answer...............

Step-by-step explanation:

in general we would need a probabilty table or a probability calculator service on the internet.

but in this case we know.

the man value is 64. and the standard deviation is 6.

so, one standard deviation +/- interval from the mean value is 70 and 58.

and the interval of 2 standard deviations from the mean value is 76 and 52.

and 64 and 76 are exactly the limits we are asked for.

so, remember the normal distribution rule :

68% are within 1 standard deviation.

95% are within 2 standard deviations.

99.7% are within 3 standard deviations.

and 50% are below (and also above) the mean value.

so, we know, 50% of the 350 (= 175) students scored below 64.

95% of the students scored between 76 and 52. as there are 5% left, half of these 5% (= 2.5%) scored even below 52).

so, 95% + 2.5% = 97.5% of the 350 (= 341.25) students scored below 76.

therefore, the number of students that scored between 64 and 76 is

341.25 - 175 = 166.25 ≈ 166

Answer:

x > 9

Step-by-step explanation:

for this inequality, we want to isolate x, so that we know the inequality of x

5x + 3 > 48

     - 3      -3        {subtract 3 from both sides to get x alone}

5x > 45

/5      /5                {divide both sides by 5 to find 1x}

x > 9

So , x > 9 is the inequality in terms of x {is the solution}

hope this helps! :)

Answer:

[tex]\huge\boxed{\sf x > 9}[/tex]

Step-by-step explanation:

5x + 3 > 48

Subtract 3 to both sides

5x > 48 - 3

5x > 45

Divide 5 to both sides

x > 9

[tex]\rule[225]{225}{2}[/tex]

Answer:

Option B is correct

Answer:

B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries

Answer:

The dog is 16 years old.

Step-by-step explanation:

X/4 + 6 = X/8 + 8

X/4-X/8 = 8-6

0.125X = 2

X = 2/0.125

X = 16

Answer:

16 years old

Step-by-step explanation

Dividing the dog’s age by 4 and adding 6

D÷4  + 6

dividing the dog’s age by 8 and adding 8

D÷8  + 8

equating both

D÷4  + 6 = D÷8 + 8

=> D÷4 - D÷8  = 2

multiplying by 8 both sides

=> 2D - D = 16

=> D = 16

hence, the dog is 16 years old

Answer:

6 green marbles should be added.

Step-by-step explanation:

If the probability of drawing a blue marble from 18 marbles is 2/3 then there are 12 blue marbles because 18 times 2/3 is 12. This means that to reduce this probability to 1/2 you need to add 6 more marbles to the total amount to get it to 24. Now the probability of getting a blue marble is 12/24 which is 1/2.

Answer:

A

Step-by-step explanation:

Given:

[tex]8-3x > 2(3x-5)[/tex]

Simplify by distributing:

[tex]8-3x > 6x-10[/tex]

Add 10 to left side and add 3x to the right side:

[tex]18 > 9x[/tex]

Answer:

1/6

Step-by-step explanation:

-2 - (-2 1/6)

multiply the number in the parentheses by -1

-2 + 2 1/6

-2 + 2  cancels out

Leaving 1/6 as your answer.

Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

n = 40, p = 0.07.

The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242[/tex]

0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

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As IJK is isosceles

Hypotenuse must not counted counted among equal sides so

Apply roots

Option C

Let's see

[tex]\boxed{\sf log_aa=1}[/tex]

Now

[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]

[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]

[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]

[tex]\\ \rm\Rrightarrow -4[/tex]

Answer:

This has already been answered correctly, but I'll add an additional perspective.  The log of (0.0001 to the base 10 is -4.

Step-by-step explanation:

log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.

[tex]10^{0}[/tex] = 1

[tex]10^{1}[/tex] = 10

[tex]10^{-1}[/tex] = 0.1

[tex]10^{-2}[/tex] = 0.01

[tex]10^{-4}[/tex] = 0.0001

The log of (0.0001) to the base 10 is -4.

Answer: No solution

Step-by-step explanation:

Both of these equations have the same number as to coefficient of x (-6) but have a different constant (-8 and 8). This means that there are no solutions to this system of equations.

