If the model plane is built at a scale of 1 inch to 32 feet
let x be the actual length of the airplane
1/32 = 8/x
cross-multiply
x = 32 times 8
x = 256 inches
Seventh grade > Y.12 Area of compound figures with triangles MRGWhat is the area of this figure?3 mm4 mm8 mm2 mm5 mm6 mm3 mmWrite your answer using decimals, if necessary.square millimeters6 mm
Area of the figure = 72mm²
Explanation:Given:
An irregular figure
To find:
the area of the figure
To determine the area, we will divide the figure into shapes with known areas
We have 1 triangle, 1 rectangle, and 1 square. We will find the area of each of the shapes
Area of triangle = 1/2 × base × height
height = 3mm
base = 4 + 3 + 1 = 8mm
[tex]\begin{gathered} Area\text{ of the triangle = }\frac{1}{2}\times8\times3 \\ \\ Area\text{ of the traingle = 12 mm}^2 \end{gathered}[/tex]Area of rectangle = length × width
length = 8mm, width = 3mm
[tex]\begin{gathered} Area\text{ of the rectangle = 8 }\times\text{ 3} \\ \\ Area\text{ of the rectangle = 24 mm}^2 \end{gathered}[/tex]Area of square = length²
length = 6 mm
[tex]\begin{gathered} Area\text{ of the square = 6}^2 \\ \\ Area\text{ of the square = 36 mm}^2 \end{gathered}[/tex]Area of the figure = Area of triangle + Area of the rectangle + Area of the square
[tex]\begin{gathered} Area\text{ of the figure = 12 + 24 + 36} \\ \\ Area\text{ of the figure = 72 mm}^2 \end{gathered}[/tex]May I please get help with finding out weather each of them can be the HL congruence property
The hypotenuse-leg theorem states that two right right triangles are congruent if the hypotenuse and a leg of one triangle are congruent to the hypotenuse and a leg of the other triangle. Looking at the given options,
For a,
We only know that two legs are congruent. We can't confirm that the hypotenuses are congruent
For b,
two legs and two hypotenuses are congruent
For c, the triangles don't have hypotenuses because they are not right triangles.
For d, the hypotenuses of both triangles is the common line. This means that they are congruent. Two legs are also congruent.
Thus, the correct options are
b. Yes
d. Yes
When a tow truck is called, the cost of the service is $150 plus $5 per mile that the car must be towed.
Write and graph a linear equation to represent the total cost of the towing service, which is dependent on the number of miles the car is towed.
Find and interpret the slope and y-intercept of the linear equation
The linear equation to represent the total cost of the towing service is;
C = 150 + 5x.
What is defined as the term linear equation?A linear equation is one in which the variable's highest power is always 1. A one-degree equation is another name for it. A linear equation inside one variable has the standard form Ax + B = 0.For the given question,
The fixed cost of towing service = $150.
The variable cost per mile = $5.
Let the number of miles be 'x'.
The total cost be 'C'.
Thus, the equation becomes;
C = 150 + 5x.
C = 5x + 150 (linear equation to represent the total cost of the towing service)
Find the slope and y-intercept of the linear equation;
Comparing the equation with the slope intercept form of line;
y = mx + c
slope m = 5
y-intercept c = 150.
Thus, the linear equation to represent the total cost of the towing service is; C = 150 + 5x.
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Find the derivatives of the following using the different rules.1. y = 3x + 29
To find the derivative of the given function, we can use the power rule.
[tex]ax^n\Rightarrow nax^{n-1}[/tex]In this rule, we multiply the exponent of the variable by its numerical coefficient and then subtract 1 from the exponent.
For this function y = 3x + 29, we have two terms. These are 3x and 29. We need to apply the power rule for each term.
Let's start with 3x.
[tex]3x^1\Rightarrow1(3)(x^{1-1})\Rightarrow3x^0\Rightarrow3[/tex]The first derivative for 3x is 3.
