Using the slope concept, supposing the horizontal distance is of 1500 feet, the angle of depression will be of 37º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we suppose an horizontal distance of 1500 feet, with a vertical distance of 2000 feet, hence:
[tex]\tan{\alpha} = \frac{1500}{2000}[/tex]
[tex]\alpha = \tan^{-1}{\left(\frac{1500}{2000}\right)}[/tex]
[tex]\alpha = 37^\circ[/tex]
The angle of depression will be of 37º.
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7. Wally invests $5,000 in a CD that earns 4% per year. Eqn:
Answer:
5000(1.04)^x, x is # of years
i need help with this quick pls
Answer:
[tex]\left[\begin{array}{cc}21&6\\-2&14\end{array}\right][/tex]
Step-by-step explanation:
[tex]x=\left[\begin{array}{ccc}8&4\\-2&3\end{array}\right][/tex]
[tex]y=\left[\begin{array}{ccc}5&-2\\2&8\end{array}\right][/tex]
To multiply an array by a constant, all you need to do is take every element in the array and multiply it by the constant, addition is similar in that you just go to each corresponding element in the arrays and add the two corresponding elements together.
[tex]2*\left[\begin{array}{cc}8&4\\-2&3\end{array}\right]+\left[\begin{array}{cc}5&-2\\2&8\end{array}\right] = \left[\begin{array}{cc}21&6\\-2&14\end{array}\right][/tex]
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
26
Part 1
Select all that apply.
A.
irrational numbers
B.
whole numbers
C.
real numbers
D.
natural numbers
E.
integers
F.
rational numbers
Answer:
26 is a:
B. Whole number
D. Natural number
E. Integer
F. Rational number
Answer:
B, C, D, E, F or all options except A
Step-by-step explanation:
26 is not an irrational number since irrational numbers cant be put in fraction form while 26 can be. ex: 26/1, 52/2 and so on
26 is a whole number.
whole numbers are 0 1 2 3 4 and so on
26 is a real number
imaginary number example: sqrt of -2
natural numbers are numbers going from 1 to infinity
integers are any number that is not a decimal.
26 is rational since it's not irrational.
The lower part of a window is square shape of side 2.1 metre and the upper part is semicircular with the side of square as the diameter. Find the total surface area covered by the window
Answer:
6.14
Step-by-step explanation:
The required area would be 6.14 m²
I hope I helped you
Answer:
6.14m^2
Step-by-step explanation:
Maybe this will help you..
Please answer number 7 thank you.
Answer:
3 is most likely
Step-by-step explanation:
5/16, 3/8, 7/16, 19/32, 1/4 least to greatest
I will mark brainliest
(Set 10)
Step-by-step explanation:
my solution is
1/4, 5/16, 3/8, 7/16, 19/32
a ruler and a pair of compasses Using only 1 Construct a Line IABI= 10cm b. Perpendicular bisector at A to C. c.Angle ABC =30. d. construct perpendicular bisector at B to Do such that AC BD. Join A to D
measure AD and angle ADB.
Answer:
Using a graduated ruler, draw a line segment AB of length 10 cm.
Draw 2 arcs of radius more than half of AB with A as the center, one above AB and one below AB.
With the same radius, similarly, draw 2 arcs with B as the center.
What is the name of the shape depicted in the graph below?
A. Rose
B. Cardioid
C. Limaçon
D. Lemniscate
The name of the shape depicted in the graph below is rose, so the answer is A.
GraphsA rose is a flat curve resembling a symbolic image of a flower. Geometrically, it is the algebraic or transcendent curve whose graph is characterized by a series of windings around a central point.
In the best known cases, these windings produce figures in the shape of a rose window, from which its name derives from.
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helpppppppppppppp this is hardddddddddd
Answer:
#1: 4) D
#2: 1) 34.89 = 3 × C
#3: 4) 6y + 18
Step-by-step explanation:
#1
Using the distributive property:
3 × 5z = 15z
3 × -3 = -9
The correct expression is 15z - 9. Hence, D is the right option.
#2
You need to find the cost of each box.
3 × C = 34.89
34.89 ÷ 3 = 11.63
3 × 11.63 = 34.89
Hence, 1) is the right option.
#3
Using the distributive property:
6 × y = 6y
6 × 3 = 18
The expression is 6y + 18. Hence, 4) is the right option.
hope this helps!! p.s. i really need brainliest :)
An event has a probability of 2/7. How would you best describe the likelihood of this event? (Hint: Change it to a decimal)
A. Impossible
B. Less likely
C. Equally likely
D. More likely
E. Certain
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]
As we can see, the probability of this event is 2/7 = 0.28 (approx), so it's even less than 50%, hence we can conclude that the given event is less likely to happen.
The Correct choice is B
The less likely would be the best description of the likelihood of the event.
The correct option is B.
What is the probability?The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?
The probability of the event is 2/7.
To describe the likelihood of the event,
we can convert the fraction to a decimal:
2/7 = 0.2857...
Since the decimal is between 0 and 0.5, we can say that the event is "less likely" to occur.
Therefore, the best answer is B. Less likely.
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What is the volume of this container?
Answer:
1,253 in³
Step-by-step explanation:
The container can be split into two rectangular prisms. Adding their volumes together will give us the volume of the container.
The formula for the volume of a rectangular prism is length×width×height or base×height
Let's substitute!
(l×w×h)+(l×w×h)
=(7×5×5)+(11×14×7)
=175+1078
=1,253 in³
Hope this helps!
Can someone please help me?
Answer:
152 ft²
Step-by-step explanation:
First, we can work out the area of the triangles using the formula 1/2 × base × height. 1/2 × 6 × 4 = 12 ft². This is the area of one triangle so we can multiply this by 2 to get the area of both triangles - 24ft².
Next, we can work out the area of the rectangular sides by multiplying the length and width together. 8 × 5 = 40ft². Again, this is the area of one rectangle so we can multiply this by 2 to get the area of both rectangles - 80ft².
Then, we can work out the area of the base by multiplying the length and width together. 8 × 6 = 48ft².
Finally, we can add all the areas together to find the total surface area of the tent. 24 + 80 + 48 = 152 ft².
Hope this helps!
what is the equation of the line with the slope -3 through the point (3,5)?
Answer:
[tex]\boxed{\sf{y=-3x+14}}[/tex]Step-by-step explanation:
The slope-intercept formula can be used to find the equation of the line.
Slope-intercept formula:
[tex]\Longrightarrow:\sf{y=mx+b}}[/tex]
The m represents the slope.The b represents the y-intercept.y-intercept is 14.y=-3x+14
Therefore, the correct answer is y=-3x+14.I hope this helps you! Let me know if my answer is wrong or not.
3. I am a cube that has a length,
width, and height of 1 unit.
A cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.
What is a Cube?A cube is a three-dimensional shape that has equal length, width, and height.
We are given that the height of a cube is 1 unit. Since the length, width, and height of a cube are always equal, therefore:
Length of the cube =1 unit
Width of the cube = 1 unit.
In summary, a cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.
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The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. what is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? use the portion of the standard normal table below to help answer the question.
The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.
Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data.
The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
The times of the runners in a marathon are normally distributed, with
Mean of 3 hours and 50 minutes Standard deviation of 30 minutes.Refere the probabiliity table attached below. The probability of Z being inside the 1 Standard daviation of mean is 0.84.
The probability of runner selected with time less than or equal to 3 hours and 20 minutes,
[tex]P=1-0.84\\P=0.16[/tex]
Thus, the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.
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A car travels 28 miles south and then 45 miles east around a lake. A boat leaves from the same place and arrives at the same place but travels directly from point A to point B. Calculate how many miles the boat and the car each traveled total. Then calculate who arrived first if the car was traveling at 40miles per hour and the boat traveled at 25 miles per hour.
Answer:
The car travelled 73 miles
The boat travelled 53 miles
The car arrived 17.7 minutes before the boat
Step-by-step explanation:
The total distance the car travelled from Point A to Point B = 28+45 = 73 miles
The total distance the boat travelled is given by the displacement; Using Pythagorean theorem = 53miles.
Time taken by the car = Distance/Speed = 73/40 = 1.825 hrs or 109.5 minutes
Time taken by the boat = Distance/speed = 53/25 = 2.12 hrs or 127.2 minutes.
The time taken by the car is the shortest, therefore it arrives first before the boat.
(◔‿◔)
a) write 2 2/3 as an improper fraction in its simplest form.
B) work out 2 2/3 x5 give your anwser as an improper
fraction in its simplest form.
Step-by-step explanation:
a) write 2 2/3 as an improper fraction in its simplest form....
[tex] = 2 \frac{2}{3} \\ [/tex]
[tex] = \frac{2 \times 3 + 2}{ 2} \\ [/tex]
[tex] = \frac{8}{2} \\ [/tex]
[tex] = \frac{8 \div 2}{2 \div 2} \\ [/tex]
[tex] = \frac{4}{1} = 4 \\ [/tex]
B) Work out 2 2/3 x5 give your anwser as an improper...
[tex] = 2 \frac{2}{3} \times 5 \\ [/tex]
[tex] = \frac{2 \times 3 + 2}{3} \times 5 \\ [/tex]
[tex] = \frac{8}{3} \times 5 \\ [/tex]
[tex] = \frac{40}{3} \\ [/tex]
Carter invested $540 in an account paying an interest rate of 4. 875 % compounded monthly. Jack invested $540 in an account paying an interest rate of 5. 5% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Carter's money to triple than for Jack's money to triple?
Using compound interest and continuous compounding, it is found that it would take 2.61 years longer for Carter's money to triple.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For Carter, we have that the rate of interest and the number of compoundings are, respectively, r = 0.04875 and n = 12. The time to triple is t for which A(t) = 3P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.04875}{12}\right)^{12t}[/tex]
[tex](1.0040625)^{12t} = 3[/tex]
[tex]\log{(1.0040625)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.0040625)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.0040625)}}[/tex]
t = 22.58.
What is continuous compounding?The amount of money is given by:
[tex]A(t) = Pe^{kt}[/tex]
For Jack, we have that the rate of interest is of k = 0.055, hence:
[tex]A(t) = Pe^{kt}[/tex]
[tex]3P = Pe^{0.055t}[/tex]
[tex]e^{0.055t} = 3[/tex]
[tex]\ln{e^{0.055t}} = \ln{3}[/tex]
[tex]0.055t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.055}[/tex]
t = 19.97.
The difference is given by:
22.58 - 19.97 = 2.61
It would take 2.61 years longer for Carter's money to triple.
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Triple u then divide 3 by the result?
Answer:
[tex]beinggreat78~is~here~to~help![/tex]
The equation should look something like this.
[tex]\frac{u(3)}{3}[/tex]
Be careful with your use between cubing and multiplying; Cubing is multiplying the number by itself multiple times, while multiplying is like repeated adding, yet much easier.
In this case, if it says triple, I highly recommend multiplying by 3, which is what I did, it only looks different because it is in parentheses.
What have we learned?
We learned how to write algebraic equations, and some further information on multiplying.John has 1010 items in his backpack, including 66 books. What is the probability that a randomly selected item from his backpack is a book?
Answer:
~6.534653% of randomly selected a book from his bag (I don't know how many decimals you need)
Step-by-step explanation:
Basically you just do (66 (books) /1010 (total items)) * 100 to find your answer because out of the total 1010 items in that bag there is only 66 that are books so its (66/1010)*100 to find your answer, the *100 is added to find the percentage.
two numbers have difference of 6 and a mean of 11. Find the numbers.
Mean is average 11 x 2 = 22
The two cards need to equal 22 when added together.
the difference is 6:
6/2 = 3
11-3 = 8
11+ 3 = 14
14 +8 = 22
the two numbers are 8 and 14
find the value of x by factoring x^2-9x-36=0
Find the sum of the following series. Round to the nearest hundredth if
necessary
5 + 10 + 20 + ... + 163840
Sum of a finite geometric series:
ai
Sn
di — airon
1 - 1
Answer:
327675
Step-by-step explanation:
the formula of the series is:
16
∑5*2^(n-1)
n=1
the formula for the sum of a geometric series is:
Sn=a(1-r^n)/(1-r)
plug in the values from above
n=16 a=5 and r=2 (values from the geometric function) so
Sn=5(1-2^16)/(1-2)
Sn=327675
Pls help me look at the picture for the question pls
Answer:
D
Step-by-step explanation:
[tex]y=-3x-14[/tex] is a function as it has:
The input (x-values)A relationship (multiply the x-value by -3 then subtract 14)The output (y-value)Linear equation in slope-intercept form: [tex]y=mx+b[/tex]
where:
m = slopeb = y-interceptTherefore, for equation [tex]y=-3x-14[/tex]
The slope is -3The y-intercept is -14So as the equation is a linear equation, its graph is a straight line.
Therefore, the only statement that is NOT true is D as the y-intercept is -14 (not 14).
Coach Morton is going on vacation! He drives 7.5 hours at an average speed of 35mph. How many miles did he travel?
Answer:
4.7m
Step-by-step explanation:
35/7.5
=4.7m
Am sure am correct
Naomi wants to take yoga classes. she can take classes at the high school for a one-time fee of $20 plus $10 per class. she can join the local gym for $50 and take classes for $5 per class. which statement is true about the average cost for the two options? the high school option costs less per class for six classes. the gym option costs less per class for six classes. the high school option costs less per class for seven classes. the gym option costs less per class for seven classes.
The gym option costs less per class for six classes(Option B), and the gym option costs less per class for seven (Option D).
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Here we're specified that:
For high school classes:
one-time fee of $20 plus $10 per class.For local gym:
she can join for $50 and take classes for $5 per class.For 6 classes:
High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 6 = $(20+60) = $80
(since $20 dollar is one time cost, and $10 was price for each class)
Similarly, joining local gym's $50 cost is one time, and rest of $5 is price for each class.
Local gym : $50 + $(5+5+5+5+5+5) = $20 + $5 × 6 = $(20+30) = $50
For 7 classes:
High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 7 = $(20+70) = $90
Local gym : $50 + $(5+5+5+5+5+5+5) = $20 + $5 × 7 = $(20+35) = $55
Thus, the statements which are true about the average cost for the two options is given by: Option B: The gym option costs less per class for six classes., Option D: The gym option costs less per class for seven classes.
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A paperweight in the shape of a rectangular prism is shown: A right rectangular prism is shown with length 10 cm, width 4 cm, and height 4 cm. If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section? Rectangle Triangle Parallelogram Hexagon
Answer:
triangleStep-by-step explanation:
draw a square and cut it from the top right corner to the bottom left corner it makes a triangle
Suppose that the coordinates of point G were (4, –3) instead of (4, 3). Would the area of the triangle be the same? Explain why or why not.
The coordinate of point G is its location on the coordinate plane
The area of the triangle would not remain the same
How to determine the area statement?From the question, we have the following points
G = (4,-3) and
G = (4,3)
The above coordinates are two different points, and so they would make the triangle have different areas.
Hence, the area of the triangle would not remain the same
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Instructions: Find the missing side of the triangle.
Answer:
x=15
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
The legs and x and 20 and the hypotenuse is 25
20 ^2+x^2 = 25^2
400 + x^2 = 625
Subtract 400 from each side
x^2 = 625-400
x^2 = 225
Take the square root of each side
sqrt(x^2) = sqrt(225)
x = 15
Which rule dilates a figure in the coordinate plane by a scale factor of 5?
Dilation involves changing the size of a figure
The dilation rule of a figure in the coordinate plane by a scale factor of 5 is (b) (x,y) [tex]\to[/tex] (5x,5y)
How to determine the dilation rule?The scale factor (k) is given as:
k = 5
Assume the coordinates of the figure is (x,y)
The dilation rule would be:
(x,y) [tex]\to[/tex] k(x,y)
Substitute 5 for k
(x,y) [tex]\to[/tex] 5(x,y)
Expand
(x,y) [tex]\to[/tex] (5x,5y)
Hence, the dilation rule is (b) (x,y) [tex]\to[/tex] (5x,5y)
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If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
Dilation of coordinateDilation is a transformation technique that changes the size and shape of an object in an xy plane
If the coordinate point (x, y) is dilated by a factor of "k", the resulting coordinate of the preimage will be (kx, ky)
If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
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