$297
Explanation:Amount taken for the trip = $900 US
Converting to Yen, amount = 80,514 Yen
Amount spent = 53,944 Yen
Amount remaining + Amount spent = Total amount for the trip
Amount remaining + 53944 = 80514
Amount remaining = 80514 - 53944
Amount remaining = 26570 Yen
We need to convert back to US dollars:
if 80,514 Yen = $900 US
let 26570 Yen = y
Cross multiply:
[tex]\begin{gathered} y(80514\text{ Yen) = \$900 (}26570\text{Yen)} \\ y\text{ = }\frac{\text{ \$}900\text{ }\times\text{ }26570}{80514} \end{gathered}[/tex][tex]y\text{ = \$297.00}[/tex]The remaining amount aftert the trip is $297 (nearest whole dollar)
how to solve (s + 5)(s - 5)
Here, we want to solve an expansion
To get this, we simply multiply the terms in the first bracket with the terms in the second, before we proceed to collect like terms
We have this as follows;
[tex]\begin{gathered} (s+5)(s-5)\text{ = s(s-5)+5(s-5)} \\ =s^2-5s+5s-25 \\ =s^2-25 \end{gathered}[/tex]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
4+4=? :))))))))))))))))))
Answer:
Step-by-step explanation:
8 :)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
:0
Rita can read 5 pages every minute and has already read 25 pages. Which is equation would match the scenario? *A. y = 25x + 5B. y - 25 = 5xC. y = 30xD. None of the aboveI would really appreciate the help as soon as possible.I will appreciate the help by marking you brainliest.
Given:
Number of pages Rita can read every minute = 5
Pages already read = 25 pages
To find the equation that represents this scenario, use the slope intercept form:
y = mx + b
Where, m is the rate of change.
m = 5
x represents the number of minutes
b represents the number of pages already read.
b = 25
Now, input values into the equation.
We have:
y = 5x + 25
From the choices given, let's rewrite the equation.
Subtract 25 from both sides:
y - 25 = 5x + 25 - 25
y - 25 = 5x
Therefore, the equation from the list that matches the scenario is:
y - 25 = 5x
ANSWER:
B. y - 25 = 5x
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]
Which of these groups of relative frequencies would be best represented by a pie chart
The data presented by a pie chart is best used when comparing significantly different groups of data.
The correct option would be the one in which all the relative frequencies are different, and they show a significant difference or variation between one another.
From the options provided, the group of relative frequencies that satisfies the problem is:
[tex]17\%,71\operatorname{\%},3\operatorname{\%},9\operatorname{\%}[/tex]OPTION A is correct.
[tex] - 15 \ \textless \ - 4x - 3[/tex]That's the Math problem
EXPLANATION
Given the inequality
-15 < -4x - 3
Adding +4x to both sides:
-15 + 4x < -4x + 4x -3
Adding +15 to both sides:
-15 + 15 + 4x < -3 + 15
Simplifying:
4x < -15 - 3
Adding like terms:
4x < -15 - 3
Dividing both sides by 4:
x < -18/4
Simplifying the fraction:
x < -4.5
The solution is x<-4.5
[tex] \frac{1}{6} (x + 12) = - 4[/tex]Can you please solve it
Problem
[tex] \frac{1}{6} (x + 12) = - 4[/tex]
Solution
For this case we have the following equation given:
[tex]\frac{1}{6}(x+12)=-4[/tex]We can multiply both sides by 6 and we got:
[tex]x+12=-24[/tex]Now we can subtract 12 in both sides and we got:
[tex]x=-24-12=-36[/tex]And the solution for this case would be x=-36
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
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.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]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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the measure of an interior angle of a regular polygon is given find the number of sides in the polygon
EXPLANATION.
1.Find the number of sides in the polygon with an interior angle of 160 degrees.
The exercise is as follows:
[tex]\begin{gathered} 160n=(n-2)\times180 \\ 160n=(180\times n)-(180\times2) \\ 160n=180n-360 \\ 160n-180n=-360 \\ -20n=-360 \\ n=\frac{-360}{-20} \\ n=18, \\ \text{the answer is 18 sides } \end{gathered}[/tex]Find the area of a square with sides 8 centimeters long.
