The functions are:
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ g(x)=3x \end{gathered}[/tex]We need to evaluate f(x) in x=-2 and g(x) in x=2, so:
[tex]\begin{gathered} f(-2)=\frac{1}{(-2)}=-\frac{1}{2}=-0.5 \\ g(2)=3\cdot2=6 \end{gathered}[/tex]Find the approximate mean and standard deviation of the following data.
Given the data in the table, to find the approximate mean we would need to find the midpoints for the given intervals.
The midpoint was gotten from the average of the upper and lower class intervals.
We can then find the approximate mean using the formula below.
[tex]\bar{x}(Mean)=\frac{\sum^{}_{}fx}{\sum^{}_{}f}[/tex]
Therefore,
[tex]\begin{gathered} \bar{x}=\frac{(8\times3.5)+(11.5\times3)+(19.5\times9)+(27.5\times5)}{8+3+9+5} \\ \bar{x}=\frac{28+34.5+175.5+137.5}{25} \\ \bar{x}=\frac{375.5}{25} \\ \bar{x}=15.02 \end{gathered}[/tex]To find the standard deviation we would use the formula below;
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}f(x-\bar{x})^2}{\sum^{}_{}f} \\ ^{} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} \sigma^2=\frac{8(3.5-15.02)^2+3(11.5-15.02)^2+9(19.5-15.02)^2+5(27.5-15.02)^2}{25} \\ =\frac{1061.6832+37.1712+180.6336+778.752}{25} \\ \sigma^2=82.3296 \\ \sigma=\sqrt[]{82.3296} \\ \sigma=9.074 \end{gathered}[/tex]Answer:
Therefore, the approximate mean and standard deviation is 15.02 and 9.074 respectively
2/7:12/7 how to divide
In order to divide two fractions, we cross-multiply them:
This way,
[tex]\frac{2}{7}\div\frac{12}{7}\rightarrow\frac{2\cdot7}{7\cdot12}\rightarrow\frac{14}{84}\rightarrow\frac{2}{12}\rightarrow\frac{1}{6}[/tex]Therefore, we can conclude that
[tex]\frac{2}{7}\div\frac{12}{7}=\frac{1}{6}[/tex]Help me please and thank you I just need part a and d please
a. To complete the table, we have to assign the corresponding study hours per week to the hours worked per week.
For example, for the first interval 0≤h<4, the credits taken are 18 (according to the first table). When the credits taken are 18, the study hours per week are 39 (according to the second table). It means that for the interval 0≤h<4, the study hours per week is 39.
The values of this table will be, respectively:
39, 32, 24, 21, 17, 14, 12.
d. An student works between 12 and 16 hours every week, that allows him take 15 credits, which means that he has to use 21 hours to study. He wants to study 32 hours per week, that way, he can take 17 credits. To achieve it he needs to reduce its working hours to 4 to 8 hours per week, that way he would be able to take 17 credits and study 32 hours per week.
you are trying to upload a photo for your school picture,but you need to reduce the size of the photo by a quarter of its original size. Which is the correct power that will reduce the picture by a quarter?A: 2^2B: 2^4C: 2^-2D: 2^-4
the scale factor is 1/4, which is equivalent to:
[tex]\frac{1}{4}=\text{ }\frac{1}{2^2}=2^{-2}[/tex]ge bank offers a checking account without monthly fees of $538 and wrote a check for $325. how much should he transfer from his savings account to avoid paying a service fee on his cheeking account. express as an inequality.
I’m here to help you. Just give me a few mins to look over your question.
Step 01:
Checking account no monthly fees (minimum balance) = $300
Daniel's balance checking account = $538
Daniel's check = $325
transfer from savings account ===> ?
Step 02:
transfer from savings account ≥ Checking account minimum balance - (Daniel's balance - Daniel's check)
transfer from savings account ≥ $300 - ($538 - $325)
transfer from savings account ≥ $300 - $213
transfer from savings account ≥ $87
The answer is:
Daniel should transfer from his savings account at least $87.
option 2 you have 1 hour of homework at the start, then amount of homework duobles every week.
As per given by the question,
There are given that to the construct of equation to reperesent the number of hours of home work.
Now,
Here, y for the total hours and x for the total weeks.
The,
From option two;
In starting, you have 1 hours of homework, then after that amount of homework double in every week.
So,
Total hours of homework is 1,
Then , y is represent the 1 hour of homework.
Now,
The amount of home work double in every week,
So,
[tex]2y[/tex]Here, x represent the week.
So, homework double in every week.
Hence, the equation is;
[tex]x=2y[/tex]what word represents when the line intersects with the y-axis
Given:
what word represents when the line intersects with the y-axis?
The intersection between a line and the y-axis gives:
the point of the y-intercept
Please help with number 8Solve each equation by completing the square.simplify all irrational and complex situations
We're going to solve by completing the square the given equation:
5x²+14x=3 (divide both sides by 5)
x² +(14/5)x=3/
Find g′(4) given that f(4)=5, f′(4)=−1, and g(x)=(√x)*f(x).
Given that:
[tex]g(x)=\sqrt[]{x}f(x)[/tex]You need to find:
[tex]g^{\prime}(x)[/tex]In order to derivate the function, you need to apply the Product Rule
[tex]\frac{d}{dx}(u\cdot v)=u\cdot v^{\prime}+v\cdot u^{\prime}[/tex]Then, you get:
[tex]g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+f(x)(\sqrt[]{x})^{\prime}[/tex]Since:
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]You know that:
[tex]\frac{d}{dx}(\sqrt[]{x})=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt[]{x}}[/tex]Hence:
[tex]\begin{gathered} g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+f(x)(\frac{1}{2\sqrt[]{x}}) \\ \\ g^{\prime}(x)=\sqrt[]{x}\cdot f^{\prime}(x)+\frac{1}{2\sqrt[]{x}}f(x) \end{gathered}[/tex]Knowing that you need to find:
[tex]g^{\prime}(4)[/tex]You can rewrite the function as follows:
[tex]g^{\prime}(4)=\sqrt[]{4}\cdot f^{\prime}(4)+\frac{1}{2\sqrt[]{4}}f(4)[/tex]Knowing that:
[tex]\begin{gathered} f\mleft(4\mright)=5 \\ f^{\prime}\mleft(4\mright)=-1 \end{gathered}[/tex]You can substitute values:
[tex]g^{\prime}(4)=(\sqrt[]{4})(-1)+(\frac{1}{2\sqrt[]{4}})(5)[/tex]Evaluating, you get:
[tex]\begin{gathered} g^{\prime}(4)=(2)(-1)+(\frac{1}{2\cdot2})(5) \\ \\ g^{\prime}(4)=-\frac{3}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]g^{\prime}(4)=-\frac{3}{4}[/tex]
Find the missing dimension of the figure shown to the right round to the nearest tenth.
On the right triangle, we know the measure of the hypotenuse and one of its sides, then, using the pythagorean theorem, we get:
[tex]x=\sqrt[]{(29)^2-(14)^2}=\sqrt[]{841-196}=\sqrt[]{645}=25.4[/tex]therefore, the missing dimension is 25.4''
Perform the indicated operation. Write your solution in scientific notation: 0.00000936 0.00000003 a. 3.12 x 102 son b. 3.12 x 10-14 C. 3.12 x 1048 3 d. 3.12 x 104
1) To write a scientific notation number we must write a rational number followed by its power of 10.
2) So we can write:
[tex]undefined[/tex]Suppose that the dollar value v(t) of a certain car that is t years old is given by the following exponential function.v (t) = 19,900(0.91)^tFind the initial value of the car.Does the function represent growth or decay?By what percent does the value of the car change each year?
The general form of an exponential function is:
[tex]f(x)=ab^x[/tex]where a = initial value and b = the rate of growth.
In the given equation that we have,
[tex]v(t)=19,900(0.91)^t[/tex]we can see that the value of a = 19, 900. Hence, this is the initial value of the function and thus, the initial value of the car is 19, 900.
We can also see that the rate of growth is 0.91. Since the rate of growth is between 0 and 1, the function represents exponential decay.
The value of the car decreases by 9% each year.
please answer both i will give brainliest and thanks!!!! please quickly!!! hurry pleaseeee!!!
1.
The nth term is given by,
[tex]\begin{gathered} f(n)=f(n-1)+7 \\ f\mleft(1\mright)=2 \end{gathered}[/tex]The common difference can be calculated as,
[tex]\begin{gathered} f(1)=2 \\ f(2)=f(1)+7=9 \\ f(3)=f(2)+7=16 \\ d=\text{ 7} \end{gathered}[/tex]Therefore the tenth term can be calculated as,
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_{10}=a_1+7\times9=2+63=65 \end{gathered}[/tex]2.
SImilarly,
[tex]\begin{gathered} f(1)=30 \\ f(n)=2(fn-1)-50 \\ f(2)=2\times30-50=10 \\ f(3)=2\times10-50=-30 \\ d=-20 \end{gathered}[/tex]Thus, the tenth term is,
[tex]f(10)=30-20\times(9)=-150[/tex]Thus, the answer is -150.
10. Find f(-3) + 1 using the following equation f(x) = 5x – 4
We are to find the value of f(-3) + 1
using the following expression for f(x):
f(x) = 5 x - 4
Then f(-3) = 5 (-3) - 4 = -15 - 4 = - 19
since we need to add 1 to this result, we get:
f(-3) + 1 = -19 + 1 = - 18
What is the lateral surface area of the prism shown below? 9 m 6m 6 m 10 m
we are asked to find the surface area of a prism. To do that, we will find the areas of each lateral rectangle and the areas of the top and bottom triangles.
The areas of the rectangles are:
[tex]\begin{gathered} A_1=(10)(6)=60 \\ A_2=(10)(6)=60 \\ A_3=(10)(50)=50 \end{gathered}[/tex]To determine the ara of the top triangle we will use the following formula:
[tex]undefined[/tex]Evaluate the expression when b= 6 and x = -5. -b+ 2x
Given the below expression;
[tex]-b+2x[/tex]Evaluating the expression when b = 6 and x = -5, we'll have;
[tex]\begin{gathered} -(6)+2(-5) \\ -6-10 \\ -16 \end{gathered}[/tex]Therefore, when b = 6 and x = -5, the expression will be -16.
Find the equation of a line parallel to2y=2x+4 and passes through the point ( -5,-1)
Slope-Intercept Equation of the Line
Given a line, we can express it in the form:
y = mx + b
Where m is the slope and b is the y-intercept.
We are given the equation of a line:
2y = 2x + 4
Dividing by 2:
y = x + 2
Comparing with the generic equation in slope-intercept form, we can see that m = 1 and b=2.
Now we have to find the equation of a line that is parallel to that line and passing through the given point.
Parallel lines have the same value of the slope. Thus, the slope of our required line is m'=1
The equation of the line is so far:
y = x + b'
We need to find the value of b'. Here comes handy the use of the point (-5,-1). Substituting in the equation:
-1 = -5 + b'
Solving for b':
b' = -1 + 5 = 4
Now we have the complete equation of the line as required:
y = x + 4
I need further explanation on number 3 please enlighten me will give 5 stars if you give me a good explanation ⭐️⭐️⭐️⭐️⭐️
To evaluate an expression at a given value means that you substitute the given value anywhere you see the variable. For example, if the expression is:
[tex]x+1[/tex]and the problem asks you to evaluate the expression at x=9, then we substitute x=9 and get:
[tex]9+1=10.[/tex]Now, question number 3 asks us to evaluate
[tex](1.42+t)\times u+\frac{0.42}{v},[/tex]at t=13.5, u=7, and v=6. Therefore substituting the given values we get:
[tex]\begin{gathered} (1.42+13.5)\times7+\frac{0.42}{6}=(14.92)\times7+0.07 \\ =104.44+0.07=104.51. \end{gathered}[/tex]Answer: 104.51
What’s the mid point of AB in the picture below
From the given linear graph, we would write out the co-ordinates of the points A and B first in the form of (x,y).
Thus, we have:
[tex]\begin{gathered} A(-6,-4) \\ B(-3,3) \end{gathered}[/tex]The mid-point of a line segment;
[tex]\begin{gathered} A(x_1,y_1)\text{ and} \\ B(x_2,y_2) \end{gathered}[/tex]is given as:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Thus, we have:
[tex]\begin{gathered} (\frac{-6+(-3)}{2},\frac{-4+3}{2}) \\ (\frac{-6-3}{2},-\frac{1}{2}) \\ (\frac{-9}{2},-\frac{1}{2}) \\ (-4.5,-0.5) \end{gathered}[/tex]Hence, the midpoint of the line segment AB is: ( -4.5, -0.5)
Rewrite the following equation in slope intercept form3x + 17y = -4Write your answer using integers, proper fractions, and improper fractions in simplest form.
the given expression is,
3x + 17y = -4
17y = -4 - 3x
y = -3/17x - 4/17
thus, the answer is,
[tex]y=-\frac{3}{17}x-\frac{4}{17}[/tex]Santa bought a jacket that was marked 55% off the original price of $48. The sales tax was 6%. What did he pay altogether for the jacket? Find the discount price first and then find the tax. Round your answer to the nearest cent.
First we need to find the discount
48 * 55%
48 *.55
26.40
Subtract this from the price of the jacket
48-26.40
21.60
The sale price is 21.60
Now we need to find the sales tax
21.60 * 6%
21.60 * .06
1.296
Rounding to the nearest cent
1.30
Add the sales tax to the price of the jacket
21.60 +1.30
22.90
Santa will have to pay 22.90 for the jacket.
Please I need help finding the equation of the parallel line and the perpendicular line.
The equation parallel to the given equation and passing through the point (8, 3) is:
[tex]y\text{ = }\frac{5}{2}x\text{ - 17}[/tex]The equation perpendicular to the given equation and passing through the point (8, 3) is:
[tex]y\text{ = }\frac{-2}{5}x\text{ + }\frac{31}{5}[/tex]Explanations:The equation of the line parallel to the line y = mx + c and passing through the point (x₁, y₁) is given as:
[tex]y-y_1=m(x-x_1)[/tex]The equation of the line perpendicular to the line y = mx + c and passing through the point (x₁, y₁) is given as:
[tex]y-y_1\text{ = }\frac{-1}{m}(x-x_1)[/tex]Now, for the equation:
[tex]\begin{gathered} y\text{ = }\frac{5}{2}x\text{ - 7} \\ m\text{ = }\frac{5}{2} \end{gathered}[/tex]The line parallel to the equation and passing through the point (8, 3) will be:
[tex]\begin{gathered} y\text{ - 3 = }\frac{5}{2}(x\text{ - 8)} \\ y\text{ - 3 = }\frac{5}{2}x\text{ - 20} \\ y\text{ = }\frac{5}{2}x\text{ - 20 + 3} \\ y\text{ = }\frac{5}{2}x\text{ - 17} \end{gathered}[/tex]The line perpendicular to the given equation and passing through the point (8, 3) will be:
[tex]\begin{gathered} y\text{ - 3 = }\frac{-2}{5}(x\text{ - 8)} \\ y\text{ - 3 = }\frac{-2}{5}x\text{ + }\frac{16}{5} \\ y\text{ = }\frac{-2}{5}x\text{ + }\frac{16}{5}+3 \\ y\text{ = }\frac{-2}{5}x\text{ + }\frac{31}{5} \end{gathered}[/tex]In this diagram, ABAC – AEDF. If thearea of ABAC = 6 in2, what is thearea of AEDF?DAE 2 inB3 inс=Area = [? ] in2Enter a decimal rounded to the tenths.a
Area of ΔBAC = 6 in^2
EF = 2 in
BC = 3 in
Both triangles are similar, so:
Area ΔBAC : Area of ΔEDF = BC^2 : EF^2
Replacing:
6 / Area of ΔEDF = 3^2 / 2^2
Cross multiply
6 * 2^2 = 3^2 * Area of ΔEDF
24 = 9 * Area of ΔEDF
24/9 = Area of ΔEDF
Area of ΔEDF = 8/3 in^2 = 2.7 in^2
Multiplication Lattice Model) 1 bicycle costs $ 215. 1. Use the lattice model to multiply 2. How much will be paid for 87 bicycles 3. Upload the work
1. Multiply the number on the top of the box with the number to the right of the box. Write the answer in the box (write the product one digit on the top of the green line and the other digit under that line:
Example 2 x 8 = 16 write the 16 as in the image above
2. Add the numbers in the box diagonally and carry to the next column when necessary. Start from right to left
Then, 215 multiplied by 87 is 18705.
For 87 bicycles cost $18705Which expression can be used to find the price of a $400 telescope after a 32% markup? Select all that apply.A.400 • 0.32B.400 • 3.2C.400 • 1.32D.400 + 400(0.32)E.400 • 400(1.32)
We want to know an expression that let us find the price of a telescope of $400, after a 32% markup. We remember that briefly, the markup determines the percent of earning you will receive from selling a product.
On this case, for finding the cost, we will have to add the percent of earnings to the cost. Then we find the excedent given by the expression:
[tex]400(0.32)[/tex]And we add it to the original price:
[tex]400+400(0.32)[/tex]which is an expression to find the price after the markup.
Another option is to find the 100% + 32% of the original price, this is, multiply the original price by 1.32. We obtain that another expression for finding the price will be:
[tex]400\cdot1.32[/tex]Those two are the only options, ok?C and D, those are the ones I wrote.Yes, I am here.Do you see what I'm writing?Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours, what isthe speed of each?Step 2 of 2: Solve the equation found in Step 1.
To answer this question, we can state the problem as follows:
1. The two planes are 1180 miles apart.
2. They fly toward each other.
3. Their speed differs by 40 mph: that is one of the planes is faster than the other 40 mph, or the other plane is slower than the other plane.
4. The time they encounter each other is 2 hours.
Then, we need to remember the formula for a constant speed:
[tex]V=\frac{d}{t}[/tex]Where
• d is the distance
,• t is the time
Then, we have that the speeds for each of the planes are:
[tex]V_{p1}=V_{p2}+40[/tex]We also have that the sum of the distance for both planes is 1180 miles:
[tex]d_{p1}+d_{p2}=1180[/tex]And we have that:
[tex]V=\frac{d}{t}\Rightarrow d=V\cdot t[/tex][tex]d_{p1}=V_{p1}\cdot t[/tex][tex]d_{p2}=V_{p2}\cdot t[/tex]But
[tex]V_{p1}=V_{p2}+40[/tex]Then, we have that:
[tex]d_{p1}+d_{p2}=1180[/tex][tex]V_{p1}\cdot t+V_{p2}\cdot t=1180\Rightarrow V_{p1}=V_{p2}+40[/tex][tex](V_{p2}+40)\cdot t+V_{p2}\cdot t=1180[/tex]Since t = 2, we have:
[tex](V_{p2}+40)\cdot2+V_{p2}\cdot2=1180[/tex][tex]2V_{p2}+80+2V_{p2}=1180\Rightarrow4V_{p2}+80=1180[/tex]Subtracting 80 from both sides of the equation:
[tex]4V_{p2}+80-80=1180-80\Rightarrow4V_{p2}=1100[/tex]Dividing both sides of the equation by 4, we have:
[tex]V_{p2}=\frac{1100}{4}\Rightarrow V_{p2}=275\text{mph}[/tex]Since we know that:
[tex]V_{p1}=V_{p2}+40[/tex]Then, we have:
[tex]V_{p1}=275\text{mph}+40\text{mph}\Rightarrow V_{p1}=315\text{mph}[/tex]In summary, therefore, the speed of each plane is:
• Speed of Plane 1 = 315 mph
,• Speed of Plane 2 = 275 mph
Tyrone's car averages 26.2 miles per gallon in the city and 12.2 more miles per gallon on the highway. The gas tank holds 15 gallons and is 2/3 of the way full. With his current gas level, approximately how many miles can Tyrone drive on the highway?
First, we need to find the nubser of miles it can rive on high-way
From the question Tyron's car can drive 26.2 + 12.2 = 38.4 miles on the high way
Next, we find gallon of gas level that is currently on his car
His car can hold 15 gallons, but his current gas level is 2/3
So we will find 2/3 of 15 gallon which is equal;
2/3 x 15 = 30/3 = 10 gallons
Now, using proportion;
Let X be the number of miles he can drive with 10 gallons
38.4 miles = 1 gallon
X = 10 gallons
X = 38.4 x 10
X = 384 miles
Therefore he can drive 384 miles on highway
Which conic section is defined by the set of all points in a plane that areequidistant from a single point and a line?A. HyperbolaB. EllipseC. ParabolaD. Circle
Given:
The conic section that is defined by the set of all points in a plane that are equidistant from a single point and a line is a parabola since the parabola is equidistant from a fixed point that we call a focus and a fixed line that we call a directrix.
Therefore, the conic section is a PARABOLA.
Hence, option (C) is correct.
What is the product of 13/78 and 78/13?
Tell whether the rational number is a reasonable approximation of the square root.1.) 277/160, square root of 3
we know that
[tex]\begin{gathered} \sqrt{3}=1.73205 \\ \frac{277}{160}=1.73125 \end{gathered}[/tex]therefore
the rational number is a reasonable approximation of the square root