9. A box contains 50 discs which are numbered 1 to 50. If one disc is drawn at random from the box. Find the probability that it bears: a 2 digit no. (ii) a perfect square no. (iii) a no. divisible by 5​

Step-by-step explanation:

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[tex]\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\[/tex]

[tex]\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\[/tex]

[tex]\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625[/tex]

Answer:

288

Step-by-step explanation:

area of the base times the height. base is 6*6=36. Then 36*8 is 288

The simplification of the expression is 28. The mistake in your calculation occurred in step 3.

TO simplify expressions involving brackets, we use a common method called BODMAS (Brackets, Of, Division, Multiplication, Addition, and Subtraction).

This means that we will first solve the expression in brackets first, followed by division, multiplication, addition, and subtraction as the case may be.

Now, from the given information, we have:
= 22+6[(14-5)÷3(17-14)]

solving parameters in the bracket first, we have:
= 22 + 6[(9) ÷3(3)]

= 22 + 6[(9) ÷9]          

= 22 + 6[(9) ÷9]    

= 22 + 6[ 1]

= 22 + 6

= 28

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Answer:

0.275

Step-by-step explanation:

Answer:

The answer to this question is -11

Answer:

The one on the top left

Step-by-step explanation:

What makes a function, a function is that the x coordinate (x,y), cannot be repeated in the tables. The y coordinate can though.

0.16 (with 6 repeating) = 1/6

3.16 = 3 1/6

Mixed Number = 3 1/6

Improper Fraction = 19/6

Hope this helps!

Answer:

3 4/25

Step-by-step explanation:

[tex]\frac{3.16}{1} \cdot \frac{100}{100} = \frac{316}{100}[/tex]

[tex]\frac{316 \div 4}{100 \div 4} = \frac{79}{25}[/tex]

[tex]= 3\frac{4}{25}[/tex]

Answer:

x = 6.3

Step-by-step explanation:

since the quadrilaterals are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{QR}{KL}[/tex] = [tex]\frac{RS}{LM}[/tex] ( substitute values )

[tex]\frac{x}{7}[/tex] = [tex]\frac{3.6}{4}[/tex] ( cross- multiply )

4x = 7 × 3.6 = 35.2 ( divide both sides by 4 )

x = 6.3

Explanation:

1) sin(37º)=x/10.3————>trigonometric ratio (sine)

2)7²+10²=c²—————-> pythagorean theorem

3) using sine—————> sin(51º)=9/x

using tangent —————> tan(51º)=9/x and x = 7.3 (rounded)

4)using pythagorean theorem————> 6²+7²=c²

angle b is tanx=6/7 where x = 40.6 degrees, angle a is tanx=7/6 where x = 49.4

Answers:

1)x= 6.2

2)x= 12.2

3)x= 11.6 (rounded)

4)x= 9.2

credit to genan for question 3 and 4

ur welcome :)

correct me if im wrong

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The area of the triangle is 608 cm².

Area is the region bounded by a plane shape.

To calculate the area of the triangle, we use the formula below.

Formula:

Where:

From the question,

Given:

If

Substitute these values into equation 1

Hence, the area is 608 cm².

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Answer:

[tex]x= 1 +5\sqrt 2,~~ x=1-5\sqrt 2[/tex]

Step-by-step explanation:

[tex]~~~~~~(x-1)^2 = 50\\\\\implies x -1 = \pm\sqrt{50}\\\\\implies x = \pm\sqrt{25 \times 2} +1\\\\\implies x= 1 \pm 5\sqrt 2[/tex]

Answer:

a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]

b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]

Step-by-step explanation:

The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]

In a), a = 3x, b = 2/x and n = 15.

You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]

Here's how to do this without the formula:

You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.

Applying this to b):

a = 2x, b = -3/x, n = 20

[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]

Answer: 123.84

Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.

From the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

When making a choice or addressing an issue, reasoning is the ability to appraise things rationally by using logic based on new or existing information.

We have:

Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names.

Mao and Cory visited cities whose names start with an S.

