The number of nails of a given length is normally distributed with a mean a length of 5 in. and a
standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are between 4.97
in. long and 5.03 in. long?
ut 57 nails
out 60 nails
out 82 nail

Answer:

-3 -2 -1 = -6 0 times 1 times 2 times 3 = 0 -12 -7 -4 = -23

Step-by-step explanation:

Answer:

36 38 40 42

and

38 40 42 44.

Step-by-step explanation:

160 / 4 = 40  so the numbers are close to 40.

38 + 40 + 42 + 44 = 164

36 + 38 + 40 + 42 = 156.

Step-by-step explanation:

Hope you'll understand

Answer:

the answer is the numbers in the expressions inside the bracket should be added not subtracted

Step-by-step explanation:

hope it helps

Answer:

Part A: 12.5 cm

Part B: 0.8 km

Step-by-step explanation:

Map scale problems can be solved with proportions.

Part A

5 cm / 2 km = x cm / 5 km

5/2 = x/5

2x = 25

x = 12.5

Answer: 12.5 cm

Part B

5 cm / 2 km = 2 cm / x km

5/2 = 2/x

5x = 4

x = 4/5

x = 0.8

Answer: 0.8 km

Answer:

75.36

hope this helps :)

Answer:

a² = 16

Step-by-step explanation:

substitute a = 4 into the expression

a² = 4² = 4 × 4 = 16

Answer:

16

Step-by-step explanation:

Answer:

[tex]27cm^{2}[/tex]

Step-by-step explanation:

Area of compound shapes = Area of shape A + Area of shape B

Area of this shape = (L x B) + (L x B)
                               = (5 x 3) + (6 x 2)
                               = 15 + 12
                               = [tex]27cm^{2}[/tex]

Answer:

A = 27 cm²

Step-by-step explanation:

the figure consists of 2 rectangles

the one on the right with dimensions 2 cm by 6 cm and

the one on the left with dimensions 5 cm by 3 cm

the total area (A) is then calculated as

A = (2 × 6) + (5 × 3) = 12 + 15 = 27 cm²

Answer:

26^2 meters

Step-by-step explanation:

l + b

16 + 10

= 26m×2

Answer:rectangle

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

24 X 8     X 1FOOT DROP =  192 FT ^3

Assuming   .40 ft^3 per MINUTE

192/.4 = 480 minutes   = 8 hours

[tex]\left[\begin{array}{cc}1&3\\0&-2& \end{array}\right] \begin{bmatrix} 3& 1&-1& 0 \\ -1& 0&3&-1\end{bmatrix}\\\\\\=\begin{bmatrix} 3-3& 1+0&-1+9&0-3\\ 0+2&0-0&0-6&0+2\end{bmatrix}\\\\\\=\begin{bmatrix} 0&1&8&-3\\2&0&-6&2\end{bmatrix}[/tex]

Answer:

B=41

Step-by-step explanation:

Triangle = 180 degrees.

108+31=139

180-139=41\

B = 41 degrees

Answer:

hope this will help you ( ◜‿◝ )♡

Step-by-step explanation:

[tex] \frac{ \sin(theta) }{ \sqrt{1 - \sin {}^{2} ( theta) } } \\ \frac{ \sin(theta) }{ \cos(theta) } \\ \tan(theta) [/tex]

Answer:

300

Step-by-step explanation:

[tex]5\% \: of \: x = 15 \\ x = 1500 \div 5 = 300[/tex]

Answer:

5/9.

Step-by-step explanation:

Theoretical probability = number of outcomes with1 or 2 blues

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

                                             number of all possible outcomes

= 5/9

Answer:

122.7 cm³

Step-by-step explanation:

    Square pyramid:

          a = 4 cm ; h = 4 cm

       [tex]\boxed{\text{Volume of square pyramid = $\dfrac{1}{3}$*base area * height}}[/tex]

                                                   [tex]\sf = \dfrac{1}{3}*a^{2}*h\\\\ =\dfrac{1}{3}*4*4*4\\\\ = 21.3 \ cm^3[/tex]

Rectangular prism:

        l = 6 cm ; w = 6 cm  ; h = 4 cm

        [tex]\boxed{\text{Volume of rectangular prism = l*w*h}}[/tex]

                                                       = 6 * 6 * 4

                                                       = 144 cm³

                       = 144 - 21.3

                       = 122.7 cm³

Considering the amount they raised and the amount they spent, it is found that the art club had $358 after the show.

The net amount is found by the subtraction of the amount raised by the amount spent.

In this problem:

Then:

A = 564 - 206 = $358.

The art club had $358 after the show.

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Answer:

im gonna say it would be around 9 inches, because the actual answer, a decimal, isnt an option so the closest would be around 9 in.

Using the normal distribution, it is found that 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 15.1, \sigma = 2.2[/tex].

The proportion of penguins from the population have a weight between 13.0 kg and 16.5 kg is the p-value of Z when X = 16.5 subtracted by the p-value of Z when X = 13.

X = 16.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{16.5 - 15.1}{2.2}[/tex]

Z = 0.64

Z = 0.64 has a p-value of 0.7389.

X = 13:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13 - 15.1}{2.2}[/tex]

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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All vertical lines intersected the curve at exactly 1 point.

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

Explanation:

If there is a case when a single vertical line crosses 2 or more points on the  curve, then it will not be a function. In this situation, it is said that the curve fails the vertical line test.

Passing the vertical line test means that every vertical line passes through exactly one point on the curve. Each x input leads to exactly one output. If such a situation happens, then we have a function.

Since Kelly concluded that the curve is a function, this means the curve passed the vertical line test, and it points us to choice D as the answer.

Answer:

for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.

Answer:

Yes.

Step-by-step explanation:

Let's first convert his speed to km/h.

[tex]\frac{105km}{1.5h} = 70\frac{km}{h}[/tex] > [tex]80\frac{km}{h}[/tex]. Therefore, Rob is traveling within the speed limit.

Answer:

Angle HEF

105*

Step-by-step explanation:

0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio

We need to  find the probability of  that the democratic candidate wins both Michigan and Ohio in the next presidential election

As 6 wons from Michigan out of 10, so it 6/10

4 wons from Ohio out of 10, so it 4/10

The probability is 6/10/×4/10

24/100=0.24

In the next year also democratic candidate wons then the probabiltiy will be same 0.24

Hence 0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election

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Answer:

20

Step-by-step explanation:

2/3(30)

=20

Answer: 1725

Step-by-step explanation: A= A+B/2 h= 50+65/2x30=1725

To find side given angle and two sides:

a² = b² + c² − 2bc cos(A)

Here given:

Solve for AC (a):

Answer:

AC = 14.8 cm (1 dp)

Step-by-step explanation:

Cosine rule

[tex]\sf b^2=a^2+c^2-2ac \cos B[/tex]

(where a, b and c are the sides, and B is the angle opposite side b)

Given:

Substituting the given values into the formula and solving for b:

[tex]\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^{\circ}[/tex]

[tex]\implies \sf AC^2=100+49+70[/tex]

[tex]\implies \sf AC^2=219[/tex]

[tex]\implies \sf AC=\pm\sqrt{219}[/tex]

As length is positive,

[tex]\implies \sf AC=\sqrt{219}\:cm[/tex]

[tex]\implies \sf AC=14.8\:cm\:(1\:dp)[/tex]

Answer:

x=4

Step-by-step explanation:

We know that in a parallelogram opposite sides are equal

Hence on equating we get,

[tex]6x - 20 = 4[/tex]

[tex]6x = 4 + 20[/tex]

[tex]6x = 24[/tex]

[tex]x = 4[/tex]