Reggie runs 5 miles per hour for 1 1/2 hours. If
Heather runs the same distance in 1 hour, then
what is Heather's average speed in miles per
hour?
A. 10
B. 9 1/2
C. 7 1/2
D. 5

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Our assumption that L(V, W) is finite-dimensional must be false. Therefore, we can conclude that L(V, W) is infinite-dimensional when V is finite-dimensional with dim V > 0 and W is infinite-dimensional.

To prove that the space of linear transformations, L(V, W), is infinite-dimensional when V is finite-dimensional with dim V > 0 and W is infinite-dimensional, we will use a proof by contradiction.

Assume that L(V, W) is finite-dimensional. This means there exists a finite basis for L(V, W) consisting of n linear transformations, where n is a positive integer. Let's denote this finite basis as {T_1, T_2, ..., T_n}.

Since V is finite-dimensional with dim V > 0, we can choose a basis for V consisting of m vectors, where m is also a positive integer. Let's denote this basis as {v_1, v_2, ..., v_m}.

Now, consider the set of vectors in W given by {T_1(v_1), T_2(v_1), ..., T_n(v_1)}. Since each T_i is a linear transformation from V to W, each T_i(v_1) is an element of W. Since W is infinite-dimensional, there must exist a linearly independent set of vectors in W of any size.

However, we have chosen n vectors {T_1(v_1), T_2(v_1), ..., T_n(v_1)} in W, which means that they span a subspace of W of dimension at most n. Since n is finite, there exists a larger linearly independent set in W.

Let's denote the larger linearly independent set in W as {w_1, w_2, ..., w_k}, where k is greater than n. Now, we can construct a linear transformation T from V to W as follows:

T(v_1) = w_1

T(v_2) = 0

T(v_3) = 0

T(v_m) = 0

By defining T in this way, we have mapped the basis vectors of V to distinct vectors in W, ensuring that T is a linear transformation. Furthermore, since {w_1, w_2, ..., w_k} is linearly independent, we can see that T is not a linear combination of the n basis vectors {T_1(v_1), T_2(v_1), ..., T_n(v_1)}. This means that T cannot be expressed as a linear combination of the n basis elements of L(V, W), contradicting the assumption that {T_1, T_2, ..., T_n} forms a basis for L(V, W).

Hence, our assumption that L(V, W) is finite-dimensional must be false. Therefore, we can conclude that L(V, W) is infinite-dimensional when V is finite-dimensional with dim V > 0 and W is infinite-dimensional.

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Answer:

J

Step-by-step explanation:

shifts to the right by 1

The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.

Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.

The PMF of x is given by the binomial probability formula:

P(x) = (n C x) * p^x * (1 - p)^(n - x)

where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).

In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).

Let's calculate the PMF for x:

P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004

P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588

P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432

P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192

The PMF for x is:

P(x = 0) = 0.0004

P(x = 1) = 0.0588

P(x = 2) = 0.3432

P(x = 3) = 0.941192

To calculate the CMF, we sum up the probabilities up to x:

F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)

Using the calculated probabilities, the CMF for x is:

F(x = 0) = 0.0004

F(x = 1) = 0.0592

F(x = 2) = 0.4024

F(x = 3) = 1.0

Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

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An absolute maximum value and a relative maximum value are both concepts used in mathematics to describe the highest point of a function.

The key difference between the two lies in their scope and the conditions under which they occur. In summary, the absolute maximum value of a function is the highest point on the entire function's domain. It represents the overall maximum value that the function can attain. On the other hand, a relative maximum value refers to the highest point within a specific interval or a local portion of the function. It is only valid within that interval and may not be the highest point on the entire function.

To explain further, let's consider a graph of a function. An absolute maximum value can be identified by examining the entire graph and finding the highest point. This point will have the highest y-coordinate on the graph, indicating the maximum value for the function. In contrast, a relative maximum value is identified by examining a specific interval or region of the graph. It represents a peak within that interval but may not be the overall highest point on the entire graph.

It's important to note that a function can have multiple relative maximum values, but it can have at most one absolute maximum value. The absolute maximum value, if it exists, will be the highest point on the entire function's domain. Relative maximum values, on the other hand, may occur at different intervals within the function, depending on the shape and behavior of the graph.

In conclusion, while both absolute maximum and relative maximum values refer to the highest points of a function, the key distinction lies in their scope. The absolute maximum value represents the overall highest point on the entire function's domain, whereas the relative maximum value represents the highest point within a specific interval or region of the function.

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Answer:

a. A point

b. Obtuse angle

c. A line segment

d. 180 degrees

e. A ray

f. An acute angle

g. 90 degrees

Step-by-step explanation:

a. A point (a place on a plane that has no dimension)

b. Obtuse angle (any angle over 90 degrees)

c. A line segment (a part of a line)

d. 180 degrees (The angle of a line or line segment)

e. A ray (a line segment with one end extending forever)

f. An acute angle (Any angle under 90 degrees)

g. 90 degrees (the pole is perpendicular to the ground)

The probability that the selected contestant received a score of 5 55 on day 2 22 or day 3 33, given that the contestant received a score of 5 55 on one of the three days is 2/3 or approximately 0.67.