For the term 29, since there is no variable, the derivative for 29 is 0.
So, the first derivative of y = 3x + 29 is y' = 3 + 0 or just y' = 3.
[tex]y^{\prime}=3[/tex]The length of an arc of a circle measures 0.3km. The radius of the circle measures 0.7km. What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π. Round your answer to the nearest tenth.
SOLUTION:
Step 1:
In this question, we are given the following:
The length of an arc of a circle measures 0.3km.
The radius of the circle measures 0.7km.
What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π.
Round your answer to the nearest tenth.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} \text{Length of an arc of a circle = 0. 3 }km \\ \text{Radius of the circle = 0. 7 }km \\ \text{Degr}ee\text{measure of the central angle of a circle = }\theta \\ \pi\text{ = 3. 14} \end{gathered}[/tex][tex]\begin{gathered} \text{Length of Arc , l = }\frac{\theta}{360^0\text{ }}\text{ x 2}\pi r \\ 0.\text{ 3 = }\frac{\theta}{360^0}\text{ x 2 x 3. 14 x 0.7} \end{gathered}[/tex][tex]\begin{gathered} 0.3\text{ = }\frac{\theta\text{ x 4.396}}{360^0} \\ \end{gathered}[/tex]cross-multiply, we have that:
[tex]\begin{gathered} 360\text{ x 0. 3 = 4.396}\theta \\ \text{Divide both sides by 4.396, we have that:} \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = }\frac{360\text{ X 0. 3}}{4.396} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta=\text{ }\frac{108}{4.396} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = 24.5677889} \\ \theta\approx24.6^{0\text{ }}(\text{ to the nearest tenth)} \end{gathered}[/tex]Factor the given polynomial completely and match your result to the correct answer below.18m³ +24m²-24mSelect one:O a. 6m(m-4)(3m + 1)O b. 6m(3m2 +6m-4)O c.6m(m+2)(3m-2)O d. The polynomial is prime.
Given:
[tex]18m^^3+24m^2-24m[/tex]Required:
We need to factorize the given polynomial completely.
Explanation:
Take out the common multiple 6m.
[tex]18m^3+24m^2-24m=6m(3m^2+4m-4)[/tex][tex]Use\text{ 4m=6m-2m.}[/tex][tex]18m^3+24m^2-24m=6m(3m^2+6m-2m-4)[/tex]Take out the common multiple.
[tex]18m^3+24m^2-24m=6m(3m(m+2)-2(m+2))[/tex][tex]18m^3+24m^2-24m=6m(m+2)(3m-2)[/tex]Final answer:
[tex]6m(m+2)(3m-2)[/tex]Which statements describe one of the transformations performed on f(x) = x²to create g(x) = 3(x+5)² -2? Choose all that apply.A. A vertical stretch with a scale factor of 3B. A translation of 2 units to the leftC. A translation of 5 units to the left□ D. A vertical stretch with a scale factor of eP
The transformations performed on the function f(x) to create g(x) include : a vertical stretch with a scale factor of 3 and a translation of 5 units to the left.
We are given a function f(x). The function f(x) is defined as x². We also have another function, g(x). The function g(x) is defined as g(x) = 3(x + 5)² - 2. The function g(x) is formed by performing several transformations on the function f(x). The first transformation is translating the function to the left by 5 units. The next transformation is stretching the function vertically by a scale factor of 3. The last transformation is translating the function downward by 2 units.
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Which inequality shows the relationship between the plotted points on the number line? O A. 3-4 O B.-4>3 O c. -4-3 O D. 3 >-4 SUBMIT
The numbers ploted in the number line are -4 and 3
The corresponding inequality will be the one that states a true statement between htese two numbers.
-4 is less than 3 → -4 < 3
You can also say that 3 is creater than -4 → 3 > -4
The correct option is d.
Select the correct choice below and fill in any answer boxes in your choice.
Answer;
[tex]x=40[/tex]Explanation;
To get the correct choice, we have to simplify the given equation as follows;
[tex]\begin{gathered} 4x-(2x+6)=3x-46 \\ 4x-2x-6=3x-46 \\ 2x-6=3x-46 \\ 3x-2x=46-6 \\ x\text{ = 40} \end{gathered}[/tex]So, the correct option is A and we fill the value 40 in the box
Can someone please help me with these, please? I’ve tried them myself already, but I got confused enough I didn’t end up with an answer
Given:
The cost for a day food, entertainment and hotes is $250.
The cost for round trip air fair is $198.
Explanation:
Let x represents the number of full days that individual can stay at the beach.
The total money available to individual is $1400. So inequality is,
[tex]\begin{gathered} 250\cdot x+198\leq1400 \\ 250x+198\leq1400 \end{gathered}[/tex]Thus inequality for number of days is,
[tex]250x+198\leq1400[/tex]The variable x represent the number of full days that individual can spend at beach trip.
(b)
Solve the inequality for x.
[tex]\begin{gathered} 250x+198-198\leq1400-198 \\ \frac{250x}{250}\leq\frac{1202}{250} \\ x\leq4.808 \end{gathered}[/tex]The maximum whole value of x is 4.
Thus individual can spend 4 complete (full) days at the beach trip.
What matrix results from the elementary row operations represented by
ANSWER:
[tex]-2R_2+3R_1=\begin{pmatrix}-12 & 20 & 8 \\ -8 & 1 & -3\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
We have the following matrix:
[tex]A=\begin{pmatrix}-3 & 5 & 2 \\ 8 & -1 & 3\end{pmatrix}[/tex]We apply the operation where R1 is the first row and R2 is the second row, therefore:
[tex]\begin{gathered} -2R_2=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-2\cdot8 & -2\cdot-1 & -2\cdot3\end{pmatrix}=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-16 & 2 & -6\end{pmatrix} \\ \\ 3R_1=\begin{pmatrix}3\cdot-3 & 3\cdot5 & 3\cdot2 \\ \:8 & -1 & 3\end{pmatrix}=\begin{pmatrix}-9 & 15 & 6 \\ \:8 & -1 & 3\end{pmatrix} \\ \\ -2R_2+3R_1=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-16 & 2 & -6\end{pmatrix}+\begin{pmatrix}-9 & 15 & 6 \\ \:8 & -1 & 3\end{pmatrix}=\begin{pmatrix}-3+-9 & 5+15 & 2+6 \\ -16+\:8 & 2+-1 & -6+3\end{pmatrix} \\ \\ -2R_2+3R_1=\begin{pmatrix}-12 & 20 & 8 \\ -8 & 1 & -3\end{pmatrix} \end{gathered}[/tex]can you help me with this question
Since B is the midpoint of AC, we can conclude:
[tex]\begin{gathered} AC=AB+BC \\ also \\ AB=BC \\ so\colon \\ 6x+1=2x+9 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 6x-2x=9-1 \\ 4x=8 \\ x=\frac{8}{4} \\ x=2 \end{gathered}[/tex]Working on how to plot the axis of symmetry and the vertex for the function:h(x)=(x-5)^2-7
A generic expression of a quadratic is
[tex]f(x)=ax^2+bx+c[/tex]We can write it using the vertex form, that is
[tex]f(x)=a(x-h)^2+k[/tex]The vertex form holds a lot of important properties because it shows us immediately where the vertex is, just by looking at the value of "h" and "k" of the formula, in fact, the vertex of the parabola is
[tex](h,k)[/tex]And the axis of symmetry of a parabola is the x-coordinate of the vertex, then, the axis of symmetry is
[tex]x=h[/tex]But how to identify h and k when we have the parabola in the vertex form? We have the following equation
[tex]h(x)=(x-5)^2-7[/tex]What's the value of the number that sums or subctract the quadratic term? In that case, it's -7, then it's the value of k
[tex]k=-7[/tex]Now to identify the "h" we must take care, it seems like h = -5 because the quadratic term is (x-5)² but we always change the signal of the number inside the quadratic term, if we have -5 inside it, the value of h is 5
[tex]h=5[/tex]Then, the vertex will be
[tex](h,k)=(5,-7)[/tex]The vertex is (5, -7) and the axis of symmetry will be the same value of h, then
[tex]\begin{gathered} x=h \\ \\ x=5 \end{gathered}[/tex]Symmetry and vertex
[tex]\begin{gathered} \text{ vertex: \lparen5, -7\rparen} \\ \\ \text{ axis of symmetry: x = 5} \end{gathered}[/tex]Now, to plot the graph precisely we must find the roots of the parabola, in other words, the value of x that makes h(x) equal to zero:
[tex]\begin{gathered} h(x)=0 \\ \\ (x-5)^2-7=0 \end{gathered}[/tex]Then, we want to solve:
[tex](x-5)^2-7=0[/tex]Put the quadratic term on one side
[tex]\begin{gathered} (x-5)^2=7 \\ \end{gathered}[/tex]Take the square root on both sides
[tex]\begin{gathered} \sqrt{(x-5)^2}=\sqrt{7} \\ \\ |x-5|=\sqrt{7} \end{gathered}[/tex]Be careful! when we do the square root of the quadratic term we must remember to put the modulus. Then we will solve this modular equation:
[tex]|x-5|=\sqrt{7}[/tex]Which is the same as solving to different equations:
[tex]|x-5|=\sqrt{7}\Rightarrow\begin{cases}x-5={\sqrt{7}} \\ x-5=-{\sqrt{7}}\end{cases}[/tex]Then the two solutions are
[tex]\begin{gathered} x=5+\sqrt{7}\approx7.65 \\ \\ x=5-\sqrt{7}\approx2.35 \end{gathered}[/tex]Then we can do the plot of the parabola with a good precision
Or using a graphing calculator
what is represented by 2 in the ordered pair (2,7)
In (2, 7), 2 is the input
Use this diagram to answer the questions
4b. 3
Part A
Which expression represents the area of the rectangle?
B. 6+ (40 - 3)
A6(4-3)
D. 2 x 6 x (40 - 3)
C
6+ (40 - 3) + 6 + (40 - 3)
Part B
Which expression is equivalent to the expression you chose in Part A?
B. 246 - 18
A
240-3
D859
C. 80+ 6
Find the area of the rectangle if = 4 Enter your answer in the box
square units
We will answer the question given in the picture.
We can see from the question a part of a linear function, and we can see an open circle at the point (4, -2). We can also see that the arrow of the linear function indicates that the function continues infinitely.
To find the domain and the range of the function we need to remember that:
• The domain of a function is, roughly speaking, all of the values for which the function is defined. In general, is represented by all of the values of x for which this function is defined.
,• The range of a function is, roughly speaking, all the values that the variable y, the dependent variable, takes for each of the values of the independent variable, x.
Therefore, if we check the graph, we have:
The domain of the function1. The values for x are not defined for x = 4 (we can see a small open circle at the point (4, -2). However, the values for x continue infinitely after that. Therefore, the domain of the part shown is as follows:
[tex]\text{ Domain=}x>4[/tex]And we can say that the domain of the function is for all of the values greater (not equal to x = 4) to positive infinity. We can write this in interval notation as follows:
[tex]\text{ Domain=}(4,\infty)[/tex]The range of the functionWe can check from the graph that the values for y start from y = -2. However, y = -2 is not included since we have a small open circle that indicates that (see above).