The table can be make to show the information provided:

Cory - city with 2 words

Molly - city with 2 words

Mao - starting with an s

Cory - starting with an s

cities are : Seattle, Santa Clara,Pittsburgh,Des Moines

The table is:

Name            City name

Cory               Santa Clare

Molly              Des Moines

Mao                Seattle

Srey               Pittsburgh

Thus, from the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

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Answer & Step-by-step explanation:

I have attached two ways you can find the number of green Jolos, by adding and/or subtracting from the other known values. Both ways will give the answer of C. 280 Jolos

Answer:

7

Step-by-step explanation:

350÷50=7

................

Answer:

r - 3

Step-by-step explanation:

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to write the verbal phrase "r decreased by 3" as an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]

Here we decrease the variable "r" by 3.

Remember, variables always represent some number.

Let's think about it this way...

///\\\////\\\\////\\\///\\\///\\\///\\\///\\\///\\///\\///\\///\\///\//\\///\\\///\\\///\\\///\\///\\\///\

So we have a number r, and we decrease it by 3.

Now its value is less than the original value.

We subtracted 3 from the original value of r, and now its value is less than the original one.

Thus, "decreased by" is the same as "subtracted" in mathematics.

r decreased by 3 ⇒ [tex]\star\large\pmb{r-3}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

A - x = 4

Step-by-step explanation:

According to The Midsegment Trapezoid Theorem the length of the midsegment is the sum of both bases divided by 2.

So to find the value of x:

x + 3 + 4x  7 = 15*2  add like terms

5x + 10 = 30 subtract 10 from both sides

5x = 20 divide both sides by 5

x = 4

The shape of experiment 1 is roughly bell shaped. This indicates that it is normally distributed. The shape of experiment 2 is asymmetrical. This indicates that it is not normally distributed.

A dot plot is a graph that is used to represent the frequency of a data set using dots. The dots represents the frequency of a number.  The results from experiment 1 is more spread out over the numbers compared to experiment 2 which is concentrated around the center.

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Answer:

the answer to the question above would be the option 3 (vertex)

Answer:

[tex]16[/tex]

Step-by-step explanation:

[tex]~~~~~~x^2 -8x = 5 \\\\\implies x^2 -2\cdot 4 \cdot x+ 4^2 = 5+ 4^2~~~~~~~~~~~~;[\text{Add}~ 4^2 = 16 ~ \text{to both sides }]\\\\\implies (x-4)^2 = 21[/tex]

The coordinate of the point is (6,-2)

The given parameters are:

A = (1,8)

B = (7,-4)

The location of the point (i.e 5/6) means that the ratio is:

m :n = 5 : (6 - 5)

m : n = 5 : 1

The coordinate of the point is then calculated as:

[tex](x,y) = \frac{1}{m + n}* (mx_2 + nx_1,my_2 + ny_1)[/tex]

So, we have:

[tex](x,y) = \frac{1}{5 + 1}* (5 * 7 + 1 * 1 , 5 * -4 + 1 * 8)[/tex]

Evaluate

[tex](x,y) = \frac{1}{6}* (36 , -12)[/tex]

Evaluate the product

(x,y) = (6,-2)

Hence, the coordinate of the point is (6,-2)

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A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.

A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.

Note that:

The power of the test shows that:

See full question below

Suppose you have the following null and alternative hypothesis:

H o: it is snowing.

H a: It is not snowing

(A) in the context of this problem, describe a Type-1 error

(B) Describe Type II error

(C)Describe power of the test

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Answer:

2/8, 3/12 and 4/16

Step-by-step explaination:

All these fractions are equivalent to 1/4 as the numerator is a multiple of 1, the denominator is a multiple of 4, and the numerators are all a quarter of their respective denominators.

The person who thinks the event is more likely is Layne. This is because she has a higher probability value than Abdul.

Probability determines the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0. The closer the event is to 1, the more likely the event would happen

Layne's probability that the event would happen = 75%

Abdul's probability that the event would happen = 3/5 x 100 = 60%

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Answer:

2.65 cm

Step-by-step explanation:

Applied Formula :

Solving :

Answer:

-2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103