SOLUTION
9. We want to find the product of c and 10.
Product means multiplication. So the product of c and 10 means
[tex]c\times10[/tex]So we bring 10 and c together, to get 10c.
Hence the answer is 10c
which situation could be written mathematically as 10÷1/2A) The amount of time it would take to watch ten 1/2 hour videos.B) The amount of time it would take to watch half of a ten minute video.C) The number of 1/2 hour videos in ten hours.D) The number of minutes in one tenth of a 1/2 hour video.I also need to show my work :)
Which situation could be written mathematically as 10÷1/2?
10 ÷ 1/2 = 10 x 2/ 1 = 20
If there are 1/2 hour videos in ten hours, then there are also 20 videos
The correct answer is Option C - The number of 1/2 hour videos in ten hours.
Consider the following data set where “x” is a positive integer: {x+2, x+4, x-4, x-3, x+6} Which of the following statements are true? Select all that apply.A. The mode is x-4B. The median is x+2C. The mean is x+1D. None of above
Before start analyzing the mode, median and mean of the data set, we must organize it from lowest to highest:
{x+2, x+4, x-4, x-3, x+6}
↓
{x-4, x-3, x+2, x+4, x+6}
ModeThe mode is the most frequently repeated data. Since every data appears just one time, then this set has not mode.
MedianThe median is the data that is in the center. We find it just by counting the same numbers from left to right and from right to left:
The median is x+2
MeanThe mean is given by the addition of all the data, and the division by the number of data.
there are 5 values, then we should divide their sum by 5:
[tex]\begin{gathered} \frac{(x-4)+(x-3)+(x+2)+(x+4)+(x+6)}{5} \\ =\frac{x-4+x-3+x+2+x+4+x+6}{5} \\ =\frac{5x+5}{5}=x+1 \end{gathered}[/tex]The mean is x+1
ANSWERS: B and CStudents in Introductory Chemistry are recording the masses of samples as part of a lab experiment. for 5 samples, Sidney has recorded these masses: 4 grams 6 grams 4 grams 8 grams 2 grams What is the mode of the masses?
Solution
For this case we have the following data given:
4, 6, 4, 8, 2
We need to remember that the mode is the most repeated value so then the answer would be:
Mode= 4
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?
The given transformation is
[tex](x,y)\rightarrow(x+2,y+4)[/tex]We have to apply this translation to each vertex.
[tex]\begin{gathered} K(-4,-2)\rightarrow K^{\prime}(-2,2) \\ L(-1,-2)\rightarrow L^{\prime}(1,2) \\ M(-1,-5)\rightarrow M^{\prime}(1,-1) \\ N(-4,-5)\rightarrow N^{\prime}(-2,-1) \\ \end{gathered}[/tex]According to this result, the right answer is C.A-Lab assistant need to create a 900 ml mixture that is 4.5% hydroelectric acid. The assistant has solutions of 3% and 5.5% in supply at the lab. Using the variables x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively, determine a system of equation that describes the situation.Enter the equations below separated by a comma.How many milliliters of the 3% solution should be used?How many milliliters of the 5.5% solution should be used?
Let x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively. Given that the volume of the mixture is 900 ml, we have
x + y = 900
The mixture should contain 4.5% hydroelectric acid. Recall, percentage is expressed in terms of 100. The concentration of the mixture is
4.5/100 * 900 = 40.5
x should contain 3% of hydroelectric acid. The concentration of x is
3/100 * x = 0.03x
y should contain 5.5% of hydroelectric acid. The concentration of y is
5.5/100 * y = 0.055y
The equation representing the concentration would be
0.03x + 0.055y = 40.5
Thus, the required system of equations is
x + y = 900
0.03x + 0.055y = 40.5
From the first equation,
x = 900 - y
Substituting x = 900 - y into the second equation, we have
0.03(900 - y) + 0.055y = 40.5
27 - 0.03y + 0.055y = 40.5
- 0.03y + 0.055y = 40.5 - 27
0.025y = 13.5
y = 13.5/0.025
y = 540
x = 900 - y = 900 - 540
x = 360
360 ml of 3% solution and 540 ml of 5.5% solution should be used.
C. How long until there are only 20 mg remaining.
Therefore, it will take 12.52 hours
A plane is 110 mi north and 189 mi east
ANSWER:
30.2°
STEP-BY-STEP EXPLANATION:
The angle x can be calculated by means of the tangent trigonometric ratio, which relates the opposite leg to the adjacent leg, just like this:
[tex]\begin{gathered} \tan x=\frac{\text{ opposite}}{\text{ adjacent }} \\ \text{ opposite = 110} \\ \text{ adjacent = 189} \end{gathered}[/tex]We substitute and calculate for x just like this:
[tex]\begin{gathered} \tan\:x\:=\:\frac{110}{189} \\ x=\tan^{-1}\left(\frac{110}{189}\right) \\ x=30.2\degree \end{gathered}[/tex]Therefore, the angle is 30.2°
the sum of pi and 3/4 is a (n)_________ numberA. RationalB. NaturalC. WholeD. Irrational
Remember that pi is an irrational number which means it has infinite decimal without a pattern.
If we add a number to pi we would still get an irrational number because the sum of a rational and an irrational won't give another type of number than an irrational.
Therefore, the right answer is D.g(x) = 2x + 3, find g(a + 1). *
ANSWER:
g(a+1) = 2a + 5
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]g(x)=2x+3[/tex]Replacing, when x is a + 1:
[tex]\begin{gathered} g(a+1)=2\cdot(a+1)+3 \\ g(a+1)=2a+2+3 \\ g(a+1)=2a+5 \end{gathered}[/tex]A survey of 130 freshmen business students at a local university produced the results listed below. How many students took only psychology?
We could draw the following Venn's diagram to solve this problem.
So, after drawing this diagram, we notice that the number of students that took only psychology were 9.
Calculator 5 ft С A window in the shape of a parallelogram has the dimensions given What is the area of this window?A.20 ftB.24 ftC.28 ftD.40 ft
Area of a parallelogram = b x h
A chemist is using 328 milliliters of a solution of acid and water. If 13.7% of the solution is acid how many milliliters of acid are there? Round to nearest tenth
Hello
Let's find 13.7% of 328
[tex]\begin{gathered} \frac{13.7}{100}=\frac{x}{328} \\ x=\frac{13.7\times328}{100} \\ x=44.94 \end{gathered}[/tex]From the calculation above, 44.94mL of acid is present in the solution
Kerala is a marine biologist studying the breeding habits of an exotic species of sea turtlesLast year she observed the number of pregnant mother titles at each beach on an isolated island in the pacific. The histogram below summarizes the data. Use the histogram to answer each question
a) The number of beaches in each class is represented by the height of the class. The class that has the least frequency is the one with 5-7.
We can see that the height is 2, thus the number of beaches in this class is 2.
b) We can see that each class has width 3:
2 to 4: 2, 3, 4
5 to 7: 5, 6, 7
and so on
The width of each class is 3.
c) The classes with 11 or more are the last two, from 11 to 13 and from 14 to 16.
The height of the class 11 to 13 is 4
The height of the class 14 to 16 is 7
The total beaches with 11 or more pregnant turtles is the sum: 4 + 7 = 11
I need to find how much does is his monthly payment.
The total amount Christian will pay is given by:
[tex]A=P(1+rt)[/tex]where P is the principal, r is the interes rate and t is the time. In this case we have that P=15000, r=0.07 and t=2. Then we have:
[tex]\begin{gathered} A=15000(1+0.07(2)) \\ A=17100 \end{gathered}[/tex]Hence he will pay $17,100 in total. Now, to find the monthly amount we divide the total by the number of months; in this case 24:
[tex]\frac{17100}{24}=712.50[/tex]Therefore he will pay $712.50 each month.
Instructions: Find the missing length indicated.x=Check81225X
Given: A right triangle is given, and an altitude is drawn to the hypotenuse of the triangle.
Required: To determine the missing side x.
Explanation: The given triangle is as follows-
Let the side of the triangle be as shown in the figure. Now triangle ABD is a right-angled triangle. Hence, by Pythagoras theorem, we have-
[tex]\begin{gathered} BD^2=AB^2+AD^2 \\ (225)^2=x^2+y^2\text{ ...}(1) \end{gathered}[/tex]Similarly, triangles ABC and ADC are right-angled triangles. Thus-
[tex]\begin{gathered} y^2=z^2+(144)^2\text{ ...}(2) \\ x^2=(81)^2+z^2\text{ }...(3) \end{gathered}[/tex]Equations (1), (2), and (3) represent equations in 3 variables. Hence solving equations (1) and (2) by substituting the value of y from equation (2) into equation (1) as follows-
[tex]\begin{gathered} x^2+z^2+(144)^2=(225)^2 \\ x^2+z^2=(225+144)(225-144) \\ x^2+z^2=369\times81 \\ x^2+z^2=29889\text{ ...}(4) \end{gathered}[/tex]Now, we can solve equations (3) and (4) for x as follows-
[tex]x^2+x^2+z^2=6561+z^2+29889[/tex]Further solving for x as-
[tex]\begin{gathered} 2x^2=36450 \\ x=\sqrt{18225} \\ x=\pm135\text{ units} \end{gathered}[/tex]Since the side of a triangle can't be negative. Hence, x=135 units.
Final Answer: The length of the missing side is-
[tex]x=135\text{ units}[/tex]After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)
Since Mike drove at 65 mph for 3 hours, we have that he traveled:
[tex]3\cdot65=195\text{ miles}[/tex]for Sandra, we have the following:
[tex]3\cdot70=210\text{ miles}[/tex]notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:
[tex]x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}[/tex]therefore, Sandra and Mike are approximately 287 miles apart after 3 hours
what is 8 × 2000? and
simple, it's a multiplication
I multiply the number of atoms with the weight of each one to find the total weight of the gas
[tex](5.04\times10^{23})\times(1.67\times10^{-24}^{})[/tex]We group
[tex](5.04\times1.67)\times(10^{23}\times10^{-24})[/tex]and solve
[tex]\begin{gathered} (8.4168)\times(10^{-1}) \\ =0.84168 \end{gathered}[/tex]the result is: 0.84 grams
Determine if the expression s3+s2+s5/4 is a polynomial or not. If it is a polynomial state the type and degree of the polynomial
Given the algebraic expression
[tex]s^3+s^2+s^{\frac{5}{4}}[/tex]For the algebraic expression to be classified as a polynomial, all expressions must have a non-negative integer exponent.
From the given expression, we can see that the last term doesn't obey this rule (an exponent that is in fraction term).
Hence, the expression given is not a polynomial.
What is the relative value of F(x) when the value of x is close to 2 for the function F(x) = 1/x+2, whose graph is shown below?A. A very large numberB. ZeroC. A very small numberD. Either a very large number or a very small number
Answer:
D. Either a very large number or a very small number
Explanation:
Given the function:
[tex]F(x)=\frac{1}{x+2}[/tex]As can be seen from the graph, the point x=2 is an asymptote of the function.
Thus, the relative value of F(x) when the value of x is close to 2 is either a very large number or a very small number.
Option D is correct.
I have a practice problem that I need answered, thank you
Given inequality:
[tex]6x^2-x\text{ }<\text{ 2}[/tex]Re-arranging:
[tex]6x^2-x\text{ - 2 }<\text{ 0}[/tex]Factorizing the expression to the left:
[tex]\begin{gathered} 6x^2-2x\text{ + x -2 }<\text{ 0} \\ 6x^2\text{ -4x +3x -2 }<\text{ 0} \\ (3x-2)(2x+1)\text{ }<\text{ 0} \end{gathered}[/tex]Hence:
[tex]\begin{gathered} 3x-2\text{ }<\text{ 0} \\ 3x\text{ }<\text{ 2} \\ x\text{ }<\text{ }\frac{2}{3} \end{gathered}[/tex]Since their product is negative. one of the factors would be positive.
[tex]\begin{gathered} 2x\text{ + 1 > 0} \\ 2x\text{ > -1} \\ \frac{2x}{2}\text{ >}-\text{ }\frac{1}{2} \\ x\text{ > -}\frac{1}{2} \end{gathered}[/tex]The solution on a number line:
The solution on interval notation:
[tex]\mleft(-\frac{1}{2},\: \frac{2}{3}\mright)[/tex]Edmond divided 8 3/4 gallons of ketchup equally into 2 smaller bottles to put on the tables in his hamburger restaurant. How much ketchup did he put in each bottle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total ketchup = 8 3/4 gallons
bottles = 2
ketchup in each bottle = ?
Step 02:
[tex]8\text{ + }\frac{3}{4}=\frac{32+3}{4}=\frac{35}{4}[/tex][tex]\frac{\frac{35}{4}}{\frac{2}{1}}=\frac{35\cdot1}{4\cdot2}=\frac{35}{8}[/tex]The answer is:
Edmond put 35/8 gallons of ketchup in each bottle.
You deposit 500$ in a savings account that earns 2.5 interest compounded yearly. Find the balance in the account after the given amount of time A. 1 yearB. 5 years C. 20 years
In order to find the balance after the given time, use the following formula:
I = P(1 + r/n)^(t·n)
where
r: interes rate = 2.5% = 0.025
n: frequency = 1
t: time = 1, 5, 20
P: principal investment = 500
replace the previous values of the parameters into the formula for I:
A. 1 year:
I = $500(1 + 0.025/1)^(1·1) = $512.5
B. 5 years:
I = $500(1 + 0.025)^(5·1) = $565.7
C. 20 years
I = $500(1 + 0.025)^(20·1) = $819.3
What is the length of the hypotensis?If necessary round to the nearest 10th
We need to use the pythagorean theorem:
In a right triangle we have:
hyppootenuse
leg1
leg2
And the theorem says:
[tex]\text{hyppotenuse}^2=\text{leg}1^2+\text{leg}2^2[/tex]In this case:
leg1 = 9cm
leg2 = 3cm
[tex]c^2=(9cm)^2+(3cm)^2[/tex]And solve for c:
[tex]\begin{gathered} c=\sqrt[]{81cm^2+9cm^2} \\ c=\sqrt[]{90cm^2} \\ c\approx9.486832\ldots \end{gathered}[/tex]To the nearest tenth:
c = 9.5cm
question number 2! I already have the answer of the number one
If we have f(x) = sin(x), then:
[tex]f(2x)=\sin2x[/tex]f(2x) = sin(2x) is a vertical shrink if we compare it with f(x) = sin(x). Then, the graph of each function is:
How to solve for area of number 6 to the nearest square unit
132 square meters
Explanations:6) The given composite function is made up of a large rectangle and a small rectangle as shown:
The area of the composite figure = Area of the rectangle A + area of rectangle B
Since area of the rectangle = Length * width, hence;
[tex]\begin{gathered} \text{Area of the figure=}LW+lw \\ \text{Area of the figure=(9m}\times12m\text{)+(}4m\times6m\text{)} \\ \text{Area of the figure=}108m^2+24m^2 \\ \text{Area of the figure=}132m^2 \end{gathered}[/tex]Hence the area of the composite figure is 132 square meters
The table below shows the value for the function y=f(x)If g(x)=1/2 which of the following are solutions to g(x) select all that applyA (-3,5.5)B(-1,-2)C(0,4)D (5,-8)
So we have a table of values that associate x values with a function f(x). The pairs (x,y) are solutions to the equation y=f(x) and they are:
[tex]\begin{gathered} (-3,5) \\ (-1,-4) \\ (0,2) \\ (5,-8) \\ (6,3) \end{gathered}[/tex]If we define a new function g(x)=(1/2)*f(x) its solutions will be those of f(x) but with their y values divided by 2. Then the solutions to g(x) are:
[tex]\begin{gathered} (-3,\frac{5}{2})=(-3,2.5) \\ (-1,-\frac{4}{2})=(-1,-2) \\ (0,\frac{2}{2})=(0,1) \\ (5,-\frac{8}{2})=(5,-4) \\ (6,\frac{3}{2})=(6,1.5) \end{gathered}[/tex]Then the only option with a solution to g(x) is the second option (-1,-2).
Use the number line to determine if each number is a solution . And don't worry this is just a practice :)
What effect does changing the function f(x)=3sin(x)+1to the function g(x)=3sin(x4)+2 have on the graph of f(x)?
Step 1
The parent function f(x) is given as;
[tex]f(x)=3\sin (x)+1[/tex]If we transform the function by adding 1 to it we will have;
[tex]\begin{gathered} f(x)=3\sin (x)+1+1 \\ f(x)=3\sin (x)+2 \end{gathered}[/tex]We have the following graph;
which means when you add 1 to the to get f(x)=3sin(x)+2, the function is shifted up by 1 unit.
Step 2
If the function is further transformed to;
[tex]f(x)=3\sin (\frac{x}{4})+1[/tex]we will have the graph below;
This means that the graph stretches horizontally by a factor of 4.
Therefore the changes f(x) passes through to g(x) are;
[tex]\begin{gathered} f(x)=2\sin (\frac{x}{4})+1_{}--(A\text{ horizontal stretch by a factor of 4)} \\ g(x)=2\sin (\frac{x}{4})+2---(A\text{ shift up by 1 unit)} \end{gathered}[/tex]Answer; The graph is stretched horizontally by a factor of 4 and shifted up by 1 unit.
Please help me solve this math question. Please explain each step clearly
a) Since the relation is proportional, the graph is a line.
In order to graph a line we only need two points and connecting them we get the line.
In this case, we know that at 4h the pool has 5200 gallons. The point woud be (4, 5200)
Now we need another point. The simplest one is the origin. When the time is zero, the amount of water in the pool is also 0, then we have another point (0, 0)
Now with the points (0, 0) and (4, 5200) we can graph the relationship.
b) We need to compair the filling rates. In the graph provided we can see that in 3 hours, there is 10,800 gallons. Since the other pool had 5,200 gallons in 4 hours, is clear that the second pool fills much more quicker.
Ahmad is putting 11 colored light bulbs into a string of lights. There are 5 green light bulbs, 4 yellow light bulbs, and 2 red light bulbs. How many distinct ordersof light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:
[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:
[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]So, Ahmad has 6,930 distinct orders