From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

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Answer:

[tex]tan(-1) \approx -0.02[/tex]

Step-by-step explanation:

The given expression is

[tex]tan(-1)[/tex]

The tangent of -1 is defined, it's around -0.02.

The tangent is a trigonometric function with a period of [tex]\pi[/tex], where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".

However, at [tex]x=-1[/tex], the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.

[tex]tan(-1) \approx -0.02[/tex]

Answer:

(a) The mean weight of beer used to fill each bottle is 16 ounces.

(b) The answer of part (a) would not change.

Step-by-step explanation:

A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle.

Ben takes a random sample of n = 48 bottles and finds the average weight to be [tex]\bar x=[/tex] 15.8 ounces. Also it is known that the standard deviation is, σ = 0.8 ounces.

(a)

The hypothesis can be defined as follows:

H₀: The mean weight of beer used to fill each bottle is 16 ounces, i.e. μ = 16.

Hₐ: The mean weight of beer used to fill each bottle is not 16 ounces, i.e. μ ≠ 16.

Assume that the significance level of the test is, α = 0.05.

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

 [tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

   [tex]=\frac{15.8-16}{0.80/\sqrt{48}}\\\\=-1.732[/tex]

The test statistic value is -1.732.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

[tex]p-value=2\cdot P(Z>-1.732)[/tex]

               [tex]=2\times [1-P(Z<1.732)]\\\\=2\times [1-0.04182]\\\\=0.08364\\\\\approx 0.084[/tex]  

*Use a z-table for the probability.

The p-value of the test is 0.084.

p-value = 0.084 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that the mean weight of beer used to fill each bottle is 16 ounces.

(b)

The standard deviation of a random variable is the square root of the variance.

[tex]SD=\sqrt{Variance}[/tex]

So, if the variance was 0.64, then the standard deviation will be:

[tex]SD=\sqrt{Variance}=\sqrt{0.64}=0.80[/tex]

Thus, the answer of part (a) would not change.

Answer:

A-40

B-140

C-140

Step-by-step explanation:

b and c are supplementary angles to angle 40.

Therefore 180-40= 140.

and opposite angles in a quadrilateral are congruent to each other.

Answer:

The  class width is  [tex]C_w \approx 13[/tex]

Step-by-step explanation:

From the question we are told that

 The  upper class limits is [tex]max = 121[/tex]

  The  lower class limits is  [tex]min = 14[/tex]

   The number of classes is  [tex]n = 8 \ classes[/tex]

The class width is mathematically represented as  

       [tex]C_w = \frac{max - min}{n }[/tex]

substituting values

       [tex]C_w = \frac{121 - 14}{8 }[/tex]

       [tex]C_w = 13.38[/tex]

      [tex]C_w \approx 13[/tex]

Since

Answer:

a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

Step-by-step explanation:

a) The velocity function is obtained after deriving the position function in time:

[tex]v (t) = -32\cdot t -27[/tex]

The velocity of the ball after 2 seconds is:

[tex]v(2\,s) = -32\cdot (2\,s) -27[/tex]

[tex]v(2\,s) = -91\,\frac{ft}{s}[/tex]

The velocity of the ball after 2 seconds is -91 feet per second.

b) The time of the ball after falling 364 feet is found after solving the position function as follows:

[tex]435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft[/tex]

[tex]-16\cdot t^{2} - 27\cdot t + 364 = 0[/tex]

The solution of this second-grade polynomial is represented by two roots:

[tex]t_{1} = 4\,s[/tex] and [tex]t_{2} = -5.688\,s[/tex].

Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:

[tex]v(4\,s) = -32\cdot (4\,s) - 27[/tex]

[tex]v(4\,s) = -155\,\frac{ft}{s}[/tex]

The velocity of the ball after falling 364 feet is 155 feet per second.

c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:

Second-order polynomial evaluated at (0, 1)

[tex]c = 1[/tex]

Slope of the tangent line evaluated at (1, 0)

[tex]5 = 2\cdot a \cdot (1) + b[/tex]

[tex]2\cdot a + b = 5[/tex]

[tex]b = 5 - 2\cdot a[/tex]

Now, let evaluate the second order polynomial at (1, 0):

[tex]0 = a\cdot (1)^{2}+b\cdot (1) + c[/tex]

[tex]a + b + c = 0[/tex]

If [tex]c = 1[/tex] and [tex]b = 5 - 2\cdot a[/tex], then:

[tex]a + (5-2\cdot a) +1 = 0[/tex]

[tex]-a +6 = 0[/tex]

[tex]a = 6[/tex]

And the value of b is: ([tex]a = 6[/tex])

[tex]b = 5 - 2\cdot (6)[/tex]

[tex]b = -7[/tex]

The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

Answer: B or square root 2^5

Step-by-step explanation: I checked on my calculator

ANSWER:

C. Place the compass on point A. Open the compass to a point between point P and point B.

EXPLANATION:

A perpendicular is a line that would be at a right angle to line BA.

The next step is to chose a radius that is greater than PB or PA so as to construct the bisector. And this can be done by placing the compass on point A, and open the compass to a point between point P and point B.

Use this radius to draw an arc above and below the line, and repeat the same using B as the center with the same radius. This would form two intersecting arcs above and below line BA. Join the point of intersection of the arcs by a straight line through P. This is the bisector of line BA through point P.

Answer:

See below

Step-by-step explanation:

Proof:

Statements                                    |  Reasons

AD ≅ BC                                         | Given

AD ║ BC                                         | Given

AC ≅ AC                                         |  Reflexive Property

∠DAC ≅ ∠ACB                               | If 2 || lines are cut by a trans., the                                                                       |  alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA                               | S.A.S  Postulate

BA ≅ DC                                         | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm             | If a quad. has its opposite sides

                                                       | congruent, the quad. is a parallelogram.

It is prove that given quadrilateral is a parallelogram.

            AD ≅ BC      and AD ║ BC              

            AC ≅ AC            

       So that,   ∠DAC ≅ ∠ACB                              

            ΔADC ≅ ΔBCA    

        So that, BA ≅ DC                                        

Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.

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Answer:

B. [tex]\frac{6}{2x^{2} - 5x}[/tex]

Step-by-step explanation:

The product of the ratioal expressions given above can be found as follows:

[tex] = \frac{2}{x} * \frac{3}{2x - 5} [/tex]

Multiply the denominators together, and the numerators together, separately to get a single expression

[tex] \frac{2(3)}{x(2x - 5)} [/tex]

[tex] = \frac{6}{x(2x) - x(5)} [/tex]

[tex]= \frac{6}{2x^{2} - 5x}[/tex]

The product of the expression [tex]\ = \frac{2}{x}*\frac{3}{2x - 5}[/tex] = [tex]\frac{6}{2x^{2} - 5x}[/tex]

The answer is B.

Answer: THe slope is 2

SO answer d

Step-by-step explanation:

-4X + 2Y = 16 add 4x to the other side so equation is

2y=16+4x divided by 2

y=8+2x

Answer:

bar graphs

Step-by-step explanation:

as in a bar graph, we don't do any calculations to graph on a paper,

so the data values, are taken RAW while graphing.

Answer:

x=-11

Step-by-step explanation:

x+8=-3

x=-3-8 :- collect like term

since we are adding two negative numbers, we will let the number be negative but add them.

x=-11

Hope it helps :)

Answer:

x=-11

Step-by-step explanation:

x+8=-3

collect like terms;

x=-3-8

x=-11

Answer: 6

Step-by-step explanation:

Lets re- write the numbers in growing order.

2,3,4,6,7,10,10

The number that stays exactly in the middle of the the sequence is the median.

Number 6 stays in the middle. So 6 is the median

Answer

Step by step explanation

Given data : 4 , 3 , 2 , 10 , 10 , 6 , 7

Arranging the data in ascending order, we have,

2 , 3 , 4 , 6 , 7 , 10 , 10

Here, n ( total number of items) = 7

Now, position of median:

[tex] {( \frac{n + 1}{2}) }^{th} [/tex] item

plug the value

[tex] = {( \frac{7 + 1}{2} )}^{th} [/tex] item

Add the numbers

[tex] =( { \frac{8}{2} )}^{th} [/tex] item

Divide

[tex] = {4}^{th} [/tex] item

i.e 4th item is the median

Median = 6

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

Further more explanation:

Let's take another example:

please see the attached picture.

In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series.

Thus, Median is the value of the middle - most observation, when the data are arranged in ascending or descending order of magnitude.

Hope I helped..

Best regards!!

Answer:

(x,y) = (5,15)

Step-by-step explanation:

y = 3x

2x + 3y = 55

2x + 3(3x) = 55

2x + 9x = 55

11x = 55

x = 5

y = 3(5)

y = 15

Hi there! :)

Answer:

2nd choice. f(x) = 4 sin x + 2

Step-by-step explanation:

Recall that the transformations form of a sine function is:

y = ±a sin(b(x-h)) + k

Where:

'a' changes the amplitude

'b' changes the period

'h' is a horizontal shift

'k' is a vertical shift, or a change in the midline.

In this instance, the function has a midline of y = 2, which means an equation representing this must have a 'k' value of 2.

The only equation that contains this value is:

f(x) = 4 sin x + 2.

Answer:

I'm pretty positive the answer is B.   f(x) = 4sinx + 2

Step-by-step explanation:

Since d = 2 and the amplitude is 4 and there is nothing else effecting the function you are going up the graph 2 vertically and the amplitude will just go up and down 4 with you midline being at y = 2.

Answer:

Well Plan D

Step-by-step explanation:

Answer:

plan D.

Step-by-step explanation:

2021 edge

Answer:

ln(2000) = 7.601

Step-by-step explanation:

For this we need to know the rules of logarithms, specifically the product rule and the power rule.  The product rule is simply ln(a*b) = ln(a) + ln(b).  The power rule is simply ln(a^b) = b ln(a).

With these rules, let's begin to simplify the expression:

4 ln(2) + 3 ln(5)

= ln(2^4) + ln(5^3)

= ln(16) + ln(125)

= ln(16 * 125)

= ln(2000)

= 7.601

Hope this helps.  Cheers.

A logarithm is a power to which a number must be raised in order to get some other number.

The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.

A logarithm is a power to which a number must be raised in order to get some other number.

Example:

log 10 = 1

log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3

log 0 = undefined

log 1 = 0

We have,

Some formulas for log:

log[tex]x^{n}[/tex] = n log x

log mn = log m + log n

Given,

4 log 2 + 3 log 5

= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]

= log 16 + log 125

= log (16 x 125)

= log 2000

= 3.30102

Thus the value of the expression 4 log 2 + 3 log 5 as a single number is

3.30102.

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Answer:

14.05

Step-by-step explanation:

We have the following:

Current Dividend = D0 = $ 1.40

g = growth rate = 2%

r = discount rate = 13%

Dividend in Year 5

= D5 = D0 * (1 + g) ^ 5

= $ 1.40 * (1 + 2%) ^ 5

= $ 1.40 * (1.02) ^ 5

Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)

= $ 1.40 * (1.02) ^ 5 / (13% -2%)

= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)

Therefore, firm stock at the end of year 4 is

P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

Option D

x = 27; m∠FDG = 62°; m∠GOF = 118°

Step-by-step explanation:

To solve this, we will need the help of the following laws of geometry:

1. We can see that the shape formed is quadrilateral. The sum of the interior angles of a quadrilateral = 360 degrees.

2. The angle between a radius and a tangent = 90 degrees. as a result of this, <OGD = <OFD = 90 degrees.

Once we have values for all the angles of the quadrilateral, we can set up an equation using the first rule mentioned above.

2x+8 + 4x+10 +90 +90 = 360 (Sum of interior angles of a quadrilateral = 360)

6x = 162

x=27 degrees

Now we have the value of x, we can find FDG and GOF as follows:

FDG = 2x + 8 = 2(27)+8 =62

FOG = 4x + 10 = 4(27)+ 10 =118

Answer:

The height of the box with the smaller base is 4  times that of the box with the larger base

Step-by-step explanation:

The volume of a box is the product of the base area and the height of the box, it is given as:

Volume = base area × height

For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm  = 25 cm². Let the height of the smaller base box be [tex]h_1[/tex]The volume of the small box = [tex]25*h_1[/tex]

For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm  = 100 cm². Let the height of the large base box be [tex]h_2[/tex]The volume of the larger base box = [tex]100*h_2[/tex]

Since both boxes have the same volume, therefore:

[tex]100*h_2[/tex] = [tex]25*h_1[/tex]

[tex]\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2[/tex]

The height of the box with the smaller base is 4  times that of the box with the larger base

We can use the formula V=lwh to compare the volume in the two boxes.

First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.

First the box with the smaller base.

V=lwh

V=5⋅5⋅1

V=25

Now the box with the larger base

V=lwh

V=10x10x1

V=100

We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.

25·h=100

h=4

The boz with the smaller base is 4 times tall

hope it helped :)

​

​

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Answer:

g(x) = x² + 4x + 5

h(x) = 3x - 5

To find (g+h)(x) add h(x) to g(x)

That's

(g+h)(x) = x² + 4x + 5 + 3x - 4

Group like terms

(g+h)(x) = x² + 4x + 3x + 5 - 4

Simplify

We have the final answer as

Hope this helps you

Answer:

8.1% decrease

Step by step

To find precentage decrease we use formula:

Percent decrease= original amount-new amount/original amount(100%)

percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%

Answer:

(a)The x-intercepts are 3, -4 and 1.

(b)f(x)=-0.5

Step-by-step explanation:

Given the function:

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}[/tex]

x-Intercepts

When y=f(x)=0

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1[/tex]

The x-intercepts are 3, -4 and 1.

y-intercepts

When x=0

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5[/tex]

The y-intercept is -0.5

Answer:

y = -(1/2)x+1

Step-by-step explanation:

-2Y - X = -2

Add x to both sides:

-2Y = X - 2

Divide both sides by -2:

Y = -(1/2)x+1

You could also use the shortcuts:

For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.

Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)

Y-intercept = C/A = (-2)/(-2) = 1

y = mx + b ---> y = -(1/2)x + 1

Answer:

y = -1/2x +1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

-2y -x = -2

Solve for y

Add x to each side

-2y = x-2

Divide by -2

-2y/2- = x/-2 -2/-2

y = -1/2x +1

Answer:

 -7x⁴+5x³-10x²-4x-7 - 4/4x+7

Step-by-step explanation:

Given the division problem, (28x⁵ + 29x⁴ + 5x³ + 86x² + 56x + 53) by (–4x – 7), find the solution in the attachment below.

The polynomial of a function is expressed as P(x) = Q(x) + R(x)/D(x)

Q(x) is the quotient

R(x) is the remainder

D(x) is the divisor

Accordin gto the divsion, Q(x) = -7x⁴+5x³-10x²-4x-7

R(x) = 4

D(x) = -4x-7

Substituting this functions in the polynomial P(x);

P(x) =  -7x⁴+5x³-10x²-4x-7 - 4/4x+7

Set up two equations:

Let a = adults and c = child:

a +  c = 289 ( rewrite as a = 289 - c)

1.50c + 4a = 746

Replace a with the rewritten formula:

1.50c + 4(289-c) = 746

SImplify:

1.50c + 1156 - 4c = 746

Combine like terms:

-2.50c + 1156 = 746

Subtract 1156 from both sides:

-2.50c = -410

Divide both sides by -2.50

c = -410 / -2.50 = 164

Number of children = 164

Number of adults = 289 - 164 = 125

Answer:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125

Step-by-step explanation:

Let x the number of children and y the number of adults. From the info given we can set up the following equations:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125