Since
[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]
it follows that
[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]
Then
[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]
so that
[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]
We also have
[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]
so we can go on to say
[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]
If the long hand of a clock is 11 and short hand is 9what is the time .help please
in poker, a royal flush is a hand with the ace, king, queen, jack and 10 of all one suit and is the best possible hand in the game. what is the probablity of a royal flush in a 5 card hand
The probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.
The combination is a way of selecting a smaller number of sets from a larger number of sets in no particular order.
If selecting r items from a set of n items, in no particular order, we use combinations, using the formula:
nCr = n!/{r!(n - r)!}.
In the question, we are asked the probability of a royal flush in a 5 card hand.
The number of ways of selecting 5 cards from a deck can be computed using a combination, 52C5, as we have 52 cards in a deck, 5 cards are to be chosen and the order is not in concern.
52C5 = 52!/{5!(52 - 5)!} = 52!/(5!.47!) = (52*51*50*49*48)/(5*4*3*2*1) = 2598960.
The number of hands that make a royal flush is only 4. 4 from each suit.
Therefore, the probability = 4/2598960 = 1/649740 or 0.0001539%.
Therefore, the probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.
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Which of the following graphs shows the
solution set to 2x < 6 and 3x + 2 >
-4?
Answer:
The third picture
Step-by-step explanation:
Solve for x in both equations
2x<6
Divide both sides by 2:
x<3
3x+2>-4
Subtract 2 from both sides:
3x>-6
Divide both sides by 3:
x>-2
There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.
When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.
The circles are not filled in because the symbol is < and > rather than [tex]\leq and \geq[/tex]. When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.
In which of the following intervals does the trigonometric inequality sec(x) < cot(x) always hold true.
The inequality for sec (x) < cot (x) is; π/2 < x < π
How to express trigonometric inequality?
We are given that;
We want to find the intervals that the trigonometric inequality sec (x) < cot (x) always hold true.
This can also be expressed as;
1/cos (x) < 1/tan (x)
Now, this can happen only in the quadrant where tan (x) is negative and cos x is positive which is in fourth quadrant where;
π/2 < x < π
The inequality for sec (x) < cot (x) is; π/2 < x < π
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Answer:
C on edge 22 for Pre-Calculus
Step-by-step explanation:
pi < x< 3pi/2
I retook the unit test, put C, and got a 100. I promise it's right
Counting by thousands, write five numerals from 1578 onwards.
Answer:
1578 + 1000 = 2578
2578 + 1000 = 3578
3578 + 1000 = 4578
4578 + 1000 = 5578
5578 + 1000 = 6578
What is the volume of this rectangular prism? A rectangular prism with a length of 6 and one-fourth foot, width of 14 feet, and height of 3 feet.
Answer:
V = 262.5 ft.
Step-by-step explanation:
Volume = length × width × height
6.25 × 14 × 3
6.25 × 42
262.5
Can someone help me please?
Answer:
7.6 units
Step-by-step explanation:
Use law of sines
12 / sin C = b / sin B
sin B * 12 / sin C = b
sin (32) * 12 / sin(57) = b = 7.6
Find the area of a rhombus.
4
30°
Answer:
[tex]13.86[/tex]
Step-by-step explanation:
you should see 2 triangles with angle 60 bounded by two equal sides of 4
[tex]=2(\frac{1}{2} (4)(4)sin 60)\\=13.86[/tex]
ZA and ZB are
supplementary angles. If mA = (7x + 24)˚ and
m/B = (7x − 26)°, then find the measure of ZA.
-
The measure of ∠A is 115˚.
Given that, ∠A and ∠B are supplementary angles. ∠A=(7x + 24)˚ and ∠B=(7x − 26)°.
What are supplementary angles?Two angles are Supplementary when they add up to 180 degrees.
Now, ∠A+∠B=180°
⇒(7x + 24)˚+(7x − 26)°=180°
⇒14x− 2°=180°
⇒14x=182°
⇒14x=182°
⇒x=13°
Now, ∠A=7×13 + 24˚
⇒∠A=91˚+ 24˚=115˚
Therefore, the measure of ∠A is 115˚.
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Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60%, percent of their plants are flowers and 40%, percent are vegetables. They have 50 plants growing in the garden. How many vegetable plants do they have?
Answer:
20 vegetable plants
Step-by-step explanation:
In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!
Please help ill give whoever answers the best the brainliest answer :00
Answer: If for every independent unit(aka x), you multiply the dependent unit by the same amount(aka y).
Step-by-step explanation:
EXAMPLE:
(0,2) (1,6) (2,18) (3,54) (4,162)
As you can see, each time x increases by unit, you multiply the y unit by 3.
As an example, if you increase x by 4, you multiply the y unit by 3^4 = 81.
If this pattern is consistent with your whole table, you have an exponential function.
Hope this is useful.
A box contains 72 cups of fruit juice. one serving size is 12 cup. how many servings can be made from the fruit juice?
Answer:
6 servings
Step-by-step explanation:
Box = 72 cups
1 serving size = 12 cups
72 ÷ 12 = 6
What is the total number of digits used when the first 2002 positive even integers are written?
Please help, 25 points.
The total number of digits used when the first 2002 positive even integers are written is 4 digits
How to find the number of sequence?Using arithmetic sequence,
nth term = a + (n - 1)d
where
a = first termd = common differencen = number of termsa = 2
d = 2
nth term = 2 + (2002 - 1)2
nth term = 2 + 4002
nth term = 4004
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For every 5 minutes that Scarlett plays on the computer, she plays outside for 12 minutes. What is the ratio of minutes Scarlett plays on the computer to minutes she plays outside?
Answer:
5:12
Step-by-step explanation:
because of the new wife
Part b assume the statement is true for n = k. prove that it must be true for n = k + 1, therefore proving it true for all natural numbers, n. t hint: since the total number of dots increases by n each time, prove that d (k) + (k + 1) = d(k+1).
The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.
To prove that the statement is true for all natural numbers, n, we can use mathematical induction.
The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.
Base Case (n = 1):
First, let's prove the statement for the base case, n = 1.
For n = 1:
d(1) + (1 + 1) = d(1) + 2
Now, consider a single square with 1 dot.
In this case, d(1) = 1.
So, we have:
1 + 2 = 3
Now, let's consider a pattern of 2 squares (n = 2).
The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.
So, the statement is true for n = 1.
Inductive Hypothesis (Assume true for n = k):
Now, assume that the statement is true for some arbitrary natural number k.
That is, assume that: d(k) + (k + 1) = d(k + 1)
Inductive Step (Prove true for n = k + 1):
To prove that the statement is true for n = k + 1.
d(k + 1) + (k + 2) = d(k + 2)
Now, consider a pattern of (k + 1) squares.
By the inductive hypothesis, assume that the statement is true for k squares:
d(k) + (k + 1) = d(k + 1)
Now, let's add one more square to the pattern.
This square will have (k + 2) dots.
So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:
d(k + 1) + (k + 2)
And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).
Therefore:
d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)
Now, simplify:
d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)
So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.
Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.
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A group of researchers wanted to measure the impact of playing classical music at bedtime to infants. They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all. For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep. At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not. None of the answer choices Experimental Survey Observational Study A group of researchers wanted to measure the impact of playing classical music at bedtime to infants . They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all . For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep . At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not . None of the answer choices Experimental Survey Observational Study
Using statistical concepts, it is found that it is an experimental study, as the music played corresponds to an experiment.
What is an experimental study?It is an study where an intervention is applied to a sample, and the effect of this intervention is studied.
In this problem, the music played is the intervention, and it's effect on the time that it takes for the infants to be asleep, hence it is an experimental study.
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\Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
Are the triangles congruent? Why or why not?
Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
By the ASA postulate, it can be said that the triangle ABC and triangle MRQ are congruent. Thus, option B is correct, Yes, they are congruent by either ASA or AAS.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Using Angle Sum Property, in ΔMRQ
<M + <R + <Q= 180
<M + 42 + 85 = 180
<M = 180 -42
<M= 53°
Now, In ΔMRQ and ΔABC
<A= <R ,
<B = <M
AB = MR
Hence, By ASA criteria ΔMRQ ≅ ΔABC.
Thus, option B is correct, Yes, they are congruent by either ASA or AAS.
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Answer: Yes, they are congruent by either ASA or AAS.
Step-by-step explanation:
What's Part of a 1 minute and 5 seconds?
62.5 seconds
Step-by-step explanation:
[tex] {3}^{2x - 2} - 28( {3}^{x - 2} ) + 3 = 0[/tex]
solve for x.....
Answer:
x = 3, x = 0
Given expression:
[tex]3^{2x-2}-28\left(3^{x-2}\right)+3=0[/tex]
rewrite expression
[tex]3^{2x} \times 3^{-2}-28\left(3^{x} \times 3^{-2}\right)+3=0[/tex]
treat [tex]\sf \s3^{x}\:as\:u[/tex], then expression
[tex]u^2 \times 3^{-2}-28\left(u \times 3^{-2}\right)+3=0[/tex]
multiply both sides by [tex]\sf 3^{2}[/tex]
[tex]u^2-28\left u+27=0[/tex]
factor expression
[tex]u^2-27\left u - u + 27=0[/tex]
factor out common terms
[tex]u(u-27) -1( u - 27)=0[/tex]
collect into groups
[tex](u-1)( u - 27)=0[/tex]
set to zero
[tex]u =1, \ u=27[/tex]
Substitute [tex]\sf 3^x = u[/tex], to find x
[tex]3^x = 1, \ 3^x = 27[/tex]
[tex]3^x = 3^0, \ 3^x =3^3[/tex]
[tex]x= 0, \ x = 3[/tex]
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help me please maths
A. 64
B. 1/12
C. 1/64
D. 12
Answer:
Step-by-step explanation:
First, since they have the same base, you can join them. Because it is division, you have to subtract the exponents.
4^(-11/3 -(-2/3)) = 4^-9/3 = 4^-3
Negative exponents turn the base into a fraction and 4^3= 64
so the answer is C. 1/64
6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp
Answer:
6xp^24
Step-by-step explanation:
Basically, there is 24 6xp's which is 6xp^24.
Hope I explained well enough.
find the midpoint of the segment with end points (-2,-1) and (0,9)
Answer:
-1 , 4
Step-by-step explanation:
x = ( -2 + 0 ) ÷ 2
y = ( -1 + 9 ) ÷ 2
-2 ÷ 2 = -1
8 ÷ 2 = 4
( -1 , 4 )
Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth.
From the least to the greatest, the solutions are:
From the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two systems of the equation:
y = log (−5.6x + 1.3)
y = −1 − x
After plotting the above equation on the graph we will see two intersections point:
(-2.12, 1.12) and (0.221, -1.221)
So the least value is x = -2.12 ≈ -2.1
The greatest value is x = 0.221 ≈ 0.2
Thus, from the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
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Divide:
5 x minus 8 StartLongDivisionSymbol 45 x squared minus 42 x minus 48 EndLongDivisionSymbol
Which of the following represents the length of the rectangle?
9x - 48
9x - 23
9x - 6
9x + 6
The length of the Rectangle is 9x +6 , Option D is the right answer.
What is a Rectangle ?A rectangle is a polygon with four sides , four angles and four vertices , The opposite sides are parallel and equal .
An expression representing the area of Rectangle is given
One of the side is 5x -8
The other side = ?
As Area of Rectangle = Length * Breadth
It can be calculated by Dividing Area by Breadth
(45x² - 45x -48 ) / (5x -8)
= 9x +6
Therefore the length of the Rectangle is 9x +6 ,Option D is the right answer.
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Answer:
9x + 6
INCLUDED WHOLE PAGE!!
☆
EDGE2022; Good Luck :3!!!
find the area of the shaded regions.
Answer: [tex]7\pi[/tex]
Step-by-step explanation:
The area of the entire circle is [tex](\pi)(3^{2})=9\pi[/tex]
The area of each of the smaller circles is [tex](1^{2})(\pi)=\pi[/tex], so their combined area is [tex]2\pi[/tex].
By subtracting areas, we get the area of the shaded region is [tex]7\pi[/tex].
Plis help! Will give brainliest!
Answer:
Q1: 62
Q2: 13
Step-by-step explanation:
Just follow Order of operations, and you get the answers.
P arenthesis
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
40 points please help!!!!
use the 3rd icon to measure 30 and 60 degrees, Then connect them with a line and add a right angle.
Answer:
Not Possible
Step-by-step explanation:
It is not possible. While it does add up to 180, if one is 90 degrees, the rest must be 45 and 45, or your not getting anything.
Let me know if this helped !!
I need help desperately! Could someone explain this math concept for me please?
The inequality that represents the range of k so that inequality 1 has real solution is -3 < k < 5
How to determine the range?Inequality 1
x^2 + (k + 1)x + k + 4 > 0
The discriminant is calculated using
D = b^2 - 4ac
So, we have:
D = (k + 1)^2 - 4 * 1 * (k + 4)
Evaluate
D = k^2 + 2k + 1 - 4k - 16
This gives
D = k^2- 2k - 15
Factorize the equation
D = (k+ 3)(k -5)
Solve for k
k = -3 and k = 5
Express the k values as inequalities
-3 < k < 5
Inequality 2
The inequality cannot be read, because of the image quality
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Jake kept track of the number of minutes it took him to assemble sandwiches at his
restaurant.
Number of
sandwiches
Minutes
1
3
2
4
4
5
6
6
7
7
Four cards are dealt at random without replacement from an ordinary deck of 52 cards. If it is known that the four cards have different face values, what is the probability that the first two cards are spades
Step-by-step explanation:
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