Answer:
[tex]a_{n}[/tex] = 8n - 19
Step-by-step explanation:
The explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 11 and d = - 3 - (- 11) = - 3 + 11 = 8, thus
[tex]a_{n}[/tex] = - 11 + 8(n - 1) = - 11 + 8n - 8 = 8n - 19
Answer:
[tex]a_{n} = 8n-19[/tex]
Step-by-step explanation:
Explicit formula is :
[tex]a_{n} = a_{1} + d(n-1)[/tex]
Where [tex]a_{1}[/tex] is the first element i.e. -11
and d is the difference between the elements i.e. 8
[tex]a_{n} = -11 + (8)(n-1)[/tex]
[tex]a_{n} = -11 + 8 (n-1)[/tex]
[tex]a_{n} = -11+8n-8\\[/tex]
[tex]a_{n} = 8n-19[/tex]
HELP!! Find the product. (6a + b)2 1. 12a2 + ab + b2 2. 36a2 + ab + 36b2 3. 36a2 + 12ab + b2 4. 36a2 + b2
Answer:
option 3
Step-by-step explanation:
Given
(6a + b)²
= (6a + b)(6a + b)
Each term in the second factor is multiplied by each term in the first factor, that is
6a(6a + b) + b(6a + b) ← distribute both parenthesis
= 36a² + 6ab + 6ab + b² ← collect like terms
= 36a² + 12ab + b²
Simplify (4x+5y) (2x-3y) + 3xy
Answer:
the answer is 8x^2+xy-15y^2
A clerical worker takes 3 times as long to finish a job as it does an executive secretary. Working together, it takes them 2 hr to finish the job. How long would it take the clerical worker, working alone, to finish the job?
Answer:
8 hours
Step-by-step explanation:
In 2 hours, the clerical secretary can do 1/4 of the job. (The executive secretary does 3/4 of the job - or 3 times as much - in the same 2 hours.)
Since it takes the clerical secretary 2 hours to do 1/4 of the job, it will take them four times that to do it themselves. 2x4=8.
Help pls!!! The diagram shows a 12 cm * 3 cm * 4 cm cuboid. Find angle GEC. Give your answer to 1 decimal place.
Answer:
m<GEC = 17.9 deg
Step-by-step explanation:
First, use the Pythagorean theorem to find the length of GE.
(GE)^2 = (E?)^2 + (?G)^2
I am using ? in place of the front right corner point name that is not visible.
(GE)^2 = 12^2 + 3^2
GE = 12.3693
In triangle EGC, for angle GEC, GE is the adjacent leg, and GC is the opposite leg. We use the tangent.
tan GEC = opp/adj
tan GEC = GC/GE
tan GEC = 4/12.3693
tan GEC = 0.32338
Use inverse tangent to find the angle.
m<GEC = 17.9 deg
The angle ∠GEC of a cuboid will be:
"17.9°"
Pythagoras TheoremAccording to the question,
Three dimensions,
AC = 4 cm
EH = 12 cm
GH = 3 cm
By using Pythagoras theorem,
→ (GE)² = (EH)² + (GH)²
By substituting the values,
= (12)² + (3)²
= 144 + 9
= 153
GE = √153
= 12.3693
Now, In ΔEGC
here, Adjacent leg = GE
Opposite leg = GC
→ tan GEC = [tex]\frac{Opposite}{Adjacent}[/tex]
= [tex]\frac{GC}{GE}[/tex]
= [tex]\frac{4}{12.3693}[/tex]
= 0.32338
Hence, by using inversing tangent
m∠GEC = 17.9°
Thus the above answer is correct.
Find out more information about Pythagoras theorem here:
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Please help. I need the answers to these. I don't get Trigonometry at all.
Answer:
below
Step-by-step explanation:
sin 24° =0.4 cos 45° =[tex]\frac{\sqrt{2} }{2}[/tex] tan 88° = 28.63Answer:
1) -.91
2) .53
3) .04
Step-by-step explanation:
[tex]sin(24)[/tex] = -.905578362
-.91 rounded to the nearest hundredth
[tex]cos(45)[/tex] = .5253219888
.53 rounded to the nearest hundredth
[tex]tan(88)[/tex]= .0354205013
.04 rounded to the nearest hundredth
Determine the solution set 2x+3(4-x)≤x<2(x+1)
Answer:
6≤x>2
Step-by-step explanation:
2x+3(4-x)≤x<2(x+1) simplify
2x+12-3x≤x<2x+2
first step:
-x+12≤x
-x+12+x≤x+x
12≤2x , then 12/2 ≤ x
6≤x or x ≥ 6
second step: x<2x+2
x-2x<2x-2x+2
-x<2 when divide by negative the sign flip in this case from less to great than
x>2
6≤x>2
In an effort to cut costs and improve profits, any US companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. What is the probability percentage that 338 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places.
Answer:
Step-by-step explanation:
This is a binomial probability distribution because there re only 2 possible outcomes. It is either a surveyed company outsourced some part of their manufacturing process in the past two to three years. The probability of success, p would be that a randomly selected company x, outsourced some part of their manufacturing process in the past two to three years. From the information given, p = 54/100 = 0.54
Number of success, x = 338
Number of samples, n = 555
We want to determine the probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years which is expressed as
P(x ≥ 338)
From the binomial probability calculator,
P(x ≥ 338) = 0.0006
The percentage is 0.0006 × 100 = 0.06%
use the grouping method to factor this polynomial.
Answer:
C
Step-by-step explanation:
Given
x³ + 3x² + 3x + 9 ( factor first/second and third/fourth terms )
= x²(x + 3) + 3(x + 3) ← factor out (x + 3) from each term
= (x² + 3)(x + 3) → C
Select the correct answer. Which statement is true for the numbers 2.5 and -2.5? A. On the horizontal number line, 2.5 and -2.5 are equal and are located on the same point. B. On the horizontal number line, -2.5 is located to the left of zero and 2.5 is located to the right of zero. C. On the horizontal number line, 2.5 and -2.5 are both located to the right of zero. D. On the horizontal number line, 2.5 is located to the left of zero and -2.5 is located to the right of zero.
Answer:
B
Step-by-step explanation:
On the horizontal number line, -2.5 is located to the left of zero and 2.5 is located to the right of zero.
On the number line, the numbers left side of zero are all negative numbers, and the numbers right side of zero are all positive numbers.
Which of the diagrams below represents the statement "If it is a square, then
it is a rectangle"?
Answer:
A
Step-by-step explanation:
Im not 100% but im sure I did this question
The diagram which correctly represents the statement "If it is a square, then it is a rectangle" is; Figure A.
From set theory;
The statement " if it is A, then it is B" simply can be translated mathematically as A is a subset of B.
As such, every element of the set A is an element of Set B.In this case, Since the statement is; "If it is a square, then it is a rectangle".
The figure A correctly represents the statement; "If it is a square, then it is a rectangle".
Read more;
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3 Sarah left home at 10:00 and cycled north in
a straight line. The diagram shows a
displacement-time graph for her journey.
a Work out Sarah's velocity between 10:00 and 11:00.
On her return journey, Sarah continued past her
home for 3 km before returning.
b Estimate the time that Sarah passed her home.
c Work out Sarah's velocity for each of the last two
stages of her journey.
d Calculate Sarah’s average speed for her entire journey.
Answer:
a) From 10 to 11, Sarah rode 12 km in one hour. That means her velocity was 12 km/hr.
b) Sarah passed by her home at 12:45.
c) From 12 to 13, Sarah rode 15 km. Thus, her velocity was 15 km/hr. From 13 to 14 she rode 3 km. Thus, her velocity was 3 km/hr.
d) Her average velocity was 12+0+15+3/4, or 30/4 which is 7.5 km/hr.
Sort each function into the correct category
f(x) = 0.45-1
Linear Functions
Quadratic Functions
Exponential Functions
f(x) = 5
f(x) = 4,5x + 1.8
f(x) = 19x2
f(x) = x2 - 3x + 4
Fx) = 2x - 6
Answer:
^ DONT LISTEN TO HIM
Step-by-step explanation:
linear - 4.5x + 1.8 and 2x - 6
quadratic - 19x^2 and x^2 - 3x + 4
exponential - 5^x and 0.45^x-1
ur welcome if ur using edge
find the volume of the cone and the curved surface area of the cone
Answer:
301.6, 188.5
Step-by-step explanation:
to find the volume of the cone is πr[tex]^{2} \frac{h}{3}[/tex]
so π x 6[tex]^{2} \frac{8}{3}[/tex]
=301.59 or 301.6
now to find the curved surface area of the cone is πrl
so π x 6 x 10
=188.49 or 188.5
Answer:
a) 301.6 cm^3.
b) 188.5 cm^2.
Both are correct to the nearest tenth.
Step-by-step explanation:
Volume = 1/3 π r^2 h
= 1/3 * π * 6^2 * 8
= 301.59 cm^3
Area of the curved surface
= π L r where L = the slant height
= π * 10 * 6
= 188.49 cm^2.
Which of the expressions are monomials?
Answer:
nx∧(-3)
Step-by-step explanation:
Since it contains one term with the variable
Rahul solved the equation 2(x – ) – 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction x = 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction . In which step did he use the addition property of equality? A table titled Rahul's Solution with 2 columns and 5 rows. The first column, Steps, has the entries 1, 2, 3, 4. The second column, Resulting equations, has the entries, 2 x minus StartFraction 1 Over 4 EndFraction minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x minus StartFraction 1 Over 4 EndFraction equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x equals StartFraction 56 Over 4 EndFraction, x equals 10. Step 1 Step 2 Step 3 Step 4
Answer:
Step 3
Step-by-step explanation:
The solution is given in the image attached. The steps are:
Step 1:
[tex]2x-\frac{1}{4} -\frac{3}{5}x=\frac{55}{4}[/tex]
Step 2: simplifying the coefficients of x:
[tex]2x -\frac{3}{5}x-\frac{1}{4}=\frac{55}{4}\\\frac{10x-3}{5} -\frac{1}{4}=\frac{55}{4}\\\frac{7x}{5} -\frac{1}{4}=\frac{55}{4}[/tex]
Step 3: Adding 1/4 to both sides
[tex]\frac{7x}{5} -\frac{1}{4}+\frac{1}{4} =\frac{55}{4}+\frac{1}{4}\\ \frac{7x}{5}=\frac{55+1}{4}\\ \frac{7x}{5}=\frac{56}{4}\\[/tex]
Step 4: Multiplying both sides by 5/7
[tex]\frac{7x}{5}*\frac{5}{7} =\frac{56}{4}*\frac{5}{7} \\x=10[/tex]
The addition property of equality states that if a number is added to both sides of an equation, the equation is still valid (i.e the equation is still the same). From the steps above, The addition property of equality was applied in step 3
Answer:
c. step 3
Step-by-step explanation:
A pack of pens costs $3.25. A pad
paper costs $1.28. If you buy two
packs of pens and five pads of paper
how much do you spend?
Answer:
$12.90
Step-by-step explanation:
In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of the cocktail is apple juice? Give your answer as a fraction in its simplest form.
Answer:
1/5
Step-by-step explanation:
Since we have given that
Quantity of orange juice = 30 ml
Quantity of apple juice = 20 ml
Quantity of coconut juice = 50 ml
Total quantity of cocktail = 100 ml
So, the ratio of orange juice to apple juice to coconut juice is given by
=30:20:50
= 3:2:5
Total ratio=3+2+5
=10
So, proportion of the cocktail of apple juice is given by
2/10×100
=1/5×100
=20%
Hence, the proportion of the cocktail is 1/5 apple juice
Identify the equation which has no solution. 3x - 21 = 3(x + 7) 3x - 21 = 3(x - 7) 3x - 21 = x - 7 All of the choices
Answer:
3x - 21 = 3(x + 7).
Step-by-step explanation:
3x - 21 = 3(x + 7)
3x - 21 = 3x + 21
3x - 3x = 21 + 21
0 = 42
Since the two are not equal, this equation has no solution.
3x - 21 = 3(x - 7)
3x - 21 = 3x - 21
3x - 3x = -21 + 21
0 = 0
Since the two are equal, this equation has infinitely many solutions.
3x - 21 = x - 7
2x = 14
x = 7
This equation has one solution.
Since there is only one choice that makes sense, the answer won't be all of the choices.
The answer is A. 3x - 21 = 3(x + 7).
Hope this helps!
Simplify the variable expression by evaluating its numerical part, and enter your answer below. g - 2/2
Answer:
g - 1
Step-by-step explanation:
g - 2/2
2/2 = 1
g - 1
PLEASE HELP I WILL MARK YOU THE BRAINIEST Using the graph, identify the slope and y-intercept. Then write an equation that represents the linear relationship.
Answer:
slope = -2
y-intercept = 2
equation: y = -2x + 2
Step-by-step explanation:
The equation of a line is
y = mx + b
We need to find the slope, m, and the y-intercept, b.
The graph crosses the y-axis at y = 2, so the y-intercept, b, equals 2.
Now we have
y = mx + 2
slope = m = rise/run
We see points (1, 0) and (0, 2) on the graph. Starting at (1, 0), we go up 2 units. That is a rise of 2. Then we go 1 unit left. That is a run of -1.
slope = m = rise/run = 2/(-1) = -2
The slope is -2.
The equation is
y = -2x + 2
Answer:
y=-2x+2
Step-by-step explanation:
Using rise over run the line travels down 2 and right one from one point to another giving u -2/1 or -2 as the slope and it passes through the y-axis at 2 giving you a y-intercept of 2 and the equation y=-2x+2.
I’m confused please help!
Answer:
A is the answer.
Step-by-step explanation:
In option A, there are 9 red boxes and 3 blue boxes
If we simlify,
9 : 3 = 3 : 1 = 1 : 1/3
Hope you understand
Answer: Grid A
Step-by-step explanation:
The ratio red:blue is simplified to 1:1/3.
To make things easier, we can expand it so that both sides add up to 12(total number of squares in a grid).
We can multiply both sides by 9.
1 x 9= 9
1/3 x 9= 3
Now the ratio red:blue is 9:3, which adds up to 12.
Grid A is the only grid where there are 9 red squares and 3 blue squares.
Justin earned scores of 85, 92, and 95 on his science tests. What does he need
to earn on his next science test to have an average (arithmetic mean) of 93%?
Answer:
Justine needs to score a 100 to have an average of 93%.
Step-by-step explanation:
Given:
Justin scores 85, 92 and 95 on his science tests.
To find:
The score that he needs to earn to have an average of 93%?
Solution:
Let the score in next science test = [tex]x[/tex]
Formula for Average/Arithmetic Mean is given as:
[tex]Average = \dfrac{\text{Sum of all observations}}{\text{Total number of observations}}[/tex]
Here we have 4 number of total observations and average is 93%.
Now, put all the values here:
[tex]93 = \dfrac{85 +92+ 95+x}{4}\\\Rightarrow 93\times 4=85 +92+ 95+x\\\Rightarrow 372=272+x\\\Rightarrow x = 372-272\\\Rightarrow x = 100[/tex]
So, Justin needs to score 100 to have an average of 93%.
Distribute and simplify the following: x(3x + 2)(-2x + 1)
Help!!!!! please!!!!!
Answer:
192.154 ft²
Step-by-step explanation:
Area of a Hexagon Formula: A = 3√3/2(x)²
x is the side of the hexagon. We simply plug in 8.6 in for x:
A = 3√3/2(8.6)²
A = 3√3/2(73.96)
A = 221.88√3/2
A = 110.94√3
A = 192.154
Answer:
~192.2
Step-by-step explanation:
The area of a regular hexagon is calculated by:
A = [3*sqrt(3)/2]x side x side = 3*sqrt(3)/2 x 8.6^2 = ~192.2
How many 9-digit palindromes are there with all the digits being even and each digit appearing no more than twice?
Answer: 96
Step-by-step explanation:
A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121
Then, we have 9 digits, and all the digits need to be even.
the options are: 0, 2, 4, 6, 8.
Now, we can tink a 9 digit number as 9 empty slots, and in each slot, we can put a number.
But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.
So we can tink it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.
For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9 digit number).
for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)
for the third digit, we have 3 options
for the fourth digit, we have 2 options
for the fifth digit, we have only one option.
The total number of combinations is equal to the product of the number of options for each selection:
C = 4*4*3*2*1 = 96
Answer:
96
Step-by-step explanation:
It says to calculate the area of the sector and t round to the nearest hundredth and to use 3.14 for Pi
Answer:
Step-by-step explanation:
The formula for the area of a sector is
[tex]A=\frac{\theta}{360}*\pi r^2[/tex] where theta is the measure of the central angle (which is the same measure as that of the arc that is intercepted by the 2 radii formig the angle), and r is the radius.
For us, theta is 90 degrees and r is 20. Filling in the formula:
[tex]A=\frac{90}{360}*(3.14)(20)^2[/tex] which simplifies down a bit to
[tex]A=\frac{1256}{4}[/tex] so
A = 314 m squared
A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5 y is 10.5 and r=3 If both containers have labels covering their lateral surfaces, which container will have less label area and by how much? Container Y by about 42 in.2. Container X by about 28 in.2. Container Y by about 9 in.2. Container X by about 85 in.2.
Answer:
Container [tex]\rm X[/tex] will have less label area than container [tex]\rm Y[/tex] by about [tex]9\; \rm in[/tex].
Step-by-step explanation:
A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.
Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of [tex]h[/tex] and a radius of [tex]r[/tex] at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width [tex]h[/tex] and length [tex]2\,\pi\, r[/tex].
Apply this reasoning to both cylinder [tex]\mathrm{X}[/tex] and [tex]\rm Y[/tex]:
For cylinder [tex]\mathrm{X}[/tex], [tex]h = 6\; \rm in[/tex] while [tex]r = 4.5\; \rm in[/tex]. Therefore, when the lateral side of this cylinder is unrolled:
The width of the rectangle will be [tex]6\; \rm in[/tex], whileThe length of the rectangle will be [tex]2 \, \pi \times 4.5\; \rm in = 9\, \pi\; \rm in[/tex].That corresponds to a lateral surface area of [tex]54\, \pi\; \rm in^2[/tex].
For cylinder [tex]\rm Y[/tex], [tex]h = 10.5\; \rm in[/tex] while [tex]r = 3\; \rm in[/tex]. Similarly, when the lateral side of this cylinder is unrolled:
The width of the rectangle will be [tex]10.5\; \rm in[/tex], whileThe length of the rectangle will be [tex]2\pi\times 3\; \rm in = 6\,\pi \; \rm in[/tex].That corresponds to a lateral surface area of [tex]63\,\pi \; \rm in^2[/tex].
Therefore, the lateral surface area of cylinder [tex]\rm X[/tex] is smaller than that of cylinder [tex]\rm Y[/tex] by [tex]9\,\pi\; \rm in^2[/tex].
The probability that Stu buys a sandwich is 0.5. The probability that Stu gets the bus is 0.7. Assuming the events are independent, what is the probability that Stu buys a sandwich and gets the bus?
Answer: 0.35
Step-by-step explanation:
First there is a 50% chance, or a 0.5 chance that Stu gets a sandwich. Then, ignoring the other .5, there is a .7 chance that he makes the bus. Thus, 1/2 of .7 is 0.35.
Hope it helps <3
Please answer it now in two minutes
Answer:
p = 67
Step-by-step explanation:
The polygon has 8 sides.
The sum of the measures of the interior angles is:
180(n - 2) = 180(8 - 2) = 180(6) = 1080
p + 49 + 2p + 7 + 2p + 142 + p + 50 + 2p + 147 + 2p + 15 = 1080
10p + 410 = 1080
10p = 670
p = 67
Can someone please provide an example problem showing multiplying and dividing rational expressions? I'm trying to get ready for a DBA tomorrow. Thank you!
Step-by-step explanation:
To multiply rational expressions, simply multiply the numerators together (the tops) and the denominators together (the bottoms).
For example:
[tex]\frac{x+a}{y+b}\times\frac{x+c}{y+d}[/tex]
[tex]= \frac{(x+a)(x+c)}{(y+b)(y+d)}[/tex]
[tex]=\frac{x^{2}+ax+cx+ac}{y^{2}+by+dy+bd}[/tex]
To divide by a rational expression, multiply by its reciprocal. In other words, flip the fraction, then multiply.
For example:
[tex]\frac{x+a}{y+b}\div\frac{x+c}{y+d}[/tex]
[tex]=\frac{x+a}{y+b}\times\frac{y+d}{x+c}[/tex]
[tex]=\frac{(x+a)(y+d)}{(x+c)(y+b)}[/tex]
[tex]=\frac{xy+dx+ay+ad}{xy+bx+cy+bc}[/tex]