Given:
Sum of three consecutive integers is more than 62.
To find:
The inequality to represent the above situation then solve your inequality.
Solution:
Let the three consecutive integers are [tex]x,x+1,x+2[/tex] respectively.
Sum of three consecutive integers is more than 62. So,
[tex]x+(x+1)+(x+2)>62[/tex]
[tex]3x+3>62[/tex]
Subtract 3 from both sides.
[tex]3x>62-3[/tex]
[tex]3x>59[/tex]
Divide both sides by 3.
[tex]x>\dfrac{59}{3}[/tex]
Therefore, the required inequality is [tex]x+(x+1)+(x+2)>62[/tex] and solution is [tex]x>\dfrac{59}{3}[/tex].
An isosceles right-angled triangle is shown.
The area of the triangle is 200 cm?.
Work out the value of x.
Answer:
[tex]\boxed{x=4}[/tex]
Step-by-step explanation:
Area of triangle = 0.5 × Base × Height
→ Substitute in the values
200 = 0.5 × 5x × 5x
→ Simplify
200 = 12.5x²
→ Divide both sides by 12.5
16 = x²
→ Square root both sides
4 = x ∴ x = 4
Answer:
Step-by-step explanation:
Kevin bought 3 dvds for 45.99 how much would 7 dvds cost?
Answer:
I am pretty sure the answer would be $107.31. Sorry if I'm wrong.
Step-by-step explanation:
First you take the total of the 3 DVD's (45.99) and you divide that by 3 (number of DVD's) to get 15.33 which is called the unit price. Then, you take your unit price and multiply that by how many items you are going to buy.
45.99 / 3 = 15.33
15.33 x 7 = 107.31
Alice, Bob, and Carl arrange to meet for lunch on a certain day. They arriveindependently at uniformly distributed times between 1 pm and 1:30 pm on that day.
Required:
a. What is the probability that Carl arrives first?
b. What is the probability that Carl will have to wait more than 10 minutes for one of the others to show up?
c. What is the probability that Carl will have to wait more than 10 minutes for both of the others to show up?
d. What is the probability that the person who arrives second will have to wait more than 5 minutes for the third person to show up?
Answer:
a. What is the probability that Carl arrives first?
Probability that Carl arrives first is ¹/₃ = 33.33% since their arrival times is uniformly distributed. The same probability applies to Bob and Alice.
b. What is the probability that Carl will have to wait more than 10 minutes for one of the others to show up?
Assuming that Carl arrived on time, 1:10 PM, we must determine the probability that Alice or Bob arrive between 1:20 and 1:30 (half the remaining time)
P = [3 · (¹/₂ - ¹/₃)] · [3 · (¹/₂ - ¹/₃)] = (3 · ¹/₆) · (3 · ¹/₆) = ¹/₂ · ¹/₂ = ¹/₄ = 25% chance that either Alice or Bob arrive more than 10 minutes later
c. What is the probability that Carl will have to wait more than 10 minutes for both of the others to show up?
P = 1 - 25% = 75%
d. What is the probability that the person who arrives second will have to wait more than 5 minutes for the third person to show up?
I divided the 20 minutes by 5 to get ¹/₄:
P (|S - T| ≤ ¹/₄) = {[(x + ¹/₄)²] / 2} + (1 / 2x) + {[(⁵/₄ - x)²] / 2} = 0.09375 + 0.25 + 0.09375 = 0.4375 = 43.75%
The ratio of 12 to 15 is ____ the ratio value of 7 to 5
A) less than
B) greater than
Answer:
a
Step-by-step explanation:
7*2=14
5*2= 10
it would be (a) because 14 is greater than 12
Answer:
Step-by-step explanation:
⬆️⬆️⬆️⬆️⬆️⬆️⬆️⬆️⬆️⬆️⬆️
What is the greatest common factor of the terms in the expression 24x + 18xy?
Answer:
GCF = 6x
Step-by-step explanation:
24x = 2 * 2 * 2 * 3 *x
18xy = 2 * 3 * 3 * x * y
GCF = 2 * 3 *x = 6x
Solve:
|11x + 10| = 22
A. x= -11/32 or x= 11/12
B. x= -32/11 or x= 12/11
C. x= -10/11 or x= 10/11
D. x= 12/11 or x= 32/11
Answer:
D. x=12/11 or x=32/11.
Answer:
D) x=12/11 or x=32/11.
