[tex] = ( \sqrt{15} - \sqrt{3} )( \sqrt{15} - \sqrt{3} ) \\ = \sqrt{15} ( \sqrt{15} - \sqrt{3} ) - \sqrt{3} ( \sqrt{15} - \sqrt{3} ) \\ = 15 - \sqrt{45} - \sqrt{45} + 3 \\ = 15 + 3 - 2 \sqrt{45} \\ = 18 - 2( \sqrt{9 \times 5} ) \\ = 1 - 2(3 \sqrt{5} ) \\ = 1 - 6 \sqrt{5} [/tex]
ATTACHED IS THE SOLUTION
a certain town is served by two hospitals. in the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. as you know, about 50% of all babies are boys. however, the exact percentage varies from day to day. sometimes it may be higher than 50%, sometimes lower.
the more compact hospital. The Law of Large Numbers, which makes intuitive sense, states that when there are more observations, the experimental average tends to approach the true proportion. Large hospitals have more observations, therefore their results are less likely to deviate from 50% or have a wide range of results.
What is the True proportion?An equation that states that two ratios are equal is a genuine proportion. You can utilise information about one ratio in a proportion to determine values in the other equal ratio.
The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) follows..
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In the diagram below, NO is parallel to KL. If KN = 24, NO = 30, and
KL = 48, find the length of N M.
Answer: NM = 40
Step-by-step explanation:
First, we will label everything. See attached.
Next, we will set up a proportion to solve. Let the missing side, ? in the picture, be equal to x.
➜ On the left side will be the "smaller top" triangle
➜ On the right side will be the larger triangle
➜ View the second attachment for a visual explanation of this if you are confused.
[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]
Next, we will cross-multiply and solve.
[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]
48x = 30(x + 24)
48x = 30x + 720
18x = 720
x = 40
Answer quick please. I need to finish this in 5 min
Answer: I got 18
Step-by-step explanation:
Substitute all the variables
18 = 2*3^2
X = 4 * 9^2
X = 4 * 81
X = 324
324/18 = 18
so the is answer is 18.
Also are you going to A+ by any chance?
20.8cm divided by 2.3g
Answer:
9.043
Step-by-step explanation:
i just divide
Answer: 9.043 centimeters/grams
Step-by-step explanation:
All you have to do it divide!
The answer is????????
Answer:
-7
Step-by-step explanation:
2(-9)+5=-7
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{xy + 5}\\\mathsf{= 2(-6) + 5}\\\mathsf{= -12 + 5}\\\mathsf{= -7}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A bottle of maple syrup in Wayne’s freezer needs to be warmed for breakfast. Sitting on the kitchen counter, the bottle temperature will go up a steady 9.6° C every hour. If the bottle temperature begins at the freezer temperature of –16° C, how many hours will it take to reach 20° C?
Change in temperature: (20 – (–16)) = 20 + 16 = 36
It will take the bottle of maple syrup 3 hours 45 minutes to reach 20° C from –16° C.
How to get the temperature changegiven data
the bottle temperature will go up a steady 9.6° C every hour
freezer temperature = –16° C
final temperature = 20° C
The temperature rise from –16° C to 20° C
from –16° C to 0° C = 16° C
from 0° C to 20° C = 20° C
adding both increments gives = 20 + 16 = 36° C
if every hour we have 9.6° C then how many hours will give 36° C
1 hour = 9.6° C
? hour = 36° C
we cross multiply to have
= 36 * 1 / 9.6
= 3.75
This is 3 hours then a fraction of some minutes, the fraction is gotten by
0.75 * 60 = 45
Therefore the time to reach 20° C is 3 hours 45 minutes
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What is the missing angle in the triangle?
A. 25
B.79
C. 126
D. 180
Answer:
25
sum of the interior angles of triangle =180
101+54=155
155-180=25
An arts academy requires there to be 4 teachers for every 68 students and for every 3 tutors for every 36 minutes. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
The given question is solved using the unitary method.
The arts academy requires 4 teacher for every 68 students
The arts academy requires 1 teacher for every 68/4 students
The arts academy requires 1 teacher for every 17 students
The academy has 17 students per teacher
It requires 3 tutors for every 36 students
3 tutor = 36 student
1 tutor = 36 /3 = 12 students
The academy has 12 students per tutor
For 72 students the total number of tutor required are 72/12 = 6
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
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If £1 is equal to 99.72 rupees and the post office only has 500 rupee papers how much can I change out of £450
£1 = 99.72 rupees -> £450 = 44874 rupees.
As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.
The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.
the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 9 years, how long will it take to triple?
Since the population increases at a rate proportional to the current number of people, the population will be three times of its initial population after 14.27 years.
The population of a community increases at a rate proportional to the number of people present at time t, means:
dP/dt = kP
where k is a constant.
