Answer:
4% per annum
Step-by-step explanation:
Recall :
Simple interest = principal * rate * time
Given that :
Time = 3 ; simple interest = 84 ; principal = 700
84 = 700 * rate * 3
84 = 2100 * rate
Rate = 84 /2100
= 0.04
= 0.04 * 100% = 4% per annum
University of Florida researchers in the Department of Materials Science and Engineering have invented a technique that rapidly detects traces of TNT (Today, Spring 2005). The method, which involves shining a laser on a potentially contaminated object, provides instantaneous results and gives no false positives. In this application, a false positive would occur if the laser detected traces of TNT when, in fact, no TNT were actually present on the object. Let A be the event that the laser light detects traces of TNT. Let B be the event that the object contains no traces of TNT. The probability of a false positive is 0.
Required:
Write this probability in terms of A and B using symbols such as U, ∩ and |.
Answer:
P(A n B) = 0
Step-by-step explanation:
Given
[tex]A \to[/tex] Traces of TNT detected
[tex]B \to[/tex] No traces of TNT
Required
Probability of false positive
From the question, we understand that A and B must occur to get a positive and the result is 0.
The probability of A and B is represented as: P(A n B)
Include the result (0), we get:
P(A n B) = 0
If the pattern shown continues, how many black keys appear on a pipe organ with a total of 120 keys? Suggestion: use equivalent ratios or a rate table to rationalize your answer.
HURRYYYYY I NEEDDD HELP
in 12 key 5 black keys are appearing so consider x key will appear in 120 keys
120/x = 12/5
solving further,
x= 50
Answer - If the pattern shown continues, 50 black keys appear on a pipe organ with a total of 120 keys!
Find the equation (in terms of x ) of the line through the points (-3,4) and (1,-8)
Answer:
A(-3,4) B(1,-8)
y-y1/x-x1 =y2-y1/x2-x1
y-4/x--3 = -8-4/1--3
y-4/x+3 = -12/1+3
y-4/x+3 =-12/4
y-4/x+3 = -3
y-4 = -3(x+3)
y-4=-3x-9
y+3x +9-4=
y+3x+5=0
Answer:
y = -3x - 5
Step-by-step explanation:
-3, 4 and 1, -8
1 - -3 = 4
-8 - 4 = -12
[tex]\frac{-12}{4}[/tex] = [tex]\frac{-3}{1}[/tex] = -3
gradient/slope = -3
now substituting in the point -3, 4 to find the y intercept:
4= -3 x -3 + c
4 = 9 + c
-5 = c
y intercept = -5
equation is y = -3x - 5
Write the equation of the quadratic whose Vertex is at ( −4,−5) and passes through the point (−3, −7)
To Find :
The equation of the quadratic whose Vertex is at ( −4,−5) and passes through the point (−3, −7).
Solution :
A quadratic equation in vertex form is given by :
[tex]y = a(x-h)^2 + k[/tex]
( Here, h, k is the vertex )
y = a(x-(-4))² + (-5)
y = a(x+4)² - 5
Now, putting (-3,-7) in above equation:
-7 = a( -3 + 4 )² - 5
a(1)² = -2
a = -2
Therefore, the equation of the quadratic is y = -2(x+4)² - 5 .
Q.6.
Lisa wanted to paint her ugly brown flower box
red. Using the given dimensions, how many square
inches will she have to paint? (remove the top
base)
Answer:
10x22x8
Step-by-step explanation:
1760 is the answer
What is the range of y= sec-'(x)? PreCal, send help please!!
Given:
The function is:
[tex]y=\sec^{-1}(x)[/tex]
To find:
The range of the given function.
Solution:
We have,
[tex]y=\sec^{-1}(x)[/tex]
The range of secant inverse function is:
[tex]Range=\{y|0\leq y\leq \pi , y\neq \dfrac{\pi}{2}\}[/tex]
The range of the given function in interval notation is:
[tex]Range=\left[0,\dfrac{\pi}{2}\right)\text{ and }\left( \dfrac{\pi}{2}, \pi\right ][/tex]
Therefore, the correct option is C.
Omar, Amare, and Jack paid a total of $68.25 for dinner and tickets to a concert. The concert
tickets cost $9.75 each. If the 3 friends split the dinner bill equally, how much did each friend
spend on dinner?
Answer:
32.5
Step-by-step explanation:
I I divided ot then added it together
A physical fitness association is including the mile run in its high school fitness test. The time for this event is known to possess a normal distribution with a mean of seconds and a standard deviation of seconds. Find the probability that a randomly selected high school student can run the mile in less than seconds. Round to four decimal places.
Answer:
This probability is the p-value of Z given [tex]Z = \frac{X - \mu}{\sigma}[/tex], considering X as less than X seconds, [tex]\mu[/tex] as the mean and [tex]\sigma[/tex] as the standard deviation.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
Find the probability that a randomly selected high school student can run the mile in less than X seconds.
This probability is the p-value of Z given [tex]Z = \frac{X - \mu}{\sigma}[/tex], considering X as less than X seconds, [tex]\mu[/tex] as the mean and [tex]\sigma[/tex] as the standard deviation.
In the given figure, which angle is complementary to <4
Answer: The definition of a complementary angle is "Either of two angles whose sum is 90°." Thus the complementary angle for 4 is angle 5.
P.S. if you feel this answer is satisfactory I would appreciate it if you would mark it brainiest.
Find the length of side y.
y=_ft
Answer:
y = 5.66388 feet, (round that to whatever you need to round to)
Step-by-step explanation:
cos (51) = y/9
cos(51)*9=
y = 5.66388 feet
Find the mean of the following data set: 8.9, 7.2, 3.3, 2.5, 9.4, 3.9, 4.5, 5.4, 8.9
A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal places
Answer:
The test statistic is t = 3.36.
Step-by-step explanation:
You're testing the claim that the mean difference is greater than 0.7.
At the null hypothesis, we test if it is 0.7 or less, that is:
[tex]H_0: \mu \leq 0.7[/tex]
At the alternate hypothesis, we test if it is greater than 0.7, that is:
[tex]H_1: \mu > 0.7[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7[/tex]
Survey of 35 people. From the sample, the mean difference was 0.95, with a standard deviation of 0.44.
This means that [tex]n = 35, X = 0.95, s = 0.44[/tex]
Calculate the test statistic
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}[/tex]
[tex]t = 3.36[/tex]
The test statistic is t = 3.36.
Mr. Reid's storage bin is 4 feet long, 3 feet wide, and 7 feet tall. Can he fit 81 boxes that each has a volume of 1 cubic foot in his bin? Explain your answer
Answer:
Mr. Reid will be able to fit 81 boxes that each has a volume of 1 cubic foot in his bin, since it has a capacity of 84 cubic feet.
Step-by-step explanation:
Given that Mr. Reid's storage bin is 4 feet long, 3 feet wide, and 7 feet tall, to determine if he can fit 81 boxes that each has a volume of 1 cubic foot in his bin, the following calculation, knowing that the volume of a rectangular prism arises from multiplying its height by its width and its length:
4 x 3 x 7 = X
12 x 7 = X
84 = X
84 - (81 x 1) = X
84 - 81 = X
3 = X
Therefore, Mr. Reid will be able to fit 81 boxes that each has a volume of 1 cubic foot in his bin, since it has a capacity of 84 cubic feet.
What's the answer to this? I thought it was -138 apparently it's not? :(
The price of an item has been reduced by 70% the original price was $20 what is the price of the item now
PLS HELP ASAP!! need the answer
Answer:
60 degrees
Step-by-step explanation:
Alan deposited $300 in an account that pays 6% interest compounded continuously. Approximately how long will it take for Alan’s money to triple?
(Use formula A=Pe^rt where A is the accumulation amount, P is the initial amount, r is the annual rate of interest, and t is the elapsed time in years.)
Show your work for credit
9514 1404 393
Answer:
18.3 years
Step-by-step explanation:
You want ...
A/P = 3 = e^(rt) . . . for r = 0.06
Taking the natural log, this gives ...
ln(3) = 0.06t
t = ln(3)/0.06 ≈ 18.31
It will take about 18.3 years for the value to triple.
The expression 4x* represents 144
Answer:
x=36
Step-by-step explanation:
because 4x36=144
Answer:
4x = 144
4 • 36 = 144
The answer to the equation is 36
Six more than quotient of 12 and a number
What is the vertical shift of this sinusoidal function?
question is in pic pls help asap :)
Answer photo math download it
Step-by-step explanation:
has everythingPLEASE HELP
what's x
cos(x+pi)-sin(x-pi)=0
please show work
sin(x+pi)=-sin(x)=sin(-x)=cos(pi/2)
cos (x+pi)=-cos(x)
So according to the question:
cos(pi/2 +x)=cos(x)
Using the solution of cos, obtain:
(pi/2) + x = 2pi +- (x)
case#1: (pi/2) + x = 2pi + (x)
But here, the value of x is canceled, just
case#2: (pi/2) + x = 2pi - (x)
answer------------>>>>>>>>> x=pi-pi/4
Can someone help me please?
the answer is 0.62
62/100 = 0.62
Answer:
0.62
Step-by-step explanation:
the 62 is the number you're mainly working with and the 100 represents the place value! so the 100 means you need to place the top number in the hundredths place (0.62)
Hope this helps! Good luck with your math work!
Simplify using order of operations.
Answer:
64 ÷ 16 = 4
Step-by-step explanation:
Using PEMDAS, you first do the parenthesis, which equals 64. Then you do the exponents, which 4² equals 16. Then you divide 64 by 16, which equals 4.
What is the exact measurement of the line segment?
Hi plz help, if you can ill mark you 5 starz! :)
Answer:
12 kg, 1200 mm, 1200 ml (twice), 12 m, and 120 mm
Answer:
12,000 is 12
120 is 120
1.2 L is 1200
1200 is 120
0.12 is 12
Find the volume of the cone. Round your answer to the nearest hundredth.
Answer:
I believe the answer is 1.36
20 points!! A. 7 1/2 ft B. 9 ft C. 10 1/2 ft D. 12 ft.
Answer:
Area of a Parallelogram = Base x height
2½ can also be expressed as 5/2
So Bxh = 3 x 5/2
Area = 15/2
Or 7½ft²
Name the two solutions of (2x – 1)^2 = 25.
Answer:
3 & -2
Step-by-step explanation:
(2x – 1)^2 = 25
2x -1 = ±√25
2x -1 = ± 5
• 2x = 5+1
2x = 6
x = 3
• 2x = -5+1
2x = -4
x = -2
Answer:
Solution given:
(2x – 1)^2 = 25.
square root on both side
[tex]\sqrt{(2x-1)²}=\sqrt{25}[/tex]
2x-1=±5
Taking positive
2x-1=+5
2x=+5+1
x=6/2=3
Taking negative
2x-1=-5
2x=-5+1
x=-4/2
x=-2
The two Solution is x=-2 and x=3.
△JKL has vertices at J(−2, 4), K(1, 6), and L(4, 4). Determine whether △JKL is a right triangle
Answer:
Not a right triangle
Obtuse isosceles triangle.
Sides: J = 3.606 K = 6 L = 3.606
Step-by-step explanation:
hope helps you
have a nice day
Match each tool with how we used it in class
Answer:
1 - b
2 - a
3 - c
Step-by-step explanation: