Given the three variable simultaneous equations;
[tex]\begin{gathered} x+y+2z=-1\ldots\ldots.i \\ x+y+8z=-7\ldots\ldots.ii \\ x-9y-2z=-37\ldots\ldots.iii \end{gathered}[/tex]To solve;
let's solve for z by subtracting equation i from ii;
[tex]\begin{gathered} x+y+8z-(x+y+2z)=-7-(-1) \\ x-x+y-y+8z-2z=-7+1 \\ 6z=-6 \\ \frac{6z}{6}=\frac{-6}{6} \\ z=-1 \end{gathered}[/tex]next let's solve for y by subtracting equation i from iii;
[tex]\begin{gathered} x-9y-2z-(x+y+2z)=-37-(-1) \\ x-x-9y-y-2z-2z=-37+1 \\ -10y-4z=-36 \\ \text{ since z=-1} \\ -10y-4(-1)=-36 \\ -10y+4=-36 \\ -10y+4-4=-36-4 \\ -10y=-40 \\ \frac{-10y}{-10}=\frac{-40}{-10} \\ y=4 \end{gathered}[/tex]We have z and y, to get x let us substitute te values of y and z into equation i;
[tex]\begin{gathered} x+y+2z=-1 \\ x+(4)+2(-1)=-1 \\ x+4-2=-1 \\ x+2=-1 \\ x+2-2=-1-2 \\ x=-3 \end{gathered}[/tex]Therefore the values of x, y and z are;
[tex]\begin{gathered} x=-3 \\ y=4 \\ z=-1 \end{gathered}[/tex]Answer is A.
proportional relationship. Vivian says that cannot be true because the constants ofMindy says that the equations p =1.59 and {o= q both represent the sameproportionality are different. Which student do you agree with? Explain.
We have two equations:
[tex]\begin{gathered} p=1.5q \\ \frac{2}{3}p=q \end{gathered}[/tex]We would like to know if those represent the same proportional relationship or don't.
For doing so, we remember that a constant of proportionality
need help on value of f(5) for function[tex]f(x) = \frac{1}{4} \times {2}^{x} [/tex]
Given
The function,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]To find:
The value of f(5).
Explanation:
It is given that,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]Then,
For x=5,
[tex]\begin{gathered} f(5)=\frac{1}{4}\times2^5 \\ f(5)=\frac{1}{4}\times32 \\ f(5)=8 \end{gathered}[/tex]Hence, the value of f(5) is 8.
Hi, can you help me answer this question please, thank you
The test statistic, z, is computed as follows:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]where:
x: sample mean
μ: population mean
σ: standard deviation
n: number of samples
Substituting with x = 89.7, μ = 84.9, σ = 13.9, and n = 61, we get:
[tex]\begin{gathered} z=\frac{\bar{89.7}-84.9}{\frac{13.9}{\sqrt[]{61}}} \\ z=2.697 \end{gathered}[/tex]There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag. What is theprobability of selecting a red marble? Your answer can be a fraction, decimal orpercent.
Given
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag
[tex]\begin{gathered} \text{Total Marbles =5+2+3} \\ \text{Total Marbles =10} \end{gathered}[/tex]Probability of selecting a red marble
[tex]\text{Probability of selecting a red marble =}\frac{2}{10}=\frac{1}{5}[/tex]The final answer
The probability of selecting a red marble
[tex]\frac{1}{5}[/tex]Find the volume of this object.Use 3 for a.Volume of a CylinderV=Tir2h4 cm7 cm8 cm]1 cm V ~ [?]cm31
Explanation
The volume of the object is the sum of the volumes of the composite solids that make up the object. Since each solid is a cylinder, we will make use of the formula below.
[tex]\text{Volume of a cylinder =}\pi r^2h[/tex]The question gives the following parameters for the solids
[tex]\begin{gathered} \text{Solid 1 }\mleft\lbrace r=\frac{4}{2}=2;h=7\mright\rbrace \\ Solid\text{ 2 }\mleft\lbrace r=\frac{8}{2}=4;h=1\mright\rbrace \\ \text{where }\pi=3 \end{gathered}[/tex]We can substitute the parameters into the formula.
[tex]\begin{gathered} \text{Volume of solid 1=}3\times2^2\times7=84\operatorname{cm}^3 \\ \text{Volume of solid 2 = }3\times4^2\times1=48cm^3 \end{gathered}[/tex]Therefore;
[tex]\text{Volume of the object }=84+48=132\operatorname{cm}^3[/tex]Answer:
[tex]132\operatorname{cm}^3[/tex]How can you compare two or more fractions so as to arrange them in ascending or descending order?