Given:
length of side = 8 cm
Area of square is:
[tex]\begin{gathered} \text{Area}=\text{side}\times\text{side} \\ =8\times8 \\ =64\operatorname{cm} \end{gathered}[/tex]so area of square is 64.
The numbers trading cards owned by 10 middle-school students are given below.(NOTE THAT THESE ARE ALREADY ORDERED FROM LEAST TO GREATEST)Suppose that the number 355 from the list changes to 415. Answer the following.
Answer:
(a) It increases by 8
(b) It stays the same
Explanation:
First, we need to calculate the mean and median of the original data. This data is
335, 393, 425, 453, 489, 542, 556, 563, 623, 661
Then, the mean is the sum of all the values divided by the number of values, so
[tex]\begin{gathered} \text{ mean = }\frac{335+393+425+453+489+542+556+563+623+661}{10} \\ \\ \text{ mean = }\frac{5040}{10} \\ \\ \text{ mean=504} \end{gathered}[/tex]The median is the value that divides the set into two sets of equal sizes. In this case, these numbers are 489 and 542 because there are 4 numbers before 489 and 4 numbers after 542
335, 393, 425, 453, 489, 542, 556, 563, 623, 661
Then, the median is
[tex]\begin{gathered} \text{ median = }\frac{489+542}{2} \\ \\ \text{ median=}\frac{1031}{2} \\ \\ \text{ median=515.5} \end{gathered}[/tex]Now, we need to calculate the mean and median when 335 is changed to 415. So, the new data set is
393, 415, 425, 453, 489, 542, 556, 563, 623, 661
Then, the mean is
[tex]\begin{gathered} \text{ mean = }\frac{393+415+425+453+489+542+556+563+623+661}{10} \\ \\ \text{ mean =}\frac{5120}{10} \\ \\ \text{ mean = 512} \end{gathered}[/tex]And the median is 515.5 because the numbers in the middle are the 489 and 542
393, 415, 425, 453, 489, 542, 556, 563, 623, 661
Therefore, we can say that:
The mean increased by 8 because 512 - 504 = 8
The median stays the same
So, the answers are
(a) It increases by 8
(b) It stays the same
(300/m) + 44n m=15 n=4
Solve (300/m) + 44n where m = 15 and n = 4
[tex]\begin{gathered} (\frac{300}{m})+44n \\ \text{Substitute for the values of m and n, and you have;} \\ (\frac{300}{15})+44(4) \\ 20+176 \\ 196 \end{gathered}[/tex]The solution to the expression is 196
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]14 + 35=7(2+_) I don't understand it I need help please
The equation is given as
14 + 35 = 7 (2 + _)
We shall represent the dash as letter y (the unknown variable)
14 + 35 = 7 (2 + y)
49 = 7 (2 + y)
Divide both sides of the equation by 7 (to eliminate it from the right side of the equation)
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
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.
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.
I was given this graph:
The points on a graph are frequently used to represent the relationships between two or more objects.
The filled out table exists as follows:
Row 1 = 2, 4, 8
Row 2 = 6, 36, 216
What is meant by graph?A graph is a visual representation or diagram used in mathematics that displays data or values in an organized manner. The points on a graph are frequently used to represent the relationships between two or more objects.
In the first row we have x² = 4. Apply the square root to both sides to get x = 2. It appears your teacher is making x positive.
So we'll have 2 in the first box of row 1.
If x = 2, then x³ = 8 after cubing both sides.
In other words, x³ = 2³ = 2 × 2 × 2 = 8
The value 8 goes in the other box of row 1.
For row 2, we use x = 6 to square that to get x² = 6² = 6 × 6 = 36.
36 will go in the blank box for row 2.
The filled out table exists as follows:
Row 1 = 2, 4, 8
Row 2 = 6, 36, 216
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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
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.
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.
the solution set of which inequality is represented by the number line below
Let's solve the last inequality
[tex]-2x+5<-3[/tex]First, we subtract 5 from each side
[tex]\begin{gathered} -2x+5-5<-3-5 \\ -2x<-8 \end{gathered}[/tex]Then, we divide the inequality by -2
[tex]\begin{gathered} \frac{-2x}{-2}>-\frac{8}{-2} \\ x>4 \end{gathered}[/tex]The solution to this inequality is all the real numbers greater than 4.