Answer: $625

Step-by-step explanation:

Total beverage sales = $2,500

Beverage cost = 25%

So, $2,500 x 25% = $2,500 x 0.25 = $625

#1

Correct version

[tex]\\ \rm\Rrightarrow (x^3+2x^2-x)-(3x^3-3x^2+2x-4)[/tex]

[tex]\\ \rm\Rrightarrow x^3+2x^2-x-3x^3+3x^2-2x+4[/tex]

[tex]\\ \rm\Rrightarrow x^3+5x^2-3x+4[/tex]

#2

[tex]\\ \rm\Rrightarrow (x^2-3x+2)(x+1)[/tex]

[tex]\\ \rm\Rrightarrow x(x^2-3x+2)+x^2-3x+2[/tex]

[tex]\\ \rm\Rrightarrow x^3-3x^2+2x+x^2-3x+2[/tex]

[tex]\\ \rm\Rrightarrow x^3-2x^2-x+2[/tex]

The path straight to the end of the hike is 6 km farther than past the scenic lookout.

The map is not given, but the question can still be answered

From the question, the positions are given as::

Maria = (4, -4)

Scenic = (2, 3)

End = (-5, 5)

The distance between Maria and the end point is calculated using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]Route\ 1 = \sqrt{(4 + 5)^2 + (-4 -5)^2}[/tex]

[tex]Route\ 1 = 13[/tex]

The distance between Maria and the scenic lookout is calculated using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]Route\ 2 = \sqrt{(4 - 2)^2 + (-4 -3)^2}[/tex]

[tex]Route\ 2 = 7[/tex]

The distance between both routes is:

Distance = 13 - 7

Evaluate

Distance = 6

Hence, the path straight to the end of the hike is 6 km farther than past the scenic lookout.

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The coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2). Then the correct option is D.

The complete options are given below.

1. (-11/2) -(11/2)

2.(-5/2)-(3/2)

3.(-5/2-(11/2)

4. (-11/2) -(-3/2)

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The end points are given below.

(-3, -7) and (-8, 4)

We have

(x₁, y₁) = (-3, -7)

(x₂, y₂) = (-8, 4)

Then the mid-point will be

x = (- 3 - 8) / 2

x = -11 / 2

y = (-7 + 4) / 2

y = -3/2

Then the coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2).

Then the correct option is D.

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Answer:

C  : (4,8)

Step-by-step explanation:

The equation y = (1/2) x

Or, 2y = x ==> x = 2y
means that, for any value of x, the y value must be one-half that value or, in other words, for any value of y, x must be twice the value of y

A, B and D will satisfy the above equation if you plug in values of x and y given

In C we have x = 4 and y =8 so x = y/2 NOT 2y

Answer:

A 3 and 8

Step-by-step explanation:

if a/b=c/d, the extremes are "a" and "d". The means would then be "b" and "c"

The extremes of the proportion are 3 and 8.

To find the extremes of a proportion, we need to identify the numbers that are positioned at the far ends of the proportion. In the given proportion:

3/4 = 6/8

The numerator of the first fraction, 3, and the denominator of the second fraction, 8, are the extremes. These numbers form the far ends of the proportion.

Therefore, the extremes of the proportion are 3 and 8.

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Answer:

80x = y

Step-by-step explanation:

Answer:

1. [tex]x = 2.45s[/tex]

2. The diving board is 45 ft high.

Step-by-step explanation:

• When Lindsey is 30 feet in the air, y = 30.

[tex]30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\[/tex]

Using quadratic formula, solve for x:

[tex]x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}[/tex]

[tex]x = 2.45s[/tex]

• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.

When she is standing on the board, x = 0 as no time has passed after jumping.

[tex]y = -16(0)^2 + 33(0) +45\\\\y = 45 ft[/tex]

Answer:

(a)9×3=37' 97 and 8 are factors of 37

Answer:

x ≈ 1.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{0.8}{x}[/tex] ( multiply both sides by x )

x × cos41° = 0.8 ( divide both sides by cos41° )

x = [tex]\frac{0.8}{cos41}[/tex] ≈ 1.1 ( to the nearest tenth )

The transformation is non-rigid because the side lengths are not preserved.

The drop-down menus and the image of the triangles are not given.

However, the question can still be solved using the available parameters.

