What is the measure of ZXYZ shown in the diagram below?S36°TХ114"ZO A. 78O B. 39OC. 36ОD. 75
Answers
In order to calculate the measure of angle XYZ, we can use the following property of secant lines to a circle:
[tex]\begin{gathered} XYZ=\frac{1}{2}(XZ-ST) \\ \text{XYZ}=\frac{1}{2}(114-36) \\ \text{XYZ}=\frac{1}{2}\cdot78 \\ \text{XYZ}=39\degree \end{gathered}[/tex]So the correct option is B.
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2.A group of students in MATH 105 start a walking program. The chart below shows eachmember's self-reported walking time in minutes during May 2022.X-300A-325B-550C-400D - 900E-150F-60G-600H - 250By what percent did X exceed or fall below the mean? it’s number 2
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Given: 300, 400, 60, 325, 900, 600, 550, 150, 250
1st we find the mean or avaerage of all the numbers.
Mean:
[tex]\frac{300+400+60+325+900+600+550+150+250}{9}=\frac{3525}{9}\approx392.778[/tex]From here we can see that X=300 falls below the mean.
So we can use this formula:
[tex]\frac{mean-actual\text{ }value}{mean}*100\%\Rightarrow\frac{392.778-300}{392.778}*100\%\approx23.688\%[/tex]Answer: X falls below the mean by 23.688%
Given that tan A= 5/12 and tan B= -4/3 such that A is an acute angle and B is an obtuse angle find the value of,a) tan (A-45°)b) tan (B+360°)
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Solve for tan(A-45°).
Recall that tan(45°) = 1
[tex]\begin{gathered} \tan (A-45\degree)=\frac{\tan A-\tan B}{1+\tan A\tan B} \\ \tan (A-45\degree)=\frac{\frac{5}{12}-1}{1+(\frac{5}{12})(1)} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{1+\frac{5}{12}} \\ \tan (A-45\degree)=\frac{-\frac{7}{12}}{\frac{17}{12}} \\ \tan (A-45\degree)=-\frac{7}{17} \end{gathered}[/tex]Therefore, tan(A-45°) = -7/17.
Solve for tan(B+360°)
Recall that tan(360°) = 0
[tex]\begin{gathered} \tan (B+360\degree)=\frac{\tan A+\tan B}{1-\tan A\tan B} \\ \tan (B+360\degree)=\frac{\frac{5}{12}+0}{1-(\frac{5}{12})(0)} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{1-\frac{5}{12}} \\ \tan (B+360\degree)=\frac{\frac{5}{12}}{\frac{7}{12}} \\ \tan (B+360\degree)=\frac{5}{7} \end{gathered}[/tex]Therefore, tan(B+360°) = 5/7.
What is the difference between a rectangle and a rhombus?
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A rhombus is a two-dimensional shape and is also characterized as a special parallelogram. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.
A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.
Rhombuses and Rectangles have the following differences:
1) A rhombus has four equal sides while in a rectangle, the opposite sides are equal.
2) The diagonals of a rhombus bisect each other at 90° while the diagonals of a rectangle bisect each other at different angles.
I have a calculus question about linear approximation. It is a doozie. High school, 12th grade senior AP Calculus. Math, not physics.
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To get the linear approximation, we follow the equation below:
[tex]y=f(a)+f^{\prime}(a)(x-a)[/tex]where "a" is the given value of x and f'(a) is the slope of the function at a given value of "a".
In the given equation, the given value of "a" or x is 5.
Let's now solve for the linear approximation. Here are the steps:
1. Solve for f(a) by replacing the x-variable in the given function with 5.
[tex]f(5)=5^5[/tex][tex]f(a)=3125[/tex]The value of f(a) is 3125.
2. Solve for the first derivative of f(x) using the power rule.
[tex]f(x)=x^5\Rightarrow f^{\prime}(x)=5x^4[/tex]The first derivative is equal to 5x⁴.
3. Replace the "x" variable in the first derivative with 5 and solve.
[tex]f^{\prime}(5)=5(5)^4[/tex][tex]f^{\prime}(5)=5(625)[/tex][tex]f^{\prime}(5)=3125[/tex]The value of the first derivative at x = 5 is also 3,125.
4. Using the linear approximation formula above, let's now replace f(a) with 3125 and f'(a) with 3125 as well since those are the calculated value in steps 1 and 3. Replace "a' with 5 too.
[tex]y=3125+3125(x-5)[/tex][tex]y=3125+3125(x-5)[/tex]5. Simplify the equation above.
[tex]y=3125+3125x-15625[/tex][tex]y=3125x-12500[/tex]Hence, the equation of the tangent line to f(x) at x = 5 is y = 3,125x - 12500 where the slope m is 3,125 and the y-intercept b is -12,500.
Now, to find our approximation for 4.7⁵, replace the "x" variable in the equation of the tangent line with 4.7 and solve.
[tex]y=3,125x-12,500[/tex][tex]y=3,125(4.7)-12,500[/tex][tex]y=14,687.5-12,500[/tex][tex]y=2187.5[/tex]
Using the approximated linear equation, the approximated value of 4.7^5 is 2, 187.5.
Need help. The ps5 cost 610 dollars And Be gets 100 dollars every week
Answers
Let x be the number of weeks after Mohammed started to save up. Since he receives $100 every week, then, after x weeks, he would receive 100x dollars.
Since he already had $50 at the beginning, then, the total amount of money y that he has saved after x weeks, is:
[tex]y=100x+50[/tex]Since the cost of the PS5 is $610, then, set y=610 and solve for x to find the number of weeks that he will need to save money:
[tex]\begin{gathered} y=610 \\ \Rightarrow610=100x+50 \\ \Rightarrow610-50=100x \\ \Rightarrow560=100x \\ \Rightarrow\frac{560}{100}=x \\ \Rightarrow x=5.6 \end{gathered}[/tex]He will need to save for at least 5.6 weeks. Nevertheless, he only receives money once a week and 5 weeks won't be enough for buying the PS5. Then, he needs to save for 6 weeks.
Study the data given,Below are the weights of 6 randomly selectedblack bears and 6 randomly selected grizzly bearsliving on a wildlife refuge.Which type of bear had morevariation in weight?Black Bear Weights (lbs): 102, 151, 248, 342,453, 498A. Black BearsMean: 299MAD: 132B. Grizzly BearsC. Both showed the same amount ofvariation in weightHaven't learned this yet.Grizzly Bear Weights (lbs): 294, 302, 347, 422,553, 596Mean: 419MAD: 104 2/3
Answers
The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.
Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.
If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.
Construct a truth table of the following statement. Jack will not play or Chris is hurtUse the symbolic representationp: Jack will playr: Chris is hurt
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ANSWER and EXPLANATION
We want to construct a truth table for the following statement:
Jack will not play or Chris is hurt
where p: Jack will play; r: Chris is hurt
"Jack will not play" will be represented by -p.
This implies that "Jack will not play or Chris is hurt" will be represented by - p v r.
Let us now construct the truth table:
That is the truth table for the statement.
find the following numbers
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We have the numbers 5, 11, 8, 8 7, 4, 10, 9, 7, 7, 6 and we have to calculate its mean.
To calculate the mean of a group of numbers we have to sum them all and then divide by the number of items we have added.
In this case we have 11 elements, so the mean can be calculated as:
[tex]M=\frac{5+11+8+8+7+4+10+9+7+7+6}{11}=\frac{82}{11}\approx7.45[/tex]The mean of this group of numbers is 7.45 periodic.
Find the percent of change and classify as a percent increase or decrease. Round to the nearest tenth of a percent when necessary. A $39 watch is now on clearance for $17.50.
Answers
The percent of increase or decrease = change/original x 100%
Since the original price of the watch is $39
Since its price now is $17.50, then
The change of the price = 39 - 17.50 = 21.50 dollars
The percentage of decrease = 21.50/39 x 100%
The percentage of decrease = 55.1282
Round it to the nearest tenth
The percentage of decrease is 55.1%
2. Two baseball players were up to bat. Consider the parabolic paths of their two hits, represented in thegraph at right. One hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet.The other hit covers a horizontal distance of 6 feet, but only reaches a maximum height of 9 feet.
Answers
Explanation:
The equation of parabola can be founded using the following equation:
[tex]y=a(x-h)^2+k[/tex]Where the point (h, k) is the vertex. So, if the hit covers a horizontal distance of 4 feet and reaches a maximum height of 20 feet, we can say that the vertex will be located at (2, 20) because the maximum height of 20 ft is reached when the horizontal distance is half of the maximum horizontal distance 4 ft.
So, the equation for the first hit is:
[tex]undefined[/tex]The engine in a airplane has a power curve approximated by x2 270 y = + 14 15000 44 where I is the RPin and y is the horsepower generated. - At what RPM is the engine putting out maximum horsepower?. Round your answer to three decimal places. RPM What is the maximum horsepower? Round your answer to three decimal places.
