==================================================
Work Shown:
T(2) = 20 means the second term is 20
T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.
Since a = 26 is the first term and d = -6 is the common difference, the nth term is
T(n) = a + d*(n-1)
T(n) = 26 + (-6)(n-1)
T(n) = 26 - 6n + 6
T(n) = -6n + 32
Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.
Plug in n = 10 to find the tenth term
T(n) = -6n + 32
T(10) = -6(10) + 32
T(10) = -60+32
T(10) = -28
Answer:
-28.
Step-by-step explanation:
T(1) = 20 + 6 = 26.
This is an arithmetic series with:
nth term T(n) = 26 - 6(n - 1).
So T(10) = 26 - 6(10-1)
= 26 -54
= -28.
A farmer uses 3/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize
Answer:
Step-by-step explanation:
Cassava = 1/3 of his land
Remaining after planting Cassava = 1 - 1/3 = 2/3 of his land
Maize = 2/5 x 2/3 = 4/15 of his land
Vegetables = 2/3 - 4/15 = 2/5 of his land
If vegetables = 10 acres
2/5 of his land = 10 acres
1/5 of his land = 10 ÷ 2 = 5 acres
5/5 of his land = 5 x 5 = 25 acres
Dustin has five hats, five shirts, five pairs of pants, and five pairs of shoes; he has one of each in blue, green, gray, silver, and gold (his five favorite colors). Dustin is picky about what he wears: he insists on his shoes being the same color as at least two other articles of clothing in the outfit. However, he refuses to wear all silver or all gold (because that's tacky). How many possible outfits can Dustin wear?
Answer:
The number of possible outfits Dustin can wear is 73 outfits
Step-by-step explanation:
The information given are;
The number of hats Dustin has = 5
The number of shirts Dustin has = 5
The number of pants Dustin has = 5
The number of shoes Dustin has = 5
The colors of Dustin's clothing are blue, green, gray, silver, and gold
Given that the shoes go with at least two other clothing of the same color, we have;
The number of ways the color of the shoes can be selected = 5 ways
The number of ways of selecting the same color for 2 of the remaining 3 clothing = 3 ways
The number of ways of selecting the color of the fourth clothing = 5 ways
The total number of ways = 5 × 3 × 5 = 75 ways
The number of ways in which all silver can be selected = 1 way
The number of ways in which all gold can be selected = 1 way
Since Dustin refuses to wear all silver and all gold, the total number of ways the outfits can be selected = 75 - 1 - 1 = 73 ways = 73 is the number of possible outfits
Therefore, the number of possible outfits Dustin can wear = 73 outfits.
HELP ME PLLEEEEASE I BEG
Surface Area of Triangular Prism
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
PLEASE HELP ME!!!
===================================================
Explanation:
Any triangle prism is composed of 2 parallel triangular faces (base faces), along with 3 rectangular lateral faces.
The bottom triangle face has a base of 10 cm and a height of 4 cm. The area is 0.5*base*height = 0.5*10*4 = 20 square cm. Two of these triangles combine to an area of 2*20 = 40 square cm. We'll use this later.
The lateral surface area of any prism can be found by multiplying the perimeter of the base by the height of the prism. The base triangle has side lengths 5, 8 and 10. The perimeter is 5+8+10 = 23. So the lateral surface area is (perimeter)*(height) = 23*9 = 207
Add this to the total base area we got earlier and the answer is 40+207 = 247. The units are in square cm, which we can write as cm^2.
Ted and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $16.88. What was the total bill?
Answer:
Total bill = $67.52
Step-by-step explanation:
Ted + 3 = 4
$16.88 × 4 = $67.52
hopefully this helped you :3
Answer:
16.88*4= 67.52 dollars
Step-by-step explanation:
Ted and 3 friends split the bill evenly, each person paid 16.88:
16.88*4= 67.52 dollars
What is the value of x
Answer:
4
Step-by-step explanation:
For the first triangle which is triangle <KJL
Hypotenuse= 8✓2
Angle=30°
Opposite = ?
Therefore we will use Sine formula
Sin30° = Y/8✓2
Y=4✓2
For the second triangle which is triangle <JML
Hypotenuse= 4✓2
Opposite=X
Angle=45°
Therefore we will use Sine formula again
Sin45°=X/4✓2
X=4
Answer:
x = 4Step-by-step explanation:
ΔJKL is half of equilateral triangle and ΔJML is half of square.
We can use properties of these triangles (picture):
m∠KJL=90° and m∠JKL = 30° ⇒ JL = 0.5KL = 0.5•8√2 = 4√2
m∠JML=90° and m∠MJL = 45° ⇒ JL = ML√2
4√2 = x√2
x = 4
plzzzz help! marking brainiest asap!
(-x^2+2x+3) + (-x^2-2x-1) = -2x^2 + 2
============================================
Explanation:
We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.
Because we must have a plus sign between the parenthesis, this means the answer is between C and D.
Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.
The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.
Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.
Help..... please math
Answer:
Ones: 91
Hundredths: 91.20
Step-by-step explanation:
All numbers that comprises the digits, 91.20, have place value.
The 9 in the digit has a place value of tens, i.e. 9*10 = 90.
The 1 has a place value of one's, i.e. 1*1 = 1
The 2, after the decimal point to the right, has a place value of tenth, i.e. 1*10-¹ = ⅒ = 0.1
While the zero has a place value of hundredth.
Therefore, the digits, in the ones place = 91
In the hundredths place = 91.20
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike? if possible, I would like a clear equation.
Answer:
He hiked 10 miles.
Step-by-step explanation:
rate x time = distance
The distance up and the distance down are equal
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
A librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections.
What is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book?
0.114
0.131
0.686
0.784
Answer:
For this case we have a total of 10 nonfiction books and 8 fiction books, we are going to assume that the selection is without replacement so then for the first case the probability of select a fiction book is:
[tex] \frac{8}{18}[/tex]
For the second selection we have 17 books remaining and the probability of select a nonfiction book is:
[tex] \frac{10}{17}[/tex]
For the last selection we have 16 books remaining and the probability of select a fiction book would be:
[tex]\frac{7}{16}[/tex]
Sinally since the events are independent the total probability would be:
[tex] \frac{8}{18} *\frac{10}{17}*\frac{7}{16}= 0.114[/tex]
Step-by-step explanation:
For this case we have a total of 10 nonfiction books and 8 fiction books, we are going to assume that the selection is without replacement so then for the first case the probability of select a fiction book is:
[tex] \frac{8}{18}[/tex]
For the second selection we have 17 books remaining and the probability of select a nonfiction book is:
[tex] \frac{10}{17}[/tex]
For the last selection we have 16 books remaining and the probability of select a fiction book would be:
[tex]\frac{7}{16}[/tex]
Sinally since the events are independent the total probability would be:
[tex] \frac{8}{18} *\frac{10}{17}*\frac{7}{16}= 0.114[/tex]
Answer:it’s A
Step-by-step explanation:
did the test
Corey owns a 50 acre vineyard and every year, depending upon conditions, worries about flooding. Corey wants rainfall amounts to be at most 12 inches per year. Which model is correct?
A: X Greater than or equal to 12?
B: X less than or equal to 12?
C: X less than 12?
Answer:
B: X less than or equal to 12
x≤12
Step-by-step explanation:
Corey owns a 50acre vineyard
Corey wants rainfall amounts to be at most 12 inches per year
Let rainfall=x
Corey wants amount of rainfall (x) to be at most 12 inches per year
x is at most 12 inches per year
In inequality, the appropriate symbol representing “at most” is the “less than or equal to”
(≤) symbol
So, substituting the symbol
We have,
x≤12
B: X less than or equal to 12
8–2|4–5y|=4 help me as quick as u can plzzz
Answer: [tex]y=\frac{2}{5}, \frac{6}{5}[/tex]
Step-by-step explanation:
When answering a problem like this, you first isolate the absolute value. TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4. Then divide both sides of the equation to get |4–5y|=2. The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.
Hope it helps <3
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
[tex]\boxed{15}[/tex]
Step-by-step explanation:
Set the output equal to 0.
[tex]-2x^2 +20x+150=0[/tex]
Factor left side of the equation.
[tex]-2(x+5)(x-15)=0[/tex]
Set factors equal to 0.
First possibility:
[tex]-2(x+5)=0\\x+5=0\\x=-5[/tex]
Second possibility:
[tex]x-15=0\\x=15[/tex]
The value or prize cannot be negative.
[tex]x\neq -5\\ x=15[/tex]
Select all the sentences that can be represented by the equation 25+p=38 A.25 is more than 38 is p B.25 times as much as p is 38 C.38 is p more than 25
Answer:
Option C: 38 is p more than 25
Step-by-step explanation:
the equation 25 + p = 38
can be read as 38 is 25 plus p units, or similarly ;
38 is p units more than 25.
Therefore from the three sentences you are showing, only the last one (option C) is the correct one.
A pair of dice is rolled. What is the probability that the sum is 9? a 1/36 b 1/18 c 1/9 d 2/9
The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set?
Answer:
[tex](\frac{2}{3},\infty)[/tex]
Step-by-step explanation:
Set builder notation is a mathematical notation used to write the elements of a set stating the conditions that the elements of the set must satisfy. A solution set is also a way of defining solutions to equations and inequalities. A solution set contains a set of all variables for which the equation is true.
