Answer:
Explanation:
Here, we are to match the correct answer given the dimensions of each of the shapes
We proceed as follows:
a) The volume of the rectangular prism
Mathematically, the volume is the product of the base rectangle and the height
We have this as:
[tex]\frac{3}{5}\times\frac{1}{5}\times\frac{2}{5}=\text{ }\frac{6}{125}cm^3[/tex]b) The volume of the rectangular prism
This is same as above
It is the product of the side lengths
Mathematically, we have this as:
[tex]\frac{3}{5}\times\frac{4}{5}\times\frac{3}{5}\text{ = }\frac{36}{125}cm^3[/tex]c) A cube with the given side length
Mathematically, the volume is the cube of the gievn side length as follows:
[tex]\frac{2}{5}\times\frac{2}{5}\times\frac{2}{5}=\frac{8}{125}cm^3[/tex]d) Cube with side length of 1/5 cm
This is the cube of the side length as follows:
[tex]\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}\text{ = }\frac{1}{125}cm^3[/tex]What are the measures of the exterior angles of the polygon shown? 1. (x + 15)° 2. (4x - 10)° 3. (3x + 10)° 4. (2x + 5)° 5. 3x°
At first for any polygon the sum of the exterior angles = 360
For the given polygon, we need to find the measures of the exterior angles
We will find the value of x, then we will evaluate the exterior angles
The given polygon has 5 sides , so, the sum of the interior angles = (n - 2) * 180
[tex]=(5-2)\cdot180=540[/tex]So, the sum of the angles is :
[tex](x+15)+(4x-10)+(3x+10)+(2x+5)+3x=540[/tex]Solve the equation for x:
[tex]\begin{gathered} 13x+20=540 \\ 13x=540-20 \\ 13x=520 \\ \\ x=\frac{520}{13}=40 \end{gathered}[/tex]So, the measures of the angles will be as following :
[tex]\begin{gathered} \angle1=180-(x+15)=180-(40+15)=125 \\ \\ \angle2=180-(4x-10)=180-(4\cdot40-10)=180-150=30 \\ \\ \angle3=180-(3x+10)=180-(3\cdot40+10)=180-130=50 \\ \\ \angle4=180-(2x+5)=180-(2\cdot40+5)=180-85=95 \\ \\ \angle5=180-3x=180-3\cdot40=180-120=60 \end{gathered}[/tex]Suppose that the functions f and f are defined as follows F(x)= 5/x g(x)=9/x+1 Find g/f then give its domain using an interval or union of intervals Simplify your answers (g/f)(x)=Domain of g/f:
Given:
[tex]\begin{gathered} f(x)=\frac{5}{x} \\ g(x)=\frac{9}{x+1} \end{gathered}[/tex]To find
[tex](\frac{g}{f})(x)[/tex]We know that,
[tex](\frac{g}{f})(x)=\frac{g(x)}{f(x)}[/tex]So,
[tex]\begin{gathered} (\frac{g}{f})(x)=\frac{\frac{9}{x+1}}{\frac{5}{x}} \\ (\frac{g}{f})(x)=\frac{9}{x+1}\times\frac{x}{5} \\ (\frac{g}{f})(x)=\frac{9x}{5(x+1)} \end{gathered}[/tex]Hence, the answer is,
[tex](\frac{g}{f})(x)=\frac{9x}{5(x+1)}[/tex]Domain of the above function is,
Let the dinominator equals to 0, we get
x+1=0
x= -1
Hence, the domain of the function is,
[tex](-\infty,-1)\cup(-1,\infty)[/tex]Evaluate the exact value of the following expression.sine and cosecant of 60°
To evaluate:
[tex]\sin 60^{\circ}\text{ and }co\sec 60^{\circ}[/tex]As we know,
Using the trigonometric ratio for sine,
[tex]\begin{gathered} \sin \theta=\frac{Opp}{\text{Hyp}} \\ \sin 60^{\circ}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Using the trigonometric ratio for cosecant,
[tex]\begin{gathered} co\sec \theta=\frac{\text{Hyp}}{\text{Opp}} \\ co\sec 60^{\circ}=\frac{2}{\sqrt[]{3}} \end{gathered}[/tex]Hence, the answers are,
[tex]\begin{gathered} \sin 60^{\circ}=\frac{\sqrt[]{3}}{2} \\ \cos ec60^{\circ}=\frac{2}{\sqrt[]{3}} \end{gathered}[/tex]Favorite coffee flavor a survey was taken asking the favorite flavor of a coffee drink a person prefers. The responses were C=caramel, H=hazelnut, M=mocha, P equals plain, And V=vanilla
It is given that Favorite coffee flavor a survey was taken asking the favorite flavor of a coffee drink a person prefers. The responses were
C=caramel, H=hazelnut, M=mocha, P equals plain, And V=vanilla
The given data is;
C M M C H H C C H M
H P V H P H V H H H
C V M H V H P C H C
H H V C H P P
Number of Caramel favorite person = 8
Number of Hazelnut favorite person = 15
Number of Mocha favorite person = 4
Number of plain favorite person = 5
Number of Vanila favorite person = 5
..
The fastest recorded lava flow moved at an average speed of 7 miles per hour. The function y = 7xdescribes the distance y the lava moved on average in x hours. Graph the function. Use the graph toestimate how many miles the lava moved after 6.5 hours.50y45403530252015105001234578910y =7x2
y =7x
We have to graph the function:
For that we have to give values to x and get y values:
For example:
x=0 ; y= 7(0) = y=0
So, we have the point (0,0)
For x =6.5
Y= 7 (6.5) = 45.5
Graph
The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10. What percentage of the scores are greater than 87? 34% 50% 84% 16%
Given
[tex]\begin{gathered} \mu=77 \\ \sigma=10 \end{gathered}[/tex]The z-score formula is
[tex]z=\frac{x-\mu}{\sigma}[/tex]In our case,
[tex]\Rightarrow z=\frac{87-77}{10}=\frac{10}{10}=1[/tex]Using a z-score table,
[tex]\Rightarrow P(X<87)=0.8413[/tex]Then,
[tex]\begin{gathered} P(X>87)=1-P(X<87)=1-0.8413=0.1587=15.87\% \\ \Rightarrow P(X>87)\approx16\% \end{gathered}[/tex]Thus, the answer is 16%What is the remainder of the quantity 4 x cubed minus 20 x minus 50 end quantity divided by the quantity x minus 3 end quantity? Show all necessary steps.
Explanation
We are given the following:
[tex]\frac{4x^3-20x-50}{x-3}[/tex]We are required to determine the remainder when the operation is carried out.
We can determine the remainder as follows:
[tex]\begin{gathered} Let\text{ }f(x)=4x^3-20x-50 \\ Let\text{ }g(x)=x-3 \\ Suppose\text{ }g(x)=0,i.e.\text{ }x-3=0\Rightarrow x=3 \\ \\ So,f(3)=4(3)^3-20(3)-50 \\ f(3)=108-60-50=-2 \end{gathered}[/tex]Hence, the remainder is:
[tex]Remainder=-2[/tex]Pay Cut Todd works for a computer firm, and last year he earned a salary of $120,000. Recently, Todd was required to take a 15% pay cut. Find Todd's salary after the pay cut.
Given:
The salary of Todd last year, C=$120,000.
The percentage rate of pay cut, R=15%.
Todd's salary after the pay cut can be calculated as,
T=C x (100-R)/100
T=120000 x (100-15)/100
T=120000 x 85/100
T=102000
Therefore, Todd's salary after the pay cut is $102000.
which number does not belong:3,6,9,12,30
we have the sequence
3,6,9,12,30
Remember that
3,6,9,12,... ----> is an arithmetic sequence
the next number would be 15
therefore
the answer is 30What is 1.57828282E5And 6.82e-8 in standard form
The standard form of a number converts a large number in short form using the power of 10.
First number is:
1.57828282E5
As you mentioned the numbers are technology generated hence E^x = 10^x. For example, in Matlab, you can write 10^5 as E^5.
Hence, the standard form of the number would be
1.57828282 x 10^5
While the ordinary form would be
157828.282
Similarly, the standard form of the second number would be:
6.82 x 10^-8
jonah sesquare started creating the following pattern in steps
Answer = the
According to the pattern he started with
The first term = 1
The common difference = 4
The nth term of a Arithmetic sequence =
Tn = a + (n - 1) d
Where a = first term , d = common difference, n = number of terms
a = 1, d = 4, and n = 15
T15 = 1 + (15 - 1) x 4
T15 = 1 + ( 14) x 4
T15 = 1 + 56
T 15 = 57
Which values are solutions to the inequality below? √x≤=4 check all that apply: A. 20 B. 12 C. 2 D. 5 E. -1. F. NO SOLUTIONS.
we can replace the value of X for each option and check the inequality
A.20
[tex]\begin{gathered} \sqrt[]{20}\le4 \\ 4.47\le4 \end{gathered}[/tex]the inequality is wrong because 4.47 is greater than 4
B.12
[tex]\begin{gathered} \sqrt[]{12}\le4 \\ 3.46\le4 \end{gathered}[/tex]The inequality is right because 3.46 is less than 4
C.2
[tex]\begin{gathered} \sqrt[]{2}\le4 \\ 1.41\le4 \end{gathered}[/tex]The inequality is right because 1.41 is less than 4
D.5
[tex]\begin{gathered} \sqrt[]{5}\le4 \\ 2.23\le4 \end{gathered}[/tex]inequality is right because 2.23 is less than 4
E. -1
[tex]\sqrt[]{-1}\le4[/tex]we can calculate the root of a negative number then the option is wrong
Find the midpoint of the two points below. Type your answer as a point (x,y) without any spaces between your characters. Be sure to include the parentheses and a comma between your x and y values. If a value is not an integer then type your answer as a decimal rounded to the nearest hundredth.(0,7) and (4,-9)The midpoint is Answer
We will use the following formula for the coordinates of the midpoint (l,m) of a segment with endpoints (x,y) and (z,k):
[tex]\begin{gathered} l=\frac{x+z}{2}, \\ m=\frac{y+k}{2}\text{.} \end{gathered}[/tex]Substituting the given points in the above formula we get:
[tex]\begin{gathered} l=\frac{0+4}{2}=\frac{4}{2}=2, \\ m=\frac{7+(-9)}{2}=\frac{-2}{2}=-1. \end{gathered}[/tex]Answer: The midpoint is
[tex](2,-1)\text{.}[/tex]If EF = 2x - 12 FG = 3x - 15. and EG = 23, find the values of x. EF, and FG. The drawing is not to scale. x =3, EF = 8, FG = 15 Ox=10, EF = 32, FG = 45 O x =3, EF = -6, FG = -6 x =10, EF = 8, FG = 15
We have the next information
EF=2x-12
FG=3x-15
EG=23
With the information above we can have the next equation in order to find x
2x-12+3x-15=23
Then we sum similar terms
5x-27=23
then we isolate the x
5x=23+27
5x=50
x=10
then we substitute the value of x for each segment
EF=2x-12=2(10)-12=20-12=8
FG=3x-15=3(10)-15=30-15=15
Wendy is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $100. Wendy will be earning a base salary of $70 per month from the gym, plus an additional $3 for every class she teaches. If Wendy teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Wendy's expenses and earnings be?
Write a system of equations, graph them, and type the solution.
Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
What is meant by the term system of equations?System of equations, also known as simultaneous equations, Two or even more equations to just be solved together in algebra. The number of equations should then equal the number of uncertainties for a system to produce a unique solution.The information regarding the teaching classes at a local gym by kickboxing instructor is given-
Total amount spent = $100.
Basic salary of Wendy = $70.
Additional salary = $3 for each class.
Let 'x' be the number of classes during first month.
The, the equation forms as;
100 = 70 + 3x (equation)
Simplifying,
x = 30/3
x = 10 (solution)
The graph is shown.
Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
To know more about the system of equations, here
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If she is working alone, Sylvia can pick a pint of raspberries in 20 minutes. If Jasmine and Sylvia work together, they can complete the job in 8 minutes. How long would it take Jasmine to pick a pint of raspberries working alone?
Given that:
- Sylvia can pick a pint of raspberries in 20 minutes working alone.
- Jasmine and Sylvia can complete the job in 8 minutes if they work together.
You can use the following Rate for Work Formula in order to solve the exercise:
[tex]\frac{t}{a}+\frac{t}{b}=1[/tex]Where "t" is the time for objects A and B to complete the work together, "a" is the time needed for object A to complete the work alone, and "b" is the time for object B to complete the work alone.
In this case, you can identify that:
[tex]\begin{gathered} t=8\text{ } \\ a=20\text{ } \end{gathered}[/tex]Therefore, by substituting values into the formula and solving for "b", you can determine how long it would take (in minutes) for Jasmin to pick a pint of raspberries working alone:
[tex]\frac{8}{20}+\frac{8}{b}=1[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]8=(\frac{3}{5})(b)[/tex][tex](8)(\frac{5}{3})=b[/tex][tex]b\approx13.3[/tex]Hence, the answer is:
[tex]13.3\text{ }minutes\text{ \lparen Approximately\rparen}[/tex]Question 15 of 25What is the approximate value of tan C?
Solution:
Question :
Find the approximate value of Tan C
To figure out the value of tan C , we will use the image below
To find the value of tan C , we will use the trigonometric ratio below
[tex]\begin{gathered} tanC=\frac{opposite}{adjacent} \\ opposite=7 \\ adjacent=16 \\ \tan C=\frac{7}{16} \\ \tan C=0.4375 \\ tanC\approx0.44 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow0.44[/tex]OPTION B is the correct answer
Which of the following expressions could be used to determine the exact value of cos 240°?
The formula we will use is the one of cos2x:
2x=240
x=120
The formula is: cos2x = 2cos²x - 1
cos240 = 2cos²(120) - 1
Which number is greater, 23 x10^3 or 11 x 10^4? How do you know? Show your work and explain your steps.
23 x 10^3 = 23,000
10^3 means that we have to move the decimal point 3 places to the right to obtain the number.
11 x 10^4 = 110,000
Now, we can compare:
110,000>23,000
11x10^4 is the greater number.
1[tex] \frac{x - 1}{2x - 4} = \frac{2x - 2}{3x} [/tex]2[tex] \frac{3}{x} + \frac{2}{x + 1} = \frac{23}{x {}^{2} + x} [/tex]3[tex] \frac{x + 2}{2} + 2[/tex]4[tex] \frac{x - 2}{2} = 4[/tex]
Find x
(x-1 )/ (2x-4) = (2x -2) / 3x
________________
Can you see the updates?
_________________
(x-1 )* 3x = (2x -2) (2x-4)
x* 3x -1*3x = 2x*2x -2*2x - 4*2x +2*4
3x^2 - 3x = 4 x^2 -4x - 8x + 8
4 x ^2 - 3x^2 -4x + 3x -8x + 8 = 0
x ^2 - 9x + 8
(x -1) (x -8) = 0
x = 1
x = 8
_____________
Answer
x = 1
x = 8
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The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, and represents the total number of dots in the figure.When n=1, there is 1 dot. When n=2, there are 3 dots. When n=3 , there are 6 dots. Notice that the total number of dots increases by n each time.Use induction to prove that d(n) = n(n+1)/2.Part AProve the statement is true for n=1 .Type your answer in the box.
From the information given
The number of dots will form the following sequence
[tex]1,3,6,10,\ldots[/tex]Where d(n
: I have 18 blocks on the bottom of my prism and I am building it to be 10 units tall what is the volume?
The volume of the prism is: area of the base*height
In this case, the base of the prism is composed of 18 blocks. Then the volume is: blocks on the bottom*height = 18*10 = 180
(Exponential Regressions)The accompanying table shows the number of bacteria present in a certain cultureover a 4 hour period, where x is the time, in hours, and y is the number ofbacteria. Write an exponential regression equation for this set of data, rounding allcoefficients to the nearest hundredth. Using this equation, determine the number ofbacteria present after 16 hours, to the nearest whole number.
Answer:
[tex]\begin{gathered} (a)y=460.30(1.10)^x \\ (b)2115\text{ bacteria} \end{gathered}[/tex]Explanation:
Part A
An exponential regression is of the form:
[tex]y=AB^x[/tex]We plug this data into an exponential regression calculator:
To the nearest hundredth, the values obtained are:
[tex]\begin{gathered} A\approx460.30 \\ B\approx1.10 \end{gathered}[/tex]An exponential regression equation for this set of data is:
[tex]y=460.30(1.10)^x[/tex]Part B
After 16 hours, when x=16
[tex]\begin{gathered} y=460.30(1.10)^{16} \\ y\approx2115\text{ (to the nearest whole number)} \end{gathered}[/tex]After 16 hours, the number of bacteria present is 2,115.
What is the value of x when f(x) = 9?
ANSWER :
A. 2
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=3^x[/tex]when f(x) = 9 :
[tex]\begin{gathered} f(x)=3^{^x} \\ 9=3^x \end{gathered}[/tex]Note that 9 is 3^2
[tex]\begin{gathered} 9=3^x \\ 3^2=3^x \\ \text{ Since the bases are equal, the exponents are equal too.} \\ 2=x \\ x=2 \end{gathered}[/tex]Solve the equation by factoring: x2 - 5x - 14 a. X = -2 or 7 b. X = 2 and - 7 c. x = -2 or -7 d. X = 2 or 7
We need to solve the quadratic equation:
x^2 - 5 x - 14 = 0 by factoring.
So we look for a pair of factors whose product is -14 and when combined render - 5. So we find the pair "-7 and 2"
Their product = (-7) * 2 = -14
combining them we get: -7 + 2 = -5
So we used them to split the middle term in the equation:
x^2 - 5 x - 14 = 0
x^2 - 7 x + 2 x - 14 = 0
Factor by grouping:
x ( x - 7) + 2 x - 14 = 0
x (x - 7) + 2 (x - 7) = 0
(x - 7) (x + 2 ) = 0
Then for this product to render zero, (x - 7) must be zero (so x = 7)
or (x + 2) is zero (and therefore x = -2)
Then we look for the answers x = -2 or x = 7
This coincides with answer (a) in your list.
what is the equation fir the graph below1. y=2/5x+42. y= -2/5x+43. y= 4/1x-2/54. y= -5/2x+4
y = -2/5 x + 4 (option 2)
Explanation:Equation of line: y = mx + b
m = slope, b = y-intercept
Slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Using points (5, 2) and (0, 4)
[tex]\begin{gathered} x_1=5,y_1=2,x_2=0,y_2\text{ = }4 \\ \text{slope = }\frac{4-2}{0-5}=\text{ }\frac{2}{-5} \\ \text{slope = -2/5} \end{gathered}[/tex]The y -intercept is point the line crosses the y axis. The point is at y = 4
b = 4
The equation of the line becomes:
y = -2/5 x + 4 (option 2)
The circumference of a circular garden is 138.16 feet. What is the diameter of the garden? Use 3.14 for pi and do not round the answer.
Find the value of f(-6).yy = f(x)108642-10-8-6-422468.10-2-4-6-8
The given graph is a downward parabola.
The roots of the equation is -2 and -8, and the vertex is (-5,7).
The general root form of parabola will be,
a(x-(-2))(x-(-8))=a(x+2)(x+8).
The value of a can be determined from the coordinate of vertex,
[tex]\begin{gathered} y=a(x+2)(x+8) \\ 7=a(-5+2)(-5+8) \\ 7=a\times(-3)(3) \\ a=\frac{-7}{9} \end{gathered}[/tex]Thus, the required quadratic is,
[tex]f(x)=\frac{-7}{9}(x+2)(x+8)[/tex]The value of f(-6) can be determined as,
[tex]\begin{gathered} f(-6)=\frac{-7}{9}(-6+2)(-6+8) \\ =6.22 \end{gathered}[/tex]Thus, the requried value of f(-6) is 6.22.
Simplify (m-5)(m^2+5m-6)
use the graph below to find the point of intersection for the functions .
The equations are in the slope-intercept form:
y= mx+b
Where:
m= slope ( rise / run )
b= y-intercept (where the line crosses the y axis)
Graph:
Both functions intersect at the point (-1,3)