There are two ways to arrange them in ascending or descending order.
The first way is to convert them into similar fractions (if they are not similar fractions yet), and arrange them in the order that you like.
[tex]\begin{gathered} \text{Example} \\ \frac{2}{3},\frac{1}{2},\frac{3}{4} \end{gathered}[/tex]Convert them to similar fractions, by getting their LCD and we have
[tex]\begin{gathered} \text{LCD}(2,3,4)=12 \\ \frac{2}{3}=\frac{8}{12} \\ \frac{1}{2}=\frac{6}{12} \\ \frac{3}{4}=\frac{9}{12} \end{gathered}[/tex]We can now arrange them based on their numerators
[tex]\begin{gathered} \text{Ascending} \\ \frac{6}{12},\frac{8}{12},\frac{9}{12}\Longrightarrow\frac{1}{2},\frac{2}{3},\frac{3}{4} \\ \\ \text{Descending} \\ \frac{9}{12},\frac{8}{12},\frac{6}{12}\Longrightarrow\frac{3}{4},\frac{2}{3},\frac{1}{2} \end{gathered}[/tex]Another way to arrange them is to get their decimal equivalent, and arrange them accordingly
[tex]\begin{gathered} \text{Example} \\ \frac{2}{3}=0.67 \\ \frac{1}{2}=0.5 \\ \frac{3}{4}=0.75 \\ \\ \text{Ascending} \\ 0.5,0.67,0.75\Longrightarrow\frac{1}{2},\frac{2}{3},\frac{3}{4} \\ \\ \text{Descending} \\ 0.75,0.67,0.5\rightarrow\frac{3}{4},\frac{2}{3},\frac{1}{2} \end{gathered}[/tex]compute the monthly cost of the cellular phone for use of the following anytime minutes.
ANSWER:
(a) $29.99
(b) $37.49
(c) $30.24
STEP-BY-STEP EXPLANATION:
We have a function by part to calculate the monthly cost of a cell phone plan.
If the consumption is between 0 and 300 minutes, the value will always be $29.99. While if the consumption is greater than 300 minutes, the value is given by the following equation:
[tex]C\mleft(x\mright)=0.25x-45.01[/tex]Knowing the above, we calculate in each case:
(a) 190 minutes.
It is in the interval between 0 and 300 minutes, therefore, the cost is $29.99.
C (190) = $29.99
(b)
[tex]\begin{gathered} C(330)=0.25\cdot330-45.01 \\ C(330)=82.5-45.01 \\ C(330)=37.49 \end{gathered}[/tex](c)
[tex]\begin{gathered} C(301)=0.25\cdot301-45.01 \\ C(301)=75.25-45.01 \\ C(301)=30.24 \end{gathered}[/tex]Find the approximated area of a circle whose circumference is 7.85.
The formula of the circumference of a circle is given by:
[tex]C=2\pi r[/tex]Where r is the radius.
By replacing the C-value, we can solve for r:
[tex]\begin{gathered} 7.85=2\pi r \\ r=\frac{7.85}{2\pi} \\ r=1.25 \end{gathered}[/tex]Now, the formula of the area is given by:
[tex]A=\pi r^2[/tex]Replace the r-value and solve for A:
[tex]\begin{gathered} A=\pi(1.25)^2 \\ A=\pi\cdot1.56 \\ A=4.91 \end{gathered}[/tex]The area of the circle is 4.91
an item is regularly priced at $30. it is on sale for 40% off the regular price. how much (in dollars) is discounted from the regular price? thank you for helping
ANSWER
$12
EXPLANATION
The item is regularly priced at $30.
It is on sale for 40% off. So, 40% of the price is cut off, so that the buyer only pays 60%.
The amount discounted from the original price is 40% of $30. That is:
[tex]\begin{gathered} \frac{40}{100}\text{ of \$30} \\ \Rightarrow\text{ }\frac{40}{100}\cdot\text{ 30} \\ =\text{ }\frac{40\cdot\text{ 30}}{100} \\ =\text{ }\frac{1200}{100} \\ =\text{ \$12} \end{gathered}[/tex]The answer is $12
If the coefficient of determination is 0.233, what percentage of the variation in the data about the regression line is explained?5.43%76.7%23.3%46.6%
We need the coefficient of determination definition
The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model
So if we have a coefficient of determination of 0.233 we multiply by 100 to get the percentage
Answer: 23.3%
simply 3 (sqrt(c^2)) if c is > or equal to 0I can upload a picture
Recall that:
[tex]\begin{gathered} \text{For all x}\in\R \\ \sqrt[]{x^2}=|x|\text{.} \end{gathered}[/tex]Therefore:
[tex]3\sqrt[]{c^2}=3|c|\text{.}[/tex]Now, since c≥0, we get that:
[tex]|c|=c\text{.}[/tex]Substituting the above result in 3|c| we get:
[tex]3\sqrt[]{c^2}=3c\text{.}[/tex]Answer:
[tex]3c\text{.}[/tex]Weight: How many grams does a 5 lb 8 oz roast weigh?The roast weighs ? grams.
Solution
For this case we have the following weight:
5 lb and 8 oz
Using the following conversion ratios
1lb = 453.592 gr
1 oz = 28.3495 gr
We need to convert into grams so we can do this:
[tex]5lb\cdot\frac{453.592gr}{1lb}=2267.96gr[/tex][tex]8oz\cdot\frac{28.3495gr}{1oz}=226.796gr[/tex]Then adding the two values we have:
2267.96gr + 226.796gr = 2494.756 gr
Solve for R in I=PRTa.) What is the variable?b.) What is happing to the variable? (list the operations from the first thing to the last thing)c.) What is the inverse (opposite) of the last thing that happened to the variable. (Make a list of the steps to solve)
a) R is the variable
b) a product, the variable is being multiplied
[tex]R=\frac{I}{PT}[/tex]Explanation
Step 1
[tex]I=\text{PRT}[/tex]the value for I depends on the value for R, it means, that I depends on the value for R
so, R is the variable
Step 2
when you have
[tex]\begin{gathered} I=\text{PRT} \\ is\text{ equal to} \\ I=P\cdot R\cdot T \end{gathered}[/tex]it is a multiplication between P, R and T,the variable is being multiplied
Step 2
solve for R
[tex]\begin{gathered} I=\text{PRT} \\ \text{you n}eed\text{ to do the inverse operation } \\ \text{Multiplication}\Rightarrow opposite\Rightarrow Division \end{gathered}[/tex]then, opposite operation is division, divide both sides by PT
[tex]\begin{gathered} \frac{I}{PT}=\frac{PRT}{PT} \\ \frac{I}{PT}=R \\ R=\frac{I}{PT} \end{gathered}[/tex]I hope this helps you
How to find the domain of y=5√(2x-7) +10?
To find the domain for this function, we can see that the restriction we need to take into account is that the values in the radical must be values equal or greater than zero, so this function can have values in the Real set of numbers. Then, we have:
[tex]y=5\sqrt[]{2x-7}+10[/tex]We need to evaluate:
[tex]2x-7\ge0[/tex]Then, add 7 to both sides of the inequality, and then dividing the inequality by 2 (at both sides again) we have:
[tex]2x-7+7\ge0+7\Rightarrow2x+0\ge7\Rightarrow2x\ge7\Rightarrow\frac{2}{2}x\ge\frac{7}{2}_{}\Rightarrow x\ge\frac{7}{2}[/tex]We have that the values for the domain of this function are those for which are equal or greater than 7/2.
We can write the domain of this function in interval notation as follows:
[tex]D=\lbrack\frac{7}{2},\infty)[/tex]The important fact here is that for this function to have a domain and a range in the Real set, we need to have this restriction for this function.
The values of 5 and 10 are 'displacements' of a parent function and do not affect the values for this function to be in the Real Set of numbers.
For example, the value of 5 multiply the function, and the values for the range are greater (for x values) if the function was not multiplied by 5 ( and this does not affect, however, the values for the domain).
The value of 10 makes the function to be shifted 10 units above in the y-axis (and it does not affect the most important restriction found above). However, it does affect the values for the range in the function.
the winner in a recent Los Angeles marathon ran the 26-mile race in 2.23 hours. How many yards per minute did he run? Round to the nearest hundredth
Distance = 26 miles
Time = 2.23 hours
1 mile = 1760 yards
26 m = 26 x 1760 = 45760 yards
1 hours = 60 minutes
2.23 h = 2.23 x 60 = 133.8 minutes
Speed rate = distance / time
Replacing:
S = 45760 y / 133.8 m = 342 yards per minute
Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, orisometry dilation.A8DD
The length of sides of the original image ABCD is
AB = 4
BC = 4
CD = 4
DA = 4
The length of the sides of ABCD after the dilation is
A'B' = 2
B'C' = 2
C'D' = 2
D'A' = 2
As you can see, the lengths are reduced by one-half (1/2).
So, it is clearly a reduction.
Therefore, the correct answer is the 2nd option.
