Step-by-step explanation:
Given : If the hypotenuse of a 30-60-90 triangle has length 15 then the shorter leg has length 5.5 , 6.5 , 7.5.
To find : What is the length of the other leg and hypotenuse ?
Solution :
For a 30-60-90 triangle, sides are in the ratio [tex]1:\sqrt{3}:2[/tex]
where, 1 is the shorter side,
[tex]\sqrt{3}[/tex] the other side
and 2 the hypotenuse.
Short leg = 5.5
Other leg = [tex]5.5\times \sqrt3=5.5\sqrt3[/tex]
Hypotenuse = [tex]5.5\times 2=11[/tex]
Short leg = 6.5
Other leg = [tex]6.5\times \sqrt3=6.5\sqrt3[/tex]
Hypotenuse = [tex]6.5\times 2=13[/tex]
Short leg = 7.5
Other leg = [tex]7.5\times \sqrt3=7.5\sqrt3[/tex]
Hypotenuse = [tex]7.5\times 2=15[/tex]
Final answer:
In a 30-60-90 triangle with a hypotenuse of 15, the shorter leg has a length of 7.5, based on the ratio 1:√3:2.
Explanation:
If the hypotenuse of a 30-60-90 triangle has length 15, then to find the length of the shorter leg, we can use the properties of this special right triangle. In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. In other words, if the shorter leg is 'x', the longer leg is 'x√3', and the hypotenuse is '2x'.
Since the hypotenuse is 15, we set '2x' equal to 15 and solve for 'x':
2x = 15
x = 15 / 2
x = 7.5
The shorter leg of the triangle has a length of 7.5.
On your first day of work, you get $1. On your second day of work, you get $4. On your third day of work, you get $9. On your fourth day of work, you get $16. It continues this way for 30 days and then once you’ve completed the 30 days you receive a completion bonus of $500,000. How much would I earn after?
Answer:
Money earned after 30 days is $509455
Step-by-step explanation:
If on the first day, that is n = 1, where n is the day and you earn $1.
On the second day (n = 2), you earn $4, On the third day (i.e n = 3) you earn $9 and on the fourth day (n = 4) you then earn $16. That is the money earned on the nth day is given by:
Money earned on the nth day = n².
That is on the 30th day, the money earned = 30² = $900
Once you’ve completed the 30 days you receive a completion bonus of $500,000, in given by:
Money earned after 30 days = [tex]\Sigma}n^2 ;n=1 to30+$500000=(1^2+2^2+3^2+4^2+5^2+...+29^2+30^2)+500000\\=9455+500000=509455[/tex]
Money earned after 30 days = $509455
Answer:
y = x^2 = 30^2 = $900
He would earn $900 on the 30th day and the bonus of $500,000
Step-by-step explanation:
Given
let y represent the amount earned
x represent the day.
At x = 1 y = 1
x = 2 y = 4
x= 3 y = 9
x = 4 y = 16
This satisfies the function;
y = x^2
So, on the 30th day;
x = 30
y = x^2 = 30^2 = $900
He would earn $900 on the 30th day and the bonus of $500,000
X^2+(y+)4^2=64 khan academy
Answer: The center is 0,4
Step-by-step explanation:
Use this form to determine the center and radius of the circle:
(
x-h)^2+(y-k)^2=r^2
Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin:
r=8
h=0
k=4
The center of the cirle is found at (h,k): (0,4)
The radius is 8
Which is an exponential decay function?
f(x) = 3/4(7/4)
f1x) = 2/3(4/5)*
f(x)= 3/3(8/7)
f(x) = 1/3(-9/2)
Answer: f(x) = 3/2 (8/7)-x
Step-by-step explanation:
Twenty less than the product of 3 and a number is -29. What is the number?
The equation representing 'twenty less than the product of 3 and a number is -29' is 3n - 20 = -29. Solving for n, we find that n equals -3.
When solving the equation twenty less than the product of 3 and a number is -29, we can translate this into a mathematical expression as 3n - 20 = -29, where n represents the unknown number. To find the value of n, add 20 to both sides of the equation, which gives us 3n = -9. Dividing both sides by 3, we find that n = -3. Thus, the number we are looking for is -3.
