In the diagram shown,\(PT=QT=QR\)

Also,\(RT=RS\) and \(\angle PTQ=36°\)

What is \(\angle PTS\)?

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Q:

In the diagram shown,\(PT=QT=QR\)

Also,\(RT=RS\) and \(\angle PTQ=36°\)

What is \(\angle PTS\)?

Q:

This is an observation tower out in Blowing Rock, NC that is 40 feet tall. If you climb to the top and view someone's campfire at an angle of depression of 3 degrees, how far from the base of the tower is the campfire?

Round your answer to the nearest foot.

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Let \((-4, 7)\) be a point on the terminal side of \(\theta\). Find the exact values of \(\sin(\theta)\), \(\csc(\theta)\), \(\cot(\theta)\).

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\(\mathrm{ABCD}\) is a quadrilateral.\(\mathrm{AB}=7\mathrm{cm}\), \(\mathrm{BC}=5\mathrm{cm}\), \(\mathrm{BC}=11\mathrm{cm}\), \(\mathrm{AD}=10\mathrm{cm}\), angle \(\mathrm{BAD}=130^{\circ}\). Work out the size of angle \(\mathrm{BCD}\).

Q:

In \(\triangle\mathrm{STU}\), the measure of \(\angle\mathrm{U}=90^{\circ},\) \(\mathrm{US}=5.9\) feet, and \(\mathrm{TU}=2.6\) feet. Find the measure of \(\angle\mathrm{T}\) to the nearest tenth of a degree.

Q:

Solve the following problems and show your solution.

1. The angle of elevation to the top of a flagpole is \(40^{\circ}\) from a point \(30\) m away from the base of the pole. How high is the flagpole to the nearest meter?

2. How high is the building whose horizontal shadow is \(60\) m when the angle of elevation of the sun is \(58^{\circ}12^{\prime}\)? Give the answer to the nearest hundredths.

Q:

If you place a \(38\)-foot ladder against the top of a \(32\)-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

Q:

In \(\triangle\mathrm{NOP}\), the measure of \(\angle\mathrm{P}=90^{\circ}\), \(\mathrm{PN}=1.1\), and \(\mathrm{NO}=3.3\) feet. Find the measure of \(\angle\mathrm{N}\) to the nearest degree.

Q:

4. You are standing on the Skydeck at Willis Tower in Chicago, 1353 feet high. You look to the southeast at an angle of depression of 10° and see Soldier Field. How far away from Willis Tower is Soldier Field? Sketch a diagram and show all work.

Q:

A sun casts a shadow of a \(50\)-foot building. If the angle of elevation to the sun is \(64^{\circ}\), how long is the shadow? Round to the nearest tenth.

\(24.4 \)feet

\(114.0\) feet

\(102.5\) feet

\(55.6\) feet

Q:

In the triangle \(\mathrm{ABC}\), \(\mathrm{C}=90\), \(\mathrm{AC}=3.2\mathrm{m}\) and \(\mathrm{BC}=4.8\mathrm{m}\). Find \(\mathrm{B}\).

Q:

In \(\triangle\mathrm{MNO}\), the measure of \(\angle\mathrm{O}=90^{\circ}\), \(\mathrm{ON}=35\), \(\mathrm{NM}=37\), and \(\mathrm{MO}=12\). What is the value of the tangent of \(\angle\mathrm{M}\) to the nearest hundredth?

Q:

When a coordinate grid is superimposed on a map of Lanesville, the middle school is located at \((15, 23)\) and the library is located at \((27, 9)\). If each unit represents \(1\) mile,, how many miles apart are the middle school and the library? Round your answer to the nearest tenth.

Q:

From the top of a building \(21\) m tall, the angle of depression to a car on the road below is \(70\) degrees. How far is the car from the base of the building? Sketch a diagram to help you...

a. \(61\) m

b. \(57.7\) m

c. \(7.6\) m

d. \(19.7\) m

Q:

The maximum slope of a wheelchair ramp is \(1:12\). For a wheelchair ramp made with these specifications, what angles does the ramp make with the ground? Round your answer to the nearest hundredth.

Q:

Find the mean, median, and mode of the following set of data:

43, 46, 47, 47, 51, 54, 59, 50

Q:

Becky Drinks her super coffee from Starbucks which contains 200mg on caffein. If the amount of caffein in a persons bloodstream decreases by 25% per hour, how much caffein will be in Becky's bloodstream after 7 hours? Round to the nearest whole number.

Q:

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between 520 and 554. What is the margin of error on the survey? Do not write on the margin of error.

Q:

Tristan has a box of toys. Four out of \(100\) toys are red, \(0.52\) of the toys are green, and \(0.1\) of the toys are blue. Write the color of toys in order from greatest to least.

Q:

The speed in miles per hour of each of Sam's last ten pitches were recorded as follows: \(\{82, 78, 83, 80, 75, 82, 79, 80, 83, 81\}\), Find the variance. Round your answer to the nearest hundredth.

Q:

Bao knows he scored inn the \(64\mathrm{th}\) percentile on a test, and that there were \(400\) people in total taking the test. How many people had a lower score than him?

Q:

\(3\), \(4\), \(4\), \(5\), \(5\), \(3\), \(2\), \(4\), \(6\), \(3\), \(6\), \(4\), \(2\)

State the mode.

Q:

Lily is a traffic engineer who is investigating the number of vehicles that travel on a certain point of expressway each day. She places a traffic counter in one direction of the expressway for 14 days. The number of vehicles counted each day are provided in the accompanying table.

Lily says that she can model the data for the number of vehicles per day to a normal distribution because the distribution is symmetric. Explain whether Lily's statement is correct, and if not, correct the statement she made.

