-3<2x+3< or equal to 5

The linear transformation T: R5 → R² defined by 7(x) = Ax, where A = [ 2₁ 23 d 4 ] can be analyzed as follows:

Firstly, to find ker(7), we need to find the null space of the matrix A. We can do this by row reducing A to its reduced row echelon form and solving for the variables that correspond to the free columns. The resulting system of equations will give us the basis for ker(7).

Secondly, to find range(T), we need to find the column space of the matrix A. This can be done by finding the pivot columns of A and taking linear combinations of them. The resulting vectors will give us the basis for range(T).

Thirdly, to find dim(ker(7)), we count the number of basis vectors obtained in step one.

Finally, to find dim(range(7)), we count the number of basis vectors obtained in step two.

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Answer:

b = 18

The mortar is 17 times ( 3 / 8 ) tall.

The brick height is equal to 18 times ( 2 + ( 1 / 4 ) ).

I don't know the options, so you have to use those values.

Step-by-step explanation:

The question uses imperial units which are generally bad.

12 inches = 1 feet;

The height of the wall should be written in inches for convenience.

4 feet = 4 * 12 inches;

4 feet = 48 inches;

The wall is short 1 + ( 1 / 8 ) inches short of 4 feet.

48 inches - ( 1 + ( 1 / 8 ) inches ) = 46 + ( 7 / 8 ) inches;

Now that the wall is done let's do the bricks. The height of the bricks is 2 + ( 1 / 4 ) inches and the mortar is ( 3 / 8 ) inches tall. The amount of mortar is the number of bricks - 1 because nobody puts extra mortar on the top of the wall.

let b;

46 + ( 7 / 8 ) = b( 2 + ( 1 / 4 ) ) + ( b - 1 )( 3 / 8 );

375 / 8 = b( 9 / 4 ) + ( 3 / 8 )b - ( 3 / 8 );

375 / 8 = ( ( 9 / 4 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( ( 18 / 8 ) + ( 3 / 8 ) )b - ( 3 / 8 );

375 / 8 = ( 21 / 8 )b - ( 3 / 8 );

Multiply both sides by 8 to get rid of those annoying fractions.

375 = 21b - 3;

Add 3 to both sides.

378 = 21b;

Divide both sides by 21.

18 = b;

Answer:

The total distance hiked altogether is;

Explanation:

Given that They hiked 4 3/8 miles to Green River and then walked another 1 9/16 miles down the riverbank.

The total distance they hike altogether is the sum of the two distance hiked;

Therefore, the total distance hiked altogether is;

The equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

To find the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0), we need to find the slope of the tangent line at that point.

The derivative of y = ln(x^2 - 5x + 1) is:

y' = (2x - 5)/(x^2 - 5x + 1)

At the point (5,0), we have:

y' = (2(5) - 5)/(5^2 - 5(5) + 1) = 0

So the slope of the tangent line at (5,0) is 0.

The equation of the tangent line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope.

Since the slope is 0, we have:

y - 0 = 0(x - 5)

which simplifies to:

y = 0

Therefore, the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

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The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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The height of a triangle is 4.8cm. The length of a perpendicular line segment starting on a side and intersecting the opposing angle defines a triangle's height. Every triangle has three sides, which results in three heights, or altitudes.

The line segment perpendicular to the base of the triangle from its point of highest point is its height. We may apply the Pythagorean Theorem to the triangle the height forms because it forms a right angle with the base. The base of the original triangle will be divided in half by the height since it is isosceles (has two equal sides). Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height. Since this is the smallest side of the triangle, the base would be equal to half of five (2.5). A triangle is said to be equilateral if its three heights are all equal.

If area and base are given: height = 2A/ b = (2 × Area) / base.

Area=8*6/2=48/2=24cm

Height=2*24/10=4.8cm

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According to the question the length of the real airplane is 63 feet and the wingspan of the airplane in the scale drawing is 10 inches.

If 1 inch in the scale drawing represents 9 feet in the real airplane, then 7 inches in the scale drawing represents:

7 inches x 9 feet/inch = 63 feet

So, the length of the real airplane is 63 feet.

(b) If 1 inch in the scale drawing represents 9 feet in the real airplane, then X inches in the scale drawing represents 90 feet in the real airplane. We can construct a ratio to find the value of X:

1 inch / 9 feet = X inches / 90 feet

Cross-multiplying, we get:

9 feet * X inches = 1 inch * 90 feet

Simplifying, we get:

X inches = 10 inches

As a result, the scale drawing's scale model's airplane has a 10 inch wingspan.

