The hundredth number in the series as defined in the task content is; 107.
What is the 100th Number?According to the task content;
The first term of the sequence of numbers is; 8 and evidently, the common difference of the sequence is; 9-8 = 1.
On this note it follows that the 100th number is;
T(100th). = 8 + 99(1) = 107.
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1.2 Fill in and complete pattern in the table below! Number of tables 4 5 6 7 Number of guests . Look at the pattern in 1.2 and describe how the number of guests who can be seated changes for each table added. Complete this sentence: To find the number of guests for each arrangement, you would 8 (2) S
The equation for the number of arrangement from the number of guest is y = 12x + 2
How to determine the equation?The pattern is given as:
x y
0 2
1 14
2 26
3 38
The above table represents a linear function;
Start by calculating the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{14 - 2}{1 - 0}[/tex]
Evaluate
m = 12
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
y = 12(x - 0) + 2
Evaluate
y = 12x + 2
Hence, the equation for the number of arrangement from the number of guest is y = 12x + 2
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There are 12 players on a baseball team. In how many different ways can the coach choose players for left field, right field,and center field?
A) 36
B) 220
C) 1320
D) 1728
Explanation:
There are 12 choices for left field.
Then there are 12-1 = 11 choices for right field.
Lastly, there are 11-1 = 10 choices for center field.
In total we have 12*11*10 = 1320 different permutations or orderings.
Solve the system of equations.
[tex]\left \{ {{y=220x-160} \atop {y=20x-400}} \right. \\[/tex]
[tex]\begin{cases} y=220x-160\\ y=20x^2-400 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{\stackrel{\textit{\Large y}}{220x-160}~~ = ~~20x^2-400} \\\\\\ -160=20x^2-220x-400\implies 0=20x^2-220x-240 \\\\\\ 0=20(x^2-11x-12)\implies 0=x^2-11x-12 \\\\\\ 0=(x-12)(x+1)\implies x= \begin{cases} 12\\ -1 \end{cases}[/tex]
[tex]\dotfill\\\\ x=12\qquad \qquad \stackrel{\textit{substituting on the 1st equation}}{y=220(12)-160}\implies y=2480 \\\\\\ x=-1\qquad \qquad \stackrel{\textit{substituting on the 1st equation}}{y=220(-1)-160}\implies y=-380 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (12~~,~~2480)\qquad (-1~~,~~-380)~\hfill[/tex]
In the diagram, quadrilateral EFGH is similar to quadrilateral PQRS. Using the graph, determine the coordinates of H. DRAG & DROP THE ANSWER
Answer:
(12,15)
Step-by-step explanation:
This is assuming you haven't answered already... Mr Cooper helped me find it
Consider the derivation of sin(2x). A 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries sine (2 x) = sine (x + x), = sine (x) cosine (x) + cosine (x) sine (x), = (sine (x) cosine (x) ) squared. Where is the error?
Answer:
D, Step 3
Step-by-step explanation:
I just did it on edge
Answer:
The answer is D Step 3 should read = 2sin(x)cos(x).
Step-by-step explanation:
PLEASE HELP ME ASAP
A radio station has a broadcast area in the shape of a circle with equation x2+ y2=5,625, where the constant represents square miles.
a. Find the intercepts of the graph
Answer:
(0, 75), (75, 0), (-75, 0), (0, -75)
Step-by-step explanation:
I used desmos graphing calculator. c:
Look at the two-way frequency table below.
Favorite Dog Breeds
Lab Terrier Poodle Other Total
Male 18 22 6 28 74
Female 14 26 8 12 60
Total 32 48 14 40 134
Which statement is true?
A
The number of males who chose a breed labeled as Other is more than two times that of females who chose Other.
B
More people chose Labs than any other breed.
C
The breed of Labs has the least difference between male and female selections.
D
Over half of the respondents preferred Terriers.
d
Step-by-step explanation:
total of terriers is 48 with is more than 3 but is lower than 134
Suppose that Felicity would like at most three Twix bars and at least two Snickers bars. Then how many ways are there for Felicity to make her selection
The number of ways that are there for Felicity to make her selection based on the combination of the twin bars is 103 ways.
How to calculate the combination?From the complete information, the combination for a twin bar is 13, 2 twin bars can be in 31 places.
3 twin bars of chocolate will be 30 and 4 twin bars will be 29. Therefore, the number of ways will be:
= 13 + 31 + 30 + 29
= 103 ways
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50 points!!!!! what is the simplified form of 6 log3x - 7 log3y + 4 log3z? log base 3 of the quantity negative xz end quantity divided by 4y end log log base 3 of 3xz divided by y end log log base 3 of the quantity x to the sixth z to the fourth end quantity divided by y to the seventh end log log base 3 of the quantity xy all raised to the twelfth end quantity divided by z to the 4th end log
log base 3 of the quantity x to the seventh z to the fourth end quantity divided by y to the sixth end log
Sure hope this helps you :D
The simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.
What are the laws involved in the simplification of logarithmic expressions?The laws involved in the simplification of logarithmic expressions are:
Power law: [tex]a log_x b= log _xb^a[/tex]Product law: [tex]log_xa + log_xb = log_xab[/tex]Quotient law: [tex]log_xa - log_xb = log_x\frac{a}{b}[/tex]Base changing law: [tex]log_ab = \frac{log_xb}{log_xa}[/tex]How to solve the question?In the question, we are asked to simplify the logarithmic expression,
6 log₃x - 7 log₃y + 4 log₃z.
The simplification of the provided logarithmic expression can be done as follows:-
6 log₃x - 7 log₃y + 4 log₃z,
= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law: [tex]a log_x b= log _xb^a[/tex]}
= log₃x⁶ + log₃z⁴ - log₃y⁷
= log₃x⁶z⁴ - log₃y⁷ {Using the Product law: [tex]log_xa + log_xb = log_xab[/tex]}
= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law: [tex]log_xa - log_xb = log_x\frac{a}{b}[/tex]}.
Thus, the simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.
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Write the equation of the circle in general form. Show all your work.
Answer:
(x + 3)^2 + (y - 2)^2 = 25
Step-by-step explanation:
Looking at the circle we can see the origin and the radius from the origin to the edge of the circle.
radius = 5
Origin of the circle (h,k) = (-3,2)
Equation of a circle: (x - h)^2 + (y - k)^2 =r^2
Plug in our (h,k) and radius into the equation.
(x - (-3))^2 + (y - (2))^2 = 5^2
(x + 3)^2 + (y - 2)^2 = 25
Which number is equivalent to 66+66+26+16
6
6
+
6
6
+
2
6
+
1
6
?
The corect answer is [tex]2\frac{3}{6}[/tex] [tex]or[/tex] [tex]2 \frac{1}{2}[/tex]
Please help!!!!!!
What is the geometric possibility of being in the square and not in the circle? The radius of the circle is five inches. Express percent’s to the nearest tenth.
A. 21.5%
B. 23.0%
C. 20.0%
Answer: A
Step-by-step explanation:
The area of the square is 10^2 = 100.
The area of the circle is (pi)(5^2) = 25pi.
So, the area of the region in the square but not in the circle is 100 - 25pi.
Thus, the desired probability is (100-25pi)/100, which is about 21.5%
Triangle ABC is transformed. Select all the
transformations that would create a shape that is
congruent to ABC.
1. Reflection across the y axis
2.Dilation by scale factor of 1
3. Rotation 90 degrees clockwise
4. Translation 4 units to the right
Answer: All four answer choices would create congruent shapes.
===================================================
Explanation:
Reflections, rotations, and translations are considered rigid transformations. What this means is that they keep the same shape, but the shape has been moved in some fashion. As such, the "before" (preimage) and "after" (image) are congruent figures.
Imagine you drew a triangle on a clear piece of glass. If you took a picture of it from one side, then took another picture from the opposite side, then you'd get reflected versions of the triangle. Notice how the triangle has not moved at all. The camera has. Therefore, this proves that reflections keep the same exact shape. The only thing different is the orientation has swapped.
Now imagine you drew a triangle etched in stone. Grab your camera to take a picture of it. Then rotate the camera to get another picture. The two triangles are rotated copies of each other. They're the same exact triangle since the figure etched in stone hasn't changed. Only the camera has. This thought exercise proves rotations are a rigid transformation, aka an isometry.
Lastly, we'll go back to the triangle etched in stone to work with translations. A translation is any shifting. Take a picture of the triangle etched in stone. Then move the camera around to pan to another location (panning is when you keep your aim at the subject but move side to side, or up and down). Imagine the camera is stuck on a train track and can only aim one direction. The camera will take two pictures of the same triangle, of course the only difference is that they have shifted in the frame. Therefore, translations are the third final type of rigid transformation.
-----------------
Dilations are not rigid transformations, but only if the scale factor was something else than 1.
If the scale factor is less than 1, then the image shrinks.
If the scale factor is greater than 1, then the image enlarges.
If the scale factor is exactly 1, then the image doesn't change at all. This is because we multiplied all sides by 1. Multiplying by 1 doesn't change the number.
So because choice (2) mentions the scale factor is 1, this places it in the "rigid transformation" category and it's one of the four answers. Change the scale factor to anything else, and it wouldn't be an answer.
A ladder reaches 2 m up a wall. the foot of the ladder is 0.4 m from the wall. for safety reasons, the slope should be between 6.3 and 9.5. is this ladder within the safe range?
Answer:
No, the ladder is not within the safe range because the slope is 5.
Step-by-step explanation:
To solve, find the slope of the ladder using the slope formula and check if the slope is between 6.3 and 9.5.
What is slope?
Slope is how steep a line is. In this case, the line is the ladder. If the ladder is too steep, them it is not safe.
How do we calculate slope?You can calculate slope using the following formula:
[tex]slope = \frac{rise}{run}[/tex]
Rise means how faraway vertically, or how high up the ladder is.
Run means the how faraway horizontally, or from the wall the ladder is.
Slope of the ladderLet's calculate slope using the formula.
[tex]\displaystyle {slope=\frac{rise}{run}}[/tex]
[tex]\displaystyle {slope=\frac{2\ m}{0.4\ m}}[/tex] Substitute the values, 2m for rise, 0.4m for run.
[tex]\displaystyle {slope=5}[/tex] Final answer
Is the ladder safe?The question tells us that a safe ladder has a slope of 6.3 to 9.5. The slope, 5, is not between that range. Therefore, the ladder is not safe.
Elijah is 2 years less than twice Michael's age. If Elijah is 18, how old is Michael?
What is the value of "c" in the following quadratic? (Make sure the equation is in
standard form: ax2 + bx+c=0)
4x² + 10X - 24 = 0
c=-24
Step-by-step explanation:
a=4, b=10 and c=-24
what’s the area and the perimeter and of the triangle?
Answer:
16.5
Step-by-step explanation:
7.5 x 2.2. formula of triangle = bh
Help?
A person can read 24 pages of a book in 3 of an hour. What is this person's reading rate in pages per hour?
72
12
8
48
How many gallons of water is being filled each minute? (8th Math)
Answer:
3 gallons
Step-by-step explanation:
its in between 2 and 4 on minute 1 and its on 6 at minute 2
Answer:
Well from looking at the graph it looks like 2 gallons in less than a minute (estimating 40 seconds) and 12 gallons every four minutes
Hope this helps :)
Slide that brainliest ;)
Which expression is equivalent to 28x + 14?
Answer:
Option B. 14(2x + 1)
Let's solve:
[tex]28x + 14=14(2x+1)=14*2x + 14*1=28x +14[/tex]
/\ /\
| |
Based on the Distributive Property of Multiplication
⇒ a number that is multiplied by the sum of two numbers, that
the number can be multiplied by both of those numbers and
then added together to get the answer
(See image attached below)
Answer: (B), 14(2x + 1)
Hope that helps!
What is the inverse of the function f(x) = 4x 8? h(x) = one-quarterx – 2 h(x) = one-quarterx 2 h(x) = one-halfx – 2 h(x) = one-halfx 2
Answer:
423 v- 69ferr
Step-by-step explanation:
£20 is divided between June, Sushil &
Fiona so that June gets twice as much as
Sushil, and Sushil gets three times as
much as Fiona. How much does June get?
