A triangle is valid if sum of its two sides is greather than the third side. If three sides are a, b and c, then three conditions should be met.
10. 5cm, 10cm, 2cm
[tex]\begin{gathered} 5+10>2 \\ 15>2\text{ -> False} \end{gathered}[/tex]This cannot be a triangle.
11. Since it has all its angles equals, that means it is a equilateral triangle.
12. 7cm, 7cm, and 15cm
[tex]\begin{gathered} 7+7>15 \\ 14>15\text{ -> False} \end{gathered}[/tex]It cannot be a triangle.
Consider the following random sample of data: 12, 24, 30, 15, 22, 5, 9, 3, 101, 20
SOLUTION
The given data in desending order is:
[tex]3,5,9,12,15,20,22,24,30,101[/tex]Recall that the median is the middle number of set of numbers arranged in ascending or descending order.
Notice that there are 10 data values Hence the area two middle value
The median is the average of the middle values:
[tex]\frac{15+20}{2}=17.5[/tex]Hence the median is 17.5
Recall that an outlier is a data point that differs significantly from other observations
Hence the outlier is 101.
Note that new data will become:
[tex]\begin{equation*} 3,5,9,12,15,20,22,24,30 \end{equation*}[/tex]Therefore the median is 15
The points U(−1,9), V(−1,5), and W(8,9) form a triangle.Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
Remember that the coordinates of the points are written in the form (x,y), the first entry represents the distance over the horizontal axis and the second entry represents the distance over the vertical axis.
Plot the given points on the coordinate plane:
The length of the segment UV is 4, and the length of the segment UW is 9. Since the triangle VUW is a right triangle, use the Pythagorean Theorem to find the length of the segment VW:
[tex]\begin{gathered} VW=\sqrt{UV^2+UW^2} \\ \\ =\sqrt{4^2+9^2} \\ \\ =\sqrt{97} \\ \\ \approx9.849 \end{gathered}[/tex]Add the lengths of all the segments to find the perimeter of the triangle:
[tex]\begin{gathered} P=UV+VW+UW \\ \\ =4+9.849...+9 \\ \\ =22.849... \\ \\ \approx22.8 \end{gathered}[/tex]Therefore, to the nearest tenth, the perimeter of the triangle is 22.8.
x = 8 is a solution for equation 3x = 27 true or false
ANSWER
False
EXPLANATION
The guven equation is:
3x = 27
For x to be a solution of the equation, the value of x must be such that the left and right hand sides of the equation must match.
So, for x = 8:
3(8) = 27
24 = 27
As we can see, the two sides do not match, so x = 8 is not a solution.
Jennifer got a new puppy and took him for a vet visit the vet said the puppy weighs 14 lb and only at 20% of it's adult weight. how much will the puppy weigh once its a an adult
If tan A = 21/20 and cos B = 28/53 and angles A and B are in Quadrant I, find the valueof tan(A - B).
Tom goes fishing with Jason. Tom catches five trout and four catfish. Jason catches twice as many trout as Tom did. How many trout did Jason catch?
We know that Tom catches five trout and four catfish and we also know that Jason catches twice as many trout as Tom did.
Knowing that Jason catches twice as many trout as Tom did we must multiply the number of trouts that Tom caught (5 trouts) by 2
[tex]5\cdot2=10[/tex]So, Jason caught 10 trouts.
Factor the following difference of squares. *Check for a GCF.
ANSWER
(x + 15)(x - 15)
EXPLANATION
The difference of squares is equivalent to the product of the sum and subtraction of the bases,
[tex]a^2-b^2=(a+b)(a-b)[/tex]So, to factor this difference of squares, we have to find the principal square roots of each term,
[tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{225}=15 \end{gathered}[/tex]So this is,
[tex]x^2-225=x^2-15^2=(x+15)(x-15)[/tex]Hence, the factored form is (x + 15)(x - 15).
