤ 2) will be 0.9298.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

\(\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}\)

q = 1 - p = 1 - 0.10 = 0.90

Let x be a binomial random variable with p = 0.1 and n = 10.

The probabilities from the binomial probability mass function P(x ≤ 2) will be

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x ≤ 2) = ¹⁰C₀ × (0.1)⁰ × (0.9)¹⁰ + ¹⁰C₁ × (0.1) × (0.9)⁹ + ¹⁰C₂ × (0.1)² × (0.9)⁸

P(x ≤ 2) = 0.3487 + 0.3874 + 0.1937

P(x ≤ 2) = 0.9298

Your question was incomplete but the complete question is given below.

Let x be a binomial random variable with p = 0.1 and n = 10. Calculate the probability from the binomial probability mass function less than or equal to 2.

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The perimeter of the figure is the sum of the lengths of all its sides. To calculate it, we need to find the perimeter of the rectangle and the circumference of the quarter circle and then add them together.

To find the perimeter of the rectangle, we need to sum up the lengths of all its sides. Let's assume the length of the rectangle is 'l' and the width is 'w'. Therefore, the perimeter of the rectangle is 2(l + w).

For the quarter circle, we need to find the circumference. The formula for the circumference of a circle is 2πr, where π is approximately 3.14 and 'r' is the radius. In this case, the radius is equal to half of the width of the rectangle. So the circumference of the quarter circle is 0.5πw.

To find the total perimeter, we add the perimeter of the rectangle and the circumference of the quarter circle:

Perimeter = 2(l + w) + 0.5πw

Now, you can substitute the given values for 'l' and 'w' to find the perimeter. Remember to use the approximation 3.14 for π.

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