Tank B originally had 80 liters of water.
Water is being drained off the tank at a rate of 2.5 liters per minute.
After 7 minutes have passed, the tank has lost 7*2.5 = 17.5 liters of water.
This means the tank still has 80 - 17.5 = 62.5 liters of water.
After 7 minutes 62.5 liters of water remain in the tank
There are 9,321 leaves on a tree. Explain why the digit 3 stays the same when9,321 is rounded to the nearest hundred.
To round the nearest hundred the digit in the hundred column and test digit in the tens column.
To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.
We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.
The 9,321 rounded to the nearest hundred is 9,300.
The boxplot shown below results from the heights (cm) of males listed in a data set. What do the numbers in that boxplot tell us?
Given:
The boxplot is given.
To fill in the blanks:
Explanation:
As we know,
The minimum value is represented by the line at the far left end of the diagram.
So, the minimum height is 153cm.
The first quartile on the left side is represented by the line between the minimum value ad the median.
So, the first quartile is 166.6cm.
The second quartile (or median) is represented by the line at the centre of the box.
So, the second quartile is 173.2cm.
The third quartile on the right side is represented by the line between the maximum value ad the median.
So, the third quartile is 180.1cm.
The maximum value is represented by the line at the far right end of the diagram.
So, the maximum height is 193cm.
Final answer:
The minimum height is 153cm, the first quartile is 166.6cm, the second quartile is 173.2cm, the third quartile is 180.1cm, and the maximum height is 193cm.
1. Knowledge: Use your Factoring Flowchart or Concept Map to factor the following Quadratic Polynomials. Copy down the question and show any necessary steps if it is a multi-step factoring process (not just a single-step solution). Question F to I
Solution
We are asked to factorize the following questions
Question F:
[tex]\begin{gathered} 4+6x+2x^2 \\ \text{ 2 is common among the terms, so we can factorize it out} \\ \\ 2(2+3x+x^2) \\ \text{ The term }3x\text{ can also be written as }2x+x.\text{ And the terms }2x\text{ and }x\text{ multiply to get }2x^2 \\ \text{ Thus, we have,} \\ \\ 2(2+3x+x^2)=2(2+2x+x+x^2) \\ \text{ In this new expression, }2\text{ is common to }2+2x\text{ while }x\text{ is common to }x+x^2 \\ \text{ Thus, we can factorize them out} \\ \\ 2(2+2x+x+x^2)=2(2(1+x)+x(1+x)) \\ \text{ Lastly, }(1+x)\text{ is common to }2(1+x)\text{ and }x(1+x) \\ \\ 2(2(1+x)+x(1+x))=2((2+x)(1+x)) \\ \\ \therefore4+6x+2x^2=2(2+x)(1+x) \end{gathered}[/tex]Question G:
[tex]\begin{gathered} 3x^2-1x-10 \\ \text{ The term }-1x\text{ can also be written as }-6x+5x\text{ and the terms }-6x\text{ and }5x\text{ multiply to get} \\ -30x^2.\text{ Thus, we have,} \\ \\ 3x^2-1x-10=3x^2-6x+5x-10 \\ 3x\text{ is common to }(3x^2-6x)\text{ and }5\text{ is common to \lparen}5x-10) \\ \text{ Thus, we can factor them out} \\ \\ 3x^2-6x+5x-10=3x(x-2)+5(x-2) \\ (x-2)\text{ is common to both terms, so we can factor again} \\ \\ 3x(x-2)+5(x-2)=(x-2)(3x+5) \\ \\ \therefore3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]Final Answer
The answers to questions F and G are:
[tex]\begin{gathered} 4+6x+2x^2=2(2+x)(1+x) \\ \\ 3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]
What is the axis of symmetry for the following quadratic?(x-3)(x+7)
The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.
[tex]x_{\text{vertex}}=\frac{-b}{2a}[/tex]Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.
[tex]\begin{gathered} (x-3)\cdot(x+7) \\ x^2+7x-3x-21 \\ x^2+4x-21 \end{gathered}[/tex]We have that a = 1 and b = 4, therefore:
[tex]x_{\text{vertex}}=\frac{-4}{2\cdot1}=-2[/tex]The axis of symmetry for this quadratic equation is x=-2.
the mean salary offered to students who are graduating from coastal state university this year is $24,215, with a standard deviation of $3712. A random sample of 80 coastal state students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more?
Given that the mean and standard deviation of the population are $24,215 and $3712 respectively,
[tex]\begin{gathered} \mu=24215 \\ \sigma=3712 \end{gathered}[/tex]The sample size taken is 80,
[tex]n=80[/tex]Consider that the salary of students in the sample is assumed to follow Normal Distribution with mean and standard deviation as follows,
[tex]\begin{gathered} \mu_x=\mu\Rightarrow\mu_x=24215 \\ \sigma_x=\frac{\sigma}{\sqrt[]{n}}=\frac{3712}{\sqrt[]{80}}\approx415 \end{gathered}[/tex]So the probability that the mean salary (X) is $24250 or more, is calculated as,
[tex]\begin{gathered} P(X\ge24250)=P(z\ge\frac{24250-24215}{415}) \\ P(X\ge24250)=P(z\ge0.084) \\ P(X\ge24250)=P(z\ge0)-P(0From the Standard Normal Distribution Table,[tex]\begin{gathered} \emptyset(0.08)=0.0319 \\ \emptyset(0.09)=0.0359 \end{gathered}[/tex]So the approximate value for z=0.084 is,
[tex]\emptyset(0.084)=\frac{0.0319+0.0359}{2}=0.0339[/tex]Substitute the value in the expression,
[tex]\begin{gathered} P(X\ge24250)=0.5-0.0339 \\ P(X\ge24250)=0.4661 \end{gathered}[/tex]Thus, there is a 0.4661 probability that the mean salary offer for these 80 students is $24,250 or more.
You have a piggy bank containing a total of 66 coins in dimes and quarters. If the piggy bank contains $10.20, how many dimes are there in the piggy bank?
I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.
Here,
x+y=66 ......(1)
1 dime values 10 cents.
1 quarter values 25 cents.
10x+25y=1020 ........(2)
x=66-y
10(66-y)+25y=1020
660-10y+25y=1020
15y=360
y=360/15
y=24
x=66-24
x=42
I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.
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given that f(x)=3x-6, determine f(8)
According to the given data we have the following function:
f(x)=3x-6
To determine f(8) we would have to plug in into the equation the 8 and then proceed to calculate it, so:
If f(x)=3x-6
Then, f(8)=3(8)-6
f(8)=24-6
f(8)=18
the probability that DeAndre missed at least 1 day of school in a given week is
Probability that Deandre missed at least 1 day is;
[tex]Pr(x\ge1)=Pr(1)+Pr(2)+Pr(3)+Pr(4)+Pr(5)[/tex]Write out the values of each probability and sum them
[tex]\begin{gathered} Pr(x\ge1)=0.25+0.18+0.34+0.12+0.04 \\ =0.93 \end{gathered}[/tex]Hence,
The probability that Deandre missed at least 1 day is 0.93
In general, what points can have coordinates reversed and still have the same location?Choose the correct answer below.O the points with x-coordinates 0o the points with y-coordinates 0o the points with the same x- and y-coordinatesO the points with opposite coordinates
SOLUTION
The Point of a co-ordinate is always written as
[tex](x,y)[/tex]Giving a point
[tex]\begin{gathered} A(x,y) \\ \text{if the coordinates of x and y are the same } \end{gathered}[/tex]For instance x=2 and y=2, the point will be
[tex](2,2)[/tex]If the coordinate of x and y are reversed, the point will remain the same
Hence
the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.
Therefore The Third option is correct (c)
Give the degree of the polynomial.
-v^8u^9 + 6x - 16u^6x^2v^6 - 5
Answer: nonic
Step-by-step explanation:
If A={a,c} and B={d,g,w} then complete the Following:a. Find AxBb. Find n(AxB)c. write a multiplication equation involving numerals related to the parts in (a) and (b)...a. AxB = {____} Type an ordered pair. Use commas to separate answers as needed
Given the two sets:
[tex]\begin{gathered} A=\mleft\lbrace a,c\mright\rbrace \\ B=\mleft\lbrace d,g,w\mright\rbrace \end{gathered}[/tex]we can write the product set of A and B in the following form:
[tex]AxB=\mleft\lbrace(a,d\mright),(a,g),(a,w),(c,d),(c,g),(c,w)\}[/tex]next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:
[tex]n(AxB)=2\cdot3=6[/tex]finally, the equation that involves the numerals of the previous parts is:
[tex]n(AxB)=n(A)\cdot n(B)[/tex]where n(A) and n(B) represents the number of elements in A and B respectively.
Mark noticed the probability that a certain player hits a home run in a single game is 0.175. Mark interested in the variability of the number of home runs if this player plays 200 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games?
The standard deviation for a total of 200 games is 5.3735.
How to calculate the standard deviation?Let X = number of home runs of this player in 200 games played by him.
p = probability that a this player hits a home run in a single game and this is given to be 0.175.
Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.
Here n = 200 and p = 0.175. So, the standard deviation for a total of 200 games is the standard deviation for a total of X
= √(200 x 0.175 x 0.825) / 2
= 5.3735
The value is 5.3735.
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If t = (- pi)/3 find the terminal point P(x,y) on the unit circle
Find the corresponding possitive angle by adding to the angle t 2pi:
[tex]-\frac{\pi}{3}+2\pi=\frac{-\pi+6\pi}{3}=\frac{5\pi}{3}[/tex]Identify the coordiantes using a unit circle:
Then, for angle t=-pi/3 the coordinates are:x=1/2y=-√3 /2Solve for x. Round to the nearest tenth ofa degree, if necessary.5.3HGto8.5F
We have a rigth triangle, where we have to find the measure of x.
We can use trigonometric ratios to relate the lengths of the sides and the measure of x.
The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:
[tex]\begin{gathered} \cos (x)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (x)=\frac{5.3}{8.5} \\ x=\arccos (\frac{5.3}{8.5})\approx\arccos (0.623)\approx51.4\degree \end{gathered}[/tex]Answer: x = 51.4°
a wood cutter measures a piece of wood to be 830 grams.There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.Whats is the mass of the wood in pounds
The mass of the wood in pounds is 1.826 pounds.
How to calculate the value?From the information, the wood cutter measures a piece of wood to be 830 grams and there are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pound.
Therefore,the mass will be represented as x
This will be:
830 grams = 0.83 kilograms
0.83/1 = x/2.2
Cross multiply
x = 2.2 × 0.83
x = 1.826 pounds.
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a computer program is in Shannon's computer carries out a single mathematical operation in 1.5 * 10 over 6 seconds how much time would the program take to complete 2.5 * 10/3 mathematical operations
Question:
Solution:
This computer program carries out a single mathematical operation in
[tex]1.5x10^{-6}\text{ seconds}[/tex]then, to complete 2.5 x 10^3 mathematical operations the program will take a time of:
[tex](1.5x10^{-6})(2.5x10^3)=3.75x10^{-3}[/tex]thus, the correct answer is:
[tex]3.75x10^{-3}[/tex]Determine whether or not the digits below are divisible by: 2,3,4,5,6,8,9,or, 10 a. 897 b. 12,000 c. 8190 d. 327
You have the following numbrs:
897
12,000
8190
327
In order to determine if the previous numbers are divisibles for numbers between 2 and 10, you take into account the following points:
- If last two digits are divisible by a number, and the part of the number without the last units is divisible too, you can consider that the complete number is divisible too.
- If the last digit is 0, then the number is divisible by 2 and 5 and 10.
- If the number is even, it is dividible by 2.
- In case a number ends in varios zeros you can consider if the digits before the zeros are divisible by a specific number.
- 897 is divisible by 3, because 97 is divisible by 3 and 800 too.
- 12,000 is divisible by 2, 3, 4, 5, 6, 8 and 10, because it is an even number, ends in 0 and the first digits are divisible by 3, 4, 6.
- 8190 is divisible by 2, 3, 5, 6, and 10, becaues it is even, ends in 0 and the number of last two digits is divisible by 3 and 6 and 8100 too.
- 327 is divisible by 3, because number of last two digits is divisible by 3 and 300 too.
The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square.
Answer: i donno
Step-by-step explanation:
ask Professor Ahmad Shaoki
If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]Which of the following equations shows the correct way to apply the Associative Property of Addition? (1 point)0 6x (2 + 3) = 6 x 2) + 3O 9+8 = 8+9O 6+2 = 4+4O 3+ (4+5) = (3+4) +5
This property indicates that when there are or more digits in these operations, the result does not depends on the way the terms are grouped. Therefore:
[tex]\begin{gathered} 3+(4+5)=(3+4)+5 \\ 3+9=7+5 \\ 12=12 \end{gathered}[/tex]therefore, the answer is the last option 3+ (4+5) = (3+4) +5
HELP PLEASEEEEE!!!!!!
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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Write the equation of the line when the slope is 1/5 and the y-intercept is 13.
Given:
• Slope, m = 1/5
,• y-intercept = 13
Let's write the equation of the line.
To write the equation of the line, apply the slope-intercept equation of a line:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept.
Thus, we have:
m = 1/5
b = 13
Plug in the values in the equation:
[tex]y=\frac{1}{5}x+13[/tex]Therefore, the equation of the line is:
[tex]y=\frac{1}{5}x+13[/tex]A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 11 choices for an entree, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entree, and a dessert?
laws of exponent : multiplication and power to a power5x3 • 2 x ²
Multiplication of coefficients and variable
It's given the expression:
[tex]5x^3\cdot2x^2[/tex]How do you find the square root of -6 by imaginary numbers
To find the square root of a negative number use the next:
[tex]\sqrt{-1}=i[/tex]For -6:
You can write -6 as the product of 6 and -1:
[tex]\sqrt{\left(6\right)*\left(-1\right)}[/tex]The square root of a product is the same as the product of the square root if each of the factors:
[tex]=\sqrt{6}*\sqrt{-1}[/tex]As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:
[tex]\begin{gathered} =\sqrt{6}*i \\ =\sqrt{6}i \end{gathered}[/tex]Then, the square root of -6 is: (√6)iWhich choice could be used in proving that the given triangles are similar? A) PO 6 DE 4 II B) PO 4 EF 9 PO 4 DE 6 D) PR 6 DE 6 allo
What’s the volume and surface area of the object shown ?
Volume of object = 42 cubic cm
Surface area of object = 96 square cm
Explanations:The given figure is a triangular prism.The formula for calculating its volume is expressed as:
[tex]volume\text{ }of\text{ prism}=BH[/tex]where:
B is the base area
H is the height of prism
[tex]\begin{gathered} volume\text{ of }prism=(\frac{1}{2}\times4\times3)\times7 \\ volume\text{ of }prism=6\times7 \\ volume\text{ of }prism=42cm^3 \end{gathered}[/tex]Determine the surface area of the prism
The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:
[tex]\begin{gathered} Surface\text{ area}=2(0.5\times3\times4)+(7\times4)+(3\times7)+(5\times7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}[/tex]Hence the surface area of the object shown is 96 square cm
a gallon of ice cream costs $4.76. How much does it cost per quart? There are 4 qts per gallon.
There are 4 quarts in a gallon so the price of one gallon that they have given us has to be split into four so $4.76/4 =$1. 19/quart
A graph the line that passes through the points (1,-5) and (5,7)and determine the equation of the line
Answer:
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Find the equation of the line that passes through the points (7,5) and (−9,5)
Hard
Updated on : 2022-09-05
Solution
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Correct option is A)
Since slope of line passing through two points (x
1
,y
1
) and (x
2
,y
2
) is m=
x
2
−x
1
y
2
−y
1
We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:
m=
−9−7
5−5
=
−16
0
=0
Therefore, the slope of the line is 0.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b
5=(0)(7)+b
b=5
Write the equation in slope intercept form as:
y=mx+b
y=(0)x+5
y=5
Hence, the equation of the line is y=5.
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope-intercept equations.
Equations of lines G & H;
Line G: y=-6x + 14
Line H: y=6x-14
O Perpendicular
O Not Enough Information
O Parallel
O Neither
POSS
10 11
12 13 14 15
Answer:
perpendicular because the slopes are opposite
Step-by-step explanation: