Volume of empty jar 8x² + 2x - 4
Volume of water poured = 4x² - 3x + 2
More number of cubic inches that the jar can still hold= (8x² +2x - 4) -(4x²- 3x+2)
= 8x² + 2x - 4 - 4x² + 3x - 2
Rearrange
=8x² - 4x² + 2x + 3x - 4 - 2
=4x² + 5x - 6
Hence, the more number of cubic inches that the jar can still hold is
4x² + 5x - 6
hey! I need help/answers to 20 questions. Heres the first question Find the volume of a pyramid with a square base, where the side length of the base is 10.9 m and the height of the pyramid is 4.7 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
The Volume of the pyramid is;
[tex]186.1\text{ }m^3[/tex]Explanation:
Given the pyramid with a square base and dimensions;
[tex]\begin{gathered} l=10.9m \\ h=\text{4}.7m \end{gathered}[/tex]Recall that the volume of a pyramid can be calculated using the formula;
[tex]V=\frac{l\times l\times h}{3}[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{10.9\times10.9\times4.7}{3} \\ V=186.1m^3 \end{gathered}[/tex]Therefore, the Volume of the pyramid is;
[tex]186.1\text{ }m^3[/tex]Circle O has a center at (2,-2) and a diameter of 8 units. Identify which point lies on Circle O. O A. (0,1) O B. (6,-2) O C. (2, 2) O D. (-3,-2)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
circle
center (2,-2)
diameter = 8
point on the circle = ?
Step 02:
equation of a circle
(x - a)² + (y - b)² = r²
r = d / 2 = 8 / 2 = 4
(x - 2)² + ( y - (-2))² = 4²
(x - 2)² + ( y + 2)² = 16
Step 03:
We must verify the points with the equation.
A. If (0 , 1)
(x - 2)² + ( y + 2)² = 16
( 0 - 2)² + ( 1 + 2)² = 16
4 + 9 = 16
15 < 16 the point is inside of the circle
B. If ( 6, -2)
(x - 2)² + ( y + 2)² = 16
(6 - 2)² + ( -2 + 2)² = 16
16 = 16 the point is on the circle
The answer is:
B. (6 , -2)
A rectangle or televisions length is 3 inches more than twice its width the perimeter of the television is 144 inches what is the width of the television
The width of the television is 23 in.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
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If AABC – ADEF, which angle corresponds with angle A in the following image?Side16deee3ce67551e9dd974313e76f08f2 webm 10Blank 1:
Answer:
Angle D corresponds to angle A
Explanations:
Since △ABC ≅ △DEF;
It means both triangles have corresponding sides and angles.
To make it obvious which angle in △DEF corresponds to angle A in △ABC, let us redraw △DEF to look like △ABC
Obviously from the diagrams I drew above,
Find the slope and y-intercept of the line.y = -3,000 + 30x
The given equation is
[tex]y=-3,000+30x[/tex]It's important to know that this is a linear equation, and it's written in the form
[tex]y=mx+b[/tex]Where m is the slope, and b is the y-intercept.
That means we only need to look for these values and that's it!
According to the given equation, we have
[tex]m=30,b=-3,000[/tex]Therefore, the slope is 30, and the y-intercept is at (0, -3000).Can you please figure out this equation and see if I have the right answer
The expression is given to be:
[tex]\tan \left(\frac{7\pi }{12}\right)[/tex]Rewrite the expression:
[tex]\frac{7\pi}{12}=\frac{\pi}{4}+\frac{\pi}{3}[/tex]Therefore, we have:
[tex]\tan\left(\frac{7\pi}{12}\right)=\tan\left(\frac{\pi}{4}+\frac{\pi}{3}\right)[/tex]Recall the summation identity:
[tex]\tan \left(x+y\right)=\frac{\tan \left(x\right)+\tan \left(y\right)}{1-\tan \left(x\right)\tan \left(y\right)}[/tex]Therefore, we have:
[tex]\tan\left(\frac{\pi}{4}+\frac{\pi}{3}\right)=\frac{\tan\left(\frac{\pi}{4}\right)+\tan\left(\frac{\pi}{3}\right)}{1-\tan\left(\frac{\pi}{4}\right)\tan\left(\frac{\pi}{3}\right)}[/tex]Recall that:
[tex]\begin{gathered} \tan \left(\frac{\pi }{4}\right)=1 \\ \tan \left(\frac{\pi }{3}\right)=\sqrt{3} \end{gathered}[/tex]Hence, the equation becomes:
[tex]\frac{\tan(\frac{\pi}{4})+\tan(\frac{\pi}{3})}{1-\tan(\pi\/4)\tan(\pi\/3)}=\frac{1+\sqrt{3}}{1-1\cdot\sqrt{3}}[/tex]Therefore, we can simplify the expression to be:
[tex]-2-\sqrt{3}[/tex]The THIRD OPTION is correct.
A time traveler can take 4 books with him, and he has 86 books to choose from. How many differentways can the books be selected?
Combination:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]n is the number of things to choose from, and r is the number of thing
Kobe is 2.07 metres tall.
Marcus is 1.79 metres tall.
Stephen is taller than Marcus by half the difference between Kobe's height and
Marcus's height.
How tall, in metres, is Stephen?
The height of Stephen is = 1.79 + 0.14 = 1.93 meters
What is unitary method ?In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple. How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used.
CalculationStep: 1
The height of Kobe is 2.07 meters
The height of Marcus is 1.79 meters
The difference between Kobe's height and Marcus's height = 2.07 - 1.79 meters
And its half is = 1/2 * 0.28 = 0.14 meters
Stephen is taller than Marcus by half the difference between Kobe's height and Marcus's height
The height of Stephen is = 1.79 + 0.14 = 1.93 meters
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A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
we have that
The area covered by grass is equal to the area of a rectangular yard minus the area of the square flower garden
so
A=(22)(19)-(10.5)^2
A=307.75 ft2Find the radius when the arc is / and / radians
The arc length formula is :
[tex]l=r\theta[/tex]where r = radius
θ = angle in radians
and l = arc length
From the problem, the arc length is 18π/7 and the angle is 6π/7.
Using the formula above :
[tex]\begin{gathered} \frac{18\pi}{7}=r(\frac{6\pi}{7}) \\ 18\pi=r(6\pi) \\ r=\frac{18\pi}{6\pi} \\ r=3 \end{gathered}[/tex]ANSWER :
The radius is 3
4. A number between 200 and 400 with 6 more tens than ones.
Answer
Question 3
Largest number where the sum of the digits is 16 is 862
Question 4
The number between 200 band 400 with 6 more tens than ones is 382
Explanation
We can only use numbers from the digit bank to answer this questions.
Question 3
Largest number where the sum of the digits is 16 is 862
Question 4
A number between 200 and 400 with 6 more tens than ones.
Noting that the tens digit is the second digit from the right in a number and the ones digit is the first number from the right for any number.
So, we are asked to form a number whose second number from the right is 6 more than the first number from the right.
So, we can easily see that
The ones number has to be 2
The tens number has to be 8 (Since 8 is 6 more than 2)
Then, for the third and last number, since the number has to be between 200 and 400, the last number has to be 3.
So, the number between 200 band 400 with 6 more tens than ones is 382
Hope this Helps!!!
Solve the equation by factoring. Separate multiple answers with a comma.
x = -4, 0, 6
Explanations:The given equation is:
[tex]x^3-24x=2x^2[/tex]The equation can be re-written as:
[tex]x^3-2x^2\text{ - 24x = 0}[/tex][tex]\begin{gathered} x(x^2\text{ - 2x - 24) = 0} \\ x\lbrack x^2\text{ - 6x + 4x - 24\rbrack = 0} \\ x\lbrack x(x-6)\text{ + 4(x - 6)\rbrack = 0} \\ x\text{ (x - 6) (x + 4) = 0} \\ x\text{ = 0} \\ x\text{ - 6 = 0} \\ x\text{ = 6} \\ x\text{ + 4 = 0} \\ x\text{ = -4} \end{gathered}[/tex]x = -4, 0, 6
what is 12 times 12?
Answer:
144
Step-by-step explanation:
Answer: 12x12=144.
I hope this helps!!!!!!!!!!!!!!!!!!!!!!!!!!
Find the GCF of 24m^4n and 16m^2n.
Answer:
[tex]8m^2n[/tex]Step-by-step explanation:
To find the GCF (greatest common factor), we have to find the prime factors of each number. Then, we have to find similar factors.
In this exercise, we have:
24m⁴n = 2 * 2 * 2 * 3 * m * m * m * m * n
16m²n = 2 * 2 * 2 * 2 * m * m * n
The GCF will be 2 * 2 * 2 * m * m * n
So, The GCF is 8m²n.
explain the meaning of the point (1, 1 .5) in terms of the situation
The graph above is a relationship between the amount of oil and the amount of vinegar use to prepare salad dressing. The point 1 is the x axis while the point 1.5 is the y axis .
In terms of the situation if the x axis represents the amount of oil required for the salad dressing and the y axis represents the amount of vinegar , the point (1, 1.5) says for every 1 table spoon of oil required , 1.5 table spoon of vinegar is also used to make the salad dressing.
Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.tan4(4x)
Solution
[tex]\begin{gathered} \tan^2(4x)=\frac{1-\cos(8x)}{1+\cos(8x)} \\ \\ \Rightarrow\tan^4(4x)=\frac{1-2\cos(8x)+\cos^2(8x)}{1+2\cos(8x)+\cos^2(8x)} \\ \\ \text{ since }\cos^2(8x)=\frac{1+\cos(16x)}{2} \\ \\ \Rightarrow\tan^4(4x)=\frac{1-2\cos(8x)+\frac{1+\cos(16x)}{2}}{1+2\cos(8x)+\frac{1+\cos(16x)}{2}} \\ \\ \Rightarrow\tan^4(4x)=\frac{2-4\cos(8x)+1+\cos(16x)}{2+4\cos(8x)+1+\cos(16x)} \\ \\ \Rightarrow\tan^4(4x)=\frac{3-4\cos(8x)+\cos(16x)}{3+4\cos(8x)+\cos(16x)} \end{gathered}[/tex]The answer is:
[tex]\frac{3-4\cos(8x)+\cos(16x)}{3+4\cos(8x)+\cos(16x)}[/tex]Show that when -9p2 + 4p + 1970 = 0, Total Revenue is at its maximum.Find the price and quantity which maximise Total Revenue.
Step 1
Write the demand function equation
[tex]Q=-9p^2+4p\text{ + 1970}[/tex]Step 2:
To find the price and quantity which maximize the revenue
You will find the derivative of Q with respect to price
[tex]\begin{gathered} \frac{dQ}{dp}\text{ = -18p + 4} \\ -18p\text{ + 4 = 0} \\ 18p\text{ = 4} \\ p\text{ = }\frac{4}{18}\text{ = }\frac{2}{9} \end{gathered}[/tex]Step 3:
Find the quantity demand by substituting p = 2/9
[tex]\begin{gathered} Q\text{ = -9 }\times\text{ (}\frac{2}{9})^2\text{ + 4 }\times\text{ }\frac{2}{9}\text{ + 1970} \\ =\text{ -0.44 + 0.888 + 1970} \\ =\text{ 1970.444} \\ =\text{ 1970} \end{gathered}[/tex]Final answer
The price which maximizes the total revenue is p = 2/9
The quantity is Q = 1970
A football team played A games last year. They lost B of those games. What was their winning percentage
Answer:
(A - B)/A x 100%
Explanation:
If they played A games last year and lost B of those games, they win the rest of the games, so they win A - B games.
Then, the percentage is calculated as the number of games that they win over the total number of games multiplied by 100, so the winning percentage is
(A - B)/A x 100%
A wire is attached from the top of a 30-foot tall telephone pole…
The diagram illustrating the given scenario is shown below
The triangle formed is a right triangle. From the diagram,
AB = height of pole
angle ACB is the angle between the and the pole
AC is the length of the wire
taking angle 48 as the reference angle,
hypotenuse = AC
adjacent side = BC = 30
θ = 48
We would find AC by applyng the Cosine trigonometric ratio which is expressed as
Cosθ = adjacent side/hypotenuse
By substituting these values into the formua, we have
Cos 48 = 30/AC
By crossmultiplying, we have
AC Cos 48 = 30
By dividing both sides of the equation by Cos 65, we have
AC = 30/Cos48
AC = 44.8
The length of the wire is 44.8 feet
Adu pick one pen from a box,
containing one blue pen, 2 red
pens and 3 green pens without.
looking into the box. What is the
probability of picking
(1) Blue Pen
if Red pen
( Green pen
(iv) green or blue pen
Red or green pen
The probability of picking Blue pen, Red pen and Green pen out of the box at random will be 1/6, 1/3 and 1/2 respectively.
