ANSWER:
Lower limit: 4.73
Upper limit: 4.78
STEP-BY-STEP EXPLANATION:
Given the following data set:
[tex]4.72,4.74,4.83,4.75,4.73,4.87,4.69,4.7,4.76,4.7,4.79,4.76[/tex]We calculate the mean and standard deviation:
[tex]\begin{gathered} \mu=\frac{4.72+4.74+4.83+4.75+4.73+4.87+4.69+4.7+4.76+4.7+4.79+4.76}{12}=\frac{57.04}{12}=4.753 \\ \\ \sigma=\sqrt{\frac{\lparen4.72-4.753^2+\left(4.74-4.753\right)^2+\lparen4.83-4.753)^2+\left(4.75-4.753\right)^2+\left(4.73-4.753\right)^2+\lparen4.87-4.753)^2+\left(4.69-4.753\right)^2+\lparen4.7-4.753)^2+\left(4.76-4.753\right)^2+\left(4.7-4.753\right)^2+\left(4.79-4.753\right)^2+\left(4.76-4.753\right)^2}{12-1}} \\ \\ \sigma=0.054 \end{gathered}[/tex]The critical limit of 90% confidence interval is 1.645
We can determine the limits as follows:
[tex]\begin{gathered} \text{ Lower limit: }\mu-Z\cdot\frac{\sigma}{\sqrt{n}}=4.753-1.645\cdot\frac{0.054}{\sqrt{12}}=4.727\cong4.73 \\ \\ \text{ Upper limit:: }\mu+Z\cdot\frac{\sigma}{\sqrt{n}}=4.753+1.645\cdot\frac{0.054}{\sqrt{12}}=4.778\cong4.78 \end{gathered}[/tex]What values of c and d would make
the following expression represent a real number?
i(2 + 3i)(c + di)
c = 2, d = 3
c = –2, d = 3
c = 3, d = –2
c = –3, d = –2
The values of c and d that would make that the given expression represent a real number are c = –3, d = –2.
What is meant by the term real number?In mathematics, a real number is a quantity that may be articulated as just an infinite decimal expansion. In comparison to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are employed in measurements of varying different quantities including such size and time.For the given question;
The expression is given as;
= i(2 + 3i)(c + di)
Simplify the expression;
= i(2c + 2di + 3ci + 3di²)
= 2ci + 2di² + 2ci² + 3di³
= (2c - 3d)i - 2d - 3c
In order is for expression to yield a real number, the coefficient of must now be zero.
Check the values from option;
2c - 3d = 2 x 2 - 3x 3 = -5
2c - 3d = 2 x -2 - 3 x -3 = -13
2c - 3d = 2 x 3 + 3 x -2 = -1
2c - 3d = 2 x -3 -3 x - 2 = 0
Thus, the correct values for the expression to becomes real number is
c = –3, d = –2.
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Of a sample of 500 students surveyed, 300 students say they listen to music when they study. In a school with 1500 students, how many students would be likely to listen to music while studying? hi 300 students 500 students 900 students 1200 students
Given:
Surveyed Sample = 500 students
Number of students who listen to music = 300
The probability of students that listens to music is given by the formula:
[tex]pr\text{ =}\frac{number\text{ of students that listen to music}}{Total\text{ number of student}}\text{ =}\frac{300}{500}[/tex][tex]pr\text{ = }\frac{3}{5}[/tex]In a sample of 1500 students, to find the probable number of students that will listen to music
we will multiply the probability we obtained initially by the sample space
=>
[tex]\begin{gathered} \frac{3}{5}\text{ x 1500} \\ \\ \frac{4500}{5} \\ \\ =900 \end{gathered}[/tex]It is likely that 900 students will listen to music while studying
Do 5 + 3 and 3 + 5 represent the same express? Explain.
5 + 3 = 8
3 + 5 = 8
The represent the same expression
You and your best friend have $10,000 each, which you would like to keep in a savings account. 5/3rd bank offers 4.23% continuous interest and bank of america will give 4.4% interest compounded quarterly. what would be the difference between the two investments after 35yrs? (round to the nearest dollar (whole number))
The difference between the two investments after 35yrs is $4700 and Bank of America is offering higher interest than 5/3rd banks.