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The correct answer is (A) stretched vertically, shifted left 2 units, and shifted down 4 units. The transformation f(x)-3(x+2)²-4 on the function f(x)-x² involves three changes to the original function.

The transformation from $f(x) = x^2$ to $f(x) = -3(x+2)^2 - 4$ involves the following changes:

Therefore, the correct answer is (A) stretched vertically, shifted left 2 units, and shifted down 4 units.

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The evaluation of the six trigonometric functions in x = -(7/6)pi can be seen below.

We want to evaluate sin(x), cos(x), tan(x), arcos(x), sec(x), arctan(x) in x = -(7/6)pi.

Now we just evaluate the trigonometric functions:

\(cos(-\frac{7pi}{6}) = -0.866\)

\(sin(-\frac{7pi}{6}) = 0.5\\\\tan(-\frac{7pi}{6})) = -0.577\\\\cosec(-\frac{7pi}{6})) = 1/sin(-\frac{7pi}{6}) = 1/0.5 = 2\\\\sec(-\frac{7pi}{6}) = 1/cos(-\frac{7pi}{6}) = -1.155\\\\arctan(-\frac{7pi}{6}) = 1/tan(-\frac{7pi}{6})) = -1.732\)

Where for the last 3 we just use the inverse of the first 3 ones.

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Answer:

The answer is C.)

Step-by-step explanation:

sine (Negative StartFraction 7 pi  Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi  Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi  Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi  Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi  Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi  Over 6 EndFraction) = Negative StartRoot 3 EndRoot

Approximately 15π tiles will be needed to make the rim of tiles on the edge of the pool.

To calculate the area and circumference of the pool, we can use the formulas for a circle.

Area of the pool:

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Given that the radius of the pool is 5 feet, we can substitute this value into the formula:

A = π(5²) = π(25) = 25π square feet.

Circumference of the pool:

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Substituting the radius value of 5 feet into the formula, we get:

C = 2π(5) = 10π feet.

Now let's calculate the number of tiles needed for the rim of the pool.

The rim of tiles is 8 inches wide, which is equivalent to 8/12 = 2/3 feet.

To find the number of tiles needed, we need to calculate the perimeter of the circular pool and divide it by the width of a single tile.

Perimeter of the pool = Circumference = 10π feet.

Number of tiles needed = Perimeter of the pool / Width of a single tile = (10π feet) / (2/3 feet) = (10π) × (3/2) = 15π tiles.

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Answer:

probability for 3 on a dice (P3) in one dice =

\( \frac{1}{6} \)

probability for even no. of a dice (Pe) =

\( \frac{3}{6} = \frac{1}{2} \)

Therefore, the probability of finding 3 on one dice and even on another (P) = P3 + Pe

\( = \frac{1}{6} + \frac{1}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3} \)

Answer:

r+3

Step-by-step explanation:

r is an expression. To get an expression that is 3 more, just add 3

r+3

Answer:

The field is 1 and 4/10 mile long.

Step-by-step explanation:

If I understand the question:

(1/2) + (9/10) =

(5/10) + (9/10) = (14/10)

(14/10) is 1 and 4/10

The field is 1 and 4/10 mile long.

Recall that the perimeter of a figure is the sum of the lengths of its sides.

From the given diagram, we get that the figure has

and each side measures 5.75 m.

Therefore, the perimeter of the figure is:

Finally, we get that the perimeter is:

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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Answer:

  67 square units

Step-by-step explanation:

The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.

The attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.

The approximate area is 67 square units.

Split up the interval [0, 6] into 6 equally spaced subintervals of length \(\Delta x = \frac{6-0}6 = 1\). So we have the partition

[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]

where the left endpoint of the \(i\)-th interval is

\(\ell_i = i - 1\)

with \(i\in\{1,2,3,4,5,6\}\).

The area under \(f(x)=x^2+2\) on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,

\(\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}\)

where we use the well-known sums,

\(\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n\)

\(\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2\)

\(\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6\)

Answer:

the answer would be 5 + 2n = 43

Step-by-step explanation:

The answer is that Point D is Circumcentre and other lengths DE,DF,DG are perpendicular bisectors of sides of triangle ABC

What is Circumcentre?

The point of intersection of Perpendicular bisectors in a triangle is called called Circumcentre.

Solution;

The circumcentre is equidistant from all sides of an triangle when we draw the perpendicular from this point to sides of triangles, the length of all perpendiculars will be same and this is its another property

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Answer:

x = 14

Step-by-step explanation:

2(x + 3) + 5 = 39

2x + 6 + 5 = 39

2x + 11 = 39

2x = 28

x = 14

\(2(x + 3) + 5 = 39 \\ \\ 2x + 6 + 5 = 39 \\ \\ 2x + 11 = 39 \\ \\ 2x = 39 - 11 \\ \\ 2x = 28 \\ \\ x = 14 \\ \\ x = 7\)

The total surface area of the pyramid is  335 square centimeters

The formula for determining the total surface area of a pyramid is expressed as;

TSI = 1/2(PI) + B

Given that;

Now, let's determine the base perimeter

Perimeter = 2( l + w)

Substitute the values

Perimeter = 2 ( 8 + 12)

Perimeter = 40 centimeters

The base area is given as;

Base area =  8(12)

Base area = 96 square centimeters

Substitute the values, we have;

Total surface area = 1/ 2 (40)(12) + 96

Total surface area = 240 + 96

Total surface area = 335 square centimeters

Hence, the value is 335 square centimeters

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Answer:

1

Step-by-step explanation:

The mathematical question that explains the process, mathematical evidence and explanation of the reasoning is discussed below.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that a good written response to a mathematical question should include your process, mathematical evidence, and explanation of your reasoning.

None of them answered the mathematical question as none of them explains the-

We can correctly answer the mathematical question as -

Given are the straight lines as shown in the graph. The plotted lines are -

2x + 3y = 24

x + y = 10

The point of intersection of both the lines represent the solution set of the given set of equations. So, (5, 5) represent the solution set of the given set of equations.

The slope of line → x + y = 10 is {m} = -1.

The slope of line → 2x + 3y = 24 is {m} = -2/3.

Therefore, the mathematical question that explains the process, mathematical evidence and explanation of the reasoning is discussed above.

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Answer:

21.6 km/hr

Step-by-step explanation:

multply the speed value by 3.6

Answer:

6m/s x 18/5

108/15 kmph

answer : 108/15 kmph

The ratio of nonfiction to fiction books is 49 : 2.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The number of fiction books is 2/7 times the number of nonfiction books.

So, If we have 7 nonfiction books then we have 2/7 fiction books.

Therefore, The ratio Nonfiction : Fiction = 7 : 2/7.

Nonfiction : Fiction = 49 : 2.

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Answer:

It would be B. Fuction 1 has the larger maximum at (4,1)  because the maximum point for Fuction 1 is at (4,1) becuase that the highest point/vertex it goes.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

One of the reasons why the aggregate demand curve is downward-sloping is the substitution effect is a "false" statement.

Aggregate demand would be a macroeconomic term which describes the total consumption of goods and services in a given period at any price level.

Some key features regarding the aggregate demand curve are-

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The solutions to the equations are

1. x = 4

2. x = -12

3. x = 0 and x = 4

The solutions to the inequalities are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

From the question, we have the following equations

1. 4x + 6 = 8x - 10

2. -3/4x - 2 = -1/2x + 1

3. |4 - 2x| + 5 = 9

Next, we split the equations to 2

So, we have

1. y = 4x + 6 and y = 8x - 10

2. y = -3/4x - 2 and y = -1/2x + 1

3. y = |4 - 2x| + 5 and y = 9

Next, we plot the system of equations (see attachment) and write out the solutions

The solutions are

1. x = 4

2. x = -12

3. x = 0 and x = 4

From the question, we have the following inequalities

4. x² + 4x - 5 < 0

5. x² - x - 12 ≥ 0

Next, we plot the system of inequalities (see attachment) and write out the solutions

The solutions are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

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The formula for the n-th term is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:

aₙ = a₁*(r)⁽ⁿ⁻¹⁾

Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.

Then the formula for the n-th term of the sequence is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

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The expressions that represent the number of hats Tracy has now will be 5j + 10x. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Tracy had 5j hats.

Barbara and Claudia each give Tracy an additional 5x hats each.

The number of hats given by Barbara will be 5x.

And the number of hats given by Claudia will be 5x.

Then the expressions that represent the number of hats Tracy has now will be

⇒ 5j + 5x + 5x

⇒ 5j + 10x

Thus, the expressions that represent the number of hats Tracy has now will be 5j + 10x.

Then the correct option is A.

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