The numeral preceding and succeeding each of the following numerals.
Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.
Adding adds 1 to the unit digit.
Subtracting 1 gives 99 because 9 is the largest digit in base 10.
So A. 100 base 8
The largest digit in base 8 is 7, so
..., 77, 100, 101,...
B. 10000 base 7
What is the largest digit in base 7?
The largest digit in base 7 is 6, so
..., 6666, 10000, 10001, ...
Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:
509 + 1 = 510.
C. 305 base 6
5 is the largest digit in base 6, so
..., 304, 305, 310, ...
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In(2e^9) in logarithmic expression
I’m having trouble with all of the “In” section and very confused
In logarithmic form, we get In(2e^9)= ln(2)+9.
LogarithmsWe define the logarithm as the power to which any number must be raised to get few other values.Exponentiation is the reverse process of logarithm.We are given,
ln(2[tex]e^{9}[/tex])
We know that, ln(ab) = ln(a) + ln(b)
So we get,
ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])
Since ln(m^n)=n ln(m)
And ln(e)= 1, we will get,
ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)
= ln(2) +9
Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.
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Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
2. Jay Smith deposited $5,000 into an annuity due at the beginning of each quarter for 3 years at 6%
compounded quarterly.
Answer:
value: $66,184.15interest: $6,184.15Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
__
formulaThe formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
calculatorThe attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
__
a)The future value of the annuity due is $66,184.15.
b)The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
On a walk through the woods, Mr. Finley saw 16 blue jays and 25 purple finches. Write the ratio of finches to blue jays three different ways.
Answer:
25:16
50:32
100:64
Step-by-step explanation:
Figure ABCD is transformed to obtain figure A′B′C′D′:
DIAGRAM INCLUDED! 100 Points!
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer. (4 points)
Answer:
Part A
Reflect over the y-axis: (x, y) → (-x, y)Part B
Two figures are congruent if they have the same shape and size. (They are allowed to be rotated, reflected and translated, but not resized).
Therefore, ABCD and A'B'C'D' are congruent. They are the same shape and size as they have only be reflected and translated.
Gabrielle's age is three times Mikhail's age. The sum of their ages is 36. What is Mikhail's age?
Answer:
Gabrielle is 27
Mikhail is 9
Step-by-step explanation:
g = 3m
g + m = 36
since g = 3m we can substitute it in the equation
g + m = 36 as
3m + m = 36
4m = 36
m = 9
3m = 27 which is g
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In AABC, a = 13, b = 14, and c = 18. Find m/A.
B
A
39.5
с
b
a
Answer:
Step-by-step explanation:
Using the Law of Cosines,
[tex]a^{2}=b^2 + c^2 - 2bc \cos A\\\\13^{2}=14^{2}+18^{2}-2(14)(18) \cos A\\\\-351=-504 \cos A\\\\\cos A=\frac{351}{504}\\\\A=\boxed{\cos^{-1} \left(\frac{351}{504} \right)}[/tex]
Darrel divided 8,675 by 87. His work is shown below
Which answer choice correctly identifies the error Darrel made when dividing?
a b c or d?
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y <2/3x + 3
y > 3/2x + 3
y > 2/3x + 3
y < 3/2x + 3
Answer:
The correct linear inequality is y<2/3x+3
Step-by-step explanation:
Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols
In the graph, the grey region corresponds to the region non-allowed by inequality. We see that for x=0, y is allowed to be only less than 3: this means that the correct inequality must be in the form y<mx+3, so only the 1st option or the 4th option.
In order to choose the correct option, we should find the value of m, the slope of the line in the graph. This slope can be found by calculating the variation of y divided by the variation of x:
m=dy/dx
Choosing for example the points x=0 (which corresponds to y=3) and x=3 , we find
So, the equation of the line is y=2/3x+3
and so the correct inequality is
y<2/3x+3
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A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?
The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0
The perimeter of the expanded rectangle is 48 units
What is a rectangle?A rectangle is a quadrilateral with its 4 angles 90°
Analysis:
First rectangle:
length = 10 + x
width = x
Second rectangle:
length = x + 14
width = x + 8
Area of expanded rectangle = 135 square unit
(x+8)(x+14) = 135
[tex]x^{2}[/tex] + 8x + 14x + 112 = 135
[tex]x^{2}[/tex] + 8x + 14x -23 = 0
[tex]x^{2}[/tex] + 22x -23 = 0
[tex]x^{2}[/tex] + 23x - x - 23 = 0
(x-1)(x+23) = 0
Therefore x = 1
Expanded length = 1+14 = 15
Expanded width = 1+8 = 9
Perimeter = 2(9+15) = 48 units
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Evaluate the expression.
