Answers
Answer:
[tex]S=\frac{12}{5}[/tex]Step-by-step explanation:
The common ratio of the following sequence is:
[tex]\frac{\frac{9}{16}}{\frac{3}{2}}=\frac{3}{8}[/tex]If the common ratio is less than 1 or greater than -1 but not 0, we can use the following expression to determine the sum of the infinite geometric series:
[tex]S=\frac{a_1}{1-r}[/tex]Therefore, if we have a common ratio of 3/8 or 0.375 and the first term of the series is 3/2.
The sum would be:
[tex]\begin{gathered} S=\frac{\frac{3}{2}}{1-\frac{3}{8}} \\ S=\frac{\frac{3}{2}}{\frac{5}{8}} \\ S=\frac{24}{10}=\frac{12}{5} \end{gathered}[/tex]Related Questions
Triangle VWX is formed by connecting the midpoints of the side of triangle STU.
The lengths of the sides of triangle VWX are shown. What is the length of SU?
Figures not necessarily drawn to scale.
Answers
The length of the side SU will be equal to 4√2.
What is a Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The formula for the Pythagorean theorem will be given as:-
H² = P² + B²
Here,
H = Hypotenuse
P = perpendicular
B= Base
The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.
Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.
H² = P² + B²
sx² = xv² + sv²
sx = √ ( 2² + 2² )
sx = √8
sx = √ ( 2 x 2 x 2 )
sx = 2√2
SU = 2 sx
SU = 2 x 2√2
SU = 4√2
Therefore, the length of the side SU will be equal to 4√2.
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(-7i)(3+3i)(a) Write the trigonometric forms of the complex numbers. (Let0 ≤ theta < 2pi.)(-7i) =(3+31) =(b) Perform the indicated operation using the trigonometric forms. (Let0 ≤ theta< 2pi.)(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
Answers
A complex number z is given in the form:
z = (x.y) = (realpart) x + imaginary part (iy)
In this case:
z1 = -7i
z2 = 3+3i
To write in trigonometric form:
[tex]\begin{gathered} z\text{ = r\lparen cos}\theta\text{ + isin}\theta) \\ For\text{ z1} \\ r\text{ = }\sqrt{0^2+7^2} \\ \text{ = 7} \\ \theta\text{ =}\tan^{-1}(\frac{7}{0} \\ Since\text{ t}he\text{ }argument\text{ }is\text{ }undefined\text{ }and\text{ y is negative,} \\ \theta=\text{ }\frac{3\pi}{2} \\ In\text{ trig form:} \\ z1\text{ = 7\lparen cos}\frac{3\pi}{2};sin\frac{3\pi}{2}) \\ For\text{ z2} \\ r\text{ = }\sqrt{3^2\text{ +3}^2} \\ \text{ =3}\sqrt{2} \\ \theta\text{ = }\tan^{-1}\frac{3}{3} \\ =\text{ }\frac{\pi}{4} \\ In\text{ trig form:} \\ z2\text{ = 3}\sqrt{2}(cos\frac{\pi}{4};sin\frac{\pi}{4}) \end{gathered}[/tex]Multiplication in trigonometric form:
[tex]z1*z2\text{ = \lparen21}\sqrt{2}\text{ \rparen \lparen cos}\frac{7\pi}{4};\text{ sin}\frac{7\pi}{4})[/tex]Multiplication in standard form:
[tex]\begin{gathered} (-7i)(3\text{ + 3i\rparen} \\ =-21i\text{ - 21i}^2 \\ i^2\text{ = -1} \\ =\text{ -21i + 21} \\ r\text{ = }\sqrt{21^2+21^2} \\ =21\sqrt{2} \end{gathered}[/tex]Solve the system of equations below for x, y, and z. (4x - 2y + 3z = 9 x - 2y = -3 2x + 3y = 1
Answers
The solutions are x = -1, y = 1 and z = 5
What is a Linear equation?In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z or a, b, c .. etc.
According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method
Here, we have three linear equations with 3 and 2 variables
4x - 2y + 3z = 9 ----(1)
x - 2y = -3 -----(2)
2x + 3y = 1 -----(3)
Here, to find x, y and z we will use Elimination method
First of all solve (2) and (3) as given below
2 × (2) ⇒ 2x - 4y = - 6 -----(4)
1 × (3) ⇒ 2x + 3y = 1
Now subtract (3) from (4)
(4) - (3) ⇒ 2x - 4y -2x - 3y = - 6 - 1
⇒ - 7y = -7
⇒ y = 1
Substitute y = 1 in (2)
(2) ⇒ x - 2(1) = -3
x - 2 = -3
x = -1
Now substitute x = -1 and y = 1 in (1)
(1) ⇒ 4(-1) - 2(1) + 3z = 9
- 6 + 3z = 9
3z = 15
z = 5
From above calculations
The values of x = -1, y = 1 and z = 5
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a pharmaceutical company knows that five percent of all users of a certain drug experience a serious side effect. a researcher examines a sample of 200 users of the drug. a. what is the probability of finding between 8 and 12 cases with side effects? (round final answer to 4 decimal places.) b. what is the probability of finding more than 16 cases with side effects? (round final answer to 4 decimal places.)
