Set
[tex]\begin{gathered} \mu_1=875,\sigma_1=80 \\ \text{and} \\ \mu_2=10000,\sigma=1500 \end{gathered}[/tex]a) The Z-score formula is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Therefore, in our case, if x=2000
[tex]\Rightarrow Z=\frac{2000-875}{80}=\frac{1125}{80}=14.0625[/tex]Using a Z-score table,
[tex]\begin{gathered} P(z\ge2000)=1-P(z<2000)\approx1-1=0 \\ \Rightarrow P(z\ge2000)=0 \end{gathered}[/tex]A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.
b) Similarly, set x=5000; then,
[tex]Z=\frac{5000-10000}{1500}=-\frac{5000}{1500}=-3.333\ldots[/tex]Thus, using a z-score table
[tex]P(z\le5000)=0.0004[/tex]The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.
c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,
[tex]\begin{gathered} Incandescent \\ \mu_1\pm3\sigma_1=\lbrack875-240,875+240\rbrack=\lbrack635,1115\rbrack \\ \text{CFL} \\ \mu_2\pm3\sigma_2=\lbrack10000-4500,10000+4500\rbrack=\lbrack5500,14500\rbrack \end{gathered}[/tex]The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.
d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.
The probability of an incandescent bulb lasting 10000 hrs is
[tex]\begin{gathered} Z=\frac{10000-875}{80}=114.0625 \\ \Rightarrow P(z\ge10000)=1-P(z<10000)=0 \end{gathered}[/tex]The event is practically impossible.
Ashley took 3 minutes to run a distance of 540 meters from point X to point YGrace took 2 minutes to run a distance of 480 meters from point Z to point YA)Find the speed of each girl.B)Which of the two girls ran faster?
First, lets determine the speed of Ashley
d/ t = speed
540meters / 3 minutes
180 meters per minute
Now determine the speed of Grace
d/t = speed
480 meters / 2 minutes
240 meters per minute
Since Grace has the larger number, Grace ran faster
I need help figuring out the answer to this problem can someone help me please ?
So the average decrease will be 50% for the season of 5 weeks as the definition of percent decrease will be "The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease".
What is percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease. The letter "%" stands for it.
Here,
The percent decrease will be,
48000-24000=24000
24000/48000*100=50%
24000-12000=12000
12000/24000*100=50%
12000-6000=6000
6000/12000*100=50%
6000-3000=3000
3000/6000*100=50%
3000-1500=1500
1500/3000*100=50%
Due to the definition of percent decrease being a season of five weeks, the average decrease will be 50% "The percentage decrease is the difference between the starting and ending values. Regardless of the units, it shows a percentage decline in value relative to the starting point. The amount of decrease is the difference between the initial and final amounts ".
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which of the binomials below is a factor of this trinomial? x^2+14x+40A. x-9B. x+10C. x+14D. x^2 + 40
Given the following trinomial expression:
[tex]x^2+14x+40[/tex]To factor the trinomial, we need two numbers:
The product of them = 40
The sum of them = 14
The factors of 40 will be as follows:
40 = 1 x 40 ⇒ sum = 41
40 = 2 x 20 ⇒ sum = 22
40 = 4 x 10 ⇒ sum = 14
40 = 5 x 8 ⇒ sum = 13
so, the numbers will be 4 and 10
The factoring of the expression will be as follows:
[tex]x^2+14x+40=(x+4)(x+10)[/tex]So, the answer will be B. x+10
if Samantha has 37 green apples and give 4 to her sister and 3 to her bestfriend. How many apples does Samantha have left?
The number of apples that has been left with Samantha is 30 apples which is calculated using subtraction.
Total number of apples that Samantha has = 37 apples
Apples that she gave to her sister = 4 apples
Apples that she gave to her bestfriend = 3 apples
Total apples that she gave will be calculated by using addition.
Total apples that she gave = 4 + 3 = 7 apples
Now, the apples left with her will be calculated using subtraction.
Apples left with her = 37 - 7 = 30 apples.
Therefore, we get that, the number of apples that has been left with Samantha is 30 apples which is calculated using subtraction.
