In an election 177 votes are cast. How many votes are needed to have a majority to have a majority of the votes in the election?

The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.

Counterexample:

Consider the following counterexample:

[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:

[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.

In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.

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Answer:

The slope-intercept equation is y = four-thirds x + 1

Step-by-step explanation:

slope:  [tex]\frac{4}{3}[/tex]

point: (3, 5)

y = mx + b

[tex]y=\frac{4}{3}x+b[/tex]

[tex]5=\frac{4}{3}(3)+b[/tex]

[tex]5=4+b[/tex]

[tex]b=5-4[/tex]

[tex]b=1[/tex]

Equation: [tex]y=\frac{4}{3}x+1[/tex]

[tex]-2=\frac{4}{3}(0)+1[/tex]

[tex]-2=0+1[/tex]

[tex]-2\neq 1[/tex]

Thus, the second statement is true!

The x- and y-intercept values in the graph for the function f and in the table for the function g(x), indicates that the correct option is option C

The x-intercept is the point at which the y-value is 0, and the coordinates of the point is specified as the x-intercept.

The x-intercept is the point at which the x-value is 0, and the coordinates of the point is specified as the y-intercept

The question compares the x- and y-intercepts of the graph and the function in the table

The x-intercept of the function f in the graph are; (0, 3)

The y-intercept of the function f in the graph are; (4, 0)

The function g(x) in the table indicates that the x- and y-intercepts are;

The value of g(x) is 0 at the ordered pair (1, 0), therefore, the x-intercept of g(x) is (1, 0)

The value of x is 0 at the ordered pair (0, 4), therefore, the function, g(x) has a y-intercept at the point (0, 4)

Therefore, the function f and g have different intercepts, but the value in the table and the graph indicates that as x approaches infinity, the y-value, approaches -1, the correct option is therefore, option C

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The mapping shown does not represents a function

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

The mapping

From the mapping, we have

(1, 7), (8, 3), (8, -1) and (3, 0)

The above ordered pair is not a function

This is so because the input value 8 have different output values 3 and -1

i.e. it would not pass the vertical line test when represented on a graph

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Cameron has 1 book left over after sorting it into group of 5

To determine the number of book left,

we need to first divide 56 by 5         [56 ÷ 5]

Quotient = 11

then find the remainder which is 1

therefore there os only 1 book left over

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In the context of a Cartesian coordinate system, the term "(-,-) quadrant" refers to the third quadrant, also known as Quadrant III.

The Cartesian coordinate system consists of four quadrants, numbered from I to IV in a counterclockwise direction. Each quadrant is defined by the signs of the x and y coordinates.

In Quadrant III, the x-coordinates are negative (represented by the "-") and the y-coordinates are also negative. This means that any point located in this quadrant will have both x and y values that are less than zero.

Visually, Quadrant III is situated below the x-axis and to the left of the y-axis. It is characterized by its lower left position in the coordinate plane.

Points in Quadrant III can be thought of as having a negative horizontal position (to the left of the origin) and a negative vertical position (below the origin).

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The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.

To find an antiderivative of f(x), we can integrate each term of f'(x) individually.

Given:

f'(x) = 2 + 15x² + 12x⁵

To integrate 2, we get:

∫2 dx = 2x + C₁, where C₁ is the constant of integration.

To integrate 15x², we get:

∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.

To integrate 12x⁵, we get:

∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.

Putting it all together, the antiderivative of f(x) is:

f(x) = 2x + 5x³ + 2x⁶ + C,

where C = C₁ + C₂ + C₃ represents the constant of integration.

To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:

0 = 2(1) + 5(1)³ + 2(1)⁶ + C,

0 = 2 + 5 + 2 + C,

0 = 9 + C.

Therefore, C = -9.

The final expression for f(x) is:

f(x) = 2x + 5x³ + 2x⁶ - 9.

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The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.

The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.

When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.

When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.

Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.

In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.

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Reason:

If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.

Let's calculate each side separately.

Both decimal values are approximate.

The two values don't match up which makes EA/EC = EB/ED to be false.

Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.

Answer:

CD is not parallel to AB

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, if CD is parallel to AB, then EA : AC = EB : BD.

Substitute the values of the line segments into the equation:

[tex]\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\\dfrac{28}{20}&=\dfrac{16}{10}\\\\1.4 &\neq 1.6\end{aligned}[/tex]

As 1.4 does not equal 1.6, then CD is not parallel to AB.

Answer:

Using the sine function, we have:

sin(angle) = opposite / hypotenuse

sin(22 degrees) = opposite / 18 feet

We can rearrange this equation to solve for the opposite side (height of the building):

opposite = sin(22 degrees) * 18 feet

Calculating this:

opposite ≈ 6.24 feet

Therefore, the base of the ladder from the base of the building is approximately 6.24 feet.

Answer:

36)

[tex]f(x) = \frac{1}{x + 3} - 1[/tex]

The equation of the function is y = 1/(x + 3) - 1

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

The reciprocal function shifted down one unit and left three units

The equation of the reciprocal function is represented as

y = 1/x

When shifted down one unit, we have

y = (1/x) - 1

When shifted left three units, we have

y = 1/(x + 3) - 1

Hence, the equation of the function is y = 1/(x + 3) - 1

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Answer:

surface area=214cm2, volume=183 cm3

Step-by-step explanation:

slanted height=√5^2+7^2 (Pythagoras theorem)

= √74

area of bottom part=π(5)^2

=25π

area of top cone part=π(5)(√74)

surface area of cone=25π+π(5)(√74)

=214 cm2(to 3 s.f.)

volume of cone=1/3π(5)^2×7

=183 cm3(to 3 s.f.)

Answer:

(a) The graph is an exponential growth curve.

(b) f(0) = 2,  f(1) = 10

(c) The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.

Step-by-step explanation:

Given function:

[tex]k(x)=2(5)^x[/tex]

[tex]\hrulefill[/tex]

The graph is an exponential growth curve.

The curve begins in quadrant II, crosses the y-axis at (0, 2) into quadrant I, and increases rapidly as x increases.

In general, an exponential growth function is in the form:

[tex]\boxed{y = ab^x}[/tex]

where:

In this case, the y-intercept is 2 and the base is 5.

As the value of a is positive, and the value of b is greater than 1, it indicates exponential growth.

[tex]\hrulefill[/tex]

The term "second coordinates" refers to the y-values of the points on a graph.

To find the second coordinates of the points with first coordinates 0 and 1, substitute x = 0 and x = 1 into the function and solve.

[tex]\begin{aligned}k(0)&=2(5)^{0}\\&=2(1)\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}k(1)&=2(5)^{1}\\&=2(5)\\&=10\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.

As 2(5)ˣ > 0, the graph is entirely above the x-axis.

The end behaviour of the function is:

Therefore, the graph increases from left to right.

In y = 2(5)ˣ, the base is 5, but it is multiplied by 2. This means that for every unit increase in x, the corresponding y-value is doubled compared to the graph of y = 5ˣ. Therefore, the multiplication by 2 makes the graph of y = 2(5)ˣ steeper than the graph of y = 5ˣ.

The graph is completely on the x-axis; It then increases from left to right. it is less steep that y = 5ˣ

The values are (0, 2) and (1, 10)

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

f(x) = 2(5ˣ)

The above function is an exponential growth curve

This means that

Here, we have

f(x) = 2(5ˣ)

This gives

f(0) = 2(5⁰)

f(0) = 2

f(1) = 2(5¹)

f(1) = 10

So, the values are (0, 2) and (1, 10)

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The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

       x           12

2      2x         24

Note: 2x/2 = x.

        24/2 = 12.

Next, we would write the expression 2x + 24 as a product as follows;

(2x + 24) = 2(x + 12).

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Answer:

379.2 in^2

Step-by-step explanation:

Each cylinder's side area is  pi *d * h = 43.98 in^2

  you need six    :     =263.89 in^2

each ned of the cylinder area = pi r^2 = 9.621 in^2

    and you have 12 ends  for 115.45 in^2

For total : 379.3  in^2       (slight difference due to the value of pi used and rounding)

Answer:

all go d Alaska causticC field lap cc feels it works happy claps dockside all letter or quip all L do all app all app all app all do all app all app all app all app 10 10 all do all app all app so we rip so do all

Step-by-step explanation:

w usually app all app all do all app so all rip so we rip do all do all app all do all do all do all do all rip trip we rip all app so all do all do all app all do all app all yep all app all app all app all app all app all app all app to

The fraction that converts to a terminating decimal number is C. 3/8.

To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.

Let's examine each option:

A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.

D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.

Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.

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The function that satisfies the given condition is y = 3x + 2.

The correct answer to the given question is option B.

We are to find the function that satisfies the condition: When x increases from a to a + 2, y increases by a difference of 6.

A statement such as this represents a linear function, where y increases at a constant rate with respect to the increase in x.Let y = mx + b, be a linear function.

We know that when x increases from a to a + 2, y increases by a difference of 6. In other words, we can express this relationship using the following equation:

2m + b − m − b = 6 ⇒ m = 3

The function has been found to be y = 3x + b.

To find the value of b, we need to use the fact that when x increases from a to a + 2, y increases by a difference of 6: y(a + 2) − y(a) = 6 ⇒ 3(a + 2) + b − 3a − b = 6 ⇒ 6 = 6

Therefore, the function that satisfies the given condition is y = 3x + 2. The correct option is B) y = 3x + 2.

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The values in the boxes that correctly complete the division model and quotient are presented as follows;

[tex]{}[/tex]                 10                   2                4    

6        [tex]{}[/tex]      60                 16                  

            76  ÷ 6 = 12 R 4  

A division area model comprises of the number being divided, representing the area of a rectangle, and a factor or the divisor, being a side length of the rectangle.

The number 76 divided by 6 using the division model can be evaluated by setting the area of the rectangle as 76 and the length of side of the rectangle as 6, asw follows;

The division model

The model for the division of 76 ÷ 6 can be presented as follows;

        [tex]{}[/tex]        10                2                 4  

6    [tex]{}[/tex]            60              16

Therefore; 76 ÷ 6 = 10 + 2 = 12 Remainder 4

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The statement is:

O True

Work/explanation:

The following statement is true, because 1x is indeed the same thing as x. So when combining like terms, 2x + x is the same thing as 2x + 1x, which evaluates to 3x.

Solution

verified

Verified by Toppr

The circumference of circle is 2πr=176

2×

7

22

×r=176

r=176×

22

7

2

1

r=7×4=28cm

Area of circle is πr

2

=

7

22

×28×28=88×28=2464cm

2

The most likely reason that Sora lists the activities of customers going through self-checkout is to prove the claim that self-checkout is eliminating jobs.

By observing and documenting the activities of customers using self-checkout, Sora may be gathering evidence to support the argument that self-checkout systems are replacing the need for human cashiers and leading to job loss in the retail industry.

By highlighting the tasks that customers can now perform independently, Sora may be emphasizing the efficiency and convenience of self-checkout systems, which can potentially lead to the reduction of cashier positions.

It's important to note that without more context, we cannot definitively determine Sora's exact intentions or motivations. However, based on the given options and the mention of activities related to self-checkout, the claim that self-checkout is eliminating jobs appears to be the most plausible reason for listing the activities of customers going through self-checkout.

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Answer: 6+9x or 9x + 6

Step-by-step explanation:

Multiply 3 by each of the numbers inside the parentheses

The answer is:

Work/explanation:

To simplify this expression, we will use the distributive property:

[tex]\sf{3(2+3x)}[/tex]

Distribute the 3:

[tex]\sf{3\cdot2+3\cdot3x}[/tex]

Simplify

[tex]\sf{6+9x}[/tex]

The best estimate for the amount of juice Barry made is 235 cups.

In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.

Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.

Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.

So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.

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Answer:

0

Step-by-step explanation:

theres only 2 people each district

The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)

Let's break down the given values and find the values of sine and tangent.

We are given:

cos θ = √(8/9)

csc θ < 0

Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.

sin^2θ + (√(8/9))^2 = 1

sin^2θ + 8/9 = 1

sin^2θ = 1 - 8/9

sin^2θ = 1/9

Taking the square root of both sides, we get:

sin θ = ±1/3

Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.

Next, let's find the value of tan θ.

tan θ = sin θ / cos θ

tan θ = (-1/3) / (√(8/9))

tan θ = -√9/√8

tan θ = -√9/√(4*2)

tan θ = -√9/(2√2)

tan θ = -3/(2√2)

So, the values are:

sin θ = -1/3

tan θ = -3/(2√2)

The best selection from the available options that matches the calculated values is:

C. sin θ = -1/3, tan θ = -3/(2√2)

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Answer:

15 coins, d + q coins

Step-by-step explanation:

If asking for the amount (in $)

5(.10) + 10(.25) = 2.5+.5 = $3

He would have 0.1d + 0.25q for d dimes and q quarters.

Answer:

1/12 is the correct answer

The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).

In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.

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Answer:

x-intercepts = (-3, 0) and (-1, 0)

y-intercept = (0, 3)

Vertex = (-2, -1)

Axis of symmetry:  x = -2

Step-by-step explanation:

Given quadratic function:

[tex]g(x) = x^2 + 4x + 3[/tex]

[tex]\hrulefill[/tex]

To find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.

Set g(x) = 0:

[tex]x^2 + 4x + 3 = 0[/tex]

Factor the quadratic equation:

[tex]x^2+x+3x+3=0[/tex]

[tex]x(x+1)+3(x+1)=0[/tex]

[tex](x + 3)(x + 1) = 0[/tex]

Set each factor equal to zero and solve for x:

[tex]x + 3 = 0 \implies x = -3[/tex]

[tex]x + 1 = 0 \implies x = -1[/tex]

Therefore, the x-intercepts are at (-3, 0) and (-1, 0).

[tex]\hrulefill[/tex]

To find the y-intercept of g(x), substitute x = 0 and solve for y.

[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]

Therefore, the y-intercept is at (0, 3).

[tex]\hrulefill[/tex]

The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.

For the function g(x), a = 1, and b = 4.

Therefore, the x-coordinate of the vertex is:

[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]

To find the y-coordinate of the vertex, substitute x = -2 into function g(x):

[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]

Therefore, the vertex is at (-2, -1).

[tex]\hrulefill[/tex]

The axis of symmetry of a vertical parabola is the x-coordinate of its vertex.

As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.

[tex]\hrulefill[/tex]

Based on the pattern we identified, the next term in the sequence would be 55.

The sequence should be 7, 10, 19, 34, 55

To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.

If we calculate the differences between consecutive terms, we get:

10 - 7 = 3

19 - 10 = 9

34 - 19 = 15

By examining the differences, we notice that they are increasing by 6 each time.

This suggests that the sequence might be formed by adding an increasing number to each term.

Let's calculate the next difference:

15 + 6 = 21

Now, let's add this difference to the last term of the sequence:

34 + 21 = 55

Therefore, based on the pattern we identified, the next term in the sequence would be 55.

To summarize:

7, 10, 19, 34, 55

It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.

Additional terms or a different pattern may emerge if more information is provided.

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