[tex]\begin{gathered} 4x+6>22 \\ 4x>22-6 \\ x>\frac{16}{4} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 6x-7\leq17 \\ 6x\leq17+7 \\ x\leq\frac{24}{6} \\ x\leq4 \end{gathered}[/tex]7. Suppose Joanna gets a 10% raise, then a 5% raise. a. What is her raise in total as a percent? (hopefully by now you have learned the answer is not 15% bc percents are tricky) (tip: make up a salary if you need/want to)b. What would her second raise need to be to make the total raise 15%?
Let
x ----> original amount
Part A
1) 10% raise
that means
100%+10%=110%=110/100=1.1
so
1.1x ---> final amount
2) 5% raise
100%+5%=105%=105/100=1.05
so
1.05(1.1x)=1.155x
therefore
1.155=115.5% ------> 115.5-100=15.5%
the answer is 15.5%part B
we have
First, raise ------> 1.1x
second raise
1.1x(a)=1.15
a=1.15/1.1
a=23/22---------> a=1.04545
1.04545-1=0.04545
therefore
The second raise must be 4.545454...%round to two decimal places 4.55%Complete the squareto find the vertexof this parabola.2y +6y+8 x+1=0(121)
Given,
The equation of the parabola is y^2+6y+8x+1=0
Required:
The vertex of the parabola.
The equation of the parabola is taken as:
[tex]\begin{gathered} y^2+6y+8x+1=0 \\ y^2+6y+1=-8x \\ y^2+6y+9-9+1=-8x \\ (y+3)^2-9+1=-8x \\ (y+3)^2-8=-8x \\ (y+3)^2=8-8x \\ -8x=(y+3)^2-8 \\ x=\frac{-(y+3)^2}{8}+1 \end{gathered}[/tex]The standard form of the equation is,
[tex]x=a(y-k)^2+h[/tex]Here, h and k are the vertex of the parabola.
On comparing the standard form with given vertex form of the parabola.
[tex](h,k)=(1,-3)[/tex]Hence, the vertex of the parabola is (1, -3).
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
On the planet of Mercury, 4-year-olds average 2.9 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that the child spends less than 2.6 hours per day unsupervised. c. What percent of the children spend over 2.5 hours per day unsupervised. % (Round to 2 decimal places)d. 72% of all children spend at least how many hours per day unsupervised? hours.
Part a.
From the given infomation, the mean is equal to
[tex]\mu=2.9\text{ hours}[/tex]and the standard deviation
[tex]\sigma=1.4\text{ hours}[/tex]Then, the distribution of X is:
[tex]N(2.9,1.4)[/tex]Part b.
In this case, we need to find the following probability:
[tex]P(X<2.6)[/tex]So, in order to find this value, we need to convert the 2.6 hours into a z-value score by means of the z-score formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]Then, by substituting the given values into the formula, we get
[tex]\begin{gathered} z=\frac{2.6-2.9}{1.4} \\ z=-0.214285 \end{gathered}[/tex]Then, the probability we must find in the z-table is:
[tex]P(z<-0.214285)[/tex]which gives
[tex]P(z<-0.214285)=0.41516[/tex]Therefore, by rounding to 4 decimal places, the answer for part b is: 0.4152
Part c.
In this case, we need to find the following probability
[tex]P(X>2.5)[/tex]Then, by converting 2.5 to a z-value, we have
[tex]\begin{gathered} z=\frac{2.5-2.9}{1.4} \\ z=-0.285714 \end{gathered}[/tex]So, we need to find on the z-table:
[tex]P(z>-0.285714)[/tex]which gives
[tex]P(z\gt-0.285714)=0.61245[/tex]Then, by multiplying this probability by 100% and rounding to the nearest hundreadth,
the answer for part c is: 61.25 %
Part d.
In this case, we have the following information:
[tex]P(z>Z)=0.72[/tex]and we need to find Z. From the z-table, we get
[tex]Z=0.58284[/tex]Then, from the z-value formula, we have
[tex]-0.58284=\frac{X-2.9}{1.4}[/tex]and we need to isolate the amount of hours given by X. Then, by multiplying both sides by 1.4, we obtain
[tex]-0.815976=X-2.9[/tex]Then, X is given by
[tex]\begin{gathered} X=2.9-0.815976 \\ X=2.0840 \end{gathered}[/tex]So, by rounding to 4 decimal places, the answer is: 2.0840 hours.