Answer:
Yes, acute
Step-by-step explanation:
Because 10 and 12 add up to more than 16, it is possible to construct an acute triangle with these side lengths. Since 10^2 + 12^2 ≠ 16^2, we know that any triangle so constructed will not be a right triangle.
The measures 10, 12, and 16 can be the side lengths of a triangle because the sum of the two shorter sides must be greater than the longest side for a triangle to exist.
In this case, 10 + 12 is greater than 16, 16 + 10 is greater than 12, and 12 + 16 is greater than 10, satisfying the triangle inequality theorem. Therefore, a triangle can be formed.
Classifying the triangle: Using the Pythagorean theorem, we can determine that the triangle with side lengths 10, 12, and 16 is a scalene triangle, and since 10^2 + 12^2 is less than 16^2, it is an obtuse triangle.
You have a wire that is 74 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
32.55 cm
Step-by-step explanation:
Let x = the length of wire that becomes a circle.
Then 74 - x = the length of wire that becomes a square
Circumference of circle + perimeter of square = 74
1. Expression for the side of the square
P = 4s = 74 - x
s = ¼(74 - x)
2. Expression for the radius of the circle
C = 2πr = x
r = x/(2π)
3. Expression for the total area
[tex]\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}[/tex]
This is the equation of a parabola.
In standard form,
ƒ(x) = 0.1421x² -9.25x + 342.24
a = 0.1421; b = -9.25; c = 342.24
The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.
The vertex of a parabola occurs at
x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55
The circumference of the circle is 32.55 cm.
The graph below shows that the area of the circle is a minimum when x = 32.55 cm
How many minutes is it from 4:00 to 4:30
Answer:
30 minutes
Step-by-step explanation:
Just look at the minutes only. Since you need 4 o'clock to 4:30, its only 30 minutes.
Answer:
30 minutes
Step-by-step explanation:
All you have to do is subtract 4:30 and 4:00 and get 30 minutes.
Keio and Taylor relapse after school to train for the baseball team the ratio of the number of laps Kyle ran to the number that Taylor 2 to 3 Kyle ran six slabs how many laps did Taylor
Answer: 9 miles
Step-by-step explanation: 6 divided by 2 is 3 and 3 times 3 is 9.
6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find the probability that all 6 are type A-. b) Find the probability that at most 4 of them are type A-. c) Find the mean and standard deviation.
Answer:
a) 7.54189*10^-8
b) 0.99999999
c) E ( X ) = 0.39 , s ( X ) = 0.604
Step-by-step explanation:
Solution:-
- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.
- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.
- The random variable is assumed to follow binomial distribution.
- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:
X ~ Bin ( 6 , 0.065 )
Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:
P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )
a) Find the probability that all 6 are type A-
- We will pmf given above and set r = 6. And evaluate the resulting probability:
P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )
= p^6
= ( 0.065 )^6
= 7.54189*10^-8
b) Find the probability that at most 4 of them are type A-
- We will pmf given above and evaluate the following expression:
P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )
P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6
= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6
= 1 - 6.50923*10^-8 - 7.54189*10^-8
= 0.99999999
c) Find the mean and standard deviation.
- The mean E ( X ) of the defined random variable distributed binomially is given by:
E ( X ) = n*p = 6*0.065 = 0.39 people
- The mean s( X ) of the defined random variable distributed binomially is given by:
s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604
Histidine has 3 nitrogens. arrange the indicated nitrogens in decreasing order of basicity (1 = most basic, 3 = least basic). if there are fewer than 3 nitrogens in the molecule, leave that answer space blank. if two nitrogens have the same basicity, give them the same number. histidine
Answer:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
Step-by-step explanation:
The basicity of amino acids is as a result f the unshared pair of electrons in the Nitrogen atoms.
Part of the rule of basicity of organic compounds(amino acids) posits that:
The more unstable an electron pair is, the more basic it is.
From the diagram attached below;
Nitrogen 7 posses and unstable electron due to the lone pair of electron in the NH₃⁺ which renders it most basic .
Nitrogen 1 and 3 are in ring form thereby they are less basic But nitrogen 1 is more basic compared to nitrogen 3 because lone pair on Nitrogen 1 is not involved in resonance unlike Nitrogen 3 that is resonance stabilized (i.e alternating by a resonance effect).
Another phenomenon to deduce the basicity of Histidine is the effect of hybridization.
Basicity of Organic Compounds increases with decreasing s character.
Therefore, the trend of basicity is as follows: sp³ > sp² > sp
Because in sp; the lone pairs are most stable, hence least basic
And in sp³; the lone pairs are least stable; hence most basic.
Therefore; From the diagram attached below:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
Advertisers often refer to CPM (Cost per thousand people reached) when quoting advertising rates. If a website
promises to reach 23,000 people for $1,540, what is the CPM? (Round to the nearest dollar.)
a) $67
b) $108
c) $150
d) $185
Answer:
$67
Step-by-step explanation:
There are 23 thousand clicks, so as it pays per thousand you need to divide $1 540 by 23, which results in 66.9.... reacurring which when rounded is (a) for $67.
SOLVE X/5+3=2
A)-5
B)25
C)5
D)-1/5
Answer:
b 25
Step-by-step explanation:
Answer:
A)-5 if its without parenthasis around 5+ 3
Step-by-step explanation
2 minus 3 is -1 and -1 times 5 is -5
20 pts if you answer
I REPORT UNNECESSARY ANSWERS
Answer:
C) 1/12
Step-by-step explanation:
P(2) = 1/6
P(Tail) = 1/2
1/6 × 1/2
1/12
Brad is putting up a 10 foot diameter circular flower garden in his yard. He will put plastic edging along the flowerbed. How many feet of edging will Brad need to enclose his flower garden?
Answer:
10π feet, or about 31.42 feet
Step-by-step explanation:
Diameter = 2 times radius, so the radius is 5 feet.
The question is asking us for the circumference - the distance around the circle. Plug our radius into the formula.
C = 2πr
C = 2π(5)
C = 10π feet = about 31.42 feet
Answer:
20 Pi feet or 62.8318530718 ft
Step-by-step explanation:
Find the circumference
Pi X diameter
radius = 1/2 diameter
radius *2 = 20
20 * Pi
Perbandingan kelereng Faiz dan Bayu 4 : 11. Jumlah kelereng mereka 60 buah. Selisih kelereng keduanya adalah
The difference in the number of their marbles is 28 Buah.
The ratio of Faiz's marbles to Bayu's marbles is given as 4:11. If the total number of marbles they have is 60, you can find the number of marbles each of them has.
Let x be the common multiplier for both parts of the ratio. Then, Faiz has 4x marbles, and Bayu has 11x marbles.
The total number of marbles is the sum of their marbles:
4x + 11x = 60
Combine like terms:
15x = 60
Divide by 15 to find x :
x = 4
Now, substitute x back into the expressions for Faiz and Bayu's marbles:
- Faiz's marbles: [tex]\( 4x = 4 \times 4 = 16 \)[/tex]
- Bayu's marbles: [tex]\( 11x = 11 \times 4 = 44 \)[/tex]
The difference in the number of their marbles is [tex]\( 44 - 16 = 28 \)[/tex].
So, the correct answer is: C. 28 Buah
Complete question:
Perbandingan kelereng Faiz dan Bayu 4:11. Their total color is 60. The best color of them is ...
16 pieces
24 pieces
28 pieces
44 pieces
What is the expression of 8 more than a number x
"more" means added to, or addition. So 8 more than 'x' is:
x + 8
What is the greatest common factor
of 48 and 120?
Answer:
24
Step-by-step explanation:
Which measure of center would you use to compare the populations represented by the box plots?
Which measure of variability would you use to compare the populations represented by the box plots?
Answer:
Median and Interquartile range (IQR)
Step-by-step explanation:
I did it :)
Two lines are perpendicular if they cross a 45° angle true or false
Answer: False
Step-by-step explanation:
in the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
Answer:
71
Step-by-step explanation:
because the theorem is sum of the square
The answer is d. hypotenuse.
Here's why:
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
So, if you have a right triangle with legs of length a and b, and hypotenuse of length c, the equation would be: a^2 + b^2 = c^2.
Therefore, the sum of the squares of the legs (a^2 + b^2) is equal to the square of the hypotenuse (c^2).
The other options are incorrect because:
a. shorter leg: The theorem doesn't differentiate between the lengths of the legs, it simply states that the sum of their squares is equal to the square of the hypotenuse.
b. longer leg: Same as above, the theorem doesn't consider the individual lengths of the legs, just their squares.
c. sum of the angles: The Pythagorean Theorem deals with the sides of a right triangle, not its angles. The sum of the angles in any triangle is always 180 degrees.
Complete Question:
In the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
a. shorter leg
b. longer leg
c. sum of the angles
d. hypotenuse
Which equations are equivalent to y = two-thirds x minus 4 when written in slope-intercept form? Check all that apply.
3 x minus 2 y = 4
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
2 (x + 6) = 3 y
2 x minus 3 y = 4
Answer:
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
Step-by-step explanation:
y = two-thirds x minus 4
y = (⅔)x - 4
Multiply the entire equation by 3
3y = 2x - 12
2x - 3y = 12
Multiply both sides by -4
-4(2x - 3y) = -4(12)
Answer:
b
Step-by-step explanation:
what is the limit of the infinite series?
Answer:
Zero
Step-by-step explanation:
There is no solution to this.
A quarter is worth of a dollar. Haley needs to exchange dollar bills to get quarters to do her laundry in coin washers and dryers. How many quarters will she get for $13?
Answer:
52 quarters
Step-by-step explanation:
-We know that a quarter dollar is equivalent to $0.25
[tex]\$1=4 \ Quarters[/tex]
-Given that Haley has $13, we multiply this amount by 4 since $1 has 4 quarters to obtain the number of quarters:
[tex]Q=13\times 4\\\\=52[/tex]
Hence, Hayley will get 52 quarters.
I need another help again my bros
Answer:
a = 15.59 c= 31.18
27 tan 30 = a
c cos 30 = 27
c = 27/cos30
c = 31.18
What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units?
Given:
The parent function is [tex]f(x)=x^2[/tex]
We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.
Shift left 9 units:
The rule to shift the graph c units to the left is given by
[tex]y=f(x+c)[/tex]
where c is the positive real number.
Hence, to shift the graph 9 units to the left is given by
[tex]f(x)=(x+9)^2[/tex]
Vertical stretch by a factor of 4:
The rule to stretch the graph vertically by a factor of c is given by
[tex]y=cf(x)[/tex]
where [tex]c>1[/tex]
Hence, to stretch the graph vertically by a factor of 4, we have;
[tex]f(x)=4(x+9)^2[/tex]
Shifting 5 units up:
The rule to shift the graph c units upward is given by
[tex]y=f(x)+c[/tex]
where c is the positive real number.
Hence, to shift the graph 5 units upward is given by
[tex]f(x)=4(x+9)^2+5[/tex]
Therefore, the function [tex]g(x)=4(x+9)^2+5[/tex] is created from the graph [tex]f(x)=x^2[/tex] by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.
Hence, the graph g(x) is [tex]g(x)=4(x+9)^2+5[/tex]
The function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units is g(x) = 4*(x+9)^2 + 5.
Explanation:To generate the function g(x) from f(x) = x^2, you will perform several transformations on it:
A horizontal shift of 9 units to the left. To do this, you change the x inside the function to (x+9). A vertical stretch by a factor of 4. To do this, you multiply the whole function by 4.A vertical shift of 5 units up. To do this, you add 5 to the entire function.So, after performing these transformations to f(x) = x^2, you get the function g(x) = 4*(x+9)^2 + 5.
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What is twice a number minus 4 is less than three times the number?
Answer:
[tex]n > -4[/tex]
Step-by-step explanation:
Step 1: Convert into an expression
Twice a number minus 4 is less than three times the number
[tex]2n - 4 < 3n[/tex]
Step 2: Solve for the number
[tex]2n - 4 - 2n < 3n - 2n[/tex]
[tex]-4 < n[/tex]
Answer: [tex]n > -4[/tex]
John goel is to have more then -7 dollors in hisaccount by the end of this mounth. the varible d is the nuber of dollor in johns bank account at the end of the mounth. Whrite an lineqwalatiy in terms of d that is true only if john meets hif monthy goal
Answer:
d > - 7
Step-by-step explanation:
John is to have more then -7 dollars in his account by the end of this month.
Now, the variable d is the number of dollars in John's bank account at the end of the month.
Therefore, the inequality in terms of d that is true only if John meets his monthly goal will be
d > - 7 (Answer)
simplify: square root 108+square root 125-square root 75
Answer:
[tex]11\sqrt{3} + 5\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{108}+\sqrt{125} - \sqrt75}[/tex]
1. [tex]\sqrt{108} = 6\sqrt{3}[/tex]\
2. [tex]\sqrt{125} = 5\sqrt{5}[/tex]
3. [tex]\sqrt{75} = 5\sqrt{3}[/tex]
4. Add [tex]6\sqrt{3} + 5\sqrt{3} = 11\sqrt{3}[/tex]
your left with [tex]11\sqrt{3}+5\sqrt{5}[/tex]
Answer:
12
Step-by-step explanation:
Please help me idk this
Answer:
34.54 inches.
Step-by-step explanation:
The formula for the circumference of the circle is given as [tex]C=\pi d[/tex], where [tex]\pi[/tex] is rounded to 3.14 and d is the diameter of the circle, 11 inches. Simply plug these values into the equation for the circumference to get your answer:
[tex]C=\pi d\\C=(3.14)*(11)[/tex]
C = 34.54 inches
Answer:
34.54 inches
Step-by-step explanation:
C=πd
d=11
C = 11 * 3.14
C = 34.54 inches
Which set of three angles could represent the interior angles of a triangle? 26 degrees, 51 degrees, 103 degrees 29 degrees, 54 degrees, 107 degrees 35 degrees, 35 degrees, 20 degrees 10 degrees, 90 degrees, 90 degrees
Answer:
26 °, 51 °, 103 °
Step-by-step explanation:
-A triangle is a 3-sided regular polygon.
-The sum of it's interior angles add up to 180°.
-Only the 26 °, 51 °, 103 ° set add exactly up to 180° and therefore satisfies the triangle's interior angles condition.
Answer:
The answer A trust me
Step-by-step explanation:
Which name accurately describes the figure shown below and why?.
Answer:
the third answer is right
Step-by-step explanation:
its a rhombus because the 4 sides are of equal length and the opposite sides are parallel but there are no right angles.
A circle has a radius of 32 inches. Find the circumference of the circle to the nearest tenth. Use 3.14 for PI.
The calculation of the circumference of a circle with a radius of 32 inches, using 3.14 for PI, gives a result of 201.0 inches.
Explanation:The subject of this question involves calculating the circumference of a circle. The formula used to find the circumference of a circle is 2πr, where r is the radius of the circle. Here, π is approximated to 3.14 as given in the question, and the radius r is given as 32 inches.
Substituting the given values into the formula, we get circumference = 2 * 3.14 * 32 = 200.96 inches. Thus, the circumference of the circle to the nearest tenth is "201.0 inches."
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If sec0= 25/24 find cot0
Answer:
cot θ = 24/7
Step-by-step explanation:
This will be difficult to explain without a diagram, but let's proceed.
Since sec θ = 25/24 (secant θ is equal to hypotenuse/adjacent) the hypotenuse of the triangle is 25 and the side adjacent to θ will be equal to 24. To find the opposite side-length you can use the Pythagorean theorem.
25^2 = 24^2 + a^2 (You can use either a or b as the variable)
625 = 576 + a^2 (Subtract 576 from each side)
a^2 = 49
a = 7 (The sqrt of 49 is 7 | This is the side-length of the opposite side relative to θ)
Since cotangent is always adjacent/opposite:
cot θ = 24/7
A growth medium is inoculated with 1,000 bacteria, witch grow at rate of 15% each day. What is the population of the culture 6 days after inoculation?
Answer: the population of the culture 6 days after inoculation is 2313.
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^ t
Where
y represents the population after t days.
t represents the number of days.
b represents the initial population.
r represents rate of growth.
From the information given,
b = 1000
r = 15% = 15/100 = 0.15
t = 6 days
Therefore
y = 1000(1 + 0.15)^6
y = 1000(1.15)^6
y = 2313
A box contains 400 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1, P(not black) + P(not red) = 1. Do you agree with him? Complete the explanation to answer the question.
I (disagree/agree) with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Answer:
I agree with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Step-by-step explanation:
If we sum the probability of not black and probability of not red, we will get 1.
The probability of not black means probability of red i.e 50/450
The probability of not red means probability of black i.e 400/450.
When we add the probability, we get 1.
50/450 + 400/450 = 450/450 = 1
Invariably, the statement is same as finding probability of black and probability of red; just that the value are interchanged.