Answer:
Step-by-step explanation:
[tex]x_{1}=7 \ ; y_{1} = -4\\\\x_{2} = -8 \ ; y_{2}=5\\\\CD = \sqrt{(-8-7)^{2}+(5-[-4])^{2}}\\\\=\sqrt{(-15)^{2}+(5+4)^{2}}\\\\=\sqrt{225+(9)^{2}}\\\\=\sqrt{225+81}\\\\=\sqrt{306}\\\\=\sqrt{3*3*2*17}\\\\=3\sqrt{34}[/tex]
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}-(y_{2}-y_{1})^{2}}[/tex]
In a family with 6 children, excluding multiple births, what is the probability of having 6 girls? Assume that a girl is as likely as a boy at each birth
Answer:
There's is a 25% chance on having all 6 births be girls. There is a 50-50 chance of a boy nor a girl. However, it is possible.
The probability of having 6 girls will be 1/64.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
In a family with 6 children, excluding multiple births.
Then the probability of having 6 girls will be
Leaving out the third gender, let's suppose that there is an equal chance of having a girl or a boy.
Any child can be either a boy or a girl, with each having equal probability of = 1/2
Each of these blank spaces can be filled in 2 ways : B and G (denoting 'B' and 'G' respectively)
Probability of first blank being a ''G' is = 1/2
and second blanks too being a “G” is = 1/2
Thus, probability of each blank individually being a “G” = 1/2
Thus, probability of all being a “G” = (1/2) (1/2) (1/2) (1/2) (1/2)* (1/2) = (1/2)6 = 1/64
Thus, probability of 6 children being all 6 girls = 1/64
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
besties can any of you help me on this because i do not know how to solve this
90 points for correct answers only
Answer:
[tex] D)\displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)[/tex]
Step-by-step explanation:
remember that
[tex] \displaystyle a \rm cis( \theta) \times b cis( \theta _{2}) = ab \cdot cis( \theta + \theta _{2})[/tex]
so we acquire:
[tex] \displaystyle \frac{ \sqrt{2} }{6} \rm cis \left( \frac{3\pi}{5} \right) \times \frac{ \sqrt{6} }{4} cis \left( \frac{2\pi}{3} \right) = \frac{ \sqrt{2} }{6} \times \frac{ \sqrt{6} }{4} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]
simplify the left hand side
[tex] \displaystyle \rm \frac{ \sqrt{12} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]
[tex] \displaystyle \rm \frac{2 \sqrt{3} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]
reduce fraction:
[tex] \displaystyle \rm \frac{ \sqrt{3} }{12} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)[/tex]
simplify addition:
[tex] \displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)[/tex]
hence our answer is D
Find three consecutive odd integers such that the sum of the first, two times the second and three times the third is 82.
A) 6x + 8 = 82
B) 6x + 16 = 82
C) 3x + 3 = 82
D) 3x + 6 = 82
Answer:
[tex]11, 13, 15[/tex]
B) 6x + 16 = 82
Note: I just kept my wrong approach.
Step-by-step explanation:
Let first define an odd integer.
Considering [tex]x\in\mathbb{Z}: 2k+1[/tex], [tex]x[/tex] is an odd integer.
Now, three consecutive odd integers are [tex]a_1 = 2k+1[/tex] , [tex]a_2 = 2k+3[/tex] and [tex]a_3 = 2k+5[/tex]
The sum of the first, two times the second and three times the third can be written as
[tex]a_1 + 2a_2 + 3a_3 = 2k+1 + 2(2k+3)+3(2k+5)[/tex]
Expanding and simplifying
[tex]2k+1 + 2(2k+3)+3(2k+5) = 2k+1 +4k+6+6k+15 = 12k+22[/tex]
This is what I have done initially, but considering [tex]x[/tex] to be an odd integer, three consecutive integers can be written as
[tex]x, x+2, x+4[/tex] such that [tex]x\in\mathbb{Z}: 2k+1[/tex]
Therefore,
[tex]x+2(x+2)+3(x+4)=82 \implies x+2x+4+3x+12 = 82 \implies 6x+16 = 82[/tex]
and [tex]6x+16 = 82 \implies 6x = 66 \implies x = 11[/tex]
The three consecutive odd integers such that the sum of the first, two times the second and three times the third is 82 are [tex]11, 13, 15[/tex]
What is the solution to the equation below? Round your answer to two
decimal places.
ex = 7.9
The value of x will be 2.067.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ eˣ = 7.9
Now,
Since, The expression is,
⇒ eˣ = 7.9
Take natural log both side, we get;
⇒ ln eˣ = ln 7.9
⇒ x = ln 79 - ln 10
⇒ x = 4.369 - 2.302
⇒ x = 2.067
Thus, The value of x = 2.067
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
The line represented by y = 3x − 2 and a line perpendicular to it intersect at R(3, 7). What is the equation of the perpendicular line? y = − negative start fraction one over three end fractionx + 4 y = − negative start fraction one over three end fractionx + 8 y = start fraction one over three end fractionx + 6 y = −3x + 7
Answer:
y= -1/3(x) + 8
Step-by-step explanation:
slope of the 1st line = 3
slope of the line perpendicular to the first is its opposite reciprocal, so
slope of the 2nd line = -1/3
now we have a point and the slope of the perpendicular line, so we use the point slope formula to get:
y-7=-1/3(x-3)
y= -1/3(x) + 1 + 7
y= -1/3(x) + 8
Dena borrowed $75,000 to buy a used car. The credit union charged 9% simple interest per year. She paid $2,025 in interest. For what period of time did she borrow the money?
Whats the...
Principal_____
Rate____
Intrest_____
PLSSSS ITS DUE IN 10 MINS
URGENT!! Use the compound interest formula A = P(1 + i)^n. Evaluate,
$1200 at 8.4% per year, compounded semi-annually, for 3 years 6 months
Answer:
$38,025.04
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 8.4/100
r = 0.084 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 1,200.00(1 + 0.084/2)(2)(42)
A = 1,200.00(1 + 0.042)(84)
A = $38,025.04
what is the area, in square feet, of the figure ?
Answer:
The answer is 24
Step-by-step explanation:
The first step is to multiply 6x3=18 Then you multiply 4x3=12/2=6 Then you add 18+6=24 Your welcome :D
Jiao works as an usher at a theater. The theater has 1000 seats that are accessed through five entrances. Each guest should use the entrance that's marked on their ticket. Jiao wants to test if the distribution of guests according to entrances matches the official distribution. He collects information about the number of guests that went through each entrance at a certain night. Here are the results: Entrance Expected # of people A 30% 398 B 30% 202 C 20% 205 D 10% 87 E 10% 108 Total 100% 1000 Jiao wants to perform a x' goodness-of-fit test to determine if these results suggest that the actual distribution of people doesn't match the expected distribution. # of people 398 202 205 87 108 1000 Jiao wants to perform a xa goodness-of-fit test to determine if these results suggest that the actua distribution of people doesn't match the expected distribution. What is the expected count of guests in entrance A in Jiao's sample? You may round your answer to the nearest hundredth.
Expected:______.
Show Calculator
Answer:
The answer is "300".
Step-by-step explanation:
Please find the complete solution in the attached file.
Answer:300
Step-by-step explanation:
uhhh i need answers on this, its hurting my BRAIN
Answer:
B. 1.8 x 10⁴
Step-by-step explanation:
6.3 / 3.5 = 1.8
10⁷/ 10³ = 10⁴
Therefor
6.3 x 10⁷ / 3.5 x 10³ = 1.8 x 10⁴
Answer:
B. 1.8 x 10⁴6.3 / 3.5 = 1.810⁷/ 10³ = 10⁴Therefor,6.3 x 10⁷ / 3.5 x 10³ =1.8 x 10⁴Hope it is helpful to you ☺️
When a particular type of thumbtack is dropped, it will land point up (A flat-top thumbtack resting on its flat top) or point down (A flat-top thumbtack resting on the edge of its flat top and the tip of its needle). This experiment was repeated times with the following results: point up: 48 times; point down: 52 times.
a. What is the experimental probability that a particular type of thumbtack will land point up?
b. What is the experimental probability that a particular type of thumbtack will land point down?
c. If the experiment was tried another 100 times would the same results occur? Why?
d. Is it expected that nearly the same results occur on a second trial? Why?
