Answer:
Step-by-step explanation:
You are to make 5 assemblies.
Each assembly requires the use of 1 Type A bolt.
To make the 5 assemblies, you need 5 Type A bolts.
The container of bolts has a total of 60 bolts.
The focus - Type A bolts - is 20 out of this 60.
The probability of obtaining a Type A bolt at all, is 20/60, which is = 1/3
(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?
- The exact number of Type A bolts you need for the 5 assemblies is 5
1/3 × 5/10 = 5/30 = 1/6 = 0.167
(B) What is the probability of taking/having less than 5 Type A bolts out of the randomly selected 10 bolts? The solution is to sum up the following:
1/3 × 4/10 = 0.133
1/3 × 3/10 = 0.1
1/3 × 2/10 = 0.067
1/3 × 1/10 = 0.033
1/3 × 0/10 = 0
TOTAL = 0.333
A wire that is centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed into the shape of a square.
Using properties of square,
a. Equation for total area = 2x² - 16x + 64
b. Area will be minimum for the value of x = 0
c. Minimum area will be 64cm².
Define a square?With four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.
Total length of wire = 32cm.
Now side of one square is given as x.
Perimeter of big square will be = 4x.
Now perimeter of small square = 32- 4x.
Side of small square = (32-4x)/4
= 4(8-x)/4
= 8-x
Area of big square = x × x
= x².
Area of small square = (8-x) ².
Now Total area, A(x) = x² + (8-x) ²
= x² + 64 + x² - 16x
= 2x² - 16x + 64
The side length that will minimize the area will be, x = 0.
Minimum area of the total figure will be = 64cm²
To know more about square, visit:
https://brainly.com/question/28776767
#SPJ1
What is the square root of 598?
the square root of 598 is 24.4540385
1) Find the mean of the following numbers: 5, 11, 8, 8, 7, 4, 10, 9, 7, 7, 6
A company created a new container in the shape of a
triangular prism that will hold sunflower seeds. A three-
dimensional image of the container is shown below, as
well as a two-dimensional image of the base.
6 in.
3.2 in.
2 in.
3.2 in.
1 in.
square inches
1 in.
The container will be made from cardboard. How many
square inches of cardboard are needed to make one
container? Assume there are no overlapping areas.
The number of square inches of cardboard that are needed to make one
the container is 18.
We have,
The volume of the triangular prism.
= Area of the triangle x height
Now,
Height = 6 in
And,
To find the area of a triangle, we can use Heron's formula.
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.
Let's calculate the area using Heron's formula:
s = (3.2 + 3.2 + 2) / 2 = 4.2
A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))
A = √(4.2 x 1 x 1 x 2.2)
A = √(9.24)
A ≈ 3.04 square inches
Now,
The volume of the triangular prism.
= Area of the triangle x height
= 3.04 x 6
= 18.24 in²
Now,
Area of one cardboard.
= 1² in²
= 1 in²
Now,
The number of square inches of cardboard that are needed to make one
container.
= The volume of the triangular prism / Area of one cardboard
= 18.24 in² / 1 in²
= 18.24
= 18
Therefore,
The number of square inches of cardboard that are needed to make one
the container is 18.
Learn more about Prism here:
https://brainly.com/question/12649592
#SPJ1
Kacie just bought a new house and needs to buy new sod for her backyard, if the dimensisons of her yard are 33.5 feet by 13.6 feet, what s the area if her yard
3. Manny's weekly wage as a welder are $520.75. He is single and claims 3 allowances. What amount is
deducted for federal taxes?
If he is single and claims 3 allowances. The amount deducted for federal taxes is $39.8
Federal taxesFederal tax withheld:
Federal tax withheld =6.2% social security + 1.45% Medicare
Federal tax withheld = 7.65%
Deduction:
Deduction= 0.0765 × $520.75
Deduction=$39.8
Therefore the amount deducted for federal taxes is $39.8
Learn more about federal taxes here:https://brainly.com/question/17354124
#SPJ1
What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
Subtract 5 - 4i from 19 - 3i.
Answer:
Step-by-step explanation:
19 - 3i - 5 + 4i
14 + i
Find the distance traveled in 25 seconds by an object traveling at a velocity of v(t) = 20 + 5cos(t) feet per second
Answer:
499.338 feet
Step-by-step explanation:
You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.
DistanceThe distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...
\(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)
The distance traveled in 25 seconds is 499.33 feet.
It is required to find the distance traveled in 25 seconds.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
We have to find the distance , we will integrate v(t) from 0 to 25 second.
Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.
Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is
1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.
