Following are the given complete statements:
(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
What is plane ?A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is a mathematical concept used in geometry and is often represented as a flat sheet or a graph on a coordinate system. In the real world, a plane can be thought of as a flat surface such as a tabletop, a piece of paper or a wall.
According to the given information :(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
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What type of figure is shown above?
Answer:
See below
Step-by-step explanation:
This is a triangular prism:
h = Perpendicular height of prism
Base shape = Triangle
t = Perpendicular height of triangle
Volume of triangular prism = Base Area × h
= Area of triangle × h
= [[tex]\frac{1}{2}[/tex] × Base of triangle × t] × h
= [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in] × 10 in
= 42.5 cubic inches
Total Surface Area = [2 × Base Area] + Lateral Surface Area
= [2 × Area of triangle] + [(Perimeter of triangle) × h]
= {2× [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in]} + [(5 in + 3 in + 3 in) × 10 in]
= 8.5 [tex]in^{2}[/tex] + 110 [tex]in^{2}[/tex]
= 118.5 square inches
Stefan is decorating a rectangular cake. He will put blue icing on the top three-fourths of the cake, as shown in this model. He will put red dots on the left one-fifth of the cake, as shown in this model. What fraction of the cake will have both blue icing and red dots? .
which expression is equivalent to 3.5b + 4.5 + 0.5b - 0.5 - 1.5b
[tex]3.5b + 4.5 + 0.5b - 0.5 - 1.5b[/tex]
Combine Like Terms:
[tex](3.5b+0.5b-1.5b)+(4.5-0.5)[/tex]
[tex]\boxed{2.5b+4}[/tex]
A human body that is performing light work generates about 700.0 BTUs of body heat per hour. If a room that is 12.0 x 13.0 x 11.0 is being painted by 3 people, how many BTUs per cubic foot do they produce in 2 hours
2.45 BTUs/ft³ is produced in 2 hours.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.It is given that a human body that is performing light work generates about 700 BTUs.
Total heat generated by 3 peoples in 1 hour -
Q{heat} = 3 x 700
Q{heat} = 2100 BTUs/hr
For the two hours -
Q{T} = 2100 x 2
Q{T} = 4200 BTUs ... { 1 }
Volume of the room -
V{R} = 12 x 13 x 11
V{R} = 1716 ft³ ... { 2 }
So, we can write as -
BTUs per cubic foot produced in 2 hours is -
{r} = Q{T}/V{R}
{r} = 4200/1716
{r} = 2.45 ft³
Therefore, 2.45 BTUs/ft³ is produced in 2 hours.
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Cory and Veronica each multiplied one/2×5/2 Cory got six/ four and Veronica Cook got five over four which student found the correct answer explain
Answer:
Veronica is correct
Step-by-step explanation:
1/2 x 5/2 = 5/4
1/2 + 5/2 = 6/4
What are the ACT math formulas that you absolutely have to know?
The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.
Here are some of the most important ACT math formulas that you should know:
1. Basic operations: addition, subtraction, multiplication, and division.
2. Exponents and roots: [tex]a^n[/tex] means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.
3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.
5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.
6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.
7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.
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A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4 6 5 7 3 5 What is the best explanation of how to find the experimental probability of rolling a 3? To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary
The best explanation of how to find the experimental probability of rolling a 3:
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have the Data as:
Number Frequency Probability
1 4 0.13
2 6 0.20
3 5 0.17
4 7 0.23
5 3 0.10
6 5 0.17
total 30 1.00
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
= 5/30
= 1/6
= 0.166
= 16.6% or 17%.
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1) A bakery used one-sixth of a bag of chocolate chips to make 8 batches of cookies. How
much of the bag did they use for each batch?
Answer:
Step-by-step explanation:
1/6 ÷ 8
1/6 × 1/8
1/48
for each batch
a process in which a number is changed, such as by adding, subtracting, dividing or multiplying is definition of _____
Answer:operation
Step-by-step explanation:
What angle in degrees does the guy wire make with the ground?
Answer:
45? I'm not 1000% sure tog
Step-by-step explanation:
A, B, C and D form the vertices of a parallelogram.
AD = 10.1cm, AB = 15.9cm and
∠
BAD = 61°.
Find the area of the parallelogram. Round to 1 DP
I thought of a number, this number doubled is 9 more than the number itself. what is my number?
Possible answer: 9
Step-by-step explanation:
9 doubled is 18, and that is 9 more than the original number itself.
Unless I'm wrong.
I NEED HELP ON THIS ASAP!!!
The system of linear inequalities (x, y) has a solution that is (-1, 2)
What is the system of linear inequalityA system of linear inequalities is identical to a system of linear equations, but instead of equations, it is made up of inequalities. Many constraint scenarios are modeled using sets of linear inequalities.
We may determine the values of x and y in the above problem as;
x + y > 1 ...eq(i)
-x + y <= 3 ...eq(ii)
Solving both inequalities;
The solution is;
1 - x < y ≤ 3 + x
This is simple to plot on a graph, and the intersection will provide the answer;
The graph below shows the inequality's (x, y) solution, which is (-1, 2)
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What is the ratio of dL to L?
Answer:
Step-by-step explanation:
The ratio of a change in a quantity (dL) to the original quantity (L) is given by:
dL/L
This ratio can also be expressed as a percentage change, which is calculated by multiplying the ratio by 100:
(dL/L) * 100 = percent change
In general, the ratio of dL/L represents the fractional change in the quantity L and is used to quantify the effect of small changes in a system or process. For example, if L is the length of an object and dL is a small change in length, then dL/L represents the fractional change in length due to this change.
The point (10, 10) is the midpoint of C and D. Given that the coordinates of C are (15, s) and the coordinates of D are (t, 3), solve for the values of the variables s and t. Show your work (HELP ME PLEASE)
Answer: T= 5 and s =17
Step-by-step explanation: Use the midpoint formula
Solve for T
^xm=^xC+^xD/2
15+t/2=10
15+t=20
Solve for S
^ym=^yC+^yD/2
s+3/2=10
s+3=20
Help pls due tomorrow
The angle measure of the missing angle is 630 - 11x.
What is the interior angle?Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."
Given:
A non-regular hexagon.
The sum of all the interior angles of the hexagon is,
= (6 - 2) 180
= 4(180)
= 720
Now, the angle measure of the missing angle,
= 720 - 2x - 3x - 2x - 4x - 90
= 630 - 11x
Therefore, 630 - 11x is the required expression.
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Solve for y. 2x - 1/4y = 1
Arial says that, for any pair of linear realtions, if the coefficients of the y-terms are equal the coefficients of the x-terms are equal, the graphs of the two lines will be parallel. Give an example for which Arial's claim is true.
Arial's claim that the graphs of the two lines will be parallel if the coefficients are equal.
How to prove the claim ?If the coefficients of the y-terms are equal and the coefficients of the x-terms are equal, the two lines represented by the equations will be parallel. Parallel lines have the same slope and do not intersect, meaning that their graphs will never cross.
To prove Arial's claim, here is an example:
y = 2x + 1 and y = 2x + 3
The coefficients of the y-terms are equal in both equations, since they both have a coefficient of 2 in front of the x-term. The coefficients of the x - terms are also equal, since they both have a coefficient of 1 in front of the constant term thereby making them parallel.
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Find x. Round your answer to the nearest tenth of a degree.
Answer:
x = 64.6 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent side / hypotenuse
cos x = 3/7
Taking the inverse cos of each side
x = cos^-1 ( 3/7)
x = 64.6 degrees
Rickquan, wants a balance of $565 in his account. He deposited $65 in
his account and will save $25 per week. How many weeks will it take
Rickquan to reach his goal?
20
Step-by-step explanation:
cause 565-65 is 500 and divide that by 25 is 20.
Answer:
20 weeks
Step-by-step explanation:
starting with an initial 65 adding money each week after 20 weeks he would've added 500
How to solve your problem: 8d+d+3d+2+4d
Answer:
d= -1/8
Step-by-step explanation:
8d+d+3d+2+4d= 16d+2
16d= -2
d= -1/8
A carnival charges $6 to enter and $.75 per ticket. Write a function rule that models this situation.
Rule:
The function rule that models this situation is that increase in the number of tickets would lead to an increase in the total cost charged for each individual.
What is a direct relationship between two values?A direct relationship between two values is said to exist when the increase in one value leads to the increase of the other.
The cost of 1 ticket = $.75
The cost to enter the carnival = $ 6
Therefore the total cost for each individual = 6+0.75 = $6.75
The cost for two tickets for two individuals = 2× 6.75 = $13.5.
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what is -3x+y=6 on a graph?
The graph of the equation -3x+y=6 is linear and is attached with the answer below.
What is a linear equation?A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given linear equation is -3x+y=6. When we plot the linear equation -3x+y=6 on the graph it will be a straight line and the x and y-intercepts are -2 and 6 respectively.
The graph of the linear equation is attached with the answer below.
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SMENT UNIT 22 SY23 / SECTION 1/1 OFS /
Kane Laboratories is studying the impact of various enriched growth mediums on different bacteria. They
are currently studying the impact of placing Bacillus Megaterium into a culture of sucrose salts. The table
below shows the growth rate of the bacteria during the growth phase. The generation time for Bacillus
Megaterium is 25 minutes in this culture.
Generation
Number, n
Bacteria
Population, P
B. P (n) = 12+2n
OC. P (n) = 12 (n+1)
OD. P (n) = 12-4-1
0
12
1
24
2
3
48 96
4
20%
192
Which function models the growth of the Bacillus Megaterium over each generation?
O A P (n) = 12-2
The function that models the growth of the Bacillus Megaterium over each generation is B. P (n) = 12 + 2n.
Determine the number of 4g cremora sachets that will make 1kg cremora box.
A total of 250 packets of 4g cremora will make 1kg cremora box.
What is function?A function is a elation between a dependent and independent variable.
Given are 4g cremora sachets.
We can write the total number of cremora sachets that will make 1kg cremora box as -
{n} = 1000/4
{n} = 250
Therefore, a total of 250 packets of 4g cremora will make 1kg cremora box.
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2x+3y=11
x-3y = 1
What is the solution (x, y) to the given system of
equations?
Answer:
(x, y) = (4, 1)
i don't have an explanation lol
If the force of two forces is 12 N acting at an angle of 90° to one forces and their greatest force is 18 N, determine the two forces.
Answer:Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.
As the resultant force makes 90
∘
with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q
2
−P
2
=R
2
Q
2
−P
2
=(12)
2
Q
2
−P
2
=144 (1)
The sum of magnitudes of two forces is given as,
P+Q=18
Q=18−P (2)
Substituting the value from equation (2) in equation (1), we get
(18−P)
2
−P
2
=144
P=5N
Substituting the value of P in equation (1), we get
Q=18−5
=13N
Thus, the magnitude of the forces are 5N and 13N.
Step-by-step explanation:
Choose ALL answers that describe the polygon QRST if QR = 12, RS = 12, ST = 12, TQ = 12, m
Answer:
quadrilaterals
ok I only guss it
1, 6, 36, 216, 1296...
Write the recursive form of the sequence above.
Tn = 6Tn-1 is the recursive form of the sequence
Finding the recursive function of a geometric sequenceA geometric sequence is determined by its common ratio. The standard recursive formula is expressed as:
Tn = rTn-1
Determine the common ratio of the sequence
r = 6/1 = 36/6
r = 6
Substitute the common ratio into the formula to have:
Tn = 6Tn-1
Hence the recursive form of the sequence above is Tn = 6Tn-1
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5. A company produced 9,800 pairs of sunglasses
in one week, and 49 of the sunglasses failed
a quality inspection. If the company produces
1,400 pairs of sunglasses in one day, how many
would you expect to fail the quality inspection
The number of sunglasses that will fail the quality inspection are 7.
What is a ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
We are given that, A company produced 9,800 pairs of sunglasses
in one week, and 49 of the sunglasses failed a quality inspection.
And based on this data we are asked to find the number of sunglasses which will fail the quality inspection If the company produces
1,400 pairs of sunglasses in one day
Let the number of sunglasses failing the quality inspection be x
hence the ratio becomes
9800/49 = 1400/x
x= 1400*49/9800
x= 7
The number of sunglasses that will fail the quality inspection are 7.
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