Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.
What does volume actually mean?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.
Here,
Let's use "x" yards to represent the other leg of the right triangle pyramid's base.
A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height
In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.
=> 168 = (1/3) * 14 * base area
The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.
=> 168 = (1/3) * 4x * 14
=> 168 = (4/3)x * 14
=> 168 = (4/3) * 14x
=> 168 = 56x
=> x = 168/56
=> x = 3
Therefore, the other leg of the right triangular pyramid's base is 3 yards long.
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Which of the following gives the circumference, C, of a circle with a radius of 4?
OC 4T
OC=4T²
OC=8T
O C=16T
The circumference of a circle with a radius of 4 is 8π.
What is the circumference of a circle with a radius of 4?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is the distance around a circle or the length of a circle. It is expressed mathematically as;
C = 2πr
Where r is radius and π is constant pi.
Given that the radius of the circle is 4 units.
Plug into the above formula.
C = 2πr
C = 2 × π × 4
C = 8π
Therefore, the circumference is 8π.
Option C) 8π is the correct answer.
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A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.
For the 2-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $7.00 / 2 lbs
Cost per pound = $3.50 per pound
For the 3-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $10.50 / 3 lbs
Cost per pound = $3.50 per pound
Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.
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The number of people applying for financial aid has gone up in the past 10 years by 6.74%. If the number of people that used to apply was 9,720,000, then how many people are applying now (10 years later)?
There are currently about 10,361,248 people requesting financial aid, which is an increase of 6.74% from ten years ago.
How are financial aid amounts determined?By reducing the financial barrier, it supports the advancement of your academic and professional ambitions.
Its current number of applications can be determined by multiplying 9,720,000 with 1.0674 (which equals a 6.74% increase)
If there were 9,720,000 people asking for financial help 10 years ago and there have been 6.74 times as many applicants since then. As a result, there are currently 10,361,248 applicants for financial aid, or 9,720,000 x 1.0674.
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Find the volume of the cone below if the radius is 12 height is 12
Answer:
Work smartly not hard.
Step-by-step explanation:
AI
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which 8 is a solution:
are x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
How find which equations is 8 a solutionThe equations for which 8 is a solution are:
x - 4 = 4 (if we substitute x=8, we get 8-4=4 which is true)
2x = 4 (if we substitute x=8, we get 2*8=16 which is true)
StartFraction x Over 2 EndFraction = 16 (if we substitute x=8, we get 8/2=4 which is not true)
StartFraction x Over 8 EndFraction = 1 (if we substitute x=8, we get 8/8=1 which is true)
So, the correct answers are:
x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
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A total of 550 tickets were sold for a game for a total of $1950. If adult tickets sold for $7 each and child tickets cost $2 each, how many of each kind of ticket were sold?
In linear equation, 170 adult and 380 children's tickets were sold.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...
7a + 2(550 -a) = $1950
7a + 1100 - 2a = 1950
5a = 1950 - 1100
5a = 850
a = 170
c = 550 - 170 = 380
170 adult and 380 children's tickets were sold.
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Find the value of the following expression when x = 5:
8x divided by 4= ?
Answer:
10
Step-by-step explanation:
Replace X with 5
The new equation should be 8×5 divided by 4
Then you would multiply 8×5, which is 40
Now, divided 40 by 4, which is 10.
Therefore 8×5 divided by 4 is 10.
SORRY IF THIS DIDN'T MAKE SENSE!
Given the definitions of f(x) and g(x) below, find the value of (fog)(-1).
f(x) =-x-12
g(x) = x² – 5x -5
Answer: 11
Step-by-step explanation: To find the value of (fog)(-1), we first need to find the value of g(-1), which means plugging -1 into the equation for g(x):
g(x) = x² – 5x - 5
g(-1) = (-1)² – 5(-1) - 5
g(-1) = 1 + 5 - 5
g(-1) = 1
Now we need to find (fog)(x) by plugging g(x) into f(x) and simplifying:
f(x) = -x - 12
fog(x) = f(g(x))
fog(x) = f(x² – 5x - 5)
fog(x) = -(x² – 5x - 5) - 12
fog(x) = -x² + 5x + 17
Finally, we can find (fog)(-1) by plugging -1 into the equation for fog(x):
fog(x) = -x² + 5x + 17
(fog)(-1) = -(-1)² + 5(-1) + 17
(fog)(-1) = -1 - 5 + 17
(fog)(-1) = 11
Therefore, the value of (fog)(-1) is 11.
if necessary.
21. A company makes specialized fish tanks, like the one shown below. If 1 gallon = 0.134 ft³, how many
gallons of water will it take to fill the fish tank completely?
9 ft
2 ft
3 ft
V = 6
It would take about 402.985 gallons of water to fill the fish tank completely.
What is the amount of water?To calculate the number of gallons of water it would take to fill the fish tank completely, we need to multiply the dimensions of the fish tank in cubic feet by the conversion factor to convert cubic feet to gallons.
Given:
Length = 9 ft
Width = 2 ft
Height = 3 ft
Conversion factor: 1 gallon = 0.134 ft³
Step 1: Calculate the volume of the fish tank in cubic feet
Volume = Length × Width × Height = 9 ft × 2 ft × 3 ft = 54 ft³
Step 2: Convert cubic feet to gallons
54 ft³ × (1 gallon / 0.134 ft³) ≈ 402.985 gallons
So, it would take approximately 402.985 gallons of water to fill the fish tank completely.
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PLS HELP!!
Which expressions are equivalent to log4 (1/4x^2)?
Answer:log₄ 1 /4 + log₄ x²
Step-by-step explanation:
please help pleaseee i need dis good grade
Answer:62.8 units
Step-by-step explanation:
Please help me! Thank You So Much in Advance!!!!!!!
The ratio between the number of people who do not enjoy reading and the number of people who do not enjoy playing videogames is given as follows:
3 to 1.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
The amounts for this problem are given as follows:
Do not enjoy reading: 8 + 1 = 9.Do not enjoy playing videogames: 2 + 1 = 3.Hence the ratio is of:
9/3 = 3/1 = 3 to 1.
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Question 3 (1 point)
Which of the choices is NOT a good example of a line of best fit?
A.
B.
C
D
Answer:
B
Step-by-step explanation:
All of the lines of best fit are close to the points in the scatter plot except B.
The line of best fit in B does not even touch any of the points in the scatter plot, so it is not a good example of a line of best fit.
if you roll a number cube 20 times. which scenario is least likely?
a) you find the experimental probability of rolling a 1 or 2 to be 0.3.
b) you find the experimental probability of rolling a 3 or 4 to be 0.4.
c) you find the experimental probability of rolling a 5 or 6 to be 0.5.
d) you find the experimental probability of rolling a number divisible by 3 to be 0.35
Use the definition of Ax
to write the vector equation as a matrix equation.
The vector equation written as a matrix equation is enter your response here
.
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
Describe vector?A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.
Here in the question,
(0, 0) is the beginning position. There should be an arrow above each vector name listed below.
Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).
Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).
These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.
Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.
Either way, the same conclusion is reached.
The terminal point of A + B is at (5, 1).
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
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An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. Be sure to address the original claim.
a) There is sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
b) There is not sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
c) There is not sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
d) There is sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
anyone can help with these?
Answer:
m∠B=63 degrees
AC≈23.6 units
AB≈26.4 units
Step-by-step explanation:
since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.
after isolating the variable, m∠B=63 degrees
we then use law of sin to find AC and AB
since [tex]\frac{sin(A)}{a}[/tex] is already given, use that to find both AC and AB
the equation for AC would be: [tex]\frac{sin(27)}{12} =\frac{sin(63)}{AC}[/tex]
the equation for AB would be: [tex]\frac{win(27)}{12} =\frac{sin(90)}{AB}[/tex]
after isolating the variables, AC≈23.6 units and AB≈26.4 units
EASY!! I ONLY NEED HELP WITH #39 & #40
39) The balance in the account after 6 years is $4,073.62.
40) The balance in the account after 6 years is $4,134.83
What is the formula for compound interest?
[tex]A = P(1 + \frac{r}{n} )^{(nt) }[/tex]
Here P is the principal,A is the balance, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the time in years.
39) Here given that P = $3500, r = 2.16% = 0.0216, n = compounded quarterly = 4 and t = 6.
So, [tex]A = 3500(1 + \frac{0.0216}{4})^{(4 \times 6)} = 4,073.62[/tex]
Therefore, the balance in the account after 6 years is $4,073.62.
40)Here given,P = $3500, r = 2.29% = 0.0229, n = 12 (compounded monthly), and t = 6.
[tex]A = 3500(1 + \frac{0.0229}{12})^{(12 \times 6)} = 4,134.83[/tex]
Therefore, the balance in the account after 6 years is $4,134.83.
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Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
co
5
H
The mapping diagram above|
Set B
✓in
-2
3
O
7
શ function since
where there
Answer:
It is not a function
Step-by-step explanation:
A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.
Here, element "1" has two images 3 and 7. Therefore it's not a function.
The owners of Applewood Farmstead tracked their fruit sales over the weekend. The graph below shows the relative frequencies of the sales of each fruit. Applewood Farmstand sold a total of 320 pieces of fruit over the weekend. How many of those were apples?
Applewood Farmstand sold 102 pieces of apples over the weekend.
What is graph?Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.
The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:
Apples = (320 pieces of fruit) x (0.32)
Apples = 102 pieces
Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.
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In the 1992 Winter Olympic trials, John Jennings pushed the USA bobsled with a force of 110 N at an angle of 42with the horizontal. Find the horizontal and vertical components of the force
Round to the nearest hundredth!!!!!!
The horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
How to determine the horizontal and vertical components of the forceThe force can be broken down into its horizontal and vertical components using trigonometry.
Horizontal component:
cos(42) = adjacent/hypotenuse
adjacent = cos(42) * 110 N
adjacent ≈ 80.34 N
Vertical component:
sin(42) = opposite/hypotenuse
opposite = sin(42) * 110 N
opposite ≈ 74.62 N
Therefore, the horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
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The diameter of a circle is 6 centimeters. What is the circle's area?
Use 3.14 for .
Answer: The area of circle is 28.26 cm^2
Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.
Area of circle = pi r^2
And the value of pi is to be taken 3.14
The area of the given circle is 28.26cm^2.
the simplest form of 4(3x+y)
An expression which is the simplest form of 4(3x + y) + (2x - 5y) + x² include the following: x² + 14x - 6y.
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
In this scenario and exercise, the simplest form of the given expression 4(3x + y) + (2x - 5y) + x² can be determined or calculated by simplifying it as follows;
4(3x + y) + (2x - 5y) + x²
12x + 4y + 2x - 5y + x²
14x + - y + x²
By rearranging, we have;
x² + 14x - 6y.
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Complete Question:
Which expression is the simplest form of 4(3x+y)+2x-5y)+x²
√ x 2 = x 2 4 = x 1 2 = √ x Based on this, the student claims that 4 √ x 2 = √ x for all values of x.
Answer:
The student's claim is incorrect. While it is true that √x^2 = x for all non-negative values of x, this property does not apply to expressions with multiple terms, such as 4√x^2.
Step-by-step explanation:
consider the case where x = -1. Then, √x^2 = √(-1)^2 = 1, but 4√x^2 = 4√1 = 4. On the other hand, √x = √(-1) is undefined, so the equation 4√x^2 = √x is not true for this value of x.
Therefore, the student's claim is not true for all values of x, and it is important to be careful when applying algebraic properties to expressions with multiple terms.
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = x2 − x − ln(x)
(a)
Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(b)
Find the local minimum and maximum value of f.
local minimum value
local maximum value
(c)
Find the inflection point.
(x, y) =
Find the interval(s) on which f is concave up. (Enter your answer using interval notation.)
Find the interval(s) on which f is concave down. (Enter your answer using interval notation.)
It should be noted that f(x) is increasing on the intervals (-1/2, 0) and (0, ∞), and decreasing on the interval (-∞, -1/2).
How to explain the functionThe derivative of f(x) is denoted as:
f'(x) = 2x - 1 - 1/x
It should be noted that to determine the critical points, set f'(x) to equal 0 and solve for x:
2x - 1 - 1/x = 0
Multiplying by x gives:
2x^2 - x - 1 = 0
On the intervals (-1/2, 0) and (0, ∞), the function f(x) exhibits increasing behaviour; in (-∞, -1/2). it's decreasing.
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Find the area of each
The areas of each figure are 5.6 sq m, 76.8 sq km, 280.8 sq units, 173.88 sq units and 332 sq units
Finding the area of each figureThe area of a shape is the amount of space on it
Using the above as a guide, we have the following:
Figure 7:
The area is calculated as
Area = 1/2 * (sum of parallel sides) * height
So, we have
Area = 1/2 * (3.9 + 1.7) * 2
Area = 5.6 sq m
Figure 8:
The area is calculated as
Area = Base * height
So, we have
Area = 9.6 * 8
Area = 76.8 sq km
Figure 9:
The area is calculated as
Area = 6 * 1/2 * Base * height
So, we have
Area = 6 * 1/2 * 9 * 10.4
Area = 280.8 sq units
Figure 10:
The area is calculated as
Area = 7 * 1/2 * Base * height
So, we have
Area = 7 * 1/2 * 6.9 * 7.2
Area = 173.88 sq units
Figure 11:
The area is calculated as
Area = 8 * 1/2 * Base * height
So, we have
Area = 8 * 1/2 * 10 * 8.3
Area = 332 sq units
Figure 12, 13 and 14:
The areas of the figures cannot be calculated with the available details and parameters
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If z is a standard normal variable, find P(z>.97)
Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
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Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
no
Yes, (3, 5) is a solution to this system of equations.
How do you calculate the equation system?
The system has a single solution if the m-values of the two equations differ. The system has no solution if the two equations have the same m-value but distinct b-values.
Substituting x = 3 and y = 5 into the equations, we get:
y = 5 (which is already given)
y = (-5/3)x + 10
y = (-5/3) * 3 + 10
y = -5 + 10
y = 5
Therefore, both equations are satisfied by the point (3, 5), making it a solution to the system of equations.
Yes, (3, 5) is a solution to this system of equations.
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What is the measure of angle x?
Enter your answer in the box.
Answer:
43
Step-by-step explanation:
at the upper horizontal plane the angles add up to 180 degrees so you add the right angle with the 47 degrees and then you subtract the answer from180 degrees.the value you obtain is oppositely equal to the value of x hence,43
A bag of M&M's has 6 red, 8 green, 2 blue, and 4 yellow M&M's. What is the probability of randomly picking:
(give answer as a reduced fraction)
1) a yellow?
There are no orange M&Ms in the bag, thus there is no probability of picking one.
What is Probability?An event is any subset of the sample space, which is the set of all potential results of a random experiment, according to probability theory. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.
Classical probability, empirical probability, and subjective likelihood are just a few of the several varieties of probability. Empirical probability is based on actual observations or experiments, as opposed to classical probability, which is predicated on the idea that all events are equally likely. On the other hand, subjective probability is dependent on opinion or conviction.
Picking a yellow M&M has a 4/20 chance, which drops to 1/5.
The likelihood of selecting a blue or green card M&M is the result of adding the odds of selecting a blue and a green:
To reduce to 1/2, 2/20 + 8/20 = 10/20.
The likelihood of choosing an orange M&M is zero because there are no orange M&Ms in the bag.
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The complete question is: