A circle has an area of 169 π in2. Which of the following is the circumference of the circle in terms of pi ( )?
13 π in
26 π in
7.5 π in
20 π in
Correct Answer : B
We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then
Substituting 169π in place of area
Dividing both sides by pi and taking square root on both sides yields
The radius of the circle from the given area is 13 in. and the circumference of the circle is given by the relation:
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Related Questions
Correct Answer is D
Explanation
To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then
Width of the rectangle= w
Length of rectangle=(w+5)
Area of the rectangle, A= Length*width=(w+5)*w
A=w(w+5)
Thus, the area of the rectangular room is w(w+5).
Correct Answer is B
Explanation
We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then
Substituting 169π in place of area
Dividing both sides by pi and taking square root on both sides yields
The radius of the circle from the given area is 13 in. and the circumference of the circle is given by the relation:
Correct Answer is D
Explanation
We use the given slope to find the minimum length of the ramp. In this case, slope is the ratio of height to length of the lamp. Thus,
If we let x be the minimum length of the ramp. Then,
Substituting the value of slope into the above equation results in,
Solve for value of x by cross-products
X = 18 Feet
Thus, the minimum length of the ramp needed to provide access to a door that is 1.5 high is 18 feet.
Correct Answer is D
Explanation
We are asked to find the number of cups of flour that will be used to make 90 cookies.
First, we convert 2 ¼ into improper fraction as:
Letting x to be the number of cups of flour, we set up a proportion equation with number of cookies on numerator and number of cups of flour on the denominator becomes:
Solve the value of x by cross-products
Dividing both sides by 60, the above equation result to
Thus, the number of cups of flour needed to make 90 cookies is 81/16 cups, which is equal to 5 1/16 cups.
Correct Answer is A
Explanation
Given the equation A(f)=92+2f
To find the value of A(f), we need to manipulate the value of f. In this case, f is the independent variable while A(f) is the dependent variable.
Correct Answer is B
Explanation
To find the circumference of a circular garden, we can use the formula:
C=π×d
Where:
- C = Circumference
- π = 3.14 (as given)
- d = Diameter
Step 1: Substitute the given values into the formula
The diameter d is 14 metres, so:
C=3.14×14
Step 2: Perform the multiplication
C=43.96 metres
Final Answer:
The circumference of the garden is 43.96 metres.
The correct answer is B. 43.96 metres.
Correct Answer is A
Explanation
Let the unknown length of the x. The resulting triangle is shown below.
We use the Pythagoras theorem as follows to find the unknown value of x as:
Thus, the value of unknown side of the triangle is 21.8 feet.
Correct Answer is A
Explanation
We are tasked to find the stock price on Thursday from the given information. Here, we need to find the stock of each day from the price increase or decrease. If the price increases, we add to the previous day’s price and subtract if the price decreases.
Monday’s stock price=$65.50
Tuesday’s stock price is Monday’s plus $1.50=65.50+1.50=$67.00
Wednesday’s stock price went down by $2.57 from Tuesday’s=67.00-2.57=$64.43
Thursday’s stock price went up by $2.25 from Wednesday’s =64.43+2.25=$66.68
From the above evaluation, the stock price on Thursday was $66.68
Correct Answer is B
Explanation
The percentage change in weight is found in three steps below:
Absolute change in weight=final weight-initial weight
Absolute change in weight=(left|120-153 ight|=left|-33 ight|=33)
Relative change in weight=(frac{absolute change}{initial weight}=frac{33}{153}=0.216)
Percent change=relative change * 100%
Percent change=0.216*100%=21.6%
The percent change in weight lost is 21.6 %, which is about 22%.
Correct Answer is B
Explanation
P-At=-kr
Subtract P on both sides
P-P-At=-kr-P
-At=-kr-P
Divide both sides by -t
-At/-t=(-kr-P)/-t
A=(kr+P)/t
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