In a sample of 30000 first borne babies, 6 were found to have Down syndrome. Find the empirical probability thay a famili’s first child will be born with this sydrome

Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

From the given figure

The 2 triangles have one equal angle of measure 88

The side of length 3 and the side of length 1 have a ratio 3: 1

The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1

That means we have one equal angle and two proportional sides

Since the angle is between the proportional sides, then

The 2 triangles are similar by the SAS postulate

Answer B

To find the area of a circle given its radius,

The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;

The area of the circle is 200.96 inches squared

Answer:

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

Step 1

Given;

Required; To factor it out into products of prime factors.

Step 2

A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number is a prime factor. Examples of prime factors are; 1,2,3,5 etc. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.

Step 3

Find the prime factor of 540

Therefore, the prime pr

16 ounces is equivalent to 453.6g when rounding to nearest tenth.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here the given data is :

1 ounce = 28.35 grams

Conversion of ounce to grams :

This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.

The easiest way about this is simply multiply 16 by 28.25g

1 ounce = 28.35 grams

16 ounce = x

x = 16 x 28.25

x= 453.6 g

From the calculations above, 16 ounces is equivalent to 453.6g.

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The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given algebraic expression is:

[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]

Apply the property of a⁻ˣ = 1/aˣ in the above term,

[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Here 64 = 4×4×4 = 4³

[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Apply the cube root property and Multiply the exponent of the variable x to 1/3

[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]

Apply the multiplication operation to the exponent of the variable x to get the solution.

[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]

Hence, the correct answer would be an option (B)

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A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.

First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows

This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY

Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.

Now, we use the slope-point formula to find the equation for the perpendicular bisector.

Where we replace the slope -3 and the point (-3,3).

The value of interior angle x for the given pentagon if found as 88 degrees.

For the given question;

The exterior angles of the pentagon are given in figure.

Find all the interior angles for given angles using linear pair as all are straight lines.

The sum of all the interior angle of pentagon is 540.

Thus,

118 + 147 + 66 + 121 + x = 540

x = 540 - 452

x = 88

Thus, the value of interior angle x for the given pentagon if found as 88 degrees.

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The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.

This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.

The cost of all the items is equal to $535

s + p + j + t = $535                 ......(1)

Sneakers cost $5 less than the jacket

s = j - $5                                 ......(2)

Pants cost $50 less than the jacket

p = j - $50                              ......(3)

T-shirt cost $10 less than three times the jacket

t = 3j - $10                              ......(4)

Putting the values of equation (2), (3) and (4) in equation (1)

j - $5 + j - $50 + j + 3j - $10 = $535

6j = $535 + $65

=> 6j = $600

=> j = $100 which is the cost Jacket.

Now, s = $100 - $5 = $95 which is the cost of Sneakers.

p = $100 - $50 = $50 which is the cost of pair of pants.

t = $300 - $10 = $290 which is the cost of t-shirt.

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Answer: 40000

+ 5000

+ 800

+ 3

Step-by-step explanation:

The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.

Answer:

You were right. The answer is (C)

Step-by-step explanation:

Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.

Let x represent the number of pounds of coffee that she bought.

From the information given,

cost per pound of coffee = $8.73

Cost of x pounds of coffee = 8.73 * x = 8.73x

Initial amount that she had = $90

After spencing $8.73x, the amount left is $63.81. This means that

90 - 8.73x = 63.81

8.73x = 90 - 63.81

8.73x = 26.19

x = 26.19/8.73

x = 3

She bought 3 pounds of coffee

Answer: x < -4

Step-by-step explanation:

➜ First thing we notice is the open circle. This means we will use either < or >

➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <

➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.

    The last thing to do is to write the inequality using the parts we pointed out above:

x < -4

Equation for the line in point-slope form is 5x + 6y = 6.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Given Data

P(6, -3)

y =1/2 x + 2

When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.

So, the points are (6,-3) and (0,2)

Formula

y₂ - y₁ = m(x₂ - x₁)

slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹

m= [tex]\frac{2-(-3)}{0-6}[/tex]

m = -[tex]\frac{5}{6}[/tex]

Equation

y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)

y +5 = -[tex]\frac{5}{6}[/tex]x + 6

y + 5 = -[tex]\frac{5+36 }{6}[/tex]

6y + 30 = -5x + 36

5x + 6y = 6

Equation for the line in point-slope form is 5x + 6y = 6.

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Answer:

This is an isosceles right triangle, so

x = 45°.

Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]

Step-by-step explanation:

The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].

Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].

Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].

Answer:

See below

Step-by-step explanation:

Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner.  Then translate down and right until rectangle A in over rectangle B

The graph of the figure is attached below.

Given equation of line:-

y = (-3/2)x - 1

First we will find the x and y intercepts of the line to plot in the line.

Putting x = 0 to find the y-intercept, we get,

y = (-3/2)(0) - 1

y = -1

Hence, the coordinates of the point are (0,-1).

Putting y = 0 to find the x-intercept, we get,

0 = (-3/2)x - 1

1 = (-3/2)x

x = -2/3

Hence, the coordinates of the point are (-2/3,0).

We can find another point on the line.

Putting x = 2, we get,

y = (-3/2)(2) - 1

y = -3 - 1

y = -4

Hence, the coordinates of the point are (2,-4).

Plotting these in a graph, we can get a straight line.

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Answer:

 65 pairs

Step-by-step explanation:

Black makes up 5/(5+8) = 5/13 of the total order, so ...

 (5/13)(169 pairs) = 65 pairs

Vinny will order 65 pairs of black high tops.

Answer:

Step-by-step explanation:

V = 4/3.pi.r^3

36 = 4/3 pi r^3

8.6 = r^3

r = 2 in

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

Area of sphere :

A = 4.pi.r^2

A = 4 . Pi . 2^2

A = 16 Pi

A = 50.26 in

Answer:  600,000 + 70,000 + 5,000 + 400 + 30 + 2

Explanation:

Each digit forms a different number depending on its place value.

The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well

First, lets perform each transformation and then take a look at its graph:

1.

The only etiquette that matches this plot is: Function decreases as x increases

2.

The only etiquette that matches this plot is: x-intercept at (1.5 , 0)

3.

The only etiquette that matches this plot is: Asymptote of x = 0

The lengths of the major and minor axis of the ellipse, are;  4√6 and 4√3 respectively.

An ellipse describes the locus of a point on a curve, such that the sum of the distance between two focal points from the points on the curve is a constant.

The function of the ellipse can be calculated as follows;

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Where (h, k) = The coordinates of the center of the ellipse

a = The length of the semi-major axis

b = The length of the semi-minor axis

Now,

[tex]\dfrac{(x-3)^2}{12} + \dfrac{(y+ 4)^2}{24} =1[/tex]

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2√6

b = √(12) = 2√3

The length of the major axis is 2a

The length of the minor axis is 2b

The length of the major axis will be;

2a = 2 × 2√6 = 4√6

The length of the minor axis will be;

2b = 2 × 2√3 = 4√3

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Given:

• AD = 3

• DC = 27

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

Where BD is the altitude.

Cross multiply:

Plug in the values and solve for x:

Take the square root of both sides:

Therefore, the value of x is 6 .

ANSWER:

d. 6

Given the expression;

Step 1:

Step 2:

Step 3:

The solution is;

Answer:

the probability is 2/8

Step-by-step explanation: