Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
How to determine the mass of the iron beam
Let suppose that the iron beam has an uniform density, the mass of the iron beam (m), in gram, is equal to the product of its density (ρ), in grams per cubic centimeter, and its volume (V), in cubic centimeters:
m = ρ · V (1)
If we know that ρ = 10504 cm³ and V = 7.8 g/cm³, then the mass of the iron beam is:
m = (7.8 g/cm³) · (10504 cm³)
m = 81931.2 g
Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
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What areC12, C31, and C22 of matrix C?
Compute the sum to simplify C :
[tex]C = \begin{bmatrix}16-0.5 & 9+0 \\ -3+5 & 0 + 8 \\ 4-3 & -10+14\end{bmatrix} = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ 1 & 4\end{bmatrix}[/tex]
Now, [tex]c_{ij}[/tex] is the entry of the matrix in row i and column j, so
[tex]C = \begin{bmatrix}15.5 & \boxed{9} \\ 2 & 8 \\ 1 & 4\end{bmatrix} \implies c_{12} = 9[/tex]
[tex]C = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ \boxed{1} & 4\end{bmatrix} \implies c_{31} = 1[/tex]
[tex]C = \begin{bmatrix}15.5 & 9 \\ 2 & \boxed{8} \\ 1 & 4\end{bmatrix} \implies c_{22} = 8[/tex]
Boris wants to sort his crayons and give out the
yellow ones. He has 360 crayons altogether.
of the crayons are blue.
18
60% of the crayons are red.
The rest are yellow.
Work out the number of crayon he gives out
Answer:
126 yellow crayons
Step-by-step explanation:
Finding the number of each of the crayons :
Blue = 18Red = 60% of total = 60% x 360 = 0.6 x 360 = 216Number of yellow crayons :
Total - [Blue + Red]360 - [18 + 216]360 - 234126 yellow crayonsThe marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 15 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. . Store Shelf Space Weekly Sales 1 5 1.3 2 5 1.6 3 5 1.4 4 10 1.7 5 10 1.9 6 10 2.3 7 15 2.2 8 15 2 9 15 1.8 10 20 2.2 11 20 2.4 12 20 2.9 13 25 2.9 14 25 2.7 15 25 2.5 Using the regression line for this problem, the approximate Weekly Sales for shelf space that is :_________,i. 30. ii. 3.12 iii. 3.1 iv. 3.04 v. 2.99
The Weekly Sales for 30 shelf spaces is 3.04
How to determine the Weekly Sales for 30 shelf spaces?The proper table is added as an attachment.
Next, we determine the regression equation using a graphing calculator.
From the graphing calculator, we have the following calculation summary:
Sum of X = 225Sum of Y = 31.8Mean X = 15Mean Y = 2.12Sum of squares (SSX) = 750Sum of products (SP) = 46The regression equation is represented as:
y = bx + a
Where
b = SP/SSX = 46/750 = 0.06133
a = MY - bMX = 2.12 - (0.06*15) = 1.2
So, we have:
ŷ = 0.06133x + 1.2
When x =30, we have:
ŷ = 0.06133 * 30 + 1.2
Evaluate
ŷ = 3.04
Hence, the Weekly Sales for 30 shelf spaces is 3.04
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What is the surface area of the right cone below?
12
A. 123 sq. units
B. 141 sq. units
C. 64 sq. units
D. 143 sq. units
3-
The surface area of the right cone is 141 sq. units. The correct option is B. 141 sq. units
Calculating surface area of a coneFrom the question, we are to determine the surface area of the given right cone
The total surface area of a cone can be calculated by using the formula,
TSA = πrl + πr²
Where TSA is the total surface area
r is the radius
and l is the slant height
From the given information,
r = 3
l = 12
Putting the parameters into the formula, we get
TSA = (π×3×12) + (π ×3²)
TSA = 36π + 9π
TSA = 45π sq. units
TSA = 141.37 sq. units
TSA ≅ 141 sq. units
Hence, the surface area of the right cone is 141 sq. units. The correct option is B. 141 sq. units
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Can some one help me please
Answer:
a) angle A = angle Z
angle B = angle X
angle C = angle Y
b) AB= ZX
AC=ZY
BC=XY
c) triangle CAB=YZX
hope it helps you
Alexei wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
2x^2 + 8x − 19.25 = 0
3x^2 + 5x − 19.25 = 0
4x^2 + 16x − 4.25 = 0
4x^2 + 16x + 15 = 0
The quadratic equation 4x² +16x - 4.25 = 0 can be used to determine the thickness of the frame option third is correct.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have:
The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long.
Let's suppose the thickness of the frame is x:
Then, the area of the rectangle:
(2x+3)(2x+5) = 19.25
4x² + 10x + 6x + 15 = 19.25
4x² +16x - 4.25 = 0
Thus, the quadratic equation 4x² +16x - 4.25 = 0 can be used to determine the thickness of the frame option third is correct.
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does anyone know proof without words ?
