Answer:
a = 9
Step-by-step explanation:
[tex]\sqrt{2a-14} = 2[/tex]
2a - 14 = 4
2a = 18
a = 9
Answer:
The answer to this question is a = 9.
Step-by-step explanation:
To solve this problem, we need isolate the variable "a" on one side of the equation. Our first step must be to remove the square root. To do this, we should perform the inverse operation, which is squaring both sides.
√2a - 14 = 2
(√(2a - 14))² = 2²
2a - 14 = 4
Next, we should add 14 to both sides of the equation to get the variable term by itself.
2a - 14 + 14 = 4 + 14
2a = 18
Finally, we should divide both sides of the equation by 2 to remove the coefficient from the variable term.
a = 9
Therefore, the correct answer is a = 9.
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Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] (−1)n xn 2n n = 0
For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
For given question,
We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]
We need to find the radius of convergence of the power series.
We use ratio test to find the radius of convergence of the power series.
Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]
[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]
Consider,
[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]
By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]
⇒ |x| < 2
So, the radius of convergence is 2.
Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
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The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth. (PLEASE ANSWER)
Answer:
29.9 cm³
Step-by-step explanation:
You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.
ConeThe volume of a cone is given by ...
V = 1/3πr²h
The volume of the cone of interest is ...
V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³
Slosh1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...
1/3(89.797 cm³) ≈ 29.9 cm³
They sloshed out about 29.9 cm³ before they drank the water.
<95141404393>
MN =7. Find AB.
3.5
10.5
14
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2
Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22
Find the Area Of each circle.
The area of the circle A and B is 86.54 inches and 124.62 mm
According to the statement
we have given that the radius of the circle A and b and we have to find the area of the given circle.
So, we know that the
The area enclosed by a circle of radius r is πr².
So, For area of the circle
For condition A :
diameter = 10.5 inches
then radius = 5.25
Area = πr²
Area = 3.14*27.56
Area = 86.54 inches
Now, For condition B :
radius = 6.3 mm
Area = πr²
Area = 3.14*39.69
Area = 124.62mm
So, The area of the circle A and B is 86.54 inches and 124.62 mm
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Match the key features of functions terms to their corresponding definitions.
The key features of the above given functions are correctly matched to their corresponding definition.
Definition of termsNegative sections of the graph: They are the parts where the graph is below the x-axis. That is option C.End behaviour: This is what happens to the graph on the far left or far right. That is option E.Positive sections of the graph: This is the parts where the graph is above the x-axis. That is option D.Intercepts: This is the points where the graph crosses an axis. That is option BRelative extrema: This is the points of relative minimum or maximum in a graph. That is option A.Learn more about graphs here:
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Identify the equation that describes the line in slope-intercept form slope = 3/4 point (2, 2) is on the line
Answer:
y = (3/4)x + 1/2
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
with a being the slope, and b the y-intercept (the y-value when x = 0).
because we got the slope and a point we can start with the point-slope form and then transform the equation.
the point-slope form is in general
y - y1 = a(x - x1)
a is again the slope (the same value), and (x1, y1) is a point on the line.
so,
y - 2 = 3/4 × (x - 2) = (3/4)x - 3/2
y = (3/4)x - 3/2 + 2 = (3/4)x - 3/2 + 4/2 = (3/4)x + 1/2
If you eat a diet with 2,000 kilocalories and 45 percent of those calories come from protein, about how many grams of protein did you eat?
The amount of Protein intake is 900 kilocalorie.
We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.
Wе have to find out the amount of protein intake.
If ' x ' students out of total ' n ' students in a class are infected by virus. Then, what percentage of students are infected.Percentage of students affected are - [tex]\frac{x}{n} \times 100[/tex]
In the question given -
Let the amount of Protein intake be y.
Then -
45 = y % of 2000
45 = [tex]\frac{y}{2000} \times100[/tex]
y = [tex]\frac{45\times2000}{100}[/tex]
y = 900 Kilocalorie
Hence, the amount of Protein intake is 900 kilocalorie.
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Identify ER rounded to the nearest tenth. The Figure shows right triangle M E R with right angle E. The length of hypotenuse M R is equal to 37 units. Angle R measures 61 degrees.
