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.
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]
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a cone is not a polyhedron. true or false?
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)
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?
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.
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.
Answer:
the answer is 192in
Step-by-step explanation:
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?
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?
helpppppppppppppppppp
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
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.
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
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)
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%.
A real estate broker sold your house for $72,000. The broker's commission was 6% of the selling price. How much would you get for the house after the commission is paid? A. $70,800 B. $76,320 C. $67,680 D. $73,200
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
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.
Suria has x apples and oranges.how many apples and oranges does suria have altogether? Give your answer in terms of x
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
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?
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.
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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?
Emma, Steve, Maria, and George are comparing the solution of a math assignment problem below.
Select the student who correctly subtracted the rational expressions.
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.
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?
What is the perimeter of this equilateral triangle?
Equilateral triangle with one side labeled 13 meters.
What do all members of the family of linear functions f(x)=1m(x+3) have in common?
All linear function has a constant slope and degree as 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Linear functions are lines in the coordinate and describe itself that the slope will be the same irrespective of the point.
A linear function is given by ;
y = mx + x where m is slope.
As we can see the degree of x and y both are 1 so the linear function has a degree of 1.
Hence "All linear function has a constant slope and degree as 1".
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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?
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
Answer: b. -3 or 2
Step-by-step explanation:
Kite QRST has sides RS, ST, TQ and QR. What are the diagonals of this figure? Select all that apply.
Write a real world problem that you would represent with the equation 4x+5=37.
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
simplify:
...............
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
Find two positive real numbers who's product is a maximum and whose sum is 156.
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.
What is the sum of 36 ounces and 4 pounds? 6 lb. 6 lb., 4 oz. 96 oz. 98 oz.
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.
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.
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%.