1/2, reduction
Find the volume of the solid who’s base is the region in the first quadrant bounded by y=x^3, y=1, and the y-acid and who’s cross sections perpendicular to the y axis are equilateral triangles
The given parameters are:
y=x^3, y=1
From the question,
I need to figure out how or where to find the standard deviation and mean for this problemGiven that z is a standard normal random variable, compute the following probabilities.a. P(z≤−1.0)b. P(z≥−1)c. P(z≥−1.5)d. P(−2.5≤z)e. P(−3
a.
P(z≤−1.0)
Using the z - score table, that gives the probabilities to the left side of the z score:
P ( z ≤−1.0) = 0.1587
b. P(z≥−1)
1 - P ( z ≤−1.0) = 1 - 0.1587 = 0.8413
c. P(z≥−1.5)
1 - P(z≤−1.5) = 1 -0.0668 = 0.9332
d. P(−2.5≤z)
P (z ≥ -2.5)
1 - P (z ≤-2.5) = 1 - 0.0062 = 0.9938
e. P(−3
P ( z≤0 ) = 0.5
P ( z ≤ -3 ) = 0.0013
P ( z ≤ 0 ) -P (z < -3) = 0.5 - 0.0013 = 0.4987
The function h(x) = 1/x-7 can be expressed in the form f(g(x)), where g(x) = x-7), and f(x) is defined as:f(x) =
Answer:
f(x) = 1 /x
Explanation:
We know that
[tex]h(x)=f(g(x))=\frac{1}{x-7}[/tex]and
[tex]g(x)=x-7[/tex]Now, what must be the form of f(x)?
Let us guess.
If we said
[tex]f(x)=\frac{1}{x}[/tex]then what would be f(g(x)) in this case?
To find out we simply replace x with g(x). This gives
[tex]f(g(x))=\frac{1}{g(x)}[/tex][tex]\Rightarrow f(g(x))=\frac{1}{x-7}[/tex]which is exactly the form we are told f(g(x)) take! This means our guess was correct and
[tex]\boxed{f(x)=\frac{1}{x}\text{.}}[/tex]A cylindrical can that is four inches tall and has a radius of 1.5 inches can hold 10¢
worth of soda. Assuming that the value of the contents is proportional to the size
(volume) of the can, what would be the value of the soda contained in a can that is 8
inches tall with a radius of 3 inches?
A. 40€
B. 90d
C. 20¢
E. None of these
D. 80¢
Find the 5 number summary for the data shownx2.72.97.27.58.511.215.418.3
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The minimum is the smallest number in the data : 2.7
The maximum is the largest number in the data : 18.3
Next, we find the median, which is the middle number in the data when arranged from smallest to largest. There are 8 numbers, so we will average the middle 2 numbers
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The middle is between the 4th and 5th numbers
( 7.5 + 8.5) / 2 = 16/2 = 8
The median(Q2) is 8
To find Q1 ( the 1st quartile), we take the numbers below the mean
2.7 ,2.9, 7.2, 7.5,
and find the median of these numbers
There are 4 numbers so the middle is between the 2nd and 3rd numbers
2.7 , 2.9, 7.2, 7.5,
(2.9+7.2) /2 =5.05
Q1 = 5.05
We will do the same process for Q3, which is the third quartile. We will use the numbers above the median
8.5, 11.2,15.4, 18.3
( 11.2 + 15.4) /2 =13.3
Q3 = 13.3
Expand the expression.3(x - 5)
solve for x
[tex]\begin{gathered} 3x=15 \\ \frac{3x}{3}=\frac{15}{3} \\ x=5 \end{gathered}[/tex]a sofa is on sale for $289, which is 32% less than the regular price what is the regular price
6149488990ay, this is the solution:
Let's use the Direct Rule of Three for answering this problem, this way:
Price Percentage
289 68
x 100
___________________
28,900 = 68x
68x/68 = 28,900/68
x = 425
The regular price of the sofa is $ 425, and you will save $ 136 if you buy it on sale.
If you don’t need any further explanation, I’ll go ahead and end our session. Feel free to let me know how I did by rating our session - all feedback is welcome and appreciated. Thanks for coming today!
Remember that the solutions from tutors are always available in your profile!
Identify the prime factorization for 75A 25x3B25x 3C 52x3
Given the number below;
[tex]75[/tex]We are asked to find the prime factorization of the number.
Step 1: Definition
"Prime Factorization" is finding which prime numbers multiply together to make the original number.
Step 2: We will use prime numbers to go through the given value until we can not divide further.
Since 75 is an odd number we will start with 3.
We can find above all the prime factors used to divide 75. Therefore;
[tex]75=3\times5\times5=3\times25^{}[/tex]Answer:
[tex]3\times25[/tex]Mr. Weinberg harvests apples from his apple tree each autumn. As the tree has matured since it's first crop, the weight in lbs, W, of the apple harvest has increased exponentially by 60% every 4 years according to the function W (t)=80(1.6)^ t/4, where the t is the number of years since the first crop.Based on this model, which is the best estimate for the percent change in the weight of the apple harvest from year to year?-26.5%-15.0%-40.0%-8.8%-12.5%
Answer:
12.5%
Explanation:
To know the percent of change from year to year, we will calculate the Weight for 2 consecutive years.
So, when t = 0, we get that W is equal to:
[tex]\begin{gathered} W_0=80(1.6)^{\text{ t/4}} \\ W_0=80(1.6)^{\text{ 0/4}} \\ W_0=80 \end{gathered}[/tex]Then, when t = 1, we get:
[tex]\begin{gathered} W_1=80(1.6)^{\text{ t/4}} \\ W_1=80(1.6)^{\text{ 1/4}} \\ W_1=89.97 \end{gathered}[/tex]Now, we can calculate the percentage of change as:
[tex]\frac{W_1-W_0}{W_0}\times100=\frac{89.97-80}{80}\times100=12.47\text{ \%}[/tex]Therefore, the best estimate is 12.5%
the ferris wheel is drawn on a coordinate plane so that the first car is located at the point ( 0, 80). what are the coordinates of the first car after a 270° counterclockwise about the originthe coordinate of the first car are........ after a rotation of 270° about the origin
We can draw the following picture:
That is, the coordinates are (80,0)
Use the following equation to solve for xf(x) = 2x-8f(6) =
The graph of Ax), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofFx)?600 = x2-5OTFC) = ?AO A. F(X) = 3(x - 2)2 - 2B. F(x) = -3(x - 2)2 - 2C. F(x) = -3(x+ 2)2 - 2D. F(x) = 3(x + 2)2 - 2
The correct answer is option C
Explanation
First observation; the graph f(x) is n- shaped, so the coefficient of x^2 must be negative. This means option A and option D cannot be the answer
We have to channel our focus to option B or C
From the graph f(x), when x = -1, f(-1) = -5
Test option B and option C by substituting x= -1 into f(x) and check which options gives -5 as the answer
Testing option c
f(-1) = -3(-1 + 2)^2 -2
=-3(1) -2
= -3 - 2
=-5
f(-1) = -5
Since f(-1) = -5, which gives a correct value as we have on the graph,
Then the answer is option C
Find the quadratic equation using the points given (-1,2), (0,1) and (-2,5).
The general equation for a quadratic equation is,
[tex]y=ax^2+bx+c[/tex]Substititute the values to obtain the equations for the coefficients.
[tex]\begin{gathered} 2=a(-1)^2+(-1)b+c \\ a-b+c=2 \end{gathered}[/tex][tex]\begin{gathered} 1=a(0)^2+b(0)+c \\ c=1 \end{gathered}[/tex]and
[tex]\begin{gathered} 5=a(-2)^2+b(-2)+c \\ 4a-2b+c=5 \end{gathered}[/tex]Substitute the value of c in the equation a-b+c=2 to obtain the equation for a and b.
[tex]\begin{gathered} a-b+1=2 \\ a=1+b \end{gathered}[/tex]Substitute the value of a and c in the equation 4a-2b+c=5 to obtain the value of b.
[tex]\begin{gathered} 4(1+b)-2b+1=5 \\ 4-2b+1=5 \\ 2b=0 \\ b=0 \end{gathered}[/tex]Substitute the value of b in the equation a=1+b to obtain the value of a.
[tex]\begin{gathered} a=1+0 \\ a=1 \end{gathered}[/tex]So quadratic equation for a=1, b=0 and c=1 is,
[tex]y=x^2+1[/tex]A line passes through the point (-1,-13) and has a slope of 6. An equation of the line is
Recall that the slope-intercept form of the equation of a line is:
[tex]y=mx+b,[/tex]where m is the slope of the line and b is the y-intercept.
To take the given equation to its slope-intercept form, first, we multiply it by x+1 and get:
[tex]\begin{gathered} y+13=6(x+1), \\ y+13=6x+6. \end{gathered}[/tex]Subtracting 13, we get:
[tex]\begin{gathered} y=6x+6-13, \\ y=6x-7. \end{gathered}[/tex]Answer:
[tex]y=6x-7.[/tex]