An elevator at a department store must carry fewer than 17 people at a time. An elevator operator is present in the elevator at all times. If x customers can travel in the elevator with the elevator operator, which inequality represents this situation? A. x + 1 < 17 B. x > 18 C. x + 1< 16 D. x < 17 E. x + 1 > 18

Answer:

C. 60,000

Step-by-step explanation:

Given

Three times as many bought tickets

24,000 * 3 = 72,000

one-sixth of them cancelled their tickets

72,000 * 1/6 = 12,000

Subtract

72,000 - 12,000 = 60,000

Answer

60,000 people are attending this week

This week, 60,000 fans are attending the football match.

To find the number of fans attending the football match this week, we need to start with the number of fans who bought tickets. This week, three times as many fans bought tickets as last week, so there were 3 * 24,000 = 72,000 fans who bought tickets. However, one-sixth of them cancelled their tickets, which means 1/6 * 72,000 = 12,000 fans cancelled. Therefore, the number of fans attending the match this week is 72,000 - 12,000 = 60,000.

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Answer:

D. 74°

Step-by-step explanation:

∠XYZ is an inscribed angle, where its vertex is located on the circle and two intersecting chords form the vertex.

An inscribed angle is equal to HALF of the intercepted arc, which is the arc that is between the two points where the chords hit.

In this picture, the intercepted arc is the red part of the outside of the circle.

Since you are given the measurement of the intercepted arc, you can find the measure of the inscribed angle by finding half of 148°.

Therefore, the inscribed angle is 148° divided by 2, giving us 74°.

The measure of the inscribed angle, ∠XYZ, is D. 74°.

Answer:

She need a interest rate of 6.25%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=16\ years\\ P=\£8,000\\ A=\£8,000*2=\£16,000\\r=?[/tex]

substitute in the formula above  and solve for r

[tex]16,000=8,000(1+16r)[/tex]

[tex]16r=2-1[/tex]

[tex]r=1/16[/tex]

[tex]r=0.0625[/tex]

Convert to percentage

[tex]r=0.0625*100=6.25\%[/tex]

Answer:

[tex]\large\boxed{A\ \cup\ B=[-5,\ 10]}[/tex]

Step-by-step explanation:

Look at the picture.

The union of two sets A and B (A ∪ B) is the set of elements which are in A, in B, or in both A and B

Answer:

y=2.4

Step-by-step explanation:

9y-2+y=5y+10

(combine like terms)

10y-2=5y+10

(subtract 5y from both sides)

5y-2=10

(add 2 to both sides)

5y=12

(divide both sides by 5)

y=2.4

Answer:

Trapezoid- A.

Answer:

A. Trapezoid

Step-by-step explanation:

The proper name of this quadrilateral is a trapezoid.

The picture might look confusing because the trapezoid is upside down.

However, it still counts as a trapezoid.

Answer:

-2

Step-by-step explanation:

6^2 = 36

5 x 6 = 30

36 - 30 - 8 = -2

Answer:

[tex]-\frac{25}{3}[/tex]

Step-by-step explanation:

To isolate for x, start by multiplying both sides by 2.5.

[tex]\frac{25}{3} =-x[/tex]

Next, divide both sides by -1.

[tex]\frac{-25}{3} =x[/tex]

Answer:

x = -25/3

Step-by-step explanation:

10/3 = x / (-5/2)

Multiply each side by (-5/2) to isolate x

-(5/2) * 10/3 = -5/2 * (x / (-5/2))

-50/6 = x

Divide the top and bottom by 2 on the left hand side

-25/3 =x

Changing to a mixed number ( if required)

3 goes into 25  8 times ( 3*8=24)   with 1 left over(25-24=1)

x = -8 1/3

Answer:

Mean Absolute Deviation = 3.

Step-by-step explanation:

The mean = (2 + 9 + 1 + 7 + 8 + 9) / 6

= 36/6

= 6.

Subtract  6 from each  number:

2 - 6 = -4 Absolute value = 4

9 - 6 = 3

1 - 6 = -5 Absolute value = 5

7 - 6 = 1

8 - 6 = 2

9 - 6 = 3

Total = 4 + 3 + 5 + 1 + 2 + 3 = 18

Mean Absolute Deviation = 18 / 6 = 3.

Answer:

B: 3

Step-by-step explanation:

First you will take the numbers and add them. The equation would be 2 + 9 + 1 + 7 + 8 + 9. That equals 36.

