1. The cards bearing letters of word “MATHEMATICS” are placed in a bag. Find the probability of getting: (a) any vowel. (b) any consonant. (c) the letter ‘m’. 2. 8 added to twice a number gives 40. Find the number

Answer:

D is correct.

Step-by-step explanation:

2x ≤ 14

x  ≤ 7

Answer:

D) x ≤ 7

Step-by-step explanation:

2x + 1 ≤ 15

2x ≤ 15 - 1

2x ≤ 14

x ≤ 14 : 2

x ≤ 7

Answer:

There are 10 perfect squares between 1 and 100;

A perfect square is basically an integer that is a square of an integer. Or simply the product of an integer with itself.

Explanation:

The perfect squares between 1 and 100 are:

1*1 = 1

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

7*7 = 49

8*8 = 64

9*9 = 81

and

10*10 = 100

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

Explanation:

Using your calculator, you should find that

Each approximate result has its decimal digits go on forever without any pattern. So we cannot write those values as a fraction of two integers. The decimal expansion must have some kind of pattern that repeats forever, so we could consider it rational.

Only choice B results in a whole number. The value 14 is the same as 14/1, showing it can be written as a fraction of two integers. Therefore choice B is rational.

Answer:

x+4

x+1-2=x-1

Step-by-step explanation:

x+4/x-1=11/16 x should be different than 1 cz 1-1=0

16(x+4)=11(x-1)

16x+64=11x-11

16x-11x=-11-64

5x=-75

x=-15

Greetings from Brasil....

From Pythagoras we have

AB² = AC² + BC²

13² = 12² + X²

Answer:

5 cm

Step-by-step explanation:

Pythagoras theorem gives us:

[tex]hypotenuse^{2} = side^{2} + side^{2}[/tex]

We know the hypotenuse is 13 cm.

We know one side is 12 cm.

[tex]13^{2} = 12^{2} + side^{2}[/tex]

[tex]169= 144 + side^{2}[/tex]

Subtracting 144 from both sides:

[tex]25 = side^{2}[/tex]

Reversing the sides:

[tex]side^{2}=25[/tex]

[tex]\sqrt{side^{2}}= \±\sqrt{25}[/tex]

[tex]side = \±\sqrt{25}[/tex]

[tex]side = \±5[/tex]

Since a distance can't be negative:

[tex]side=5[/tex]

The third side is 5 cm.

Answer:  see proof below

Step-by-step explanation:

Proof LHS → RHS

[tex]\dfrac{1}{3-2\sqrt2}-\dfrac{1}{2\sqrt2-7}+\dfrac{1}{\sqrt7-\sqrt6}-\dfrac{1}{\sqrt6-\sqrt5}+\dfrac{1}{\sqrt5-2}\\\\\\\text{Rationalize the denominator (multiply by same numbers but opposite sign)}\\\dfrac{3+2\sqrt2}{1}-\dfrac{2\sqrt2+7}{1}+\dfrac{\sqrt7+\sqrt6}{1}+\dfrac{\sqrt6+\sqrt5}{1}+\dfrac{\sqrt5+2}{1}\\\\\\\text{Group like terms:}\\3+(2\sqrt2-2\sqrt2)+(-\sqrt7+\sqrt7)+(\sqrt6-\sqrt6)+(-\sqrt5+\sqrt5)+2\\\\\\\text{Simplify:}\\3 + 0+0+0+0+2 \\= 5[/tex]

LHS = RHS:  5 = 5  [tex]\checkmark[/tex]

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A sin B = cos (A - B) - cos (A + B)

2 sin A cos B = sin (A + B) + sin (A - B)

Use the Unit Circle to evaluate: cos 120 = -1/2    &      sin 60 = √3/2

Proof LHS → RHS

LHS:                                            sin 20 · sin 40 · sin 80

Regroup:                              (1/2) sin 20 · 2 sin 40 · sin 80

Product to Sum Identity:     (1/2) sin 20 [cos(80-40) - cos (80+40)]

Simplify:                                (1/2) sin 20 [cos 40 - cos 120]

Unit Circle:                            (1/2) sin 20 [cos 40 + (1/2)]

Distribute:                             (1/2) sin 20 cos 40 + (1/4) sin 20

Product to Sum Identity:       (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20

Simplify:                                 (1/4)[sin 60 + sin (-20)] + (1/4) sin 20

                                           = (1/4)[sin 60 - sin 20] + (1/4) sin 20

Unit Circle:                             (1/4)[(√3/2) - sin 20] + (1/4) sin 20

Distribute:                              (√3/8) -  (1/4) sin 20 + (1/4) sin 20

Simplify:                                  √3/8

LHS = RHS:   √3/8 = √3/8  [tex]\checkmark[/tex]

We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.

