Determine the system of transformations, by writing the algebraic notations, that can
be used to map ∆RST onto ∆UVW.

To determine if a linear transformation is onto, we need to check if every vector in the range has at least one pre-image in the domain.

Let T be a linear transformation from R^3 to R^2 given by:

T (x, y, z) = (2x - y, x + 3y - 4z)

(a) To check if T is one-to-one, we need to check if for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3, we have T (x1, y1, z1) ≠ T (x2, y2, z2). Equivalently, we can check if T (x1, y1, z1) - T (x2, y2, z2) ≠ 0 for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3.

So, let (x1, y1, z1) and (x2, y2, z2) be two distinct vectors in R^3. Then:

T (x1, y1, z1) - T (x2, y2, z2) = (2x1 - y1, x1 + 3y1 - 4z1) - (2x2 - y2, x2 + 3y2 - 4z2)

= (2x1 - y1 - 2x2 + y2, x1 + 3y1 - 4z1 - x2 - 3y2 + 4z2)

= (2(x1 - x2) - (y1 - y2), x1 - x2 + 3(y1 - y2) - 4(z1 - z2))

For T to be one-to-one, the only solution to T (x1, y1, z1) - T (x2, y2, z2) = 0 must be (x1, y1, z1) = (x2, y2, z2). So, we need to solve the equation above and check if the only solution is (x1, y1, z1) = (x2, y2, z2).

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Table one and table four represent a linear function.

A linear function is simply a function that represents a straight line on the coordinate plane.

For a function to be linear, the differences of the y-values must be constant.

For table 1.

Let get the differences of the y-values

-1 - (-2) = 1

0 - (-1) = 1

1 - 0 = 1

2 - 1 = 1

Since the differences of the y-values are all 1 ( constant ), table one is a linear function.

For table 2.

2 - (-3) = 5

0 - 2 = -2

-2 - 0 = -2

3 - (-2) = 5

Since the differences of the y-values are not the same ( constant ), table two is not a linear function.

For table 3.

0 - 2 = -2

-1 - 0 = -1

0 - (-1) = 1

2 - 0 = 2

Since the differences of the y-values are not the same ( constant ), table three is not a linear function.

For table 4.

1 - 3 = -2

-1 - 1 = -2

-3 - (-1) = -2

-5 - (-3) = -2

Since the differences of the y-values are all -2 ( constant ), table four is a linear function.

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(a) The probability that Shelia is diagnosed as having gestational diabetes is  0.1586.

(b) The probability that Shelia is diagnosed as needing further testing for gestational diabetes is 0.0416.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy).

There is variation both in the actual glucose level and in the blood test that measures the level.

In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 120 milligrams per deciliter (mg/dL) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 105 mg/dL and = 15 mg/dL.

(a) The sample mean [tex]\bar{X}[/tex] = 120

The mean = 105

And standard deviation = 15

t = 1 - P(X ≤ 120 - 105/15)

t = 1 - P(X ≤ 15/15)

The P-Value is 0.158655.

(b) The sample mean [tex]\bar{X}[/tex] = 120

The mean = 105

And standard error = 15/√3 =

t = 1 - P(X ≤ 120 - 105/8.66025403784)

t = 1 - P(X ≤ 15/8.66025403784)

The P-Value is 0.041637.

Therefore, the P-Value is 0.041637.

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The measure of m∠5 of the quadrilateral is m∠5 = 27° because of alternate interior angles

The solution is Option C. Angle A B D is angle 5

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the quadrilateral be represented as ABCD

Now , the diagonal DB is the transversal line passing through the 2 parallel lines of the quadrilateral

And , the measure of m∠2 = 27°

The measure of m∠2 = measure of m∠5 ( alternate interior angles are equal )

So , the angles m∠2 and m∠5 are alternate interior angles

And , the measure of m∠5 = 27°

Hence , the measure of m∠5 = 27° ( interior angles )

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The expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.