Step-by-step explanation:
it shows that all the small triangles that together make the complete square (c²) under the Hypotenuse consist of exactly all the composing triangles of the squares above the legs (a² and b²).
we find the 2 purple, the 2 orange, the 2 yellow and the 2 blue triangles there.
so, the area of c² must be the same as the sum of the areas of a² and b².
help plea i am beg screenshot in
Answer:
SA = 105 in^2
Step-by-step explanation:
To find surface area, find the area of all the shapes and add it all together. This shape has 4 triangle faces. They are all the same. So we can find one of them and times by 4.
Area of a triangle:
A = 1/2b•h
= 1/2• 5 • 8
= 1/2 • 40
= 20
One triangle has area 20, so times by 4 (bc four triangles)
4•20
= 80
Area of square 5•5
= 25
Add the areas:
80 + 25
= 105 sq in
Find the measure of the missing angles.
Answer:
I think it's
G: 71
H: 109
K: 151
M: 29
Step-by-step explanation:
This shows many straight angles, which we can use to find the answers.
H and 71 are on one, every right angle is 180 degrees, so we subtract 71 from 180 and get 109. G and 71 are vertical angles which makes them the same, therefore G is also 61.
M and 151 are on another straight angle, so we do the same thing, subtract 151 from 180 and we get 29. There is a line under that and M and the little unmarked angle are vertical angles so they are the same making the little one 29, making K also 151.
Hope this helps
How is the quotient of 874 and 23 determined using an area model?
Enter your answers in the boxes to complete the equations.
874 ÷ 23 = (
÷ 23 ) + (
÷ 23 )
874 ÷ 23 =
+
874 ÷ 23 =
The quotient of 874 and 23 determined using an area model is 38.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
= 874 ÷ 23
= (800 + 74 + 4) ÷ 23
We can get the answer by using the area model:
If divide 874 with 23 we get 184 as a remainder and 030 as a quotient
Further, if we divide 184 with 23 we get 0 as a remainder and 008
874 ÷ 23 = 030 + 008 = 38
Thus, the quotient of 874 and 23 determined using an area model is 38.
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PLEASE HELP ASAP KING OF BRAINLY WORLD OR ANY ONE WILL GIVE 25 POINTS
Answer:
(10,7)
Step-by-step explanation:
4x -3y = 19
2x-3y = -1 <======= multiply this equation by - 2
-4x + 6y = 2 <======= now add this to the top equation
3y = 21 <===== y = 7
use this value in one of the equations to find x = 10
What is the probability that the spinner will land on a number greater than 4 or on a shaded section? two-ninths one-half two-thirds five-sixths
The probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
How to determine the probability?The given parameters are:
Sections = 6Numbers greater than 4 = 2Shaded section = 3Shaded section and greater than 4 = 1Using the above parameters, we have the following probabilities
P(Greater than 4) = 2/6
P(Shaded) = 3/6
P(Shaded section and greater than 4) = 1/6
The required probability is then calculated using:
P = 2/6 + 3/6 - 1/6
Evaluate
P = 4/6
Simplify
P = 2/3
Hence, the probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
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In the following table of values, what would be the value of "b" in ax² + bx + c
-2 7
-1 10
0 15
1 22
2 31
Using a system of equations, it is found that the value of b in the function would be of 6.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, considering that when x = 0, y = 15, we have that c = 15.
Then, when x = -1, y = 10, hence:
a - b + 15 = 10.
a - b = -5.
a = b - 5.
When x = 1, y = 22, hence:
a + b + 15 = 22.
a + b = 7.
Since a = b - 5:
b - 5 + b = 7.
2b = 12.
b = 6.
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Answer:
B) 6
Step-by-step explanation:
I took the exam for alg 2
The dual bar chart shows the hair colour of boys and girls in a year group.
20
18
16
14
12
10
8
6
4
Black
Brown
Blonde
What fraction of the students are girls?
Give your answer in its simplest form
Frequency
20
Hair colour
Red
Boys
Girls
Anyone know how to solve this???
Answer:
m=15/14
Step-by-step explanation:
y2-y1
x2-x1
(3, 0) (-11, -15)
x1 y1 x2 y2
-15-0
-11-3 = -15/-14 m=-15/-14 = 15/14
#72 i will give brainliest to the best answer!
Step-by-step explanation:
Select all of the following that are quadratic equations.
x² + 3x - 5 = 0 ✓
x² - x = 3x + 7 ✓
5x - 7 = 0 X
7x² + 14x = 0 ✓
x³ - 3x² + 1 = 0 X
x - 5 = 9x + 7 X
What is quadratic equations?
Quadratic equations is a equation that has a general form like "ax² + bx = c"
For example :
x² + 3x - 5 = 0
x² + 3x = 5
x² → ax²
3x → bx
5 → c
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled y with entries 19, 16, 13, 10, 7.
Use the values in the table to determine the slope.
m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction
none
Three-halves
0
Negative three-halves
I NEED IT ASAP I HAVE 10 MINUTES
3. the stem-and-leaf plot shows the cost of lamps at a department store.
(a) what is the median cost?
(b) is there a mode? if so, what is it?
(c) what is the difference between the most expensive and least expensive lamps?
(d) how many lamps cost more than $20 but less than $40?
