Given the measurement: 0.003 m
Following the rules:
• non-zero digits are always significant.
,• zeroes that come after the decimal point are only significant if the number is greater than 1 or if they are sandwiched between two non-zero digits for numbers that are smaller than 1.
,• if a zero is leading a number, before or after the decimal, it is not significant.
Hence:
ANSWER
number of significant figures = 1.
[tex]1599 + 45.60 + 2223 + 149 + 123.5 + 299 + 741 = [/tex]what's the answer
The answer for this sum:
1599 + 45.60 + 2223 + 149 + 123.5 + 299 + 741 is 5180.1.
Factor the following trinomialsA) x^2-13x+30B) x^2+3x-54
In factoring trinomials, the knowledge of basic factoring comes to play.
For example, the factors of 30 are 6 and 5, -5 and -6, 10 and 3, -10 and -3, 2 and 15, and -2 and -15.
For letters A and B, what we need to consider only here is the constant term, +30 and -54, because our first term x² has 1 as its numerical coefficient only. We need to list down the factors of +30 and -54.
Factors of +30 are:
1. 6 and 5
2. -6 and -5
3. 10 and 3
4. -10 and -3
5. 2 and 15
6. -2 and -15
Out of these 6 factors, which would result in -13 (the second term in the trinomial)?
6 and 5 = 11
-6 and -5 = -11
10 and 3 = 13
-10 and -3 = -13
2 and 15 = 17
-2 and -15 = -17
SInce -10 and -3 would result in -13 when added, the factors of our trinomial in letter A is:
[tex](x-10)(x-3)[/tex]Now, let's factor B.
Let's list down the factors of -54 and add them.
1. -9 and 6 = -3
2. -6 and 9 = 3
We don't need to list down all the factors since we already have here the result "3" in the list of factors. Again, we are looking for the second term to come up and the second term in Letter B is 3x.
Therefore, the factors of the trinomial in Letter B are:
[tex](x-6)(x+9)[/tex]Find the greatest common factor of 33 and 36.
Factors of 33 = 1 , 3 , 11 , 33
Factors of 36 = 1,2 . 3, 4 , 6 . 9, 12 , 18 , 36
There are 2 common factors of 33 and 36:
1 and 3
The greatest is 3
Evaluate the expression when w=-1, x= 6.7, and -=-14.510+X+
Substitute the given values for each variable and make calculations:
[tex]\begin{gathered} =-1+6.7-14.5 \\ =-8.8 \end{gathered}[/tex]If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all cards are picture cards. The probability is?
To find the probability of an event A to occur, we use the formula:
[tex]P(A)=\frac{favorable\text{ }outcomes}{total\text{ }outcomes}[/tex]Also, the probability of two independent events, A and B, to occur at the same time is:
[tex]P(A\text{ }and\text{ }B)=P(A)\cdot P(B)[/tex]First, we need to find how many picture cards are in a deck.
The picture cards of each suit are: Jack, Queen, and King. Since there are 4 suits:
[tex]Picture\text{ }cards=3\cdot4=12[/tex]Now, for the first card dealt we have 52 total outcomes (the total cards in the deck) and the favorable outcomes are the 12 picture cards in the deck. We calculate:
[tex]P(1st\text{ }card)=\frac{12}{52}=\frac{3}{13}[/tex]For the second card dealt, now there is one less card in the deck, and also there is one picture card less:
[tex]P(2nd\text{ }card)=\frac{11}{51}[/tex]Similar to the second card, now there is one card less in the deck, and there is one picture card less:
[tex]P(3rd\text{ }card)=\frac{10}{50}=\frac{1}{5}[/tex]Finally, for the fourth card:
[tex]P(4th\text{ }card)=\frac{9}{49}[/tex]To find the probability of all these events happening at the same time, we multiply all the probabilities:
[tex]P(4\text{ }picture\text{ }cards)=\frac{3}{13}\cdot\frac{11}{51}\cdot\frac{1}{5}\cdot\frac{9}{49}=\frac{99}{54145}[/tex]Thus, the answer is:
[tex]Probability\text{ }dealt\text{ }4\text{ }picture\text{ }cards=\frac{99}{54145}\approx0.0018284[/tex]
In decimal, rounded to 6 decimal places, the probability is 0.001828.