Answers
Using the normal distribution, the probabilities are given as follows:
a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.
b. More than 16 cases with side effects: 0.0174 = 1.74%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
p = 0.05, n = 200.
Hence the mean and the standard deviation of the approximation are given as follows:
E(X) = np = 200 x 0.05 = 10.[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{200(0.05)(0.95)} = 3.08[/tex]For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:
X = 12.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (12.5 - 10)/3.08
Z = 0.81
Z = 0.81 has a p-value of 0.7910
X = 7.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7.5 - 10)/3.08
Z = -0.81
Z = -0.81 has a p-value of 0.2090.
0.7910 - 0.2090 = 0.582 probability.
For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (16.5 - 10)/3.08
Z = 2.11
Z = 2.11 has a probability of 0.9826.
1 - 0.9826 = 0.0174 = 1.74% probability.
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help me pls and explain to me how to find y intercept
Answers
Answer:
y = -x + 4
Step-by-step explanation:
(-1, 5), (2. 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - 5 -3 -3
m = ----------- = ----------- = --------- = ------- = -1
x₂ - x₁ 2 - (-1) 2 + 1 3
y - y₁ = m(x - x₁)
y - 5 = -1(x - (-1))
y - 5 = -1(x + 1)
y - 5 = -x - 1
+5 +5
----------------------
y = -x + 4
I hope this helps!
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = 8, - 4) and (x₂, y₂ ) = (- 1, 5) ← 2 ordered pairs from the table
m = [tex]\frac{5-(-4)}{-1-8}[/tex] = [tex]\frac{5+4}{-9}[/tex] = [tex]\frac{9}{-9}[/tex] = - 1 , then
y = - x + c
to find c use any ordered pair from the table
using (2, 2 ) , then
2 = - 2 + c ⇒ c = 2 + 2 = 4
y = - x + 4 ← in slope- intercept form
with y- intercept c = 4
3. Determine the percent of each quantity.
a. 7% of 80
c. 12% of 320
b. 15% of 55
d. 8% of 300
Answers
Answer:
a. 5.6
b. 38.4
c. 8.25
d. 24
Step-by-step explanation:
Which number is the greatest?
-8
-10
-7
Answers
Answer:
-7
Step-by-step explanation:
-7 is the greatest because it is closer to 0 on the number line.
x^2+6x+? complete the square
Answers
Answer:
+ 9
Step-by-step explanation:
x²+ 6x
to complete the square
add ( half the coefficient of the x- term )² to x² + 6x
x² + 2(3)x + 3²
= x² + 6x + 9
= (x + 3)² ← a perfect square
how many elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements? how many ways are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each? (assume that no student can have more than one major.) how many ways are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6?
Answers
a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.
b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.
c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.
The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set B or including more sets
For the first problem, the sets contain:
n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0
So, n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)
= 10 +15+25-0-0-0-0-0
= 50
For the second problem, since no student can have more than one major.
So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)
As we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17
So , (A∪B∪C∪D∪E∪F∪G) = 31+88+19+11+41+22+17= 229
For the third problem, we have
n(A)=5
n(B)=3
n(C)=2
n(D)=7
n(E)=6
So, the number of elements will be (A∪B∪C∪D∪E) = 5+3+2+7+6 =23
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Divide $180 in the ratio of 2 : 3 : 4
Answers
By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
Solution
Find the sum of the ratios2 + 3 + 4 = 9
Divide the amount from the sum of the ratios180 ÷ 9 = 20
Hence, we get the quotient of 20.
Multiply the quotient by the ratios20 × 2 = 40
20 × 3 = 60
20 × 4 = 80
Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
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Please helppp as fast as possible
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
Answers
THE DOMAIN & RANGE OF THE FUNCTION g(x)=|x + 4| is
Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]This is further explained below.
What is the domain?Generally, The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
[tex](-\infty, \infty)[/tex]
Set-Builder Notation:
[tex]$\{x \mid x \in \mathbb{R}\}$[/tex]
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
[tex]$[0, \infty)$[/tex]
Set-Builder Notation:
[tex]$\{y \mid y \geq 0\}$[/tex]
Determine the domain and range.
Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]
Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]
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A metal pole to hang banners and advertisements is attached to a brick
building to form a right angle. A diagonal brace is placed 5 feet below the
pole to give support. What is the length in feet of the pole?
13 ft
5 ft
Answers
The length in feet of the pole is 13 ft.
What is Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.
Use the Pythagorean relationship:
c²= a² + b²
= 5² + 12²
= 25 + 144
= 169
c = 13
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can you tell me if my answer is correct
Answers
Answer:
(a)Vertex
(c)3 seconds
Explanation:
Part A
The maximum point on a parabola is called the Vertex.
Part C
To find out how much the plain was in the air, find the values of t at which the height, h=0.
Next, subtract the second value of t from the first value.
[tex]h=-16t^2+32t+48[/tex]First, set h=0:
[tex]\begin{gathered} h=-16t^2+32t+48=0 \\ -16t^2+32t+48=0 \end{gathered}[/tex]Factorize:
[tex]\begin{gathered} -16(t^2-2t-3)=0 \\ t^2-2t-3=0 \\ t^2-3t+t-3=0 \\ t(t-3)+1(t-3)=0 \\ (t+1)(t-3)=0 \\ t+1=0\text{ or }t-3=0 \\ t=-1\text{ or }t=3 \end{gathered}[/tex]Therefore, the plane hits the ground after 3 seconds.
what is the anwser
-2|7x-1|= 14
Answers
Answer: -3/4
Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.
Nice helping out!
Answer:
There are no solutions.
Step-by-step explanation:
Hello!
Isolate the absolute value equation first:
-2|7x - 1| = 14|7x - 1| = -7Now stop and think.
An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.
So the solution is No Solutions.
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the House blend with the Organic Free Trade blend, but always in the same proportion. Yesterday, you mixed 140 pounds of the House blend with 168 pounds of the Organic Free Trade blend. Today, there is 130 pounds of the House coffee left in stock. How many pounds of the Organic Free Trade coffee should you mix with it to get your secret blend?
Answers
The ratio House blend/Organic Free Trade blend is the same and must remain the same.
So, the proportion is:
[tex]\frac{140}{168}=\frac{130}{x}[/tex]Where x is the unknown amount of the Organic Free Trade blend.
So, from the proportion, we have:
[tex]\begin{gathered} 140\cdot x=168\cdot130 \\ 140x=21840 \\ \frac{140x}{140}=\frac{21840}{140} \\ x=156 \end{gathered}[/tex]Answer: 156 pounds of Organic Free Trade blend
What is the scale factor that takes circle m to circle n? Solve on paper if you need to. Then, enter your answer on Zearn
Answers
The scale factor which takes circle m to circle n as depicted in the attached image is; 3.
What is the scale factor that takes circle m to circle n as required?It follows from the task content that the scale factor which takes circle m and transforms it to circle n is to be determined.
Hence, since both circles have the same center, the center can be taken as a point of reference.
Therefore, the distances between the center of the circles m and n to any point on their circumferences are; 3 units and 9 units respectively.
On this note, since circle n is; 9/3 = 3 times as large as circle m, it follows that the required scale factor is; 3.
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solve the following equation 7x + 14=28
Answers
Answer:
x = 2
Step-by-step explanation:
The Question was:
7x + 14 = 28
Subtract 14 from both sides.
7x = 28 − 14
Subtract 14 from 28 to get 14.
7x = 14
Divide both sides by 7.
x = 14/7
Divide 14 by 7 to get 2.
x = 2
Answer:
x=2
Step-by-step explanation:
To solve a question like that, we have to isolate the variable.
What is the variable? A variable is a letter partaking in an equation that is in place of a number or solution that makes the equation true.
In this case, the variable is x.
To isolate the variable, we must do the opposite action that is being done to the number.
For example, if a number was added to one side by 28, we can subtract both sides by 28 so it negates the addition and does not alter the original equation.
7x+14=28 We can subtract the 14 on both sides to negate the -14 -14 addition.
7x=14 Divide each side by 7 to isolate x.
x=2
8 times the quantity of X and 8 Translate it into expression
Answers
Given
8 times the quantity of X and 8
Find
Translate into an expression
Explanation
Quantity be X
so , according to the question ,
8 (X + 8)
Final Answer
Hence , the required expression is 8 (X + 8)
Help please:)! Really STUCK on this question!
Answers
Answer:
Step-by-step explanation:
it 10
Which equation illustrates the associative property
Answers
Associative property of the sum states that the order the operations are done doesn't matter as long as the sequence of operands also doesn't change. This property is given by:
[tex](x+y)+z=x+(y+z)[/tex]Therefore, the equation that illustrates the associative property is:
[tex]a+(b+c)=(a+b)+c[/tex]allison drove home at 58 mph, but her brother austin, who left at the same time, could drive at only 46 mph. when allison arrived, austin still had 24 miles to go. how far did allison drive?
Answers
When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph. Allison arrived, Austin still had 24 miles to go.
Let t be the time they drove.
Then you have this "distance" equation
58t = 46t + 24
saying that both parts of the equation represent the same distance. Then
58t - 46t = 24
12t = 24
t = 2 hours.
Hence the distance is, 2 x 58 = 116 mph.
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Write a number that satisfies the given condition. An integer between - 0.6 and 0.4. The integer between -0.6 and 0.4 is
Answers
Answer:
I think the answer is 0.
Step-by-step explanation:
-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4
in addition to the facts in the diagram which other statements are necessary to prove that? ABC is congruent to? EFG by the ASA criterion
Answers
Triangle ABC and the triangle EFG are congruent by the first and third statement.
What is the congruent diagram?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
In the given example triangle ABC and triangle EFG having one same side of length 2.
By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.
When "m ∠ B and m ∠ F" and "m ∠ A and m ∠ E" are same then the triangles are congruent.
Therefore, the first option is correct.
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what is ( -8.7) times (-10)?
Answers
Answer:
87
Step-by-step explanation:
Answer:87
Step-by-step explanation:
an article is $68000 and sold at a profit of 14%. Find the selling price
Answers
Answer:
The selling price is: [tex]\$77,520[/tex]
Step-by-step explanation:
Step 1: Identify the profit made
A profit of 14% is made on the article.
This means that the article was sold at a price that had 14% of its original price added to it.
The 14% of the original price is:
[tex]14\% \times 68000\\=\frac{14}{100}\times 68000\\\\\text{Calculate the value}\\\frac{14}{100}\times 68000\\=9520[/tex]
So, a profit of $9520 was made
Step 2: Calculate the selling price
The selling price will be the sum of the original price and the profit.
The selling price is:
[tex]68000+9520\\=77520[/tex]
Eric ordered a set of red and yellow pins. He received 70 pins in all. 21 of the pins were red. What percentage of the pins were red?
Answers
Answer:
The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100
Percentage of red pins = (21÷70)×100
= 30%
What is the value of x?
Answers
Answer:
15
Step-by-step explanation:
If (-6,-38) and (5,28) are twoanchor points on the trend line,then find the equation of the line..y = 6x + [?]
Answers
Step 1
Write the slope, y-intercept form of the equation of a line.
[tex]undefined[/tex]The average change in a company's sales income was $9 million over 3 moths. Determine the average change in sales income per month.
Answers
The average change in sales income per month is $ 3 million.
What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.
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21. What are the modes of the following sets of numbers?
a. 3, 13, 6, 8, 10, 5, 6
b. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
Answers
Answer:
a. 6
b. 16
Step-by-step explanation:
a.
The mode is the number that appears the most
3 appears once
13 appears once
6 appears twice
8 appears once
10 appears once
5 appears once
Since 6 appears the most, it is the mode in this set of numbers
b.
Again, The mode is the number that appears the most
12 appears once
0 appears once
15 appears twice
13 appears twice
19 appears once
16 appears three times
Since 16 appears the most, it is the mode in this set of numbers
The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
____________________
Step-by-step explanation:
The question asks to find the modes of the following sets of numbers:
Set a) "{3, 13, 6, 8, 10, 5, 6}."
Set b) "{12, 0, 15, 15, 13, 19, 16, 13, 16, 16}."
Note that the mode is the number that occurs most frequently within a data set.
To begin: let's find the mode of Set: a:
_____
First, let's list all the values within Set: a: in order of smallest to largest—to simplify matters:
→ " { 3, 5, 6, 6, 8, 10, 13 }."
In this data set, there is only one value that occurs more than once—
which is 6. As such, the mode of "Data Set: a" is 6 .
Then: To continue: let's find the mode of Set: b:
_____
Second, Let's list all the values within Set: b: in order of smallest to largest—again; to simplify matters:
→ " { 0, 12, 13, 13, 15, 15, 16, 16, 16, 19 } ."
In this data set, we see the following:
Each of the three values: 0, 12, and 19 appear only once;
13 and 15 individually, appear twice; and:
16 appears "three times".
As such:
The value, 16 appears the most in this data set; and:
→ The mode of "Data Set: b"—is 16.
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The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
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