[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]

[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]

[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

And if we further simplify the expression, we should receive the following...

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]

Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.

The rule we use here is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

If the font size is too small, then it says (a^b)/(a^c) = a^(b-c)

We subtract the exponents when dividing exponentials like this. The bases must be the same.

So this means the exponents 13 and 3 subtract to get 13-3 = 10

We either have an exponent of "13-3" or an exponent of "10" as an equivalent expression. The base stays at 2 the entire time.

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

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Answer:

y=kx

20=10k

k=20/10

k=2

Answer:

28

Step-by-step explanation:

[tex]5x -7\\x =7[/tex]

Substitute 7 for x in the given equation

[tex]5x -7\\\\= 5(7) -7\\\\= 35-7\\\\= 28[/tex]

Answer:

28 is the answer

Step-by-step explanation:

5(7)= 35

35-7=28

Answer:

B. No solutions

Step-by-step explanation:

8x+2y=14

8x+2y=4

These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y).  The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.

Answer:

b

..........

Step-by-step explanation:

0≠14-4

...

Answer:

x=2

Step-by-step explanation:

1+4x=7+x

↦4x-x=7-1

↦3x=6

↦x=6/3

↦x=2

.°. x=2

Hope you understand it

Answer:

x = 2

Step-by-step explanation:

For this equation, we simply need to solve for x.

1 + 4x = 7 + x

1 + -1 + 4x = 7 + -1 + x

4x = 6 + x

4x + -x = 6 + x + -x

3x = 6

3x * (1/3) = 6 * (1/3)

x = 2

So the solution to this equation is x = 2.

Cheers.

Answer:

A

Step-by-step explanation:

125 is the amount of discount, so for example if p was 500 and discounted by 125 (p-125), you'd get 375(example of reduced price).

Answer:

(x + 5)(x + 1)

Step-by-step explanation:

First, notice that because this is a trinomial (has three terms separated by some operation), we will use a basic factoring technique.

The parent function for a quadratic is ax²+bx+c=0.

Therefore, the factoring technique is to see what factors of C add up to give you B.

Factors of 5 are 5 and 1, and 5 + 1 = 6.

So, therefore, your factors are (x + 5) (x + 1).

Performing the FOIL function on this gives you x² + 1x + 5x + 5. Simplify by adding like terms and your final answer is x² + 6x + 5.

Answer:The graph f(x)   is shifted 2 units to left and shifted down by 6 units to form the graph r(x) .

Step-by-step explanation:

Answer:

B)1-x≤-1 OR 1-x≥1

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Step-by-step explanation:

[tex]2|1-x|+1\geq 3[/tex]

[tex]2|1-x|\geq 2[/tex]

[tex]|1-x|\geq 1[/tex]

Once we have an absolute value inequality, remember that:

For a > 0

[tex]\boxed{\text{If } |x|\leq a \Longleftrightarrow -a\leq x \leq a}[/tex]

[tex]\boxed{\text{If } |x|\geq a \Longleftrightarrow x\leq -a \text{ or } x\geq a }[/tex]

Therefore,

[tex]1-x\le -1\quad \text{or}\quad 1-x\ge 1[/tex]

Solving

[tex]1-x\le -1 \Longleftrightarrow x\geq 2[/tex]

[tex]1-x\ge 1 \Longleftrightarrow x\leq 0[/tex]

We have

[tex]x\geq 2 \quad \cup \quad x \leq 0[/tex]

[tex](-\infty, 0] \cup [2, \infty)[/tex]

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Answer:

F: 48

Step-by-step explanation:

Let x be the length of the side of the cube. RQ can be expressed as a triangle consisting of a diagonal of a face of the cube and the side length x. By the pythagorean theorem, we know that a^2+b^2=c^2. So, we can express the diagonal as x^2+x^2=c^2, giving us the value of c to be [tex]x\sqrt{2}[/tex]. Now, we can once again use the pythagorean theorem to find RQ^2=2x^2+x^2=3x^2, so RQ=[tex]x\sqrt{3}[/tex]=12, so x=[tex]4\sqrt{3}[/tex]. To find the area of the shaded part, we multiply the length times width which gives us [tex](4\sqrt{3})^2=48[/tex]. So, the area of the shaded face of the cube is F: 48.

Answer:

x = 1

y = 5

Step-by-step explanation:

5x - 2y = -5

5x + 6y = 35

=> 5x + 6y = 35

=> 5x - 5x + 6y = 35 - 5x

=> 6y = 35 - 5x

=> 6y/6 = 35/6 - 5/6x

=> y = 35/6 - 5/6x

=> 5x - 2 (35/6 - 5/6x) = -5

=> 5x - 35/3 + 5/3x = -5

=> 15/3x -35/3 + 5/3 = -15/3

=> 20/3x -35/3 = -15/3

=> 20/3x -35/3 + 35/3 = -15/3 + 35/3

=> 20/3x = 20/3

=> 20/3x * 3 = 20/3 * 3

=> 20x = 20

=> 20x/20 = 20/20

=> x = 1

=> 5x + 6y = 35

=> 5(1) + 6y = 35

=> 5 + 6y = 35

=> 5 -5 + 6y = 35 -5

=> 6y = 30

=> 6y/6 = 30/6

=> y = 5

So, x = 1

     y = 5

Answer:

2x + 22

Explanation

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

Factor 2 out of  the Expression

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

- × - is +

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

Collect like terms

2(x+7+4)

2(x+11)

2x + 22

Answer:  0.753.

Step-by-step explanation:

The value of the correlation coefficient is denoted by 'r'. It is used to describe the strength and direction of the relationship between two variables.

Given: The relationship between the number of hours a person practices a task and the time it takes them to complete the task is calculated to have R-sq = 56.7%.

= 0.567

Then, [tex]r=\sqrt{R^2}[/tex]

[tex]=\sqrt{0.567}\approx0.753[/tex]

Hence, the value of the correlation coefficient is 0.753.

Answer:

Step-by-step explanation:

since it is 100% and the pie chart circle is 360°, then for each % it will be 3.6°

applying this into drawing, just times 3.6° to the percentage and then get the final angle for the data.

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

if you don't need to be so concise, just see as you fit

☆ The relation between x and y is y = a cos x° +b

Taking 1st condition from the table .

→ x = 0 and y = 9

→ y = a + cos 0° + b

→ 9 = a + cos 0° + b

☆ We know that cos 0° = 1

→ 9 = a(1) + b

Now taking other condition

→ x = 90° and y = 1

→ y = a cos 90° + b

→ 1 = a cos 90° + b

☆ We know that cos 90° is 0

→ 1 = a(0) + b

Putting the value of b in equation 1st .

→ 9 = a + 1

→ a = 8 .

Now taking the value of x according to the question .

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

So the answer is 4√2+1

Answer:

160

Step-by-step explanation:

Divide 24 by 15 percent (.15)

24/.15

=160

Answer:

160

Step-by-step explanation:

from the question, we know that 24 balloons are 15% of total.

make equation:

[tex]\frac{15}{100} =\frac{24}{x}[/tex]

calculate:

100*24/15=160 balloons

Answer: $1.8

Step-by-step explanation:

From the question, we are informed that the price for 2 kilograms of ham is $36.00. We should remember that 1000 gram = 1 kilogram; therefore, 2 kilograms = 2000 grams.

The cost of a gram of ham will then be:

= $36.00/2000

= $0.018

The unit price of ham per 100 grams will be:

= 100 × 0.018

= $1.8

Answer:

x=35°

Step-by-step explanation:

So first, recall that the interior angles of a triangle must total 180°.

The sum of the angles for the given triangle can be described by:

[tex]110+x+x\\=2x+110[/tex]

Since the total must equal 180°, set the expression equal to 180°.

[tex]2x+110=180[/tex]

To find the value of x, we just need to solve for x.

To start, subtract 110 from both sides. The 110s on the left cancels:

[tex](2x+110)-110=(180)-110\\2x=70[/tex]

Now, divide both sides by 2. The 2s on the left cancel.

[tex]\frac{(2x)}{2}=\frac{(70)}{2}\\ x=35 \textdegree[/tex]

Therefore, the value of x is 35°.

Step-by-step explanation:

[tex]180 - 110 = 60 - 2 = 30 \\ so \: x = 30[/tex]

Answer:

Domain= possible x values

Range= possible y values.

Domain= all real numbers

Range= all numbers greater than -2.

Let me know if this helps :)

Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph

" Domain of exponential function y = aˣ is all the values of x and range is the all calculated values of 'y' after substituting value of x."

General exponential function

y = aˣ

According to the graph,

Given exponential function,

y = 3ˣ - 2

x represents the domain of the function.

y represents the range of the function

compare with exponential equation

a= 3 >1

As the value of 'x' increases value of 'y' moves to infinity.

Therefore, value of y defined for all the values of 'x'.

Therefore,

Domain is set of all real numbers.

Function y is transformed by -2.

Substitute x=0 in y = 3ˣ-2 we get,

y = -2

Therefore,

Range = (-2 , ∞)

Hence, Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph.

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Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)