Answer:
18
Step-by-step explanation:
Using order of operations:
[tex] \frac{15 - 9}{3} (19 - 10)[/tex]
[tex] \frac{6}{3} (9)[/tex]
[tex]2(9) = 18[/tex]
Which of the following displays is a relative frequency bar graph?
A bar graph titled eye color has color on the x-axis. Blue, 8; brown, 10; green, 6; hazel, 5; gray, 1.
A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
A bar graph titled Caffeinated Drinks has drink on the x-axis. Coffee, 9; tea, 8; soda, 8; energy, 3.
A bar graph titled social media preferences has platform on the x-axis . Upstart, 4; Aster, 18; Babble, 15; Techy, 12.
Mark this and return
The answer choice which represents a relative frequency bar graph is; A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
What is Relative frequency?The statistical definition of relative frequency is simply the ratio of the frequency of an event in a statistical experiment with respect to the total frequency. Hence, since the frequencies in the social media bar chart as decimals (fractions of a whole), it follows that it is a relative frequency representation.
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Answer Its B
Step-by-step explanation:Edge 2022 I guess
what are the solutions in the following equations?
Answer: (0, -6) and (1, -5)
Step-by-step explanation:
If [tex]x-y=6[/tex], then [tex]y=x-6[/tex]. Substituting this into the second equation,
[tex]x-6=x^{2}-6\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x=0, 1[/tex]
If x=0, y=-6.
If x=1, y=-5.
So, the solutions are (0, -6) and (1, -5)
Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answer:
operant conditioning and schedules of reinforcement
Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.
Answer:
4. They are supplementary
Answer:
4 they are supplemental
2. (06.03)
What is the solution to the following system of equations? (2 points)
y = -x2 – 5x − 4
y = -x² + 9x - 18
O (-1,-10)
O (1,-10)
O (-1,10)
(1.10)
Answer: (1, -10)
Step-by-step explanation:
Since both of the equations are set equal to y, we can conclude that:
[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]
If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]
Thus, the solution is (1, -10)
Consider the equation below. "-2(5x+8)=14+6x" The equation was solved using the following steps.
The equation -2(5x+8) = 14+6x solved using step by step representation is x = -15/8.
Solving steps for the EquationThe equation to be considered as given in the task content is; -2(5x+8)=14+6x.
It follows from the task content that the steps for solving the equation are as follows;
-2(5x+8) = 14+6x
Step 1: opening parenthesis-10x - 16 = 14 + 6x
Step 2: collect like terms-10x - 6x = 14 + 16
Step 3: evaluate-16x = 30
Step 4: Divisionx = 30/-16
x = -15/8
Hence, the value of x upon solving the equation is; -15/8.
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25. (01.05)
Given the point (2, 3) and the slope of 4, find y when x = 22. (1 point)
I 78
O83
O88
091
Answer: 83
Step-by-step explanation:
The equation of the line in point-slope form is
[tex]y-3=4(x-2)[/tex]
Substituting in x = 22,
y - 3 = 4(22-2) [substitution]y -3 = 80 [simplify right hand side]y = 83 [add 3 to both sides]find in factord form -9n+n^2=0
Answer:
n(-9+ n) =0
Step-by-step explanation:
-9n+n^2=0 Kind of use 'reverse distributive' property
n (-9 + n) = 0
Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
72 Degrees
Step-by-step explanation:
We know that its 72 because of VAT, the vertical angle theorem.
2 Math questions! Offering the brainliest to who answers
Answer:
first one L second one D
Step-by-step explanation:
Hi. how can i Find the *number* of terms of a finite geometric sequence?
r= .75
a= 40
sum= 280
We have to use the formula [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex] to find the number of terms of a finite geometric sequence.
If a be the first term of a finite sequence, r be the common ratio between consecutive terms and n be the number of terms.
So, we have to use the formula of sum of sequence and then calculate it to reduce the equation to find the value of number of terms, that is n.
Then, Sum of the sequence (Sn) = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
Here, in the given problem,
Sum(Sn) = 280, First term of the sequence(a) = 40, Common ratio(r) = 0.75
So, Sn = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
⇒ [tex]1-r^{n} =\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]r^{n} =1+\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]
Now you have to put the values and get the number of terms.
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2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2x+4+5x+25=4x-32+2x-4
7x+29=6x-36
7x-6X=-36-29
X=-65
Answer:
x = -65
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Distribute:
2(x + 2): 2x + 4
5(x + 5): 5x + 25
=
4(x - 8): 4x - 32
2(x - 2): 2x - 4
Combine like terms:
(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)
5x + 2x: 7x = 4x + 2x: 6x
4 + 25 = 29 = -32 - 4: -36
7x + 29 = 6x - 36
Now we want to separate like terms,
subtract 29 from both sides
subtract 6x from both sides
7x + 29 - 29 - 6x = 6x - 29 - 6x- 36
7x - 6x = - 29 - 36
x = -65
F
10
A. 18
B. 28
C. 38
D. 48
G
8
H
If ZG ZH, find the perimeter of AFGH.
Answer:
The answer is 28
Step-by-step explanation:
ms..s.s..snskkzkzklzlzls
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.6 years.
If you randomly purchase one item, what is the probability it will last longer than 2 years?
The probability will last longer than 2 years will be 3.3%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
First let us calculate the z score using the formula:
[tex]z = \dfrac{(x- \mu)} { s}[/tex]
where x = 2, u is the mean = 3.1 years, and s is the standard deviation
[tex]z =\dfrac{ (2 - 3.1) }{ 0.6}[/tex]
z = -1.83
From the standard probability tables, the p-value at z = -1.83 is:
P = 0.033 = 3.3%
Therefore the probability that will last longer than 2 years will be 3.3%.
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Write this expression in simplified terms.
3×√3×6×√6
Answer:
54√2
Step-by-step explanation:
Line l has a slope of 2/3 The line through which of the following pair of points is perpendicular to l?
We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
The line through which of the following pair of points is perpendicular to l?Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.
So, if line l has the slope 2/3.
Then the perpendicular lines have a slope equal to -3/2.
Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.
If we define (x₁, y₁) = (0, 0), then the other point must be:
[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]
Then we can write the other point as (2, -3).
So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
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1) point)
Problem 2. Fill out the blank to make the given table a discrete probability distribution.
1) point)
2
3
4
P(x)
0.03
0.14
0.65
0.08
Explanation:
Add up the given decimal values
0.03+0.14+0.65+0.08 = 0.90
Recall that all of the P(X) values must add to 1 to represent 100% of all possible outcomes. So far we added to 0.90, so we're missing 1 - 0.90 = 0.10
As a check,
0.03+0.14+0.65+0.08 + 0.10 = 1
What is the area of the polygon given below?
Answer:
340 i am pretty sure
Step-by-step explanation:
A uniform density curve goes from negative 5 to positive 1.
What would the height need to be for this curve to be a density curve?
Negative one-sixth
One-sixth
One-fifth
1
Picture posted below
Answer: Choice B) One-sixth
In other words, the fraction 1/6
===========================================================
Explanation:
The base, aka horizontal component, is 6 units long. Count out the spaces from -5 to 1 to get a result of 6.
Or you could subtract and use absolute value in either of these two ways
|A - B| = |-5 - 1| = |-6| = 6|B - A| = |1 - (-5)| = |1 + 5| = |6| = 6Where A = -5 and B = 1 are the endpoints mentioned. Absolute value is used to ensure the result of the subtraction isn't negative. Negative distance on a number line doesn't make sense.
----------
However you determine the base, we'll multiply it by the unknown height which we'll call h. This leads to the area of the rectangle. The area is 6h.
Rule: The area under a probability density curve must always be 1.
So the area 6h must be 1 which helps us see that...
6h = 1
h = 1/6
Divide both sides by 6 to isolate h fully.
Answer:
B
Step-by-step explanation:
Rewrite, using the distributive
property (Algebra 1)
Answer:
[tex]24m + 32[/tex]
Step-by-step explanation:
[tex]8(3m + 4) = 24m + 32[/tex]