Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?
The possible values of b are 4 and 5
How to determine the possible numbers of b?The conditions are given as:
b is at least 2When 197 in base b has 4 digits.So, we start by converting 197 to base 2 and above.
This is done as follows:
197 to base 2
2 | 197
98 R 1
49 R 0
24 R 1
12 R 0
6 R 0
3 R 0
1 R 1
0 R 1
So, we have:
197 = 11000101 in base 2
11000101 has more than 4 digits.
This means that b cannot be 2
Using the above method of conversion, we have:
197 = 21022 in base 3197 = 3011 in base 4197 = 1242 in base 5197 = 525 in base 6197 = 401 in base 7See that as the base increases, the number of digits decreases.
The numbers in base 4 and 5 have 4 digits.
Hence, the possible values of b are 4 and 5
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Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
14r4y6
718y2
OA 24
14
B.
7y3
12
OC. 7r4y4
OD. 2x²y³
Reset
Next
The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
[tex]= \rm \dfrac{\left(14x^4y^6\right)}{\left(7x^8y^2\right)}[/tex]
[tex]\rm =\dfrac{7\cdot \:2x^4y^6}{7x^8y^2}[/tex]
[tex]\rm =\dfrac{2x^4y^6}{x^8y^2}[/tex]
[tex]\rm =\dfrac{2y^4}{x^4}[/tex]
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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Answer:
A
Step-by-step explanation:
imagine explaining
Using a standard six-sided die, janice rolled either a 2 or a 5on the last 6 rolls of the die. what is the probability of janice rolling a 2or a 5 on her 7th toss of the die?
Answer:
1/3
Step-by-step explanation:
probability = favorable outcomes/total possible outcomes
There are two favorable outcomes, 2 and 5.
There are 6 total possible outcomes.
Make your fraction.
2/6
reduce
1/3
3. The probability of winning a balloon dart game is 0.25. The odds of winning a ring toss game are 2:7. Which game gives you a better chance of winning?
Please help
Answer:
Ring toss game
Step-by-step explanation:
[tex]2:7[/tex] can be rewritten as [tex]\frac{2}{7}[/tex], which is [tex]\approx0.286[/tex].
We can now compare the probabilities of winning for each game.
[tex]0.286 > 0.25[/tex]
This means the odds of winning the ring toss game ([tex]0.286[/tex]) are higher than the odds of winning the balloon dart game [tex](0.25)[/tex].
Answers to the questions?
Based on the relationship of special angles, the values of x are:
1. x = 34
2. x = 9
3. x = 6
What are The Relationship of Angles Formed by a Transversal and Parallel Lines?Alternate interior angles are equals and corresponding angles are also equal.
Linear pair angles are supplementary.
1. Angles j and a are linear pair angles, therefore:
3x + 15 + 2x - 5 = 180
5x + 10 = 180
5x = 180 - 10
5x = 170
x = 170/5
x = 34
2. Angles m and g are corresponding angles, therefore:
4x + 12 = 2x + 30
4x - 2x = -12 + 30
2x = 18
x = 9
3. Angles c and v are alternate interior angles, therefore:
6x + 9 = 3x + 27
6x - 3x = -9 + 27
3x = 18
x = 6
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Quadrilateral abcd has the vertices a(-6,4) , b(-4,5) , c(-3,3) , d(-5,1) . determine if quadrilateral abcd is a rhombus
Answer:
No
Step-by-step explanation:
The defining property of a rhombus is that it has equal side lengths.
=============================================================
Finding all side lengths :
AB
⇒ √(-4 + 6)² + (5 - 4)²
⇒ √2² + 1²
⇒ √5 units
BC
⇒ √(-3 + 4)² + (3 - 5)²
⇒ √1² + (-2)²
⇒ √5 units
CD
⇒ √(-5 + 3)² + (1 - 3)²
⇒ √(-2)² + (-2)²
⇒ √8 units
DA
⇒ √(-6 + 5)² + (4 - 1)²
⇒ √(-1)² + 3²
⇒ √10 units
As all side lengths of the quadrilateral are not equal, ABCD is not a rhombus.
Kofi brought 6 books and 10 pencils from a store ama brought 3 books and 20 pencils of the same kind from the store if each of them paid $ 17000.00 from the items find the cost of each pencil each book two books and 4 pencils
Answer:
Answer by josgarithmetic(37226) (Show Source): You can put this solution on YOUR website!
system%2810b%2B6p=17000%2C3b%2B20p=17000%29
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let +a+ = the cost of 1 pencil
Let +b+ = the cost of 1 book
---------------------------
(1) +6b+%2B+10a+=+17000+
(2) +3b+%2B+22a+=+17000+
----------------------
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +6b+%2B+44a+=+34000+
(1) +-6b+-+10a+=+-17000+
-------------------------
+34a+=+17000+
+a+=+500+
and
(1) +6b+%2B+10a+=+17000+
(1) +3b+%2B+5a+=+8500+
(1) +3b+%2B+5%2A500+=+8500+
(1) +3b+=+8500+-+2500+
(1) +3b+=+6000+
(1) +b+=+2000+
------------------
Step-by-step explanation:
IT,LL
HELP
(05.06)Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Which graph best represents the scenario described?
The graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Based on the information given we can say graph third represents the situation.
First Keisha ran to swim practice so the line first increases and then she but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes which means the line should be constant.
Again they both ran so line increases.
Then they both stayed for 1 hour, so the line should be constant.
Thus, the graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
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Onyx surveys students at his school and finds that 80% have a pet. He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
To estimate this probability, he lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet and 5 represent a student who does NOT have a pet. He then has a computer randomly select 4 numbers and repeats this 20 times.
Based on this simulation, what is the estimated probability that at least one student who have NO PETS?
Represent your answer as a decimal and show your work as to how you determined the answer. pls help this one will give you 50 points
The estimated probability that at least one student who have NO PETS is 1/4.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Onyx surveys students at his school and finds that 80% have a pet.
He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet, and 5 represent a student who does NOT have a pet.
He then has a computer randomly select 4 numbers and repeats this 20 times.
The estimated probability that at least one student who have NO PETS
= 1/4
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2. make sure you show all your work for full points. what is z?
Answer:
I don't understand what the means
The perimeter of a square is 56cm. State the length of one of its sides.
Answer:
The length of one of the sides would be 14 cm.
Step-by-step explanation:
There are 4 sides to a square and the total perimeter is 56 cm meaning that we need to divide 56 by 4 to get the length of one side. 56 divided by 4 is equal to 14 cm, getting your answer. I hope this helps! Have a great day! :)
Here are four digit cards 6 5 5 7
arrange the cards to give the greatest possible answer to the calculation
Answer:
7 6 5 5
Step-by-step explanation:
the highest numbers should go in the leftmost digits place, as these are worth more
here, we put 7 in the thousands place, which is 2 thousand higher than if we put 5 in the thousands place
What is the surface area? 2 mm 3 mm 1 mm square millimeters
What is the surface area? 2 mm 3 mm 1 mm square millimeters.
[tex] \mathbb{SOLUTION:} [/tex][tex] \sf{SA = 2mm \times3mm \times 1mm } [/tex][tex] \sf{SA = 2x(2 \times 3 + 2 \times 1 + 3 \times 1)}[/tex][tex] \sf{SA= 22 \: square \: millimeters^{2} } [/tex]••••••••••••••••••••••••••••••••••••••••••••
- Hence,The square millimeters is 22sqm².
"Problem has been Solve"
(ノ^_^)ノ
Answer :
Surface area is 22mm²
Required solution :
After noticing the question we got to knew that we need to calculate the surface area of cuboid and we've been provided with the values of length, breadth and height of it.
★ Surface area of cuboid :
S.A. =2 (lb + lh + hb)Substituting values,
>> S.A. = 2 (2 × 3 + 2 × 1 + 3 × 1)
>> S.A. = 2 (6 + 2 + 3)
>> S.A. = 2 (8 + 3)
>> S.A. = 2 (11)
>> S.A. = 2 × 11
>> S.A. = 22
Can someone help me with 2. I will reward brainliest
Answer:
[tex]\tan 2 x = \dfrac{24}7[/tex]
Step by step explanation:
[tex]\textbf{2)}\\\\\text{Given that,} \\\\~~~~~\cos x = -\dfrac 45\\\\\implies \cos^2 x = \dfrac{16}{25}~~~~~~~~~~;[\text{Square both sides}]\\\\\implies 1- \sin^2 x= \dfrac{16}{25}\\\\\implies \sin^2 x = 1- \dfrac{16}{25}\\\\\implies \sin^2 x = \dfrac{9}{25}\\\\\implies \sin x =\pm\sqrt{\dfrac{9}{25}}\\\\\implies \sin x = \pm \dfrac 35\\\\[/tex]
[tex]\text{Since,}~ \pi \leq x \leq \dfrac{3\pi}{2}, ~ \text{the angle lies in the 3rd quadrant, where}~ \sin x ~ \text{is negative.}\\\\\text{So,}~ \sin x = -\dfrac 35[/tex]
[tex]\text{Now,}~\\\\\tan x = \dfrac{\sin x }{\cos x} = \dfrac{-\tfrac 35}{-\tfrac 45} = \dfrac 35 \times \dfrac 54 = \dfrac 34\\\\\\\tan 2x =\dfrac{2 \tan x }{ 1- \tan^2 x}\\\\\\~~~~~~~~~=\dfrac{2 \left( \tfrac 34 \right)}{1- \left( \tfrac 34 \right)^2}\\\\~~~~~~~~~=\dfrac{\tfrac 64}{1-\tfrac {9}{16}}\\\\\\~~~~~~~~~=\dfrac{\tfrac 32 }{\tfrac 7{16}}\\\\\\~~~~~~~~~=\dfrac 32 \times \dfrac{16}7\\\\\\~~~~~~~~~=\dfrac{24}7[/tex]
what is the value of x if 105% of 90 is equal to 200% of x?
help please it says name the property
ABC is shown on the coordinate plane below
What is the perimeter of △ABC? If necessary, round your answer to the nearest tenth.
Using the distance formula, the perimeter of triangle ABC is approximately 40.5 units.
What is the Perimeter of a Triangle?Perimeter = sum of all three sides.
Use the distance formula, [tex]d = \sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex] to find the distance between each of the vertices of the triangle.
The given vertices are:
A = (-6, 4)B = (8, -1)C = (0, -9)AB = √[(8−(−6))² + (−1−4)²]
AB = √221
AB ≈ 14.9 units
BC = √[(8−0)² + (−1−(−9))²]
BC = √128
BC ≈ 11.3 units
AC = √[(−6−0)² + (4−(−9))²
AC = √205
AC ≈ 14.3 units
Perimeter of △ABC = 14.9 + 11.3 + 14.3
Perimeter of △ABC ≈ 40.5 units
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Match the tan R, cos R and sin R to the correct ratios
What is the exact value of x?
Click the keyboard icon to type your answer using the math keyboard. If needed, use "/" to create a fraction.
x
8
60°
Jade and chet get a weekly allowance plus x dollars for each time the pair walks the dog. they plan to save 40% of their combined earnings in one week to purchase a new app for their smart tablet. their earnings in a certain week are represented in the table. earnings ($) jade 8+2x chet 4x+6 if their parents pay $2.50 each time they walk the dog, how much money will they have to purchase the app?
The amount of money Jade and chet will have to purchase the app is $11.6
How to solve equation?Jade = 8 + 2xChet = 4x + 6Where,
x = $2.50
Amount each earned:
Jade = 8 + 2x
= 8 + 2(2.50)
= 8 + 5
= $13
Chet = 4x + 6
= 4(2.50) + 6
= 10 + 6
= $16
Combined earnings = $13 + $16
= $29
Amount planned to save = 40% of combined earnings
= 40% × $29
= 0.4 × 29
= $11.6
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When flipping a penny, what is the theoretical probability of landing on heads? What is the theoretical probability of landing on tails?
Answer:.5 for either side
Step-by-step explanation:there are two sides, both equally likely so their probability must be equal and sun to 1. This condition is met when both probabilities are .5
Answer:
50/50 probability
Step-by-step explanation:
x-3y=4
2х-бу=Q
I’m trying to find the value of Q.
Answer:
Q=8
Step-by-step explanation:
Just multiply the entire first function by 2
therfore
(x-3y=4) * 2
therefore
=2x-6y=8
This is the same as the second function and in it, the coefficient of x is 2, therefore
Q=8
Help For points
-100
-120
-140
Answer:
x = 140°
Step-by-step explanation:
the secant- secant angle 10° is half the difference of the intercepted arcs
10° = [tex]\frac{1}{2}[/tex] (30 - ? )° ( multiply both sides by 2 to clear the fraction )
20° = 30 - ? ( subtract 30° from both sides )
- 10 = - ? ( multiply both sides by - 1 )
10° = ?
the lower arc is a semicircle = 180°
the sum of the arcs in a circle = 360° , then
x = 360° - 180° - 30° - 10° = 360° - 220° = 140°
Which represents the polynomial written in standard form?
8x²y²-3x³y + 4x²-,7xy³
O −7xy³ + 8x²y² – 3x³y + 4x4
○ 4x² - 7xy³_ 3x³y + 8x²y²
O
2
O 4x4 + 8x²y²-3x³-7xy³
2
O-7xy³ - 3x³y + 8x²y² + 4x²
2
The polynomial written in standard from is -7xy³ - 3x³y + 8x²y² + 4x².
How to write polynomial in standard form?The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
In other words the terms are arranged by decreasing order of degrees.
The degree of a polynomial is the exponential value of the variables.
Therefore, the polynomial written in standard from in the options is as follows:
-7xy³ - 3x³y + 8x²y² + 4x²
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using suitable property find 1/2*3/7-5/7*1/2+2
Answer:
13/7
Step-by-step explanation:
Method 1 :
1/2*3/7-5/7*1/2+2 = (3/14)- (5/14) + 2
= -2/14 + 2
= -2/14 + 28/14
= 26/14
= 13/7
Method 2 :
1/2*3/7-5/7*1/2+2 = (1/2) [3/7 - 5/7] + 2
= (1/2)(-2/7) + 2
= (-1/7) + 14/7
= 13/7
What figure is graphed from the following points? Graph the figure. (6, 3) (9, 3) (9, 9)
Answer:
RIght triangle
Step-by-step explanation:
Solve number 11 pls
Answer:
b. x = 123
Step-by-step explanation:
Which statement proves that quadrilateral JKLM is a kite?
The statement that proves that quadrilateral JKLM is a kite is (b) LM = JM = 3 and JK = LK = √17
The complete questionSee attachment for the complete question, the graph and the options
How to determine the true statement?The coordinates of the quadrilateral are:
J = (4,5)
K = (5,1)
L = (1,2)
M = (1,5)
Calculate the lengths of the kite using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]JK = \sqrt{(4 -5)^2 + (5 -1)^2} = \sqrt{17[/tex]
[tex]LK = \sqrt{(1 -5)^2 + (2 -1)^2} = \sqrt{17[/tex]
[tex]LM = \sqrt{(1 -1)^2 + (5 -2)^2} = 3[/tex]
[tex]JM = \sqrt{(1 -4)^2 + (5 -5)^2} = 3[/tex]
On a kite, the adjacent sides are of equal lengths
Because LM = JM = 3 and JK = LK = √17, we can conclude that the quadrilateral JKLM is a kite
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Ok, so I have a math assignment that is due on Monday (so in 2 days), but I don't understand it. Here are the instructions:
You buy a pair of jeans at a department store.
Jeans_____ $39.99
Discount___ -10.00
Subtotal____ 29.99
Sales Tax___ 31.94
I have the first two questions done for this question, and I just need help on the last one. Here it is:
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The percent of markup is __%.
Can anyone please help me?
Thanks!
What is the answer to 5x+5y=0 -8x+y=36 in ordered pairs?
Fill in the missing numbers:
Answer:
Step-by-step explanation:
2| 1 -3 -10 24
| 2 -2 -24
_______________
1 -1 -12 |0
b=2
c=-1
d=-2