By using the long division method:

x + 4 | x^2 + 2x - a

-x^2 - 2x + 4x    

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

      -a + 6x    

-x^2 - a + 6x    

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

        2x - a

-x^2 - 2x + 4x    

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

          0

The remainder is 0 a = 6x.

Hence, the expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

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Answer:

2 pieces of sc and 1 piece of rc

Step-by-step explanation:

The cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.

What is potential energy (PE)?

The potential energy formula is affected by the force operating on the two objects. The formula for gravitational force is P.E. = mgh, where m is mass in kilograms, g is gravity's acceleration (9.8 m/s2 at the earth's surface), and h is height in meters.

The potential energy (PE) possessed by the cliff-jumper of mass m at height h above the base of the cliff is given by the formula:

PE = mgh

where g is the acceleration due to gravity (9.81 m/s²).

In this problem, the cliff-jumper has a mass of 68.0 kg and possesses 16,800 J of potential energy. We can use the formula above to find the height h:

PE = mgh

h = PE / (mg)

Substituting the given values, we get:

h = 16800 J / (68.0 kg x 9.81 m/s^2)

h = 24.7 meters (rounded to two decimal places)

Therefore, the cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.

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Answer:

20

Step-by-step explanation:

592--------16hours

740---------x hours

x=740 ×16÷592 =20

Answer:

20 hours

Step-by-step explanation:

Find speed from distace and time taken to reach uncle's house

s = d/t = 592/16

s = 37 miles/hr

then find time from distance to chicago and time taken to reach there:

t = d/s = 740/37

t = 20 hours

Hope this helps!

Hence, if i > j, then (AB)ij is a sum of products of zeros, and is therefore zero. This means that all the entries below the main diagonal in the matrix AB are zero. Therefore, AB is also an upper triangular matrix.

To show that if a and b are square, upper triangular matrices, then so is ab, we need to prove that all the entries below the main diagonal in the matrix ab are zero.

Let A and B be square, upper triangular matrices of size n x n.

Then the (i,j)th entry of AB is given by:

(AB)ij = Σk=1n AikBkj

For i > j, we have:

(AB)ij = Σk=1n AikBkj = Σk=1j AikBkj + Σk=j+1n AikBkj

Since A is upper triangular, we have Aik = 0 for k > i.

Therefore, the first sum above is non-zero only for k ≤ i. Since B is also upper triangular, we have Bkj = 0 for k > j.

Therefore, the second sum above is non-zero only for k > j.

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The SAS congruence criteria, option (c), is the appropriate response. The acronym SAS stands for "side-angle-side," and it denotes that two sides and the included angle of one triangle must be congruent to two sides and the incorporated angle of another triangle for the triangles to be considered congruent.

"Right-angle-hypotenuse-side" (or option a) refers to a particular instance of the SAS criteria that only applies to right triangles.

The acronym ASA (option b) stands for "angle-side-angle," and it denotes that two angles and the included side of one triangle must be congruent with two angles and the included side of some other triangle for the triangles to be considered congruent.

Side-side-side, or SSS (option d), refers to the situation in which all three sides of one triangle are congruent with all three sides of another triangle.

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The question is -

Two triangles are congruent if two angles and the side included between them in one triangle are equal to the two angles and the side included between them in the other triangle. This is known as:

a. RHS congruence criterion

b. ASA congruence criterion

c. SAS congruence criterion

d. SSS congruence criterion

Answer:

C

Step-by-step explanation:

Cause 13/17 is 0.76 so c is nearer to 1 about 0.76

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{13}{17}}\\\\\mathsf{\rightarrow 13\div17}\\\\\mathsf{\rightarrow 0.764705882352941}}\\\\\mathsf{\approx 0.764\approx 0.75\ (in\ this\ case)}}[/tex]

[tex]\huge\text{Therefore your answer should be:} \\\\\huge\boxed{\mathsf{Point\ C.}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

No, the function aren't inverse of each other.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it's defined is known as the sphere. The entire set of values that the function's affair can produce is appertained to as the range. The set of values that could be a function's labors is known as the co-domain.

Given

f( x) = 3x 6

g( x) = x5/3

So, the find the that both function are inverse of each other we've to prove

f( g( x)) = g( f( x))

So, f( g( x))

f( x+ 5/3)

= 3 (x+ 5/3) + 6

= 3x + 15 + 6

= 3x + 21

and, g( f( x))

= g(3x+ 6)

= 3x + 6 + 5/3

= 3x + 23/3

So, f( g( x)) ≠ g( f( x))

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Answer: a) A 95% confidence interval based on n = 10 randomly selected observations would use a t*-value from the t-distribution with (n - 1 = 9) degrees of freedom.

b) A 99% confidence interval from an SRS of 20 observations would use a t*-value from the t-distribution with

Step-by-step explanation:

Answer:

1/50

Step-by-step explanation:

Divide 2/100 by 2 to get the simplest form.

The missing values in the ratio table on pages and minutes is :

Pages         1 / 4    3 / 4    1 ¹ / ₂     5

Minutes      1 / 2      1 ¹ / ₂     3       10

To fill the ratio table, find the relationship between Minutes and Pages :

= 1 / 2 ÷ 1 / 4

= 2 mins per page

This means that every page is read in 2 minutes.

3 / 4 pages would be read in :

= 3 / 4  x 2

= 1 ¹ / ₂ minutes

3 minutes would allow for the reading of :

= 3  / 2

= 1 ¹ / ₂ pages

5 pages would be read in:

= 5 x 2

= 10 mins

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The Sampling Distribution used when making inferences about a single population's variance is a(n) Chi Square distribution.

The Chi Square distribution is defined as a continuous probability distribution that takes only non-negative values. It is used to analyze the variability of a set of data and is frequently used in hypothesis testing and confidence interval estimation.

In this test, the test statistic follows a chi-square distribution with (n - 1)  degrees of freedom, where n = sample size. The larger the size of the sample , the closer the sampling distribution of test statistic will approach to  a Normal Distribution .

Therefore , the chi-square distribution is a statistical tool which the researchers use to draw conclusions about the variability of a population based on a sample.

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Answer:

Step-by-step explanation:

The answer is TRUE, If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.

Answer: 1.75 yards

Step-by-step explanation:

You need to divide 7 by 4 to get 4 equal sections.

7/4 = 1.75

Therefore, 1.75 is your answer

The maximum profit that the company will be left with is $11,450 from the laptops and tablets.

Your profit is the amount left over after paying all necessary business expenses. The three main categories of profit are gross, operational, and net. Gross revenue is the most profitable. After paying for the items and services that were sold, the remaining balance is shown.

1.The daily constraints on the company according to the plan are:

70 <= x <= 130 (number of laptops produced)

50 <= y <= 110 (number of tablets produced)

x + y >= 150 (total number of devices produced)

x + y <= 220 (total number of devices produced)

2.The objective function for maximizing profit is:

Profit = 65x + 45y

4.The vertices of the feasible region are:

(70, 80)

(70, 110)

(100, 50)

(110, 40)

(130, 20)

(130, 30)

(130, 50)

(100, 110)

5.Evaluating the objective function at the vertices of each feasible region:

(70, 80): Profit = 65(70) + 45(80) = $8,150

(70, 110): Profit = 65(70) + 45(110) = $9,500

(100, 50): Profit = 65(100) + 45(50) = $8,750

(110, 40): Profit = 65(110) + 45(40) = $8,950

(130, 20): Profit = 65(130) + 45(20) = $9,350

(130, 30): Profit = 65(130) + 45(30) = $9,800

(130, 50): Profit = 65(130) + 45(50) = $10,700

(100, 110): Profit = 65(100) + 45(110) = $11,450

6.To maximize profit, the company should make 100 laptops and 110 tablets.

7.The maximum profit is $11,450.

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La intensidad de la luz afecta la tasa de fotosíntesis, cuanto mayor es la intensidad de la luz, mayor es la tasa de fotosíntesis y viceversa. ver explicacion.

Important structures in plant development are buds, shoots, roots, leaves, and flowers; plants produce these tissues and structures throughout their life from meristems located at the tips of organs, or between mature tissues. Thus, a living plant always has embryonic tissues.