Rearrange it:
(1/P) dP = k dt
Take the integral:
∫ (1/P) dP = ∫ k dt
ln P = kt + C, where C is a constant
Substitute t = 0, from the problem, it is known that P(t = 0) = P₀
Hence,
P(t) = P₀. e^(kt)
The population doubles after 9 years, means if we substitute t = 9
P(9) = P₀. e^(9k)
2P₀ = P₀. e^(9k)
2 = e^(9k)
Take the natural logarithmic:
ln 2 = 9k
k = (ln 2)/9 = 0.077
When the population grows to triple, it means P(t) = 3P₀
3P₀ = P₀. e^(kt)
ln 3 = kt
ln 3 = 0.077 t
t = (ln 3)/0.077 = 14.27 years.
Hence, the population will be three times of its initial population after 14.27 years.
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Step
1
try
Angle
m/IKL=54"
m/
CL
F
H
54°
Reason
Given
Select a Reason
Answer:
<DKF IS 54° BECAUSE IT IS VERTICALLY OPPOSITE ANGLE OF THE<IKL.
if gas is 4.83 per gallon and johnny's car has a 107 gallon tank how much money would it take for him to fill the tank?
Answer:
Step-by-step explanation:
Fuel cost = (Distance / Consumption) × Cost per gallon.
107 X 4.83 = 516.81
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Help with this asap
Please and thank you
a) 7 video games;
26 - x = 40 - 3x
x = 7
please help 8th grade math!
what is the answer to 6x+4
Answer:
2(3x+2)
Step-by-step explanation:
i think that's what it is
Answer:
What do you need done here?
Step-by-step explanation:
6x + 4 means nothing unless you want to factor the binomial.
I assume you want to factor.
Factor out 2.
2(3x + 2)
Is this what you are looking for?
Ben's rent a car has a security deposit of $200.00 and it cost $180.00 per day to rent a car. dave's car rental services has a security deposit of $380.00, and it cost $120.00 per day to rent the same car. how many days, d, will it take for the costs to be the same on both car rentals?
It will take 3 days for the cost of the car to be the same which is $740.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So,
Ben's car rental:
Security Deposit - $200; rental each day - $180Dave's car rental:
Security Deposit - $380; rental each day - $120Now,
Days after which the cost will be the same:
Day 1:
Ben's car rental: $380Daves car rental: $500Day 2:
Ben's car rental: $560 (+180)Daves car rental: $620 (+120)Day 3:
Ben's car rental: $740 (+180)Daves car rental: $740 (+120)Therefore, it will take 3 days for the cost of the car to be the same.
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The Distributive Property- 6( x + 3)
Answer:
-6x-18
Step-by-step explanation:
in class
Answer:-24
Step-by-step explanation: you do -6(x)+(-6)(3) and u get -6+-18 and get -24 hope it helps .
The line parallel to y=-2/5x+7 that passes through the point (-1,3)
Answer:
y=-2/5x +13/5
Step-by-step explanation:
y= -0.4x+b
3=0.4+b
b=2.6
y=-2/5x +13/5
Answer: [tex]\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}[/tex]
===============================================
Work Shown:
I'll be using point slope form to get these steps
[tex]\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-3 = -\frac{2}{5}(\text{x}-(-1))\\\\\text{y}-3 = -\frac{2}{5}(\text{x}+1)\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}*1\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}\\\\[/tex]
[tex]\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+3\\\\\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+\frac{15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{-2+15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}\\\\[/tex]
This answer has a slope of -2/5 and y intercept of 13/5.
Parallel lines have equal slopes but different y intercepts.
To verify this equation, plugging in x = -1 leads to y = 3.
Use the graph of y=x^2 to graph the quadratic equation f(x)=(x+4)^2+5
Answer:
shifted 5 up and 4 to the left
Step-by-step explanation:
solve the following expression
Answer:
2
Step-by-step explanation:
substitute s for 8
then substitute f for 2
that means 2*2 or 4
8/4 is 2
Answer: the answer would be 2
Step-by-step explanation: since f = 2 you would multiple 2 x2 then you would get 4 then you divid 8 and 4 and you get 2
A bracelet is 8.0 inches long. One bead on the bracelet is
0.8 inch long.
One bead is
times the length of the bracelet.
Answer:
8.0/0.8
=10times
create a linear equation that has infinitely many solutions. Must start with 18=
Answer:
Step-by-step explanation:
18=18+x-x*x/x
A pair of shoes usually sells for $68 if the shoes are 40% off and sales tax is 6% what is the total price of the shoes including tax
Usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.
As given in the question,
Given that:
Usual selling price of shoes = $68
Discount on shoes =40%
Discounts an amount or percentage from something that they are selling, they take the amount or percentage off the usual price.
so, remove 40% from the price and you have left 60%
reduced price = 60% of $68
=60/100 * 68 = $40.8
Sales tax is 6% of reduced price= 6% of $40.8
=$2.448 upto 3 decimal digits
Now , price including tax =$40.8+$2.448 =$43.248
Hence, total price including tax= $43.248
Therefore, usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.
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HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
Based on the equation of the line that is parallel to the first line, the equation of the line in slope-intercept form is y = 3/4x - 6³/₄
How to write the equation?First, find the slope of 3x + 4y = 7:
( 3x + 4y = 7) x 1/4
3/4x + y = 7/4
The slope is therefore 3/4x.
Lines that are parallel to each other have the same slope. You can therefore use this slope to find the formula of the other line by first solving for the y-intercept:
y = Slope(x) + y-intercept
-9 = 3/4(-3) + y-intercept
y-intercept = -6³/₄
The equation of the line is:
y = 3/4x - 6³/₄
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how many nonzero complex numbers zz have the property that 0, z,0,z, and z^3,z 3 , when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?
Consequently, there exist four numbers z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z
=(z^2-e^±iπ/3)z=0⟺z=0
or z^2=e^±iπ/3
Since we have z[tex]\neq[/tex]0, z=e^±iπ/6= ±(√3/2 ± I 1/2 )
There are thus four numbers in z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
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⚠URGENT!!!⚠The larger prism has had two identical holes carved out of it, each of which is a rectangular prism. Find the volume of the remaining solid, writing your answer correct to 2 decimal places. Note that all measurements are in meters.
Volume=_____m^3
The volume of the remaining solid correct to 2 decimal places is 3634.60 m³
Calculating VolumeFrom the question, we are to determine the volume of the remaining solid
Volume of the remaining solid = Volume of the larger prism - Volume of the rectangular prisms carved out
First, we will determine the volume of the larger prism
Volume of the larger prism = 17 × 17 × 17
Volume of the larger prism = 4913 m³
Now, we will determine the volume of one of the rectangular prism that was carved out
Volume = 4 × 9.4 × 17
Volume = 639.2 m³
∴ Volume of the two identical holes carved out = 2 × 639.2 m³
= 1278.4 m³
Thus,
Volume of the remaining solid = 4913 m³ - 1278.4 m³
Volume of the remaining solid = 3634.60 m³
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Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
The figure RSTU can represent Quadrilateral, Parallelogram and Rectangle
The figure KLMN represents Quadrilateral and Parallelogram
The figure ABCD represents only Quadrilateral
Given,
The figures;
RSTU, KLMN and ABCD
We have to identify the true facts about the figure.
All figure are drawn like a rectangle.
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Parallelogram;
A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.
Now here,
RSTU; This figure can represent all the options.
That is,
Quadrilateral, Parallelogram and Rectangle
KLMN; This figure represents Quadrilateral and Parallelogram
ABCD; This figure represents only Quadrilateral
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Please answer this question to 1 decimal place
The side x of the rectangle is 36.0 cm
How to find side of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
All four angles of a rectangle are right angles.
The diagonal of a rectangle are equal in length to each other and they bisect each other at there point of intersection.
Therefore,
∠ COD = 48°
∠OCD = ∠ODC = 132 / 2 = 66°
Using sin law
OD / sin 66 = 16 / sin 48
OD sin 48 = 16 sin 66
OD = 16 sin 66 / sin 48
OD = 14.6167273223 / 0.74314482547
OD = 19.6687105931
OD = 19.7 cm
∠AOD = 180 - 48
∠AOD = 132°
∠OAD = ∠ODA = 48 / 2 = 24°
Hence, using sine law let's find x
19.7 / sin 24 = x / sin 132
x sin 24 = 19.7 sin 132
x = 19.7 sin 132 / sin 24
x = 14.6399530619 / 0.40673664307
x = 35.9935605802
Therefore,
x = 36.0 cm
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solve the inequlaity 2(4x+1)<3(2x-3)
Answer:
x<-5.5 or x<-11/2
Step-by-step explanation:
2(4x+1)<3(2x-3)
1. First we need to expand the brackets
8x+2<6x-9
2. get the x on one side so we would -6x and -2 on each side
2x<-11
3. divide by 2 on each side as we want to get the value of x which gives
x<-11/2
the fraction can also be written as a decimal
x<-5.5
4) so, the final answer is
x<-5.5 or <-11/2
The graph of line p passes through the point (-3,-4) and has a slope of 2. What is the y-coordinate of the y-intercept of line p?
Answer: m= -1/2
Step-by-step explanation: Equation of line in slope intercept form is represented by,. y= mx+c —-(1). Given that the line p passes through A (- 2, 4) and has a slope m= -1/2.