The given parameters are:

Pre-image: 6, 10, 8

Image: 3, 5, 8

See that the side lengths of the image and the pre-image are not the same

This means that the transformation is a non-rigid transformation

Hence, the complete statement is the transformation is non-rigid because the side lengths are not preserved.

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Answer:

$72

Step-by-step explanation:

Answer: a

Step-by-step explanation:

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

Therefore, the HCF is a.

Answer:

a

Step-by-step explanation:

Factorizing both terms :

The HCF of the terms is a.

Answer:

2/5

Step-by-step explanation:

22/11=2

55/11=5

The  is probability P(B|A) expressed in simplest form is 1/2 (Option B) See computation below.

P (A) = [[tex][\mathrm{C}_{5}^{1} \mathrm{C}_{8}^{1}]/ \mathrm{A}_{9}^{2}[/tex]

= ('5 x 8)/(9 x 8)

P (A) = '5/9

P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]

= ('5 x 4)/(9 x 8)

= '5/18

P(B|A) = P (AB)/P(A)

= ('5/18)/('5/9)

P(B|A)  = 1/2

From the above we already have P (AB)

this is given as

P (AB) = [tex][\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1}]/ \mathrm{A}_{9}^{2}[/tex]

= ('5 x 4)/(9 x 8)

P(AB) = '5/18

Note that:

Event A = drawing a white marble on the first draw

Event B = drawing a red marble on the second draw

P(A) = 8/13; while

P (B) = (5/12) because the first marble was not replaced, thus reducing th sample to 12.

Thus

P(A and B) = P(A)*P(B) = 8/13 * 5/12

P(A and B) =  10/39 (Option B)

Event A - Probability of Drawing a Green Marble is 8/20

Event B - Probability of Drawing a Blue Marble is 5/19

Thus P(B|A) = (8/20) * (5/19)

= [tex]\frac{8 * 5 }{20 * 19}[/tex]

= 40/380; divide numerator and denominator by 20

P(B|A) = 2/19 (Option A)

Event A = Probability of Drawing a red ball = 3/12

Event A = Probability of Drawing a pink ball without replacing the read in Event A = 3/11

Thus P (B and A) =

3/12 x 3/11

P (B and A) = 3/44 (Option A)

The conditions given are as follows:

The sum total of ways thus is

9 x 8

= 72 ways........X

Recall that

Event A is defined as selecting 8 as the first numeral

The only way to select this is one way

Event B is defined as choosing a number less than 6 as the second digit, that is 1, 2, 3, 4, 5

Thus, the possible number of ways to fill second digit = 5/8

Thus, the possible number of ways to form two digits 'AnB' =
('AnB') = 1 x 5 = 5 .................y

Hence Probability (AnB) = 5/72 (Option B)

Given that the non-zero digits are in a combination are not repeated and range from 3 through 8, thus the odd numbers between 3 and 8 are:

3, 5, 7

total numbers is 3, 4, 5, 6, 7, 8

Hence; Event A = choosing an odd number for the first digit = 3/6

Event B = choosing an odd number for the second digit (recall that the numbers are not repeated) = 2/5

= [tex]\frac{2*3}{3*6}[/tex]

= 6/30

= 1/5 (Option A)

If a combination is picked at random with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?

Event A = the first digit is an odd number

Event B = the second digit is an odd number

The numbers from 2 to 9 are:
2,3,4,5,6,7,8,9

The odd numbers between 2 and 9 are:

3,5,7,9

P (A) = 4/8

P (B) = 3/7

P(B|A) = (3/7)/(4/8)

P(B|A) = 3/7

Event A = drawing a white tile on the first draw

Event B = drawing a purple tile on the second draw

|n| = 15 * 14 = 210

| A| = 3*14 = 42

| AnB| = 3*7 = 21

P (A) = 42/210 = 6/30

P (AnB) = 21/210 = 1/10

P(B|A) = (1/10)/6/30)

P(B|A) = 1/10 * 30/6

P(B|A) = 30/60
P(B|A) = 1/2 (Option D)

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Answer:

-5x=-23

Or

X=23/5

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

8x-5(x-3) = 18

The first step is to distribute

8x -5x+15 = 18

Combine like terms

3x+15 = 18

Subtract 15 from each side

3x+15-15=18-15

3x=3

Divide by 3

3x/3 =3/3

x=1