Then, you may divide that by 6 (how many numbers there were) and that is your mean (also 6).

Next, you find the how far each number is from the mean using absolutes. Those values are 4, 3, 5, 1, 2, and 3.

Finally, add those together to get 18, then divide by how many numbers there were (6) that to get the mean absolute deviation (3).

Hope this helped! :)

Answer:

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Step-by-step explanation:

The given complex number equation is:

[tex]\frac{1-2i}{2+i}+\frac{4-i}{3+2i}=x+yi[/tex]

We simplify the LHS and compare with the RHS

We collect LCD on the left to get:

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

[tex]\frac{3+2i-6i+4+8+4i-2i+1}{6+4i+3i-2}=x+yi[/tex]

Simplify to get:

[tex]\frac{16-2i}{4+7i}=x+yi[/tex]

Rationalize the LHS:

[tex]\frac{(16-2i)(4-7i)}{(4+7i)(4-7i)}=x+yi[/tex]

Expand the numerator using the distributive property and the denominator using difference  of two squares.

[tex]\frac{64-112i-8i-14}{16+49}=x+yi[/tex]

Simplify to get:

[tex]\frac{50-120i}{65}=x+yi[/tex]

[tex]\frac{10-24i}{13}=x+yi[/tex]

[tex]\frac{10}{13}-\frac{24}{13}i=x+yi[/tex]

By comparing real parts and imaginary parts; we have;

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Answer: The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}, where:

x_2 is the second point in the function

x_1 is the first point in the function

f(x_2) is the function evaluated at the second point

f(x_1) is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so x_1=1 and x_2=10. Replacing values:

Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}

Av=\frac{-100+200+50-[-1+20+50]}{9}

Av=\frac{150-[69]}{9}

Av=\frac{150-69}{9}

Av=\frac{81}{9}

Av=9

Since f(x) represents the number of pounds per acre and x the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is where all the points are in the form (positive, negative).

The center and radius of [tex](x-h)^2+(y-k)^2=r^2[/tex] is (h,k) and r, respectively.

Let's look at the centers and the radius of each of these choices:

A) This one has center (4,-2) and radius [tex]\sqrt{32} \approx 5.7[/tex].

If you add 5.7 to -2 you get a positive number and we needed it negative.

Not this choice; moving on.

B) This one has center (-3,2) and radius [tex]\sqrt{25}=5[/tex].

The center is not even in quadrant 4; moving on.

C) This one has a center (3,-4) and radius 1.

Add 1 to 3 you get 4.

Subtract 1 from 3 you get 2.

Those x's are positive so that looks good so far.

Add 1 to -4 you get -3.

Subtract 1 from -4 you get -5.

Those y's are negative so that looks good.

This circle is in quadrant 4 and doesn't go outside it.

D) This one has center (5,-7) and radius 4.

Add 4 to 5 you get 9.

Subtract 4 from 5 you get 1.

Positive x's is good.

Add 4 to -7 you get -3.

Subtract 4 from -7 you get -11.

Those are negative so that looks good.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

Quadrant IV: The fourth quadrant is in the bottom right corner of the plane. In this coordinate X has positive values and y has negative values.

According to the question

We have to find the circles lie completely within the fourth quadrant.

Observing the below graph, These two circle lie  completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex]

[tex](x-5)^{2} +(y+7)^{2} =16[/tex]

These circles lie bottom right corner of the plane.

From the given graphs below Option C and D lie completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

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Answer:

A strong positive correlation

Step-by-step explanation:

A strong correlation when the correlation coefficient is close to 1 or -1. If the correlation coefficient is close to positive 1, then it is a positive strong correlation coefficient. If the correlation coefficient is close to negative 1, then it is a negative strong correlation coefficient.

Answer:

The r-value indicate A strong positive correlation

Step-by -step-explanation:

The following information should be considered:

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so shes 72 i think

hope i'm right

Answer: 58 would be my guess, but need more info

For this case we must multiply the following expression:

[tex](2x-6) (3x ^ 2-4x-5)[/tex]

Applying distributive property we have:

[tex](2x) (3x ^ 2) - (2x) (4x) - (2x) (5) - (6) (3x ^ 2) + (6) (4x) + (6) (5) =[/tex]

By definition of multiplication of powers of the same base, we have to put the same base and add the exponents:

[tex]6x ^ 3-8x ^ 2-10x-18x ^ 2 + 24x + 30 =[/tex]

Adding similar terms:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

9*4

Step-by-step explanation:

We can Factor out a 9 from each term

9 + 27

9 (1+3)

9 (4)

9*4

Answer:

* cos 211.7 not equal the other values

Step-by-step explanation:

* Lets revise the angles in the four quadrant

- If the angle in the first quadrant is Ф, then the equivalent angles to

 it in the other three quadrant are

# 180° - Ф ⇒ 2nd quadrant (sin only +ve)

# 180° + Ф ⇒ 3rd quadrant (tan only +ve)

# 360° - Ф ⇒ 4th quadrant (cos only +ve)

# -Ф ⇒ 4th quadrant (cos only +ve)

# -180 + Ф ⇒ 3rd quadrant (tan only +ve)

# -180 - Ф ⇒ 2nd quadrant (sin only +ve)

# -360 + Ф ⇒ 1st quadrant (all are +ve)

* Lets solve the problem

∵ Ф = 31.7°

∵ cos 31.7 = +ve value

∵ 180° + Ф° = 180° + 31.7° = 211.7°

∵ cos (180° + Ф°) = - cos Ф° ⇒ cos (180° + Ф°) in the 3rd quadrant is

  same value as cos Ф but with -ve sign

∴ cos 211.7° = - cos 31.7°

∴ cos 31.7° ≠ cos 211.7°

∵ 360° - Ф° = 360° - 31.7° = 328.3°

∵ cos (360° - Ф°) = cos Ф° ⇒ cos (360° - Ф°) in the 4th quadrant has the

  same value and sign with cos Ф°

∴ cos 328.3° = cos 31.7°

∴ cos 31.7° = cos 328.3°

∵ -391.7° + 360° = -31.7° ⇒ more then clockwise turn by 31.7°

∵ cos (-Ф°) = cos Ф° ⇒ cos (-Ф°) in the 4th quadrant has the same value

  and sign with cos Ф°

∴ cos (-31.7°) = cos 31.7°

∴ cos 31.7° = cos (-390.7°)

* cos 211.7 not equal the other values

ANSWER

The diagonal of the square is 6 units.

EXPLANATION

A diagonal of a square divides the square into two congruent right isosceles triangles.

Let the sides of the square be 's' units. Then, the Pythagoras Theorem says that, the sum of the squares of the shorter legs will be equal to the square of the hypotenuse.

Let the diagonal which is the hypotenuse be 'd' units.

Then,

[tex] {d}^{2} = {s}^{2} + {s}^{2} [/tex]

[tex] \implies \: {d}^{2} = 2{s}^{2}[/tex]

From the question, the side length of the square is

[tex]s = 3 \sqrt{2} \: units[/tex]

We plug in this value to obtain:

[tex]\implies \: {d}^{2} = 2{(3 \sqrt{2} )}^{2}[/tex]

Or

[tex]\implies \: {d}^{2} = 2 \times { {3}^{2} (\sqrt{2} )}^{2}[/tex]

[tex]\implies \: {d}^{2} = 9 \times 2 \times 2 = 36[/tex]

We take the positive square root of both sides to get:

[tex]d = \sqrt{36} [/tex]

[tex]d = 6 \: units[/tex]

Answer:

Part 1) [tex](x+4)(x-1)(x-2)(x-4)[/tex]

The related polynomial equation has a total of four roots, all four roots are real

Part 2) [tex](x+1)(x-1)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) [tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) [tex](x+i)(x-i)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Step-by-step explanation:

we know that

The Fundamental Theorem of Algebra  states that:  Any polynomial of degree n has n roots

so

Part 1) we have

[tex](x+4)(x-1)(x-2)(x-4)[/tex]

The roots of this polynomial are

x=-4, x=1,x=2,x=4

therefore

The related polynomial equation has a total of four roots, all four roots are real

Part 2) we have

[tex](x+1)(x-1)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-1, x=1,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) we have

[tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The roots of this polynomial are

x=-3, x=4,x=(2-i),x=-(2-i)

therefore    

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) we have

[tex](x+i)(x-i)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-i, x=i,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (4, 2)

m = [tex]\frac{2-1}{4-2}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\huge\boxed{\frac{1}{2}}[/tex]

We can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope, where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.

Plug in the values. [tex]\frac{2-1}{4-2}[/tex]

Subtract. [tex]\frac{1}{2}[/tex]

(9x^2 + 8x) – (2x^2 + 3x)

Subtract like terms:

9x^2 - 2x^2 = 7x^2

8x - 3x = 5x

The difference is 7x^2 + 5x

Answer:

The multiplicative inverse is -5/3

Step-by-step explanation:

Multiplicative inverse means we want to end up with 1

-3/5 * what =1

Multiply by 5 to clear the fraction

-3/5 * what *5 = 1*5

-3 * what = 5

Divide by -3 to isolate what

-3*what /-3 = 5/-3

what = -5/3

The multiplicative inverse is -5/3

Answer:

A) x² + 7x - 9

Step-by-step explanation:

Deduct\Add each like-term to arrive at your answer.

Answer:

[tex]\large\boxed{x=3\dfrac{3}{4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3}{4x}=\dfrac{1}{5}\qquad\text{cross multiply}\\\\(4x)(1)=(3)(5)\\\\4x=15\qquad\text{divide both sides by 4}\\\\x=\dfrac{15}{4}\\\\x=3\dfrac{3}{4}[/tex]

Answer:

its 4/15 because u will get the answer i got 100% for that

Final answer:

To identify which function the graph represents, analyze the shape and pattern of the graph. The correct function could either be a polynomial such as y = x^4, which has a sharply rising curve, or a logarithmic function with a declining curve due to having a base between 0 and 1, like y = log(1/4)x, but not y = log1x as this is not mathematically valid.

Explanation:

The question requires the identification of a function based on its graph. Since the properties of functions are known, such as the logarithmic function increasing as x increases, and the behavior of exponential functions and their inverses, we can analyze the options given. The function y = log1x is not valid as the base of a logarithm cannot be 1. The function y = x4 is a polynomial function with a graph that rises sharply for positive and negative values of x. Lastly, y = log(1/4)x represents a logarithmic function with base 1/4, which is a declining curve because the base is between 0 and 1.

To choose the correct function that a graph represents, one should look for key characteristics such as the shape of the graph, increase or decrease pattern, as well as specific points like asymptotes or intercepts. If the graph is increasing as x increases and resembles a typical logarithmic curve, the correct choice is a logarithmic function. If the given graph is a sharp rising curve for all x-values and looks like a polynomial, then y = x4 would be correct. The given functions need to be analyzed based on their mathematical properties to select the one that best describes the graph in question.

Answer:

We can find the answer to your question by using a computational tool or any similar software

The equation is

-8/2*y - 8 = 5/y + 4 -7y + 8/y^2 - 18

-4*y + (- 8-4 + 18) = 5/y  -7y + 8/y^2

-4*y + 6 = 5/y  -7y + 8/y^2

-4*y + 7y + 6 = 5/y  + 8/y^2

3y + 6 = 5/y  + 8/y^2

We multiply by y^2

3y^3 + 6y^2 = 5y  + 8

3y^3 + 6y^2 -5y - 8 = 0

See image below for result of the equation

Answer:

(1,1)

Step-by-step explanation:

We have the following system:

[tex]y=x^2-x+1[/tex]

[tex]y=x[/tex]

We are going to plug the 2nd equation into the 1st eqaution giving us:

[tex]x=x^2-x+1[/tex]

Now time to solve [tex]x=x^2-x+1[/tex].

[tex]x=x^2-x+1[/tex]

Subtract x on both sides:

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

Now this actually not too bad.  This a perfect square trinomial.  That is it is of the form [tex]a^2x^2+2abx+b^2[/tex] which equals [tex](ax+b)^2[/tex].

So solving [tex]0=x^2-2x+1[/tex] is equivalent to solving [tex]0=(x-1)^2[/tex]

In order to solve  [tex]0=(x-1)^2[/tex], we just need to know when x-1=0 which is at x=1.  I got by adding 1 on both sides of x-1=0

Now remember y=x means we have the solution (1,1).

Okay, I'm going to leave all of this algebra here.  I'm going to graph this without a graphing calculator.

[tex]y=x[/tex] is a line with slope 1 and y-intercept 0.

[tex]y=x^2-x+1[/tex] is a parabola.  The vertex isn't obvious to me right now without the algebra but I do know the parabola is open up because the coefficient of x^2 being positive.

So let's find the vertex.

