Answer:
The probability that the weight of a candy randomly selected is more than 0.8537 is 0.7486
Step-by-step explanation:
The given parameters are;
The mean candle weight = 0.8552 g
The standard deviation = 0.0519 g
The number in the sample, n = 442 candles
By central limit theorem, the sample standard deviation, [tex]\sigma _{\bar x}[/tex] is given by the relationship;
[tex]\sigma _{\bar x} = \dfrac{\sigma}{\sqrt{n} } = \dfrac{0.0519}{\sqrt{442} } = 0.002469[/tex]
The probability is given by the relation;
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-\mu }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-\mu }{\dfrac{\sigma }{\sqrt{n}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-0.8552 }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-0.8552 }{\dfrac{0.0519 }{\sqrt{442}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (z>-0.6076\right )[/tex]
The from the z-score table we have = 0.2514
The probability of P (z > -6076) = 1 - 0.2514 = 0.7486
The probability that the weight of a candy randomly selected is more than 0.8537 = 0.7486.
What equation could be used to find the missing leg length a in a right triangle with a hypotenuse of 60 and leg length of 51?
Answer:
Pythagorean Theorem: a² + b² = c² should be used.
Step-by-step explanation:
51² + b² = 60²
b² = 60² - 51²
b = 3√111
b = 31.607
Pythagorean Theorem is used to find any missing side of a right triangle if 2 other sides are present.
Answer:
Pythagoras theorem
EXPLANATION
HYPOTHENUS SQUARE =OPPOSITE SQUARE + ADJACENT SQUARE
i.e 60^2= 51^2+x^2
i.e 3600=2601+x^2
collecting like terms we have
3600-2601=x^2
999=x^2
√999=x
x=31.6
Compare the two functions. [tex]f(x) = \frac{1}{50} (3)^x[/tex] [tex]g(x) = \frac{1}{5} x^{2}[/tex] Which statement is true?
Answer:
As x increases, the rate of change of f(x) exceeds the rate of change of g(x).
Step-by-step explanation:
Hope this helps :)
A rectangular carton has twice the height, one-
third the length, and four times the width of a
second carton. The ratio of the volume of the
first carton to that of the second is
A)16:3
B)3:1
C)8:3
D)3:8
Find the product of:additive inverse of−5/6, multiplicative inverse of 4/12 and reciprocal of 9/5.
Answer:
25/18
Step-by-step explanation:
Additive inverse of a number X is the number which when is added to X =0
ex: additive inverse of 2 is -2 since 2 +(-2)=0
Multiplicative inverse of a number N is the number which when multiplied by N gives 1
ex: multiplicative inverse of 6/7 is 7/6
6/7*7/6=1
Ex of reciprocal is
5/9 & 9/5
7/6 & 6/7
Additive inverse of -5/6=5/6
Multiplicative inverse of 4/12 is 12/4
Reciprocal of 9/5 is 5/9
(5/6)*(12/4)*(5/9)=25/18
Answer:
(5/6)*(12/4)*(5/9)=25/18
Step-by-step explanation:
PLEASE HELPPP. Or explain what the question is even asking im so confused.
Step-by-step explanation:
f(x) = y
so f(4.999) = -5 when x = 4.999
f(5)= undefined because open circles means > or < with out the line underneath that means equal to
f(5.0001)= 7 when x=5.0001
f(9)= 7 when x=9 because the closed circle means ≥ or ≤ or equal to
Answer:
see attached
The function in the graph is:f(x)= -6, when x= [-9, 2)f(x)= -5, when x= [2, 5)f(x)= 7, when x= (5, 9]Therefore,f(4.999)= -5, f(5)= undefined,f(5, 0001)= 7,f(9)= 7What is the slope of the line?
Answer:
5/3
Step-by-step explanation:
it should be y/x
you can count 5 up and 3 over
Answer:
8/5
Step-by-step explanation:
You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.
URGENT HELP NEEDED! YOU WILL GET BRAINLIEST! Convert to a product: cot(α) - 1
Answer:
WHAT
Step-by-step explanation:
Determine the approximate area of a sector with a central angle of 75° and a radius of 14 yards. Question 16 options: A) 9.2 yards2 B) 128.3 yards2 C) 40.8 yards2 D) 0.21 yards2
Answer:
B) 128.3 square yards
Step-by-step explanation:
A = (n/360 deg)(pi)r^2
where n = central angle of sector.
A = (75/360)(3.14159)(14 yd)^2
A = 128.3 yd^2
Answer:
B. 128.3 yards
Step-by-step explanation:
Area of a Sector Formula: A = ∅/360πr²
Simply plug in our variables:
A = 75/360(π)(14)²
A = 5π/24(196
A = 128.3
in which number does the digit 5 have a value that is 10 times as great as the digit 5 in the number 4.59?
Answer:
B) 2775.9
Step-by-step explanation:
The missing options are:
A) 578
B) 2775.9
C) 134.591
D) 31.757
The digit 5 is in the tenths in 4.59. This means that its value is 0.5. A value 10 times greater is 10*0.5 = 5, that is, a 5 in the ones, like in 2775.9.
Write an algebraic expression for the verbal description.
The total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40
Step-by-step explanation:
45X + 2000 = Y
Where X = Number of units
Y = Total Cost
The total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40 is T(x) = 40x + 2500.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40.
Assuming total cost to be T.
∴ T(x) = 40x + 2500.
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PLEASE HELP WITH THIS I WILL MARK EVERYONE THAT ANSWERS BRAINLY
Answer:
125.6 cubed inches
Step-by-step explanation:
1. 3.14(2)^2(10) - Multiply 3.14 with 2 squared and 10.
2. First find out what is 2 squared, which is 4. Then, multiply 4 with 3.14, which is 12.56.
3. Now, multiply 12.56 with 10 or just move the decimal point one place to the right, which gives you 125.6 cubed inches.
which mathematical operation is represented in the phrase "15 more than q"
A) +
B) ×
C) ÷
D) -
Answer:
[tex]\boxed{OptionA}[/tex]
Step-by-step explanation:
More than always indicates "ADDITION". So the mathematical operation is "+".
Answer:
A. +
Step-by-step explanation:
The key word in the phrase is "more than"
That signifies an increase of value which is addition's main function
If the number that was represented in the phrase is x, then we could write out an equation
x=q+15
how to find the gradient of the line segment joining each pair points?
(1,3) (7,-1)
(6,1) (2,5)
(4,5) (-5,-7)
(-2,2) (2,8)
Answer:
1. -0.66666666666667
2. -1
3. 1.333
4. 1.5
Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package. She planted 15 saplings and has at most 20 left. How many packages of saplings did she start with? What would the solution look like on a number line graph?
When Rita started, she had (blank)(at least 7, at most 7, at least 4, at most 4) packages of saplings. The solution can be represented as(blank)(an open circle, a closed circle) with an arrow to the (blank)(left, right).
Answer:
7 packages
Step-by-step explanation:
Total number of saplings = 15 + 20 = 35
Number of saplings per package = 5
Number of packages = Total saplings ÷ Number of saplings per package
= 35 ÷ 5
= 7
Answer:
7
Step-by-step explanation:
The perimeter of the rectangle below is 74 units. Find the length of side RS
Write your answer without variables.
Answer:
20 units
Step-by-step explanation:
The perimeter of a rectangle is
P = 2(l+w)
P = 2( 3x+2 + 4x)
Adding like terms
P = 2( 7x+2)
We know the perimeter is 74 units
74 = 2 ( 7x+2)
Divide by 2
74/2 = 2/2 (7x+2)
37 = 7x+2
Subtract 2 from each side
37-2 = 7x+2-2
35 = 7x
Divide by 7
35/7 = 7x/7
5 =x
We want to find the length RS = PQ = 4x
RS = 4x = 4*5 = 20
there are 1600 students in school.47.5% are male.how many are female
Answer:
840 female students
Step-by-step explanation:
The total percentage of students is 100%, so, the percentage of female students = 100% - 47.5%
=52.5%
Multiply the total no. of students by the percentage to get the no. of female students.