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8 Kiara has a bag with 9 oranges. She shares the oranges between 3 friends and herself. Write an equation to model the situation. How many oranges does each person receive?
9 oranges shared between 4 persons
x = 9/4
Oranges for each person = 9/(number of persons)
In this case, number of persons = 4
Oranges for each person = 9/4
Oranges for each person = 2.25 oranges (also we can write 2 1/4)
Find the y-intercept and x-intercept of the line 6x-2y=12
The expression we have is:
[tex]6x-2y=12[/tex]This is the equation of the line.
To find the y-intercept, we need to find the value for y, when x is equal to 0. So we plug x=0 into our equation:
[tex]6(0)-2y=12[/tex]And we solve for y:
[tex]-2y=12[/tex]Divide both sides by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{12}{-2} \\ y=-6 \end{gathered}[/tex]The y-intercept is at y=-6
In the coordinate form, the y-intercept is (0,-6)
Now, to find the x-intercept, we need to find the value of x, when y=0.
So we plug y=0 into the equation:
[tex]6x-2(0)=12[/tex]And we solve for x:
[tex]6x=12[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{12}{6} \\ x=2 \end{gathered}[/tex]The x-intercept is at x=2
In coordinate form, the x-intercept is: (2,0)
Answer:
2,-6
Step-by-step explanation:
the app is desmos btw- very helpful
Please break down how to do these pls
The value of given expressions is -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] = 19 and 2[tex]x^{0}[/tex][tex]y^{-2}[/tex] = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] 2. 2[tex]x^{0}[/tex][tex]y^{-2}[/tex]
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] = 19 and 2[tex]x^{0}[/tex][tex]y^{-2}[/tex] = 0.08
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Hello! Would you please explain if Questions 7 and 8 are the same? I'm confused if I need to sub x for 23 for number 8
In question 7, the exercise only wants an explanation, in text form, of the meaning of the substitutions. That is, that the value of x=5 indicates the time that has passed, 5 hours, and that f(5)=32 indicates the number of riders.
In question 8, you need to pick some values for x, make a table with those values and the respective values of the function when you substitute those values of x, and put the points on the graph.
Evaluating a Function In Exercises 5-12, evaluate the function at the given value(s) of the independent variable. Simplify the results. 5. f(x) = 3x - 2 (a) f(0) (b) f(5) (c) f(b) (d) f(x - 1)
Since the given function is
[tex]f(x)=3x-2[/tex]We want to evaluate it at some values of x
a) To find f(0), substitute x by 0
[tex]\begin{gathered} x=0 \\ f(0)=3(0)-2 \\ f(0)=0-2 \\ f(0)=-2 \end{gathered}[/tex]b) To find f(5), substitute x by 5
[tex]\begin{gathered} x=5 \\ f(5)=3(5)-2 \\ f(5)=15-2 \\ f(5)=13 \end{gathered}[/tex]c) To find f(b), substitute x by b
[tex]\begin{gathered} x=b \\ f(b)=3(b)-2 \\ f(b)=3b-2 \end{gathered}[/tex]d) To find f(x-1), substitute x by (x - 1)
[tex]\begin{gathered} x=(x-1) \\ f(x-1)=3(x-1)-2 \end{gathered}[/tex]Simplify it by multiply 3 by the bracket
[tex]\begin{gathered} f(x-1)=3(x)-3(1)-2 \\ f(x-1)=3x-3-2 \end{gathered}[/tex]Add the like term
[tex]\begin{gathered} f(x-1)=3x+(-3-2) \\ f(x-1)=3x+(-5) \\ f(x-1)=3x-5 \end{gathered}[/tex]Identify the slope and y-intercept of the line y = -3(x - 1) + 5. Also, graph this line.
The slope is -3, and y-intercept is 8
The graph is shown below:
Explanation:Given the line:
y= -3(x - 1) + 5
Let us write this in the form:
y = mx + b
Where m is the slope and b is the y-intercept
Removing the parentheses, we have:
y = -3x + 3 + 5
= -3x + 8
Therefore,
The slope is -3, and y-intercept is 8
C. Two angles are supplementary. One angle measures 2° less than 3 times the other. What are the measures of the two angles?
C.
if x one of the angles, then, the other angle is 3x - 2. Due to these angles are supplementary, you can write:
x + 3x - 2 = 180
by solving for x you obtain:
x + 3x - 2 = 180 simplify like terms left side
4x - 2 = 180 add 2 both sides and divide by 4 both sides
4x = 180 - 2
4x = 178
x = 178/4
x = 44.5
the other angle is then:
3x - 2 = 3(44.5) - 2 = 131.5
Hence, the two angles are 44.5° and 131.5°
need help find the crimcumference of each circles round your answer to the nearest tenth.
The formula in getting the circumference of a circle is:
[tex]C=2\pi r[/tex]where r = length of the radius and π = 3.14159.
Since the radius is already given in the circle which is 9.9 km, let's use this value to replace "r" in the formula. Use 3.14159 to replace π as well.
[tex]C=2\times3.14159\times9.9km[/tex]Then, multiply.
[tex]C=62.203482km\approx62.2km[/tex]Hence, the circumference of the given circle is approximately 62.2 km.
SCS_20-21 Math GR_CFA2 3 Chandler sadelta Naseen an Solana are the theater asks them to the expression shown. Each students answer is shown in 3 Which student answers carece b Doe here anarch
Given:
The expression is,
[tex]\frac{1}{3}(12+3\times6)-5[/tex]The objective is to find which students answer is correct.
By BODMAS rule, the order of arithmetic expression is Bracket, Order of power, Division, Multiplication, Addition, Subtraction.
So as per the rule of BODMAS, first perform the bracket operation.
Inside the bracket, the first operation to be perfoemed in multiplication.
[tex]\frac{1}{3}(12+18)-5[/tex]Now, perform addition inside bracket.
[tex]\frac{1}{3}(30)-5[/tex]Next operation after bracket is division.
[tex]10-5[/tex]Finally by performing the subtracting operation, the answer will be 5.
Hence, the answer of the student naSahar is correct.
What is the radius for a circle whose equation is x2 + y2 = 36?A. 18B. 36C. 1296D. 6
Answer:
D. 6
Explanation:
The general equation for a circle centered at the origin (0,0) is:
[tex]x^2+y^2=r^2[/tex]Given the equation of the circle:
[tex]\begin{gathered} x^2+y^2=36 \\ \implies r^2=36 \\ r^2=6^2 \\ r=6 \end{gathered}[/tex]Thus, the radius of the given circle is 6.
Help with question 13 ( the D just represents the word angle )
Using the law of sines, we would have that:
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Solving for C,
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C}\rightarrow\frac{\sin C\cdot b}{\sin B}=c\rightarrow\sin C\cdot b=c\cdot\sin B \\ \\ \rightarrow\sin C=\frac{c\cdot\sin B}{b}_{}\rightarrow C=\sin ^{-1}(\frac{c\cdot\sin B}{b}_{}) \end{gathered}[/tex]Plugging in the data given,
[tex]\begin{gathered} C=\sin ^{-1}(\frac{(10.3)\cdot\sin (58.8)}{(10.5)}_{}) \\ \\ \Rightarrow C=57 \end{gathered}[/tex]Therefore, we can conclude that:
I am needing help on how to this step by step please
The pattern will look like this:
[tex]\begin{gathered} \frac{20}{10}=2=2(10)^0 \\ \frac{20}{10^2}=\frac{2}{10}=2(10)^{-1} \\ \frac{20}{10^3}=\frac{2}{100}=2(10)^{-2} \\ \frac{20}{10^4}=\frac{2}{1000}=2(10)^{-3} \end{gathered}[/tex]The next number will have index of 10 as -4,-5 and so on.
A group of workers. an plant 2/3 acres in 7/8 days. Write the unit in acres per day?
To write the unit in acres per day. We have 2/3 acres and 7/8 days:
[tex]\frac{\frac{2}{3}}{\frac{7}{8}}\frac{\text{ acres}}{\text{ days}}=\frac{2\times8}{3\times7}\frac{\text{ acres}}{\text{ days}}=\frac{16}{21}\frac{\text{ acres}}{\text{days}}[/tex]Answer: 16/21 acres per day
This graph shows the distance that a robot walks. What is the rate of change of the robot's location?
Solution:
The rate of change, m, is;
[tex]\begin{gathered} m=\frac{d_2-d_1}{t_2-t_1} \\ \\ \text{ Where }d=distance,t=time \end{gathered}[/tex]Thus;
[tex]\begin{gathered} (1,10),(3,30) \\ \\ m=\frac{30-10}{3-1} \\ \\ m=\frac{20}{2} \\ \\ m=10 \end{gathered}[/tex]ANSWER: (D) 10 feet per minute
Learning Target #1: Creating and Solving Linear Equations11. Short Response #1: The perimeter of a rectangle is 130 ft. The length of the rectangle is 9 feetshorter than it is wide. What are the dimensions of the rectangle? (Hint: P = 2w + 2L) (4 points)Length:Width:
P = 2w + 2L
w = L - 9
The elevation of a city is positive if the city is above sea level and negative if below sea level.The elevation of New Orleans is -0.3 m.What does an elevation of -0.3 m represent in this situation?
If the elevation of New Orleans is -0.3m, then it is below sea level.
This is because it is a negative number and any
A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.
A. What is the area, in square meters, of 6 triangles? If you get stuck, draw a diagram.
The area of the 6 required triangles is 1/3m².
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. The seven different kinds of triangles that can be found in nature—equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene—must be studied and built.So, one square meter is equal to one huge square.
The larger square has now been divided into nine smaller squares.9 tiny square meters of space equals 1 square meter of space.So, using the unitary method, we can discover a single little square.1 tiny square is equal to 1/9 square meter.Each little square now has two similar triangles on each side of it.Now,
One triangle's surface area equals half that of a small square, or (1/2) (1/9) = 1/18 square meters.Using the unitary approach once more, determine the area of 6 triangles.The area of 6 triangles is equal to the 6 * area of 1 triangle, which is:6 * (1/18) = 1/3 square meter.Therefore, the area of the 6 required triangles is 1/3m².
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Solve. Leave a fraction in your in your answer, if necessary. 45 is what percent of 70.
The following can be written as,
[tex]\frac{45\times100}{70}=\frac{4500}{70}=64.29\text{ \%}[/tex]So 45 is 64.29% of 70.
Find the midpoint of the segment with the given endpoints.(-10,9) and (-3,4)
Let's apply the midpoint formula
((x1+x2)/2, (y1+y2)/2)
[tex](\frac{-3-10}{2},\frac{4+9}{2})[/tex][tex](\frac{-13}{2},\frac{13}{2})[/tex]can u help me fix what i did wrong in the equation
Based on the question, the vertical asymptote is x = -4 and x = 3. This means the denominator cannot have these x-values or else, the function becomes undefined. Hence, from these x-values, we can say that the factors of the denominator are:
[tex](x+4)(x-3)[/tex]Multiplying the factors, we get:
[tex]\begin{gathered} \Rightarrow x^2-3x+4x-12 \\ \Rightarrow x^2+x-12 \end{gathered}[/tex]So, the denominator of our rational function must be x² + x - 12 in order to have those vertical asymptotes.
Another given information is that our x-intercepts are at x = -2 and x = 5. This means that the numerator must be zero at these x-values. Hence, we can say that some factors of the numerator are:
[tex](x+2)(x-5)[/tex]Multiplying these two factors, we get:
[tex]\begin{gathered} \Rightarrow x^2-5x+2x-10 \\ \Rightarrow x^2-3x-10 \end{gathered}[/tex]This means x² - 3x - 10 should be part of our numerator.
Another given information is that the horizontal asymptote is at y = 4. This means that the ratio between the leading coefficients of the numerator and denominator is 4. (since both have the same degree)
So, in order to have a ratio of 4, we will multiply our numerator by 4.
[tex]4(x^2-3x-10)\Rightarrow4x^2-12x-40[/tex]Therefore, our numerator must be 4x² - 12x - 40. And as mentioned above, the denominator must be x² + x - 12. So, the rational function is:
[tex]y=\frac{4x^2-12x-40}{x^2+x-12}[/tex]i need help please, i am desperate. Im fully crying right now so please.
We have a triangular prism.
The volume of a triangular prism is given by,
[tex]V=\frac{1}{2}*b*h*l[/tex]where,
b is the base,
h is the height, and,
l is the length,
for this problem:
b = 3 yd
h = 2 yd
l = 6 yd
Therefore, the volume is,
[tex]V=\frac{1}{2}*3*2*6=18[/tex]Thus, the answer is 18 cubic yards
hello I've been stuck on this question and it is a plane trigonometry question hopefully you can help me answer it and thank you for your time
let us start by writing out our parameters
linear velocity v = 50mi/hr
diameter d = 44 in
[tex]\text{Angular Velocity = }\frac{Angle\text{ turned through}}{\text{time}}[/tex]from the diagram above, let the angle turned through be
The perimeter of ΔPQR below is 55 units. What is the length of side QR?P to Q 2x+4 P to R x+3 Q to R has an x there.
Given:
In ΔPQR, Perimeter is 55 units.
The length of PQ = 2x+4
The length of PR = x+3
The length of Q+R = x
To find the length of QR, that is x:
Perimeter of the triangle formula is,
[tex]P=\text{ Sum of the length of thre}e\text{ sides}[/tex]So, we have
[tex]\begin{gathered} 2x+4+x+3+x=55 \\ 4x+7=55_{} \\ 4x=48 \\ x=12 \end{gathered}[/tex]Then, the length of QR is, 12 units.
Logarithm 9) solve for P ( in terms of Q)Log (P - Q) = lop P - log Q
we have the expression
[tex]\text{log (P}-Q)=\log P-\log Q[/tex]Applying properties of log right side
[tex]\text{log (P}-Q)=\log (\frac{P}{Q})[/tex]Equate the numbers inside the parenthesis
[tex]P-Q=\frac{P}{Q}_{}[/tex]Solve for P
[tex]P-\frac{P}{Q}=Q[/tex][tex]P\lbrack1-\frac{1}{Q}\rbrack=Q[/tex][tex]P=\frac{Q}{\lbrack1-\frac{1}{Q}\rbrack}[/tex]Simplify
[tex]P=\frac{Q^2}{Q-1}[/tex]Convert the expression from radical form to exponential expression in rational form, multiply and simplify then divide no need to evaluate just simplify
Solution
Given:
[tex]\sqrt[]{5^7}\text{ }\cdot\sqrt[]{5^6}\div\sqrt[5]{5^3}[/tex]Recall from the law of indices that;
[tex]\begin{gathered} a^{\frac{b}{c}}=\sqrt[c]{a^b}=(\sqrt[c]{a})^b \\ a^{\frac{b}{2}}=\sqrt[]{a^b}^{} \end{gathered}[/tex][tex]undefined[/tex]14. Factor x4 + 3x2 - 28.(x2 - 7)(x - 2)(x + 2)(x2 - 2)(x2 + 14)(x2 + 7)(x - 2)(x + 2)(x2 + 4)(x2 - 7)
Answer:
[tex]x^4+3x^2-28=(x^2+7)(x-2)(x+2)[/tex]Step-by-step explanation:
To factorize the expression, we can use a variable substitution. Let's say that z=x^2.
[tex]\begin{gathered} x^4+3x^2-28 \\ z^2+3z-28 \end{gathered}[/tex]Then, to factorize this we need to factor in the form:
[tex](z+\text{?)(z}+\text{?)}[/tex]The numbers that go in the blanks, have to:
*Add together to get 3
[tex]-4+7=3[/tex]*Multiply together to get -28
[tex]-4\cdot7=-28[/tex]So, we get:
[tex]z^2+3z-28=(z-4)(z+7)[/tex]Substitute the equation z=x^2
[tex](x^2-4)(x^2+7)[/tex]Factorizing the perfect square binomial:
[tex]x^4+3x^2-28=(x^2+7)(x-2)(x+2)[/tex]