Answer:
0.48
0.52
No
Yes
Step-by-step explanation:
Result of experiment :
Point up = 48
Point down = 52
Total number of trials = 100
Recall :
Experimental probability = number of outcomes / number of trials
1.)
P(Landing point up) = 48 / 100 = 0.48
2.)
P(Landing point down) = 52 / 100 = 0.52
3.)
The same result will not occur has the outcomes of trials aren't fixed.
4.) Yes, nearly the same result could occur on the second trial, as the number of possible outcubes are just 2 and the number if trials is high.
Name two numbers that are 25 units from 3 on the number line.
Answer:
-22 and 28
Step-by-step explanation:
You move 25 units down from the number and 25 units up from the number.
PLS HELP!! need the answer asap
Answer:
1.) 113 degrees and 2.) 67 degrees
Step-by-step explanation:
(x + 33) + (x - 13) = 180
Add like terms:
2x + 20 = 180
2x = 160
x = 80
x + 33 =
80 + 33 =
113 =
x - 13 =
80 - 13 =
67 =
anyone know the missing angle ?
Answer:48.013
Step-by-step explanation: just found it
What is the radius of a sphere with a volume of 384\text{ ft}^3,384 ft
3
, to the nearest tenth of a foot?
Answer:
r≈4.5 ft
Step-by-step explanation:
r≈4.5 ft
\text{Volume of a Sphere:}
Volume of a Sphere:
V=\frac{4}{3}\pi r^3
V=
3
4
πr
3
384=
384=
\,\,\left(\frac{4}{3}\pi\right) r^3
(
3
4
π)r
3
384=
384=
\,\,(4.1887902)r^3
(4.1887902)r
3
Evaluate 4/3pi in calc
\frac{384}{4.1887902}=
4.1887902
384
=
\,\,\frac{(4.1887902)r^3}{4.1887902}
4.1887902
(4.1887902)r
3
Evaluate \frac{4}{3}\pi
3
4
π in calc
91.6732472=
91.6732472=
\,\,r^3
r
3
\sqrt[3]{91.6732472}=
3
91.6732472
=
\,\,\sqrt[3]{r^3}
3
r
3
Cube root both sides
4.5090066=
4.5090066=
\,\,r
r
\text{Final Answer:}
Final Answer:
r\approx 4.5\text{ ft}
r≈4.5 ft
Round to nearest tenth
The radius of the sphere is approximately 4.2 feet.
What is the volume of the sphere?To find the volume of a specific sphere, we need to know its radius. Once we have the radius, we can plug it into the formula and calculate the volume.
The formula for the volume of a sphere is:
V = (4/3) x π x r^3
where V is the volume of the sphere, r is its radius, and π is a mathematical constant approximately equal to 3.14.
We are given the volume of the sphere, so we can plug it into the formula and solve for the radius:
384 = (4/3) x π x r^3
Dividing both sides by (4/3) x π, we get:
r³ = 384 / ((4/3) x π)
r³ = 72.825
Taking the cube root of both sides, we get:
r ≈ 4.243
The radius of the sphere is approximately 4.2 feet.
To know more about volume follow
https://brainly.com/question/29091596
#SPJ2
Find the number of terms in this polynomial.
–3p9 − 7p
Answer:
ans: 2 terms
Step-by-step explanation:
1st term: -3p^9
2nd term: -7p
A ladder leans against the side of a house. The angle of elevation of the ladder is 65° when the bottom of the ladder is 14 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth. (PLZ HELP I LIST BRAINLIST AND LIKE COMMENTS)
Answer:
33.1
Step-by-step explanation:
cos(65)=14/x
x=33.1
Find the measure of the missing angle
Answer: a=
Answer:
Hello! answer: a = 68
Step-by-step explanation:
This is a complementary angle meaning it will add up to 90 degrees so...