Answers;
a) ER ≈ 66.7
b) ER ≈ 32.4
c) ER ≈ 17.9
d) ER ≈ 22.3
Please give an explanation! :)
The value of length ER rounded to the nearest tenth is 17.9 units (Option C)
Trigonometric ratiosThe trigonometric ratios which has been proven as regarding right angle triangles are given below:
Sine θ = Opposite / Hypothenus
Cos θ = Adjacent / Hypothenus
Tan θ = Opposite / Adjacent
With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:
How to determine the length of ERFrom the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:
Hypothenus (MR) = 37 unitsAngle R = 61 °Adjacent (ER) = ?Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 61 = ER / 37
Cross multiply
ER = 37 × Cos 61
ER = 37 × 0.4848
ER = 17.9 units
Thus, the length of ER to the nearest tenth is 17.9 units
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QUICK!!!HELP!!!!!!!!!!!!!!!!!!
Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
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Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Cos C
C
21
B
35
28
A
HELP! A city pays a manufacturing company to produce more stop signs for the city due to an increase in traffic incidents at intersections. After doing some research, the company manager reads that a standard stop sign is a regular octagon that is 30 inches wide and 30 inches tall.
The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59
How to solve for the octagonThe side of the octagon is given by x inches
the interior side of the angles can be gotten by:
8-2 * 180 / 8 sides
= 135
We have to find the value of the angles
<abc = 180 - 135 = 45 degree
<acb = 180 - 135 = 45 degrees
x² = 2AB²
AB = x/√2
30 = x/√2 + x + x/√2
x = 30 / 1 + √2
The apothem = 30 / 2
= 15
perimeter = 8x
= 8(30 / 1 + √2)
= 99.4 inches
area = 0.5 x 15 x 99.4
= 745.59
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A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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The area of a circle is 9pi cm². Find its radius.
Please do this question with full solution:)
Answer:
3 cm
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A = \pi r^2[/tex]
Where "r" represents the radius of the circle. We can substitute the given value for Area into the equation to solve for the radius.
Solve for Radius[tex]A=\pi r^2\\9\pi = \pi r^2[/tex]
Divide both sides by π
[tex]9=r^2[/tex]
Take the square root of both sides
[tex]\sqrt9=\sqrt {r^2}\\r=3[/tex]
The radius of the circle is 3 cm.
A bag contains 4 blue marbles and 7 red marbles. Two marbles are randomly drawn without replacement. Find the probability of the event ""the first marble is red and the second marble is blue""?
Answer:
8/11
Step-by-step explanation:
In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:
P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.
Which system of measurement uses the minim as the basic unit of liquid measure?
The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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In a certain company, there were five candidates running for President. After the vots were tallied, it turned out that Victor, like in the election, finished in thir place, and david beat him. Greg said that he didn't come in first, but he also didn't come in last. Mac in an interview, said that in this election he wasn't able to win, but at least he was one place hight than his old rival Bill. What place did each candidate come in?
Considering the situation described, the classification of the elections is given as follows:
David came in first place.Greg came in second place.Victor came in third place.Mac came in fourth place.Bill came in fifth place.How to find the classification of the elections?We take the situation that is described, and build the classification from it. The classification has the following format:
P1 - P2 - P3 - P4 - P5
With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.
From the text given in this problem, we have that:
Victor finished in third place, and David beat him, hence P3 = Victor, David = P1 or P2.Greg didn't come in first nor in last, hence, considering that Victor is P3, Greg = P2 or P4.Mac didn't win, but he finished higher than Bill, hence, considering that Mac didn't win and that Victor is P3, Mac = P4, Bill = P5.From the bullet points above, we can conclude that David = P1, Greg = P2.Hence the places of each candidate are given as follows:
David came in first place.Greg came in second place.Victor came in third place.Mac came in fourth place.Bill came in fifth place.A similar problem, in which a situation is interpreted, is given at https://brainly.com/question/5660603
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You deal 7 cards off of a 52-card deck and line them up in a row. how many possible lineups are there in which no card is a club?
Answer:
39C7 or 15380937
Step-by-step explanation:
There are 13 clubs in a 52 card deck. We can remove these from the possibilities. 52-13=39. The rest is simple, choose 7 from 39 using the choose function is 39!/(32!*7!)=15380937. Or just say 39C7 as your answer.
Write the algebraic expression that represents the following: Forty more than a number
Answer:
x+40
Step-by-step explanation:
Let's say the the "number" is x.
"Forty more than a number" would be x+40
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{40+n}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Letting n be the number
[tex]\bold n[/tex]
⇨ Add 40 to n (40 more)
[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)
Hope that helped
HELP PLEASE
if a function representing distance (feet) as a function of time (minutes), what does f(30) represent in terms of the situation?
We know
In a function
y=f(x)x represents the input and y represents output
So
f(30)x is time
So
f(30) represents distance traveled in 30mins
PLEASE HELP ME !!!
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the
cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
base area for cone= B
base area for pyramid= B, 3r heigh
A. V = pi r³
B. V = 1/3 pi r²
C. V = 2 pi r²
D. V = 1/9 pi r³
E. V = 3 pi r³
Answer:
The answer is A. V=pi r³
Step-by-step explanation:
:)
The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.
The cone is a three-dimensional figure with a vertex and a flat base.
The volume of a pyramid is given by the formula:
[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]
Given that:
The base area of the pyramid = B
The height is 3r
The base area of the pyramid is the same as that of the cone.
The base of the cone = [tex]\pi r^2[/tex]
The volume of the pyramid is calculated as:
[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]
V =[tex]\pi r^3[/tex]
Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.
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Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
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Bob needs to send out a mailing for his company. Working alone, it will take him 10 hours to get the job done. Ellen can do the job in 8 hours by herself. They work together for 2 hours, and then Ellen finishes the job by herself. Which choice is the best estimate for how long the job will take in all?
Answer:
6 2/5 hrs or 6.4 hours total
Step-by-step explanation:
In two hours, Bob completes 2/10 = 1/5 of the job
Ellen completes 2/ 8 = 1/4
Find amount left
1 - 1/5 -1/4 = 1 - 4/20 - 5/20 = 11/20 left
Ellen will need 8hrs * 11/20 = 88/20 = 4 2/5 hours to finish the job
2 hours to start + 4 2/5 hours to finish = 6 2/5 hours total
Someone please explain.50 points available.Thankyou so much!
Answers:
a) 49 square tiles - did the work on paper.
b) 83 circular tiles - did the work on paper.
c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.
Step-by-step explanation:
I did all the work on paper it took a while to do it. pls mark brainliest
Express 324000000 in scientific natation
Answer:
[tex]3.24*10^8[/tex]
Step-by-step explanation:
First, it is even so you don't need a negative power. Secondly, you put the decimal point after the first number which is three, and the next numbers which are not zeros go after it. Then you count the two numbers behind the decimal and the rest of the zeros. Then the number you get is the power of 10. And then just multiply and check your answer. :)
Round 51.6172 to the
thousandths place.
Answer:
51.617
Step-by-step explanation:
tythe answer is 51.617 hope it helps
Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.
Answer: 51.617
:)
What is the exponent of x in in the expression -4x^3y^2 + 6
Answer:
3
Step-by-step explanation:
- 4x³y² + 6
the x is raised to the power of 3 , that is exponent of x is 3
Urve revolves around the x-axis. if you cannot evaluate the integral exactly, use your calculator to approximate it. (round your answer to four decimal places. ) y = 16 − x2 from x = −1 to x = 1
The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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Someone help me please
30-60-90 triangles
Answer:
Short leg = 10
Longer leg = 10[tex]\sqrt{3}[/tex]
Hypotenuse = 20
Step-by-step explanation:
The given is a special right triangle, its angle measures are as follows:
30-60-90 and the side lengths will follow as:
x, x[tex]\sqrt{3}[/tex], 2x respectively.
The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20
We can conclude x = 10 from this
So the length of short leg is 10
Then the length of longer leg is 10[tex]\sqrt{3}[/tex]
The length of hypotenuse is already given as 20
Halfway through the season, the USF Bulls football team had the highest average final score. What was the USF Bulls' average score if their final
scores were 31, 36, 28, 52, and 27
Answer:
D 34.8
Step-by-step explanation:
[tex]\frac{31+36+28+52+27}{5}[/tex]