Explain compound interest and continuous interest.Most interest is compounded semiannually, quarterly, or monthly. Continuous compounding assumes that interest is compounded indefinitely and reentered on the balance sheet. The continuous compounding formula takes into account four variables.
For the given question,
5/3rd bank offers continuous interest:
For continuous interest, A = P[tex]e^{rt}[/tex]
where,
P = the initial amount
A = the final amount
r = the rate of interest
t = time
e is a mathematical constant where e ≈ 2.7183.
A = 10000 × [tex]2.71^{0.042*35}[/tex]
A = 10000 × 4.04
A = $40400 approximately
Interest = Amount - Principle
Interest = 40400 - 10,000
Interest = $30400
Bank of America offers compound interest:
For compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A = 10000 × 4.51
A = $45100
Interest = Amount - Principle
Interest = 45100 - 10,000
Interest = $35100
The above calculation explains Bank of America is offering higher interest than 5/3rd bank by $35100 - $30400 = $4700
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Set up a proportion and soive for
side TV (y):
ATUV-AXWV
As we Know that, ΔTUV[tex]\sim[/tex] ΔXWV
So, for the given proportion TV(y) = 21.
What is Proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
What is Ratio?
The link between two or more things in terms of quantity, amount, or size.
Given that,
ΔTUV[tex]\sim[/tex] ΔXWV
∠T = ∠X
∠U = ∠W
∠TUV = ∠XWV
So, TU/WX = TV/WV
10/10 = TV/21
1 = TV/21
TV = 21
So, for the given proportion the value for the side TV(y) = 21
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If point (x, y) is reflected over the line y = x, the resulting point is (y,x).TrueFalse
When we reflect a point over y = x, the x and y coordinates become swapped and switch places, that is why (x,y) results to (y,x).
Therefore, the answer is true.
Write 280,000,000 in scientific notation.
0.28 × 109
28 × 108
2.8 × 108
2.8 × 109
Answer:
= 4.875 × 105
(scientific notation)
= 4.875e5
(scientific e notation)
= 487.5 × 103
(engineering notation)
(thousand; prefix kilo- (k))
|x - 7| ≥ 1?
what is the solution?
Answer: Inequality form: x is less then or equal to 6 or xis greater then or equal to 8
Interval Notation: (-infinity,6] u [8,infinity)
Answer:
x ≤ 6 ∨ x ≥ 8
Step-by-step explanation:
x-7 ≥ 0
when
x≥7
if x≥7
x-7≥ 1
x ≥ 7 + 1
x ≥ 8
if x < 7
-x + 7 ≥ 1
-x ≥ -7 + 1
-x ≥ -6
x ≤ 6
Final solution
x≤ 6 ∨ x ≥ 8
How many solutions does this equation have?
–8y + 1 = –8y
Answer:
-8 + 1 = -8
+8 +8
1 = 0
no solution
Jasper opened a savings account and deposited 200.00 the account earns 9%interest compounded annually if he wants to use the money to buy a new bicycle in 2 years how much will he able to spend on the bike
The formula for calculating the amount of money after compounding for a period of time is expressed as;
A = P(1+r/n)^nt
P is the principal (amount deposited)
r is the rate
t is the time
n is the time of compounding
Given
P = 200.00
r = 9% = 0.09
t = 2 years
n = 1 year
Substitute the given parameters into the formula
A = 200(1+0.09/1)^1(2)
A = 200(1.09)^2
A = 200(1.1881)
A = 237.62
Hence he will be able to spend 237.62 on the bike
What is the value of x in the equation 3/2(4x - 1) – 3x = 5/4-(x + 2)? Pick one below. 1. 1/16 2. 3/16 3. 19/164. 3X= ???