Therefore, the range of the function is given by:
[tex]y<-2[/tex]And we can say that the values of the range are less than y = -2 (not equal), and they are all smaller than y = -2 (for instance, -3, -4, -5.001, -10.222, and so on). The latter values are less than y = -2. We can write this in interval notation as follows:
[tex]\text{ Range=}(-2,-\infty)_[/tex]Therefore, in summary, we can say that:
1. The inequality to represent the domain of the part shown is x > 4. It means that the domain is those values of the independent variable greater than x = 4 (not equal to 4), and these values extend to positive infinity.
2. The inequality to represent the range of the part shown is y < -2. It means that the range is those values of the dependent variable less than y = -2 (not equal to y = -2), and these values extend to negative infinity.
how much simple interest can be earned in one year on $800 at 6%
The simple interest is defined as
[tex]I=P\cdot r\cdot t[/tex]Where P is the principal, r is the interest rate and t is times in years. Replacing all given information, and using 0.06 as 6%, we have
[tex]I=800\cdot0.06\cdot1=48[/tex]Therefore, the simple interest is $48.In ARST, the measure of ZT=90°, the measure of ZR=9°, and RS = 46 feet. Find thelength of ST to the nearest tenth of a foot.
Question:
Solution:
Since it is a right triangle, and the side opposite the angle is unknown, we can use the following trigonometric identity:
[tex]\sin (9^{\circ})=\text{ }\frac{x}{46}[/tex]solving for x, we get:
[tex]x\text{ = sin(9) x 46 = 7.19}\approx7.2[/tex]then the correct solution is:
[tex]x\text{ =}7.2[/tex]
Can you please explain how to differentiate an equation? specifically, how to get from this:h(t) = -16t^2 + 72t + 24 to this:h'(t) = -32t + 72I am a parent trying to help my child. looks vaguely familiar but it's been a long time, if you know what I mean! Thank you!
To differentiate an equation as given you can use the next:
Derivates of powers:
[tex]\begin{gathered} f(x)=x^n \\ f^{\prime}(x)=nx^{n-1} \\ \\ \\ f\mleft(x\mright)=x \\ f^{\prime}(x)=1 \\ \end{gathered}[/tex]Derivate of a constant:
[tex]\begin{gathered} f(x)=c \\ f^{\prime}(x)=0 \end{gathered}[/tex]You have in the given equation two powers (the fist two terms) and a constant (las term (24)):
[tex]\begin{gathered} h^{\prime}(t)=-2(16t)^{2-1}+72(1)+0 \\ \\ h^{\prime}(t)=-32t+72 \end{gathered}[/tex]the speed of a stream is 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream. what is the speed of the boat in still water?
The speed of the boat in still water is 10 mph.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the speed of a stream as 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream.
Assume the speed of the boat in still water be [x] mph.
We know that -
time [t] = distance[x]/speed[s]
Then, we can write -
6/(x - 4) = 14/(x + 4)
6(x + 4) = 14(x - 4)
6x + 24 = 14x - 56
56 + 24 = 8x
80 = 8x
x = 10 mph
Therefore, the speed of the boat in still water is 10 mph.
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2 3/5 •3= ?A 13/15B 1 2/13C 6 3/5D 7 4/5
Given:
[tex]2\frac{3}{5}\times3=?[/tex]First of all,we multiply 5 and 2 i.e.
[tex]\begin{gathered} 5\times2=10 \\ \end{gathered}[/tex]Then,add 3 to this value.
It becomes 10+3=13
Hence,
[tex]2\frac{3}{5}\times3=\frac{13}{5}\times3[/tex][tex]=\frac{39}{5}[/tex]Now, we convert the obtained value in mixed fraction.
First we divide 39 by 5 and then write the remainder in numerator and dividend in the side as shown.
[tex]\frac{39}{5}=7\frac{4}{5}[/tex]Here, when we divide we get 6 as divident and 4 as remainder, so we express it like this.
Hence, option (4) is correct.