I'm going to start with the x-coordinate which is -b/(2a).

Compare [tex]x^2-x+1[/tex] to [tex]ax^2+bx+c[/tex] and you should see that [tex]a=1,b=-1,c=1[/tex].

So [tex]-\frac{b}{2a}=-\frac{-1}{2(1)}=\frac{1}{2}[/tex]

So the vertex occurs when the x-coordinate is 1/2.

To find the correspond y-value just use the equation that relations x and y.

That is use [tex]x^2-x+1[/tex].

Replace x with 1/2.

[tex](\frac{1}{2})^2-(\frac{1}{2})+1[/tex]

[tex]\frac{1}{4}-\frac{1}{2}+1[/tex]

Find a common denominator.

[tex]\frac{1}{4}-\frac{2}{4}+\frac{4}{4}[/tex]

[tex]\frac{1-2+4}{4}[/tex]

[tex]\frac{3}{4}[/tex]

So the vertex is at (1/2,3/4) and the parabola is open up.

When you plug in 0 into [tex]x^2-x+1[/tex] you get [tex]0^2-0+1=1[/tex] so the ordered pair (0,1) is on the parabola.

Using symmetry about the line x=1/2 we know that (1,1) is also on this graph.

Let's use this information to produce a graph now.

Now our answer appears to be (1,1) in the graph.

We can check this answer by plugging in (1,1) into our system and see if both equations check out:

[tex]y=x[/tex]  gives us 1=1 which is true.  So we are good there.

[tex]y=x^2-x+1[/tex] gives us [tex]1=1^2-1+1[/tex] which is true. So we are good there.

The work for showing [tex]1=1^2-1+1[/tex].

[tex]1^2-1+1[/tex]

[tex]1-1+1[/tex]

[tex]0+1[/tex]

1

So the point (1,1) checks out for both of our equations which means it is a common point amongst the equations given.

Answer:

y = 2 when x= 4

y=3 when x = 8

y = 4 when x=12 ....

Step-by-step explanation:

The given rule is:

y=1/4x+1

We have given the values of x. We have to find the values of y by substituting the values of x in the given rule:

y=1/4x+1

x=4

Substitute the value of x in the rule:

y=1/4 * 4+1

y=4/4 +1

By taking L.C.M of the denominator:

y= 4+4/4

y=8/4

Cancel out 8/4 by the table of 4

y= 2

y = 2 when x= 4

y=1/4x+1

x=8

Substitute the value in the given rule:

y= 1/4 * 8+1

y= 8/4 +1

By taking L.C.M we get,

y = 8+4/4

y= 12/4

Cancel out 12/4 by the table of 4

y= 3

y=3 when x = 8

Then,

y=1/4x+1

x= 12

Substitute the value in the given rule:

y = 1/4*12+1

y= 12/4+1

By taking L.C.M we get,

y=12+4/4

y=16/4

Cancel out 16/4 by the table of 4

y =4

y = 4 when x=12 ....

Answer:

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

[tex]a + 6d[/tex]

The eleventh term of an AP is written as:

[tex]a + 10d[/tex]

If the 7th term is 11 times the 11th term, then;

[tex]a + 6d = 11(a + 10d)[/tex]

Expand to get:

[tex]a + 6d = 11a + 110d[/tex]

[tex]11a - a = 6d - 110d[/tex]

[tex]10a = - 104d[/tex]

[tex] \frac{a}{d} = - \frac{104}{10} [/tex]

[tex] \frac{a}{d} = - \frac{52}{5} [/tex]

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

[tex] - 52 + 5 \times 17 = 33[/tex]

For the second case,

[tex]52 - 5 \times17 = - 33[/tex]

Answer:

C. $6 per hour.

Step-by-step explanation:

Pick a convenient point on the graph. The rate of change  is the

y coordinate /  x coordinate.

So we pick the point near the top right corner where y = 30 and x = 5 which gives us the answer 30/5 = 6.

The rate of change shown in the graph is option B that is $3 per hour.

The rate of change in a line is the difference between vertical values divided by horizontal values. It is also known as slope. It can be calculated as under:

Rate of change= y2-y1/x2-x1

To calculate the rate of change we need to first select two points which are in the given graph are (0,0) and (1,3)

Rate of change is equal to (3-0)/(1-0)

=3/1

means $ 3 is paid for 1 hour.

Hence the rate of change in the given graph is $3 per hour.

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