The answer is √7.
What is Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Step-by-step explanation:
Using the pythagorean theorem, we know that
a^2 + b^2 = c^2
In this case,
c = 4, which means that a^2 + b^2 = 16
Since we know that a = 3, this means that a^2 is also 9. So, we know that b^2 = 16-9
Therefore, b^2 = 7
So, the answer is √7.
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which value is a solution to the inequality 9 - y >12?
Answer:
(A) -6
Step-by-step explanation: hope this helps!
Answer:
answer is -3 did like 5 days ago
A researcher investigated whether following a vegetarian diet could help to reduce blood pressure. For a sample of 85 people who followed a vegetarian diet for 4 months, the mean systolic blood pressure was 124 mmHg. For a sample of 75 people who followed a non-vegetarian diet for 4 months, the mean systolic blood pressure was 138 mmHg. Methods of statistics show that if a vegetarian diet had no effect on blood pressure, there would be less than 1 chance in 100 of getting these results. Does the result have statistical significance? Why or why not? Does the result have practical significance?
Answer:
Yes, the result does not have statistical significance
Yes, the result has practical significance
Step-by-step explanation:
An experiment or claim may be said to be statistically significant if it's occurence is likely not due to chance for a certain level of stated significance. From the scenario described, it is stated that if vegetarian diet has no effect on blood, then the result obtained wipukd likely occur in less Than 1 of 100 ; this is < 0.01. This means that the effect of vegetarian diet on blood could not have occurred by chance. Hence, result is statistically significant.
The result does have practical significance too, since there is a distinctive difference in blood pressure of non - vegetarians(138mmHg) and Vegetarians (124mmHg).
Derive the equation of the parabola with a focus at (2,4) and a directrix of y=8
Answer:
The equation of the parabola with a focus at (2,4) and a directrix of y=8 is,
48-8y=(x-2)²
Ethan had planned to visit his local post office on Saturday to exchange $400
or euros. The exchange rate for that day was $1 = 1.25 E
However, due to unforseen circumstances, Ethan arrived at the post office after
it closed on that day. He therefore had to wait until the following Monday to
exchange his $400 for euros. The exchange rate on Monday was $1 = 1.20 E
a) How many fewer euros did he receive due to this delay? |20
b) What percentage loss was caused by this delay?
The amount of fewer euros he would receive as a result of the delay is 20 E.
The percentage loss that was caused by the delay is -4%.
What is the fewer euros received and the percentage loss?
Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.
Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday
Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E
Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E
Difference = 500 E - 480 E = 20 E
Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1
Percentage loss = (480 / 500) - 1 = -0.04 = -4%
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A rabbit doubles every 6 months there are currently 5 rabbits the function f(x)=5(2)x models the rabbit population where x is the number of times the rabbit pupilation doubles how many rabbits will there be in two years?
Answer:
40 rabbits
Step-by-step explanation:
...
help please! I added extra points
Answer:
a
Step-by-step explanation:
Answer:
A. The first option.
Step-by-step explanation:
Using the distributive property you can see that when you distribute them you would get something like (8 x 4) + (3 x 4) = 44. The first option is the only one that states this.
Hope this helps :)
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\(\huge\underline\bold{A} \underline\frak{nswer :}\)
\(✠===============✠\)
\( \large \boxed{b.pound}\)\( \large\sf\to\green{explanation}\)
Pound is defined as the basic unit for weight in the Foot Pound Second (F.P.S) system and is equal to 16 ounces\(✠===============✠\)
The basic units for length or distance measurements in the English system are the inch, foot, yard, and mile. Other units of length also include the rod, furlong, and chain. survey foot definition. In the English system, areas are typically given in square feet or square yards.
\(✠===============✠\)
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mark me brainliest please
hey um, so i’m learning ab percentages in my math class so can someone please explain to me how to solve percent problems if that’s ok? thank you.
Answer:
It's pretty simple. For example, if it says there is a percentage increase on something like there is a jacket for $25 and there was a 15% increase, you multiply 25 by 1.15 to see what the new price is. But say if the same $25 jacket is on sale for 15%, then you can multiply 25 by .15, then subtract that from 25 or originally subtract the 15% from 100 which is 85 and multiply 25x.85 and get the answer directly.
Hope this helps! But this would be easier to explain with an example
The equation of the line is y=_. The slope indicates that the temperature decreases by 3.5 F for each 1000 foot increase in altitude
The slope of the function is m = -3.5, which indicates that the temperature decreases by 3.5 degrees for each 1000 feet increase in elevation.
The temperature at Sea level is 87 °F
What is the slope of a function?The slope of a straight line function is the ratio of the rise to the run of the function.
Parts of the question that appear missing includes; The slope and the temperature at Sea level is required.
A point on the table of the graph is that at 4 feet, the temperature is 73 °F
The rate at which the the temperature changes = -3.5 °F per 1,000 feet
The slope of the equation is therefore;
y - 73 = -3.5·(x - 4)
y = -3.5·x + 14 + 73 = -3.5·x + 87
y = -3.5·x + 87
The equation of the the line of the temperature above Sea level is an equation of a straight line, which is of the form; y = m·x + c
Where;
m = The slope of the function
By comparison, the slope of the equation of the line the function is; m = -3.5
The temperature at Sea level, which is the y-intercept is found at the point where x = 0, which gives;
y = -3.5 × 0 + 87 = 87
The temperature at Sea level is 87 °F
The slope of line of the graph of the function, m = -3.5
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( 25 POINTS ) simplify: \/ \'/ \/ \/ \/ \/ \/ \/ \
Answer:
-17/12
Step-by-step explanation:
║5/6 - 7/12║- ║5/3║
= ║10/12 - 7/12║ - ║5/3║
= ║3/12║- ║5/3║
= 3/12 - 5/3
= 3/12 - 20/12
= -17/12
A bag contains 8 counters labeled with the numbers 3, 4, 4, 5, 5, 6, 6, and 6. Select all of the true statements The probability of drawing a 2 is 0. The probability of drawing a 7 is 1. The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5. The probability of drawing a 3 or a 6 is 12 . The least likely number to draw is 4.
The true statements are, The probability of drawing a 2 is 0 and The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
What is probability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here the given , Total number of outcomes = N {3,4,4,5,5,6,6,6} = 8
Now probability = No of Favorable outcome/ Total outcome.
Here Option A , Number of 2 = 0.
Then probability of getting 2 = 0/8 = 0.
Option B, Number of 7 = 0
Then probability of getting 7 =0/8 = 0
Option C , Number of 5's = 2
probability of getting 5 = 2/8 = 1/4
Number of less than 5 = 3
Probability of getting less than 5 = 3/8
Here 1/4 > 3/8 . Then The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
Option D, Here least number in given is 3 not 5.
Hence the true statements are, The probability of drawing a 2 is 0 and The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
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the exact value of sin 5pi/12 is
The exact value of sin(5π/12) is (√6 + √2)/4
Calculating the exact value of sin 5pi/12From the question, we have the following parameters that can be used in our computation:
sin 5pi/12
Express properly
So, we have
sin(5π/12)
Convert the angle to degrees
This gives
sin(5π/12) = sin(5/12 * 180)
Evaluate
sin(5π/12) = sin(75)
The actual value of sin(75) is (√6 + √2)/4
This means that
sin(5π/12) = (√6 + √2)/4
Hence, the exact value of sin(5π/12) is (√6 + √2)/4
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The exact value of sin 5π/12 is (√6 + √2)/4
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Angle in trigonometry can be measured in either degree or radian.
π is a measurement in radian which is equivalent to 180° in degrees.
Therefore:
5π/12 = 5 × 180/12
= 75°
Therefore sin5π/12 = sin75°
sin75 = sin( 45+30) = sin45cos30+ cos 45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= √3/2√2 + 1/2√2
= (√3+1)/2√2
rationalizing;
(2√6 + 2√2)/8
dividing through by 2
=(√6 + √2)/4
therefore tan75 =(√6 + √2)/4
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Y=x^2 - x - 3, y=-3X + 5. What are the solutions Of this system of equations?
Answer: \((x,y)=\{(-4,17), (2,-1) \}\)
Step-by-step explanation:
\(x^2 -x-3=-3x+5\\\\x^2 +2x-8=0\\\\(x+4)(x-2)=0\\\\x=-4, 2\\\\x=-4 \longrightarrow y=17\\\\x=2 \longrightarrow y=-1\\\\\therefore (x,y)=\{(-4,17), (2,-1) \}\)
I need help with this PLEASE!!!
Answer:
See the image for marked congruences.
1. JM ≅ LM | Given
2. △JML is isosceles | definition of isosceles
3. ∠MJL ≅ ∠MLJ | isosceles triangle theorem
4. m∠MJL = m∠MLJ | definition of ≅
5. JK ≅ LK | Given
6. △JKL is isosceles | definition of isosceles
7. m∠KJL = m∠KLJ | isosceles triangle theorem
8. m∠MJL + m∠KJM = m∠KJL | adjacent angle theorem
9. m∠MLJ + m∠KMJ = m∠KLJ | adjacent angle theorem
10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM | transitive property of =
11. m∠MJL + m∠KJM = m∠MJL + m∠KLM | substitution
12. m∠KJM = m∠KMJ | subtraction
13. ∠KJM ≅ ∠KLM | definition of ≅
14. △KJM ≅ △KLM | SAS theorem
15. ∠JKM ≅ ∠LKM | CPCTC
16. KM bisects ∠JKL | definition of bisector
A bus holds 39 passengers. How many buses will 420 people need
Answer:
11 buses
Step-by-step explanation:
Y is a random variable that is distributed N(-16, 1.21). Find k such that Prob(-15.043 < Y ≤ k) = 0.1546. (Round your answer with 4 digits after the decimal.)
Transform Y to Z, which is distributed N(0, 1), using the formula
Y = µ + σZ
where µ = -16 and σ = 1.21.
Pr[-15.043 < Y ≤ k] = 0.1546
Pr[(-15.043 + 16)/1.21 < (Y + 16)/1.21 ≤ (k + 16)/1.21] = 0.1546
Pr[0.791 < Z ≤ (k + 16)/1.21] ≈ 0.1546
Pr[Z ≤ (k + 16)/1.21] - Pr[Z < 0.791] = 0.1546
Pr[Z ≤ (k + 16)/1.21] = 0.1546 + Pr[Z < 0.791]
Pr[Z ≤ (k + 16)/1.21] ≈ 0.1546 + 0.786
Pr[Z ≤ (k + 16)/1.21] ≈ 0.940
Take the inverse CDF of both sides (Φ(x) denotes the CDF itself):
(k + 16)/1.21 ≈ Φ⁻¹ (0.940) ≈ 1.556
Solve for k :
k + 16 = 1.21 • 1.556
k ≈ -14.118
Hurry please I will give brainly need this in about 15 mins help me help meee
Answer:
x = -2
Step-by-step explanation:
The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.
Using the above information, we can construct the equation:
3x + 2 = 2x
and solve it for x.
x = -2
The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.
True or false question please help :)
Answer:
TrueStep-by-step explanation:
:D
Can someone help? I don’t know the equation to use and how to solve. Thank you!! Anything will helps!
Answer:
\(x=55\\\)
Step-by-step explanation:
this is because the angles in a right angle should add up to 90
x is simplified to 2x and 20 is added to both sides
2x = 110
divide by 2 on both sides answer is 55
double check by doing the inverse
The triangle above has the following measures.
s = 29 m
r= 63 m
Find the m/Q.
Round to the nearest tenth and include correct units.
Show all your work.
The value of m∠Q as shown in the right-angled triangle below is 62.59°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
s = 29 m
r = 63 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(29/63)
m∠Q = cos⁻¹(0.46)
m∠Q = 62.59°
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A contractor better job at $750 for materials plus $43 per hour for labor. The total cost for the job can be modeled by C= 43H+ 750$.
Find the number of hours that he has for the job if the owner would like the total cost to be under $2000, rounded to the nearest hour.
The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.
To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.
Since the owner wants the total cost to be under $2000, we can set up the inequality:
43H + 750 < 2000
Now, let's solve this inequality for H, the number of hours:
43H < 2000 - 750
43H < 1250
Dividing both sides of the inequality by 43:
H < 1250/43
To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.
Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:
H < 29
Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.
By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.
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Find the volume of a pyramid that has a rectangular base that is 12 inches 10 inches and a vertical height of 9 inches.
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
Consider this equation. cos(0) = 4√47/41.
If 0 is an angle in quadrant IV, what is the value of sin(0)
Therefore, sin(0) = -√305/41 when 0 is an angle in quadrant IV.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It is used to solve problems in many fields, including engineering, physics, astronomy, and architecture. Trigonometry involves the use of functions such as sine, cosine, and tangent to relate the angles and sides of a right triangle. It also includes the study of trigonometric identities, equations, and graphs, as well as applications of trigonometry in real-world situations.
Here,
If 0 is an angle in quadrant IV, then cosine is positive and sine is negative. We can use the Pythagorean identity to find the value of sin(0):
sin²(0) + cos²(0) = 1
sin²(0) = 1 - cos²(0)
sin(0) = -√(1 - cos²(0))
substituting the given value of cos(0):
sin(0) = -√(1 - (4√47/41)²)
sin(0) = -√(1 - (16*47/41))
sin(0) = -√(1 - 736/41)
sin(0) = -√(305/41)
sin(0) = -(√305)/√(41)
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Determine the surface area and volume. Note: The base is a square.
Answer:
volume=60cm3, surface area=96cm2
Step-by-step explanation:
volume=1/3×(6×6)×5
=60cm3
surface area= 4(1/2×6×5)+(6×6)
=96cm2
A camp needs 900kg of food for 40 campers to last for 20 days. For how many days, will 540 kg of food last for 30 campers?
Answer:
The food will last for 16 days
Step-by-step explanation:
Proportions
We need to know how the variables depend on each other.
It's clear that:
The more campers, the more food the camp needs.
The more time, the more food the camp needs.
Therefore, the amount of food (F) is directly proportional to the number of campers (c) and the time (t).
This can be written as:
F = k.c.t
Where k is a constant that we'll be found by knowing the camp needs F=900 Kg of food for c=40 campers and t=20 days:
900 = k*40*20=800k
Thus:
k=9/8
And:
F = 9/8 c.t
We now need to find how many days will F=540 kg of food will last for c=30 campers. So we solve the equation for t:
t = 8/9 * F/c
t = 8/9 * 540/30
t = 16 days
The food will last for 16 days
Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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Anne made a recipe for a miniture bread loaves that called for 7/8 of a cup of whole-wheat flour. If the recipe made 7 equal sized loaves of bread, how many cups of whole-wheat flour did each loaf contain
Answer:
1/8 cups
Step-by-step explanation:
All you have to do is divide 7/8 and 7.
Let's do the problem together! :)
7 ÷ 7 = 1
8 1 = 8
And this is the work!
Hope this helped! :)
Point b is at (1,1) on a graph. transformed using matrix A
In the above scenario, The point that B is transformed to are coordinates (10, 6). This means that it is translated to the right by 9 units and upwards by 5 units.
In order to derive the new location of point B after the transformation by matrix A, we need to perform matrix multiplication of A with the column vector representing point B.
\(\left[\begin{array}{cc}8&2\\7&1\\\end{array}\right]\) = \(\left[\begin{array}{cc}1\\1\\\end{array}\right]\)
\(\left[\begin{array}{cc}(8 * 1) + &(2 *1)\\(7 *1)&(1 *1)\\\end{array}\right]\) = \(\left[\begin{array}{cc}10\\6\\\end{array}\right]\)
As a result, the converted point B is situated at (10, 6). As a result of the transformation provided by matrix A, point B has been translated to the right by 9 units (from x = 1 to x = 10) and upwards by 5 units (from y = 1 to y = 6).
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What is the distance between the following points?
Answer:
D. d = \(\sqrt{58}\)
Step-by-step explanation:
Use the distance formula: d = \(\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2} }\)
The two points are (6, -2) and (3, -9)
Plug the values into the formula:
d = \(\sqrt{(3 - 6)^{2}+ (-9 + 2)^{2} }\)
Simplify
d = \(\sqrt{(-3)^{2}+ (-7)^{2} }\)
d = \(\sqrt{9+ 49 }\)
d = \(\sqrt{58}\)
I hope this helps :))