1600 x 52.5%
= 840 female students
You can also obtain the same answer by first multiplying the male percentage to find the no. of male students, then subtracting it from the total 1600.
plz help!!
will give the brainliest!!
Answer:
x = 3
Inverse matrix:
[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]
Step-by-step explanation:
Determinant: ad - bc
a = 3, b = 2, c = 3, d = -1
3 * (-1) - (2 * x) = -9
-3 - 2x = -9
-2x = -6
x = 3
For matrix
[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]
the inverse is
[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]
Here we have: det = -9
a = 3, b = 2, c = 3, d = -1
Inverse matrix:
[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]
[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]
[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]
PLEASE HELP WITH THIS(INORDER FOR ME TO GIVE YOU A BRIANLIST,EXPLAIN HOW U GOT IT)(will give brainlist and thanks)(Find the perimeter)
Answer:
7x+10 cm
Step-by-step explanation:
To find the perimeter add up all the sides
There are 5 sides
3x+ 5+ 2x+2x+5
Combine like terms
3x+2x+2x +5+5
7x + 10
The perimeter is 7x+10 cm
What are the zeros of f(x) = x2 + x - 30?
O A. x= -6 and x = 5
B. x= -2 and x= 15
o
C. x= -5 and x = 6
D. x= -15 and x = 2
SS
Answer:
A
Step-by-step explanation:
The zeroes of the function are the x values when f(x) = 0 so we can write:
0 = x² + x - 30
0 = (x + 6)(x - 5) (To factor this we need to find 2 numbers that have a sum of 1 and a product of -30; these numbers are 6 and -5)
x + 6 = 0 or x - 5 = 0 (Use Zero Product Property)
x = -6, 5
Hey there! :)
Answer:
A. x = -6 and x = 5.
Step-by-step explanation:
Given:
f(x) = x² + x - 30
Factor the equation by finding two numbers that sum up to 1 and multiply into -30. We get:
-5, 6
Use these to express this quadratic function in factored form:
f(x) = (x - 5) (x + 6)
Set each factor equal to 0 to solve for the zeros of the equation:
0 = x - 5
x = 5
-------------
0 = x + 6
x = -6
Therefore, the correct answer is A. x = -6 and x = 5.
Mathematics IV
Nathan receives $28 each month for his allowance. If each month has approximately 4
weeks in it, how much money does he receive each week?
Answer:
$7
Step-by-step explanation:
So since he gets $28 in one month and there are 4 weeks in a month, -->
28/4 = 7 so, $7
What is the inverse of the function below?
f(x) =X/3-2
A. f^-1(1x) = 2(x-3)
B. f^-(1x) = 3(x-2)
c. f^-1(x) = 3(x + 2)
D. f^-1(x) = 2(x + 3)
Answer: C
Step-by-step explanation: With inverse equations, you switch y and x (y=f(x)) and undo/reverse the steps towards x.
1. Multiply by 3
2. Add 2
Equation by itself
0. x
1. 3(x)
2. 3(x+2)
The inverse of the given function is f⁻¹(x) = 3(x + 2).
What is the inverse of a function?The inverse function of a function f(x) in mathematics is a function that reverses the operation of f(x).
The given function in the question:
f(x) = (x/3) - 2
f(x) + 2 = x/3
x + 2 = f⁻¹(x)/3
f⁻¹(x) = 3(x + 2)
Hence, the inverse of the given function is f⁻¹(x) = 3(x + 2).
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Simplify: (2 cot(−240°)cos(-1050°)− cot^2(50°)) / (sec^2(40°))
Thanks! (:
Answer:
\frac{2\cot \left(-240^{\circ \:}\right)\cos \left(-1050^{\circ \:}\right)-\cot ^2\left(50^{\circ \:}\right)}{\sec ^2\left(40^{\circ \:}\right)}
Step-by-step explanation:
ok
How many non-congruent triangles can be formed by connecting 3 of the vertices of the cube?