Step-by-step explanation:
because i just know math
Which equation below would be perpendicular to the line x = 5?
Answer:Any equation that when solved will be y=(number)
Step-by-step explanation:
Well you didn't add any "equations below" so I can't help too much bite you need to solve the equations they listed and the result of the equation must be y=(number), there cannot be any other variable in the equation when simplified if that makes sense. Sorry i can't help more.
Mack, Jason, and Yuri invested a total of $14,500 in the stock market. After one year, they earned a profit equal to 1/5 of their investment Mack receives 2/5 of the profit, Jason Receives 1/4 of the profit, and Yuri receives the rest of the profitWhat is the amount of each person's profit?
Answer:
The amount of each person's profit is:
Mack
= $1160
Jason
= $725
Yuri
= $1015
Step-by-step explanation:
Mack, Jason, and Yuri invested a total of $14,500 in the stock market. After one year, they earned a profit equal to 1/5 of their investment Mack receives 2/5 of the profit, Jason Receives 1/4 of the profit, and Yuri receives the rest of the profitWhat is the amount of each person's profit?
Step 1
We calculate how much the profit is.
Mack, Jason, and Yuri invested a total of $14,500 in the stock market. After one year, they earned a profit equal to 1/5 of their investment
The profit = 1/5 of Investment
Hence = 1/5 × $14500
Profit = $2900
Step 2
We calculate the amount each of them receives.
Mack receives 2/5 of the profit,
= 2/5 × $2900
= $ 1160
Jason Receives 1/4 of the profit
= 1/4 × $2900
= $725
Yuri receives the rest of the profit
This is calculated as:
$2900 -($1160 + $725)
$2900 - $1885
= $1015
The amount of each person's profit is:
Mack
= $1160
Jason
= $725
Yuri
= $1015
(3w^2 + 7W + 2) + (w^2 + 2W + 8)
Answer:
4w^2+9w+10
Step-by-step explanation:
(3w^2+7w+10+w^2+2W
Combine like terms
4w^2+7w+10+2w
Combine like terms
4w^2+9w+10
Answer:
4w^2+9w+10
Step-by-step explanation:
11 purple hats 14 yellow hats 45 purple hats 70 yellow hats
Answer:
140 hats is the answer i guess
h(n)=-15•6^n complete the recursive formula
h(1)=
h(n)=h(n-1)•
ILL MARK BRAINLIEST
Answer:
h(1)= -90 h(n)=h(n-1) ⋅ 6
Step-by-step explanation:
Im smart :D
Beatriz has a big hot chocolate. She drank 7 ounces so far, how large is her entire hot chocolate
Answer:
larger than 7 ounces
Step-by-step explanation:
Answer:
lol
Step-by-step explanation:
lol
I have a rectangular garden. I usually grow cucumbers in 2/3 of my garden, but I want to take 3/4 of the cucumber section to grow
radishes. After I make this change, how much of my whole garden will
be radishes?
Answer:
[tex]\frac{1}{2}[/tex] of the garden will be radishes.
Step-by-step explanation:
Given a rectangular garden which grows cucumbers in [tex]\frac{2}{3}[/tex] of the garden.
[tex]\frac{3}{4}[/tex] of the cucumber section to grow radishes.
To find:
How much of the whole garden will be radishes?
Solution:
Let the total area of the garden = [tex]x[/tex] sq units
Then as per our assumption, total area to grow cucumbers:
[tex]\frac{2x}{3}[/tex] sq units
Cucumber area to grow radishes = [tex]\frac{3}{4}[/tex] of cucumber area
[tex]= \dfrac{3}{4}\times \dfrac{2x}{3}\\\Rightarrow \dfrac{x}{2}\ sq\ units[/tex]
Fraction of whole garden to grow radishes = Area to grow radishes divided by whole area of garden
[tex]\Rightarrow \dfrac{\frac{x}{2}}{x}\\\\\Rightarrow \bold{\dfrac{1}{2}}[/tex]
Therefore, [tex]\frac{1}{2}[/tex] of the garden will be radishes.
PLEASE HELPP‼️‼️ write in factored form g(x)= x^3 - 4x^2 - x + 22
Answer:
[tex]g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22[/tex] in the factored form will be:
[tex]g\left(x\right)=x^3-4x^2-x+22=\:\left(x+2\right)\left(x^2-6x+11\right)[/tex]Step-by-step explanation:
Given the function
[tex]g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22[/tex]
Use the rational root theorem.
[tex]a_0=22,\:\quad a_n=1[/tex]
[tex]\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:11,\:22,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1[/tex]
[tex]\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:11,\:22}{1}[/tex]
[tex]-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2[/tex]
[tex]=\left(x+2\right)\frac{x^3-4x^2-x+22}{x+2}[/tex]
as
[tex]\frac{x^3-4x^2-x+22}{x+2}=x^2-6x+11[/tex] ∵ [tex]x^3-4x^2-x+22=\left(x+2\right)\left(x^2-6x+11\right)[/tex]
so the expression becomes
[tex]x^3\:-\:4x^2\:-\:x\:+\:22=\left(x+2\right)\left(x^2-6x+11\right)[/tex]
Therefore,
[tex]g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22[/tex] in the factored form will be:
[tex]g\left(x\right)=x^3-4x^2-x+22=\:\left(x+2\right)\left(x^2-6x+11\right)[/tex]
Find the number of different ways that an instructor can choose 6 students from a class of 25 students for a field trip.
Answer:
177100
Step-by-step explanation:
I just used the combinations formula.
c(n,r) = (n over r) = n over (r(n-r)
69% of Americans have $1,000 or less in a savings account, leaving them
vulnerable to common expense spikes such as a major car repair or a job loss.
What savings strategies have proven to be most effective?
. My Question is The Cost of Admission to the Zoo is 14.75 for each Adult, and 6.25 of 2 Adults and 1 child plan to spend the day at the zoo. How much does all the admission for the entire Family Cost?
Answer:
35.75
Step-by-step explanation:
Hope this helps. :)
Answer: $35.75
Step-by-step explanation:
2 adults $29.50 one child $6.95 In total they will be paying $35.75
Paying 12$ to whoever can answer this question i created. MUST BE CORRECT
Answer:
x = 10
I used the Interior Angles of a Triangle Rule --The sum of all 3 interior angles in a triangle is always 180°.
(3x + 28) + (5x - 18) + 90° = 180°
Now i can get rid of the parentheses and combine like terms.
3x + 5x + 28 - 18 + 90 = 180
8x + 10 + 90 = 180
8x + 100 = 180
Then i subtract 100 from both sides to isolate x.
8x + 100 - 100 = 180 - 100
8x = 80
Then, i divide both sides by 8 to find x.
8x ÷ 8 = 80 ÷ 8
x = 10
How do you solve
C= 3 - 17
Answer: C = -14
Step-by-step explanation: 3 - 17 = -14
HELP 25 Points CALC multiple choice
Alligators captured in Florida are found to have a mean length of 2 meters and a standard deviation of 0.35 meters. The lengths of alligators are believed to be approximately normally distributed. What is the approximate length of an alligator at the 67th percentile of alligator lengths?
a. 2.01 meters.
b. 2.44 meters.
c. 2.21 meters.
d. 2.15 meters.
e. 2.09 meters.
Answer:
The correct option is (d). 2.15 meters.
Step-by-step explanation:
According to the given scenario, the approximate length of an alligator at the 67th percentile is as follows:
The length of an alligator is [tex]X \sim N(2,0.35)[/tex] .
Let us assume the [tex]P_{67}[/tex] be the 67th percentile
[tex]P(X <P67) = 0.67\\\\P(Z < \frac{P_{67 - 2 }}{0.35} ) = 0.67\\\\\emptyset (\frac{P_{67 - 2 }}{0.35} ) = 0.67\\\\ (\frac{P_{67 - 2 }}{0.35} ) = \emptyset^{-1 (0.67)\\\\[/tex]
[tex]\frac{P_{67 - 2 }}{0.35} = 0.44\\\\P_{67} = 2.154[/tex]
Hence, the correct option is (d). 2.15 meters
Set up and evaluate the optimization problems. (Enter your answers as comma-separated lists.) Find two positive integers such that their sum is 14, and the sum of their squares is minimized. Find two positive integers such that their sum is 14, and the sum of their squares is maximized.
Answer and Step-by-step explanation:
Let x and y be two positive integers and their sum is 14:
X + y = 14
And the sum of square of this number is:
f = x2 + y2
= x2+ (14 – x)2
Differentiate with respect to x, we get:
F’(x) = [ x2 + (14 – x)2]’ = 0
2x + 2(14-x)(-1) = 0
2x +( 28 – 2x)(-1) = 0
2x – 28 +2x = 0
2x + 2x = 28
4x = 28
X = 7
Hence, y = 14 – x = 14 -7 = 7
Now taking second derivative test:
F”(x) > 0
For x = y = 7,f reaches its maximum value:
(7)2 + (7)2 = 49 + 49
= 98
F at endpoints x Є [ 0, 14]
F(0) = 02 + (14 – 0)2
= 196
F(14) = (14)2 + (14 – 14)2
= 196
Hence the sum of squares of these numbers is minimum when x = y = 7
And maximum when numbers are 0 and 14.
Solve the following equation. Only enter the numeric answer (no variables). 30=2.5(10-2x)
Answer:
x = -1
Step-by-step explanation:
30 = 2.5(10)(-2x) - you multiply by each
30 = 25 - 5x - then pass 25 to the other side and subract
5x = - 5x - then divide 5 / -5
x = -1 - and you have the answer
Answer:
x= -1
Step-by-step explanation:
distribute 2.5 through the parenthese
30=25-5x
move variable to the left hand side an change its sign
5x+30 =25
move constant to the right hand side and change the sign
5x=25 -30
calculate the difference
5x= -5
divide both sides of the equation by 5
x= -1
Hope this helps!!! I would really appreciate a brainliest???
There is 1/4 of a pizza left to split between 2 of your friends if u split the pizza equally what fraction of the pizza will each of your friends get
Answer:
1/8
Step-by-step explanation:
1/4 ÷ 2
~Turn 2 into a fraction
1/4 ÷ 2/1
~Copy dot flip
1/4 * 1/2
~Multiply
1/8
Best of Luck!
Answer:
1/8
Step-by-step explanation:
1/4 also = 2/8
2/8 divided by 2 = 1/8
The hockey team team won 8 out of their 14 games, At the same rate how many games should they expect to win out of 84?
Answer:
48 Games
Step-by-step explanation:
8/14 = 0.57142857142
84 x 0.57142857142 = 48 games
Hope that helps have a lovely night!
find mode of following
stem | leaves
4. 8
5 0,16
6 2,2,4
7 3,5
Answer:
62.
Step-by-step explanation:
A mode is a number that appears most frequently on a set of data. As you can see, there is a double of 62 while the rest is not repeated, so 62 is the mode.
1+6÷5×4
please help
SOLVING STEPS...
CALCULATE 6÷5×4
IT'S 4.8
ADD 1 WITH 4.8
CALCULATE THE SUM...
WE WILL GET THE ANSWER...
SO THE ANSWER IS
[tex]5.8[/tex]
GAVE ME THE BRAINLIEST IF MY ANSWER WAS HELPFUL...
Help plz:))) I’ll mark u brainliest ASAP 10 points(:(: Xx thank you....!!!
Answer:
D
Step-by-step explanation:
D because K to M is the shortest line in the diagram. Please mark brainllest if you want you dont have to.
if 4 oranges make 1 cup of juice then how much will 6 oranges make
Answer:
1 and 1/2 cups
Step-by-step explanation:
4 oranges = 1 cup
6 oranges / 4 oranges in a cup = 1 1/2 cups
If 4 oranges make 1 cup of juice, then that means 1 orange makes 1/4 cup of juice.
So we know that each orange makes 1/4 cup of juice. We need to find how much juice 6 oranges will make. To do that, multiply 1/4 by 6.
1/4 times 6 equals 6/4 or 1 and 1/2.
6 oranges will make 1 and 1/2 cups of juice.
Suppose that a phone that originally sold for $800 and loses 3/5 of its value each year after it is released.
3. Write an equation for the value of the phone, p, t years after it is released.
Answer:
p=(800)(3/5)^t
Step-by-step explanation:
Answer: 800 - (3/5xt)
Step-by-step explanation:
800 is the base value and you have to multiply 3/5 by t