The equation is given as
[tex]\frac{3(4x-1)}{2}-3x=\frac{5}{4}-(x+2)[/tex][tex]\begin{gathered} \frac{3(4x-1)-2\ast3x}{2}=\frac{5-4\ast(x+2)}{4} \\ \frac{3(4x-1)-6x}{2}=\frac{5-4x-8}{4} \\ \frac{12x-3-6x}{1}=\frac{-3-4x}{2} \\ (6x-3)=\frac{-3-4x}{2} \\ (6x-3)\ast2=-3-4x \\ 12x-6=-3-4x \\ 12x+4x=-3+6 \\ 16x=3 \\ x=\frac{3}{16} \end{gathered}[/tex]The value of x is 3/16.
1/3(x+18)= 7 sole for x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
1/3(x+18)= 7
x = ?
Step 02:
We must apply the algebraic rules to find the solution.
[tex]\begin{gathered} \frac{1}{3}\cdot(x+18)=7 \\ x\text{ + 18 = 3}\cdot7 \\ x=21-18\text{ = 3} \end{gathered}[/tex]The answer is:
x = 3
A regular pentagon is inscribed in a circle as shown. 1. Find the measure of minor arc cut off by one of the diagonals.2. Find the length of the same minor arc in problem 16a, given the radius of the circle is 10 cm. Leave the answer is terms of pi.
SOLUTION:
Step 1:
we are to find the measure of minor arc cut off by one of the diagonals;
The sum of interior angles in a pentagon is:
[tex]\begin{gathered} (n-2)\text{ x 180} \\ (5-2)\text{ x 180} \\ 3\text{ x 180} \\ 540 \end{gathered}[/tex]Each interior angle of a regular pentagon is
[tex]\frac{540}{5}\text{ = 108}[/tex]So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.
[tex]\text{The major arc = 2 x 108 = 216}[/tex]Then recall,
[tex]\begin{gathered} \text{The major arc + the minor arc = 360 (sum of angles at a point)} \\ 216\text{ + the minor arc = 360} \\ \text{The minor arc = 360 - 216} \\ \text{The minor arc =144} \end{gathered}[/tex]Step 2:
We are to find the length of the same minor arc in problem;
[tex]\frac{\theta}{360}\text{ x 2 }\pi\text{ r}[/tex]Where our angle (titan) is 144 and radius is 10
[tex]\begin{gathered} \frac{144}{360}\text{ x 2 x }\pi\text{ x 10} \\ \\ 8\pi \end{gathered}[/tex]So the length of the minor arc, given that the radius is 10 cm is 8 pi
- 3(x + 7) - 3x - 18 ? Please I really need help because our long-term sub won’t explain it in a way I can understand
Answer:
-6x - 39
Step-by-step explanation:
-3(x + 7) -3x -18 Fist distribute the -3
-3(x) + -3(7) -3x -18 Simplify (a negative times a positive is a negative)
-3x -21 -3x -18 Now combine like terms
-6x -39
LaDawn needed wire for her Halloween wreath. How many 1/4 inch pieces can be cut from a piece of wire that is 5/8 inches long?
The length of each piece of wire is 2.5 inches.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
Let the number of pieces = x
The length of the wire = 5/8 inches
The length of one piece of wire = 1/4 inch
According to the question,
1/4 x = 5/8
So, x = 5/8 × 4
x = 20/ 8
x = 5/2
x = 2.5 inch
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Which of the linear equations represents the graphed line?
Responses
A y = 32x + 1y = 3 2 x + 1
B y = −23x + 1y = − 2 3 x + 1
C y = −32x + 1y = − 3 2 x + 1
D y = 23x + 1
The linear equations of the graph are y = 2/3x + 1. Option D.
Solution:
Let's find the slope of the graph using the coordinates (0, 1) (-3, -1)
m = y₂ - y₁ / x₂ - x₁
m = -1 - 1 / -3 - 0
m = -2/-3
m = 2/3
Using the slope-intercept form,
y = MX + c
where
m = slope
c = y-intercept(This is when x = 0)
Therefore,
c = 1
Finally, the equation will be y = 2/3 x + 1.
An equation is a mathematical statement consisting of two expressions joined by an equal sign. The ID applies to all values of the variable. Constraint expressions apply only to specific values of variables. A mathematical expression that expresses the relationship between two terms on either side of a letter.
