Find the missing Side of the triangle

Given:

The inequality is:

[tex]|2x-1|>3[/tex]

To find:

The solution set for the given inequality.

Solution:

We know that, if [tex]|x|>a[/tex], then [tex]x<-a[/tex] and [tex]x>a[/tex].

We have,

[tex]|2x-1|>3[/tex]

It can be written as:

[tex]2x-1<-3[/tex] or [tex]2x-1>3[/tex]

Case I:

[tex]2x-1<-3[/tex]

[tex]2x<-3+1[/tex]

[tex]2x<-2[/tex]

[tex]x<\dfrac{-2}{2}[/tex]

[tex]x<-1[/tex]

Case II:

[tex]2x-1>3[/tex]

[tex]2x>3+1[/tex]

[tex]2x>4[/tex]

[tex]x>\dfrac{4}{2}[/tex]

[tex]x>2[/tex]

The required solution for the given inequality is [tex]x<-1[/tex] or [tex]x>2[/tex]. The solution set in the interval notation is [tex](-\infty,-1)\cup (2,\infty)[/tex].

Therefore, the required solution set is [tex](-\infty,-1)\cup (2,\infty)[/tex].

Every morning there are expected 240 customers who arrive at bank for the customer service.

There are on average 240 customers arriving to the bank every morning.

There are total 5 bank tellers and they take average 3 minutes to help customer.

The average time each bank teller spends on satisfying a customer will be calculated using the linear model,

Using wait time calculator:

Average service time / standard deviation

Ce = 3/1.5 = 2

The spent time on a customer is 3.4 minutes.

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Answer:

Customers spend 3.4 minutes in the bank on average.

Step-by-step explanation:

The customer arrives at the bank every morning. There is a line at bank goes to 5 bank teller. The customer takes 3 minutes with a 1.5-minute standard deviation.

The customer = 240

Time = 3

Where R = (240/4)

=60/hr

Where CVa = 1

Answers:

================================================

Explanation:

If it's sold at a loss of 15%, then the store owner loses 0.15*330 = 49.50 dollars

So it was sold for 330- 49.50 =  280.50 dollars

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

An alternative method:

If the store owner loses 15%, then they keep the remaining 85% since 15%+85% = 100%.

85% of 330 = 280.50 dollars is the discount price

This means 330-280.50 = 49.50 dollars is the amount lost.

Answer:

3x ( x+2)(x^2−2x+4)

Step-by-step explanation:

3x^4 + 24x.

Factor out the greatest common factor

3x*x^3 + 3x*8

3x(x^3+8)

Then factor the cubic term

The sum of cubes is a^3+b^3=(a+b)(a^2−ab+b^2)

3x ( x+2)(x^2−2x+4)

Answer:

x=24, y = 33/360 π×24^2/(sin^2(33° (degrees)))

Step-by-step explanation:

notice that x = MK = HM = 24.

Let the center of the circle be C.

Also, notice the radius of the circle can be expressed as the hypotenuse of HMC. Using some trig, we figure out that the radius is 24/sin(33 degrees).

Using the radius of the circle, we can figure out the circumference. The circumference is pi*r^2=(24/sin(33 degrees))^2*pi=pi*24^2/(sin(33 degrees)^2)

Lastly, notice that y = 33/360*circumference = 33/360 π×24^2/(sin^2(33° (degrees)))

hopefully this helped

Answer:

The number is 448.

Step-by-step explanation:

Hope it helps

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

x=35

vertical opposite angles are equal.

Answer:

(-2, 2)

Step-by-step explanation:

If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)

So, if the original point is (-8, 8)

And we do a dilation by a scale factor k = 1/4

Then the image of the point will be:

(-8*(1/4), 8*(1/4))

(-8/4, 8/4)

(-2, 2)

Answer: 1.28571428571. This number is infinite.

Step-by-step explanation:

Answer:

1.29 rounded

Step-by-step explanation:

Answer:

√29

Step-by-step explanation:

This is due to A^2+b^2=c^2. you know that side a and b are 2 and 5, so it beocmes 25+4/=c^2, which means that 29=c^2, and you root it to get rid of the power of 2, so you obtain c=√29

Answer:

<4 = <1

Step-by-step explanation:

Judging from the picture, <1 and <4 are opposite angles. Opposite angles are always congruent. Hope this helps!

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

The solid is described as a three-dimensional solid made from

two parallel and congruent discs, not in the same plane, and all the points

between them is a Cylinder.

Hence, the correct option is A.

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Hey there!

2w^2 - 3w + 7

= 2(-2)^2 - 3(-2) + 7

(-2)^2

= (-2)(-2)

= 4

= 2(4) - 3(-2) + 7

2(4) = 8

3(-2) = -6

= 8 - (-6) + 7

= 8 + 6 + 7

8 + 6 = 14

14 + 7

= 21

Answer: 21

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

The graph would be compressed vertically by a factor of 1/3.

Step-by-step explanation:

Multiplying a function by some constant is a way to stretch or compress that function. If the magnitude of the constant is greater than 1, you are vertically stretching, if the magnitude of the constant is less than one but greater than 0 you are vertically compressing your function.

Answer:

[tex]C=27inch\ by\ 27inch[/tex]

Step-by-step explanation:

Squares [tex]h=4inch[/tex]

Volume [tex]v=1444in^3[/tex]

Generally the equation for Volume of box is mathematically given by

 [tex]V=l^2h[/tex]

 [tex]1444=l^2*4[/tex]

 [tex]l^2=361[/tex]

 [tex]l=19in[/tex]

Since

Length of cardboard is

 [tex]l_c=19+4+4[/tex]

 [tex]l_c=27in[/tex]

Therefore

Dimensions of the piece of cardboard is

[tex]C=27inch\ by\ 27inch[/tex]

Answer:

1  3 5 2 4 6

Step-by-step explanation:

Answer:

8 1/8 units^3

Step-by-step explanation:

This figure is a rectangular prism, and the volume of a rectangular prism is given by the formula:

lwh

But since we have the area of the base snd the height of the figure, there is also one formula that we can use to find the volume:

bh

Which means area of base times the height.

USE THE FORMULA bh:

16 1/4 x 1/2

= 65/4 x 1/2

= 65/8

SIMPLIFIED: 8 1/8

Volume is measured in cubic units

SO YOUR ANSWER IS 8 1/8 units^3

Answer:

6,78

Step-by-step explanat

ion:data size :10

Sample mean:15

Standard sample deviation :6,782

Answer:

6,78

Step-by-step explanation:

We are given a system of equations,

[tex]\begin{cases}-x+2y=0\\y=-2\\ \end{cases}[/tex]

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

[tex]\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}[/tex]

The matrix will then be applied to the vector (lower dimensions on top),

[tex]\begin{bmatrix}x\\y\\ \end{bmatrix}[/tex]

And the result vector will be whats on the other side of equals sign,

[tex]\begin{bmatrix}0\\-2\\ \end{bmatrix}[/tex]

So to put everything together,

[tex]\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}[/tex]

Hope this helps :)

Answer:

The volume of this cone would be approximately equal to 2787.64 [tex]yd.^2[/tex].

Step-by-step explanation:

The formula used to calculate the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex] where [tex]r[/tex] represents the radius of the circle at the base of the cone, and [tex]h[/tex] represents the vertical height of the cone. In this case, [tex]r[/tex] equals the diameter of the base divided by two, which is [tex]\frac{22}{2}[/tex] or 11 yards; and [tex]h[/tex] is equivalent to 22 yards. Insert these values into the formula and you'll get that the volume of this cone is equal to [tex]11^2*\pi*\frac{22}{3} = 121\pi * \frac{22}{3}[/tex] ≈ 2787.64 [tex]yd.^2[/tex], so that is the correct answer.

Answer:

C. all possible input values of the function

Step-by-step explanation:

Answer:

C is right

Step-by-step explanation:

domain is f(x)=x^2 is all real numbers but domain g(x)=1/x is all real numbers except for 0 which is x but domains and the rang can be the same also

Answer:

[tex]14<15[/tex]

[tex]0<2x+10<62[/tex]

[tex]-10<2x<52[/tex]

[tex]-5<x<26[/tex]

~OAmalOHopeO

Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

They are different exponents but they have the same bas so you add them up.

4x^5+3 = 4x^8

[tex] \pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: as \: we \: know \: that \\ \\ \bf\: \: \rightarrow \: {(xy)}^{n} = {x}^{n} . {y}^{n} \\ \\ \bf \rightarrow \: {( {a}^{m} })^{n} = {a}^{m \times n} \\ \\ \bf \: now \\ \: \\ \blue{ {\boxed{\begin{array}{cc} \maltese \bf\: \: \: {(4 {x}^{5} })^{3} \\ \bf = {4}^{3} \times ({x}^{5} )^{3} \\ \bf = {4}^{3} \times {x}^{5 \times 3} \end{array}}}}\end{array}}}}[/tex]

So option D) is the correct answer

Answer:

the correct answer is |x – 18| ≤ 4

just took the test

Step-by-step explanation:

P(even)=1/2. P(odd)=1/2. Let x= number of even in ten rolls

P(x<=8) = 1-P(x>=9) = 1-[C(10,9)(1/2)^9 *(1/2)^1 + C(10,10)(1/2)*(1/2)^0]

=1-[C(10,9)(1/2)^10 +C(10,10)(1/2)^10]

=1-(1/2)^10[10+1

=1–11/1024

=1013/1024

It does not appear that police can use a shoe print length to estimate the height of a​ male.

The given parameters are:

[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

Rewrite as:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

See attachment for scatter plot

To determine the correlation coefficient, we extend the table as follows:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]

The correlation coefficient (r) is:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

We have:

[tex]n =5[/tex]

[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]

[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]

[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]

[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]

[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]

Calculate mean of x and y

[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]

[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]

Calculate SSx and SSy

[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]

[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]

Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]

[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]

So:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]

[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]

[tex]r = \frac{9.098}{63.90}[/tex]

[tex]r = 0.142[/tex]

Calculate test statistic:

[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]

[tex]t = \frac{0.142}{0.5715}[/tex]

[tex]t = 0.248[/tex]

Calculate the degrees of freedom

[tex]df = n - 2 = 5 - 2 = 3[/tex]

The [tex]t_{\alpha/2}[/tex] value at:

[tex]df =3[/tex]

[tex]t = 0.248[/tex]

[tex]\alpha = 0.01[/tex]

The value is:

[tex]t_{0.01/2} = \±5.841[/tex]

This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841

We calculate the t value as:

[tex]t = 0.248[/tex]

[tex]-5.841 < 0.248 < 5.841[/tex]

Hence, we do not reject the null hypothesis because they do not appear to have any correlation.

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Answer:

It is shifted left 5 units and up 2 units from the parent function.

Step-by-step explanation:

Given

[tex]y = \frac{1}{x}[/tex]

[tex]y' = \frac{1}{x+5} + 2[/tex]

Required

Compare both functions

First, translate y, 5 units left.

The rule is:

[tex](x,y) \to (x + 5,y)[/tex]

So, we have:

[tex]y = \frac{1}{x}[/tex]

[tex]y_1 = \frac{1}{x + 5}[/tex]

Next, translate y1, 2 units up.

The rule is:

[tex](x,y) \to (x,y+2)[/tex]

So, we have:

[tex]y' = y_1 + 2[/tex]

[tex]y' = \frac{1}{x + 5} + 2[/tex]

Hence, the transformation is:

5 units left and 2 units up

Answer:

b

Step-by-step explanation: