Answer:
55 x 224 yards
Step-by-step explanation:
w + w + 2 * ( 4 + 4w) = 558 (given)
10 w + 8 =558
w = 55 then L = 4 + 4w = 224 yards
1+2-3+4+5-6+7+8-9...+97+98-99
Answer:
1584
Step-by-step explanation:
The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.
__
series of partial sumsThe partial sums, taken 3 terms at a time, are
1+2-3 = 0
4+5-6 = 3
7+8-9 = 6
...
97+98-99 = 96
So the original series is equivalent to ...
0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)
That is, the sum is 3 times the sum of the consecutive integers 1..32.
__
consecutive integersThe sum of integers 1..n is given by the equation ...
s(n) = n(n+1)/2
__
series sumUsing this to find the sum of our series, we find it to be ...
series sum = 3 × (32)(33)/2 = 1584
_____
Alternate solution
The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...
1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)
Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).
Computed that way, we find the sum to be ...
(99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584
Bob wants to take his wife, Mary, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $25,000 inheritance from an uncle, which he plans to put towards the trip. Bill calculates that the trip will cost $30,000 and that he can earn 6% yearly compound interest on his investment. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
To calculate the future value, fill out the table below. Will he be able to pay for the trip with the money he has saved up? (Round up your totals to the nearest whole dollar amount.)
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
(pls give brainliest)
Solve f (9) for f(x) = -13 + 2x
ƒ(9) = [?]
The value of f(9) for the given function is 5
Evaluating the value of a functionFrom the question, we are to determine the value of f(9)
The given function is
f(x) = -13 + 2x
To determine f(9), we will put x = 9 in the given function
That is,
f(x) = -13 + 2x becomes
f(9) = -13 + 2(9)
f(9) = -13 + 18
f(9) = 5
Hence, the value of f(9) for the given function is 5
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Will give 50 points for answer to this question please help
Answer:
The 3rd one (y_< 2/3 x + 1/5) If this helps please mark brainiest! :)
A petri dish contains cells of a certain strain of bacteria. Each bacterial cell in the dish divides in half approximately every 6 minutes. The curve of best fit that models the number of bacterial cells in the dish is given by the equation f(x) = 4.2 • 1.1x, where x represents the number of minutes and y represents the number of cells. Approximately how many bacterial cells will be in the petri dish after 30 minutes?
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of cells after x minutes, hence:
y = 4.2(1.1)ˣ
After 30 minutes:
y = 4.2(1.1)³⁰ = 73.3
The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3
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3. Which test do you stretch your muscles by reaching for your toes?
Answer:
I think it's sit and reach sorry if I'm wrong
URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A
Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta
Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity
Step 3: 1 + tan2 θ
Step 4: sec2 θ Student B
Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta
Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta
Step 3: secant squared theta over tangent squared theta
Step 4: csc2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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I need help I don’t get this
Answer:
Your answer is 368
Step-by-step explanation:
Separate 92 into 90 + 2
4 * 92 = 4 * (90 + 2)
Distribute 4.
= 4 * 90 + 4 * 2
Multiply and Add
= 360 + 8
= 368
The function fis defined as follows.
f(x)=2x²+3
If the graph of fis translated vertically downward by 6 units, it becomes the graph of a function g.
Find the expression for g(x).
The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3
How to Interpret Graph Translations?
We are given the function;
f(x) = 2x² + 3
Now, when we translate a function f(x) downwards, the new function becomes;
g(x) = f(x) - a
where a is the amount of units by which the graph was translated.
Thus for translation of 6 units vertically downwards;
g(x) = 2x² + 3 - 6
g(x) = 2x² - 3
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In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
x > 64 and x < 68
x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Another way of writing the inequality 64 < x < 68, where x represents the height of the actor, is x>64 and x< 68. Hence, the correct option is A.
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Solve the equation using the Square Root Property
2(x+1)^2=50
SHOW ALL YOUR STEPS/WORK
Jimmy invests $25,000 into the stock market which generates 5% interest compounded every month. How much money will he have after 7 years?
Answer:
35177.51057 (Rounded - 35177.5)
Step-by-step explanation:
Compound Interest -
- Recalculates how much you should be getting
The format will ALWAYS be y=[tex]ab^x[/tex]
A = Starting Value
B = Multiplier
X = Time (years)
5% = .05
1.00 + .05 = 1.05%
y=25,000(1.05)^7
= 35177.51057
Let me know if i did anything wrong <3
find the area and the circumference of a circle with the diameter 6 yards
Answer:
area = 28.27
circumference = 18.85
Step-by-step explanation:
Using the formulas for area,
A = πr^2
d = 2r
Solving for area,
A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²
Using the formulas for circumference,
C = 2 πr
d = 2r
Solving for circumference,
C = πd = π × 6 ≈ 18.85yd
Solve the system of equations 4x + 3y = 3 and y = 2x + 6.
O The solution is (-0,3).
O The solution is (-1,5).
O The solution is (-2,3).
O There are no solutions.
Step-by-step explanation:
4x + 3y = 3
y = 2x + 6 ->
2x - y = -6
let's multiply the modified second equation by 3 and add both equations :
4x + 3y = 3
6x - 3y = -18
--------------------
10x + 0 = -15
x = -1.5
4x + 3y = 3
4×-1.5 + 3y = 3
-6 + 3y = 3
3y = 9
y = 3
and so the solution is (-1.5, 3).
which is not in the list of your answer options.
so, something must have been wrong in your problem definition.
either you changed something in the 2 equations, or subverting is missing in the answer options, or you even mixed up problem and answer options of 2 different questions.
but I also checked by using the numbers in the 2 equations, but (-1.5, 3) is indeed the correct solution for the given 2 equations.
A group of 25 classmates visits an amusement park. When they arrive, 3/5 of the students want to ride the fastest roller coaster first. How many students is this?
Find 3/5th of the classmates
3/5 of 253/5(25)3(5)15studentsThey are 15 students
Answer:
15 students
Step-by-step explanation:
To find 3/5 of 25 students, simply swap the word "of" for the multiplication symbol and calculate:
[tex]\begin{aligned}\sf \dfrac{3}{5}\:of\:25\:students & = \sf \dfrac{3}{5} \times 25\\\\& = \sf \dfrac{3 \times 25}{5}\\\\& = \sf \dfrac{75}{5}\\\\& = \sf 15\:students\end{aligned}[/tex]
A play has tickets available for 8 orchestra seats and 12 balcony seats. The next person to buy a ticket will be randomly assigned to one of those seats. What is the probability that the next person will be assigned an orchestra seats?
The probability that the next person will be assigned an orchestra seats is 2/5.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, Available Orchestra seats = 8
Balcony seats = 12
Total available seats = 12 + 8 = 20
Probability = Favorable Outcome / Total Outcome
Probability of getting orchestra ticket = 8/20
= 2/5
Thus, the probability that the next person will be assigned an orchestra seats is 2/5.
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CIRCLE THEOREM (CHECK PHOTO)
O is the centre of this circle.
Calculate the size of angle x.
Show all of your working and state any theorems that you use.
N = 80°
M and J are common arcs
K = 128⁰
L & J are common arcs
Not drawn accurately
I got 52 but it’s not right and I’ve tried this question twice - would love to know if you get something different
I used cyclic quad theorem and angles to the centre is x2 circumference rule
HELP ILL GIVE MONEY
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 27 liters per minute. There are 700 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating W to T. Then use this equation to find the total amount of water after 17 minutes.
Equation:__
Total amount of water after 17 minutes: __liters
Answer: Equation: 27t +700 = w
Total amount of water after 17 minutes: 1159 L
Step-by-step explanation:
Equation: 27t +700 = w
let t = minutes
let w = total amount of water in pond (liters)
Total amount of water after 17 minutes: 1159 L
t = 17
therefore
27(17) +700 = 1159
Answer:
425 l
Step-by-step explanation:
Multiply 2/3 • 5/8 simplify your answer , if possible
Answer:
5/12
Step-by-step explanation: 2/3 x 5/8 Multiply the numerators ( top numbers) and the denominators ( bottom numbers ) 2x 5= 10 3x8=12 Simplify by 2 Answer=5/12
PLEASE I NEED THE ANSWER (JUST THE ANSWER)
People of different ages were asked the question "Do you listen to audiobooks?” The bar chart displays the percentage of "yes” responses in each age group.
A bar graph titled audiobook listeners has age on the x-axis and relative frequency on the y-axis. 13 to 17, 0.08; 18 to 25, 0.15; 26 to 35, 0.23; 36 to 45, 0.45; 46 and over, 0.47.
Based on the bar graph, the true statement is that: C. more 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.
What is a bar graph?A bar graph is used for the graphical representation of data, especially by using rectangular bars or vertical columns.
How to interpret the bar graph?From the information provided, we can deduce the following points about the audiobook listeners:
Age Relative frequency
13 to 17 0.08
18 to 25 0.15
26 to 35 0.23
36 to 45 0.45
46 and over 0.47
Based on the frequency table for the bar graph, we can logically deduce that more 36 to 45-year-olds with a frequency of "0.45" listen to audiobooks than 26 to 35-year-olds with a frequency of "0.23."
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Complete Question:
People of different ages were asked the question "Do you listen to audiobooks?" The bar chart displays the percentage of "yes" responses in each age group. Which of the following statements is correct?
A. More 18- to 25-year-olds listen to audiobooks than 26- to 35-year-olds.
B. Fewer 18- to 25-year-olds listen to audiobooks than 13- to 17-year-olds.
C. More 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.
D. Fewer 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.
Solve for x.
Your answer must be simplified.
−x<−29
Step-by-step explanation:
if you made no typo or left things out, this is very simple :
-x < -29
x > 29
remember that when you multiply an inequality by -1 (or any negative value), the orientation of the inequality changes.
Find the area of the yellow region.
Round to the nearest tenth.
DCH
6 in
-6 in-
Area = [?] in²
Answer:
A = 3.9 in²
Step-by-step explanation:
To find the area of the shaded region, you need to find the (1) area of the entire square, then (2) find the area of the 1/2 circles, then (3) subtract them and divide by 2. Because the 1/2 circles are identical, you can combine them and just use the circle area equation.
Area of the Square:
A = l x w
A = 6 in x 6 in
A = 36 in²
Area of Combined 1/2 Circles:
A = πr²
r = 6 in / 2
r = 3 in
A = π(3)²
A = 9π -----> 28.3 in²
Area of Shaded Region:
A = (Area Square - Area Circle) / 2
A = (36 in² - 28.3 in²) / 2
A = 7.7 in² / 2
A = 3.9 in²
Find the area of the sector
Answer:
10:
7/4π = 5.5(1decimql place)
11:
50π = 157.1(1 decimal place)
Step-by-step explanation:
the equation is (angle/360) X πr^2
Volume of a cube with a side length of 18.8m
Answer:
[tex]6644.672~ m^3[/tex]
Step-by-step explanation:
[tex]\text{Volume} = (18.8)^3~ m^3 = 6644.672~ m^3[/tex]
Which pair of angles is an example of supplementary angles?
Answer:
Angle1 and Angle2 are supplementary.
Step-by-step explanation:
There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.
Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:
1&2
2&4
3&4
1&3
5&6
6&8
7&8
5&7
Since angles don't have to touch in order to be supplementary there are many more pairs.
EASY POINTS Which of the following statements is true?
Answer:
B.
Step-by-step explanation:
They form a right angle.
Answer:
B
Step-by-step explanation:
if A were true, this hole shape could not be a triangle as AC and BC would be parallel and never have an intersecting point.
C - the line BC intersects the line EC but only at the very end point. but to bisected means to split it in half, so the intersection would have to be in the middle.
D - the line AC is only perpendicular to DE, and while DE is a perpendicular bisector to AC, AC itself does not split anything in half.
Select the graph of y=cot x.
Answer:Suppose y= cot x is our parent function then remember general rules of transformation.1) y= -f(x), reflects the graph of f(x) across x-axis.2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.Now, apply these rules to y= -4 cot(x)the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.
Every day carla spends 2/3 of a hour cleaning her room. How long will she spend cleaning her room in 4 days
Answer:
see photo
Step-by-step explanation:
see photo for answer
sometimes when there is a fraction in the question it's a good idea to keep things as fractions and not decimals
PLEASE HELP ME I HAVE A F IN MATH
Answer:
pattern 0 i believe would be just the 4 red squares
Step-by-step explanation:
its adding a blue square on the 3 sides and adding enough green squares to cover the middle, or however many blue squares there are on the top and side, multiply them together. like in figure 1 i noticed that 1×1=1 so that's how many green squares there are. Figure 2: 2 blue× 2 blue= 4 green. if that makes sense. Figure 3: 3×3=9 i dont know if that made sense. but that's what i could think of!!