Answer:
5
Step-by-step explanation:
area of rectangle = l(ength)×w(idth)
perimeter = 2×l + 2×w
diagonal = sqrt(l² + w²) (Pythagoras)
l×w = 12. => l = 12/w
2×l + 2×w = 14
2×12/w + 2×w =14
12/w + w = 7
12 + w² = 7w
w² - 7w + 12 = 0
=> (after a little thinking and trying : what 2 numbers multiply to 12 and add to -7 ? -3 and -4
=> (w-3)×(w-4) = 0
so, we get 2 solutions for w : 3 and 4
that gives us 2 solutions for l : 4 and 3
so, one is 3 and the other 4. it does not matter which is which. length 4 and width 3 produce the same diagonal as length 3 and width 4.
diagonal = sqrt(l² + w²) = sqrt(16 +9) = sqrt(25) = 5
Which equation is written in factor form?
Fat Kat's offers a special on large two topping pizzas. In how many different ways can you order a two topping pizza if you can choose from 18 toppings? NO LINKS!!!
=======================================================
Explanation:
There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.
If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.
So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations
------------------------
The alternative method involves using the nCr combination formula
Use n = 18 and r = 2 in this formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
the exclamation marks indicate factorial.
what should be added to -13/25+21/5+-21/18 to get 5?
ATQ,
= [tex] \dfrac{ - 13}{25} + \dfrac{21}{5} + \frac{ - 21}{18} + x = 5[/tex]
Take the lcm of 25,5,18 and then manipulate it accordingly.= [tex] \dfrac{ 377}{150} + x = 5[/tex]
= [tex] x = 5 - \dfrac{ 377}{150}[/tex]
= [tex] x = \dfrac{ 373}{150}[/tex]
Answer
=727/150
Step-by-step explanation:
-13/25 + 21/18 + 21/18
= -13 + 105/25 + 21/18
= 92/25 + 21/18
= 1656 + 525/450
= 2181/450 = 727/150
Have nice day
Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = 0.14.
Step-by-step explanation:
Venn probabilities:
Suppose we have two events, A and B. The probability P(A and B) is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]
So
P(A and B) = 0.14.
please help what's the exact value for x?
cos(x+pi)-sin(x-pi)=0
SHOW WORK PLEASE
Step-by-step explanation:
Recall that
[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]
and
[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]
But we also know that
[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]
so the above relations reduce to
[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]
Therefore,
[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]
HELP PLSS I DONT UNDERSTAND A THING
Answer:
1 no
angle 1 =53 degree (being vertically opposite angle)
angle 2=127 degree(being linear piar)
angle 3 =127 degree(being vertically opposite angles)
2 no
angle 1=155.1(being linear pair)
angle 2=24.9(being vertically opposite angles)
angle 3=155.1(beinf linear pair)
3 no
angle 1=68 degree(being linear pair)
angle 2=112 degree(being vertically opposite angle)
angle 3=68 degree(being vertically opposite angle)
4 no
angle 1=54.5 degree(being linear pair)
angle 2=125.5 degree(being vertically opposite angle)
angle 3=54.5 degree(being vertically oppostie angle)
Step-by-step explanation:
A box is filled with 2 red carts, 3 green cards, and 8 brown cards. A card is chosen at random from the box, What is the grobability that the card is not green?
Write your answer as a fraction in simplest form.
Answer:
10/13
Step-by-step explanation:
High. Very High
The total number of cards is 8 + 3 + 2 = 13
There are 3 green ones and 10 others.
P(~G) = 10/13 = 0.769
Find the 8th term of the geometric sequence 7, 28, 112, ...
A watering can contained 5 1/2 quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
Answer:
4 1/2 quarts.
Step-by-step explanation:
So 5 1/2 quarts to start. 4 left over.
Theres 4 cups in a quart.
So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.
if u can answer this that would rlly help:)
Answer:
x = 12
Step-by-step explanation:
First, we need to find the last interior angle of the triangle. Since we know the exterior angle next to it is 140° and they are supplementary, meaning they form a 180° angle, we can make an equation to solve for the last angle.
∠SRT + 140° = 180°
∠SRT = 40°
Now we know that the last interior angle is 40°. All triangles have a sum of 180°, therefore we can once again set up an equation to solve for x.
3x + 4 + 8x + 4 + 40 = 180
11x + 48 = 180
11x = 132
x = 12
Therefore, x = 12.
Help with volume all help is appreciated :)
Answer:
It would be 0.41 ft^3
Step-by-step explanation:
Alright, to start, lets get the volume of the entire cinder block and the holes within it.
1.31 * 0.66 * 0.66 ---> 0.5706...
Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.
0.33 * 0.39 * 0.66 ---> 0.0849...
Since there's two of them: 0.1698...
To finish it, subtract the hole volume from the total volume;
0.5806 - 0.1698 = 0.4108
Rounds to 0.41 ft^3
Imagine a simple process in which 5 ticket booths are selling tickets for an opera. If customers are coming at a rate of 15 / hour, and the utilization of the 5 booths is 50%, then how long does a customer spend at a booth (each customer goes to only one booth)?
Answer: The customer spends 10 minutes at a booth.
Step-by-step explanation:
Let n= number of booths, [tex]\rho[/tex] = utilization, [tex]\lambda[/tex] = arrival rate, [tex]\mu=[/tex]Service rate
We know that
[tex]\rho=\dfrac{\lambda}{\mu\times n}[/tex]
As per given,
[tex]0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6[/tex]
Service rate = 6 customers per hour.
Time taken by each customer = [tex]\frac{1}{\mu}[/tex]
[tex]=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes[/tex]
Hence, the customer spends 10 minutes at a booth.
I need help
1−(−3)−5
answer is -1 you can check it on the calculator
pleaseeee mark me as the BRAINLIEST pleaseeee
Step-by-step explanation:
(-)(-)=+
1−(−3)−5
1+3-5
4-5
-1
The step function f(x) is graphed
What is the value of f(-1)?
0-3
O-1
ОО
0 1
The value of f(-1) in the graph is 1.
What is Function?In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The graph leads to the following finding:
The values of f(-1) for x = -1 are -1 and -3.
The function does, however, have a closed circle at f(-1) = 1.
The function has an open circle at f(-1) = -3.
A closed circle represents inclusive principles.
Hence, the graph's value for f(-1) is 1.
Learn more about functions here:
brainly.com/question/13136492
#SPJ7
he slope distance between two points BM1 and TP1 is 600.00 ft. These two points arelocated on an inclined plane. A level is used to measure the backsight on BM1 (2.50 ft) andthe foresight on TP1 (10.20 ft). What is the horizontal length of the line to nearest 0.01 f
Answer:
the height is 599.950
Step-by-step explanation:
The computation of the horizontal length of the line is shown below:
The vertical distance is
= 10.20ft - 2.50ft
= 7.70 ft
Now use the pythagoreans theorem to determine the length of the line horizontally i.e presented below;
√horizontal distance^2 + √vertical distance^2 = Slope
√horizontal distance^2 + √7.7^2 = 600
So the height is 599.950
20 POINTS AND I WILL MARK YOU BRAINLIEST !!!
the london ferris wheel has a maximum height of 443 ft and a diameter of 394 ft . the wheel takes 30 mins to rotate
#1. what is the minimum height of the ferris wheel ?
94 , 85 , 49 , or 40
#2. where would the midline of the graph be ?
y=246 , y=221.5 , or y=197
#3. what is the amplitude of the graph ?
246 ft , 221.5 ft , or 197 ft
#4. what is the period of the function ?
15 , 30 , or 60 minutes
Step-by-step explanation:
#1 . the minimum height =
443 - 394 = 49 ft
#2. y = (394/2) + 49 = 197+49
=> y =246
#3. the amplitude is ½× diameter
= ½×394 = 197 ft
#4. the period of function is
the time that the wheel takes
one rotation =>30 minutes
If y is inversely proportional to (tan x) and y = 2
when x = 30°, find the value of y when this value
of x is doubled.
Answer:
When something is inversely proportional it can be solved by using the equation:
y = k/x
where k is the constant.
So using this we can plug in x and y to find the value of k.
3 = k/4.
Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.
Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.
In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.
Thus, y must be divided by 2.
Thus, y = 3/2 or 1.5.
Answer:
Step-by-step explanation:
y is inversely proportional to tan x means
[tex]y \ \alpha \ \frac{1}{tan x}\\\\y = k \times \frac{1}{tanx}[/tex]
Given y = 2 when x =30° . So we will find k.
[tex]y =k \times \frac{1}{tanx } \\\\2 = k \times \frac{1}{tan 30}\\\\k = 2 \times tan 30 = 2 \times \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3} }[/tex]
Now x is doubled, x = 60°, find y
[tex]y = k \times \frac{1}{tanx}\\[/tex]
[tex]= \frac{2}{\sqrt{3}} \times \frac{1}{tan 60}\\\\= \frac{2}{\sqrt{3}} \times \sqrt{3}\\\\=2[/tex]
Lil' HydroPhil owns five pieces of precious apparel and wants to choose two to wear to the awards show. He defines his precious apparel as: platinum nose ring, diamond shirt, titanium boots, suede pants, and beryllium hat. Assuming the selection is random and each has an equally likely outcome, determine the probability HydroPhil chooses a combination that includes the suede pants.
Answer:
The probability HydroPhil chooses a combination that includes the suede pants is 0.40
Step-by-step explanation:
Given
Let
[tex]P \to Platin um\ no se\ ri ng[/tex]
[tex]D \to Diamond\ shirt[/tex]
[tex]T \to Titanium\ boots[/tex]
[tex]S\to Suede\ pants[/tex]
[tex]B\to Beryllium\ hat[/tex]
Required
Probability of selecting a combination that has S
First, list out all possible combinations (A) of 2
[tex]A = \{PD, PT, PS, PB, DT, DS, DB, TS, TB, SB\}[/tex]
The sample size is:
[tex]n(A) = 10[/tex]
The combinations that has S are:
[tex]S \to \{PS, DS, TS, SB\}[/tex]
The size is:
[tex]n(S) = 4[/tex]
So, the probability that he choose the combination that has S is:
[tex]Pr = \frac{n(S)}{n(A)}[/tex]
[tex]Pr = \frac{4}{10}[/tex]
[tex]Pr = 0.40[/tex]
What do u multiply first?
Answer:
Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.
pls Mark me as brainliest trust me..
please help!! 15 points i’m stressed out :/
Answer:
Since this (looks) like a homework assignment/test, I'll give you a hint.
Step-by-step explanation:
A function is where you have a input, that usually involves an equation that you have to replace the unknown with, to get the output.
Don't get it? Well, I didn't either.
What's great about this problem that you don't neccessarily have to know what the definition is.
A function can only output. So if you inputted the number 6, and got the output -3, you can't have another number that also had the output -3, and vice versa. This is my hint for the number 1.
Number 4 is a bit harder, but here's my hint:
Look for a pattern.
1. Points scored by a basketball player are 12, 15, 8, 12, 15, 10, 3, 14, and 15
Calculate the:
a) mean
b) median
c) mode
d) midrange
e) Use the relative location of the mean, median, and mode calculated describe the sets as
symmetric, skewed left, or skewed right.
Answer:
mean : add all of them and divide by how much they are
mode: is what repeats it self like 15 is the most repeated.
READ PIC! PLEASE HELP
Answer:
B. 0< b < 1
Step-by-step explanation:
b is a fraction that less than 1, so 0 < b < 1
Plz help me well mark brainliest if correct!!....
Answer:
I'm pretty sure it is line plot
brainliest and many poitns FAST
Answer:
you're answer is, 22
Answer:
Solution given;
[tex]11 \div \frac{1 }{2} = \frac{11}{ \frac{1}{2} } = 11 \times 2 = 22[/tex]
22 is a required answer:.
Find the Surface Area of this Prism
Answer:
formula - 2 (wl + hl + hw)
559,872 is the answer from how I learned it.
If i'm right, please mark me brainliest ! (๑・ω-)～♥”
Round 2.873 to the nearest tenth
Answer:
2.9
hope this helps
have a good day :)
Step-by-step explanation:
Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½:
N(t) = 300 • 0.5t/8
What is the half-life for the zombie population?
Answer:
The half-life for the zombie population is of 8 years.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
[tex]N(t) = N(0)(1-r)^t[/tex]
In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.
In this question:
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
Thus N(0) = 300, that is, initial population of 300.
What is the half-life for the zombie population?
This is t for which N(t) = 0.5*300 = 150. So
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]
[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]
[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]
[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]
Equal exponents, so:
[tex]\frac{t}{8} = 1[/tex]
[tex]t = 8[/tex]
The half-life for the zombie population is of 8 years.
PLEASE PLEASE HELP I will give BRAINLIEST
Anthony deposits 1,250 in a savings account with an interest rate of 6% if the Interest rate is compounded monthly than the account balance after t years is given by the expression below 1250(1+0.06/12)^12t what does (1+0.06/12t) represent
(nevermind srry, that was wrong)
Answer: represents the growth factor which reveals the monthly interest rate.
Step-by-step explanation:
Anthony's account balance can be modeled by the general compound interest formula shown below, where P is the initial amount, r is the annual interest rate, n is the number of times that the interest in the account is compounded per year, and t is the time period.
Consider the given expression.
1250(1+0.06/12)^12t
In the given expression, "1" represents 100% of the money in the account at the start of the month and "" represents the percentage of the account balance that gets added into the account at the end of each month. This is the monthly interest rate and the entire expression,(1+0.06/12t) , is the factor of growth.
Therefore, (1+0.06/12t)represents the growth factor which reveals the monthly interest rate.
Kelly is using a rectangular container to fill up a bucket of water. The container is 3.8 inches long, 2.5 inches wide, and 7.2 inches tall. If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket
Answer:
Kelly will have to fill the cup 20 times.
Step-by-step explanation:
Volume of the cube:
Rectangular cube, so the volume of the cube is the multiplication of its three dimensions(3.8 inches, 2.5 inches and 7.2 inches).
V = 3.8*2.5*7.2 = 68.4 cubic inches.
If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket?
Solved by proportions, using a rule of three.
1 time - 68.4 cubic inches
x times - 1368 cubic inches
Applying cross multiplication:
[tex]68.4x = 1368[/tex]
[tex]x = \frac{1368}{68.4}[/tex]
[tex]x = 20[/tex]
Kelly will have to fill the cup 20 times.
Plzzz help as soon as possible
Answer:
Step-by-step explanation:
8 is not a function
9 is a function
10 is a function