Given the following rule, describe the transformation. (x , y) ---> (x + 9, y - 2)
The given rule is
[tex](x,y)\to(x+9,y-2)[/tex]The transformations shown indicate translations if the original point.
Any value (k) added/subtracted to the x-coordinate of a point results in a horizontal movement.
If the value is added to the x-coordinate → the resulting movement is k units to the rigth.
If the value is subtracted to the x-coordinate → the resulting movement is k units to the left.
Any value (m) added/subtracted to the y-coordinate of a point results in a vertical movement.
If the value is added to the y-cordinate → the resulting movement is m units up.
If the value is subtracted to the y-coordinate → the resulting movement is m units down.
In the given rule, 9 units are added to the x-coordinate, which indicates a translation 9 units to the right.
And there are 2 units subtracted to the y-coordinate, which indicates a translation 2 units down.
A box is filled with 12 red cards 2 blue cards and 4 green cards a card is chosen at random from the box what is the probability that the card is not blue write your answer as a fraction in simplest form
There are 12+2+4=18 cards in total. The probability to get a not-blue card is
[tex]\begin{gathered} P(\text{not blue) = 1 - P(blue)} \\ P(\text{not blue) =}1-\frac{2}{18} \end{gathered}[/tex]which gives
[tex]\begin{gathered} P(\text{not blue})=1-\frac{1}{9} \\ P(\text{not blue})=\frac{9}{9}-\frac{1}{9} \\ P(\text{not blue})=\frac{9-1}{9} \\ P(\text{not blue})=\frac{8}{9} \end{gathered}[/tex]then, the probability that the card is not blue is 8/9.
How many ounces are in 10 1/2 pounds?1 pound = 16 ounces
hello
to solve this question, we simply need to equate this
[tex]\begin{gathered} 1\text{pound}=16\text{ounces} \\ 10\frac{1}{2}=x\text{ ounces} \\ \text{cross multiply both sides } \\ x\times1=10.5\times16 \\ x=168\text{ounces} \end{gathered}[/tex]from the calculation above, 10.5 pounds would be equal to 168 ounces
I took a screenshot I didn’t want to type it again
You have a 52 standard deck.
There are 4 suites on the deck: diamonds, hearts, spades, and clubs.
Each suite has 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, Jack, Queen, and King → This means that there are 4 cards with each rank on the deck.
The "9 of clubs is missing on your deck"
This means that:
1) Your deck has one less card, the total number of cards is 51.
2) Your deck has one less club, instead of 13 club cards, you have 12.
3) Your deck has one 9 less, which means that there are 3 nines on your deck.
a) You have to select one event, whose probability decreased due to the missing 9 of clubs.
For example, the event "you draw a card at random and it's a 9"
The expected probability of drawing a 9 of the deck can be determined as the number of nines divided by the number of cards on the deck:
[tex]\begin{gathered} P(9)=\frac{4}{52} \\ P(9)=\frac{1}{13} \\ P(9)=0.076\approx7.6\% \end{gathered}[/tex]But in reality, there is one 9 is missing from the deck, so you have 3 nines and 51 cards on the deck, its probability is:
[tex]\begin{gathered} P(9)=\frac{3}{51} \\ P(9)=\frac{1}{17} \\ P(9)=0.059\approx5.9\% \end{gathered}[/tex]The expected probability of drawing a card at random and the card being a 9 is 7.6%, but due to the missing card, the probability dropped to 5.9%.
This means that drawing a card at random and selecting a 9 is less likely than expected.
b) You have to select one event whose probability increased due to the missing card.
For example, the probability of drawing an Ace, knowing that the card is a club:
On a normal deck there are 13 clubs and "one Ace of clubs", the expected probability of drawing the ace, given that the card is a club can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{13} \\ P(\text{Ace}|\text{Club)}=0.076\approx7.6\% \end{gathered}[/tex]But we are missing one club, which means that the total number of clubs is missing, so instead of having 13 clubs, we have twelve. The probability can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{12} \\ P(\text{Ace}|\text{Club)}=0.083\approx8.3\% \end{gathered}[/tex]The expected probability of drawing the Ace, given that the card is a club, on a normal deck is 7.6%, but due to the missing 9 of clubs, this probability has increased to 8.3%.
So this event is more likely due to the missing card.
c) You have to select an event whose probability hasn't changed due to the missing card.
For example, the event "draw a card at random and is a Heart"
The expected probability of drawing a heart from the deck is equal to the quotient between the number of hearts and the total number of cards on the deck:
[tex]\begin{gathered} P(H)=\frac{13}{52} \\ P(H)=\frac{1}{4} \\ P(H)=0.25\approx25\% \end{gathered}[/tex]Your deck is missing one card, so there are 13 Hearts and a total of 51 cards, the probability can be determined as follows:
[tex]\begin{gathered} P(H)=\frac{13}{51} \\ P(H)\approx0.254\approx25.4\% \end{gathered}[/tex]The probability of drawing a heart is around 25% when the deck is complete or missing one card.
Find the number of CDs that will produce maximum revenue.
Given data:
Price of CD is,
[tex]p(x)=90-\frac{x}{6}[/tex]The total revenue is,
[tex]R(x)=90x-\frac{x^2}{6}[/tex]First find the derivative of revenue function and then equate it to zero we have,
[tex]\begin{gathered} R^{\prime}(x)=0 \\ 90-\frac{2x}{6}=0 \end{gathered}[/tex][tex]\begin{gathered} \frac{x}{3}=90 \\ x=90\times3 \\ x=270 \end{gathered}[/tex]Now, to prove the maximize find the double derivative of revenue function
[tex]\begin{gathered} R^{\doubleprime}(x)<0 \\ \frac{-2}{6}=\frac{-1}{3}<0 \end{gathered}[/tex]Thus, 270 CD's will produce maximum revenue.
Answer: Option (c) that is 270.
Our university consists of three colleges: business, engineering, and fine arts. There are 2,900 students in the business college, 1,500 students in the engineering college, and 1,000 students in the fine arts college. What percent of the total number of students are in the fine arts college. Round your answer to the nearest percent.
Given data:
The numbers of students in business college is B=2,900.
The numbers of students in engineering college is E=1,500.
The numbers of students in fine arts is A=1,000.
The percentage of total number of students in fine arts is,
[tex]\begin{gathered} P=\frac{A}{B+E+A}\times100 \\ =\frac{1,000}{2,900+1,500+1,000}\times100 \\ =18.52\text{ percent} \\ \approx18\text{ percent} \end{gathered}[/tex]Thus, the percentage of the students in fine arts is 18 %.
Find the reference angle for a rotation of 297º.
We have the following angle:
We know that the reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. In this case, we have the following reference angle:
To find the value of the reference angle, we substract 297 from 360:
[tex]x=360-297=63[/tex]therefore, the reference angle for a rotation of 297° is 63°
the doll collector store has an inventory of 420 dolls a total of 70 dogs are made of porcelain and the remainder are made of plastic which of the following is the ratio of the plastic dolls to the total number of dolls in store inventory
let:
P = Number of plastic dolls = 420 - 70 = 350
N = total number of dolls in store inventory
[tex]\begin{gathered} P\colon N \\ 350\colon420=\frac{350}{420}=\frac{5}{6} \end{gathered}[/tex]To determine whether or not it is sensible to do a regression analysis, look atQuestion 20 options: the slope y-intercept scatter plot correlation
Explanation
Regression analysis is a set of statistical methods used to estimate relationships between a dependent variable and one or more independent variables.
Before one determines if one will do a regression analysis, we will have to check for the scatter plot
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
Thus, the answer is a scatter plot
your freezer should be kept at -18 C. One day you woke up and noticed the door was left open and the temperature is now -4 degrees C. How many degrees warmer is the freezer now?
where are given that the reference temperature of a freezer is -18 C, if the temperature is -4 C. the difference in temperature will give us how many degrees warmer the freezer is:
[tex]\Delta T=-4-(-18)[/tex]To solve the operations we need first change the sing inside the parenthesis since it is preceded by a minus sing.
[tex]\Delta T=-4+18[/tex]Solving the operations:
[tex]\Delta T=14[/tex]Therefore, the freezer is 14C warmer.
Solve the inequality for A:-3 (9 – 4A) > 3 (2A – 11).
Given the inequality
-3 (9 – 4A) > 3 (2A – 11).
expand
-27 + 12A > 6A -33
Collect like terms
12A - 6A > -33 +27
6A > -6
Divide both sides by 6
A > -1
A piece of cheese contains 34.9 g of fat per 100 g. Calculate the number of g of fat in a 30 g serving of this cheese. Give your answer in g correct
to one decimal place.
The number of grams of fat in 30 grams of the pack will be 11.9 grams.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a piece of cheese contains 34.9 g of fat per 100 g. The number of grams of fat in a 30g pack will be calculated as,
100 g of pack ⇒ 34.9 g of fat
1 g of pack ⇒ 34.9 / 100 g of fat
30 g of pack ⇒ (34.9 x 30 ) / 100 g pf fat
30 g of pack ⇒ 11.9 g of fat
Therefore, the number of grams of fat in 30 grams of the pack will be 11.9 grams.
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I'm going to show u the picture of the question
First, we need to know the number that chose vanilla flavor
Total number of classmate = 300
percentage of those that love Vanilla = 100% - 14% - 42% - 18% = 26%
Number of people that love Vanilla = 26% of 300 =
[tex]=\frac{26}{100}\times300[/tex][tex]=78[/tex]Next, find the number of those that chose strawberry
Number of people that love Strawberry = 18% of 300
[tex]=\frac{18}{100}\times300[/tex][tex]=54[/tex]
The number that chose vanilla than strawberry is 78 - 54= 24
Look at the graph below and use the vertical line test to determine whether or not the graph represents a function. The determine if it is a one-to-one function.positive cube root functionThis graph Answer represent a function.This graph Answer represent a one-to-one function.
By using the vertical line test with the given graph
Since a vertical line can intersect the graph in any position in only ONE point
Then the graph represents a function
To test if it is a one-one function, draw a horizontal line and check if it intersects the graph at any position in only ONE point or not
Since a horizontal line can intersect the given graph in only ONE point in any position, then
The graph represents a one-one function
The current, I, in an electrical conductor varies inversely as the resistance,R, of the conductor. The current is 5 amperes when the resistance is 882ohms. What is the current when the resistance is 428 ohms? Round youranswer to two decimal places if necessary.
ANSWER:
10.30 A
SOLUTION
I=k/R this is base on the definition of I is inversely proportional to R
we need to find the constant k
5=k/882
k=4410
substitute k and R value to get I
I=4410/428
I=10.30
A company charges (c) a flat fee of $4 for shipping plus $0.85 per pound (p). Which equation expresses this relatioship?
The cost of shipping is the flat rate plus the cost per pound times the number of pounds
c = flat rate + rate* pounds
c = 4 + 0.85*p
The write the second part in the opposite order
c = 0.85p +4
When we add the order doesn't matter
Answer B c = 0.85p + 4
Susan's television was damaged during her move and she decides to replace it. She finds the television she wants at the BigBox Store. She can buy the television on consignment for $982 with a 14% down payment. How much must Susan pay as down payment? Round your answer to the nearest cent. Do not include a dollar sign in your answer.
ANSWER
$137.48
EXPLANATION
We have to find the 14% of $982,
[tex]982\cdot\frac{14}{100}=982\cdot0.14=137.48[/tex]Hence, she must pay
$137.48
PLS HELP 5 MATH QUESTIONS WILL MARK BRAINLIEST
The function f(x) = x³ - 2x is an odd function.
From the question, we have
f(x) = x³ - 2x,
The function to be odd if f(-x) = -f(x)
put x = -x in the function,
f(-x) = (-x)³ - 2(-x)
f(-x) = -x³ + 2x
Therefore, the function f(x) = x³ - 2x is an odd function.
Multiplication:
Mathematicians multiply the numbers to find the sum of two or more. It is a fundamental mathematical operation that is frequently employed in daily life. When we need to combine groups of similar sizes, we multiply. The fundamental concept of repeatedly adding the same number is represented by multiplication. The product of two or more numbers is the result of the multiplication of the factors, which are the amounts being multiplied. It is easier to repeatedly add the same number when the numbers have been multiplied.
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Graph the function. f(x) = -3 sin x Use 3.14 for Use the sine tool to graph the function. The first point m value on the graph closest to the first point....I'll send pic of the problem
This is an example of how the graph should look like. What you can do is to find the sine of 2 angles, let's choose pi and 3pi/2. Find the function for these values
[tex]\begin{gathered} -3\cdot\sin \pi=-3\cdot0=0 \\ -3\cdot\sin (\frac{3\pi}{2})=-3\cdot-1=3 \end{gathered}[/tex]Plot these points and graph the function: (3.14,0) and (4.71,-3)
Can I please get someone to help me with this?
First, notice that the line intersects the y-axis at the point (0,5), and that it also passes through the point (2,4). Then, we can use the equation for the slope given two points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we get the following:
[tex]\begin{gathered} (x_1,y_1)=(2,4)_{} \\ (x_2,y_2)=(0,5) \\ \Rightarrow m=\frac{5-4}{0-2}=-\frac{1}{2} \\ m=-\frac{1}{2} \end{gathered}[/tex]now that we have that the slope is m = -1/2 and that the y-intercept is 5 (since the intersection is the point (0,5)), then, the equation of the line in slope intercept form is:
[tex]y=-\frac{1}{2}x+5[/tex]Statistics and probil
we know that
Minimum value=838
Maximum value=1443
Difference=1443-838=605
we have that
Lower Class Limit Upper-Class Limit
838 838+x
838+x 838+2x
838+2x 838+3x
838+3x 838+4x
838+4x 838+5x
838+5x 838+6x=1443
Find out the value of x
838+6x=1443
6x=1443-838
6x=605
x=100.83
therefore
the answer is
Lower Class Limit Upper-Class Limit
838 838+100.83=938.83
938.83 1039.66
1039.66 1140.49
1140.49 1241.32
1241.32 1342.15
1342.15 1443
Find out the frequency for each class
838-938.83 ----> (838,842) ---------> frequency=2 ok
938.83- 1039.66 -----> (945,1034,1025) --------> frequency=3 ok
1039.66-1140.49 -----> (1124,1136,1057,1130) ----> frequency=4 ok
1140.49-1241.32 -----> (1184) ----> frequency=1 ok
1241.32-1342.15 ----> (1247, 1249,1256) -----> frequency=3 ok
1342.15- 1443 -----> (1352,1439,1439,1368,1381,1342,1395) -----> frequency=7
Draw the image of a triangle after a dilation with a scale factor of 2.
Let's begin by listing out the information given to us:
The vertices of the triangle is given as:
[tex](0,0),(0,5),(-4,2)[/tex]Dilation by a scale factor of 2 means the triangle will be enlarged, the coordinate of the vertices become:
[tex]\begin{gathered} (0,0)\rightarrow2(0,0)=(0,0) \\ (0,5)\rightarrow2(0,5)=(0,10) \\ (-4,2)\rightarrow2(-4,2)=(-8,4)_{} \end{gathered}[/tex]We will then graph this
how many 1/5s are in 20?
there are 100 1/5s in 20