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a14. What are the lengths of b and c? Write your answer to the nearest tenth of a metre, where appropriate. b 5m 3 m-k3 m
Solution:
As you can see in the diagram, there are two triangles. We will separate the two triangles into the smaller and the bigger one.
For the smaller triangle:
Now we will use the Pythagorean Theorem. The theorem states that the square of the longest side is equal to the sum of the squares of the two other sides.
To solve for the value of b, we will have:
[tex]\begin{gathered} 5^2=3^2+b^2 \\ b^2=5^2-3^2 \\ b=\sqrt[]{5^2-3^2} \\ b=\sqrt[]{25-9} \\ b=\sqrt[]{16} \\ b=4 \end{gathered}[/tex]For the bigger triangle:
We will also use the pythagorean theorem to find the value of c and by using the value of b we got from the smaller triangle.
[tex]\begin{gathered} c^2=b^2+6^2 \\ c^2=4^2+6^2 \\ c=\sqrt[]{4^2+6^2} \\ c=\sqrt[]{16+36} \\ c=\sqrt[]{52} \\ c=2\sqrt[]{13} \\ c=7.211102551 \end{gathered}[/tex]ANSWER:
b = 4 cm
c = 7.2 cm
Sketch the graph of y= sin x° for 0≤x≤360
Answer:
Step-by-step explanation:
This is a sketch graph of y= sin x° for 0 ≤ x ≤360.
It is called as Sine curve. A mathematical curve described in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
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What percent of 120 is 180%
What percent of 120 is 180
we know that
120 represent the 100%
so
Applying proportion
100/120=x/180
solve for x
x=(100/120)*180
x=150%
the answer is 150%The total number of participants who went on the seventh-grade field trip to the Pink Palace consisted of all of the seventh-grade students and 13 adult chaperones. Four-ninth of the total participants rode a large bus, and the rest rode a smaller bus. If 156 people rode the larger bus, how many students went on the field trip?
338 students went on the field trip.
Given:
Four-ninth of the total participants rode a large bus, and the rest rode a smaller bus.
156 people rode the larger bus.
Let x be the total participants.
4/9 x = 156
multiply by 9 on both sides
4*9/9 x = 156*9
4x = 156*9
4x = 1404
divide by 4 on both sides
4x/4 = 1404/4
x = 1404/4
x = 351.
number of students = total participants - adult chaperones.
= 351 -13
= 338 students
Therefore 338 students went on the field trip.
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What is the best approximation of the solution to the system to the nearest integer values?
A (3, 4)
B (2, 3)
C (1, 3)
D (3, 2)
Answer:
B (2, 3)
The two lines intersect near that point.
√20 - 2√5solve with using adding and subtracting radicals
the initial expression is:
[tex]\sqrt[]{20}-2\cdot\sqrt[]{5}[/tex]so to rest them we want to have the same radical so we can rewrite the root of 20 so:
[tex]\begin{gathered} \sqrt[]{4\cdot5}-2\cdot\sqrt[]{5} \\ 2\cdot\sqrt[]{5}-2\cdot\sqrt[]{5}=0 \end{gathered}[/tex]a line that passes through the point (2,1) and is parallel to the line y = -2x + 5
A line in slope-intercept form is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Parallel lines have the same slope, then if the line is parallel to the line y=-2x+5, the slope of the parallel line would be -2 too.
Now, by the given point (2,1) and knowing the slope of the line, we can use the slope-point form of the line equation to get the slope-intercept form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where,} \\ (x_0,y_0)\text{ is the given point} \\ m\text{ is the slope} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} y-1=-2(x-2) \\ y=-2x+4+1 \\ y=-2x+5 \end{gathered}[/tex]Notice that the parallel line would be the same original line, y=-2x+5.
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Libby wants to draw a scale diagram of the Sun and the Earth.
The diameter of the Sun is 1.4 million km to 2 s.f.
The diameter of the Earth is 13,000 km to 2 s.f.
k to task
Libby decides to draw the Earth with a diameter of 2 cm.
Work out the diameter of the Sun that she needs to draw.
Give your answer in metres to 2 significant figures.
Watch video
The diameter of the Sun that she needs to draw, considering the scale, is of:
2.15 m.
What is a scale?The meaning of the scale of a drawing is how much each unit in the drawing represents in actual distance.
In this problem, the actual diameters are given as follows:
Sun: 1,400,000 km.Earth: 13,000 km.The drawn diameters are given as follows:
Sun: x cm.Earth: 2 cm.From the scale of the earth, the number of km represented with each cm is given as follows:
13000/2 = 6500 km represented by each cm.
(division of the actual distance by the scale).
Hence the number of cm that is needed to represent 1,400,000 km is of:
1400000/6500 = 215 cm.
(division of the total distance by the scale).
Each cm is composed by 100, the diameter of the Sun in meters is of:
215/100 = 2.15 m.
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In 8 days, the temperature dropped 12 degrees. How many degrees per day did the temperature drop
Answer:
x = 1.5°
Step-by-step explanation:
8 days = 12°
1 day = x
cross-multiply
8x = 12
Divide both sides by the coefficient of x, which is 8
8x/8 = 12/8
x = 1.5°
Hence, 1 day = 1.5°
What is an equation of the line that passes through the points (6,0) and (3, 4)?
The slope-intercept form of the equation of a straight line is given to be:
[tex]y=mx+b[/tex]where m is the slope and b is the intercept on the y-axis.
The slope is calculated using two points on the line by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, for this line, the slope will be:
[tex]m=\frac{4-0}{3-6}=-\frac{4}{3}[/tex]Therefore, this value for the slope is substituted back into the equation for the line:
[tex]y=-\frac{4}{3}x+b[/tex]At the point (6, 0), we can calculate the value of b to be:
[tex]\begin{gathered} 0=-\frac{4}{3}(6)+b \\ b=\frac{4}{3}(6) \\ b=8 \end{gathered}[/tex]Therefore, the equation is:
[tex]y=-\frac{4}{3}x+8[/tex]15. Which of the following relations defines y as a function of x?
Remember that
The data set is a function if every element of the domain corresponds to exactly one element of the range
so
Verify each option
I ------> is a function (every element of the domain corresponds to exactly one element of the range)
II -----> is not a function (every element of the domain does not correspond to exactly one element of the range)
III ---> is a function (every element of the domain corresponds to exactly one element of the range)
IV ----> is not a function (every element of the domain does not correspond to exactly one element of the range)
therefore
The answer is
Both I and III define a y as function of xWhat number will complete the point-slope equation that models this scenario?
y−50,000=[_______](x−10)
−3,000
−2,000
2,000
3,000
A Point-Slope equation of a straight line models this scenario: y -50,000 = -3,000(x -10).
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
We can recognize any points of the graph.
(0,80000) ; (10,50000)
Given that;
y -50,000 =______(x -10)
We need to find the slope.
Slope = Change in y / Change in x
Slope = 80,000 - 50,000 / 0 - 10 = 30,000 / -10
= -3,000
The slope is equal to -3000 that is Choice A; y -50,000 = -3,000(x -10)
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The complete question is;
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario.
Graph each system and determine the number of solutions that it has. If there is no solution, type NS. Ifit has a solution, state it. When entering solutions, enter them as a coordinate pair. Do not includespaces in answers.3x +y = -33x +y = 3Number of Solutions:Solution:
we have the system
3x +y = -3
3x +y = 3
In this problem we have two different parallel lines
Remember that the solution of the system is the intersection point both lines
In this problem the lines don't intersect (are parallel)
therefore
the system has no solution NS
isolate the variable y in the first equation
y=-3x-3 -----> equation 1
isolate the variable y in the second equation
y=-3x+3 -----> equation 2
Solve the system of equations
equate equation 1 and equation 2
-3x-3=-3x+3
solve for x
-3x+3x=3+3
0=6 ------> is not true
that means
the system has no solution (NS)
Can someone help? :)
The slope of the given line is [tex]-\frac{3}{5}[/tex]
What is slope of a line?
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]
The given line passes through ( -1, -5) and (4, -8)
Slope of the line =
[tex]\frac{-8-(-5)}{4-(-1)}\\-\frac{3}{5}\\\\[/tex]
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