Answers
A)For this question, we will use the first and second derivative criteria. First, we compute the first and second derivative of the given function:
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{2x}{15000}+\frac{27}{44} \\ \frac{d^{2}y}{dx^{2}}=-\frac{2}{15000} \end{gathered}[/tex]Setting the first derivative equal to zero and solving for x we get:
[tex]\begin{gathered} -\frac{2x}{15000}+\frac{27}{44}=0 \\ \frac{2x}{15000}=\frac{27}{44} \\ x=\frac{27(15000)}{44(2)}=4602.273 \end{gathered}[/tex]Evaluating the first second derivative at x=4602.273 we get a negative number, therefore the function has a maximum value at x=4602.273. At 4602.273 RPM the engine puts out its maximum horsepower.
B) Now, to compute the maximum horsepower we evaluate the given function at x=4602.273:
[tex]\begin{gathered} y=-\frac{(4602.273)^{2}}{15000}+\frac{27}{44}(4602.273)-14 \\ y=1398.061 \end{gathered}[/tex]Therefore, the maximum horsepower is 1398.061.
Match the appropriate graph to each equation. t(x)= 1/x+3t(x) = -1/x +3
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The graph of the function is attached below.
[tex]t(x)=\frac{1}{x+3}[/tex]This matches with the 3rd graph.
Part B
The graph of the function is attached below
[tex]t(x)=-\frac{1}{x}+3[/tex]This matches with the 2nd graph.
Over 12 hours, the water in Julia's pool drained a total of 534.72 liters. It drained the same number of liters each hour. Write an equation to represent the change in the number of liters of water in Julia's pool each hour.
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Answer:
the pool lost 44.56 liters per hour
Step-by-step explanation:
Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)
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We have the following equation to solve
[tex]E=I\cdot Z[/tex]Where E, I, and Z are complex numbers, therefore let's put it in numbers
[tex]E=(4+4i)(7+3i)[/tex]We can solve it directly into the rectangular form by doing the distrutive
Then
[tex](4+4i)(7+3i)=28+12i+28i+12i^2[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} (4+4\imaginaryI)(7+3\imaginaryI)=28+12i+28i-12 \\ \\ (4+4\imaginaryI)(7+3\imaginaryI)=16+40i \end{gathered}[/tex]Now we have completely solved the problem!
[tex]E=16+40i[/tex]______________________
The second solution (usual)
When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form
[tex]\begin{gathered} I=4+4i=4\sqrt{2}\angle45° \\ \\ Z=7+3i=\sqrt{58}\angle23.2° \end{gathered}[/tex]Now to do the multiplication we multiple the magnitude and sum the phases (angles)
[tex]\begin{gathered} ZI=4\sqrt{2}\cdot\sqrt{58}\angle45°+23.2° \\ \\ ZI=4\sqrt{116}\operatorname{\angle}68.2° \end{gathered}[/tex]We already have the result, now just put it in the rectangular form
[tex]\begin{gathered} ZI=4\sqrt{116}\cdot\cos(68.2)+i4\sqrt{116}\sin(68.2) \\ \\ E=16+40i \end{gathered}[/tex]The school that Imani goes to is selling tickets to a spring musical. On the first day of ticketsales the school sold 6 senior citizen tickets and 8 child tickets for a total of $122. The schooltook in $167 on the second day by selling 9 senior citizen tickets and 8 child tickets. WriteaSOE and solve it to find the price of a senior citizen ticket and the price of a child ticket
Answers
Define the system of equations to solve the problem
Take x as the price of a senior citizen ticket and y as the price of a child ticket
[tex]\begin{gathered} 6x+8y=122 \\ 9x+8y=167 \end{gathered}[/tex]Solve the system
[tex]\begin{gathered} 6x+8y=122 \\ 8y=122-6x \\ 9x+8y=167 \\ 8y=167-9x \end{gathered}[/tex][tex]\begin{gathered} 122-6x=167-9x \\ 9x-6x=167-122 \\ 3x=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex][tex]\begin{gathered} 8y=122-6x \\ y=\frac{122-6x}{8} \\ y=\frac{122-6\cdot15}{8} \\ y=\frac{122-90}{8} \\ y=\frac{32}{8} \\ y=4 \end{gathered}[/tex]The price of a senior citizen ticket is $15 and for child is $4
Solve for y:2x – 3y = 5
Answers
y = (2x-5)/3
Explanation:
[tex]\begin{gathered} 2x\text{ - 3y = 5} \\ To\text{ solve for y, we need to make y the subject of formula} \end{gathered}[/tex][tex]\begin{gathered} \text{Let's take every other thing not attached to y to the right side of the equation:} \\ -3y\text{ = 5 - 2x} \\ To\text{ make y stand alone, we will divide through by -3} \\ \frac{-3y}{-3}=\text{ }\frac{5-2x}{-3} \\ y\text{ = }\frac{-(5-2x)}{3}\text{ or }\frac{-5\text{ +2x}}{3}\text{ } \\ y\text{ = }\frac{2x\text{ -5}}{3} \end{gathered}[/tex]Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.45≥4x+5 and 53>4x+5
Answers
Expression given:
[tex]45\ge4x+5[/tex][tex]53>4x+5[/tex]Procedure:
• Solving for ,x ,in first inequality
[tex]-4x\ge-45+5[/tex][tex]-4x\ge-40[/tex][tex]x\le\frac{-40}{-4}[/tex][tex]x\le10[/tex]• Solving for ,x ,in second inequality
[tex]-4x>-53+5[/tex][tex]x<\frac{-48}{-4}[/tex][tex]x<12[/tex]Thus, the graph would be:
If the solution is for both inequalities, then the answer is in which both are included:
[tex]x\le10[/tex]-14x > -3 all I have to do is simplify it
Answers
The first step in simplifying the inequality is to divide both sides by -14:
[tex]\frac{1}{-14}\times-14x>-3\times\frac{1}{-14}[/tex]Since we are dividing both sides by a negative number, the inequality reverses direction, and hence it becomes
[tex]\textcolor{#FF7968}{x<\frac{3}{14}}\text{\textcolor{#FF7968}{.}}[/tex]This is the farthest we can go in simplifying the inequality; therefore, the above inequality is our answer
A door to playhouse is 50 inches tall.Which of the following is another measure eaqual to the height?A.4 ft 2 in.B.4 ft 1 in.C.4 ft 1/2 in.D.5 ft
Answers
Dereo, this is the solution:
All we need to do is to convert inches to feet, as follows:
Let's recall that:
12 inches = 1 feet
In consequence,
50 inches = 50/12 feet
50 inches = 4 feet + 2 inches
The correct answer is A.
Which statement describes a key feature of the function g if g(x) =f(x)-7
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The graph of the function f(x)=e^x is given.
To determine the function g(x),
g(x)=f(x)-7.
Then the graph of function g(x) is
Then from the graph above , the horizontal asymptote is y=-7.
Hence the correct option is D.
pls help with this. just the answer
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Answer:
Step-by-step explanation:
“y” should be the first step of the system.
this composed figure is made up of three similar shapes what is the area of the figure
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Given data:
The given figure is shown.
The area of the composite figure is,
[tex]\begin{gathered} A=(10\text{ cm)}\times(5\text{ cm)+}(3\text{ cm)(6 cm)+}\frac{1}{2}(3\text{ cm)(4 cm)} \\ =50cm^2+18cm^2+6cm^2 \\ =74cm^2 \end{gathered}[/tex]Thus, the area of the composite figure is 74 square-cm.
please help due in 5 minutes would mean a lot
Answers
Answer:
150 degrees
Explanation:
Given: m∠8=150 degrees
Angles 8 and 5 are vertically opposite angles.
Vertical angles are equal, therefore:
[tex]\begin{gathered} m\angle5=m\angle8 \\ m\angle5=150\degree \end{gathered}[/tex]Next, angles 1 and 5 are corresponding angles.
Corresponding angles are equal, therefore:
[tex]\begin{gathered} m\angle1=m\angle5 \\ m\angle1=150\degree \end{gathered}[/tex]The measure of angle 1 is 150 degrees.
I don't understandDescribe in words and by using function notation
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f(x) = 2(x +3)^2 + 1
1. Scale f(x) by 1/2 ==> (1/2) f(x) = (x + 3)^2 + 1
2. Reflect f(x) through x axis ==> -(x+3)^2 + 1
3. Shirt f(x) to the right by 5 units ==> -(x + 3)^2 - 4
4. Shift f(x) down by 5 units ==> -(x - 2) - 4 = g(x)
Consider the following functions.Step 3 of 4: Find (f g)(-1). Simplify your answer.Answerf(x) = x² + 6 and g(x) = -x +5(-2)-1)=
Answers
Solving for (f•g)(-1)
[tex]\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+6)\cdot(-x+5) \\ (f\operatorname{\cdot}g)(-1)=((-1)^2+6)\operatorname{\cdot}(-(-1)+5) \\ (f\operatorname{\cdot}g)(-1)=(1+6)\cdot(1+5) \\ (f\operatorname{\cdot}g)(-1)=7\cdot6 \\ \\ \text{Therefore, }(f\operatorname{\cdot}g)(-1)=42 \end{gathered}[/tex]Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow menure recipe helps produce more or less energy. Me collected random samples of menure and benenes from the farm, prepared 15 bottles each of both matures, and placed oballeen on top of each bottle. Alter two weeks, he measured the circumference of each balloon in centimeters: the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below. Which description most accurately summarizes the sample results? 10. 11. 13. 13. 14. 15. 15. 15. 18. 18. 19 20. 22. 25. 26 22.22.26 29 30 31 36. 36 38. 39. 43 46. 46. 49. 50 MORE CONSISTENT LESS S OUT THE Autor behind ONE CON nece MORE
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Notice the smaller range and values of the experiment with cow manure (smaller box diagram and also located at smaller values of total energy.
The banana mixture clearly generates a wider box diagram (so less consistent) and also located at higher values (to the right).
Therefore, the answer we choose is the last one (bottom right) that says that the cow manure data is more consistent than the other one, and also, since the mashed banana data is so much higher, combined with the previous will clearly give larger amounts of biogas.
Please select the bottom right option.
Determine whether the ordered pair is a solution of linear equation.Y = x - 1/2, ( -5, -2 ) A- yes it is a solution B- no it is not a solution
Answers
The ordered pair is (- 5, - 2)
This means that when x = - 5, y = - 2
To determine if the ordered pair is a solution of the linear equation, We would substitute the values into the equation. If we substitute x = - 5 into the equation and y gives us - 2, then it is a solution.
Therefore,
y = - 5 - 1/2 = - 5 - 0.5
y = - 5.5
Since it is not - 2, then the answer is B
B- no it is not a solution
ed pai
please help me please please please please please please please please please please please please please please
Answers
EXPLANATION
The Area of a square shape is:
Area= side*side = s^2
If we have that:
Area = 121 yd^2, then:
121=s^2
Isolating s:
[tex]s=\sqrt[]{121}=11\text{ ---> The answer is 11}[/tex]Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5
Answers
For the first equation:
y = (x + 5)(x + 1)
apply distribution property:
y = (x + 5)(x) + (x + 5)(1)
y = x·x + 5·x + x·1 + 5·1
y = x² + 5x + x + 5
y = x² + 6x + 5
For the second equation:
y = (x + 3)² - 4
use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:
y = x² + 2·x·3 + 3² - 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
The third equation is already in the convenient form.
Then, you can notice that all three equations are the same equations.
In 2018 the scores of students on the May SAT had a normal distribution with mean u = 1450 and a standard deviation of o = 120.a. What is the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?b. If a sample of 50 students is taken from the population, what is the probability that the sample mean score of these students is 1470 or higher?
Answers
From the question,
[tex]\begin{gathered} \mu\text{ = 1450, } \\ \sigma\text{ = 120} \end{gathered}[/tex]a. We are to find the probability that a single student randomly chosen from all those taking the test scores 1500 or higher?
we will do this using
[tex]\begin{gathered} P(x<\text{ z) such that } \\ z\text{ = }\frac{x\text{ -}\mu}{\sigma} \end{gathered}[/tex]From the question, x = 1500.
Therefore
[tex]\begin{gathered} z\text{ =}\frac{1500\text{ - 1450}}{120} \\ z\text{ = }\frac{50}{120} \\ z\text{ = 0.417} \end{gathered}[/tex]applying z - test
[tex]\begin{gathered} P(xThus, the probability that a single student is randomly chosen from all those taking the test scores 1500 or higher is approximately 34%b. From the question
[tex]\begin{gathered} n\text{ = 50, }^{}\text{ }\mu\text{ = 1450} \\ \bar{x}\text{ = 1470},\text{ }\sigma\text{ = 120} \end{gathered}[/tex]we will be using
[tex]\begin{gathered} z\text{ = }\frac{\bar{x}\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ \end{gathered}[/tex]inserting values
[tex]\begin{gathered} z\text{ = }\frac{1470\text{ - 1450}}{\frac{120}{\sqrt[]{50}}} \\ z\text{ = }20\text{ }\times\frac{\sqrt[]{50}}{120} \\ z\text{ = }\frac{\sqrt[]{50}}{6} \\ z\text{ = 1.18} \end{gathered}[/tex]Applying z-test
[tex]\begin{gathered} P(xHence,
The probability that the sample mean score of these students is 1470 or higher is approximately 12%