Mark has three 4 1/2 oz cans and five 8 1/4 oz cans. How many ounces of tomatoes does Mark need?
Answer:
54.74 ounces of tomatoes mark need.
Step-by-step explanation:
Given : Mark has three [tex]4\frac{1}{2}[/tex] oz cans and five [tex]8\frac{1}{4}[/tex] oz cans.
To find : How many ounces of tomatoes does Mark need?
Solution :
Mark has three [tex]4\frac{1}{2}[/tex] oz cans.
i.e. [tex]3\times 4\frac{1}{2}=3\times \frac{9}{2}=\frac{27}{2}[/tex]
Mark has five [tex]8\frac{1}{4}[/tex] oz cans.
i.e. [tex]5\times 8\frac{1}{4}=5\times \frac{33}{4}=\frac{165}{4}[/tex]
Total ounces of tomatoes does Mark need is
[tex]T=\frac{27}{2}+\frac{165}{4}[/tex]
[tex]T=\frac{54+165}{4}[/tex]
[tex]T=\frac{219}{4}[/tex]
[tex]T=54.75[/tex]
Therefore, 54.74 ounces of tomatoes mark need.
Three ballet dancers are positioned on stage. Elizabeth is straight behind Hannah and directly left of Manuel. If Hannah and Elizabeth are 3 meters apart, and Manuel and Hannah are 5 meters apart, what is the distance between Elizabeth and Manuel?
Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Final answer:
To calculate the distance between Elizabeth and Manuel, the Pythagorean theorem is used. Given the 3-meter distance between Hannah and Elizabeth, and the 5-meter distance between Hannah and Manuel, the distance between Elizabeth and Manuel is calculated to be the square root of 34, which is approximately 5.83 meters.
Explanation:
The question pertains to finding the distance between Elizabeth and Manuel, given their respective positions on a stage in relation to Hannah.
To find the distance between Elizabeth and Manuel, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the distances between Hannah and the other two dancers form two sides of a right-angled triangle with Elizabeth and Manuel's positions marking the ends of the hypotenuse.
Since Hannah is 3 meters from Elizabeth and 5 meters from Manuel, we can calculate the distance between Elizabeth and Manuel (hypotenuse) with the following equation:
c^2 = a^2 + b^2
Where c is the distance between Elizabeth and Manuel, a is the distance between Hannah and Elizabeth (3 meters), and b is the distance between Hannah and Manuel (5 meters).
So, c^2 = 3^2 + 5^2 which simplifies to c^2 = 9 + 25, and further to c^2 = 34. This implies that c = [tex]\sqrt{34}[/tex].
Therefore, the distance between Elizabeth and Manuel is the square root of 34, which is approximately 5.83 meters. We can round this to the nearest hundredth for a precise measurement.
The distance between Elizabeth and Manuel is approximately 5.83 meters.
Simplify: (x - 7)(6x - 3)
Answer:
C. 6x² -45x + 21
Step-by-step explanation:
( x - 7) (6x - 3)
= x(6x - 3) -7 ( 6x - 3)
= 6x² - 3x - 42x + 21
= 6x² - 45x + 21
Hope it will help you :)
Answer
the answer is c
Step-by-step explanation:
Given that a randomly chosen quadrilateral has four right
angles, what is the probability that the quadrilateral also
has four equal side lengths? Express your answer in
percent form, rounded to the nearest whole percent.
25%
33%
40%
67%
Answer: 25%
Step-by-step explanation:
Bc I’m smort boi
A randomly chosen quadrilateral has four right angles, has a probability that the quadrilateral also has four equal side lengths is 33%.
What is probability?Probability is a measure of the likelihood of an event to occur.
Many events cannot be predicted with total certainty.
We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
Given is a Venn diagram,
In the Venn diagram, we can see that we have 9 elements, 6 of these belong to the set R, 3 of them belong to the set E, and 2 belong to both sets.
Now we want to find the probability that, if a figure has four right angles (belongs to R) it also has 4 equal side lengths (belongs to E).
So, given that an element belongs to R (6 elements there).
The probability that it also belongs to E,
2 out of these 6 elements belong to E, so the probability will be:
P = 2/6 = 1/3 = 0.33
To get this in percent form, we need to multiply it by 100%, we will get:
0.33x100% = 33%
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All else being equal, a study with which of the following error ranges would be
the most reliable?
O
A. 17 percentage points
O
B. +22 percentage points
O
C. 17 percentage points
O
D. 112 percentage points
Answer:
it would be A and C because they are the lowest
Step-by-step explanation:
The correct option is C
Percentage point : It is defined as a unit for the arithmetic difference of two percentages and greater the difference more will be the error range.
So, the most reliable error range is the one whose percentage point is minimum.
Now, among the provided options , 2 percentage points is minimum so it will be the most reliable error range.
Hence, Option C. 2 percentage points is correct
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If ABC Is an equilateral triangle, solve for both x and y
Answer:
X=16
Y=5
Step-by-step explanation:
For equilateral triangle, length of both sides are equal hence 18y-41=3x+1=49
Solving for x
Given that 3x+1=49
Rearranging like terms
3x=49-1=48
x=48/3=16 units
Solving for y
Considering that 18y-41=49
18y=49+41=90
y=90/18=5 units
The value of x = 16 and y = 5.
Given that [tex]\( \triangle ABC \)[/tex] is an equilateral triangle, all sides are equal. Therefore, we have:
[tex]\[ AB = BC = AC \][/tex]
Given the side lengths:
[tex]\( AB = 49 \)[/tex] meters
[tex]\( BC = 3x + 1 \)[/tex] meters
[tex]\( AC = 18y - 41 \)[/tex] meters
Since [tex]\( AB = BC \)[/tex]:
[tex]\[ 49 = 3x + 1 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 49 - 1 = 3x \][/tex]
[tex]\[ 48 = 3x \][/tex]
[tex]\[ x = \frac{48}{3} \][/tex]
[tex]\[ x = 16 \][/tex]
Next, since [tex]\( AB = AC \)[/tex]:
[tex]\[ 49 = 18y - 41 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ 49 + 41 = 18y \][/tex]
[tex]\[ 90 = 18y \][/tex]
[tex]\[ y = \frac{90}{18} \][/tex]
[tex]\[ y = 5 \][/tex]
The complete question is:
If ABC Is an equilateral triangle, solve for both x and y.
x = _____.
y = _____.
The door code outside a house often consists of either pressing A or B and then a code with free digits. Suppose you do not know the code, but try your way. How long would it take to test all combinations if each trial takes 10 seconds?
Round to whole hours.
Answer:
6 hours
Step-by-step explanation:
2 option for letter
10 for each digit
2×10×10×10
2000 trials
2000×10
20,000 seconds
20000/3600
5.5555555556 hours
The total number of combinations is 2000. Testing each one at a rate of 10 seconds per test would take approximately 20,000 seconds, which is around 6 hours when rounded to the nearest hour.
Explanation:This problem deals with the concept of combinations in mathematics. To find out how long it would take to try all possible combinations, you first need to determine how many combinations there are. The door code consists of either A or B (2 options) followed by a three-digit code (10 options for each digit, from 0-9). Therefore, there are 2 * 10 * 10 * 10 = 2000 possible combinations. If each combination takes 10 seconds to try, it would take 2000 * 10 = 20,000 seconds. To convert this to hours, divide by 3600 (as there are 3600 seconds in one hour), rounding to the nearest whole number, would give approximately 6 hours.
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If a line is 10 feet long but needs to be enlarged 150%, how long will the new line be?
Answer:
23
Step-by-step explanation:
find 10 percent and times the rest
−8 ≤ −3; Add 11 to both sides
a town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number
Answer: P(t) = 5000(1.02)^5
Step-by-step explanation:
an international company has 24,500 employees in one country. if this repersents 24.8% of the company's employees, how many employees does it have in total?
Answer:
98,790
Step-by-step explanation:
The given relation is ...
0.248 · (total employees) = 24,500
Dividing by the coefficient of the variable, we have ...
(total employees) = 24,500/0.248 = 98,790
The company has 98,790 employees in total.
Which model shows
64
−
−
√
3
=4
643=4
?
In the equation √64 - 3 = 4, we first take the square root of 64 to get 8, then subtract 3 to get 5, NOT 4. Thus, the given equation is not accurate.
Explanation:The model to represent the mathematical expression √64 - 3 = 4 is firstly taking the square root of 64 which gives 8, and then subtracting 3 from it to get 4. The complete equation is as follows:
Take square root of 64 which is 8.Then subtract 3 from 8, which equals 5 NOT 4, meaning the given equation is incorrect.
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0.4(5x – 12) + 0.5x = 15.2
Look at the attached picture ⤴
Hope it will help u..
0.4(5x-12)+0.5x=15.2
We move all terms to the left:
0.4(5x-12)+0.5x-(15.2)=0
We add all the numbers together, and all the variables
0.5x+0.4(5x-12)-15.2=0
We multiply parentheses
0.5x+2x-4.8-15.2=0
We add all the numbers together, and all the variables
2.5x-20=0
We move all terms containing x to the left, all other terms to the right
2.5x=20
x=20/2.5
x=8
What is the product enter your answer as a fraction in simplest form in the box -4/5 • 10/16
Answer:
-1/2
Step-by-step explanation:
The first thing you do is cross cancel because when you cross cancel 4 and 16 it would be -1/5 * 10/4 then you cross cancel 5 and 10 and then you faction would look like -1/1 * 2/4 then you multiply those fractions together and get -2/4 but simplified would be -1/2.
One cup is equal to 14.4375 in^3. If a 1-cup measuring cylinder has a radius of 3 in., what is its height? If
the radius is 1 in., what is its height? Round to the nearest tenth.
If the measuring cup has a radius of 3 in. then its height is
height is _____ in., and it it has a radius of 1 in. then it’s height is _____ in.
Answer:
The height of the cup is 0.51 in.
The height of the cup is 4.59 in.
Step-by-step explanation:
The volume of the cylinder is [tex]\pi r^2 h[/tex]
Given that,
The volume of the cup is 14.4375 in³.
If the measuring cup has a radius of 3 in.
Then,
[tex]\pi r^2h=14.4375[/tex]
Plug r= 3 in.
[tex]\pi (3)^2h=14.4375[/tex]
[tex]\Rightarrow h=\frac{14.475}{9\pi }[/tex]
⇒h=0.51 in.
The height of the cup is 0.51 in.
If it has radius of 1 in.
Then,
[tex]\pi r^2h=14.4375[/tex]
Plug r= 1 in.
[tex]\pi (1)^2h=14.4375[/tex]
[tex]\Rightarrow h=\frac{14.475}{1\pi }[/tex]
⇒h=4.59 in.
The height of the cup is 4.59 in.
A grain silo is composed of a cylinder and a hemisphere.
The diameter is 4.4 meters. The height of its cylindrical
portion is 6.2 meters
What is the approximate total volume of the silo? Use 3.14
forn and round the answer to the nearest tenth of a cubic
meter.
37.1 m3
71.9 m
116,5 m
130.8 m3
Answer:
C.
Step-by-step explanation:
[tex]116.5^{3}[/tex]
The approximate total volume of the silo is 116.9 m^3, the correct option is C. 116.5 m^3.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
Diameter=4.4m
Height=6.2meter
Now,
The radius of the silo is half of its diameter, which is 4.4/2 = 2.2 meters. So, plugging in the given values and using 3.14 for π, we get:
V = πr^2h + (2/3)πr^3
V = 3.14(2.2^2)(6.2) + (2/3)3.14(2.2^3)
V = 94.25 + 22.64
V = 116.89
Therefore, the volume of silo will be 116.5 m^3.
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Which expression is the as 400.902
Answer:
4*100+.9*0.1+.002*.001
Step-by-step explanation:
The student's question is unclear and lacks clarity. It is recommended that they provide more information or context so that an accurate explanation can be given.
Explanation:The question seems to be unclear. As a tutor, I would ask the student to clarify their question more specifically. The number '400.902' is indeed an expression, however, it's not clear what it's supposed to be equivalent to. Understanding the context can help provide a more accurate answer, as '400.902' could represent a multitude of things, such as a decimal, a fraction, a percentage or even part of a scientific notation. Without this information, I can't provide a reliable explanation or comparison.
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What is the volume of this container ? HELP
Answer:
56 [tex]in^{3}[/tex]
Step-by-step explanation:
Volume of bigger rectangular prism is 4*3*4 (48[tex]in^{3}[/tex]).
Volume of smaller rectangular prism is 1*2*4 (8[tex]in^{3}[/tex]).
48 + 8 = 56[tex]in^{3}[/tex].
The mean of 4 data values is calculated. One of the data values is 3 above
the mean. Another value is 4 above the mean. A third value is 1 above the
mean. What is true about the fourth data value? olla
A It is 8 below the mean.
B It is 6 below the mean.
C It is equal to the mean.
D It is 2 above the mean.
Answer:
It is 2 above the mean
9514 1404 393
Answer:
A. It is 8 below the mean
Step-by-step explanation:
The sum of differences from the mean is always zero. If x is the difference from the mean that the fourth data value has, then we must have ...
3 + 4 + 1 + x = 0
x = -8 . . . . . . . . . subtract 8
The fourth data value must be 8 below the mean.
_____
Additional comment
I find this property of the mean to be very useful in solving any number of problems related to differences from an actual or a desired mean.
What is the area of triangle ABC?
3 square units
7 square units
11 square units
15 square units
Answer:
7 units
Step-by-step explanation:
use the distnce formula to get the riangles legs, multiply them and divide by two
The expression 1.5t + 20 predicts the height in centimeters of a plant t days from today. What is the predicted height of the plant 15 days from today?
Answer:
42.5
Step-by-step explanation:
so you start with adding 15 to the equations because that is how many days
1.5 15 +20
1.5 x 15 =22.5
22.5+20=42.5
so 42.5 is the answer
The predicted height of the plant 15 days from today is 42.5 cm.
The given expression for the height of a plant is 1.5t + 20, where t represents the number of days from today. To find the predicted height of the plant 15 days from today, we need to substitute t = 15 into the expression.
Substitute t = 15 into the expression:height of the plant 15 days from today = 1.5(15)+20 cm
height of the plant 15 days from today = 22.5 + 20 cm = 42.5 cm
Therefore, the predicted height of the plant 15 days from today is 42.5 cm.
solve the inequality: 5x + 14 greater than or equal too 54
Answer:
5*8+14=54
Step-by-step explanation:
5*x+14= 54
so
54-14= 40
40/5=8
so x=8
A sphere and cylinder have same radius and height the volume of cylinder is 27 which equation give volume of sphere
Answer:
the answer is A≈9160.88
Step-by-step explanation:
A=4πr2=4·π·272≈9160.88418where as a = areaAnswer:
The correct answer is A on Edge 2020.
Step-by-step explanation:
A sphere has 2/3 the volume of a cylinder given that the radius and height are equal. Because the volume of the cylinder is 27 pi (on Edge 2020), you need the equation: 2/3(27 pi) or A.
What gives the range of the function y=|x-1|+7
The range of the function y=|x-1|+7 is all real numbers greater than or equal to 7, as the absolute value ensures non-negative values to which 7 is added.
The range of the function y=|x-1|+7 can be determined by analyzing the nature of the absolute value function and the constant term. The absolute value function, |x-1|, ensures that the output is always non-negative for any value of x, since it represents the distance from 1 on the number line, which cannot be negative. Therefore, when we add 7 to this non-negative value, the smallest value y can take is when |x-1|=0, which is when x=1. So, at x=1, y will be 7 since we have 0+7. For any other value of x, |x-1| will be positive, and when adding 7, y will be greater than 7. Hence, the range of y is all values greater than or equal to 7.
A book normally cost $21.50. Today it was on sale for $15.05. What percentage discount was offered during the sale. ( Please explain, i'm desperate!)
Answer: 30%
Step-by-step explanation:
Subtract the original cost from the on sale price.
21.50 - 15.05 = 6.45
Divide the savings by the original cost.
6.45/21.50 = .3
Multiply by 100
.3 * 100 = 30
Answer:
30% percent
Step-by-step explanation:
21.50-15.05=6.45
21.50÷6.45=3.
3×100=30%
we times 100 because 1 equal 100%.So you need to do is just to multiply the number by 100 and add at the end symbol %
The number e is an irrational number approximately equal to 2.718 between which pair of square roots does e fall
Answer:
It falls between √7 and √8
Step-by-step explanation:
Please kindly check the attached file for explanation.