Answer:
Given:-Side length ( perpendicular = 60 cm)
Hypotenuse = 61 cm
To find :-Base length
Solution:By Pythagoras theorem ,
Hypotenuse² = Perpendicular² + Base²
61² = 60² + base²
3721-3600 = Base²
√121 = base
11cm = base
Answer:
Base = x = 11 cmStep-by-step explanation:
In the question we are given ,
Side length ( Perpendicular ) = 60 cm Hypotenuse = 61 cmAnd we have asked to find the length of base that is denoted by x .
Solution : -
According to Pythagoras Theorem ,
[tex] \longrightarrow \purple{\boxed{H {}^{2} = P {}^{2} + B {}^{2} }} \longleftarrow[/tex]
Where ,
H = HypotenuseP = PerpendicularB = BaseNow , substituting value of hypotenuse, perpendicular and base :
[tex] \hookrightarrow \: 61 {}^{2} = 60 {}^{2} + x {}^{2} [/tex]
Now by squaring 61 and 60 , we get :
[tex] \hookrightarrow \:3721 = 3600 + x {}^{2} [/tex]
Now transposing 3600 to left hand side :
[tex] \hookrightarrow \:3721 - 3600 = x {}^{2} [/tex]
Now subtracting 3600 from 3721 :
[tex] \hookrightarrow \:121 = x {}^{2} [/tex]
[tex] \hookrightarrow \: \sqrt{121} = x[/tex]
We know that 11 × 11 is equal to 121 that means square root of 121 is 11 . So :
[tex] \hookrightarrow \: \red{ \boxed{11 \: cm = x}}[/tex]
x = baseHenceforth, length of base of right triangle is 11 cm .#Keep LearningPlease help! Refer to the image below.
If u = ⟨-4, 8⟩ and v = ⟨5, -18⟩, then we have
2u - 4v = ⟨-8, 16⟩ + ⟨-20, 72⟩ = ⟨-28, 88⟩
To this vector, we want to add another vector w = ⟨a, b⟩ such that
2u - 4v + w = ⟨0, 1⟩
Solve for w :
w = ⟨0, 1⟩ - ⟨-28, 88⟩ = ⟨28, -87⟩ … … … [C]
Determine whether each statement correctly describes the likelihood of an event based on the given number cube. Select True or
False for each statement.
True or False
The statement that correctly descrives the likelilhood of an event based on the given numbered cube is: Option A: It is likely that a number less than 6 is occured.
How to decide the likelihood of an event?Suppose that for a considered sample space, we consider an event E
Then, E is likely to occur if:
[tex]P(E) \geq P(E')[/tex]
where [tex]E_i '[/tex] is complementary event of E (ie, E' occurs whenever E doesn't occur and vice versa)
If so, then we say that E is likely to occur as the outcome of the considered random experiment, else unlikely.
Since we have:
[tex]P(E) = 1- P(E')[/tex] due to E and E' being complement of each other, therefore, we get:
[tex]P(E) \geq 1 - P(E)\\P(E) \geq 0.5[/tex]
Thus, event E is said to be likely if its probability is greater or equal to 0.5, else not.
It is given that the cube is 6 faced (assuming all equally likely), numbered from 1 to 6.
Evaluating likelihood of each event:
It is likely that a number less than 6 is obtained on the number cube.P(Getting a number < 6 on that cube) = [tex]\dfrac{5}{6}[/tex] (since a number out of 6 numbers can occur in 6 ways, but it being < 6 can be done in 5 ways).
Thus, we have:
P(Getting a number < 6 on that cube) =5/6 > 0.5
So it is likely to get a number < 6 on the considered cube. So this statement correctly describes the likelihood of its considered event.
It is unlikely that a number < 4 is obtained on the number cube.Ways to get a number on the considered cube = 6
Ways to get a number < 4 on the considered cube = 3
Thus, we get:
P(Getting a number < 4 on that cube) = 3/6 = 0.5
Thus, it is likely to get a number < 4 on that cube, so this option is wrong.
It is certain that an odd or even number is obtained on the number cubeYes it is certain, but we're considering only those options which correctly describe likelihood instead of certainity.
So, this option is not considerable.
It is unlikely that a number > 1 is obtained on the number cube.Ways to get a number on the considered cube = 6
Ways to get a number > 1 on the considered cube = 5
Thus, we get:
P(Getting a number > 1 on that cube) = 5/6 > 0.5
Thus, it is likely to get a number > 1 on that cube, so this option is wrong.
Thus, the statement that correctly descrives the likelilhood of an event based on the given numbered cube is: Option A: It is likely that a number less than 6 is occured.
Learn more about likelihood of events here:
https://brainly.com/question/14954386
#SPJ1
Need help with 115/120 please and thank you
Answer:
115: a) -4
120: a) 11
Step-by-step explanation:
115: Use the formula
[tex]m = \frac{rise}{run} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
= (-5)-(3) / (6) - (4)
= -8 / 2
= -4
120: Count the units between point B and point F
PLEASE HELP ME WITH THIS!!!! I BEG
Answer:
D. turns
Step-by-step explanation:
Rotation is the process of turning around a center or an axis.
(Sorry if it's wrong. I hope I helped somewhat.)
Upon review of production results, it was determined that 130 pieces out of 3,500 were "out of spec." What percent of the production was "out of spec"?
A. 0.03 percent .
B. 3.71 percent .
C. 30 percent
D. 37.1 percent
Answer:
Option B
Step-by-step explanation:
Given:
130 pieces of 3500 were out of specTo determine the percentage of the production was out of spec, we need to use the percentage formula (x/y × 100).
[tex]\implies \dfrac{x}{y} \times 100[/tex]
The value of "x" is the the number of pieces that were out of spec and the value of "y" is the total pieces in the production results.
[tex]\implies \dfrac{130}{3500} \times 100[/tex]
Simplify the expression to determine the percentage of the pieces that were out of spec.
[tex]\implies \dfrac{13000}{3500}[/tex]
[tex]\implies \dfrac{130}{35} = \dfrac{130 \div 5}{35 \div 5} = \dfrac{26}{7} = 3.714... \%[/tex]
When the percentage is estimated to nearest hundredth, we get 3.71%
(Option B)
Answer:
B) 3.71%
Step-by-step explanation:
[tex]\textsf{130 out of 3500}\sf =\dfrac{130}{3500}[/tex]
To convert to a percentage, multiply by 100:
[tex]\implies \sf \dfrac{130}{3500} \times 100\%=0.03714.. \times 100\%=3.71\%[/tex]
Henry was thinking of a number. Henry adds 2, then divides by 5 to get an answer of -10. What was the original number?
need help pls i will give brainliest.
Answer:
g= 60°
i= 70°
h= 50°
Step-by-step explanation:
g=180-120 = 60°
i= 180-110 = 70°
h=180-60-70 = 50°
hope this helps =)
Kindly rate and mark brainliest. Thank you.
60 point help What are domain restrictions of rational functions? What do domain restrictions mean for the graph of a rational function?
Answer:
1. The use of a domain for a function that is smaller than the function's domain of definition. Note: Restricted domains are commonly used to specify a one-to-one section of a function.
2. Domain restrictions can be calculated by finding singularities, which are the x -values for which the denominator Q(x) is zero.
Answer:
by setting the denominator equal to zero and solving. The x -values at which the denominator equals zero are called singularities and are not in the domain of the function.
Step-by-step explanation:
what type of angle is this?
Answer:
This is an acute angle since it measures less than 90 degrees.
50 paise × 1000 give your answer in rupees
Answer:
10 rs
Step-by-step explanation:
I hope it's helpful for youWhich function is equivalent to g(x)= x2 +11x-60?
Find the circumstance of a circle with the diameter of 13 meters use 3.14 as an approximation
Answer:
okay so the circumference is 40.82m
[tex]circumference = 2\pi \: \times r \\ = 2 \times 3.14 \times 6.5 \\ = 40.82m[/tex]
the diameter will be divided by 2 to give 6.5
Is 5 1/2 2.5 or 5.5?
Answer:
Volume = 92.15
Step-by-step explanation:
V=πr2h/3=π·42·5.5/3≈92.15
Add. Write the answer as a fraction simplified to lowest terms.
2+1 15 20 =
Answer:
Step-by-step explanation:
LCD (15,20) = 60
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{20}[/tex] = [tex]\frac{8}{60}[/tex] + [tex]\frac{3}{60}[/tex] = [tex]\frac{11}{60}[/tex]
Answer:
2/15 + 1/20 = 11/60
Step-by-step explanation:
1. Find the least common denominator or LCM of the two denominators:
15 and 20.
Steps to find LCM:
1. Find the prime factorization of 15
15 = 3 × 5
2. Find the prime factorization of 20
20 = 2 × 2 × 5
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 3 × 5
LCM = 60
2. Next, find the equivalent fraction of both fractional numbers with denominator 60.
For the 1st fraction, since 15 × 4 = 60,
2/15 = 2 * 4 / 15 * 4 = 8/60
Likewise, for the 2nd fraction, since 20 × 3 = 60,
1/20 = 1 * 3 / 20 × 3 = 3/60
Add the two like fractions:
8/60 + 3/60 = 8 + 3/60 = 11/60
What is the interquartile range for 8 9 3 12 4 4 8 7 2 10
Answer: 5
Step-by-step explanation:
lower quartile: 4
upper quartile: 9
9-4=5
IQR=5
Find the derivative.
[tex]\dfrac{d}{dx} \left[ \sin^{-1}(\cos e^x)-\cos^{-1}(\sin e^x) \right][/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex]\qquad \tt \dashrightarrow \:\dfrac{d}{dx} \left[ \sin^{-1}(\cos e^x)-\cos^{-1}(\sin e^x) \right][/tex]
[tex]\qquad \tt \dashrightarrow \:\dfrac{d}{dx} \sin^{-1}(\cos e^x) - \dfrac{d}{dx}\cos^{-1}(\sin e^x) [/tex]
[tex]\qquad \tt \dashrightarrow \: \bigg(\dfrac{1}{ \sqrt{1 - ( \cos( {e}^{x} ) ) {}^{2} } } \times - \sin( {e}^{x} ) \times {e}^{x} \bigg) - \bigg( - \dfrac{1}{ \sqrt{1 - ( \sin( {e}^{x} )) {}^{2} } } \times \cos( {e}^{x} ) \times {e}^{x} \bigg)[/tex]
[tex]\qquad \tt \dashrightarrow \: \bigg(\dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{1 - ( \cos( {e}^{x} ) ) {}^{2} } } \bigg) - \bigg( - \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{1 - ( \sin( {e}^{x} )) {}^{2} } } \bigg)[/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{1 - \cos {}^{2} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{1 - \sin {}^{2} ( {e}^{x} ) {}^{} } } [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ \sqrt{ { \sin}^{2} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ \sqrt{ \cos {}^{2} ( {e}^{x} ) {}^{} } } [/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{ - {e}^{x} \sin( {e}^{x} ) }{ { { \sin}^{} ( {e}^{x} ) {}^{} } } + \dfrac{ {e}^{x} \cos( {e}^{x} ) }{ { \cos {}^{} ( {e}^{x} ) {}^{} } } [/tex]
[tex]\qquad \tt \dashrightarrow \: - {e}^{x} + {e}^{x} [/tex]
[tex]\qquad \tt \dashrightarrow \:0[/tex]
I hope this helps, if you find any problem with steps or got a mistake in my explanation then feel free to ask me ~
Question 3 on math!
Please help me 15 points
Answer:
2nd one
Step-by-step explanation:
if you were to look on a grid the slope would point up
Lisa cut out 36 paper snowflakes to decorate her room.
Then her brother gave her 28 paper snowflakes that he had made.
If she chooses to use only half of the snowflakes to decorate, how many will
she have left over?
Answer: 32
Step-by-step explanation:
We know that the original number of paper snowflakes was 36, plus 28 given by her brother. The new total would be 64 paper snowflakes and she only uses half of the paper snowflakes. The answer would be 32.
Find the area of the shaded region. Round to the nearest hundredth where necessary. Hint: Could you find the radius?
Answer:
13.72 cm²
Step-by-step explanation:
The formula to find the area of a shaded region: Area of the bigger shape - area of the smaller shape.
The formula to find the area of a square: [tex]a^{2}[/tex], where [tex]a[/tex] is the side.
The formula to find the area of a circle: [tex]\pi r^{2}[/tex], where [tex]\pi[/tex] is 3.14 or [tex]\frac{22}{7}[/tex] or 3.142 or similar, [tex]r[/tex] is the radius (diameter ÷ 2).
1) Find the area of the circle using the formula. The radius is 4 because the diameter is 8 (8 ÷ 2 = 4).
= [tex]\frac{22}{7}*4^{2}[/tex]
= [tex]\frac{22}{7}*16[/tex]
= 50.285
2) Find the area of the square using the formula.
= [tex]8^{2}[/tex]
= 64
3) Apply: area of the bigger shape - area of the smaller shape.
= 64 - 50.285
= 13.715
4) Round it off to the nearest hundredth.
= 13.72
15 x 18 + 12 ÷ 3 + 9
1. 15 x 18 =270
2. 270 + 12 divided by 3 + 9
3. 12 divided by 3 = 4
4. 270 + 3 + 9
5. 270 + 3= 273
6. 273 + 9 = 282
The answer is 282.
Answer:
283
Step-by-step explanation:
[tex]15 \times 18 + 12 \div 3 + 9 \\ 270 + 4 + 9 \\ 283[/tex]
By using BODMAS rule
Before adding the 12 u have to divide 12 by 3 =4 then u will add 4
Answer:
Your wrong the correct answer is 283
Step-by-step explanation:
[tex]15 \times 18 + 12 \div 3 + 9 \\ = 270 + 4 + 9 \\ = 283 \\ [/tex]
{ The algorithm, multiplication and division comes first, then addition}
Help would be very appreciated!!
11 points
Answer:
29 candy bars
Step-by-step explanation:
13 movie pases= $9.50x13= $123.50
3 gift cards= $25×3 =$75
amount of money she has left over to buy candy bars = $250- $75- $123.5 = $51.50
Amount of candy bars she can buy = $51.50÷$1.75 = 29.43 candy bars, but u can only buy full candy bars and there for 29 candy bars is the final answer
The square of a negative number is 8 more than 2 times the negative number. Find the number. The number =
Answer:
the number = -23 because there are different ways to do this don't bother
Use the associative property to rewrite the expression: -6+(3+7)
2x<5x-15 Solve check use x = 10)
Answer:
x= -5
Step-by-step explanation:
not right its -5
The intrest of 3 years on Rs.2400 is Rs 576. Find the rate of intrest...
Answer:
The answer is 8%
Step-by-step explanation:
Given,
Principle=Ra.2400
Time=3 years
Simple Interest= Rs.576
Rate=?
Now,
Rate=100*Simple Interest%P*T
=100*576%2400*3
=57600%7200
=8%
Therefore, the rate of Interest is
8%
(can you give me BRAINLIEST)
What number increased by ¼ of itself is equal to 30?
Answer:
x = 24
Step-by-step explanation:
let x be the number we want to determine its value
The statement x increased by ¼ of itself is equal to 30
is equivalent to :
[tex]x + \frac{x}{4}=30\\\\then[/tex]
[tex]\frac{4x+x}{4} = 30\\\\then[/tex]
[tex]\frac{5x}{4} = 30\\\\then[/tex]
5x = 4× 30
then
5x = 120
then
x = 120/5
then
x = 24
i have another very simple question before this thats worth 100 points go answer it. whats 2,231.5 milligrams to grams, dont delete this question for christ sake
Answer:
te paso mi canal subcribete y la respueta
Step-by-step explanation:
2.2315
mi canal es navegando con incognito subcribete
Question 1 of 10
How many solutions are there to the equation below?
x = -5
A. 2
B.1
C.0
D.25
Answer:
Answer is either 1 or 2
Step-by-step explanation:
Find the lateral surface area of the
cylinder 7mm 19mm. Round your answer to the nearest tenth
We can use the lateral surface area equation 2πrh. Assuming π = 3.14 we can plug all of the information into the equation to get 2 * 3.14 * 7 * 19.
multiplying everything you get 835.24, rounded to the nearest tenth is 835.2
If The radius of a quarter circle is 3 miles. What is the quarter circle's perimeter?
Answer:
6pi miles
Step-by-step explanation:
Answer: 6pi
formula for perimeter: pi*diameter
diameter=radius*2
diameter=3*2=6
6*pi=6pi