The notation {x l x > two-thirds} is a set of all real numbers greater than 2/3, it can also be represented as:
[tex](\frac{2}{3},\infty)[/tex]
Answer:
c) (two-thirds, ∞)
Step-by-step explanation:
edg2020
what is the value of the digit 6 in the number 48.061?
Answer:
The hundredths place.
Step-by-step explanation:
48 is the whole number, and .061 is the decimals. As you probably know, this is the whole numbers place value.
ones, tens, hundreds, thousand, 10 thousand, 100 thousand, million...ect.
The decimal places are different
in this case the 0 is the tenths
the 6 is the hundredths
and the 1 is the thousandths.
Mostly, the decimal points are just with added ths to the end.
Hope this helped :D
As per the given number, the place value of 6 is that it is at hundredths place.
What is Place Value?Place value is the value assigned to each digit in a number. Depending on its location, each digit in such a number has a unique value. Because a digit's value relies on where it appears in an integer, it is possible for an amount to have two equivalent digits with different values.
The decimal equivalent of 48 is .061. The entire number is 48. This is the entire integer's place value, as you are surely aware.
The decimal places are different
In the given question, the 0 is at tenths place ,6 is the hundredths place and 1 is the thousandths place.
The decimal points are typically only inserted at the end.
To know more about Place Value:
https://brainly.com/question/27734142
#SPJ3
Anita plans to cover a solid cone with construction paper for a science project. The cone has a diameter of 11 inches and a slant height of 28.5 inches. How many square inches of paper will she need to cover the entire cone? (Use 3.14 for Pi and round to the nearest hundredth. Recall the formula S A = pi r l + pi r squared.) 492.20 in.2 587.18 in.2 982.82 in.2 984..39 in.2
Answer:
587.18 in²
Step-by-step explanation:
In the above question, we are given the following values
Diameter = 11 inches
Radius = Diameter/2 = 11 inches/2 = 5.5 inches
Slant height = 28.5 inches.
We were asked to find how many square inches of paper will she need to cover the ENTIRE cone.
To solve for this, we would use formula for Total Surface Area of a Cone
Total Surface Area of a Cone = πrl + πr²
= πr(r + l)
Using 3.14 for π
Total Surface Area of a Cone
= 3.14 × 5.5( 5.5 + 28.5)
= 3.14 × 5.5 × (34)
= 587.18 in²
Therefore, Anita will need 587.18 square inches of paper to cover the entire cone.
Answer:
B
Step-by-step explanation: Just trust me bro
somebody plz answer.
Answer:
IT'S D
Step-by-step explanation:
LOOK AT THE PATTERN AND YOU WILL UNDERSTAND.
Answer:
ii honestly think d
Step-by-step explanation:
Please help meeee I need help finding x y and z :)
Answer:
Hey there!
We see that z is equal to 40, because angles in a triangle add to 180 degrees.
We see that x is equal to 70, because an isosceles triangle has two angles that are congruent to each other, and can be represented using the equation 2x+y=180.
We see that y is equal to 110, because x+y needs to equal 180.
Hope this helps :)
Answer:
∠x = 70º, ∠y = 110º, ∠z = 40º
Step-by-step explanation:
to find ∠z: 180 - (71 + 69) = 40º = ∠z
the smaller triangle is an isosceles triangle, therefore ∠x is equal to the angle on its left.
so 180 - ∠z = 2 x ∠x
180 - 40 = 140 / 2 = 70º = ∠x
the angle to the left of ∠x forms 180º with ∠y.
as that angle is 70º, ∠y = 180 - 70 = 110º
WILL GIVE BRAINLIEST FOR BEST ANSWER Maya wants to perform an experiment with a spinner labeled A, B, and C. The theoretical probabilities for each section are: P(A) = ½, P(B) = ¼, and P(C) = ¼. Which spinner could she use?
Answer: The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.
Answer:
spinner B
Step-by-step explanation:
there's 8 sides to the spinner and half of them have A on it.
Please help I will give out brainliest
Answer:
All the points change, there are no invariant points
Step-by-step explanation:
The given parameters are
To translate the square OABC by the vector [tex]\dbinom{1}{3}[/tex], we have;
The coordinates of the point O is (0, 0)
The coordinates of the point A is (3, 0)
The coordinates of the point B is (3, 3)
The coordinates of the point C is (0. 3)
The translation is by moving 1 step right and three steps up to give;
O' is (0+1, 0+3) which is (1, 3)
A' is (3+1, 0+3) which is (4, 3)
B' is (3+1, 3+3) which gives (4, 6)
C' is (0+1, 3+3) which gives (1, 6)
As all the points change, there are no invariant points and the number of invariant points is zero.
Please help! I know its either B or D but im not sure how to tell
Answer:
D.
Step-by-step explanation:
To find the equation of g(x), we can substitute the point into each of the equations.
A. g(x) = (1/4x)^2
1 = (1/4 * 2)^2
1 = (1/2)^2
1 = 1/4
This statement is false, so this is not the equation.
B. g(x) = 1/2 * x^2
1 = 1/2 * (2)^2
1 = 1/2 * 4
1 = 2
This statement is false, so this is not the equation.
C. g(x) = 2x^2
1 = 2 * 2^2
1 = 2 * 4
1 = 8
This statement is false, so this is not the equation.
D. g(x) = (1/2x)^2.
1 = (1/2 * 2)^2
1 = 1^2
1 = 1
This statement is true, so this is your answer.
Hope this helps!
Need help quick quick quico
Answer:
7 batches
Step-by-step explanation:
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.
The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713
Given that:
[tex]Entrance\ Fee = \$18[/tex]
[tex]Rate = \$0.08[/tex] per ball
Let:
[tex]B \to Balls[/tex]
The amount (A) Carolina can spend on B balls is:
A = Entrance Fee + Rate * B
This gives:
[tex]A = 18 + 0.08 * B[/tex]
[tex]A = 18 + 0.08B[/tex]
To get $10, Carolina must spend $75 or more.
This means:
[tex]A \ge 75[/tex]
So, the inequality is:
[tex]18 + 0.08B \ge 75[/tex]
The smallest number of balls is calculated as follows:
[tex]18 + 0.08B \ge 75[/tex]
Collect like terms
[tex]0.08B \ge 75 - 18[/tex]
[tex]0.08B \ge 57[/tex]
Divide both sides by 0.08
[tex]B \ge 712.5[/tex]
Round up
[tex]B \ge 713[/tex]
Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713
Learn more about inequalities at:
brainly.com/question/20383699
Using a linear function, it is found that:
1. [tex]18 + 0.08B \geq 75[/tex], given by option B.2. She has to buy at least 713 paintballs.-----------
The linear function for the cost of B paintballs has the following format:
[tex]C(B) = C(0) + aB[/tex]
In which
C(0) is the fixed cost.a is the cost per paintball.-----------
Question 1:
Entrance fee of $18, thus [tex]C(0) = 18[/tex].Cost of $0.08 per ball, thus, [tex]a = 0.08[/tex]Thus:
[tex]C(B) = 18 + 0.08B[/tex]
The promotion is valid if the cost is of at least 75, thus:[tex]C(B) \geq 75[/tex]
[tex]18 + 0.08B \geq 75[/tex], given by option B.
-----------
Question 2:
The smallest number is the solution of the inequality for B, thus:[tex]18 + 0.08B \geq 75[/tex]
[tex]0.08B \geq 57[/tex]
[tex]B \geq \frac{57}{0.08}[/tex]
[tex]B \geq 712.5[/tex]
Rounding up, she has to buy at least 713 paintballs.
A similar problem is given at https://brainly.com/question/24583430
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation
Answer:
ANSWER LINK
Need Help ASAP!!!! thanks
Answer: 35 m3
Step-by-step explanation:
Hi, to answer this question, first we have to calculate the base of the pyramid:
Base area = 1/2x base length x height
Base area = 1/2 x 6 x 5 = 15 m2
Volume of a pyramid = 1/3 x base area x height
Replacing with the values given:
V = 1/3 x 15 x 7 = 35 m3
Feel free to ask for more if needed or if you did not understand something.
EXPLANATION NEEDED:
In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =
a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²
Answer:
C. xStep-by-step explanation:
AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:
[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]
pleaz!!! some body help with number #4 at the bottom
Answer:
See my explanation
Step-by-step explanation:
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22 <- this is wrong in question writing as x = 22
so, x = -22
a coat was marked down by 60 percent from its original price of $99 . including an 8% sale tax , what is the final cost of the coat?
Answer:
i think its 42.77... might be wrong tho
Step-by-step explanation:
being marked down by 60 percent means to multiply original number by 0.4
so we get 39.6
the multiply it by 1.08 to get 42.768
Answer:
See below.
Step-by-step explanation:
To find the marked down price, multiply the total by the percentage.
[tex]99*.6=59.4[/tex]
Next, subtract the amount from the total.
[tex]99-59.4=39.6[/tex]
Then, multiply to find the sales tax.
[tex]39.6*0.08=3.168[/tex]
[tex]39.6+3.168=42.768[/tex]
Answer: $42.77