Answer:
The number of non-congruent triangles that can be formed by connecting 3 of the vertices of the cube is 3 non-congruent triangles
Step-by-step explanation:
From the three dimensional shape of a cube, triangles can be constructed from;
1) 6 side faces
2) 4 front face to opposite vertices triangles
3) 4 rear face to opposite vertices triangles
Each face can produce ₄C₃ = 4 triangles
Therefore;
The total number of triangles that can be formed = 4 × 6 + 4 × 4 + 4 × 4 = 56 triangles
Of the 56 triangles, it will be found that all 24 triangles from the different 6 direct faces will have the same dimension of 1, 1, √2 are congruent
The 24 triangles formed by the sides of the faces and an adjacent diagonal have the same dimension of 1, √2, √3 and are congruent
The 8 triangles formed by joining the three diagonals have the same dimension of √2, √2, √2 are congruent
Therefore, the 56 triangles comprises of a combination of three non-congruent triangle.
There are only 3 observed non congruent triangles formed by connecting three of the vertices of the cube.
Answer:
Answer is 3, i had it for homework
Step-by-step explanation:
PRE CALC, helppp please
Hey there! :)
Answer:
Choice B.
Step-by-step explanation:
Since h(x) equals (g o f)(x):
f(x) is substituted for x in the equation g(x). We can go through the answer choices and choose the most suitable choice by substitution:
A. f(x) = x, g(x) = x/ x + 1
(g o f)(x) = x / x + 1. This is incorrect.
B. f(x) = x², g(x) = x / x + 1
(g o f)(x) = x² / x² + 1. This matches h(x), so this is correct.
C. f(x) = x + 1, g(x) = 1/x²
(g o f)(x) = 1/(x² + 2x + 1). This is incorrect.
D. f(x) = x + 1, g(x) = x²
(g o f)(x) = x² + 2x + 1. This is incorrect.
Therefore, B is the correct answer.
Suppose you pick and replace marbles from a bag, one after another. If the bag
contains 3 red marbles, 3 white marbles, and 6 blue marbles, what is the probability of
picking a red marble and then a blue marble?
Answer:
1/8
Step-by-step explanation:
There are 3 + 3 + 6 = 12 marbles in the bag and 12 * 12 = 144 ways to choose two marbles when replacing. There are 3 * 6 = 18 ways to choose a red marble and then a blue marble so the probability is 18 / 144 = 1 / 8.
Thuy is substituting t = 3 and t = 8 to determine if the two expressions are equivalent.
Answer:
The expressions are not equivalent.
Step-by-step explanation:
The answers would be 196 and 193 for t = 8
The answers would be 76 and 73 for t = 3
The points in a plane in a fixed distance from a given point
is called a circle. What is the fixed distance called?
a. chord
b. radius
c. diameter
d. not given
Answer:
radius
Step-by-step explanation:
That "fixed distance" is the 'radius' of the circle.
Find the area of the shaded polygon
There’s no measurements, use square unit. One square is 1
Answer:
6 Units squared.
Look at file for explanation.
If sin(21°) = 0.36, and cosθ = 0.36, what's the measure of ∠θ? ANSWERS: A) m∠θ = 21° B) m∠θ = 0.36° C) m∠θ = 90° D) m∠θ = 69°
Hey there! :)
Answer:
m∠θ = 69°.
Step-by-step explanation:
If sin (21°) = 0.36 and cos θ = 0.36, the two angles are complementary because the sine and cosine values are equivalent. Therefore:
90 - 21 = 69°.
The correct answer is D) m∠θ = 69°.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
the equation of the line in slope-intercept form is;
[tex]y=8x-26[/tex]
Step-by-step explanation:
First use the formula for the slope of the segment that joins the two given points:
[tex]slope=\frac{y_2-y_1}{x_2-x_1} =\frac{6-(-2)}{4-3}=\frac{8}{1} =8[/tex]
now that we have the slope, we can use the point-slope form of a line to find the line with slope 8 that passes through any of the given points, for example through (3, -2):
[tex]y-y_0=m\,(x-x_0)\\y-(-2)=8\,(x-3)\\y+2=8\,(x-3)\\y=8x-24-2\\y=8x-26[/tex]