According to given question we have
Given a velocity function v, the distance s is figured by taking the integral. In this case,
v = 20 + 5 cos(t)
s = 20t + 5 sin(t) from 0 to 25
= s(45)-s(0)
s(0) = 0
so, the distance is
s(25) = 20*25 + 5sin(25)
= 500 -0.661
=499.33 feet.
Therefore, the distance traveled in 25 seconds is 499.33 feet.
Learn more about distance here:
brainly.com/question/28304899
#SPJ1
You are starting your first job as a salesperson at a clothing store. You receive a base salary of $10.00 per hour with time-and-a half for hours in excess of 40 hours per week. You also receive a 3% commission on your total sales.
Calculate your paycheck if you work 40 hours both weeks, plus you sell $3,000 worth of merchandise.
a
800
b
830
c
890
d
970
The paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.
How is the paycheck calculated?The paycheck can be computed by working out the base salary, overtime pay if any, and the sales commission separately and adding up these.
Some deductions (withholding taxes and insurance) are made to the gross pay to arrive at the paycheck, which is known as the net pay.
Data and Calculations:Base salary = $10.00 per hour
Overtime pay = 1.5 of the base salary per hour
Work week = 40 hours
Commission on total sales = 3%
Sales for a month = $3,000
Commission on $3,000 sales = $900 ($3,000 x 3%)
Base salary for two weeks = $800 ($10 x 40 x 2)
Paycheck = $890 ($800 + $900)
Thus, the paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.
Learn more about calculating paychecks at https://brainly.com/question/14972403
#SPJ1
solve ~
\(x {}^{2} - 5x + 6 = 0\)
thankyou ~
Answer:
x = 3, 2
Explanation:
⇒ x² - 5(x) + 6 = 0
breakdown
⇒ x² - 3(x) - 2(x) + 6 = 0
takeout common terms
⇒ x(x - 3) - 2(x - 3) = 0
factor
⇒ (x-3) ( x-2) = 0
simplify
⇒ (x-3)=0, ( x-2) = 0
final answer
⇒ x = 3, 2
I need help asap I’ll also give brainliest
Answer:
15
Step-by-step explanation:
Find the distance represented by 4.9 inches if 1 inch = 50 miles.
Answer:
245 miles
Step-by-step explanation:
To complete this, you want to use the unit conversion technique in fraction form. The units for the numerator of the first fraction (thing you want to convert) should match the units of the denominator in the multiplying fraction.
Answer:
4.9 inches = 7.73359e-5 miles
Step-by-step explanation:
:)
Round 143.596 to the nearest hundredth
Answer:
143.6
Step-by-step explanation: i swear its right
Need help pleasee.
Using Rational Zero Theorem
Consider the function f(x)=2x^3-8x^2+5x+3
List all the possible rational zeros of f based on the Rational zero Theorem
The possible rational zeros of f are:
±1/1, ±3/1, ±1/2, ±3/2
What is the Rational Zero Theorem?
The Rational Zero Theorem states that if a polynomial function f(x) has integer coefficients, then every rational zero of f has the form p/q, where p is a factor of the constant term of f and q is a factor of the leading coefficient of f.
In the case of the function f(x) = 2x³ - 8x² + 5x + 3, the constant term is 3 and the leading coefficient is 2. Therefore, the possible rational zeros of f are of the form:
p/q, where p is a factor of 3 and q is a factor of 2.
The factors of 3 are 1 and 3, and the factors of 2 are 1 and 2. Therefore, the possible rational zeros of f are:
±1/1, ±3/1, ±1/2, ±3/2
These are the possible rational zeros of f(x) based on the Rational Zero Theorem. However, not all of them may be actual zeros of f(x).
To determine which of these possible zeros are actual zeros of f(x), we can use synthetic division or other methods to test each possible zero.
Therefore, the possible rational zeros of f are:
±1/1, ±3/1, ±1/2, ±3/2
To learn more about the Rational Zero Theorem visit:
https://brainly.com/question/28828052
#SPJ1
Arătati ca numărul ab1 + a1b + 1ab
Answer:
a plus b equals 9923
Step-by-step explanation:
What is the value of the expression 2,160/30
Answer:
72
Step-by-step explanation:
Find the area of the polygon
Answer:
Area of a regular polygon formulas
Step-by-step explanation:
area = n * a * ri / 2 , having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides)
area = perimeter * ri / 2 , given ri and polygon perimeter.
area = n * (ri)² * tan(π/n) , given ri.
