A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer's claim based on this observation?

Answer:

x = 9.8

Step-by-step explanation:

Please see attached photo for diagram.

We'll begin by calculating the value of y. This can be obtained as follow:

Angle θ = 45

Opposite = 6

Hypothenus = y

Sine θ = Opposite /Hypothenus

Sine 45 = 6/y

0.7071 = 6/y

Cross multiply

y × 0.7071 = 6

Divide both side by 0.7071

y = 6 / 0.7071

y = 8.5

Finally, we shall determine the value of x. This can be obtained as follow:

Angle θ = 60

Opposite = 8.5

Hypothenus = x

Sine θ = Opposite /Hypothenus

Sine 60 = 8.5 / x

Cross multiply

x Sine 60 = 8.5

Divide both side by sine 60

x = 8.5 / sine 60

x = 8.5 / 0.8660

x = 9.8

Answer:

b

Step-by-step explanation:

the square root of 8 is 2 and the square root of 18 is 4.5 and both simplified is 4/9.

Aslo did this last week.

90/-10

= 9/-1

= -9

So, -9 is the quotient.

Answer:

Below.

Step-by-step explanation:

Area = 5(x + 3)

= 5x + 15

Perimeter = 2(x + 3) + 2(5)

= 2x + 6 + 10

= 2x + 16.

Answer:

The answer closest to 36.10425. So 36.10 or 36.1

Step-by-step explanation:

x = 44.85 ( 1 - 0.195) = 36.10425

If this helps, it would be nice if 5 stars are given, and a brainliest :)

The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

For this case, we can assume the amount of bill without tip being A.

Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:

Total price of the bill = Bill amount before tip + Tip

44.85 = A + (19.5 % of A)

(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))

44.85 = A + (19.5 % of A)

or

[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]

Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

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Answer:

response bias

Step-by-step explanation:

because whan you are asked a question you expect response in return

Answer:

It is a parallelogram!

Step-by-step explanation:

This is because it has four sides and all the sides have parallel lines if that makes sence.

Hi there!

[tex]\large\boxed{x \approx 19.6}[/tex]

We can use right triangle trigonometry to solve.

We are given the angle's adjacent side and are trying to solve for the hypotenuse, so:

Use cosine: cos Ф = A / H

Thus:

cos 30° = 17 / H

Simplify:

0.866 = 17 / H

Isolate for H:

H · 0.866 = 17

H = 17 / 0.866

H = 19.63 ≈ 19.6

Answer:

x = 19.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = 17/x

x cos 30 = 17

x = 17/cos 30

x=19.62990

To the nearest tenth

x = 19.6

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.

By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

Answer:

In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?

There are 4 colours of balls - green, blue, yellow and white.

Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.

Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.

Check: Total number of balls = 12+6+4+26 = 48

Answer: 6 balls are blue....

Answer: 3/8

Step-by-step explanation:

A=3

B=5

3/3+5=3/8

c.write the fact,organize your thoughts and define your strategy.

Answer:

c

Step-by-step explanation:

Answer:

8.204786801 in

Step-by-step explanation:

cos (79°) = BE/BG= adjacent/hypotenuse

cos ( 79°) = BE/43 in

BE = cos (79°) × 43 in= 8.204786801 in

Hi,

no need to use discriminant for that.

3(m)^2 = -6

m^2 = -6/3

m^2= -2

in R, there is no

solution as a square can not be negative.

Answer:

y = 4

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : √3 : 2

The sides in this triangle are in the order:

y : 4√3 : x

y/1 = 4√3/√3

y = 4

Step-by-step explanation:

jejejebe. s shs sjs sibskkw

Answer:

[tex]1.5,1.2,0.96,0.768[/tex]

Common ratio between successive terms

[tex]=\frac{1.2}{1.5}[/tex]

[tex]=0.8[/tex]

OAmalOHopeO

The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The sequence is,

⇒ 1.5, 1.2, 0.96, 0.768,...

Hence, The value of the common ratio between successive terms in the sequence is,

⇒ 1.2 / 1.5

⇒ 12/15

⇒ 0.8

Thus, The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

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a) The equation has a root in the interval (-1,0)

b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]

a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.

"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"

So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:

[tex]2x+3cos(x)+e^{x}[/tex]

[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]

Let's now test for x=0

[tex]2x+3cos(x)+e^{x}[/tex]

[tex]2(0)+3cos(0)+e^{0}=4[/tex]

So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.

b) The zero is located at x=-0.9977

The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:

x=-1 and x=0

so we find the value in the middle by using the following formula:

[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]

so we get:

[tex]mid-value=\frac{-1+0}{2}[/tex]

mid-value=-0.5

Next, we evaluate the given function for that value:

[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]

Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:

[tex]mid-value=\frac{-1-0.5}{2}[/tex]

mid-value=-0.75

Next, we evaluate the given function for that value:

[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]

and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.

Learn more about the intermediate zero theorem here:

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Step-by-step explanation:

you cannot just put the actual numbers in and calculate ?

and you can't provide the correct problem statement, as it seems.

I assume you mean

an = 3n² - 1

a sequence starts with a1, so, n>=1

a1 = 3×1² - 1 = 3-1 = 2

a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11

a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26

a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47

a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74

there, that is all there is to it. you really needed help with that ?

Answer:

50

Step-by-step explanation:

19-7=12

6+6+7+19+12

Answer:

d the median if the data is 55

Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Step-by-step explanation:

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]

Applying Pythagoras theorem

[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]

[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]

[tex]\bf \large \implies \: \: x \: = \: 52[/tex]

Hence , the length of hypotenuse is 52.