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.20). What is the slope of the graph? What is the unit rate? Complete the explanation.
The slope is ________. The unit rate is $______/min. If the graph of a proportional relationship passes through the point (____, r), then r equals the slope and unit rate.
The formula rise/run can be used to determine the slope of a graph by choosing any two points on it. Picking two locations and using the equation (y2 - y1) / (x2 - x1) will also get the answer. A horizontal line's slope is always zero. A vertical line has an unknown slope at all times.
Explain about the slope of graph?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").
The unit rate will be represented by the graph's slope.
The cost for one minute is the unit rate.
The rate is $3.20 according to the graph at x = 1.
To learn more about slope of graph refer to:
https://brainly.com/question/19376563
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16. A thick human hair is about 1.81 x 10^-4 meter in diameter. Write this measurement in standard notation. I hanges to the original content are the responsibility of the instructor. 4
1.81 x 10^-4
Since 10 is raised to a negative power, we have to move the decimal point 4 places to the left.
0.000181
What does the P represent in the formula's for simple and compound interest?A The initial amount of the loanB The interest rate as a decimalC The length of the loan in years
Given the formula for simple interest:
[tex]I=P\ast R\ast T[/tex]Given the formula for compound interest:
[tex]undefined[/tex]If O is an angle in standard position and its terminal side passes through the point(9,-7), find the exact value of csc O in simplest radical form.
SOLUTION
Let us make a simple diagram to illustrate the question and see the position of the angle
From the right-angled triangle in the diagram, the opposite side is 7, and the adjacent side is 9, we need to find the hypotenuse h.
From Pythagoras theorem,
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ h^2=7^2+9^2 \\ h^2=49+81 \\ h=\sqrt[]{130} \end{gathered}[/tex]Now we know that
[tex]\begin{gathered} \sin \theta=\frac{opposite}{\text{hypotenuse}} \\ \sin \theta=\frac{7}{\sqrt[]{130}} \\ This\text{ position of the angle }\theta\text{ is the 4th quadrant.} \\ In\text{ the 4th quadrant, only cos }\theta\text{ is positive, sin }\theta\text{ and tan }\theta\text{ are negative.} \\ \text{Hence } \\ \sin \theta=-\frac{7}{\sqrt[]{130}} \end{gathered}[/tex]Also
[tex]\begin{gathered} co\sec \theta=\frac{1}{\sin \theta} \\ co\sec \theta=-\frac{\sqrt[]{130}}{7} \end{gathered}[/tex]Hence, the answer is
[tex]-\frac{\sqrt[]{130}}{7}[/tex]Use the properties of sigma notation and the summation formulas to evaluate
Since the given question is
[tex]\sum_{i\mathop{=}1}^{10}(i^2+3i-2)[/tex]We will substitute i by 1 to 10, then add all the answers
[tex]\begin{gathered} 1^2+3(1)-2=2 \\ 2^2+3(2)-2=8 \\ 3^2+3(3)-2=16 \\ 4^2+3(4)-2=26 \\ 5^2+3(5)-2=38 \end{gathered}[/tex][tex]\begin{gathered} 6^2+3(6)-2=52 \\ 7^2+3(7)-2=68 \\ 8^2+3(8)-2=86 \\ 9^2+3(9)-2=106 \\ 10^2+3(10)-2=128 \end{gathered}[/tex]Now, we will add the answers
[tex]\sum_{i\mathop{=}1}^{10}(2+8+16+26+38+52+68+86+106+128)=530[/tex]The answer is the 1st choice
For each absolute value equation , list characteristics. I’m stuck on b. I’m not sure if it’s a horizontal stretch or horizontal shrink.
Given:
[tex]y=-\lvert\frac{1}{3}x-2\rvert+9[/tex]For the absolute value equation,
[tex]\begin{gathered} f(x)=a|bx-h|+k \\ a\text{ denote the graph shrinks or stretched} \\ h\text{ denote graph goes left or right} \\ k\text{ denote graph goes up or down} \\ b\text{ denote the horizontal stretched or shrink} \end{gathered}[/tex]So, the given equation,
The graph is reflected over x-axis. since, f(x) = -f(x).