Q:

Marlena has a bag of coins. The bag contains 8 quarters, 10 dimes, 4 nickels, and 2 pennies. She will randomly select a coin from the bag. What is the probability that Marlena will select a nickel?

A.\(\frac{1}{12}\) B.\(\frac{1}{3}\) C.\(\frac{1}{6}\) D.\(\frac{1}{5}\)

Q:

4) For lunch at school, you get 3 choices for the main food item, 2 choices of fruit, 2 choices for vegetable, and 3 choices for drink. Use the Fundamental Counting Principle to find how many . different possible outcomes (lunch combinations) you have to choose from. Show your work.

a) 1 lunch combination b) 18lunch combinations c) 36 lunch combinations

Q:

A carnival roulette wheel contains \(22\) slots numbered \(00\), \(0\), \(1\), \(2\), \(3\), ..., \(20\). \(10\) of the slots numbered \(1\) through \(20\) are colored red, and \(10\) are colored black. and \(10\) are colored black. The \(00\) and \(0\) slots are uncolored. The wheel is spun, and a ball is rolled around the rim until it falls into a slot. What is the probability that the ball falls into a black or red slot.

Q:

Event \(\mathrm{A}\) and \(\mathrm{B}\) are independent. Find the indicated Probability.

\(P(A)=0.44\)

\(P(B)=\fbox{\phantom{?????????}}\) (round answer to three decimal places)

\(P(A~\mathrm{and}~B)=0.16\)

Q:

A pizza shop has available toppings of anchovies, mushrooms, peppers, onions, olives, bacon, pepperoni and sausage. How many different ways can a pizza be made with \(4\) toppings.

Q:

Gwen has two boxes of accessories. One contains scarfs and the other contains gloves. The probability of her selecting a red scarf from the first box is 3/4 and the probability of her selecting a pair of golden gloves from the other box is 1/4. Gwen is getting ready to go out, what is the probability that Gwen selects a red scarf from the first box and a pair of golden gloves from the second box?

Q:

Two marbles are drawn randomly one after the other without replacement from a jar that contains \(7\) red marbles, \(8\) white marbles, and \(9\) yellow marbles. Find the probability of the following events.

(a) A red marbles is drawn first followed by a white marble.

(b) A white marble is drawn first followed by a white marble.

(c) A yellow marble is not drawn at all.

Q:

Are the sets equal?

\(\mathrm{A}=\{15, 16, 16, 17, 17, 17, 18, 18, 18, 18\}\)

\(\mathrm{B}=\{18, 17, 17, 15\}\)

Q:

In a survey of a group of people, it was found that \(60\%\) of the people liked apple, \(70\%\) liked orange and \(400\) people liked both of them. If \(10\%\) people liked non of them, then

(i) Represent the above information in a Venn-diagram

(ii) Find the total number of people in the survey

(iii) Find the number of people who like apple only.

Q:

Suppose we want to choose \(6\) objects, without replacement, from \(15\) distinct objects.

(a) How many ways can this be done, if the order of the choices does not matter?

(b) How many ways can this be done, if the order of the choices matters?

Q:

If \(f(x)=3x^2+1\) and \(g(x)=1-x\), what is the value of \((f-g)(2)\)

\(12\)

\(14\)

\(36\)

\(38\)

Q:

If \(f(x)=x^2-6x+2\) and \(g(x)=-2x\), find the following composition.

\((g\circ f)(-5)\)

Q:

The length of a rectangle is increasing at a rate of \(2\) ft/s, and its width is increasing at a rate of \(5\) ft/s. At what rate is the area of the rectangle increasing when the length is 5ft and the width is \(10\mathrm{ft}\).

Q:

Suppose Salma places \(\$9500\) in an account that pays \(16\%\) interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding.

(a) Find the amount in the account at the end of \(1\) year.

(b) Find the amount in the account at the end of \(2\) years.

Q:

In the figure below, \(\mathrm{m}\overline{\mathrm{AB}}=55^{\circ}\) and \(\mathrm{m}\overline{\mathrm{CD}}=59^{\circ}\). Find \(\mathrm{m}\angle\mathrm{CED}\).

Q:

If \(\mathrm{RT}=36\), find the value of \(x\).

Q:

In the diagram below,\(\overline{PR}\) and \(\overline{QS}\) intersect at \(T\) such that \(\overline{PQ} \left | \right |\overline{RS}\). If \(PQ=6,PT=8,TQ=7\), and \(RT=10\) then which of the following is the length of \(\overline{SR}\)?

Q:

In the diagram below, \(\overline{\mathrm{BE}}\cong\overline{\mathrm{EC}}\), \(\mathrm{m}\angle\mathrm{BEC}=54^{\circ}\) and \(\mathrm{m}\angle\mathrm{A}=40^{\circ}\). Find \(\mathrm{m}\angle\mathrm{AEB}\).

Q:

Find the sum of the following series, Round to the nearest hundredth if necessary.

4+12+36+...+234196

Sum of a finite geometric series:

\(S_n=\frac{a_1-a_1r^n}{1-r}\)

Q:

Calculate the area of a circle with a diameter of 10.8 centimeters.

Q:

Which of the following sets of lengths can represent the measures of the sides of a right triangle?

A. 4, 5, 6

B. 5, 12, 15

C. 8, 10, 17

D. 20, 21, 29

Q:

The circumference of a circle is 16π cm. What is the area, in square centimeters? Express your answer in terms of π.

Q:

Find an equation of the circle that has center (-6, 4) and passes through (-1, -2).

Q:

A rectangular athletic field is \(100\) yards wide and \(500\) yards long. How many square yards are there in the field?

Q:

What is the measure of each angle of a regular \(16\)-gon? If necessary, round to the nearest tenth.