Hi can you please help meThe cut off part:On the same grid, line k passes through
line j and k are perpendicular (option B)
Explanation:J passes through points (8, 2) and (-2, -2)
line K passes through (-4, 3) and (-6, 8)
We need to find the relationship betwen the lines by using the slope from both lines
slope formula is given by:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let's find slope of each line:
[tex]\begin{gathered} \text{for line J: }x_1=8,y_1=2,x_2=-2,y_2\text{ = -}2 \\ \text{slope = m = }\frac{-2-2}{-2-8} \\ \text{slope = }\frac{-4}{-10} \\ \text{slope = 2/5} \\ \\ \text{for line K: }x_1=-4,y_1=3,x_2=-6,y_2\text{ = 8} \\ \text{slope = m = }\frac{8-3}{-6-(-4)} \\ \text{slope = }\frac{5}{-6+4}\text{ = 5/-2} \\ \text{slope = }\frac{\text{-5}}{2} \end{gathered}[/tex]For two lines to be parallel, their slope will be the same:
Since the slopes are not the same, they are not parallel
For two lines to be perpendicular, the slope of one line will be negative reciprocal of the other line:
slope of one line = 2/5
reciprocal of the line = 5/2
negative reciprocal of the line = -5/2
We can see -5/2 is the slope of the other line.
As aresult, line j and k are perpendicular
fifty four percent of the items in a refrigerator are dairy products what percent of the items are non dairy products
Given :
54% of the items are dairy products.
If the ratio of AB to BC is 11:6, at what fraction of AC is point B located? Round to the nearesthundredth, if necessary.
For this case we know that the ratio of AB to BC is 11:6 and we can set up the following ratio:
[tex]\frac{AB}{AC}=\frac{11}{6}[/tex]And we want to identify what fraction of AC is point B located
We can assume that the lenght of AC is lower than AB
So then we can answer this problem with this operation:
[tex]\frac{6}{11}=0.545[/tex]And the answer for this case would be 0.545
tell me if the way I did it include commutative, associative, distributive or combined like terms in my problem
Explanation:
The commutative property said that:
a + b = b + a
The associative property said that:
a + b + c = (a + b) + c
So, in the first step, you apply commutative property when you reorganize the terms, and then, you apply associative property when you add the brackets
Finally, on the second step, you combined like terms because 6x, -x, and 2x are like terms.
I need help with this practice problem I need to know if I’m correct.
Let's draw a picture of our problem:
The trigonometric value function of the angle beta will have the same value of the trigonometric value function of theta. Then, in order to find the cosine of beta, we can use the following right triangle
Therefore,
[tex]\cos \beta=\cos \theta=\frac{-4}{\sqrt[]{61}}[/tex]or equivalently
[tex]\cos \beta=\frac{-4}{61}\sqrt[]{61}[/tex]Therefore, the answer is correct.
Instead, now suppose that P(x) = 5band b = 2. What is the weekly percent growth rate in thiscase? What does this mean in every-day language?
According to the given value of b, we can determine the growth rate by substracting 1 from the value of b, that is 2, and converting the result to a percent:
[tex]\begin{gathered} 2-1=1 \\ 1\cdot100=100\% \end{gathered}[/tex]It means that the weekly growth rate is 100%.
In every day language, it means that every week, the number of fish in the lake doubles the number of the last week.
A TV set is offered for sale for P1, 800 down payment, and P950 every month for thebalance for 2 years. If interest is to be computed at 6% compounded monthly, what isthe cash price equivalent of the TV set?
Answer:
The cash equivalent price of the tv set is P5849.37
Explanation:
The total amount paid monthly is:
The initial down payment of P1800 and 24 payments of P950 (2 years = 24 months)
Then, the price paid with interest is:
[tex]1800+24\cdot950=24600[/tex]
Now, the formula for the monthly compound interest is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]Where:
A is the amount after t years
P is the initial amount (what we want to find)
R is the rate of compound in decimal
t is the number of years of compounding
In this case:
• A = 24600 (the total paid if compounded)
,• P is what we want to find
,• r = 0.06 ( to convert percentage to decimal, we divide by 100: 6%/100 = 0.06)
,• t = 24 (2 years)
[tex]\begin{gathered} 24600=P(1+\frac{0.06}{12})^{12\cdot24} \\ . \\ 24600=P\cdot1.005^{288} \\ . \\ P=\frac{24600}{4.2056} \\ . \\ P=5849.373 \end{gathered}[/tex]To the nearest cent, the cash price is 5849.37
In the Itty Bitty High School, there are 85 students. There are 27 students whotake French, 51 who take Geometry and 38 who take History. There are 10 thattake Geometry and French, 7 that take History and French and 15 that takeGeometry and History. There are 2 students who take all 3 and 5 that take noneof these subjects.What it the probability that you randomly select a person who is a female giventhey are brown headed? *Fair ColorBrom Blonde Red87682SaleFemale34861271666Your answer
ANSWER:
2.2%
STEP-BY-STEP EXPLANATION:
The probability would be the quotient between the number of people with these characteristics (female, brown hair) and the total number of people
[tex]\begin{gathered} p(\text{female and brown) }=\frac{66}{548+876+82+612+716+66}=\frac{66}{1450}=0.022 \\ p(\text{female and brown) }=2.2\text{\%} \end{gathered}[/tex]After completing the fraction division 5 divided by 5/3, Miko used the multiplication shown to check her work. 3x5/3=3/1x5/3=15/3 or 5
Answer:
Miko found the correct quotient and checked her work using multiplication correctly
Explanation:
When we divided 5 by 5/3, we get:
[tex]5\div\frac{5}{3}=5\times\frac{3}{5}=\frac{5\times3}{5}=\frac{15}{5}=3[/tex]Therefore, the quotient is 3.
Then, to check the division, we need to multiply the quotient 3 by the divisor 5/3. If we get the dividend 5, the division was correct, so
[tex]3\times\frac{5}{3}=\frac{3}{1}\times\frac{5}{3}=\frac{15}{3}=5[/tex]Therefore, Miko found the correct quotient and checked her work using multiplication correctly.
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe^(−x^2/98), [−3, 14]
absolute minimum value?
absolute maximum value?
Absolute minimum value and maximum value at f(-3) = -2.7 and
f(14) = 12.14 respectively.
Define function.An association between a number of inputs and outputs is called a function. A function is, to put it simply, an association of inputs where each input is connected to exactly one output. For each function, there is a corresponding range, codomain, and domain.
Given function is -
f(x) = x*e^(−x^2/98)
By differentiating the function, we will get
f'(x) = (1)([tex]e^{-x^{2} /98}[/tex])+ x([tex]\frac{-2x}{98}[/tex] * [tex]e^{-x^{2} /98}[/tex])
f'(x) = ([tex]e^{-x^{2} /98}[/tex] ) - ([tex]\frac{x^{2} }{49}[/tex] * [tex]e^{-x^{2} /98}[/tex])
f'(x) = ([tex]e^{-x^{2} /98}[/tex]) (1 - [tex]\frac{x^{2} }{49}[/tex])
To calculate the maximum and minimum value, (1 - [tex]\frac{x^{2} }{49}[/tex]) must be zero or ([tex]e^{-x^{2} /98}[/tex]) must be zero.
=> (1 - [tex]\frac{x^{2} }{49}[/tex]) =0
=> [tex]\frac{x^{2} }{49}[/tex] = 1
=> [tex]x^{2}[/tex] = 49
=> x = 7 or x= -7
However, -7 is not within our given interval and does not need to be tested. Therefore, put the x = -3,7,14 in given function.
f(-3) = -3 [tex]e^{-9/98}[/tex] = -2.7
f(7) = 7 [tex]e^{-1/2}[/tex] = 4.24
f(14) = 14 [tex]e^{-1/7}[/tex] = 12.14
Absolute minimum value at f(-3) = -2.7 and
Absolute maximum value at f(14) = 12.14
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