9514 1404 393
Answer:
21.6 in³
Step-by-step explanation:
The volume of a square pyramid is given in terms of perimeter and height by ...
V = (1/48)P²h
V = (1/48)(10.4 in)²(9.6 in) ≈ 21.6 in³
The volume is about 21.6 cubic inches.
In(3x2 - 1) = In(191)
Given:
The equation is:
[tex]\ln(3x^2-1)=\ln(191)[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\ln(3x^2-1)=\ln(191)[/tex]
On comparing both sides, we get
[tex]3x^2-1=191[/tex]
[tex]3x^2=191+1[/tex]
[tex]3x^2=192[/tex]
Divide both sides by 3.
[tex]x^2=\dfrac{192}{3}[/tex]
[tex]x^2=64[/tex]
Taking square root on both sides, we get
[tex]x=\pm \sqrt{64}[/tex]
[tex]x=\pm 8[/tex]
Therefore, the solutions of the given equation are -8 and 8.
wht is the answer ???
The equation to represent the height of a glass slab is y=11x+2.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, we have (2, 24) and (4, 46).
Substitute (x₁, y₁)=(2, 24) and (x₂, y₂)=(4, 46) in m=(y₂-y₁)/(x₂-x₁)
= (46-24)/(4-2)
= 22/2
= 11
Substitute m=11 and (x, y)=(2, 24) in y=mx+c, we get
24=11(2)+c
c=2
Substitute m=11 and c=2 in y=mx+c, we get
y=11x+2
Therefore, the equation to represent the height of a glass slab is y=11x+2.
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A quantity with an initial value of 800 grows continuously at a rate of 4.5% per year. What is the value of the quantity after 96 months, to the nearest hundredth?
The value of the quantity after 96 months, to the nearest hundredth is 1146.66
Exponential equationsThe standard expression for an exponential equation is expressed as:
P(t) = P0e^rt
Given the following parameters
Po = 800
rate r = 4.5% = 0.045
time t = 8 years
Substitute
P(8) = 800e^0.045(8)
P(8) = 1146.66
Hence the value of the quantity after 96 months, to the nearest hundredth is 1146.66
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Supplementary solving for x
Answer:
7x-5=72( vertically opposite angle are equal)
7x=72-5
x=67/7
x=9.57
hope it helps.
Find the sum and express it in simplest form.
(7t³ + 3t - 1) + (-9t³ + 2t)
DO
Enter the correct answer.
Answer:
-2[tex]t^{3}[/tex] + 5t - 1
Step-by-step explanation:
(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)
7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1 Combine like terms
-2[tex]t^{3}[/tex] + 5t - 1
Like terms have to have the same variable and the same exponents to be like terms.
If enrollment in a class went from 30 people last term to 25 people this term, what is the percent decrease? Round to the nearest percent.
====================================================
Explanation:
The change in value is 30-25 = 5, so the amount has dropped by 5
Divide this change over the original amount to get 5/30 = 0.1667 approximately. This converts to 16.67% roughly, and that rounds to 17%
----------------
Here's a way to do it using a formula
A = old value = 30
B = new value = 25
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (25-30)/30 ] * 100%
C = -0.1667 * 100%
C = -16.67%
C = -17%
The negative percent change means we have a percent decrease. The class size went down by about 17%.
correct 0.00798516 to three significant figures
Explanation:
The zeros in 0.00798516 are not considered significant because they are not between nonzero values.
If we had something like 1.207, then that zero would be considered significant.
The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.
Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.
Answer: 0.00799
0.00798516 rounded off to three significant figures is 0.00799
hope that helps...
8-2z+3(x+y), when x=4, y=9, Z=3
[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3
Substitute:
[tex]8-2(3)+3(4+9)[/tex]
[tex]8-6+39[/tex]
Solve:
[tex]8-6+39\\=\fbox{23}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]
[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]
[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]
[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]
[tex]\mathsf{= 2 + 12 + 27}[/tex]
[tex]\mathsf{= 14 + 27}[/tex]
[tex]\mathsf{= 41}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
For each expression, select all equivalent expressions from the list.
(a) 4(5x-2)
1) 20x-2
2) 20x - 8
3) 9x-2
4) 4.5x-4.2
(b) 8y + 5y + 7y
1) 8y+12y
2) 12y-8y
3) 20y
4) 20+ y
Answer:
A. 2 20x-8
B. 3 20y
What is the IQR?
a. 20
b. 41
c. 11.5
d. 61
Hello friend, (づ｡◕‿‿◕｡)づ I'm here to help you solve this
Answer:
IQR = 35.25
Step-by-step explanation:
First Quartile Q1 = 15.75
Second Quartile Q2 = 30.5
Third Quartile Q3 = 51
Interquartile Range IQR = 35.25
Median = Q2 x˜ = 30.5
Minimum Min = 11.5
Maximum Max = 61
Range R = 49.5
~~Best regards
~Akmp
tan( 4/3 + 12/5 )= what
Answer:
[tex]tan\frac{56}{15}[/tex]
Step-by-step explanation:
We are given the trigonometrical equation of tan( 4/3 + 12/5) and are asked to find the answer.
To solve this, keep in mind that even though this has tan, the process of adding fractions is no different from the original format.
First, find the LCM of 3 and 5, this would be 15. Multiply the numbers to get to 15 (3 and 5) by both denominators and numerators.
[tex]\frac{4*5}{3*5} + \frac{12*3}{5*3}[/tex]
[tex]\frac{20}{15}+\frac{36}{15}[/tex]
[tex]\frac{56}{15}[/tex]
Our answer would be [tex]tan\frac{56}{15}[/tex]
Answer:
tan(56/15)
Step-by-step explanation:
tan( 4/3 + 12/5 ) =
tan( 20/15 + 36/15) =
tan( 56/15 )
Todd caught at least three times as many fish this year than last year. He caught 63
fish this year. Which inequality represents how many fish he caught last year?
Answer:
3y ≥ 63
Step-by-step explanation:
Ill tell you how I did it hold on
Answer:
3y ≤ 63
Step-by-step explanation:
3y ≤ 63
y ≤ 21
this means that last year ('y') he caught, at most, 21 fish - this is 1/3 less than this year
Which defines a line segment?
Answer: A line segment is a part of a line having two endpoints.
Im not sure if you meant to put a picture there. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
What is the solution to the system of equations graphed below?
PLEASE HELP!! It takes Sheila 36 minutes to edit a commercial. How many commercials can
she edit in 144 minutes?
Answer:
she can edit 4 commericals in 144 minutes.
Step-by-step explanation:
144 divided by 36 is 4
Answer:
180
Step-by-step explanation:
you have to add 36/144 to get your answer our welcome.
Please Help ASAP I don't know this well
Answer:
Step-by-step explanation:
First of all I'm going to presume it means an eight-grader chosen at random from the instrument players, if this is incorrect the question should have specified the total amount of students.
You have to add the amount of students of each of instrument to get the total:
5+9+10+9=33
then it says to not include the drum playing students so it goes from
[tex]\frac{33}{33}[/tex] to [tex]\frac{33-10}{33}[/tex] so its [tex]\frac{23}{33}[/tex] which we must now turn to a percentage.
so you divide the 23 by the 33:
23/33=0.6969....
then you multiply by 100 as it's a percentage:
0.6969...×100=69.6969...
and finally we round it do the nearest integer/whole number:
70 (we look at the tenths digit and it's a 6 so it's rounded up)
The equation of the line passing through the points (−1, 2) and (4, 0) is given by ax + by = 16. What is the value of b?
Answer:
8/5
Step-by-step explanation:
Slope of the line = (-1-4)/(2-0)= -5/2
Equation of the line :
=> y - y1 = m(x - x1)
=> y - 0 = (-5/2)(x - 4)
=> 2(y - 0) = - 5x + 20
=> 2y + 5x = 20
To make the RHS 16, divide both sides by 20 and multiply by 16:
=> (2y/20)*16 + (5x/20)*16 = (20/20)*16
=> 8y/5 + 4x = 16
compare the equation with ax + by = 16 for y, b = 8/5
What is the differences between solving an equation and solving an inequality?
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
when we have to solve an equation, it does not has an equal sign and inequalities.
When we have to solve an inequality equations usually are exact answers.
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
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Sidney surveyed 14 students at her school about their favorite classes. Of the students surveyed, 8 said their favorite class was Math. What is the experimental probability that the next student Sidney talks to will pick Math? Fraction answer and reduce!
Answer:
4/7
Step-by-step explanation:
8/14=4/7
14. A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid, What could be the x- and y-coordinates of another vertex of the square?
Answer:
For a square of side length L, the perimeter is:
P = 4*L
Then if the perimeter of our square is 36 units, we have:
36 units = 4*L
(36 units)/4 = L = 9 units.
Now we know that one vertex of the square is located at (3, 5)
Then another vertex of the square can be at:
A distance of 9 units of this point (such that these vertices are connected by one side of the square)
Some examples can be:
(3 + 9, 5) = (12, 5)
or
(3, 5 + 9) = (3, 14)
These are the simpler options, there are a lot of other possible points that can be another vertes (we can have a circle of radius 9 units centered in the point (3, 5), all these points can be another vertex of the square).
We also can have a vertex that is connected by the diagonal, this point can be:
(3 + 9, 5 + 9) = (12, 14)
or
(3 - 9, 5 - 9) = (-6, -4)
Again, there are a lot of other possible points that can be this vertex (A circle of radius √2*9 units centered in the point (3, 5)).
please please help me Please help for my math rpoject!!!!!
a. The table for the relation is given by the image shown at the end of the answer.
b. The domain and range of the relation are given as follows:
Domain: {0, 1, 2, 3, 4, ...}.Range: {0, 0.75, 1.5, 2.25, ...}.c. The relation is a function, as it value of the input is mapped to a single value of the output.
How to represent the situation?The ratio between the total cost and the number of vehicles is obtained as follows:
k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.
Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:
y = 0.75x.
For which:
x is the number of cars.y is the total cost.The domain and range are given as follows:
Domain: {0, 1, 2, 3, 4, ...}. -> possible amounts of cars.Range: {0, 0.75, 1.5, 2.25, ...}. -> possible prices.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Katrina buys a 76-ft roll of fencing to make a rectangular play area for her dogs. Use
2({+w) = 76 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation? Explain.
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
Here,
We have the following for the rectangle's perimeter:
2 ( l + w ) = 64
Here,
W = width, and L = length.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
Now,
2 ( l + w ) = 64
l + w = 32
Thus, the sum of the length and breadth measurements must equal 32.
The possible widths are 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We think about
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
Values for width and length are used as the x- and y-axes, respectively.
Below is a graph of the data.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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What is the difference between solving an equation and solving an inequality
Note that solving an equation involves finding the value(s) of the variable(s) that make the equation true. For example, solving the equation 2x + 3 = 7 would give the solution x = 2.
On the other hand, solving an inequality involves finding the set of all values of the variable(s) that make the inequality true. For example, solving the inequality 2x + 3 > 7 would give the solution x > 1.
What is inequality in Math?An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
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the cylindrical toothbrush holder modeled below has a diameter of 6.5 centimeters and a height of 9 centimeters. The shaded part represents the base of the cylinder.
A formula for finding the volume for a cylinder is V= Bh which equation can be used to find b, the area of the cylinders base in square centimeters?
A B= 3.14(6.5/2)^2
B B = 3.14(6.5/2)
C B = 3.14(6.5)^2
D B = 3.14(6.5)
Answer: B
Step-by-step explanation:
1) A publisher wants to determine the thickness of a book they will print soon. The book has a front cover and a back cover, each of which have a thickness of
1/4 in. The publisher can choose on what type of paper to print the book.
Bond paper has a thickness of 1/4 in. per 100 pages.
Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper.
Ledger paper has a thickness of 2/5 in. per `100` pages. Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on ledger paper.
2) If the publisher selects front and back covers with a thickness of 1/3 in. each, how would this change the equations you wrote on the previous slides?
1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x
1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x
2) The equation will be; y = ²/₃ +¹/₄x
How to solve Algebraic Word Problems?1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;
The addition of both gives to the book thickness of;
1/4 + 1/4 = 1/2 inch, despite how many pages the book has.
We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:
y = ¹/₂ + ¹/₄x
where;
y is the width of the book in inches.
x is every hundred pages printed on bond paper.
1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;
y = ¹/₂ + ²/₅x
2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;
y = 2(1/3) +¹/₄x
y = ²/₃ +¹/₄x
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(16,1), (17,7) find the slope of line through each pair of points
The slope of the line through each pair of points (16,1), (17,7) is 6.
A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.
The slope of a line can be positive, negative, zero, or undefined.
In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.
To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula
m = (y2 - y1) ÷ (x2 - x1)
where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the slope of the line through the points (16,1) and (17,7) is:
m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6
So the slope of the line is 6.
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Unit test Which of the x-values are solutions to the following inequality? 2 > 111
Answer: C
Step-by-step explanation: It is C because X is greater than (>) 111, and 119 is greater than 111. Good luck on the test!
Mike went on a bicycle trip. Every 4 days he travels 230 miles.
Create a proportional table comparing miles traveled to days spent traveling.
Calculating the ratio between each pair of values in a table allows you to determine whether a proportional relationship is present. The table depicts a proportional relationship if all of those ratios are the same.
How should an equation for a proportional table be written?y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to depict proportional relationships.
How should a proportional relationship be written?The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
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the inaugural attendance of an annual film festival is 20,000. The attendance y increases by 5% each year
1. about how many people will attend the festival in the fifth year?
Answer:
24,241 people
Step-by-step explanation:
To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.
1st year: 20,000
2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)
3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)
4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)
5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)
So, in the fifth year the festival will be attended by approximately 24,241 people.
Two cars leave the same parking lot, with one heading north and the other heading'east. After several minutes, the northbound car has
traveled 12 kilometers and the eastbound car has traveled 9 kilometers, measured in a straight line. How far apart are the two cars? Round
to the nearest tenth, if a decimal.
Answer:
I DONT KNOW DO YOU?