1. Answer True or False to the
Answer:
umm the photo is blurry
Step-by-step explanation:
Does the expression x^3-1 divided by x^2 -1 simplify to x?
No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.
To simplify the expression, let's first factorize both the numerator and denominator.
The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).
The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).
Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:
[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]
The (x - 1) terms cancel out, leaving us with:
x^2 + x + 1 / (x + 1)
So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.
Know more about numerator here:
https://brainly.com/question/1217611
#SPJ8
Select the expression that represents the following statement: multiply the difference of 5 and 2 by 7, and then add 6. 7 x (5 − 2) + 6
5 + 2 x 7 + 6
7 x (5 + 2) − 6
6 − 2 + (7 x 5)
Answer:
7(5-2)+6
Step-by-step explanation:
difference - subtraction
putting the 7 next to it means that it will multiply times that first
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
ILL GIVE A BRAINLIEST TO WHOEVER HELPS!!
Answer:
10x^2-4x+6??????????
Answer:
10x^2-4x+6
Step-by-step explanation:
Multiply the length and width and you will get 2*(5x^2-2x+3) = 10x^2-4x+6!
HELP ME PLEASEEEEEEEEEEEEEEEE
Answer:
15.7
Step-by-step explanation:
Because the width has to be bigger than the length since its a rectangle and 15.7 matches the equation of 43.8 and 12.4
Answer:
P = 2(l + w)
43.8 = 2(12.4 + x )
43.8 = 24.8 + 2x
43.8 - 24.8 = 2x
19 = 2x
Divide both side by two;
x = 9.5 ft
The answer choices in the picture are:
A. a reflection over the line x=6
B. a dilation with a scale factor of 6
C. a 180 degrees clockwise rotation about the origin
D. a 90 degree clockwise rotation about the origin
Answer:
A. A reflection over the line x = 6
Step-by-step explanation:
You can see in the picture if you follow the line every edge has the same
Number x=6
find the product 3/8 x 2 help plz
Answer:
3/4
Step-by-step explanation:
hope this helps. I have to wrote this random think so it can be 20 characters hope this helps enjoy
Solve for x xx. Enter the solutions from least to greatest. Round to two decimal places. ( x + 3 ) 2 − 3 = 0 (x+3) 2 −3=0
The solution of the equation (x + 3)² − 3 = 0 least to greatest will be negative 4.73 and negative 1.27.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
(x + 3)² − 3 = 0
Simplify the equation, then the value of the variable 'x' is given as,
(x + 3)² − 3 = 0
(x + 3)² = 3
x + 3 = ± √3
x = - 3 ± √3
x = - 3 ± 1.73
x = -4.73, -1.27
The solution of the equation (x + 3)² − 3 = 0 least to greatest will be negative 4.73 and negative 1.27.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Please help song for b
please help me solve this problem
The features related to vectors are listed below:
Case A: u' = (- 4√41 / 41, - 5√41/ 41)
Case B: Tip coordinantes of vector v: (x, y) = (10, 10)
Case C: r = 11.402
How to determine vectors
In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.
Case A - Unit vector
Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:
u' = u / ||u||
Where:
u' - Unit vector.u - Vectoru - ||u|| - Magnitude of the vector.Please notice that the magnitude of the vector is determined by Pythagorean theorem:
r = √[(Δx)² + (Δy)²]
Where:
r - MagnitudeΔx - Change in the x-direction.Δy - Change in the y-direction.Thus, the unit vector of u is:
u' = (- 4, - 5) / √[(- 4)² + (- 5)²]
u' = (- 4, - 5) / √41
u' = (- 4 / √41, - 5 / √41)
u' = (- 4√41 / 41, - 5√41/ 41)
Case B - Definition of a vector
This can be found easily by vector subtraction:
v = Tip coordinates - Base coordinates
(3, 4) = (x, y) - (7, 6)
(x, y) = (3, 4) + (7, 6)
(x, y) = (10, 10)
Case C - Magnitude of a vector
The magnitude is found by means of Pyhtagorean theorem:
r = √[(- 4 - 3)² + (- 5 - 4)²]
r = √[(- 7)² + (- 9)²]
r = 11.402
To learn more on unit vectors: https://brainly.com/question/28028700
#SPJ1
What is the equation of the line that passes through the point (-5,2)and has undefined slope
Step-by-step explanation:
a line with undefined slope is a vertical line, because x does not change on this line at all, and therefore the shoe is y/0.
a vertical line is parallel to the y-axis.
and to go through the given point, it has to use the x- coordinate.
so, the equation is
x = -5
that's really it.
this is the line of all points with the x-coordinate = -5. any value for y is valid.