-the amount of regular unleaded gasoline purchased every week at a gas station follows the normal distribution with mean 50000 gallons and standard deviation 10000 gallons. the starting supply of gasoline is 74000 gallons, and there is a scheduled weekly delivery of 47000 gallons. (a) find the probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons. (b) how much should the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%?

Answer:

peanut butter jelly

Step-by-step explanation:

I love that!

The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

3 ¹/₅ and 1/3

Convert the mixed fraction number into a fraction number. Then we have

3 ¹/₅ = 16 / 5

Then the division of the numbers 16/5 and 1/3 will be given by putting a division sign between them. Then we have

⇒ 16/5 ÷ 1/3

⇒ (16/5) / (1/3)

⇒ (16/5) x (3)

⇒ 48/5

⇒ 9.6

The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.

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The required graph of the inequality has been shown and the solution is; 8 Nickels  and 12 dimes.

Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).

Let the number of nickels be x and let the number of dimes be y,

We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;

x + y = 20

x = 20 - y - - - - (1)

0.05x + 0.10y ≤ 1.60 - - - -(2)

We are also told that no less than 4 of the coins are dimes. Thus;

x ≥ 4

From the graph, one solution is given as 8 Nickels and 12 dimes.

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The bacteria culture has an initial size of 79.7409

Given,

The count in a bacteria culture;

After 10 minutes is 400

After 30 minutes is 2000

Assume that the count grows exponentially;

We have to find the initial size of the culture;

Here,

The growth of population can be calculated using;

P = P₀ (1 + r)^t

Here,

Count of bacteria, P = 400 and 2000

Time period, t = 15 and 30

Initial size =  P₀

So,

400 = P₀ × (1 + r)¹⁰

2000 = P₀ × (1 + r)³⁰

Take P₀ common.

Then,

400/(1 + r)¹⁰ = 2000/(1 + r)³⁰

(1 + r)³⁰/ (1 + r)¹⁰ = 2000/400

(1 + r)¹⁰ = 5

1 + r = 1.175

r = 0.175

Now,

The value of P₀ should be determined from the above equation;

That is,

400 = P₀ × (1 + 0.175)¹⁰

P₀ = 400/ (1 + 0.175)¹⁰

P₀ = 79.7409

Therefore,

The initial size of the bacterial culture is 79.7409

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The wave function that satisfies wave equation is D(x,t) = A cos(kx + ωt) that is option C is correct.

This wave function satisfies the wave equation because it can be rewritten as:

D(x,t) = A cos(kx) cos(ωt) - A sin(kx) sin(ωt)

And the left-hand side of the wave equation is simply the sum of the second derivatives of the two cosine and sine functions with respect to x, while the right-hand side is the product of the second derivative of the cosine function with respect to t and the second derivative of the sine function with respect to t.

For the transverse velocity of a particle at point x, the function is given by:

v(x,t) = -Aω sin(kx) cos(ωt) - Ak cos(kx) sin(ωt)

And for the transverse acceleration, the function is given by:

a(x,t) = -Aω^2 cos(kx) cos(ωt) + Ak^2 sin(kx) sin(ωt)

These functions can be derived by taking the first and second derivatives of the wave function with respect to time.

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Answer: 12 miles

Step-by-step explanation:

Let y represent the cost and x represent the number of miles!

y = 1.25x + 3

Now put the $18 in for y

18= 1.25x + 3

15 = 1.25x

x = 12 miles

Answer:

Step-by-step explanation:

We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:

18 = 1.25x + 3

15 = 1.25x (subtracted 3 from both sides)

12 = x (divided each side by 1.25)

So, the trip was 12 miles

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

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By the information provided in the question, we got to know that - there are 2598960 ways.

Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.

[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]

You are choosing a subset of size 5 from a set of size 52.

[tex]Note that the order you are dealt these 5 cards is irrelevant.[/tex] Thus, order doesn’t matter.

Thus, this is a combination problem. The formula for this is:

[tex]Comb(52,5) = \frac{52!}{5! 13!} = 2598960.[/tex]

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The proportion of the class that scored higher than the student will be 0.0912.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The class normal is 85% and the standard deviation is 3%. Then the student from the class who earned 89% higher will be given as,

z = (0.89 - 0.85) / 0.03

z = 0.04 / 0.03

z = 1.3333

Then the probability is given as,

P(x > 89%) = P(z > 1.3333)

P(x > 89%) = 0.091211

The proportion of the class that scored higher than the student will be 0.0912.

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Answer:

Check below/above

Step-by-step explanation:

A) The graph passes through the point (0,1).

The domain is all real numbers.

The range is y>0.

B) it would be a linear equation that shifts the graph vertically.

C) the slope of an exponential function continues to increase, while the slope of a linear function stays the same.

Answer:

z = 22

Step-by-step explanation:

Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).

Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:

2z = z + 22

Now, all we have to do is solve for z

2z = z + 22

-z   - z

z = 22

Answer: A, B, C, E

Step-by-step explanation:

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R

Full question is:

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)

If we have a level surface, then it will give us

f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.

Now let us calculate the ∇ gradient of f at point (0,0,7):

∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)

= (1, 1, 1)

We get the equation for the tangent plane A:

A: 1(x−0) + 1(y−0) + 1(z−7)=0

This can also be written as:

x+y+z = 7 ------------------------------------------------------------------(a)

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)

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The equation is false (we can remove the dependence with the variable x) that is why the equation has no solutions.

Here we have the following linear equation:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

We want to see why we don't have any solutions, to check that, we need to simplify both sides of the equation. Let's start by grouping like terms:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

(5 - 7) + (-4x - 10x) = (-4 - 10) + (-8x - 6x)

-2 - 14x = -14 - 14x

Notice that now we can add 14x in both sides of the equation, then we will get:

-2 -14x + 14x = -14 - 14x + 14x

-2 = -14

So we have a false equation, this happens because the equation does not truly depend of the value of x.

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The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

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Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

The measure of z in the polygon is (a) z = 15

From the question, we have the following parameters that can be used in our computation:

Shape = 9-sided polygon

Parameter to calculate = the measure of z

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where n is the number of sides

In this case

n = 9

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (9 − 2) × 180∘

Evaluate

The sum of the interior angles = 1260∘

So, the internal angle is

Angle = 1260/9

Evaluate

Angle = 140

This means that

5z + 65 = 140

So, we have

5z = 75

Divide by 5

z = 15

Hence, the angle is (a) z = 15

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The polynomial of third degree whose zeros and degree are given, for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

From the question statement, a third degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.

We need to determine the polynomial.

Since, (-2) is a zero of the polynomial, then (x+ 2) will be a factor of the polynomial. for zero of (-2), multiplicity is 1, means that the factor of (x + 2) is only multiplied once.

Similarly, (3) is another zero of the polynomial, then (x - 3) will be a factor of the polynomial.

For zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice

Hence, our required polynomial is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]

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Answer:

91 cents per ounce

Step-by-step explanation:

Divide 13.59 by 15

Answer: $0.91

Step-by-step explanation:

Take $13.59 divided by 15 = $0.91 per ounce

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A linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

The mathematical assertion that two linear expressions, or a linear expression and a constant, are not equal is made via a linear equation.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept).

Therefore, a linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

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The 50% of students who passed the second exam also passed the first exam.

The question is about Conditional Probability. Conditional probability is defined as the measure of the probability of event A given that event B has already occurred. It is denoted by P(A | B). Also, the formula for finding the conditional probability is given below:
P(A | B) = P(A ∩ B)/P(B)         ....(1)
In the given question, We have the following information:
A = Students who passed both exams = 40% = 0.4
B = Students who passed only the second = 80% = 0.8
Now, Let
Probability of Students who passed the second exam and first exam = P (A | B) =?

We can find P(A | B) by putting the values of A and B in equation (1)
By putting values we get:
P (A | B) = [tex]=\frac{40\%}{80\%}[/tex] = [tex]\frac{0.4}{0.8}[/tex]

P (A| B) = 0.5 = 50%

So there are half or 50% of the students passed the second exam and also passed the first exam.

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The area is 0.25

What is a tangent line?

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.  A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.

[tex]$$\begin{aligned}& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3-2 x\right] \\& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3\right]-\frac{\mathrm{d}}{\mathrm{d} x}[2 x] \quad \text { Sum } / \text { Rest rule } \\& f^{\prime}(x)=3 x^{3-1}-2 \quad \text { Power rule } \\& f^{\prime}(x)=3 x^2-2 \\&\end{aligned}$$[/tex]

Now finding tangent for a=-1,

[tex]\begin{aligned}& y=f^{\prime}(a)(x-a)+f(a) \\& y=f^{\prime}(-1)(x+1)+f(-1) \\& y=\left(3(-1)^2-2\right)(x+1)+(-1)^3-2(-1) \\& \mathbf{y}=\mathbf{x}+\mathbf{2}\end{aligned}$$[/tex]

For the first area,

[tex]$$\begin{aligned}& A_1: \int_{-2}^{-\sqrt{2}} x+2 d x=\frac{1}{2} x^2+\left.2 x\right|_{-2} ^{-\sqrt{2}} \\& A_1=\frac{1}{2}(-\sqrt{2})^2+2(-\sqrt{2})-\left(\frac{1}{2}(-2)^2+2(-2)\right) \\& A_1=\mathbf{3}-\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{1}} \approx \mathbf{0 . 1 7 1 5 7 2 8 7 6} \ldots\end{aligned}$$[/tex]

For the second area,

[tex]$$\begin{aligned}& A_2: \int_{-\sqrt{2}}^{-1} x+2-\left(x^3-2 x\right) d x=-\frac{1}{4} x^4+\frac{3}{2} x^2+\left.2 x\right|_{-\sqrt{2}} ^{-1} \\& A_2=-\frac{1}{4}(-1)^4+\frac{3}{2}(-1)^2+2(-1)-\left(-\frac{1}{4}(-\sqrt{2})^4+\frac{3}{2}(-\sqrt{2})^2+2(-\sqrt{2})\right) \\& A_2=-\frac{\mathbf{1 1}}{\mathbf{4}}+\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{2}} \approx \mathbf{0 . 0 7 8 4 2 7 1 2 4} \ldots .\end{aligned}$$[/tex]

Hence, required area is

[tex]$$\begin{aligned}& A=A_1+A_2 \\& A=3-2 \sqrt{2}-\frac{11}{4}+2 \sqrt{2} \\& \mathbf{A}=\frac{\mathbf{1}}{\mathbf{4}}=\mathbf{0 . 2 5}\end{aligned}$$[/tex]

The area is 0.25

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Answer: 43 small tanks

Step-by-step explanation:

First, take 900 - 212 = 688 fish in small tanks

Then take 688 divided by 16 fish in each tank = 43

So there are 43 smaller tanks

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &13 \end{cases} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}} \end{array}} ~\hfill[/tex]

well, let's instead find when will there be 1 gram first off, then after that it's all downhill, so A = 1

[tex]\stackrel{A}{1}=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \cfrac{1}{2.5}=\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \log\left( \cfrac{1}{2.5} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{t}{13}} \right][/tex]

[tex]\log\left( \cfrac{1}{2.5} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]\implies \cfrac{\log\left( \frac{1}{2.5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]}=t\stackrel{\textit{after about 17 days and 5 hours}}{\implies 17.19\approx t ~\hfill }[/tex]

The measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.

What is an isosceles triangle?

An isosceles triangle, therefore, has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg)

In an isosceles triangle, the two base angles are equal. Therefore, the measure of each base angle is (4x + 5)°.

An exterior angle of a triangle is supplementary to one of the base angles if it forms a straight line with the base angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two base angles.

Therefore, the measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.

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Answer:

[tex]\textsf{1)} \quad x=\dfrac{y-b}{a}[/tex]

[tex]\textsf{2)} \quad x=\dfrac{y+b}{a}[/tex]

[tex]\textsf{3)} \quad x=2y-2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa+b\\\\&\textsf{Subtract $b$ from both sides}: \quad & y-b&=xa+b-b \\\\&\textsf{Simplify}: \quad &y-b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y-b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y-b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y-b}{a}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa-b\\\\&\textsf{Add $b$ to both sides}: \quad & y+b&=xa-b+b \\\\&\textsf{Simplify}: \quad &y+b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y+b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y+b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y+b}{a}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad & y&=\dfrac{x+2}{2} \\\\&\textsf{Multiply both sides by $2$}: \quad & 2 \cdot y&=2 \cdot \dfrac{x+2}{2} \\\\&\textsf{Simplify}: \quad & 2y&=x+2 \\\\&\textsf{Subtract $2$ from both sides}: \quad & 2y-2&=x+2-2 \\\\&\textsf{Simplify}: \quad & 2y-2&=x \\\\&\textsf{Switch sides}: \quad &x&=2y-2\end{aligned}}[/tex]

Answer:

7

Step-by-step explanation:

The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:

$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$

We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:

$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$

Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.

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A negative result does not mean that you do not have the disease. It could be a false negative.

The reasons that could be there for a negative result when there is  actually the presence of the disease

The ELISA may not be sensitive enough to detect very low concentration  of the disease agent, as might occur when one is tested soon after infection before a proper immune response occurs.

As HIV buds from the surface of the host cell, it incorporates some of the host cell Human leukocyte antigen into its envelope. False negatives usually occurs during the window between infection and an antibody response to the virus which is known as seroconversion.

Therefore, if the sample gave a negative result for the disease-causing agent, it does not mean that you do not have the disease

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Answer:

120

Step-by-step explanation:

Let the unknown number be x.

Therefore, if 5.76 is 4.8% of x:

[tex]\boxed{\begin{aligned}4.8\%\; \textsf{of} \; x&=5.76\\\\\implies \dfrac{4.8}{100}x&=5.76\\\\4.8x&=576\\\\x&=\dfrac{576}{4.8}\\\\x&=120 \end{aligned}}[/tex]

So the unknown number is 120.

Answer:

8750 Rs

Step-by-step explanation:

Saves

12.5 : 100 = x : 10 000

x = 10 000 * 12.5 / 100

x = 100 * 12.5

x = 1250 Rs

Total he spends

10 000 - 1250 = 8750 Rs

We can shown that the triangles are congruent by a translation of 2 units left and then a reflection over the y-axis.

Congruent triangles are triangles that have the same side lengths.

Transformations that keep  the congruence of a triangle are given as follows:

One vertex of the original triangle is given as follows:

A(8,8).

The equivalent vertex on the reflected and translated triangle is given as follows:

A'(6,-8).

Considering the reflection over the y-axis that we can see from the image, the complete rule is given as follows:

(x,y) -> (x - 2, - y).

Meaning that the translation was two units left.

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