If [tex]251_x\equiv100_{10}[/tex], then this translates to the equation
[tex]251_x = 2x^2 + 5x + 1 = 100[/tex]
Solve for [tex]x[/tex].
[tex]2x^2 + 5x = 99[/tex]
[tex]2\left(x^2 + \dfrac52 x\right) = 99[/tex]
[tex]2 \left(x^2 + \dfrac52 x + \dfrac{25}{16}\right) - \dfrac{25}8 = 99[/tex]
[tex]2 \left(x + \dfrac54\right)^2 = \dfrac{817}8[/tex]
[tex]\left(x + \dfrac54\right)^2 = \dfrac{817}{16}[/tex]
[tex]x + \dfrac54 = \pm \dfrac{\sqrt{817}}4[/tex]
[tex]x = \dfrac{-5\pm\sqrt{817}}4[/tex]
though it is a bit unusual (but not entirely out of the question) to have an irrational base number system.
In case you meant [tex]100_2[/tex] on the right side, then [tex]100_2 = 2^2 = 4_{10}[/tex], so that
[tex]2x^2 + 5x + 1 = 4 \\\\ 2x^2 + 5x - 3 = 0 \\\\ (x+3) (2x-1) = 0 \\\\ x=-3 \text{ or } x = \dfrac12[/tex]
which at first glance seem like more reasonable choices of base.
Find the rate of change for the given table of values.
Answer:
-40
Step-by-step explanation:
First you have to look at the difference between 8 and 10. which is 80, then because it takes two steps to go from 8 to 10 you divide 80 by two, which is 40. And because the values are decreasing it is -40.
The table shows the information about the length of time, in minutes, it took students to do their maths homework.
Draw a histogram.
The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart. The histogram for the given data is attached with the answer below.
What is a histogram?The histogram is a diagram with rectangles whose width is similar to the specified range and whose area is equal to the regularity of variables.
The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart.
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look at image.............
Answer:
answer is -3 ....is this correct
What is the sum of k° + i°?
180°
360°
110°
290°
Answer:
k+i =290
Step-by-step explanation:
The three angles added together form a circle, which is 360 degrees
k+i + 70 = 360
We want to find the sum of k+i, so we subtract 70 from each side
k+i + 70-70 = 360-70
k+i =290
whats the distance between -3 and -12
Answer:
9
Step-by-step explanation:
We can just count from -3 to -12 and get 9 as the distance
Assume that all conditions are met. The mean of the differences was 1. 33 and the standard deviation of those differences was 2. 90. What is the test statistic for this procedure?.
The test static used for this procedure is Aspin Welch's t-test.
What is Aspin Welch's T-test?
A variation of the Student's t-test used to determine if two sample means are substantially different is known as the Aspin Welch's T - test for Unequal Variances (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.
The means being equal is the test's null hypothesis.The notion that the means are not equal serves as the test's alternate hypothesis.Formula for Aspin Welch's T - test
The t-statistic in Aspin Welch's T-test is given as,
t = [tex]\frac{X' - X}{\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } }[/tex]
Here, X' is the mean of the sample
X is the mean of the population
S1 and S2 are the respective standard deviations for the two samples
N1 and N2 are the respective strength of samples.
Calculating t-statistic for Aspin Welch's T-test
Given that,
X'-X = 1.33
[tex]\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } = 2.90[/tex]
∴ t = 1.33/2.90
t=0.458
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In a school, lessons are 55 minutes long.
A maths lesson starts at 9:15am
At what time does the lesson end?
Answer:
6:10am from my point of view
Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.
Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.
Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
The correct option regarding whether the triangles are similar is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
What are similar triangles?Similar triangles are triangles that have congruent angles, that is, angles with the same measure.
Considering that the sum of the internal angles of a triangle is of 180º, the third angle of triangle FGH is given as follows:
98.6 + 61.1 + x = 180
x = 180 - (98.6 + 61.1)
x = 20.3º.
The second triangle has an angle of 20.3º, hence they are not similar, and the correct option is given by:
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.
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convert the Function to Degrees Fahrenheit:
3. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)? (2 points: 1 point for each transformation)
Note: The conversion rule for Celsius to Fahrenheit is .
F(t)=95(-0.30(t-12)2+40)+32
f(t)=-0.54(t-12)2+72+32
4. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24. (2 points: 1 point for each row)
t
0
12
(12,24)
c(0)=95(24)+32
24
5. Use the conversion formula to write the equation for the new function, F(t).
(4 points: 2 points for setting up the equation, 2 points for the answer)
Hint: Substitute the equation for C(t) into .
6. Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted points to sketch out the graph of F(t). (3 points: 2 points for correct coordinates, 1 point for correct shape)
7. Compare the graph in question 6 (F(t)) with the graph in question 2 (C(t)). What changes were made to the graph of C(t) to transform it to F(t)? (1 point)
The changes that transform C(t) to F(t) is that the function C(t) is stretched vertically to form the function F(t)
How to transform the function?The Fahrenheit function
The Celsius function is given as:
C(t) = -0.30 (t – 12)² + 40
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
Hence, the Fahrenheit function is F(t) = 9/5 * C(t)
Convert values from Celsius to Fahrenheit
The values are t = 0, 12 and 24.
So, we have:
F(0) = -0.54(0 - 12)² + 72 = -5.76
F(12) = -0.54(12 - 12)² + 72 = 72
F(24) = -0.54(24 - 12)² + 72 = -5.76
The new function F(t)
The conversion from Celsius to Fahrenheit is
F(t) = 9/5 * C(t)
So, we have:
F(t) = 9/5 * (-0.30 (t – 12)² + 40)
Expand
F(t) = -0.54(t – 12)² + 72
Hence, the new function is F(t) = -0.54(t – 12)² + 72
The graph of function F(t)
See attachment for the graph of function F(t)
The changes that transform C(t) to F(t)
We have:
C(t) = -0.30 (t – 12)² + 40
F(t) = 9/5 * C(t)
The above implies that the function C(t) is stretched vertically to form the function F(t)
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Jim’s Gym has an initial fee of $300 to join the gym and then charges $3 per visit. Sally’s Salon has an initial fee of $250 and then charges $5 per visit. Write a system of equations that represent the total fees charged for each plan. How many visits does it take before the plans are equal? Separate your equations and final number of visits by comas
The system of equation is y = 300 + 3x and y = 250 + 5x and the number of visits is 25
The system of equationsThe given parameters are:
Jim's Gym
Initial fee = $300Charges = $3 per visitSally's Salon
Initial fee = $250Charges = $5 per visitThe equation is calculated as:
Total (y) = Initial * Charges * Number of visits (x)
So, the system of equation is
y = 300 + 3x
y = 250 + 5x
Number of visits before the plans are equalWe have:
y = 300 + 3x
y = 250 + 5x
Substitute y = 300 + 3x in y = 250 + 5x
300 + 3x = 250 + 5x
Evaluate the like terms
-2x = -50
Divide by -2
x= 25
Hence, the number of visits is 25
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In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that four of the five digits are the same.
The probability that four of the five digits are the same is 0.036.
There are 10,000 (10*10*10*10) possible sequences. There are 4C3 ways, 4, of having exactly three digits be the same value. The differing digit can be any of the four positions. There are 10P2 ways, 90 (10*9), to choose the digits of the sequence since we have 10 choices for the digit to be repeated, then 9 more options or the differing digit. The product of the combination arrangements and permutation selection, 4*90, shows there are 360 sequences with three of the same digit. Thus the probability is 360/10,000 or 0.036 or 3.6%.
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MATHEMATICS
Find (A-B) n B when A={a,e,i,o,u} and B={a,b,c,d}
a.
b. A
zia
d. A-B
Answer:
( A - B).
A = { a, e, I, o, u}
B = { a, b, c, d }
{ e, I, o, u}
A - B = subtracting elements of B from A ( all the common elements)
Which table represents a proportional relationship?
how do u not know this
Step-by-step explanation:
my guy
A chemical company sells a specialized industrial lubricant in 20 liter containers. A
random sample of the latest production lot shows the contents of 10 containers to be
20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, and 20.2 liters. Find the
standard deviation of the sampled containers' contents.
A. o = 0.55
B. o = 0.53
C. o = 0.36
D. o = 0.42
The standard deviation of the sampled containers' contents is 0.36
How to determine the meanData = 20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, 20.2Number of data (n) = 10Summation of data = 20.72 + 20.6 + 20.71 + 20.92 + 19.79 + 20.93 + 20.09 + 20.27 + 20.49 + 20.2 = 204.72Mean (μ) =?Mean = summation of data / number
μ = 204.72 / 10
μ = 20.472
How to determine the standard deviationData = 20.72, 20.6, 20.71, 20.92, 19.79, 20.93, 20.09, 20.27, 20.49, 20.2Number of data (n) = 10Mean (μ) = 20.472Standard deviation (σ) =?σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)² + (x₆ - μ)² + (x₇ - μ)² + (x₈ - μ)² + (x₉ - μ)² + (x₁₀ - μ)²] / n]
σ = √[[(20.72 - 20.472)² + (20.6 - 20.472)² + (20.71 - 20.472)² + (20.92 - 20.472)² + (19.79 - 20.472)² + (20.93 - 20.472)² + (20.09 - 20.472)² + (20.27 - 20.472)² + (20.49 - 20.472)² + (20.2 - 20.472)²] / 10]
σ = 0.36
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Determine the seating capacity of an auditorium with 34 rows of seats if there are 16 seats in the first row, 20 seats in the second row, 24 seats in the third row, and so on.
Answer:
2788.
Step-by-step explanation:
This is represented by an arithmetic series with first term 16 and common difference 4.
The number of rows n = 34.
The capacity
= sum of 34 terms
= (34/2)[2*16 + 4(34-1)]
= 2788.
Answer:
2788
Step-by-step explanation:
16,20,24,.. This is a arithmetic progression with common difference of 4
Sn=? , d=4 , a =16 , n=34[tex]Sn=\frac{34}{2}[2(16)+(34-1)4] \\\\Sn=17[32+33(4)]\\\\Sn=17[164]\\\\Sn=2788[/tex]
The graph of the function f(x) = -(x+3)(x-1) is shown
below.
64-2
Mark this and return
6
A
2
-2-
-4
-6
2
4
6
X
Which statement about the function is true?
O The function is positive for all real values of x where
x < -1.
The function is negative for all real values of x where
x <-3 and where .x > 1.
O The function is positive for all real values of x where
x > 0.
O The function is negative for all real values of x where
x <-3 or x>-1.
Save and Exit
Next
Submit
The true statement about this function is that: B. the function is negative for all real values of x, where x < -3 and where x > 1.
What is a function?A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.
By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.
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help me please eeeeeeeeee
Answer:
A
Step-by-step explanation:
Fundamental Theorem of Algebra:
This states that any polynomial with degree n will have n solutions which are real or complex.
Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.
End Behavior of Polynomial Functions:
So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.
In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.
Using these two things, we can exclude answers
B can't be the answer, it only has 3 zeroes, this has at least 4.
C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions
D can't be the answer, it has a positive leading coefficient so the right side would be going up
This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.
Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.
What is the length of GF?
units
Based on the calculations, the length of GF is equal to 26 units.
How to find the length of GF?In Geometry, the centroid of any triangle always divides the lines in a ratio of 2:1. Thus, G divides line B F as follows:
2DG = BD
2(9x + 2) = 40
18x + 4 = 40
18x = 40 - 4
x = 36/18
x = 2.
Similarly, G divides line A F as follows:
2GF = A F
GF = A F/2
GF = (19x + 14)/2
GF = (19(2) + 14)/2
GF = 52/2
GF = 26 units.
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Answer: 26 units
Step-by-step explanation: Trust Me!
The answer is correct on Edge. I did it and got it right!
Solve. Set up the Table.
$2,000 at 2.50% for 50 years.
$2,000 at 5.00% for 50 years.
Answer:
can you explain more i dont get what u mean if you mean 2,000 a year and you get 2.50% or 5.00% and you get it for 50 years your answer for each would be 50 and 100
What is the following product?
(√14-√3)(√12+√7)
O 2√√42+7√√2-6-√√21
O√√14-6+√√7
O√26+ √21-√15-/10
O2√42-√√21
Answer: [tex]3\sqrt{21}+7\sqrt{2}-6[/tex]
Step-by-step explanation:
[tex](\sqrt{14}-\sqrt{3})(\sqrt{12}+\sqrt{7})\\\\=(\sqrt{2}\sqrt{7}-\sqrt{3})(2\sqrt{3}+\sqrt{7})\\\\=4\sqrt{21}+7\sqrt{2}-6-\sqrt{21}\\\\=\boxed{3\sqrt{21}+7\sqrt{2}-6}[/tex]
The product on the equation is A = 2√42 - 6 + 7√2 - √21
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( √14 - √3 ) ( √12 + √7 )
On simplifying , we get
A = √14 ( √12 ) - √3 ( √12 ) + √14 ( √7 ) - √3 ( √7 )
A = √168 - √36 + √98 - √21
On further simplification , we get
A = 2√42 - 6 + 7√2 - √21
Therefore , the value of A is 2√42 - 6 + 7√2 - √21
Hence , the product is A = 2√42 - 6 + 7√2 - √21
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Question 2 of 10
If a basketball player missed 53 free throws out of 100, what fraction and
what percentage of free throws did the player make? Choose two answers.
Answer:
47/100 and 47%
Step-by-step explanation:
He missed 53 out of 100 so that means he made 47 out of a 100 and there you go... 47/100 and 47%
3 metres of material cost £1.56
Work out the cost of 5 metres of the same material.
Answer:
2.6
Step-by-step explanation:
1.56 ÷3 = 0.52 ( cost of 1 meter of material )5 × 0.52 = 2.6 ( cost of 5 meter of material )The distance between adelaide and melbourne is 450 miles. For the first 200 miles, Mila drives her car at X miles per hour. For the remaining distance, Mila drives her car at (X+30) mph. The average speed of the whole trip is 30 mph. What is the value of X?
5. Sally took money from her bank account to go
out of town for an audition. She spent $54.00
for a round-trip ticket and 1/2 of the remaining
money for her hotel bill. She spent $7.90 for
food and arrived home with $15.10. How much
money did Sally take from her bank account?
Answer:
110
Step-by-step explanation:
Sally takes $110 from her bank account if she spent $54.00 for a round-trip ticket.
What are expenses?It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.
We have:
Sally took money from her bank account to go out of town for an audition.
The expeses = (7.90 + 15.10) ÷ (1 - 1/2) = $46
Total money = 54 + 46
Total money = $110
Thus, Sally takes $110 from her bank account if she spent $54.00 on a round-trip ticket.
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HELP HELP HELP
I have so many 50 point easy algebra 1 questions, just look into my profile and click questions I really need help.
Tysm! :)
Find the interquartile range for a data set having the five-number summary: 6.6, 14, 21, 27.5, 36.4
A box plot has 5 data descriptions. The interquartile range for the given data set is 13.5.
How does a boxplot shows the data points?A box plot has 5 data descriptions.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.The given following information can be written as,
The minimum value in the data = 6.6The leftmost line in the box shows the first quartile = 14The middle line shows the median, also called the second quartile = 21The last line of the box shows the third quartile = 27.5The maximum value in the data = 36.4Thus, the interquartile range for the given data is,
Interquartile range = 27.5 - 14 = 13.5
Hence, the interquartile range for the given data set is 13.5.
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Identify the expression that has two terms.
6 x + 4
x/4
2 x
5
Answer:
A
Step-by-step explanation:
Comment
The first one. Such an expression requires an isolation plus or minus sign and two terms that are not alike.
Answer
A
Answer:
6x+4
Step-by-step explanation:
A term can be a constant(like 7,4,3 etc) or a variable (x,y etc) which is separated by a multiplication, division,addition or subtraction sign.
Brainliest + 25, Urgent
For all values of x, there is a function h such that 4h(x) = h(4x). What is the value of h(6) if h(24) = 20 ?
Ty!
The value of h(6) = 5
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
4h(x) = h(4x)
It is also given that
h(24) = 20
now to determine the value of h(6)
4* h(6) = h(6 *4)
4* h(6) = h(24)
4 * h(6) = 20
h(6) = 5
Therefore the value of h(6) = 5.
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what is the probability of hitting a triangle on this dashboard?
Answer: 9/110
Step-by-step explanation:
11*20=220
3*3/2*4=18
18/220=9/110
Answer:
P = 9/110
Step-by-step explanation:
Area of all triangles
[tex]4(\frac{(3)(3)}{2}) =4(\frac{9}{2}) =18[/tex]
Area of the rectangle
[tex](20)(11)=220[/tex]
Probability of hit
[tex]P=\frac{18}{220}= \frac{9}{110}[/tex]
Hope this helps
In the equation y=kx, where k is a constant. when y=12, then x=5. when y=60, what does x equal?
Answer:
If y = 60 then x = 25
Step-by-step explanation:
You know that when y = 12 then x = 5
So when y = 60, x = 25
The reason for this is because 12 * 5 = 60.
Which means that since the y = 12 was multiplied by 5, the x = 5 should be multiplied by 5 too.
Since 5 * 5 = 25, then we know that if y = 60, then x will equal 25.
Hope this helped! :D