To see why, note that there are three possible cases: the contestant received a score of 5 55 on day 1 11, day 2 22, or day 3 33. We know that the contestant received a score of 5 55 on one of the days, so we can ignore the first case.

Now, since no contestant received the same score on two different days, the contestant who received a score of 5 55 on day 2 22 cannot have received that same score on day 3 33. Similarly, the contestant who received a score of 5 55 on day 3 33 cannot have received that same score on day 2 22. Therefore, if a contestant received a score of 5 55 on one of the days, there are only two possible days on which that could have happened (day 2 or day 3), and both of these have an equal chance of being the correct day. So, the probability is 2/3.

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Answer:

It is (x - 2y)/xy

Step-by-step explanation:

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

carry out LCM method:

LCM of y and x is xy

\( = \frac{x - 2y}{xy} \)

Answer:

i need more info, like how much r the CDs and the phones

Step-by-step explanation:

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

Answer:4

Step-by-step explanation:

The poles and zeros are the roots of the numerator and denominator polynomials of the transfer functions.

a) To convert the transfer functions into state space representation, we need to express them in the form:

ẋ = Ax + Bu

y = Cx + Du

where ẋ represents the derivative of the state vector x, u represents the input, y represents the output, A is the state matrix, B is the input matrix, C is the output matrix, and D is the feedforward matrix.

1) For G1(s):

G1(s) = (s^2 + 4s + 5) / (3s + 9)

To convert it into state space representation, we introduce a state vector x = [x1, x2]^T and rewrite the transfer function as follows:

s^2 + 4s + 5 = x1' - 4x1 - 5x2

3s + 9 = x2'

Therefore, the state space representation for G1(s) is:

ẋ1 = x2

ẋ2 = -4x1 - 5x2

y = x1

2) For G2(s):

G2(s) = (s+3)(s^2 + 2s + 2) / (12s + 24)

Again, we introduce a state vector x = [x1, x2, x3]^T and rewrite the transfer function as follows:

s+3 = x1' - 3x1

s^2 + 2s + 2 = x2'

12s + 24 = x3'

Therefore, the state space representation for G2(s) is:

ẋ1 = -3x1

ẋ2 = x3

ẋ3 = -2x1 - 2x2

y = x1

b) The block diagram representation of the state space system for G1(s) and G2(s) can be drawn as follows:

For G1(s):

```

        |--------|       |----|

u ----->|        |-----> |    | ---> y

       | ẋ = Ax |       | C  |

x ----->|        |-----> |----|

        |--------|

```

Where A = [0 -5; -4 0], B = [0; 1], C = [1 0], and D = 0.

For G2(s):

```

        |--------|       |----|

u ----->|        |-----> |    | ---> y

       | ẋ = Ax |       | C  |

x ----->|        |-----> |----|

        |--------|

```

Where A = [0 0 0; 0 0 -2; 0 1 0], B = [0; 0; 1], C = [1 0 0], and D = 0.

c) The poles and zeros for G1(s) and G2(s) can be determined by examining the coefficients of the transfer functions.

For G1(s):

Poles: -3

Zeros: None

For G2(s):

Poles: -3, -1+√3i, -1-√3i

Zeros: -3

Note: The poles and zeros are the roots of the numerator and denominator polynomials of the transfer functions.

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Answer:

did u have any options in that..so I can tell u

Answer:

18 times in a day

Step-by-step explanation:

1 day - 24 hours

1 hours - 60 minutes

24 hours - 24 × 60

= 1440

1 day - 1440 minutes

therefore, 1440/ 80 = 18

Answer:

(C)(5,9.2)

Step-by-step explanation:

Given points Q(2, 5) and R(7, 12). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 3 to 2.

For internal division of a line segment, the coordinate of the point which partitions the segment in the ratio m:n is given as:

\(\left(\dfrac{mx_2+nx_1}{m+n} , \dfrac{my_2+ny_1}{m+n}\right)\)

m:n =3:2

\((x_1,y_1)=Q(2,5)\\(x_2,y_2)=R(7,12)\)

Therefore:

\(P(x,y)=\left(\dfrac{3*7+2*2}{3+2} , \dfrac{3*12+2*5}{3+2}\right)\\=\left(\dfrac{25}{5} , \dfrac{46}{5}\right)\\P(x,y)=(5,9.2)\)

Answer:

\(\frac{9}{16}\)

Step-by-step explanation:

\((-\frac{3}{4}) ^{2}\)

= - \(\frac{3}{4}\) × - \(\frac{3}{4}\) ← multiply numerators/ denominators

= \(\frac{3(3)}{4(4)}\)

=\(\frac{9}{16}\)

Answer:

3 8 + 3 7  divided by 8

Step-by-step explanation:

What is a Matrix?

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

A)

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)

B)

\(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

C)

A x B = C

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)  X    \(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

=

\(\left[\begin{array}{c}183.46\\159.66\\179.51\end{array}\right]_{3x1}\)

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Answer:

Unlike the previous problem, this one requires application of the Law of Cosines.  You want to find angle Q when you know the lengths of all 3 sides of the triangle.

Law of Cosines:  a^2 = b^2 + c^2 - 2bc cos A

Applying that here:

                          40^2 = 32^2 + 64^2 - 2(32)(64)cos Q

Do the math.  Solve for cos Q, and then find Q in degrees and Q in radians.

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

this is an isosceles triangle, which mean that PRQ and PQR are equal.

all sides of a triangle equal 180.

using this, you can make the following equation:

x + (2x + 15) + (2x + 15) = 180

combine like terms

5x + 30 = 180

subtract 30 from both sides

5x = 150

divide both sides by 5

x = 30

The correct answer is option a. The slope of the least-squares regression line is 0.0298. This means that for every additional one mile increase in the flight distance, the predicted air fare increases by $0.0298.

In other words, there is a positive relationship between the distance of the flight and the air fare. As the distance of the flight increases, the air fare also increases. It is important to note that this is only a rough linear relationship and there may be other factors that affect the air fare such as seasonality, demand, and competition. The slope of the least-squares regression line helps us understand the direction and strength of the relationship between the two variables (distance and air fare). However, it is important to interpret this slope in context with other information such as the correlation coefficient, residual plots, and other regression diagnostics.

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Answer:

The cause is the independent variable. In your study, its value is independent of other variables. The affect is the dependent variable. Its value depends on the independent variable being changed.

Step-by-step explanation:

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

Step-by-step explanation:

4x + 2y = 1 is linear because it's straight on a graph.

y - x² + 3x = 1 - x² is also linear.

Answer:

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

The major difference between linear and nonlinear equations is given here for the students to understand it in a more natural way. The differences are provided in a tabular form with examples.

Step-by-step explanation:

Answer:

C2H5OH + 3O2 --> 2CO2 + 3H2O

Step-by-step explanation:

Balanced, there is:

- 2 Carbons coming from the ethanol going into the Carbon Dioxide.

- 6 Hydrogens coming from the ethanol going into the water

- 1 Oxygen coming from the ethanol and 6 Oxygens coming from 3O2 going (so 7 in reactants) going to 4 in the Carbon Dioxide and 3 to the Water

The balanced form of the chemical equation is:

C2H5OH(l) + 3O2(g) → 2H2O(g) + 2CO2(g)

A balanced chemical equation is a representation of a chemical reaction using the chemical formulas of the reactants and products, with stoichiometric coefficients indicating the relative numbers of molecules or moles of each substance involved.

We have,

In this balanced equation, the stoichiometric coefficients have been adjusted to ensure that the same number of atoms of each element appears on both sides of the equation.

The balanced equation shows that one molecule of ethanol (C2H5OH) reacts with three molecules of oxygen (O2) to produce two molecules of water (H2O) and two molecules of carbon dioxide (CO2).

Note that the state of matter is also included in the balanced equation

(l = liquid, g = gas).

Thus,

The balanced form of the chemical equation is:

C2H5OH(l) + 3O2(g) → 2H2O(g) + 2CO2(g)

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Answer:

The arteries

Step-by-step explanation:

Answer:

Question 1: Artery

Question 2: Cardiovascular Activity

Step-by-step explanation:

Answer:

She can swin 3.6 km in 1 hour using freestyle.

Step-by-step explanation:

If she can swin 0.3 kilometers in 10 minutes or 1/6 hours using backstroke, then her speed on that style is:

\(v_{backstroke} = \frac{0.3}{\frac{1}{6}} = 0.3*6 = 1.8 \text{ } \frac{\text{km}}{\text{h}}\)

If she can swim twice the distance in the same time for freestyle, then her speed on that is twice the one in backstroke. Therefore, her speed on freestyle is:

\(v_{freestyle} = 2*v_{backstroke} = 2*1.8 = 3.6 \text{ } \frac{\text{km}}{\text{h}}\)

Since her speed in freestyle is 3.6 km per hour, this means that she can swim a total of 3.6 km in one hour.

ANSWER: 155.25

EXPLANATION: -81 ÷ (-9)× 23(3/4)

9×69/4

621/4

155.25 answer

please mark as brainliest if it helps

Answer:

\( \frac{621}{4} \)

or

\(155.25\)

Answer:

\(\angle ABC\) corresponds to the \(\angle D EF\)

\(\angle BCA\) corresponds to the \(\angle EFD\)

Segment AC corresponds to segment DF.

Segment BA corresponds to segment ED.

Step-by-step explanation:

As per the given statements, kindly refer to the attached figure for the diagrammatic representation of the situation.

Given two triangles: \(\triangle ABC, \triangle D EF\).

Horizontal sides are AB and DE with points B and E are on the right side of A and D respectively.

Points C and F are directly above the corresponding sides AB and DE respectively.

Kindly refer to the attached diagram for the representation as per the given situation.

Scaled version of a figure and the original figure are similar to each other.

It means that corresponding sides and angles are equal to each other.

\(\angle ABC\) corresponds to the \(\angle D EF\)

\(\angle BCA\) corresponds to the \(\angle EFD\)

Segment AC corresponds to segment DF.

Segment BA corresponds to segment ED.

Answer:

no

Step-by-step explanation: