Answers
.. (27 in^2)*(8/12)^2 = 27*(4/9) in^2 = 12 in^2
Related Questions
Cesar is building a shelf at an angle so that it appears to be leaning against the wall. The shelf touches the wall 7 ft. above the floor and the distance between the floor from the wall to the front of the shelf is 1.5 ft. What is the angle the shelf makes with the floor?
A. 77.9 degrees.
B. 77.6 degrees.
C. 12.1 degrees.
D. 12.4 degrees.
A 15-ft. building casts a shadow of 12 ft. What is the approximate angle of inclination of the sun?
A. 51.3 degrees.
B. 53.1 degrees.
C. 36.9 degrees.
D. 19.2 degrees.
Answers
- The shelf touches the wall 7 feet above the floor.
-The distance between the floor from the wall to the front of the shelf is 1.5 feet
Then:
Tan^-1(α)=Opposite Leg/Adjacent leg
Opposite leg=7
Adjacent leg=1.5
When you substitute the values, you obtain:
Tan^-1(α)=7/1.5
α=77.9°
What is the angle the shelf makes with the floor?
The correct answer is: A) 77.9 degrees.
2) The problem says that the 15-feet building casts a shadow of 12 feet. Then:
Tan^-1(β)=Opposite Leg/Adjacent leg
Opposite leg=15
Adjacent leg=12
When you substitute, you obtain:
Tan^-1(β)=15/12
β=51.3°
What is the approximate angle of inclination of the sun?
The correct answer is: A) 51.3 degrees.
1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)
2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)
How to apply trigonometric relations to determine angles
1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]
[tex]\theta \approx 77.905^{\circ}[/tex]
The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]
2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]
[tex]\theta \approx 51.340^{\circ}[/tex]
The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]
To learn more on trigonometric relations, we kindly invite to check this verified question: https://brainly.com/question/6904750
Jermaine did this work to solve an equation. Did he make an error?
Answers
The solution for the below equation is required:
4x + 6 - x = 2x + 3
The work done by the Jermaine is presented below :
4x + 6 - x = 2x + 3
5x + 6 = 2x + 3
Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.
So, the correct option is
Jermaine did make an error. He should have combined 4x and -1x to make 3x
3x + 6 = 2x + 3
Hope it helps..!!
Answer:
Step-by-step explanation:
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th
The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.
Answers
the std deviation of the sample will be:
σ/√n
plugging the values we obtain:
15/√36
=15/6
=2.5
hence the z-score when x=264 will be:
z=(264-264)/2.5
z=0
thus:
P(x<264)=P(z<0)=0.5
the z-score when x=266 will be:
z=(266-264)/2.5
z=0.8
hence
P(x<266)=P(z<0.8)=0.7881
thus
P(264<x<266)=P(0.5<z<0.7881)
=0.7881-0.5
=0.2881
Answer: 0.2881
The probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is 0.2881. The percentage is 28.81%.
The correct probability that the mean pregnancy length of 36 randomly selected women falls between 264 days and 266 days is given by the cumulative distribution function (CDF) of the normal distribution with a mean of 264 days, a standard deviation of 15 days, and a sample size of 36.
To find this probability, we first need to determine the standard error of the mean (SEM), which is calculated by dividing the standard deviation by the square root of the sample size:
[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{36}} = \frac{15}{6} = 2.5 \][/tex]
To find the z-scores corresponding to the mean pregnancy lengths of 264 days and 266 days. The z-score for a value x is calculated by:
[tex]\[ z = \frac{x - \mu}{SEM} \][/tex]
For 264 days:
[tex]\[ z_{264} = \frac{264 - 264}{2.5} = 0 \][/tex]
For 266 days:
[tex]\[ z_{266} = \frac{266 - 264}{2.5} = \frac{2}{2.5} = 0.8 \][/tex]
Now, we look up these z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities.
The probability of a z-score less than 0 is 0.5, and the probability of a z-score less than 0.8 is approximately 0.7881.
The probability that the mean pregnancy length is between 264 days and 266 days is the difference between these two probabilities:
[tex]\[ P(264 < \bar{x} < 266) = P(z < 0.8) - P(z < 0) \] \[ P(264 < \bar{x} < 266) = 0.7881 - 0.5 \] \[ P(264 < \bar{x} < 266) = 0.2881 \][/tex]
Therefore, the probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is approximately 0.2881.
To express this as a percentage, we multiply by 100:
[tex]\[ 0.2881 \times 100 \approx 28.81\% \][/tex]
The answer is: 28.81%.
How do you write
2/4
as a percentage?
Answers
Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4
Answers
First we rewrite the quadratic equation:
4x2 - 7x - 3x - 24 = 0
4x2 - 10x - 24 = 0
The solutions to the quadratic equation in this case are:
x1 = 4
x2 = -1.5
Answer:
x = -3/2
x = 4
Answer: b. -3 or 2
Step-by-step explanation:
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
4x + 5 = 37
4x + 5 (-5) = 37 (-5)
4x = 32
4x/4 = 32/4
x = 8
It will take Bob ~8 seconds to reach 37 feet*
*Problem & answer
hope this helps
helpppppppppppppppppp
Answers
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
the trig unit circle
[tex]tan \frac{3π}{4} [/tex] = [tex] - tan \frac{π}{4} [/tex]
= -1
Remember,
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
= 1 ÷ -1
= -1
Then, when you substitute the values, you obtain:
Cot(3π/4)=-(√2/2)/(√2/2)
When you simplify the expression, you have the following result:
Cot(3π/4)=-1
What is the exact value of Cot(3π/4)?
The answer is: The exact value of Cot(3π/4) is -1
The graph of y=|x|y=∣x∣y, equals, vertical bar, x, vertical bar is reflected across the xxx-axis and then scaled vertically by a factor of \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. What is the equation of the new graph?
Answers
Justification:
The statement is confusing, so I will re-write it to avoid confusions:
"The graph of y=|x| is reflected across the x-axis and then scaled vertically by a factor of 1/4. What is the equation of the new graph? "
Answer
Solution:
1) Reflection acros the x-axis means (a,b) transforms into (a, -b). That is for the given x the reflected function will return the negative of the original value, that is:
y = - |x|
2) Scaling by a factor of 1/4 means that the new function is multiplied by 1/4
=> y = - (1/4) |x| which is the answer
Your teacher took a survey of student’s eye colors. She found that 15 students have brown eyes, 6 students have green eyes, and 4 students have blue eyes. Make a table showing the frequency
Answers
Green- 6
Blue- 4
15+6+4= 25
green: 6/25 = 6/25 * 4/4 = 24/100 = 24%
blue: 4/25 = 4/25 * 4/4 = 16/100 = 16%
Find two positive real numbers who's product is a maximum and whose sum is 156.
Answers
The sum of two numbers is 156, so we can write:
x+ y = 156
or
y = 156 - x
The product of two numbers = xy
Using the value of y in previous equation we can write:
Product = x(156 - x) = - x² + 156x
The above equation is a quadratic equation and results in a parabola. The maximum value of parabola with negative coefficient of x² lies at its vertex.
The x component of vertex will be = [tex] \frac{-b}{2a} [/tex]
Here b is the coefficient of x term, and a is the coefficient of x² term.
So,
a = -1
b = 156
Using the values in the formula we get the x component of vertex x = [tex] \frac{-156}{-2}=78 [/tex]
So x = 78
and
y = 156 - x = 156 - 78 = 78
Thus, the two numbers whose sum is 156 and which result in maximum product are 78, 78
Final answer:
To maximize the product of two numbers with a fixed sum of 156, we set up an equation for the product, differentiate, and find that the maximum product is obtained when both numbers are 78.
Explanation:
To find two positive real numbers whose product is a maximum and whose sum is 156, we need to use the concept of optimization in calculus. This involves taking the derivative of the function representing the product of the two numbers and setting it equal to zero to find the critical points. Since the sum of the numbers is fixed at 156, we can express one number in terms of the other, for example, x and 156 - x. The product of these two numbers is x(156 - x). To find the maximum product, we differentiate this function with respect to x:
[tex]\frac{d}{dx} [x(156 - x)] = 156 - 2x[/tex]
Setting this derivative equal to zero gives us 156 - 2x = 0, solving for x we find-
x = 78.
This gives us the two numbers as 78 and 78, because the sum must be 156 and the other number would be 156 - 78. To confirm that this gives a maximum, we would test the second derivative or use the first derivative test. However, by symmetry, when the sum of two numbers is fixed, their product is maximized when the two numbers are equal. In this case, both numbers are 78.
The length of a rectangle is 3 m less than double the width, and the area of the rectangle is 65 m2 . find the dimensions of the rectangle.
Answers
a cone is not a polyhedron. true or false?
Answers
Answer:
The answer is true
Step-by-step explanation:
we know that
A polyhedron is is a solid with flat faces and a cone is a solid with a curved side
therefore
A cone is not a polyhedron ( Is true)
What is the perimeter of this equilateral triangle?
Equilateral triangle with one side labeled 13 meters.
Answers
What is the sum of 36 ounces and 4 pounds? 6 lb. 6 lb., 4 oz. 96 oz. 98 oz.
Answers
Answer:
6 lb 4 oz
Step-by-step explanation:
Since, 1 lb = 16 oz,
Here, the given phrase,
The sum of 36 ounces and 4 pounds,
[tex]= 36\text{ oz}+4\text{ lb}[/tex]
[tex]=36\text{ oz}+64\text{ lb}[/tex]
[tex]=100\text{ oz}[/tex]
Again,
1 oz = 1/16 lb,
[tex]100\text{ oz}=\frac{100}{16}=6.25\text{ lb} = 6\text{ lb}+0.25\text{ lb}=6\text{ lb }4\text{ oz}[/tex]
Hence, The sum of 36 ounces and 4 pounds is 6 lb 4 oz
Second option is correct.
simplify:
...............
Answers
Exact form:
[tex] \sqrt{61 - 24}\sqrt{5} [/tex]
Decimal form:
2.70820393...
I hope this helps!
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Michaela uses measuring tape to measure a piece of paper. The measuring tape has an accuracy to the nearest centimeter. She uses her measurements to calculate the area of the piece of paper. Which of the answer choices show the degree of precision she can use to report the area?
Answers
Suria has x apples and oranges.how many apples and oranges does suria have altogether? Give your answer in terms of x
Answers
Answer:
It is given that Suria has x apples and Oranges.
Which means ,total number of fruits which includes apple and Orange is equal to x.
Suppose, number of Oranges Suria has = A
And, Number of Apples Possessed by Suria= B
→Number of Oranges +Number of Apple=x
→ A + B =x
So,total number of apples and Oranges does Suria have altogether = x
Which statement best describes the polynomial 2x + 8?
A. first degree polynomial with two terms
B. first degree polynomial with eight terms
C. second degree monomial
D. second degree binomial
Answers
Selection A is appropriate.
The heights (in inches) of 13 plants are 6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, and 17. What is the interquartile range of this data set? A) 3.5 B) 6 C) 10.5 D) 11
Answers
6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, 17.
The first step is to find Median in order to divide the above series into lower and upper quartiles.
To find the median, just cross out the first and the last value until you left with the single value, as the number of elements is odd.
Like first 6 would cancel the last 17,
second number 9 would cancel the second last number 16,
and so on.
By doing above exercise, we are left with 11.
So the median = 11.
Now any number below the median 11 would be in lower quartile series, while other half would be in upper one.
To find the lower quartile, find the median of 6, 9, 10, 10, 10, 11:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:
The two elements are: 10, 10.
Take average = (10 + 10) / 2 = 10
So lower quartile = 10
To find the upper quartile, find the median of 12, 12, 13, 14, 16, 17:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:
The two elements are: 13, 14.
Take average = (13 + 14) / 2 = 13.5
So Upper quartile = 13.5
The interquartile range = Upper Quartile - Lower Quartile = 13.5 - 10.0 = 3.5
So the correct option is (A) 3.5
-i
Let's first find the second quartile. This is also known as the Median. It is the middle value in your list of numbers. The middle number in your data is 11.
6, 9, 10, 10, 10, 11, (11 = Median), 12, 12, 13, 14, 16, 17
There are six numbers to the left of the middle number and six to the right. We have divided the data into two groups.
The first quartile is the middle number of the first group. Since there are 6 numbers there technically isn't a middle number, so we take the average of the two numbers closest to the middle. These are in parenthesis below:
6, 9, (10), (10), 11
Since the two number are the same (10) their average is also 10. The first quartile (denoted q1 = 10).
Now let's look at the numbers to the right of the median. Again there are 6 numbers here so none is technically in the middle but I have put in parenthesis the two closest to the middle.
12, 12, (13), (14), 16, 17.
The third quartile q3 is the average of 13 & 14. This is found by adding 13 + 14 and dividing the sum by 2. The third quartile is 13.5
Going back to our original list of data we have now split the data into four groups of 3 numbers each as follows:
6, 9, 10, (q1= 10), 10, 10, 11, (Median = 11), 12, 12, 13, (q3=13.5), 14, 16, 17
The interquartile range is the third quartile minus the first quartile. Here it is 13.5 - 10 = 3.5. It gives the range (the distance) between the first and third quartiles.
Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike. What is the measure of the angle of elevation of the ramp to the nearest degree?
Answers
Answer:
[tex]3^{\circ}[/tex]
Step-by-step explanation:
Let x represent the angle of elevation.
We have been given that Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike.
Upon looking at our attached file, we can see that 20 feet board and 1 foot board forms a right triangle with respect to ground, where side of 1 foot is opposite side and 20 feet side is hypotenuse.
We know that sine relates the opposite side of right triangle to its hypotenuse, so we can set an equation as:
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(x)=\frac{1}{20}[/tex]
Using arcsin we will get,
[tex]x=\text{sin}^{-1}(\frac{1}{20})[/tex]
[tex]x=2.865983982599^{\circ}[/tex]
Upon rounding our answer to nearest degree we will get,
[tex]x\approx 3^{\circ}[/tex]
Therefore, the measure of the angle of elevation of the ramp is 3 degrees.
The gum you like to is on sale. it is regularly priced at $1.59. Write and equation that will help determine how much you’ll save if you buy the pack today.
S=sale price
C=cost savings
Answers
The temperature of a liquid during an experiment can be modeled by the function f(x)=3.8cos(πx20)+2.2 , where f(x) is the temperature in °C and x is the number of minutes into the experiment.
What is the lowest temperature the liquid reached during the experiment?
Answers
the function is f(x)=3.8cos(πx20)+2.2
using a graph tool
see the attached figure
the answer is
the lowest temperature the liquid reached during the experiment is -1.6 °C
Emma, Steve, Maria, and George are comparing the solution of a math assignment problem below.
Select the student who correctly subtracted the rational expressions.
Answers
Answer:
A. Steve
Step-by-step explanation:
We are given the expression, [tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex].
So, upon simplifying the expression, we get,
[tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex]
implies [tex]\frac{1}{x-1}-\frac{3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{1(x+3)-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x+3-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x}{(x-1)(x+3)}[/tex]
So, from the options, we see that,
Steve has correctly subtracted the rational expressions.
Thus, option A is correct.
What is the area of this trapezoid? 44 in² 64 in² 168 in² 192 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 2 inches, F E is 14 inches, E C is 2 inches, A B is 14 inches., and E B is 12 inches.
Answers
we know that
[the area of the trapezoid]=[area rectangle]+2*[area triangle]
[the area of the trapezoid]=[14*12]+2*[12*2/2]=192 in²
the answer is 192 in²
Answer:
the answer is 192in
Step-by-step explanation:
A horse race has 14 entries and one person owns 5 of those horses. assuming that there are no ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of order)
Answers
entries------------ > 14 in total.
the owner has-----------> 5 horses.
if each horse has the same probability of winning, then the probability that the owner's horses will come in first, second, third, fourth and fifth will be as follows:
we have 5 spots.
the probability that one of those 5 horses will be first is 5/14
the probability that one of the remaining 4 horses will be second is 4/13.
the probability that one of the remaining 3 horses will be third is 3/12.
the probability that one of the remaining 2 horses will be fourth is 2/11.
the probability that the remaining horse will be fifth is 1/10.
the total probability is [5/14 * 4/13 *3/12 *2/11 *1/10]
(120/240240)=1/2002=0.0004995
the answer is 0.0004995
Final answer:
The probability that the five horses finish first through fifth in any order is 0.0004995 or 0.04995%.
Explanation:
The probability that the five horses owned by one person finish first through fifth, regardless of order, in a horse race with 14 entries can be calculated using combinatorics. First, we determine the number of ways to choose 5 horses out of 14 to finish in the top 5 positions, which is C(14,5). Then we calculate the number of favorable outcomes, which, since the order doesn't matter for the set of horses owned by the person, is just 1. To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes, resulting in 1/C(14,5). Using the formula for combinations C(n,r) = n! / (r! * (n-r)!), where n is the total number of entries and r is the number of horses owned by the person, we can calculate the exact probability.
The formula gives us C(14,5) = 14! / (5! * (14-5)!) = 14! / (5! * 9!) = 2002. Therefore, the probability is 1/2002, which simplifies to 0.0004995 or 0.04995%.
If the minute hand of a clock is 20 degrees behind the hour hand at this moment, then in 18 minutes, the minute hand will be how many degrees ahead of the hour hand?
Answers
Answer:
I got 79 degrees in my pocket, gonna solve this math problem, its just like a pick on a locket, no wonder your grades are gonna skyrocket.
Step-by-step explanation:
The number of degrees ahead of the hour hand will be 128 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
If the minute hand of a clock is 20 degrees behind the hour hand at this moment.
We know that the rotation of the minute hand in each minute is 6°.
The angle when minutes shows 18 minutes is given as,
⇒ 18 x 6°
⇒ 108°
The number of degrees ahead of the hour hand will be given as,
⇒ 108° + 20°
⇒ 128°
The number of degrees ahead of the hour hand will be 128 degrees.
More about the angled link is given below.
https://brainly.com/question/15767203
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You asked your classmates to name their favorite type of music. You found that 12 students like rock, 8 like rap, 6 like R&B, and 4 like jazz. Suppose you made a pie chart to display the data. How many degrees of the circle should represent rock music?
Answers
12+8+6+4=30
then we should divide the number 30 by 360(because the pie chart is 360 degrees):
[tex]360 \div 30 = 12[/tex]
now we should multiply 12(the number of students who likes rock) by 12
[tex]12 \times 12 = 144[/tex]
the answer is 144 degrees
PLEASE HELP!!!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x^2 + 2x +2
Answers
We are given this equation
[tex] y=-2x^{2} +2x+2 [/tex]
The vertex form is given by:
[tex] y=a(x-h)^{2} +k [/tex]
Now let us try to convert our equation into vertex form:
[tex] y=-2x^{2} +2x+2 [/tex]
Vertex form is given by:
[tex] y=-2(x-0.5)^{2} +2.5 [/tex]
comparing our equation with vertex form ,
The vertex (h,k) is (0.5, 2.5)
Next we have to find y when x=6, plugging x as 6 in the given equation,
[tex] y=-2(6)^{2} +2(6)+2 [/tex]
y=-58
So at x=6, y=-58.
Joseph wants to cover a rectangular box with wrapping paper. The length of the box is 2 feet, its width is 1 foot, and its height is 1 foot. The cost of wrapping paper is $0.80 per square foot. How much will it cost Joseph to cover the box with wrapping paper?
Answers
Let's find it with plugging it in.
2(2×1) + 2(2×1) + 2(1×1)
4+4+2=10
Now the surface area is 10 ft², let's just multiply .8 by that to find the price.
.8×10= 8
It'll cost $8 for Joseph to cover the box with wrapping paper.
Tell me if this helps!!
Kite QRST has sides RS, ST, TQ and QR. What are the diagonals of this figure? Select all that apply.