Given data:
The expression for the total age of Darris, Miles, and Alan is D+M+A= 48 years.
The expression for Darris is twice as old as Miles is D=2M or M=D/2.
The expression for Alan is 3 years older than Darris is A=D+3.
Substitute (D/2) for M, and (D+3) for A in the first equation.
[tex]\begin{gathered} D+\frac{D}{2}+D+3=48 \\ 2D+\frac{D}{2}=45 \\ \frac{5D}{2}=45 \\ 5D=90 \\ D=18\text{ years} \end{gathered}[/tex]The Miles age is,
[tex]\begin{gathered} M=\frac{18}{2}\text{ years} \\ =9\text{ years} \end{gathered}[/tex]The Alan age is,
[tex]\begin{gathered} A=(18\text{ years)+3 years} \\ =21\text{ years} \end{gathered}[/tex]Thus, the Dorris age is 18 years, Miles age is 9 years, and Alan age is 21 years.
Which inequality is equivalent to the following? 5 x/2+ 3 < 12
We can isolate x to find an equivalent inequality:
[tex]\begin{gathered} \frac{5}{2}\cdot x+3<12 \\ \frac{5}{2}\cdot x<12-3 \\ x<9\cdot\frac{2}{5} \\ x<\frac{18}{5} \end{gathered}[/tex]I need help with this problem Harry made 4 hits in 9 times at-bat. If she keeps the same success level, how many hits should she make in 18 timesat-bat?
We need to find the expected value, first:
[tex]E(x)=p(x)\cdot n[/tex]Where:
[tex]\begin{gathered} p(x)=\frac{4}{9} \\ n=18 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} E(x)=\frac{4}{9}\cdot18 \\ E(x)=8 \end{gathered}[/tex]Answer:
8 hits
5) Solve the following systems of linear equations: (10pts each) Sy=44-7 (use substitution) Ly=-2x+5 i) ii) (2x - 3y=8 (use elimination) 16x+5y = -4
The given set of equations are:
[tex]\begin{gathered} 2x-3y=8\ldots\text{.}\mathrm{}(1) \\ 6x+5y=-4\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]Multiply equation 1 by 5 and equation 2 by 3, we get,
[tex]\begin{gathered} 5(2x-3y)=8\times5\rightarrow10x-15y=40\ldots\text{.}(3) \\ 3(6x+5y)=3\times(-4)\rightarrow18x+15y=-12\ldots\text{.}(4) \end{gathered}[/tex]Now, add equation 3 and 4, we get,
[tex]\begin{gathered} 10x-15y+18x+15y=40-12 \\ 28x=28 \\ x=1 \end{gathered}[/tex]Therefore, from equation 1, with the value of x, we get,
[tex]\begin{gathered} 2-3y=8 \\ 2-8=3y \\ -6=3y \\ y=-\frac{6}{3}=-2 \end{gathered}[/tex]Thus, the solution is, x = 1 and y = -2
i need to fine the common denominator and the answer
To find the common denominators
Find the unit rate if it costs $2.48 for 10 slices
10 slices costs $2.48
The unit rate will be the cost of 1 slice.
Therefore:
[tex]\begin{gathered} \text{Unit Rate}=\frac{\$2.48}{10\text{ Slices}} \\ =\$0.248\text{ per slice} \end{gathered}[/tex]To the nearest cent, the unit rate will be:
$0.25 per slice.
write the equation of the line in fully simplified intercept form.
We have the following:
The equation in its slope-intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]we calculate the slope like this
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing the points (-8,11) and (10, 2)
[tex]m=\frac{2-11}{10-)-8)}=\frac{-9}{10+8}=\frac{-9}{18}=-\frac{1}{2}[/tex]In this case the y-intercept can be seen in the graph y is (0,7), therefore the value of b is 7
Therefore, the equation would be:
[tex]y=-\frac{1}{2}x+7[/tex]what letters do you need to get rid of first to solve the equation [tex] \frac{x}{z } [/tex][tex] - c for x[/tex]
You have the following equation:
[tex]y=\frac{x}{z}-c[/tex]In order to determine which of the previous letter you need to get rid off, to solve for x, you consider it is necessary to eliminate additional terms in the side of the equation where the variable is.
In this case, such additional term is - c.
Hence, the letter you need to get rid off is letter c.
Select all the expressions that are equivalent to 797(–
5).
The expressions that are equivalent to 797(–5) include the expressions that his a value of -3985.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case you will multiply the values. This will be:
= 797 × (-5)
= -3985
Therefore, the values given must so he equal to -3985.
Note that an overview was given as the options aren't given.
Learn more expressions on:
brainly.com/question/723406
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Elena went to a store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces of spicy popcorn for $2.50. 1. How much does popcorn cost per ounce? Show your work.
Okay, here we have this:
Considering that we know that 10 ounces of popcorn cost $2.50, let's calculate how much does popcorn cost per ounce:
Cost of one ounce of popcorn=Cost of 10 ounces/10
Replacing we obtain:
Cost of one ounce of popcorn=$2.50/10
Cost of one ounce of popcorn=$0.25
It says to find the volume of the figure and round to the nearest hundredth where necessary. Please help!
Solution:
Given:
A frustrum with a rectangular top and base.
To find the volume of the figure, we make the sketch as shown below.
The volume of the frustrum is given by;
[tex]Volume\text{ of frustum}=volume\text{ of big pyramid}-volume\text{ of small pyramid}[/tex]The volume of a pyramid is given by;
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ where; \\ A\text{ is the base area} \\ h\text{ is the height} \end{gathered}[/tex]Hence, we get the heights of both pyramids by similarity;
[tex]\begin{gathered} height\text{ of big pyramid}=25.7+x \\ height\text{ of small pyramid}=x \\ base\text{ of small pyramid}=15 \\ base\text{ of big pyramid}=37 \\ \\ Hence,\text{ by similarity,} \\ \frac{h_1}{b_1}=\frac{h_2}{b_2} \\ \frac{25.7+x}{37}=\frac{x}{15} \\ \\ Cross\text{ multiplying,} \\ 15\left(25.7+x\right)=37\times x \\ 385.5+15x=37x \\ Collecting\text{ the like terms,} \\ 385.5=37x-15x \\ 385.5=22x \\ Dividing\text{ both sides by 22;} \\ \frac{385.5}{22}=x \\ x=17.52cm \\ \\ Thus, \\ he\imaginaryI ght\text{ of b}\imaginaryI\text{g pyram}\imaginaryI\text{d}=25.7+x=25.7+17.52 \\ he\mathrm{i}ght\text{ of b}\mathrm{i}\text{g pyram}\mathrm{i}\text{d}=43.22cm \\ \\ he\mathrm{i}ght\text{ of small pyram}\mathrm{i}\text{d}=x \\ he\mathrm{i}ght\text{ of small pyram}\mathrm{i}\text{d}=17.52cm \end{gathered}[/tex]Hence, the volume of the pyramids is calculated;
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ Volume\text{ of the big pyramid}=\frac{1}{3}\times l\times b\times h \\ Volume\text{ of the big pyramid}=\frac{1}{3}\times37\times20\times43.22=31,982.8cm^3 \\ \\ Volume\text{ of the small pyram}\imaginaryI\text{d}=\frac{1}{3}\times l\times b\times h \\ Volume\text{ of the small pyram}\imaginaryI\text{d}=\frac{1}{3}\times15\times20\times17.52=5256cm^3 \\ \\ \\ Volume\text{ of the figure}=31982.8-5256 \\ Volume\text{ of the figure}=26726.80cm^3 \end{gathered}[/tex]Therefore, the volume of the figure to the nearest hundredth is 26,726.80 cubic centimeters.
One positive integer is 1 less than twice another. The sum of their squares is 34. Find the integers.
Let's define the following variable.
x = first integer
y = second integer
If the sum of their squares is 34, then we can form the equation below:
[tex]x^2+y^2=34[/tex]If the other integer, say x, is 1 less than twice the other (y), then we can form this second equation:
[tex]x=2y-1[/tex]From these two equations, we can now solve for the values of x and y.
Here are the steps.
1. Replace the value of "x" in equation 1 using the value in equation 2.
[tex](2y-1)^2+y^2=34[/tex]2. Apply the exponent.
[tex]\begin{gathered} (4y^2-4y+1)+y^2=34 \\ 4y^2-4y+1+y^2=34 \end{gathered}[/tex]3. Rearrange the terms. Subtract 34 on both sides of the equation then, combine similar terms.
[tex]\begin{gathered} 4y^2+y^2-4y+1=34 \\ 4y^2+y^2-4y+1-34=34-34 \\ 5y^2-4y-33=0 \end{gathered}[/tex]In step3, we are able to create a quadratic equation in a standard form that is ax² + bx + c wherein a = 5, b = -4, and c = -33.
To solve for the value of y, we can use the Quadratic formula.
[tex]y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Since we have already determined the values of a, b, and c, let's plug them into the formula above.
[tex]y=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(5)(-33)}_{}}{2(5)}[/tex]Then, solve for y.
[tex]\begin{gathered} y=\frac{4\pm\sqrt[]{16+660}}{10} \\ y=\frac{4\pm\sqrt[]{676}}{10} \\ y=\frac{4\pm26}{10} \end{gathered}[/tex]Separate the plus and minus signs.
[tex]\begin{gathered} y=\frac{4+26}{10}=\frac{30}{10}=3 \\ y=\frac{4-26}{10}=-\frac{22}{10}=-2.2 \end{gathered}[/tex]There are two possible values y but only one is an integer. So, we will use y = 3.
To solve for the other integer x, let's use the second equation plugin y = 3.
[tex]\begin{gathered} x=2y-1 \\ x=2(3)-1 \\ x=6-1 \\ x=5 \end{gathered}[/tex]Therefore, the integers are 5 and 3.
Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 1 tile the firstday. She started to go faster and by the end of day 4, she had placed 31 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.Lizzy took______days to place all the tiles. Ok so I was working on this and I have y-1=10(x-1) is this correct so far and what do I do next?
Answer:
Equation: y - 1 = 10( x - 1)
Explanation:
If we call x the number of days and y the number of tiles placed, then the word problem gives us two points that lie on the line we are trying to find the equation for. These points are (1,1) and (4, 31).
First, we find the slope of the line. The slope is found by dividing the difference in y coordinates by the difference in x -coordinates.
[tex]m=\frac{31-1}{4-1}=\frac{30}{3}[/tex][tex]\boxed{m=3.}[/tex]With the value of the slope in hand, we now use the point (1,1) to write the point-slope equation of the line.
[tex]\boxed{y-1=10\mleft(x-1\mright)_{}}[/tex]With this equation in hand, now let us find how many days it will take Lizzy to place 100 tiles. To find out we substitute y = 100 into the above equation and solve for x.
[tex]100-1=10(x-1)[/tex][tex]\Rightarrow99=10(x-1)[/tex]dividing both sides by 10 gives
[tex]9.9=x-1[/tex]finally, adding 1 to both sides gives
[tex]x=9.9+1[/tex][tex]\boxed{x=10.9.}[/tex]which is about 11 days.
Hence, it took lizzy exactly 10.9 days to place all the tiles.
wwmuch money, in dollars, does each person earn per lawn hard earns per lawn. omanas per lawn
Both are proportional functions.
Divide the earnings by the number of lawns in each case, pick one point.
Richard: 40 / 5 = $8 per lawn
Tom = 22.50 / 3 = $7.5 per lawn
[tex] \frac{2}{n } = \frac{2}{3} \: \\ \\ \\ \: \: a \: deh \\ [/tex]A. n= 30B. n= 3\4C. n=3D. n=1 1/3
Answer:
The solution is;
[tex]n=3[/tex]Explanation:
Given the equation;
[tex]\frac{2}{n}=\frac{2}{3}[/tex]We want to solve for n;
Let us cross multiply;
[tex]\begin{gathered} \frac{2}{n}=\frac{2}{3} \\ n(2)=2(3) \\ 2n=6 \\ \text{divide both sides by 2;} \\ \frac{2n}{2}=\frac{6}{2} \\ n=3 \end{gathered}[/tex]Therefore, the solution is;
[tex]n=3[/tex]If sin(0)1213and O is in Quadrant III, then what is coss)
Answer:
cos(θ/2) = -2(√2)/13
Explanation:
To find cos(θ/2), we will use the following trigonometric identity
[tex]\cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]Now, we know that sin(θ) = -12/13 and sin(θ) is also equal to the opposite side over the hypotenuse, so we can represent the angle with the following triangle
Then, using the Pythagorean theorem, we can find the value of the adjacent side x, so
[tex]\begin{gathered} x=\sqrt[]{13^2-(-12)^2} \\ x=\sqrt[]{169-144} \\ x=\sqrt[]{25}=5 \end{gathered}[/tex]Therefore, cos(θ) will be equal to:
[tex]\cos (\theta)=\frac{\text{Adjacent}}{\text{Hypotenusa}}=\frac{-5}{13}[/tex]Where we use the negative sign because θ is in quadrant III. Now, we can use the trigonometric identity
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{1+\cos\theta}{2}}_{} \\ \cos (\frac{\theta}{2}_{})=\pm\sqrt[]{\frac{1-\frac{5}{13}}{13}} \\ \cos (\frac{\theta}{2})=\pm\sqrt[]{\frac{8}{169}} \\ \cos (\frac{\theta}{2})=\pm\frac{2\sqrt[]{2}}{13} \end{gathered}[/tex]Since θ is in quadrant III, θ/2 should be in quadrant II, so cos(θ/2) is negative. then, the answer is
[tex]\cos (\frac{\theta}{2}_{})=-\frac{2\sqrt[]{2}}{13}[/tex]Factor completely.50u^2 - 18
Given:
[tex]50u^2-18[/tex]To factor the given equation completely, we factor out common term 2 first:
[tex]2(25u^2-9)[/tex]We can also rewrite this into:
[tex]2((5u)^2-3^2)[/tex]For (5u)^2-3^2, we apply Difference of Two Squares Formula:
[tex]x^2-y^2=(x+y)(x-y)[/tex]where:
x=5u
y=3
So,
[tex](5u)^2-3^2=(5u+3)(5u-3)[/tex]Therefore, the answer is:
[tex]2(5u+3)(5u-3)[/tex]HELP MEEE PLEASEEEEEEEE
Step-by-step explanation:
The answer is going to be B
Answer:
B
Step-by-step explanation:
0.5x - 18 >= -14
0.5x >= 4
x >= 4/0.5 = 8
so,
x >= 8
therefore, 8 is the smallest number to make that inequality true.
P'Q' is a translation of PQ. Write the translation rule.(x, y) -> (____,____)
Let:
[tex]\begin{gathered} P=(-2,-9) \\ Q=(-7,-4) \\ P^{\prime}=(9,2) \\ Q^{\prime}=(4,7) \end{gathered}[/tex]so:
[tex]\begin{gathered} P\to(x,y)\to P^{\prime} \\ -2+x=9 \\ so\colon \\ x=11 \\ ----- \\ -9+y=2 \\ y=11 \end{gathered}[/tex]Therefore:
[tex](x,y)\to(11,11)[/tex]You might need:The equation of a circle is given below.(x-0.5)² + (y - 3,5)² = 16What is its center?(______)What is its radius?If necessary, round your answer to two decimal places.
Center = (0.5, 3.5) and radius = 4
Explanation:Given the equation:
[tex](x-0.5)^2+(y-3.5)^2=16[/tex]This may be written as:
[tex](x-0.5)^2+(y-3.5)^2=4^2[/tex]Comparing this with the general form of the equation of a circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]With the center = (a, b) and radius = r, we have:
Center = (0.5, 3.5) and radius = 4
I’m confused about this and the other answer is the 1.7 in the trial one
The most likely error in the data shown would be the .64 in trial 2 because as you may have noticed on all the data in the table, the amount of growth are all more than 1.
The following summarizes the number of fiction books read last summer by a sample of 33 students.Number of students 2,7,16,8Number of books read per student 2,3,4,7What is the mean number of books read? Round your answer to the nearest tenth.
The mean is 4
To find the mean of a data set, we use:
[tex]Mean=\frac{Sum\text{ }of\text{ }values}{Total\text{ }number\text{ }of\text{ }values}[/tex]The values given are:
2, 3, 4, 7
The total number of values are 4. Then:
[tex]Mean=\frac{2+3+4+7}{4}=\frac{16}{4}=4[/tex]-2 -6-5-4-3-2-1 + 71 2 3 4 5 6 7 8 9 -2 A If this is the graph of f(x) = a*+h nk + k, then: O A. 0 1 O c. ao O a Da > 1
For the graph given in the question, we have the function
[tex]f(x)=a^{x+h}+k[/tex]If the given graph is for for the function f(x) the
[tex]a>1[/tex]Therefore, the correct option is D
The table below shows a student's quiz scores on four quizzes. Scores 16 15 15 13 Find this student's mean quiz score
We are given the following data set:
[tex]1\text{6 15 15 13}[/tex]We are asked to find the mean value, to do that we need to add them all together and divide the result by the number of digits we have, in this case we have 4 numbers, therefore the mean value is the following
[tex]\operatorname{mean}value\text{ = }\frac{16\text{ +15+15+13}}{4}=\frac{59}{4}=14.75[/tex]The student's mean quiz score is 14.75
.
Thanks and have a great day!
line L is shown in the coordinate plane. which of the following is located on line L
Given the line L.
As shown the line passes through the points (0, 0) and (4, 5)
So, the slope of the line =
[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]The equation of the line will be:
[tex]y=\frac{5}{4}x[/tex]We will check which point is located on the line L
As we can see from the equation the ratio of y/x = 5/4
So, we will find the ratio of y/x for the given points
[tex]\begin{gathered} (20,25)\rightarrow\frac{y}{x}=\frac{25}{20}=\frac{5}{4} \\ \\ (22,27)\rightarrow\frac{y}{x}=\frac{27}{22} \\ \\ (15,18)\rightarrow\frac{y}{x}=\frac{18}{15}=\frac{6}{5} \end{gathered}[/tex]From the previous results, the answer will be:
The point that is located on the line is (20, 25)
fraction worksheet 6/7 = -----/56
The missing number is 48
Explanation:Let the missing number be x, then
x/6 = 56/7
x/6 = 8
x = 8 * 6
= 48
Use the slope-intercept form to graph the equation y=2/9x+3
we are given the following equation of a line
[tex]y=\frac{2}{9}x+3[/tex]This is written in the slope-intercept form, which means it follows the general form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the intercept. We are asked to find the graph, to do that, we can begin by using the intercept since that is the point where the line touches the y-axis, this means that it represents the point (0,b), in our case, this is: (0,3).
Now we need to find a second point, we can use the point where the line touches the x-axis, that is, the point where y = 0, so we set y = 0 in the equation for the line and solve for "x", like this:
[tex]\begin{gathered} y=\frac{2}{9}x+3 \\ 0=\frac{2}{9}x+3 \end{gathered}[/tex]subtracting 3 on both sides
[tex]-3=\frac{2}{9}x[/tex]multipliying by 9 on both sides
[tex]-3(9)=2x[/tex]Dividing by 2 on both sides
[tex]\begin{gathered} \frac{-3(9)}{2}=x \\ -\frac{27}{2}=x \end{gathered}[/tex]therefore, the second point is (-27/2,0). Now we plot both points and join them with a line, like this:
Any two points can be use to plot a line, so one could also use a different value for "x", evaluate that value in the equation for the line and get a value for "y". That point, together with the intercept can be use to plot the line.
We could use for example x = -5, if we replace that value in the equation we get.
[tex]y=\frac{2}{9}(-5)+3=\frac{17}{9}[/tex]we get the point (-5,17/9), and the plot would look like this:
In AGHI, the measure of angle I=90^ °, HI = 1.1 feet , and IG = 7.5 feet. Find the measure of angle G to the nearest tenth of a degree.
To find angle x we can use the tangent function. Remember that the tangent function is defined as:
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]For angle x the opposite leg is 1.1 and the adjacent leg is 7.5, plugging this values into the equation above and solving for x we have:
[tex]\begin{gathered} \tan x=\frac{1.1}{7.5} \\ x=\tan ^{-1}(\frac{1.1}{7.5}) \\ x=8.3 \end{gathered}[/tex]Therefore x is equal to 8.3°
A triangle has side lengths of (1.2u + 1.8v) centimeters, (6.5u + 8.7w) centimeters, and (5.8W – 6.9v) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 0 13.5uw + 3.6vw 7.7u + 1.8w + 7.6v -1.lvw + 15.2uw + 3uv 0 14.5w – 5.1v + 7.7u Submit Answer i dont get this?
1) The Perimeter (2P) is the sum of the side lengths so let's sum those given measures:
2P=(1.2u+1.8v) +(6.5u+8.7w)+(5.8w-6.9v) Combining Like terms
2P=1.2u +6.5u +1.8v -6.9v +8.7w+5.8w
2P= 7.7u-5.1v+14.5w
2) Reordering
2p= 14.5w -5.1v +7.7u
2. Last year, Mr. Leon had a rectangular gardenwith an area of 208 square feet. This year thedimensions of the garden are the size of thedimensions of last year's garden. What is thearea of Mr. Leon's garden this year?A. 104 ft2B. 416 ft2C. 52 ft2D. 208 ft2
Answer:
C. 52 ft2
Step-by-step explanation:
Rectangle:
Has two dimensions, which are height(h) and base(b).
The area is: A = b*h
In this question:
We have that that A = b*h = 208.
New dimensions:
Both the dimensions are half(1/2) of last year.
So
A = (b/2)*(h/2) = (b*h)/4
Since b*h = 208
A = (b*h)/4 = 208/4 = 52
The UN's measures gender equality. The mean number of hours spent on household chores is another measure of gender equality for a nation. Suppose that a UN study aims to estimate the mean hours spent on household chores by adults 15 years and older for a particular country within 0.2 hour. The desired level of confidence is 96%. From the previous studies, the the population standard deviation is 0.8 hours.What is the necessary sample size to achieve the above margin of error?
We have to find the minimum sample size.
The margin of error that it is aimed is ±0.2 hours from the real mean.
The population standard deviation is 0.8 hours.
The desired level of confidence is 96%. This corresponds to a z-score of 2.054.
We can relate sample size with the given information as:
[tex]\begin{gathered} e=\frac{\sigma}{\sqrt{n}}\cdot z \\ \sqrt{n}=\frac{\sigma}{e}\cdot z \\ n=(\frac{\sigma\cdot z}{e})^2 \end{gathered}[/tex]If we replace e = 0.2, σ = 0.8 and z = 2.054 we can calculate the sample size n as:
[tex]\begin{gathered} n=(\frac{0.8*2.054}{0.2})^2 \\ \\ n=(8.216)^2 \\ n\approx67.5 \\ n\approx68 \end{gathered}[/tex]Answer: the sample size has to be at least 68 people.
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