(e) what is the ratio of lamps that cost less than $40 to lamps that cost more than $40? write the ratio in simplest form.
Answer:
I don't know F but if y'all do let me now.
Step-by-step explanation:
(b) the price in the very middle of a data set, with exactly half of the houses priced for less and half priced for more.
(c) The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.
(d) The two biggest things that come to mind right away is how is it going to be used and who is going to be using it? While we would all love to get the highest quality that’s just not always possible. So, that’s a good starting point for me is considering the answer to those two questions.
(e) Price and other details may vary based on product size and color.
The difference between the most and least expensive lamps represented on the stem and leaf plot is 66.
The median costThe stem and leaf plot that completes the question is added as an attachment.
The median cost is the leaf element at the middle.
The plot has 18 leaves.
So, the median position is:
Median = (18 + 1)/2 = 9.5th
This means that the median is the mean of the 9th and the 10th items.
So, we have:
Median = (58 + 58)/2
Median = 58
Hence, the median cost is $58
The modal costThis is the element with the highest frequency in the plot.
From the attached plot 65 has the highest frequency of 3
Hence, the modal cost is 65
The difference between the most and least expensive lampsFrom the plot, we have:
Most expensive = 78
Least expensive = 12
The difference (d) is:
d = 78 - 12
d = 66
Hence, the difference between the most and least expensive lamps is 66.
Number of lamps that cost more than $20 but less than $40This means that we check the items in the range 20 to 40 (exclusive)
The elements in this range are:
25, 28, 30, 32 and 34
Hence, 5 lamps that cost more than $20 but less than $40
Ratio of lamps that cost less than $40 to more than $40From the plot, we have:
Less than $40 = 6
More than $40 = 12
The ratio is represented as:
Ratio = 6 : 12
Simplify
Ratio = 1 : 2
Hence, the ratio of lamps that cost less than $40 to more than $40 is 1 : 2
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How many variables are displayed in a scatterplot?
A. one along the x-axis, and one along the y-axis
B. one along the x-axis, and two along the y-axis
C. two along the x-axis, and one along the y-axis
D. two along the x-axis, and two along the y-axis
Answer:
A. one along the x-axis, and one along the y-axis
Step-by-step explanation:
For any kind of a plot, one variable is displayed along each axis.
__
A scatter plot has variables displayed one along the x-axis, and one along the y-axis.
Answer:
A. one along the x-axis, and one along the y-axis
Step-by-step explanation:
Edge 2023
Only 4 students have won the track races this year gina has won 4 times Hal has won 3 times Isabel has won 3 times and Jamal has won 4 times
Solve the inequality
2b + 5< 30
Answer:
b < 12.5
Step-by-step explanation:
2b + 5 < 30
1. Subtract 5 from both sides:
2b < 25
2. Divide both sides by 2:
b < 12.5
Final answer: b < 12.5
The value of b is any value that is less (smaller) than 12.5.
Hope this helps!
5a+3-4a²+2a³ sandard form
Please help me answer the question to the picture attached!!! I need help REALLY BAD!!!!
Answer:
Step-by-step explanation:
it might be like this but im not sure
The area of the rectangle is 20 square units. Find the length and width of the rectangle
which graph corresponds with the equation [tex]f(x)=\frac{1}{2 } (x+1)^{2} +2[/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The given equation is a Quadratic equation, so it's graph must be a parabola, and the Coefficient of x² is positive that means the parabola must have an opening upward.
And 2 is added to the ideal equation, so the parabola must have shift 2 units up from x - axis.
From the above information, we can easily conclude that the Correct representation is done in graph 4
What is the measure is OMN (explain please)
Answer:
90°
radius is perpendicular to tangent.
Step-by-step explanation:
HELP ME WITH THIS STORY PROBLEM SOMEONE
There are 5 posts supporting the guardrail for the steps to your home. The tallest post is 3 feet tall. The height of each of the other posts is 5/6 the height of the next larger post. Write an expression for the height of the shortest post. What is the height of the shortest post?
(also show work)
Answer:
3(5/6)^4
Step-by-step explanation:
The heights are changing by a constant factor. g1 is the first term, r is the common ratio, and n is the term number. Since the tallest pole is 3 ft so itll be g1=3. Heights are decreasing by 5/6 so r=(5/6). Since there are 5 posts shortest post will be n=5. Expression for the shortest pole is g5=3(5/6)^5-1 it simplifies to the answer
Rational function h is continuous, with a horizontal asymptote at y = 1. which function could be function h?
The function that could be the function h is option A.
What is a Rational Function?This refers to the type of function that can be defined by a rational fraction and contains polynomials.
Hence, we can see that option A is correct because x²+16 never turns 0, and this makes this function continuous and both the numerator and denominator are both polynomials of the second degree.
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The probability distribution shows the results of a survey of people's fear of flying on an airplane. find the probability that a person who is afraid of flying has never flown before. round to the nearest thousandth.
Answer:
0.070
Step-by-step explanation:
Bc I know how to do math
Calculate the average velocity of a motor cycle that travels 72km/hr in 20 seconds.
Answer:
400m/s
Step-by-step explanation:
72×1000÷3600
=20
20×20
=400m/s