La fotosíntesis es el proceso mediante el cual las plantas verdes fabrican su propio alimento en presencia de luz solar, clorofila, dióxido de carbono y agua.

La intensidad de la luz afecta la tasa de fotosíntesis, cuanto mayor es la intensidad de la luz, mayor es la tasa de fotosíntesis y viceversa. Cuando hay una mayor intensidad de luz, hay más luz disponible para impulsar las reacciones de la fotosíntesis.

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Answer:

t ≤ 8

Step-by-step explanation:

Equation Total

1 hour 32 + 9.4 41.4

2 hours 32 + 2(9.4) 50.8

3 hours 32 + 3(9.4.) 60.2

4 hours 32 + 4(9.4.) 69.6

5 hours 32 + 5(9.4.) 79.0

6 hours 32 + 6(9.4.) 88.4

7 hours 32 + 7(9.4.) 97.8

8 hours 32 + 8(9.4.) 107.2

So we know the maximum amount of time is 8 hours. So now let's express this as an inequality:

32 + 9.4t ≤ 107.2 Now let's solve for t

9.4t ≤ 75.2

t ≤ 8

The parametric equations for the tangent line to the curve

x = 26+27, t = 10+6t, z = 27+27t

In the given question points are given and we have to find the parametric equations for the tangent line to the curve.

given r(t) = <t³-1 , t²+1 , t³>

taking differentiation

r'(t) = <3t² , 2t , 3t² >

parameters corresponding to point at the point (26, 10, 27)

t²+1 = 10

=> t² = 9

=> t = √9

=>t=3

r'(t) at t = 3 is

r'(t) = <27, 6, 27 >

So the parametric equations for the tangent line to the curve

x = 26+27

t = 10+6t

z = 27+27t

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The complete question is :

Find the parametric equations for the tangent line to the curve

x = t³ - 1,

y = t² + 1,

z = t³

at the point (26, 10, 27). Use the variable t for your parameter.

The solutions to the equation 3x²-18x=-15 by completing the square are x = 1 and x = 5.

In order to make an equation a perfect square, something must be added. This is known as "completing the square." This makes a number of equations simple to solve. In fact, by solving the square, all quadratic problems can be resolved.

To complete the square for the equation 3x²-18x=-15, we can follow these steps:

Move the constant term to the right side of the equation:

3x² - 18x + 15 = 0

Divide both sides by the coefficient of x^2 to make the coefficient 1:

x² - 6x + 5 = 0

To complete the square, we need to add and subtract the square of half of the coefficient of x:

x² - 6x + 9 - 4 = 0

(x - 3)² = 4

Take the square root of both sides to solve for x:

x - 3 = ±2

x = 3 ± 2

x = 1 or x = 5

Therefore, the solutions to the equation 3x²-18x=-15 by completing the square are x = 1 and x = 5.

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To determine whether these sequences of vertices are paths in this directed graph:

A) path is a series of edges that starts at a vertex and moves along a graph's edges from vertex to vertex.

B) "A circuit begins at the same vertex and terminates there.".

C) "The number of edges determines length.".

D) "A path or circuit is simple if there are no repeated instances of the same edge."

E) No path

F) No path

In most cases, "a simple path" means that you can only enter or exit a vertex once (in the case of cycles, you do both but only once, i. e. It's still ok because there is only one entrance and exit). The phrase "simple path" can mean: simple curve, a continuous injective function from a real number set interval or, more generally, to a topological or metric space.

In graph theory, a simple path is a path through a graph without repeating vertices.

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Note that the graph is: (check attached image)

Answer:

Part A: PR ≈ 16.06

Part B: QR≈ 9.60

Step-by-step explanation:

Part A)

The length of rod PR can be found using the Pythagorean theorem.

In this case, rod PQ is one leg, rod QR is the other leg, and rod PR is the hypotenuse. So, we have: PQ^2 + QR^2 = PR^2

Substituting the given lengths, we have:

14^2 + 8^2 = PR^2

Solving for PR, we get:

PR^2 = 14^2 + 8^2 = 196 + 64 = 260

Taking the square root of both sides, we have:

PR = √260

PR ≈ 16.06

Part B)

If the length of rod PR is adjusted to 17 feet, we can use the Pythagorean theorem to find the new height QR.

PQ^2 + QR^2 = 17^2

Substituting the given length of PQ, we have:

14^2 + QR^2 = 17^2

Expanding both sides, we have:

196 + QR^2 = 289

Subtracting 196 from both sides, we have:

QR^2 = 289 - 196 = 93

Taking the square root of both sides, we have:

QR = √93

QR ≈ 9.60

An equation that is equivalent to 3y - 5=45, but written only in terms of x include the following: B. 9x - 6 = 50.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

3y - 5 = 45      .......equation 1.

y = 3x - 2          .......equation 2.

By using the substitution method to substitute equation 2 into equation 1, we have the following:

3(3x - 2) - 5 = 45

9x - 6 - 5 = 45

9x - 6 = 45 + 5

9x - 6 = 50.

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The rate at which the water level is rising when the water level is 3 cm,

⇒ 0.65 cm / sec

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let us assume it is a regular pyramid. The (altitude) height "h" of apex from base square, slanting height and the side "a" of the base square rise uniformly and proportionally when we move from the apex point to the base.

Now, If height (altitude) h becomes x times, then side "a" of the base square becomes x times, the slanting height also becomes x times.  Thus, the area b of the base square rises x² times.

Δh / h = Δa / a  

Δb / b  = 2 Δa / a = 2 Δh / h    

Or,     h₁/h₂ = a₁/a₂

Since, We know that;

⇒ V = 1/3 b h = 1/3 a² h

⇒ d V / dt = 1/3 a² dh/dt  + 1/3 h a da/dt

                 = 1/3 a² dh /dt + 2/3 h a  (a/h) (dh/dt)

                 = 1/3 a² dh / dt + 2/3 a² dh/dt

Hence, We get;

dV/dt  = a² dh/dt        

dh/dt = (1/a²) dV/dt

We have;

h₀ = 5 cm and a₀ = 3 cm    

At the base;

When h = 5cm,  

Hence,  h / h₀ = a/a₀ ;

⇒ a = a₀ h / h₀ = 5×5/3 = 8.3 cm

And, dh/dt = 1/8.3² × 45 = 45/68.89 cm/sec = 0.65 cm / sec

Thus, The rate at which the water level is rising when the water level is 3 cm,

⇒ 0.65 cm / sec

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The number  ways can make change for 70 cents using only​ nickels, dimes, and​ quarters is,

7 dimes, 0 nickels

6 dimes, 2 nickels

5 dimes, 4 nickels

4 dimes, 6 nickels

3 dimes, 8 nickels

2 dimes, 10 nickels

1 dime, 12 nickels

0 dimes, 14 nickels

In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.

Formula for selection of a objects from the n objects,

N = ⁿCₐ

To find the number of ways to make change for 70 cents using only nickels, dimes, and quarters, we can use a combination of systematic listing and counting.

One approach is to consider the number of quarters used to make the change, which can be 0, 1, or 2, since using more than 2 quarters would exceed the total value of 70 cents.

Here are the possible combinations of coins to make change for 70 cents:

Using 0 quarters:

7 dimes, 0 nickels

6 dimes, 2 nickels

5 dimes, 4 nickels

4 dimes, 6 nickels

3 dimes, 8 nickels

2 dimes, 10 nickels

1 dime, 12 nickels

0 dimes, 14 nickels

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7 minutes will it be until there are 120 grams of the element remaining.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

We have,

An element with a mass of 820 grams decays by 24% per minute. To the nearest minute.

Now, 100 - 24 = 76% of the element remains after each minute.

So, 820 x (0.76[tex])^t[/tex] = 120 where t is number of minutes.

(0.76[tex])^t[/tex]  = 0.146

Taking log both side we get

t log 0.76 = log 0.146

t = 7.00724

t = 7 minutes

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