As per the question statement, we are supposed to find the probability of picking Blue pen, Red pen and Green pen out of the box at random.
It is given that the box contains one blue pen, 2 red pens and 3 green pens.
Total pen = 6
Probability of Blue pen = 1/6
Probability of Red pen = 2/6 = 1/3
Probability of Green pen = 3/6 = 1/2
Hence, the probability of picking Blue pen, Red pen and Green pen out of the box at random will be 1/6, 1/3 and 1/2 respectively.
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As shown above a classical deck of card is made up 52 cards suppose one card is selected at random and calculate the following proper ability
To determine the probability of selecting a classical deck of card
(a) Probability of selecting a 7 or club
[tex]\begin{gathered} Pr(\text{selecting a 7 or club) = pr( selecting a 7) + pr(selecting a club )} \\ \text{pr( selecting a 7) = }\frac{4}{52} \\ \text{pr( selecting a club) = }\frac{13}{52} \\ Pr(\text{selecting a 7 or club) = }\frac{4}{52}+\frac{13}{52}=\text{ }\frac{4+13}{52}=\frac{17}{52}\text{ = 0.3269} \\ Pr(\text{selecting a 7 or club) = }0.327\text{ (3dp)} \end{gathered}[/tex](b) Probability of selecting a face card or heart
[tex]\begin{gathered} Pr(\text{selecting a face card or heart) = pr(selecting a face card) + pr(selecting a heart)} \\ Pr(\text{selecting a face card) = }\frac{12}{52} \\ Pr(\text{selecting a heart) = }\frac{13}{52} \\ Pr(\text{selecting a face card or heart) = }\frac{12}{52}+\frac{13}{52}=\frac{12+13}{52}=\frac{25}{52}=0.4807 \\ Pr(\text{selecting a face card or heart) }=\text{ 0.481 (3dp)} \end{gathered}[/tex](c) Probability of selecting both a face card and a club
[tex]\begin{gathered} Pr(\text{selecting both a face card and a club) = pr(selecting a face card)+pr(selecting a club)} \\ \text{pr(selecting a face card) = }\frac{12}{52} \\ \text{pr(selecting a club) = }\frac{13}{52} \\ Pr(\text{selecting both a face card and a club) = }\frac{12}{52}\text{ }\times\frac{13}{52}=\text{ }\frac{3}{52}=0.0577 \\ Pr(\text{selecting both a face card and a club) = 0.058 (3dp)} \end{gathered}[/tex]
equation allows the nurse to use theratio and proportion method todetermine how many tablets the patientrequires?O 100 mg/50 mg x 1 tabletO 50 mg/100 mg x 1 tablet50 mg/1 tablet = 100 mg/ x tablets
SOLUTION
From the question, the patient needs 100 mg but the drug is available in 50 mg tablets.
We can see that 100 is twice of 50, so using 50 mg tablets should be twice that to make it 100 mg
If the number of tablets is given as x, so the requirement will be calculated as
[tex]x\text{ tablets = }\frac{1\text{ tablet }}{50\text{ mg}}\times100\text{ mg/1 tablet }[/tex]Hence the last option is the correct answer
What is 3 times 5????
For natural numbers, a multiplication can be seen as a repetitive addition. In this case, 3 times 5 is the same as addign 5+5+5. Then:
[tex]3\times5=5+5+5=15[/tex]Divide the stars into 3 equal groups. How many stars are in each group? 8 What is 13 of 9?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total stars = 9
equal groups = 3
stars per group = ?
1/3 of 9 = ?
Step 02:
stars per group = total stars / equal groups
stars per group = 9 / 3
stars per group = 3
1/3 of 9 = 1/3 * 9 = 9/3 = 3
The answer:
There are 3 stars per group.
1/3 of 9 is 3.
repeat the following procedure for the four given numbers. multiply the number by 2. add 10 to the product. divide the sum by 2. subtract 5 from the quotient. the first number is 2, the 2nd number is 4, the 3rd number is 8,the 4th number is 10
Lets start with the first case (the number is 2). Then, we get
Now, for the second case (the number is 4), the result is
Now, for 3rd case ( the number is 8), we have
And for 4th case (the number is 10) we get
a) As we can note, the result is always the same number we started with.
Then, if we represent the first number by n, the result is n.
b) Let n be the given number, then, we can write:
-Multiply the number by 2:
[tex]2n[/tex]-Add 10 to the product:
[tex]2n+10[/tex]- Divide the sum by 2:
[tex]\frac{2n+10}{2}[/tex]but this is equal to
[tex]\frac{2n+10}{2}=\frac{2n}{2}+\frac{10}{2}=n+5[/tex]- Substract 5 from the quotient:
[tex]\frac{2n+10}{2}-5[/tex]but (from our last result) this is equal to
[tex]n+5-5=n[/tex]which is our first number n. Thats why the answer in all cases is the same number we started with.
list 6 different types of geometric principles represented in the picture.
We need to list 6 geometric principles represented in the picture.
We can see the vertices of something that looks like leaves, arranged in a spiral.
Those vertices form angles. Also, the leaves seem to be tridimensional, so they have a surface area and a volume.
Also, notice that leaves equidistant from the center of the spiral seem to be congruent.
Therefore, we can list the following types of geometric principles:
• vertices
,• spiral
,• angles
,• surface area
,• volume
,• equidistance
,• congruent
The table below represents the data collected at a sandwich shop for the last six months withrespect to the type of bread people ordered (sourdough or wheat) and whether or not theygot cheese on their sandwich.With cheeseWithout cheeseSourdough800425Wheat1200700What is the P(cheese | wheat)? Show all work to receive full credit. You can place your workin this box or attach it in the box on the final question.
Given:
The table represents the data collected at a sandwich shop for the last six months with respect to the type of bread
We will find P(cheese | wheat)
We will use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Let A represents cheese, and B represents wheat
From the table:
[tex]\begin{gathered} A\cap B=1200 \\ B=1200+700=1900 \end{gathered}[/tex]So, the probability will be as follows;
[tex]P\left(cheese|wheat\right)=\frac{1200}{1900}=\frac{12}{19}[/tex]So, the answer will be:
P(cheese | wheat) = 12/19 = 0.63
an airplane is flying at an altitude of 5000 ft in starseed sitting at a rate of 150 ft per minute what we'd altitude of the plane after 10 minutes
Problem
An airplane is flying at an altitude of 5000 ft in starseed sitting at a rate of 150 ft per minute what we'd altitude of the plane after 10 minutes
Solution
For this case we can define the following notation:
y= altitude
x= time in minutes
We can find the altitude at any time with the following formula:
y = 5000 - 150 x
And we can find the value for the altitude at x=10 we got:
y = 5000 -150(10) =3500 ft
Drag each label to the correct location on the image. Are these functions even, odd , or neither?
We know that if a function is even then the graph of the function is symmetrical about y-axis.
Look at the first function, it is symmetrical about y-axis, henve it is even,
if a function is odd then the graph of the function is symmetrical about origin
Look at the second function, it is symmetrical about origin, henve it is odd,
And the third function is neither symmetrical about y-axis nor symmetrical about origin and so it neither odd nor even.
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
A cone-shaped pile of sawdust has a base diameter of 30 feet, and is 10 feet tall. Find the volume of the pile. Round your answer to the nearest tenth if necessary.
The formula for calculating the volume of a cone (pile) is expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]r is the radius
h is the height of the cone (pile)
Given
Base diameter = 30 feet
radius = diameter/2
radius = 30/2
radius = 15 feet
height = 10feet
Required
Volume of the pile
To get the volume, you will substitute the given data into the formula as shown;
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\pi(15)^2(10) \\ V\text{ = }\frac{1}{3}\pi(225)(10) \\ V=\frac{1}{3}(3.14)(2250) \end{gathered}[/tex]Evaluate the final expression;
[tex]\begin{gathered} V\text{ =}\frac{7065}{3} \\ V\text{ = }2355ft^3 \end{gathered}[/tex]Hence the volume of the pile is 2355ft^3