90 - 22 = 68 therefore a = 68 hope that helps!
Answer:
68°
Step-by-step explanation:
That's an right angle so it's equal to 90°
To find a
90-22=68°
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
You can get a car loan with a term of three years at an APR of 5%. If you can afford a monthly payment of $450, how much can you borrow? (Round your answer to the nearest cent.)
$
Answer:
15014.57
Step-by-step explanation:
effective rate: .05/12= .004166667
[tex]450*\frac{1-(1+.004166667)^{-36}}{.004166667}=15014.5655[/tex]
Step-by-step explanation:
15014.57
Step-by-step explanation:
effective rate: .05/12= .004166667
450*\frac{1-(1+.004166667)^{-36}}{.004166667}=15014.5655450∗
.004166667
1−(1+.004166667)
−36
=15014.5655
A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation y = mx + b.
A line is drawn on the coordinate plane that passes through the point (3,-6) and has a slope of 4. The y-intercept of the line is
Answer:
b=-18
Step-by-step explanation:
If a line that passes through the point [tex]P(x_o,y_o)[/tex]and it has slope [tex]m[/tex], the equation of the line is:
[tex]y-y_o=m(x-x_o)~=>y=mx+y_o-mx_o~=>b=y_o-mx_o\\\\b=-6-4(3)=-18[/tex]
Answer:
-18
Step-by-step explanation:
Challenge: Solve x+3y=-6 for x. Then use your value for x to solve for y.
X=
Y=
Answer:
X = -6 - 3y
Y = -1
Step-by-step explanation: Solve for X first using basic algebra. Plug in X vaalue to original equation and solve. -6 - 3y + 3y = -6. Solve by adding 6 to both sides of the equation and dividing -3y by 3y.
What is the value of -42+(5-2)(-6)?
0-34
-2
0 10
34
Answer:
-60
Step-by-step explanation:
-42+3*-6
-42-18
-60
which is the mode of the data given below 24686424664
Someone please help me I’m stuck on this question
9514 1404 393
Answer:
-9
Step-by-step explanation:
You are given a point and a slope, so you can write the equation of the line in point-slope form:
y -k = m(x -h) . . . . . line of slope m through point (h, k)
y -7 = 4(x +5) . . . . using the given point
Putting in the x- and y-values of the other point, we have ...
-9 -7 = 4(w +5)
-4 = w +5 . . . . . . . . . divide by 4
-9 = w . . . . . . . . . . subtract 5
The value of w is -9.
3. What is the perimeter of the rectangle
given below?
Geometry
P=2l+2s
Plugin both numbers.
P=24+38
P=62
The value of x in the solution to the system
2x - 3y = -2
3x – 2y = 12
Answer:
(8,6)
Step-by-step explanation:
See image below:)
FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free:)
find the area of the shape below 22226
Answer:
12 units²
Step-by-step explanation:
A(triangle) = 1/2(2)(2) = 2 units²
A(triangle) = 1/2(2)(6) = 6 units²
A(Square) = 2(2) = 4 units²
A(Shape) = 2 + 6 + 4 = 12 units²
What is the explicit formula for this sequence?
-5, -3,-1,1, 3, ...
A. an = (-5) + (n − 1)2
B. an = (-5) + (n - 1)(-2)
C. an = 5 + (n - 1)2
D. an = 2 + (n - 1)(-5)
Answer:
Step-by-step explanation:
A.-5+(n-1)*2 and n belong to 1 to ponitive infinity
Find the GCF of 21m^5n^2 and 28m^4n2
Answer: 7m⁴n²
Step-by-step explanation:
Find the GCF of 21m⁵n² and 28m⁴n².
Find the prime factors of each term in order to find the greatest common factor (GCF).
21m⁵n² = 7 · 3 · m · m · m · m · m · n · n
28m⁴n² = 7 · 2 · 2 · m · m · m · m · n · n
The product of these common prime factors will be the Greatest Common Factor: 7 · m · m · m · m · n · n = 7m⁴n²
Horizontal lines are always perpendicular to _________ lines.
Answer:
Vertical
Step-by-step explanation:
/_