kurt drives a total of 32 miles to and from work everyday. he works 5 days a week. how many miles does kurt drive in a week for his job?

The water that was lost between 9 and 11 am is 52 liters by using integration.

An integral in mathematics assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that come from merging infinitesimal data. The process of determining integrals is known as integration. Along with differentiation, integration is a fundamental, essential operation of calculus and is used to answer issues in mathematics and physics involving the area of an arbitrary form, the length of a curve, and the volume of a solid, among others.

The integrals listed below are definite integrals, which can be defined as the signed area of the plane region circumscribed by the graph of a given function between two points on the real line.

Rate of leaking R'(t)=2+8t

Here t is the number of hours.

Total water lost from 9 and 11 am

=\(\int\limits^8_2\) (2+8t)dt

=(2t+(8t²/2))⁴₂

=(8+64)-(4+16)

=72-20

=52 liters.

The water that was lost between 9 and 11 am is 52 liters.

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Answer:

$12

Step-by-step explanation:

36÷3=12

Each ticket costs $12

Answer:

$12 per ticket

Step-by-step explanation:

$36 / 3 = 12

$12 per ticket

Therefore, each ticket costs 12 dollars.

Can I please have brainliest, thanks:)

Therefore, the solutions that make sense for the situation are in the first quadrant, where x and y are both positive.

Inequality is a mathematical statement that compares two values or expressions using an inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). Inequalities can be solved like equations, but the solution is typically a range of values rather than a single value. Inequalities are commonly used in algebra and other branches of mathematics, as well as in real-world situations such as economics, where they can represent constraints or limitations on resources or options.

Here,

A) Let x be the pounds of strawberries and y be the pounds of blueberries.

To make at least 30 pounds of fruit, we have:

x + y ≥ 30

To spend at most $132, we have:

3x + 4y ≤ 132

B) The graph of the system will include points in all four quadrants of the xy-coordinate plane. However, in the context of this problem, only the positive quadrant makes sense because it doesn't make sense to have negative pounds of fruit.

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The exact numerical value of the expressions given cannot be determined without additional information or clarification.

The given expressions involve various calculations and summations involving complex numbers and exponentials. However, the specific values of the variables, such as V, k, n, or t, are not provided. Additionally, the patterns or series mentioned in the expressions are not clearly defined.

To determine the exact numerical values, we would need more information, such as the values of V, k, n, or t, and the specific patterns or rules for the series mentioned. Without these details, it is not possible to calculate the exact numerical values of the expressions.

Therefore, based on the given information, the exact numerical values cannot be determined, and additional clarification or information is required to solve the expressions.

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Answer:

124.8 and 39.6

Step-by-step explanation:

120 * .04 = 4.8

it says to increase so 120 + 4.8 = 124.8

45 * .12 = 5.4

it says to decrease so 45 - 5.4 = 39.6

Expected value of the net reward is:

E(net reward) = \(n^2p^2\sum[(n-1)\) choose \((X-1)]p^(^X^-^2^)(1-p)^(^n^-^X^)(X-1)\)\(+ np\sum\)[(n choose X)\(p^(^X^-^1^)(1-p)^(^n^-^X^)\)(1+b)] - nd

Expected value of the reward is:

\(E(reward) = \sum [(n choose X) * (ap)^X * (1-p)^n-X]\)

For the first part of the question, we can use the binomial distribution to find the probability of obtaining X heads in n tosses of a fair coin. Let p be the probability of getting a head in a single toss, which is 0.5. Then, the probability of getting X heads in n tosses is:

P(X) = (n choose X) \(* p^X * (1-p)^(^n^-^X^)\)

where (n choose X) is the binomial coefficient, which is equal to n! / (X! * (n-X)!).

The expected value of the net reward is the sum of the expected rewards for all possible numbers of heads, minus the cost of performing n tosses:

E(net reward) = Σ [P(X) * (\(X^{2}\) + bX)] - nd

where Σ is the sum over all possible values of X from 0 to n.

Using the formula for the binomial coefficient and simplifying, we can write:

E(net reward) = Σ [(n choose X) \(* p^X * (1-p)^(^n^-^X^) * (X^2 + bX)] - nd\)

E(net reward) = \(n^2p^2\)Σ[(n-1) choose (X-1)]\(p^(^X^-^2^)(1-p)^(^n^-^X^)(X-1)\) + npΣ[(n choose X)\(p^(^X^-^1^)(1-p)^(^n^-^X^)\)(1+b)] - nd

where Σ is the sum over all possible values of X from 1 to n.

For the second part of the question, we can use the same approach but replace (\(X^2\) + bX) with \(a^X\):

E(reward) = Σ [P(X) *\(a^X\)]

E(reward) = Σ [(n choose X) *\(p^X * (1-p)^(^n^-^X^) * a^X]\)

E(reward) = Σ [(n choose X) * \((ap)^X * (1-p)^n-X]\)

where Σ is the sum over all possible values of X from 0 to n.

The expected value of the net reward and the expected value of the reward can be negative if the cost d is greater than the expected reward or if a is less than 1, respectively.

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The total number of observations of bivariate data can be obtained from the frequencies in a contingency table by using the following three methods:

By summing the row totals, the column totals, or the frequencies in the cells, we can obtain the total number of observations in the bivariate data. These methods are all based on the fact that the frequencies in a contingency table represent the number of observations in each category.

By adding up these frequencies, we can determine the total number of observations in the data. Therefore, alternatives A, B and D are correct.

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Answer:

19.04

Step-by-step explanation:

find the length of AB,BC,CD , and AD

distance=√(x2-x1)^2+(y2-y1)^2

A(-3,5), B(2,6),C(0,2),D(-5,1)

line AB :d=√(2−(−3))^2+(6−6)^2

AB=5

BC=d=√(0−2)^2+(2−6)^2=√20=2√5

CD:√26

DA:√20

perimeter=AB+BC+CD+DA=5+√20+√20+√26=19.04

The equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.

Two lines that lie parallel to each other will have a slope (m) that is of the same value. The equation can be written as y = mx + b in slope-intercept form.

Find the slope of the line that passes through (4, 5) and (3, 2):

Slope (m) = change in y / change in x = (5 - 2)/(4 - 3)

Slope (m) = 3/1

Slope (m) = 3

The slope of a parallel line would also be 3.

Substitute (a, b) = (2, -3) and m = 3 into y - b = m(x - a):

y - (-3) = 3(x - 2)

y + 3 = 3x - 6

Subtract 3 to both sides of the equation

y + 3 - 3 = 3x - 6 - 3

y = 3x - 6 - 3

y = 3x - 9

Therefore, the equation for the parallel street that passes through (2, -3) is: B. y = 3x - 9.

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The question is an illustration of combination, and there are 1820 ways to select the 12 students

The distribution of the students is given as:

Senior = 7

Junior = 5

Sophomore = 4

The total number of students is:

Total = 7 + 5 + 4

Evaluate

Total = 16

To select 12 students from the 16 students, we make use of the following combination formula

Ways = 16C12

Evaluate the expression using a calculator

Ways = 1820

Hence, there are 1820 ways to select the 12 students

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The creation of a scatter plot is the first step in the analysis of two quantitative variables.

A scatter plot is a form of a graph where each data point is shown separately to show the relationship between two quantitative variables. A scatter plot graph shows the link between the variables to one another after learning the concept of a sample statistic through examples.

In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

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The type of bacterial pneumonia is most often seen in children and young adults is; Pneumococcal infection.

The correct type of Bacterial pneumonia that is most often seen in children and young adult is called Pneumococcal infection. This is because it is a name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.

Thus, we can conclude that the type of Bacterial pneumonia here is called Pneumococcal infection.

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Answer:

76

Step-by-step explanation:

Answer:

(x+7)(x+6)

Step-by-step explanation:

x²+13x+42

x²+6x+7x+42

x(x+6)+7(x+6)

(x+6)(x+7)

Answer:

a) (x+7) (x+6)

Step-by-step explanation:

That is the correct answer because you get it when you factor the current equation.

Hope it helps

Answer:

C. 215.12 feet per second

Step-by-step explanation:

Sergei's car was clocked in a quarter mile race at 146.67 miles per hour.

How many feet per second is this to the nearest hundredth if there are 5280 feet in one mile?

From the above question

1 mile = 5280 feet

1 hour = 60 minutes

1 minutes = 60 seconds

1 hour = 60 × 60 seconds = 3600 seconds

We are to convert 146.67 miles per hour = feet per second

Hence:

146.67 miles /1 ft × 5280 feet/1 miles × 1 hr/3600 seconds

= 146.67 × 5280 feet/3600 seconds

= 774417.6 feet / 3600 seconds

= 215.116 feet per second.

Approximately = 215.12 feet per second

Option C is correct

The largest angle is \(\frac{7a}{4}\) and the smallest angle is \(\frac{3a}{4}\).

In this case, we have the angles \(\frac{5a}{2}, \frac{3a}{4}, and \frac{7a}{4}\). So we can set up the equation:

\(\frac{5a}{2} + \frac{3a}{4} + \frac{7a}{4} = 180\)

To solve for "a", we can simplify the left side of the equation by finding a common denominator:

\(\frac{(10a + 3a + 7a)}{4} = 180\)

Simplifying the left side gives:

\(\frac{20a}{4} = 180\)

And further simplifying gives:

5a = 180

Dividing both sides by 5 gives:

a = 36

Now that we know the value of "a", we can substitute it back into each angle expression to find their actual values:

\(\frac{5a}{2} = \frac{5(36)}{2} = \frac{903a}{4} = \frac{3(36)}{4} = \frac{277a}{4} = \frac{7(36)}{4} = 63\)

Therefore, \(\frac{7a}{4} = 63\) is the largest angle and \(\frac{3a}{4} = 27\) is the smallest angle.

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According to the given information, equivalent ratios are 25 : 50 : 100 : 200

What are equivalent ratios?

Equivalent ratios are ratios that have the same value or result in the same proportion when simplified. In other words, if two ratios have the same value or represent the same proportion, then they are equivalent ratios.  For example, the ratios 2:4 and 3:6 are equivalent because both simplify to 1:2. Likewise, the ratios 6:8 and 9:12 are equivalent because both simplify to 3:4.

Ratio table:

25, 50, 100, 200

1/3, 2/3, 1, 4/3

Equivalent ratios:

1/3 : 2/3 : 1 : 4/3

25 : 50 : 100 : 200

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Answer:

Step-by-step explanation:

Uh sorry but there is no picture here

Answer:

no graph is attached

Step-by-step explanation:

The formula for the distance from P to B is √(25-10y+y²+z²)  and the formula for L(x, y) the total length of the connector joining P to A, B, and C is √(5²+y²+z²)+√((5-x)²+y²+z²)+√(x²+y²+(5-z)²).

Given, Domain: 5, 5, and A, B, C are not given and unknown.

2. To find the formula for the distance from P to B, first we need to consider the triangle PBA and the Pythagoras theorem. The distance from P to B is the hypotenuse of the right triangle PBA and can be obtained by the formula using the Pythagorean theorem as follows; h² = p² + b²

Where, h = hypotenuse, p = perpendicular, b = base

Let's use the information given in the problem, where B is on the x-axis, which means the distance from P to B is the length of the segment BP. Then, the value of p is (5 - y) and the value of b is z.

So, the formula for the distance from P to B will be; BP = √(5-y)²+z²= √(25-10y+y²+z²)

3. Now, to find a formula for L(x,y), we need to consider the distance between A, B, and C. We have already found the length of the connector joining B to P, which is BP.

To find the length of connector AP and CP, we have to use the distance formula for 3D space that is the formula for the Euclidean distance between two points (x1, y1, z1) and (x2, y2, z2).

The formula is given by;d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Therefore, the formula for the total length of the connector joining P to A, B, and C can be given as follows;

L(x, y) = AB + AP + CP = √(5²+y²+z²)+√((5-x)²+y²+z²)+√(x²+y²+(5-z)²)

4. Now, we need to find the minimum value of L(x,y) over all (x,y,z) that satisfy the equation x+y+z=5.

To do this, we have to differentiate L(x,y) with respect to x and y. We assume that partial derivatives are equal to zero since we are looking for the minimum value.

L(x,y) = AB + AP + CP = √(5²+y²+z²)+√((5-x)²+y²+z²)+√(x²+y²+(5-z)²)∂L/∂x = -√((5-x)²+y²+z²)/(√((5-x)²+y²+z²)+√(x²+y²+(5-z)²)) = √(x²+y²+(5-z)²)/(√((5-x)²+y²+z²)+√(x²+y²+(5-z)²))∂L/∂y + -√(y²+z²+25)/(√(5²+y²+z²)+√((5x)²+y²+z²)) = √(y²+z²+25)/(√(5²+y²+z²)+√((5-x)²+y²+z²))

The minimum value occurs when the partial derivatives are equal to zero.

Therefore, we have the following two equations; x²+y²+(5-z)² = (5-x)²+y²+z² ……………(1)

y²+z²+25 = 5²+y²+z²+2√((5-x)²+y²+z²) ……(2)

Simplify equation (2) : 5√((5-x)²+y²+z²) = 5² - 25 + 2x√((5-x)²+y²+z²)

Squaring both sides25(5-x)² + 25y² + 25z² = 25x² + 625 - 50x

Substituting z = 5-x-y in the above equation

25(2x² - 10x + 25) + 25y² - 50xy = 625 …………….(3)

Now, we have to minimize equation (3) subject to the condition x + y + z = 5.

We will use the Lagrange multiplier method for this.

Let's assume that F(x,y,z,λ) = 25(2x² - 10x + 25) + 25y² - 50xy + λ(5-x-y-z)∂F/∂x = 100x - 250 + λ = 0∂F/∂y = 50y - 50x + λ = 0∂F/∂z = λ - 25 = 0∂F/∂λ = 5 - x - y - z = 0

Solving these equations, we get x = 5/3, y = 5/3, z = 5/3

Now we can substitute these values in equation (1) or (2) to find the minimum value of L(x,y).

Using equation (2), we get25 = 5² + 2√((5/3)²+y²+(5/3)²)√((5/3)²+y²+(5/3)²) = 10/3

Substituting back into the equation for L(x,y) we get L(x,y) = √50+√50+√50=3√50

the minimum value of L(x,y) over all (x,y,z) that satisfy the equation x+y+z=5 is 3√50

Therefore, the formula for L(x, y) is √(5²+y²+z²)+√((5-x)²+y²+z²)+√(x²+y²+(5-z)²).

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Answer:

Step-by-step explanation:

2)f(x) = 2x² +4x - 3    

a = 2 ; b = 4 ; c = -3

1) Put x = -1 in the equation

f(x) = 2*(-1)² + 4*(-1) -3 = 2 - 4 -3 = -5

Vertex = (-1,-5)

2) Upward

3) Minimum

4) axis of symmetry = -b/2a = -4/2*2=-4/4= -1

x = -1

5) domain: all real numbers  (-∞ ,∞)

Range : y ≥ -5 ; [-5 , ∞)

3) f(x) = 3x² - 6x + 4

Vertex : (1,1)

Opening : upward

Minimum

Axis of symmetry: x = 1

Domain: all real numbers

Range: y ≥ 1 ; [1, ∞)

4)f(x) = -x² - 2x - 3

a) Vertex:  f(x) = -(-1)² - 2*(-1) - 3 = -1 + 2 - 3 = -2

Vertex( -1,-2)

b) downward

c) Maximum

d) Axis of symmetry: x = 2/-2 = -1  

x = -1

e) Domain: all real numbers

Range: y ≤ -2 ; (-∞ , -2]

5)f(x) = 2(x -2)²

a) Vertex: (2, 0)

b) Opening: upward

c) Minimum

d) x = 2

e)Domain: all real numbers

Range: y ≥ 0 ; [0,∞)

In this problem, we are given a set S with 13 elements and two subsets A and B. We need to perform various operations and calculations related to these subsets.

Additionally, we are asked to calculate the number of different license plates possible with four digits followed by four letters, considering both cases where repetition is not allowed and where repetition is permitted.

a. The Venn diagram for the given sets A and B can be drawn as follows:

  - Set A contains elements {a, b, m, q}.

  - Set B contains elements {a, d, m, p, q}.

  The overlapping region represents the elements common to both sets A and B.

b. Operations:

  - Ac represents the complement of set A, which contains all the elements in set S except those in set A.

  - AUB represents the union of sets A and B, which contains all the elements that are in either set A or set B or both.

  - (AUB)c represents the complement of the union of sets A and B, which contains all the elements in set S except those in the union of A and B.

c. Calculations:

  - n(Ac) represents the number of elements in the complement of set A.

  - n(AUB) represents the number of elements in the union of sets A and B.

  - n() represents the number of elements in the overlapping region of sets A and B.

  - n((AUB)c) represents the number of elements in the complement of the union of sets A and B.

d. Combinations and Permutations:

  - C(3, 2) represents the number of combinations of selecting 2 elements from a set of 3 elements without repetition.

  - P(3, 2) represents the number of permutations of selecting 2 elements from a set of 3 elements without repetition.

  - C(3, 2) * 2! represents the product of C(3, 2) and 2 factorial (2!), which can be compared with P(3, 2).

19. License plates:

  a. If digits and letters are not repeated on a plate, we have 10 choices for each digit and 26 choices for each letter. Therefore, the total number of possible license plates is 10 * 10 * 10 * 10 * 26 * 26 * 26 * 26.

  b. If repetition of digits and letters is permitted, we still have 10 choices for each digit and 26 choices for each letter. Therefore, the total number of possible license plates is 10 * 10 * 10 * 10 * 26 * 26 * 26 * 26.

Hence, the number of different license plates possible can be calculated based on whether repetition is allowed or not.

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The cliff rises 10.8 metres in height.

To determine the height of the cliff, we can use similar triangles and apply the concept of proportions.

Let's denote the height of the cliff as "h."

According to the given information, Sandra is 1.8 m tall and stands 0.9 m from the base of the mirror. The distance between the base of the mirror and the base of the cliff is 5.4 m.

We can form a proportion based on the similar triangles formed by Sandra, the mirror, and the cliff:

(Height of Sandra) / (Distance from Sandra to Mirror) = (Height of Cliff) / (Distance from Mirror to Cliff)

Plugging in the values we know:

1.8 m / 0.9 m = h / 5.4 m

Simplifying the equation:

2 = h / 5.4

To solve for h, we can multiply both sides of the equation by 5.4:

2 * 5.4 = h

10.8 = h

Therefore, the height of the cliff is 10.8 meters.

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Answer:

(240 × 60)/100 = 144

Step-by-step explanation:

(Whole × Percent)/100 = Part

Answer:

25%

Step-by-step explanation:

60 times 4 is equal to 240.

1/4 is 25%

60 is 25% of 240

Answer:x= - 23/54

x= 3/20

Step-by-step explanation:

i hope this helps

Answer:

1.x= -23/54

2.x= 4/15

Step-by-step explanation:

1.5x-2x= -7/18 - 8/9

3x= -23/18 .......divide both sides by 3

x = -23/18 × 1/3

x = -23/54

2.3x-6x = -2/10 - 3/5

-3x = -1/5 - 3/5

-3x = -4/5......... divide both sides by -3

x = -4/5 × 1/-3

x = 4/15

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

The sum of the first 20 integers is 420.

Step-by-step explanation:

So x+(x+2)+(x+4)+(x+6)=420.

4X+12=420

4X=408

X=102

102+104+106+108 =420

The calculated correlation coefficient (r) is approximately -0.291.

To calculate the correlation coefficient between telomere length and chronicity, we can utilize the given summary data. The correlation coefficient, often denoted as r, measures the strength and direction of the linear relationship between two variables.

Let's denote the sum of products as Σxy, the sum of squares for chronicity as Σx², the sum of squares for telomere length as Σy², and the total sample size as n.

From the given data, we have the following values:

Σxy = -8.822

Σx² = 318.817

Σy² = 2.868

n = 38

The correlation coefficient (r) can be calculated using the following formula:

r = Σxy / √(Σx² * Σy²)

Substituting the given values into the formula:

r = -8.822 / √(318.817 * 2.868)

Now, let's solve this equation step by step:

First, multiply the values inside the square root:

r = -8.822 / √(913.350956)

Next, calculate the square root:

r = -8.822 / 30.219307

Finally, divide Σxy by the square root of the product of Σx² and Σy²:

r ≈ -0.291

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Answer:

The probability of drawing a purple marble is 3/10