The probability that a family’s first child will be born with down syndrome is 1/5000
Number of first borne babies = 30000
Number of first borne babies having Down syndrome = 6
Probability is defined as the ratio of number of favorable outcomes to the total outcome.
Probability = (number of favorable outcomes)/(total outcome)
We have to find the probability that a family’s first child will be born with down syndrome. So, Number of first borne babies having Down syndrome is equal to the total number of favorable outcomes and Number of first borne babies will also be equal to total outcome. Hence we can write,
Probability = (number of favorable outcomes)/(total outcome)
Probability = 6/30000
Probability = 1/5000
So, the required probability is 1/5000.
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What is the Expanded form of 45,803
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.
Write the equation of the perpendicular bisector of XY if endpoint X is at (-9,1) and endpoint Y is at (3,5). A) y = -X B) y = 3x - 6 C) y = -3x - 6 D) y = 3x + 12
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
[tex]\begin{gathered} M=(\frac{-9+3}{2},\frac{1+5}{2}) \\ M=(\frac{-6}{2},\frac{6}{2}) \\ M=(-3,3) \end{gathered}[/tex]This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-1}{3-(-9)}=\frac{4}{3+9}=\frac{4}{12} \\ m=\frac{1}{3} \end{gathered}[/tex]Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.
[tex]\begin{gathered} m_1\cdot m=-1 \\ m_1=\frac{-1}{m} \\ m_1=-\frac{1}{\frac{1}{3}}=-3 \end{gathered}[/tex]Now, we use the slope-point formula to find the equation for the perpendicular bisector.
[tex]y-y_1=m(x-x_1)[/tex]Where we replace the slope -3 and the point (-3,3).
[tex]\begin{gathered} y-3=-3(x-(-3)) \\ y-3=-3x-9 \\ y=-3x-9+3 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the right answer is C.Which graph shows a proportional relationship between the number of hours of renting a pair of roller skates and the total amount spent to
rent the roller skates?
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.
number in expended form
675,432
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
One ounce is 28.35 grams. Convert16 ounces into grams. Round to nearest tenth
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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Find the area of this circle.Use 3.14 to approximate n.Α = πη28 inA = [ ? ] in?
To find the area of a circle given its radius,
[tex]\text{Area}=\pi\times r^2[/tex]The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;
[tex]\begin{gathered} \text{Area}=3.14\times8^2 \\ \text{Area}=3.14\times64 \\ \text{Area}=200.96in^2 \end{gathered}[/tex]The area of the circle is 200.96 inches squared
Y=-3/2x-1. Graph integers?
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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45. Write an inequality that represents the graph. Explain it step by step please.
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
radicals that have the same index and the same radicand is this true
Given the expression;
[tex]\frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}[/tex]Step 1:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2} \\ \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} \sqrt[]{2}\times\sqrt[]{2}=2 \\ \sqrt[]{7}\times\sqrt[]{7}=7 \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{7}\times\sqrt[]{2}=\frac{2\times7}{7} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=\frac{2\times7}{7} \\ \frac{\sqrt[]{2}}{7}\times\sqrt[]{7}\times\sqrt[]{14}=2 \end{gathered}[/tex]The solution is;
[tex]2[/tex]in the standard (x y) coordínate plane what’s the slope of a line that’s perpendicular to
Answer:
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
Stanley bought sneakers, a pair of pants, a t-shirt and a jacket for $535.00. The sneakers cost 5 less than the jacket, the pants cost $50 less than the jacket, and the t-shirt cost $10 less than three times the jacket. Find the cost of each item.
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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This is my practice review me I have unlimited attempts. I need help with this question
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
Carolyn leases a new Hyundai Elantra by paying $2600 up front and $170 a month over three years. The lease also stipulates he will be charged $0.12 per mile for every mile over 36,000. If she puts 40,693 miles on the car, what will be the total cost of the lease?
Find the constant of proportionality for the proportional relationship between weight and cost shown in the table. Then find the cost of 10 oz of green beans. Cost of Green Beans Weight (oz) Cost($) 8 1.12 12 1.68 16 2.24 The constant of proportionality is $0.14 per ounce. The cost of 10 oz of green beans is $ VE S 4.1 More 10 Enter your answer in each of the answer boxes. Next Back of 16 Question 1 Review progress
Need help with a geometry problem. it is a scalene triangle with a parallel line through it which is x+1. the base is going to be 3x-2 and is parallel with x+1. on the right of x+1 there should be 12 at the top then 20 will split it . I need to solve for x
Does anyone understand this geometry question
Answer:
This is an isosceles right triangle, so
x = 45°.
Select the reason why these triangles are similar. If they are not, select "Not similar". 88 3 2 88 B. SAS A. AA D. Not similar C. SSS
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
Factor 540 into product of prime factors
Step 1
Given;
[tex]540[/tex]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
Describe a series of transformations Matt can perform to decide if the two windows are congruent
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
Given f(x) = ln(x), which is the correct answers ?
First, lets perform each transformation and then take a look at its graph:
1.
[tex]\begin{gathered} g(x)=-\frac{1}{2}f(x-2) \\ \\ \Rightarrow g(x)=-\frac{1}{2}\ln (x-2) \end{gathered}[/tex]The only etiquette that matches this plot is: Function decreases as x increases
2.
[tex]\begin{gathered} h(x)=f(x-\frac{1}{2}) \\ \\ \Rightarrow h(x)=\ln (x-\frac{1}{2}) \end{gathered}[/tex]The only etiquette that matches this plot is: x-intercept at (1.5 , 0)
3.
[tex]\begin{gathered} j(x)=f(x)-\frac{1}{2} \\ \\ \Rightarrow j(x)=\ln (x)-\frac{1}{2} \end{gathered}[/tex]The only etiquette that matches this plot is: Asymptote of x = 0
Please help!
The volume of a sphere is 36 in³. What is the surface area?
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
vinny has decided to order high tops in black and white at a 5.8 ratio. he beleives he will need a total of 169 pairs. how many black high tops will he order
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.
What is the answer pleasee
The value of interior angle x for the given pentagon if found as 88 degrees.
What is termed as the pentagon?A pentagon is a two-dimensional polygon with 5 sides and 5 angles.This shape should have five sides and form a closed two-dimensional figure. A closed figure consists of each of its sides intersecting to form vertices.Five diagonals connect the five vertices to one‘s opposite vertices in a pentagon shape.Each interior angle in a regular pentagon is 108°, so each exterior angle is 72°.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.
180 - 62 = 118180 - 33 = 147180 - 114 = 66180 - 59 = 121The 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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P(6, -3); y =1/2 x + 2
Write an equation for the line in point-slope form.
Equation for the line in point-slope form is 5x + 6y = 6.
What is point slope form?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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six times the sum of four and a number is 7. what is the number?
Step-by-step explanation:
6×(4 + x) = 7
24 + 6x = 7
6x = -17
x = -17/6 = -2.833333333... = -2 5/6
HELP ME WITH IS PROBLEM THANK YOU
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)
What is the algebraic expression?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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What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
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].
MARKING BRAINLIEST What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
The lengths of the major and minor axis of the ellipse, are; 4√6 and 4√3 respectively.
What is an ellipse in coordinate geometry?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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From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Given:
• AD = 3
,• DC = 27
,• BD = x + 3
Let's solve for x.
To solve for x, apply the altitude formula:
[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]Where BD is the altitude.
Cross multiply:
[tex]BD^2=AD*DC[/tex]Plug in the values and solve for x:
[tex]\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}[/tex]Therefore, the value of x is 6 .
ANSWER:
d. 6
I need help with this question but no one is helping me! Can someone please help me
Answer:
the probability is 2/8
Step-by-step explanation: