Answer: see explanation below
Step-by-step explanation:
A rational number terminates.
9.6 terminates at six-tenths.
Jack received $300 for his 13th birthday. If he saves it in a bank account with 8% interest compounded yearly, how much money will he have in the bank by his 18th birthday?
300(1.08)^5
440.798423
A round wading pool has a diameter of 115cm deep. A hose is filling the pool at a rate of 34000cm^3, cubed per minute. How long will it take to fill the pool to a depth of 20cm?
Answer:
It will take 6.118 minutes to fill up the pool to a depth of 20 cm
Step-by-step explanation:
The first step is to calculate the volume of the wading pool.
we will assume it is a cylinder, hence the volume will be = [tex]\pi r^{2}h[/tex]
Where r= radius of the pool = 115/2 = 57.5cm
h = depth of the pool =20 cm
The volume of the pool will be [tex]\pi \times57.5^{2} \times 20 =2.08 \times 10^{5} cm ^{3}[/tex]
We are filling a pool of 208,000cm ^{3} at the rate of 34000cm^3, cubed per minute.
To get the time it will take to fill up the pool, we will have to divide as follows:
208,000cm ^{3} / 34000cm^3 =6.118 minutes
Therefore it will take 6.118 minutes to fill up the pool to a depth of 20 cm
Numbers 1-6 please and thank you This is really hard and I really really need help. I appreciate all the help I can get.
Area of prism = base area × altitude
1. (2x²-10)(x+4)
= 3x³-2x - 40
2. Base area = 2πr
Volume = (2πr)(r²+ 5r)
=2πr³ + 10πr²
3. Base area=½(6)(x-4)(x+3)=3(x-4)(x+3)
Volume= 3(x-4)(x+3)(⅓)
=(x-4)(x+3)= x² - x -12
4. Base circumference= 10π
Base radius = 10π/(2π) = 5
Base area = πr² = 25π
Volume = 25π(3x²-2x)
=125πx²-50πx
5. Volume = 3π√50
=15π√2
6. Base diameter = 16
Base radius = 16/2 = 8
Base area = 2πr = 16π
Volume = 16π(23a²)
=368πa²
Help.. ~Probability
7. Find the probability of choosing a red counter if a counter is chosen from a box that contains the following counters.
A. 3 red and 3 yellow
B. 3 red and 5 yellow
C. 1 red, 1 yellow and 2 blue
D. 5 red, 12 green and 7 orange
E. 10 red only
F. 6 blue and 4 green
A.
[tex]|\Omega|=6\\|A|=3\\\\P(A)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
B.
[tex]|\Omega|=8\\|A|=3\\\\P(A)=\dfrac{3}{8}[/tex]
C.
[tex]|\Omega|=4\\|A|=1\\\\P(A)=\dfrac{1}{4}[/tex]
D.
[tex]|\Omega|=24\\|A|=5\\\\P(A)=\dfrac{5}{24}[/tex]
E.
[tex]|\Omega|=10\\|A|=10\\\\P(A)=\dfrac{10}{10}=1[/tex]
F.
[tex]|\Omega|=10\\|A|=0\\\\P(A)=\dfrac{0}{10}=0[/tex]
Josephine is going on a run around the lake. She knows the distance around the lake. but she would like to complete her run in a certain amount of time. Josephine knows she can used the formula d=rt Which equation correctly rearranges the formula to find the time it will take her to run around the lake? (Solve for t)
Answer:
D
Step-by-step explanation:
To solve for T in this, you need to to divide r from both sides of the equation.
d=rt
divide r
d/r=t
The correct equation is t= d/r.
The answer is option D.
How do you reorganize an equation?Rearrange the equation in order that the unknown variable is by itself on one aspect of the equals sign (=) and all the different variables are on the opposite side. Rule 1: you could add, subtract, multiply and divide by means of something, so long as you do the identical aspect to both aspects of the equals sign.
What does it mean to rearrange a formula?We can express an equation in phrases of the opposite variable. For example, to arrange the equation in order that it's far written as taking each time period and circulate to the opposite side of the equal sign the usage of the opposite operation till you most effective have.
Learn more about the equation here: https://brainly.com/question/1214333
#SPJ2
A train moves at a speed of 90 km/hr. How far will it travel in 36 minutes?
Answer:
(90/60)*36 = 54 km
Step-by-step explanation:
Select the correct answer. If x and y are positive real numbers, which expression is equivalent to the expression below? (125x^4y3/2)1/3÷(xy)1/2
Answer:
5x^(5/6)
Step-by-step explanation:
we will use properties of exponents
x^a/x^b = x^(a-b)
and
x^a * x^b = x^(a+b)
___________________________________
(125x^4y3/2)1/3÷(xy)1/2\\
expanding each term by taking power for each component of expression
=>125^(1/3) x^(4/3) y(3/2*1/3) ÷ x(1/2)y(1/2)
=>5*x^(4/3) y(1/2) ÷ x(1/2)y(1/2)
using property = x^a/x^b = x^(a-b)
=>5x^(4/3 - 1/2) y^(1/2 -1/2)
y^(0) = 1
=> 5x^((4*2-3)/3*2) *1
=> 5x^(5/6)
Thus, value of expression is 5x^(5/6)
Calculate:
a) QR
b) PS
c) The area of quadrilateral PQRS
Greetings from Brasil...
For QR: we need to use the Sine Law in Any Triangle....
QS/SEN 72 = QR/SEN 25
6/SEN 72 = QR/SEN 25
6,3 = QR/SEN 25
QR = 2,66For PS: we need to use the Cosine Law in Any Triangle....
PS² = PQ² + QS² - 2.PQ.QS.COS Q
PS² = 7,4² + 6² - 2.(7,4).6.COS 34
PS² = 90,76 - 73,61
PS = √17,14
PS = 4,14For area we use Heron's Formula 2x.....
for ΔQRS = A1:
A1 = √[P.(P - QR).(P - RS).(P - QS)]
where P = (QR + RS + QS)/2
A1 = √[P.(P - QR).(P - RS).(P - QS)]
RS = 6,26 (using RS/SEN 97 = QS/SEN 72)
P = (2,66 + 6,26 + 6)/2
P = 14,92/2 ⇒ P = 7,46
A1 = √[7,46.(7,46 - 2,66).(7,46 - 6,26).(7,46 - 6)]
A1 = 7,92
for ΔPQS = A2:
A2 = √[P.(P - PQ).(P - PS).(P - QS)]
P = (7,4 + 4,14 + 6)/2 = 8,77
A2 = √[8,77.(8,77 - 7,4).(8,77 - 4,14).(8,77 - 6)]
A2 = 12,41
Total Area = A1 + A2
Total Area = 7,92 + 12,41
Total Area = 20,33see more:
https://brainly.com/question/17138076
If BH = 66, find DE. Round your answer to two decimal places if necessary.
Answer:
BH= 66
DE= ...?
We know that
BH is 1 to 6 = 66
DE is only take one space of that--> 3 to 4
so 66/6 = 11
1 space = 11 = DE
Hope it helps ^_^
find the interquartile range for the data {5, 7, 9, 5, 6, 6, 6, 11, 11, 3, 3}
Answer:
4
Step-by-step explanation:
i dont really know how to explain i used an algebra calculator
What is the area of the following figure: A) 30 cm 2 B) 36 cm 2 C) 18 cm 2 D) 15 cm 2
Answer:
15 cm^2
Step-by-step explanation:
The area of the triangle is
A = 1/2 bh
A = 1/2 ( 10) * 3
= 1/2 (30)
= 15
Answer:
D) 15cm^2
Step-by-step explanation:
The area of the triangle is
A = 1/2 bh
A = 1/2 ( 10) * 3
= 1/2 (30)
= 15
Match the graph with the correct equation. Please help!
Answer:
y = -x -2
Step-by-step explanation:
The graph has a slope of -1 and a y-intercept of -2.
The equation is therefore
y = -x -2
what are the prime numbers
Answer:
numbers that cannot be reduced when squared, ex: 1,3,5,
Step-by-step explanation:
These numbers factors are themselves and 1, to find if it is a prime number you can try to find the factors and if it is just itself and 1, then it is a prime number
The average age of cars owned by residents of a small city is 6 years with a standard deviation of 2.2 years. A simple random sample of 400 cars is to be selected, and the sample mean age of these cars is to be computed. We know the random variable has approximately a normal distribution because of
Answer:
The random variable [tex]\bar x[/tex] has approximately a normal distribution because of the central limit theorem.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Let the random variable X be defined as the age of cars owned by residents of a small city.
It is provided that:
μ = 6 years
σ = 2.2 years
n = 400
As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean ([tex]\bar x[/tex]) will be approximately normally distributed.
What is the volume of the following rectangular prism?
Answer:
1/10 units ^3
Step-by-step explanation:
The formula for the volume is given by
V = Bh where B is the area of the base and h is the height
V = 3/20 units ^2 * 2/3 units
= 3/20 * 2/3
= 1/10 units ^3
Para la función f(x) = x + 6, ¿ cuál es
resultado de la función si x=2 ?
Answer:
f(x) = 8
Step-by-step explanation:
Como x = 2, simplemente lo sustituiría por x en la función y sumaría.
f(x) = 2+6
f(x) = 8
Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.
Answer:
For Sprint
Cell phone plan would be;
$29.95 + $0.15n
For At & t
we have;
$4.95 + $0.39n
Step-by-step explanation:
Okay , here in this question, we are interested in creating equations for the cell phone plans.
Let’s start with Sprint
Sprint charges $29.95 monthly and $0.15 per text message.
Let the number of text messages sent be n
So the value of the cell phone plan will be;
$29.95 + $0.15(n) = $(29.95 + 0.15n)
For the At& t
Let the number of texts sent per month be n
The monthly plan is thus;
$4.95 + $0.39n
The Tama, Japan, monorail carries 92,700 riders
each day. If the monorail usually carries
5,150 riders per hour, how many hours does
the monorail run each day?
Answer:
The monorail runs 18 hours runs every day.
Step-by-step explanation:
You know that the total number of riders the monorail carry each day is 92700 and the number of riders the monorail carry per hour is 5150.
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
A direct proportionality relationship is established between two quantities if:
The greater the quantity in one quantity, the greater the quantity in the other quantity, in the same proportion. The less quantity in the magnitude corresponds to the less quantity in the other magnitude, in the same proportion.If the relationship between the magnitudes is direct the direct rule of three must be applied and to solve a direct rule of three, the following formula must be followed:
a ⇒ b
c ⇒ x
Being
[tex]x=\frac{c*b}{a}[/tex]
In this case the rule of three can be applied in the following way: if the monorail carries 5,150 passengers in 1 hour, the monorail will transport 92,700 passengers in how many hours?
[tex]amount of hours=\frac{92,700 passengers*1hour}{5,150 passengers}[/tex]
amount of hours= 18 hours
So the monorail runs 18 hours runs every day.
How many planes can be drawn through any three noncollinear points?
Answer:
1 plane
I hope this helps!
A retailer allowed 4%. discount on her his
goods to make 20 %profit and sold a refrigerator
for Rs.10848 with 13%. VAT . By how much
is the discount percent to be increased so that
she lhe gained only 15 % profit ?
Answer:
8%
Step-by-step explanation:
Let the cost price of the goods be $y. Let us assume the selling price of the goods is $x. The retailer sold at 4% discount, this means it was sold for 0.96x (100% - 4% = 96%). Since the goods was sold to make 20% profit, therefore it was sold for 1.2y (100% + 20% = 120%).
The refrigerator was sold at 13% VAT at Rs. 10848:
1.2y + 13%(1.2y) = 10848
1.2y + 0.13(1.2y) = 10848
1.2y + 0.156y = 10848
1.356y = 10848
y = 8000
The cost price is Rs 8000.
The selling price is:
0.96x = 1.2y
0.96x = 1.2(8000)
x = 10000
The selling price is Rs. 10000
For a profit of 15%, that is 1.15(8000) = 9200, the discount is:
(1 - discount)10000 = 9200
1 - discount = 0.92
Discount = 1 - 0.92 = 0.08
Discount = 8%
hey guys i need help again with this plzz help me
Answer: A) -4
================================================
Explanation:
The 3^0 in the denominator is equal to 1. Any nonzero number raised to an exponent of 0 is always 1. So this equation x^0 = 1 is true when x is nonzero.
This allows us to simplify to the equation 3^x = 1/81
Note how 81 = 3^4. Taking the reciprocal of 81 means the exponent goes from positive to negative. So 3^(-4) = 1/81. The rule is x^(-k) = 1/( x^k ). We could use logarithms to solve 3^x = 1/81.
if your ans is correct i will choose you as a brainlist when the number of student of a school was increased by 30% it became 455. Find the previous number student.
Step-by-step explanation:
find 30% of 455
which is = 136.5
then subtract 136.5 from the original number(455)
455 - 136.5
=318.5 student
A gear ratio is the ratio of the teeth on the rear sprocket. If a bike has 36 teeth on the front and 12 teeth on the rear sprocket, what is the gear ratio for the bike?
Answer: the ratio of the bike is 3
Step-by-step explanation:
its simply easy all you have to do is divide 36/12
Hey There!!
The answer to this is: (3:1) 36:12. 36 is the teeth on the front socket and 12 is the teeth on the rear socket. All you need to do is simplify by finding the greatest common factor (GCF) of 36 and 12-which is 12, then divide by the GCF. This gives you 3:1. The gear ratio for the bike is 3 teeth on the front socket for every 1 teeth on the rear socket (3:1).
Hope It Helped!~ ♡
ItsNobody~ ☆
What value of x is in the solution set of –5x – 15 > 10 + 20x? –2 –1 0 1
Answer:
-2
Step-by-step explanation:
5x – 15 > 10 + 20x
Subtract 5x from each side
5x – 15-5x > 10 + 20x-5x
-15 > 10+15x
Subtract 10 from each side
-15-10 >15x
-25 > 15x
Divide each side by 15
-25/15 > x
-5/3 > x
X must be less than -1 2/3
The only value that is less than -1 2/3 is -2
Answer:
x< -5/3x is less than -5/3 , so answer = -2Step-by-step explanation:
[tex]5x - 15 > 10 + 20x\\\mathrm{Add\:}15\mathrm{\:to\:both\:sides}\\\\5x-15+15>10+20x+15\\\mathrm{Simplify}\\\\5x>20x+25\\\\\mathrm{Subtract\:}20x\mathrm{\:from\:both\:sides}\\\\5x-20x>20x+25-20x\\\\\mathrm{Simplify}\\\\-15x>25\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-15x\right)\left(-1\right)<25\left(-1\right)\\\\\mathrm{Simplify}\\\\15x<-25\\\\\mathrm{Divide\:both\:sides\:by\:}15\\\\\frac{15x}{15}<\frac{-25}{15}\\\\x<-\frac{5}{3}[/tex]
Insert 2 rational numbers between -1/3 and -1/2
Answer:
-11/24 and -4/9
Step-by-step explanation:
A rational number is a fraction in the form a/b where both a and b are integers and b is not equal to zero.
Given the numbers -1/3 and -1/2, to place two numbers between them, we have to first find the width between the two numbers.
Width = -1/3 - (-1/2) = -1/3 + 1/2 = 1/2 - 1/3 = 1/6
Since two numbers are to be placed between -1/3 and -1/2, we have to divide the width into 3 which results to 1/6 ÷ 3 = 1/18
The first number placed is -1/3 - 1/18 = -11/24
The second number is -11/24 - 1/18 = -4/9
What is the solution for 5x-9 is less than or equal to 21
Answer:
Step-by-step explanation:
5x - 9 <= 21
5x <=30
x <= 6
2% of the students at Hamilton Middle School have red hair. There are 700 students at Hamilton Middle
School
How many students at Hamilton Middle School have red hair?
Answer:
14 students
Step-by-step explanation:
We can set up a percentage proportion to find 2% of 700.
[tex]\frac{x}{700} = \frac{2}{100}[/tex], and we can use the cross products property to find the value of x.
[tex]700\cdot2=1400\\\\1400\div100=14[/tex]
Hope this helped!
Answer:
14 students
Step-by-step explanation:
If two percent of Hamilton Middle School students have red hair, it means that the number of students who have red hair is given by (0.02) * (700) =14 students.
The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? need to know right now ASAP!! –270 cents per week –90 cents per week –87 cents per week –30 cents per week
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
It decreased by 30 cents per week.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The average rate of change is calculated as:
the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)
Rate of change = [tex]\frac{-60 -10 -20}{3}[/tex].
(-60 + -10 + -20 = -90). So, to simplify it:
[tex]\frac{-90}{3}[/tex] = -30
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Incase you are confused:
Since the average rate of change is negative, this means that the stock price has decreased.
SOMEBODY PLS HALP ;( According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answer:
B
Step-by-step explanation:
B sqrtb is right in front of 2, so 2 squared is 4, so a little bit more than 2 squared will be a little more than four.
Answer:
C) C < 4
Step-by-step explanation:
because c is on the right side of four on the number line
Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
Answer:
The second week had 10 more golfers than the first week.
Step-by-step explanation:
The graph clearly shows that the second week golfer are more than the first week. The median for week 2 is greater than the median of week 1. The graph of week 2 shows that number of golfers had increased and their age is between 60 to 80 years of age. The median of week 2 is 79 where as median of week 1 is 75.