[tex]b=\frac{1}{3}<1\Rightarrow\text{ horizontal stretched}[/tex]The graph is 6 units right and 9 units up.
Write the equation in slope-intercept form.y= -3(x – 4) + 5(2x - 1)
Given equation is
[tex]y=-3(x-4)+5(2x-1)[/tex]On simplifying the equation,
[tex]\begin{gathered} y=-3x+12+10x-5 \\ y=7x+7 \end{gathered}[/tex]Hence the slope intercept form of the given equation is
[tex]y=7x+7[/tex]What is the probability that the random selection of the four-person group willresult in three math majors and 1 computer science major?
We have 18 students,
There are 11 math majors and 7 computer science majors.
We need to find the probability that randomly selecting four persons in the group will result in three math majors and 1 computer science major.
Now,
For select 3 math majors of 11, we use a combination:
11C3
Where the formula is given by:
[tex]\text{nCr}=\frac{n!}{(n-r)!r!}[/tex]Where n is the number of the total group and r the sample:
Then:
[tex]11C3=\frac{11!}{3(11-7)!}=165[/tex]Now, for the selection 1 computer science major of 7:
n=7 and r=1
[tex]7C1=\frac{7!}{1!(7-1)!}=7[/tex]Now, the selection 4 persons of the group of 18 students:
18C4, where n=18 and r=4
[tex]18C4=\frac{18!}{4!(18-4)!}=3060[/tex]The probability of the chose three math majors and 1 computer science major, is given by:
[tex]P=\frac{7C1\cdot11C3}{18C4}=\frac{7\cdot165}{3060}[/tex]Therefore:
[tex]P=0.38[/tex]which linear equation represents the same relationship shown in the graph Below?
Notice that the y-intercept of the line in the graph is 5. Set x=0 on the given equations to find which of them satisfy that condition. It turns out that there are two possibilities:
[tex]y=-\frac{2}{5}x+5[/tex][tex]y=-\frac{5}{2}x+5[/tex]Furthermore, we can see that when x=2, then y=0 on the graph. substitute x=2 on those equations to find which of them satisfy that condition:
[tex]\begin{gathered} y=-\frac{2}{5}(2)+5 \\ =-\frac{4}{5}+5 \\ =4.2 \end{gathered}[/tex][tex]\begin{gathered} y=-\frac{5}{2}(2)+5 \\ =-5+5 \\ =0 \end{gathered}[/tex]Then, the equation:
[tex]y=-\frac{5}{2}x+5[/tex]is the only one which matches the line on the image.
Hey can you help me with this quick equation ?
We were given the following information:
There are 158 empty seats
There are 237 occupied seats
Total number of seats = 395 seats
The percentage of seats that are empty is given by:
[tex]\begin{gathered} \text{\%}Empty.Seat=\frac{No.of.empty.seat}{Total.number.of.seats}\times100\text{\%} \\ \text{\%}Empty.Seat=\frac{158}{395}\times100\text{\%} \\ \text{\%}Empty.Seat=0.4\times100\text{\%} \\ \text{\%}Empty.Seat=40\text{\%} \\ \\ \therefore\text{\%}Empty.Seat=40\text{\%} \end{gathered}[/tex]Therefore, the percentage of empty seats is 40%
The speed (in mph) of randomly selected bicyclists were measured as they were approaching a hill. The results arepresented in the following histogram.How many of those bicyclists were traveling at least 8.5 and less than 11.5 mph as they were approaching the hill?
Number of bicyclists that traveled at leat 8.5 and less than 11.5 = 22
Explanations:To get the number of bicyclists that traveled within this range, add all the frequencies between the range 8.5 and 11.5
Number of bicyclists that traveled between 8.5 and 9.5 = 4
Number of bicyclists that traveled between 9.5 and 10.5 = 5
Number of bicyclists that traveled between 10.5 and 11.5 = 13
Number of bicyclists that traveled at leat 8.5 and less than 11.5 = 4 + 5 + 13
Number of bicyclists that traveled at leat 8.5 and less than 11.5 = 22
What is the sum of 3 x 10^6 and 4 x 10^6
Unit 3 Exam Free ResponseSolve the problems below. Clearly indicate your final answers. Be sure your final answer is in SMALLEST form.A. 27 - 23/В І0 7 10000 Word Limit
can someone please help me find the value of X?
Ok, so:
We know that a circle has angles from 0° to 360°.
For this problem, we have to apply the equation for tangent chord angle, which is:
Tangent chord angle = 1/2 (intercepted minor arc)
So, x = 1/2(360 - 274)
And this is 42°.
please help me asap..
Therefore, the answer is x=3.
Dr. Coleman is ordering PHS t-shirts for the staff. Half of the shirts are maroon and the other half are grey. A local store sells t-shirts for $5 per shirt and a starting fee of $80. What would be the cost of buying 200 t-shirts?
Dr. Coleman is ordering PHS t-shirts for the staff. Half of the shirts are maroon and the other half are grey. A local store sells t-shirts for $5 per shirt and a starting fee of $80. What would be the cost of buying 200 t-shirts?
Let
y -----> the total cost
x ----> the number of shirts
we ahve that
the linear equation is
y=5x+80
For x=200
substitute
y=5(200)+80
y=$1,-080
therefore
the answer is $1,080What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.A) 288B) 360C) 72D) 162thank you ! :)
ANSWER :
B. 360π in^2
EXPLANATION :
Recall the surface area of a cylinder :
[tex]SA=2\pi r^2+2\pi rh[/tex]From the problem, the radius is 6 inches and the height is 24 inches.
Using the formula above :
[tex]\begin{gathered} SA=2\pi(6)^2+2\pi(6)(24) \\ =72\pi+288\pi \\ =360\pi\text{ }in^2 \end{gathered}[/tex]area and decmale the answer has a) b) and c)
a) $2.58 of material has been wasted.
b) 21.52% of that material has been wasted.
c) So each circle costs $4.71
1) Since the plate are going to be cut to make 2 identical circles,
a) The Amount of waste
$ 12 each piece of stock
The radius of each circle is 6 inches
The area of both circles: 2[π(6)²] = 2π36 = 72π in² =226.19 in²
The area of the rectangle: 24 x 12 =288 in
Calculate the waste:
288-226=62
$12------------------------ 288 inches
x-----------------------------62
288x =744
x=$2.58
$2.58 of material has been wasted.
b) Let's consider a similar proportion to calculate that:
100%------------288 inches
y -----------------62 inches
y=21.52% of that material has been wasted.
c) Since each circle has an area of 36π inches ≅ 113 inches
Then, we can set another proportion
$12------------288
z---------------113
z=1356 ÷ 288 z ≅ 4.71
So each circle costs $4.71
A manufacturer has a monthly fixed cost of $60,000 and a production cost of $10 for each unit produced. The product sells for $15/unit.A.) what is the cost function?B.) what is the revenue function?C.) what is the profit function?D.) compute the profit (loss) corresponding to production levels of 10,000 and 14,000 units/months
Given the word problem, we can deduce the following information:
Fixed Cost = $60,000
Production Cost = $10 for each unit produced
To solve the following based on the given information, we let x be the number of units. So,
a)
The get the cost function, we note first that the cost would be:
Cost = Fixed Cost + Production Cost per unit produced
Hence, the cost function is:
C(x)=60,000+10x
b)
The revenue is the gross sales, so the revenue function would be:
R(x) = 15x
c)
We also note that the formula to get the profit is:
Profit= Revenue - Cost
So the profit function would be:
P(x)= 15x-(60,000+10x) = 15x-60,000-10x
Simplify
P(x)= 5x-60,000
d)
To compute the profit or loss, we plug in x=10,000 and x = 14,000 into the profit function:
When x =10,000:
[tex]\begin{gathered} P(x)=5x-60000 \\ P(10000)=5(10000)-60000 \\ \text{Simplify} \\ P(10000)=-10,000 \end{gathered}[/tex]It means that when x=10,000, there would be a $10,000 loss.
When x=14,000:
[tex]\begin{gathered} P(x)=5x-60000 \\ P(14000)=5(14000)-60000 \\ \text{Calculate} \\ P(14000)=10000 \end{gathered}[/tex]It means that when the production is 14,000 units/month, there would be a $10,000 profit.
what is 9.86 rounded to the nearest integer what is 2.17 rounded to the nearest integer what is 13.41 rounded to the nearest integer
Given data:
The firts number given is a=9.86.
The second number given is b=2.17.
The third number given is c=13.41.
The roundoff of first number is,
a=10
The rounoff of the second number is,
b=2
The roundoff to the third number is,
c=13
Thus, the first integer is a=10, second integer is b=2, and the third integer is c=13.
The sum of a number, n, and a number 5 larger than it is 41. Which of the following equations could be used to solve for the number?1. n+5n=412. n+n+5=413. 5(n+1)=414. 5n+n+1=41
We have the sum of two terms: "a number n", and "a number 5 larger than n". We also know that the sum is equal to 41.
5 larger than n is equivalent to: n + 5
Then, the equation is:
n + (n + 5) = 41
n + n + 5 = 41
a Dairy Farmer uses a storage Silo that is the shape of a right cylinder below if the volume of the silo is 72 cubic yards what is the diameter of the base of the cylinder in yards
The volume of a cylinder is given by:
[tex]V=\pi\cdot r^2\cdot h[/tex]where:
r = radius
h = height = 8yd
V = 72π
so:
[tex]\begin{gathered} 72\pi=\pi_{}\cdot r^2\cdot8 \\ \end{gathered}[/tex]solve for r:
[tex]\begin{gathered} r^2=\frac{72\pi}{8\pi} \\ r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Since the diameter is equal to:
[tex]\begin{gathered} d=2r \\ d=2\cdot3 \\ d=6 \end{gathered}[/tex]Answer:
6yd
Determine whether each ratio or rate is proportional. Explain your reasoning and write the proportion. 15 songs for $5; 45 songs for $15
Given
15 songs for $5; 45 songs for $15
Procedure
Let's calculate the fraction associated with the two ratios given to us.
[tex]\frac{15\text{ songs}}{5\text{ \$}}=3\text{ songs/\$}[/tex][tex]\frac{45\text{ songs}}{15\text{ \$}}=3\text{ songs/\$}[/tex]In this case, we can see that the two fractions have the same ratio, therefore they have the same proportion.
Let f (x) = x– 3 and g(x) = x² – 7. Find g (f(x))
We are given the following functions:
[tex]\begin{gathered} f(x)=x-3 \\ g(x)=x^2-7 \end{gathered}[/tex]We are asked to find:
[tex]g(f(x))[/tex]That means that in the function g(x), wherever we find "x" we are going to replace it with the value of the function f(x}, like this:
[tex]g(f(x))=(x-3)^2-7[/tex]Now we simplify the parenthesis using the following property:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Applying the property we get:
[tex]g(f(x))=x^2-6x+9-7[/tex]Now we solve the operations:
[tex]g(f(x))=x^2-6x+2[/tex]An animal is running at a rate of 40 ft per sec.(a) If the animal runs for 5 sec, what is its distance?(b) If the animal travels d ft, what is its time?If the animal travels d ft, it’s time is : _____(Use integers or fractions for any numbers)Is the answer in ft per sec, ft., or just sec.?
ANSWERS
(a) d = 200 ft
(b) t = d/40 sec
EXPLANATION
The animal is running at a rate of 40 feet per second. Given the units of this rate, we can conclude that this rate is the quotiend between distance (in feet) and time (in seconds),
[tex]40\frac{ft}{sec}=\frac{d}{t}[/tex](a) Now, if the animal runs for a time t = 5 seconds, we have to find what is its distance traveled, d. To do so, we solve the expression above for d by multiplying both sides by t,
[tex]d=40\frac{ft}{sec}\cdot t=40\frac{ft}{sec}\cdot5sec=200ft[/tex]Hence, in 5 seconds the animal travels 200 feet.
(b) For this part of the question, we have to find the other variable, t, knowing that the distance traveled is d. Since the distance is not given as a number, we will find an expression as a function of d,
[tex]40\frac{ft}{sec}=\frac{d\text{ }ft}{t}[/tex]Solving for t,
[tex]t=\frac{d\text{ }ft}{40\frac{ft}{sec}}[/tex]The unit of distance, feet, cancels out, and we have the result in seconds,
[tex]t=\frac{d}{40}\text{ }sec[/tex]Hence, the time for a distance traveled of d feet is d/40 sec.