Answer:
Therefore, June gets £6
Step-by-step explanation:
Total amount = £20
Assume:
June's share = a
Sushil's share = b
Fiona's share = c
a = 2b -----------------------(1)
b = 3c -----------------------(2)
c = b ÷ 3 -------------------(3)
a + b + c = £20 --------(4)
Substitute equations (1) and (3) in equation (4)
2b + b + (b ÷ 3) = £20
10b ÷ 3 = £20
b = £20 * 3 ÷ 10 = £6
a = 2 * £6 = £12
c = £6 ÷ 3 = £3
Therefore, June gets £6
A company has three sales departments (local, regional, and national) at each of several locations across the United
States. Each local sales department has 120 employees. The company wants to survey its employees to determine
the most effective sales method.
Which sample should the company use to arrive at the most reliable conclusion?
Answer:
Each local sales department has 120 employees. The company wants to survey its employees to determine the most effective sales method.
Step-by-step explanation:
Answer:
they should used a random sample including the staff members
Step-by-step explanation:
A baby giraffe was born at a wildlife preserve. The giraffe was 6 feet tall when it was born, and it grew 1.75 feet over the next 7 months.
If the giraffe continues to grow at the same rate, at what age will it reach a height of 15 feet?
The age of the giraffe when he is 15 feet tall be 1 year 1 month and 16 days.
What is fraction?
A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Giraffe height = 6 feet
Height grew in 7 months= 1.75 feet
Giraffe's height in 7 month = 7.75 feet
Giraffe's height, 1 feet= [tex]\frac{7}{7.75}[/tex] month
= 0.9032 months
Giraffe's height, 15 feet= 0.9032 x 15 month
= 13.548 month
= 13 months 16 days approx.
= 1 year 1 month 16 days
Hence, the age of giraffe will be 1 year, 1 month and 16 days
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a 250g bag of maize flour, contains 195 g of carbohydrate, use percentages to work out the amount of carbohydrate
Answer:
78%
Step-by-step explanation:
195/ 250 = 0.78 then we multiply .78 by 100 to get the percentage
(.78)(100) = 78%
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink \star\underline{\underline{\boxed{ \sf{ \frac{value}{T. value} * 100 \%}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
[tex]\sf{ \frac{value}{T. value} * 100 \%}[/tex]
[tex]\sf{\frac{195}{250}*100\%}[/tex]
[tex]\sf{0.78 * 100 \%}[/tex]
[tex]\sf{78 \%}[/tex]
The amount of carbohydrate is 78 %
Find the distance between the points. Round to two decimal places if necessary.
Answer:
The distance is 17.20
Step-by-step explanation:
The solution is in the image
Find the range values. y= -x + 6 domain (-2,-11)
Answer:
range = {8,17}
Step-by-step explanation:
plug in -2 & -11 where x is
y= -(-2) + 6
y= +2 + 6
y= +8
y= -(-11) + 6
y= +11 + 6
y= +17
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Eric 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, more than 2 would 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.
The results of these trials are shown in this list.
5533, 2245, 1555, 3341, 4252,5335, 5321, 4155, 2131, 3414,1532, 4251, 2523, 3311, 2352,2332, 5451, 3344, 1121, 5243
Based on this simulation, what is the estimated probability that more than 2 of 4 randomly selected students would have a pet?
Enter your answer, as a decimal, in the box.
==========================================================
Explanation:
You'll look at each four digit group separately.
Since we want more than 2 people having a pet, this means the group of four must have 3 pet owners or all 4 are pet owners.
The digit 5 represents "no pet". If we see it show up twice or more, then we must cross the group off the list. Something like 5533 has the first two people that don't own pets, while the last two people do own pets. In this case, we don't have a "more than 2 pet owners" situation happening. So we must cross it off the list.
Here is the list of groups to cross off
55331555533541555451There are five such groups we have eliminated. That leaves 20-5 = 15 groups where there are more than 2 pet owners.
We have 15 groups we want out of 20 total. It leads to the probability of 15/20 = 0.75
Answer:
0.75
Step-by-step explanation:
I took the quiz :)
Chris bought 37 pounds of peanuts that cost $0.93 per pound. How much did he pay for peanuts?
Answer:
$34.41
Step-by-step explanation:
rate = 0.93$/lb
amount = 37 lb
total = amount x rate
= 37 lb x 0.93$/lb
=34.41$
Identify the inverse of f(x)=x^2-9
