Answer:
The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The sample consist of 64 people and 48 of them are 'successful'. Hence, the proportion of 'successful' people is:
[tex]p = \frac{n}{N}[/tex]
Where:
[tex]N[/tex] - People that forms the sample, dimensionless.
[tex]n[/tex] - People classified as 'successful', dimensionless.
Given that [tex]n = 48[/tex] and [tex]N = 64[/tex], the sample proportion of 'successful' people is:
[tex]p = \frac{48}{64}[/tex]
[tex]p = \frac{3}{4}[/tex]
The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].
What is the slope of the line shown below?
A. -13/6
B. 6/13
C. 13/6
D. -6/13
-
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
Find the value of x.
Answer:
5
Step-by-step explanation:
This shape is formed by two right triangles.
Let's start by the little one.
Let y be the third side.
Using the Pythagorian theorem we get:
y^2 = 6^2 + 3^2
y^2 = 36 + 9
y^2 = 45
y = 3√(5)
●●●●●●●●●●●●●●●●●●●●●●●●
Now let's focus on the second triangle. Let z be the third side.
The Pythagorian theorem:
6^2 + x^2 = z^2
Using the Pythagorian theorem on the big triangle :
[3√(5)]^2 + z^2 = (3+x)^2
45 + z^2 = 3x^2 + 6x + 9
36 +z^2 = 3x^2 +6x
So we have a system of equations.
36+ x^2 = z^2
36 +z^2 = 3x^2 +6x
We want to khow the value of x so we will eliminate z .
Add (36+x^2 -z^2 =0) to the second one.
36 + x^2-z^2+36+z^2 = 3x^2+6x
72 + x^2 = 3x^2 +6x
72 - 2x^2 -6x = 0
Multipy it by -1 to reduce the number of - signs
2x^2 + 6x -72 = 0
This is a quadratic equation
Let A be the discriminant
● a = 2
● b = 6
● c = -72
A = b^2-4ac
A = 36 -4*2*(-72) = 36 + 8*72 =612
So this equation has two solutions
The root square of 612 is approximatively 25.
● (-6-25)/4 = -31/4 = -7.75
● (-6+25)/4 = 19/4 = 4.75 wich is approximatively 5
A distance cannot be negative so x = 5
Please help. I’ll mark you as brainliest if correct! Thank you
Answer:
8 pounds of cheaper candy,
17.5 pounds of expensive candy
Step-by-step explanation:
Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!
x + y = 25.5
[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]
We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:
y = 17.5
Plugging this in, we find that:
x = 8.
Consider the given function and the given interval.
f(x) = 8 sin x - 4 sin 2x, [0,pi]
(a) Find the average value f ave of f on the given interval.
(b) Find c such that f ave = f(c).
(a) The average value of f(x) on the closed interval [0, π] is
[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]
(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :
8 sin(c) - 4 sin(2c) = 16/π
8 sin(c) - 8 sin(c) cos(c) = 16/π
sin(c) - sin(c) cos(c) = 2/π
Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.
(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=75 and s =5. assuming normality, the 99% confidence interval for the population mean is:__________
Answer:
The 99% confidence interval is [tex]71.67 < \mu < 78.33[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 75[/tex]
The standard deviation is [tex]s = 5[/tex]
Given that confidence is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical values of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Generally the margin for error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 5}{ \sqrt{15} }[/tex]
=> [tex]E = 3.3307[/tex]
The 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]75 - 3.3307 < \mu <75 + 3.3307[/tex]
=> [tex]71.67 < \mu < 78.33[/tex]
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?
Answer:
6720 in ^3
Step-by-step explanation:
Volume = length * width * height
= 30*16*14
=6720 in ^3
Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
Help please, I don't understand :(
Answer:
38 = JKL
Step-by-step explanation:
JKM = JKL + LKN + NKM
Substituting what we know
104 = JKL + LKN +33
KN bisects LKM so NKM = LKN
33 = LKN
104 = JKL + 33 +33
104 = JKL + 33 +33
Combine like terms
104 = JKL +66
104 - 66 = JKL
38 = JKL
Answer: ∡JKL=38°
Step-by-step explanation:
KN bidects ∡LKM => ∠KLN=∡NKM=33°
=> ∡LKM=∠KLN+∡NKM=33°+33°=66°
=>∡JKL= ∡JKM-∡LKM= 104°-66°=38°
∡JKL=38°
If the length of the legs of a right triangle are 13 and 13,what is the length of the hypotenuse? Round your answer to the nearest tenth,if necessary.
Answer:
a² + b² = c²
13² + 13² = c²
169 + 169 = c²
338 = c²
c = √338 or 18.385 or 13√2
Answer:
18.4
Step-by-step explanation:
13² + 13² = x²
169 + 169 = x²
338 = x²
x = 18.38477....
Which option is correct and how would one solve for it?
Answer:
2+4+6+8
Step-by-step explanation:
We have the sum of 2n where n runs from 1 to 4
n=1 2(1) = 2
n=2 2(2) = 4
n=3 2(3) = 6
n=4 2(4) = 8
The sum is add
2+4+6+8
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Learn more on equations :https://brainly.com/question/2972832
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The graph of g(x) is the result of translating the graph of f(x) = (one-half) Superscript x three units to the left. What is the equation of g(x)?
Answer:
[tex]g(x) = 0.5^{(x+3)}[/tex]
Step-by-step explanation:
Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),
the way to translate three units to the left is to change x to x+3. This gives our answer: [tex]g(x) = 0.5^{(x+3)}[/tex]
Answer:
B. g(x) = (1/2)⁽ˣ⁺³⁾
Hope this helps!
Step-by-step explanation:
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
Find the sum. 31.25 + 9.38
Answer:
40.63
Step-by-step explanation:
31.25+9.38= 40.63
Hope this helps
Answer: 40.63
Look at the image for shown work.
Please help. I’ll mark you as brainliest if correct!
Answer:
x and y can have many values
Step-by-step explanation:
-24x - 12y = -16
Then: 24x + 12y = 16
We know: 6x + 3y = 4
X and Y can have a lot of valoues.
6x + 3y = 4
3 ( 2x + y) = 4
2x + y= 4/3
2x+y= 1.333...
how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
ΔABC is similar to ΔMNO. The scale factor from ΔMNO to ΔABC is 3∕2 . If the area of ΔMNO is 10 square units, what's the area of ΔABC? Question 12 options: A) 45 square units B) 90 square units C) 22.5 square units D) 15 square units
Answer:
The area of ΔABC= 6.667 square units
Step-by-step explanation:
ΔABC is similar to ΔMNO.
The scale factor from ΔMNO to ΔABC is 3∕2
the area of ΔMNO is 10 square units,
The area of ΔABC/the area of ΔMNO
= 2/3
The area of ΔABC/10= 2/3
The area of ΔABC= 2/3 * 10
The area of ΔABC= 20/3
The area of ΔABC= 6 2/3
The area of ΔABC= 6.667 square units
Answer:
22.5 square units
Step-by-step explanation:
i multiplied 10 by 2 to get 20 and went with the closest answer and got it right.
i dont know how to do math but i guess it worked
GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
A 16-inch piece of string is 40.64 centimeters long. To the nearest 0.01 centimeter, how long will a 42-inch price of string be?
A. 56.64 cm
B. 82.64 cm
C. 106.68 cm
D. 1,706.88 cm
Please show ALL work! <3
Answer:
106.68 centimeters
Step-by-step explanation:
40.64 cm/16 in = x cm/42 in
Cross multiplying, we get:
16x = 40.64(42)
16x = 1706.88
x = 106.68 centimeters
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
Which relationships have the same constant of proportionality between y and x as the equation 3y=2x? SELECT 3 ANSWERS
*Correct Question:
Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?
Answer:
A, B, C
Step-by-step explanation:
Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus
[tex] 3y = 27x [/tex]
Divide both sides by 3
[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]
[tex] y = 9x [/tex]
Thus, we can say, y would always be 9 times the quantity of x.
From the options given, examine which options have this proportionality statement as well.
Option A, y = 9x is same as the statement.
Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x
Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.
Option D and E do not have same constant of proportionality.
The right options are A, B, and C.
perform the indicated operation (8-15i)(-3 + 2i)
Answer:
[tex] - 24 + 16i + 45i + 15 = 9 + 61i[/tex]
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
Whats 18x^3 divided by 7x?????
A computer store sells new computers for $500 and refurbished computers for
$200. In March, the store sold 20 computers for $6,400, meaning they sold ?
refurbished computers.
Answer:
no of new computers sold : 8
no. of refurbished computer sold : 12
Step-by-step explanation:
Let the no. of new computers sold be x
let the no. of refurbished computers sold be y
Given
In March, the store sold 20 computers
x + y = 20
y = 20-x ----- equation 2
selling price of new computer = $500
selling price of x new computer = 500*x = 500x
selling price of refurbished computer = $200
selling price of y refurbished computer = 200*y = 200y
Total selling price of x new computer and y refurbished computers = 500x+200y
given that
total prioce of computer is $6400
thus
500x+200y = 6400
using y = 20-x from equation 2
500x+200(20-x) = 6400
=> 500x+ 4000 - 200x = 6400
=> 300x = 6400 - 4000 = 2400
=> x = 2400/300 = 8
Thus,
no of new computers sold = 8
no. of refurbished computer sold = 20 -8 = 12
ASAP!!!!!!!asap!!!!!!!!!!!! asap asap asap
Answer:
7). x = 3.2, AC = 42.8
8). a = 6, YZ = 38
Step-by-step explanation:
It is given in the question that a point B is between A and C of the line segment AC.
⇒ AB + BC = AC
By substituting the values of segments,
5x + (9x - 2) = (11x + 7.6)
14x - 2 = 11x + 7.6
14x - 11x = 7.6 + 2
3x = 9.6
x = 3.2
Therefore, AC = 11x + 7.6
= 11(3.2) + 7.6
= 35.2 + 7.6
= 42.8
Question (8).
If Y is a point between X and Z,
⇒ XY + YZ = XZ
By substituting the measures of these segments given in the question,
(3a - 4) + (6a + 2) = (5a + 22)
9a - 2 = 5a + 22
9a - 5a = 22 + 2
4a = 24
a = 6
Since, length of segment YZ = 6a + 2
= 6(6) + 2
= 38
Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?
Answer:
Reserve rate = 9%
Step-by-step explanation:
Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.
first, let us calculate the reserve amount as follows:
Reserve = Deposit - (free amount to lend out)
Reserve = 28,000 - 25,480 = $2,520
[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]
Therefore the reserve rate = 9%
a department store regularly sells a pair of pants for $49.95. they are having a sale where clothing 30% off.
after including an 8% sales tax, how much do the pants cost on sale?
A. $30.97
B. $38.96
C. $37.76
D. $32.17
Answer:
C. $37.76
Step-by-step explanation:
30% of $49.95
=30/100×49.95
=$14.99
selling price = 49.95 -14.99
= $34.96
8% sales tax included
=8/100×34.96
=$2.80
new price= 34.96+2.80
=$37.76
if the LCM and the HCF of two numbers are 9 and 3, respectively, what are the numbers?
Hey There!
Answer:
HCF = 9 (With the two numbers) - 18,9LCM = 3 (with the two numbers) - 6,9Step-by-step explanation:
HCF
If HCF is ''9'' that means that ''9'' is the divisible of two numbers.
So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.
And always remeber the answer is a ''Prime factor.''
LCM
If LCM is ''3'' that means ''3'' is the lowest common multiple out of two numbers.
Hope this helps!
Have a nice Day!:)
