Answer: 158
Step-by-step explanation:
Okay so the total is 9 5/10.
Each party goer needs 6/10
So 95/10 / 6/0=. 95/10x10/6
=950/6 = 158.
MODELING WITH MATHEMATICS The population P (in thousands) of Austin, Texas, during a recent decade can be approximated by y = 494.29 * (1.03) ^ f , where is the number of years since the beginning of the decade. a. Tell whether the model represents exponential growth or exponential decay b. Identify the annual percent increase or decrease in population . Estimate when the population was about 590,000 .
Show work
Answer:
a) growth
b) 3%
c) 6 years (since the beginning of the decade)
Step-by-step explanation:
Given:
The population P (in thousands) of Austin, Texas during a recent decade can be approximated by [tex]y=494.29(1.03)^t[/tex] when t is the number of years since the beginning of the decade.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the y-intercept (or initial value)b is the base (or growth factor)x is the independent variabley is the dependent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
a) The model represents exponential growth as 1.03 > 1
b) The annual percent increase of the population is 3%
1.03 - 1 = 0.03
0.03 x 100 = 3%
c) To estimate when was population about 590,000 set y = 590 and solve for t:
[tex]\implies 590=494.29(1.03)^t[/tex]
[tex]\implies \dfrac{590}{494.29}=(1.03)^t[/tex]
Take natural logs of both sides:
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t[/tex]
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)[/tex]
[tex]\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}[/tex]
[tex]\implies t=5.988069001...[/tex]
Therefore the population was about 590,000 6 years since the beginning of the decade.
A square box s 12cm wide. What is the area of the box?
Answer: 9cm
Step-by-step explanation:
What decimal number is 17/22 equal to?
( Plato)
Answer:
0.773 thousandths place
Answer:
0.772
Step-by-step explanation:
Thats what i got!
Hope this helps! :)
vertex (-3, -3), point (2,97) find equation of parabola in vertex form
Answer:
y = 4(x+3)^2 - 3
Step-by-step explanation:
Vertex form y = a(x+3)^2 -3 sub in 2,97 to calculate a
97 = a(2+3)^2 - 3
a = 4
If a car travels 213 miles in 3 hours, how many miles will the car drive in 5 hours? pls help
Answer:
355 miles
Step-by-step explanation:
Figure out how far the car travelled in 1 hour - 3 hours can be divided by 3 for 1 hour, so do the same for the miles - 213 / 3 = 71 miles.
So we know the car travelled 71 miles in 1 hour.
Now just multiply the miles by 5 to figure out the answer - 71 * 5 = 355 miles
:)
Solve the right triangle.
Round your answers to the nearest tenth.
Answer: A= 42 degrees
Step-by-step explanation:
A= 180-90-48=42 (degrees)
Answer:
A= 42 degrees
a = 27
c= 40.4
Step-by-step explanation:
48 - 90 = 42 (we know the remaining angle area is 90 because its a right triangle and a traingle is 180 degrees)
to find the answer of a we need to use tan(48) and when you convert that to radians you get 1.1106 ish tan is opposite over adjacent and we know the opposite is 30 but we dont know a so we put [tex]\frac{30}{a}[/tex] = 1.1106 and put a on both sides so you divide 30 by 1.1106 and dget 27.0124 and round to the nearest tenth to get 27
to find c you need to find the hypotanuse which is [tex]a^{2}[/tex]+[tex]b^{2} =c^{2}[/tex]
30 squared is 900 add that to 27 squared which is 729 and you get 1629
find the square root of 1629 to get 40.3608 and then round that to the nearest tentth to get 40.4
20 points and brainliest to the best correct answer, do and show work for numbers 13 and 15. Questions are in the photo, thank you.
Answer:
13. x=11; MN=65°; NP=115°; NQP=245°
15. x=9; AD=108°; BC=23°; DC=139°; DBC=221°
Step-by-step explanation:
13.The marked arcs are congruent, so we can equate the given expressions for their measures:
10x -45 = 6x -1
4x = 44 . . . . . . . . . add 45-6x
x = 11 . . . . . . . . . . divide by 4
The arc measures are found by using the value of x in the corresponding expression. Arcs around a circle total 360°.
arc MN = (10(11) -45)° = 65°
arc NP = 180° -65° = 115°
arc NQP = 360° -NP = 245°
__
15.The sum of arcs around a circle is 360°. We can use this fact to write an equation involving the given expressions. Clockwise from A, we have ...
90 +(2x +5) +(17x -14) +12x = 360
31x = 279 . . . . . . . subtract 81, collect terms
x = 9 . . . . . . . . . divide by 31
The arc measures are found by using the value of x in the corresponding expression.
arc AD = 12(9)° = 108°
arc BC = (2(9) +5)° = 23°
arc DC = (17(9) -14)° = 139°
arc DBC = 360° -DC = 221°
(3x-4)^2=22 identify the solutions to the quadratic equation by taking the square root
[tex]~~~~(3x-4)^2 = 22\\\\\implies 3x-4 = \pm\sqrt{22}\\\\\implies 3x = 4 \pm\sqrt{22}\\\\\implies x = \dfrac{4\pm \sqrt{22}}3 \\\\\text{Hence,}~~ x = \dfrac{4+ \sqrt{22}}3~~ \text{and}~~ x = \dfrac{4-\sqrt{22}}3[/tex]
A farmer need to build a goat pen. The pen will be 5 meters wide and 16 meters long. The fencing material costs $8. 00 per meter. How much will it cost to buy enough fencing material to build the goat pen
Answer:
$336
Step-by-step explanation:
Find the perimeter, 5x2 + 16x2 = 10 + 32 = 42
Fencing material = $8 per 1 meter
42 meters, so 42 * 8 = $336
Which system of equations is better represented by this graph
find the area of this triangle, round to the nearest tenth. I will give brainliest
Answer:
108.8yd²
Step-by-step explanation:
Area of a Side Angle Side triangle : Area = 1/2 ( a × b ) × sin(c)
where a and b = the side lengths and c = the angle
Here the given side lengths are 23yds and 9.5yds and the angle given has a measure of 85° so a = 23, b = 9.5 and c = 85
Area = = 1/2 ( a × b ) × sin(c)
a = 23 , b = 9.5 and c = 85
Area = 1/2 ( 23 × 9.5 ) × sin(85)
==> multiply 23 and 9.5
Area = 1/2 ( 218.5 ) × sin(85)
==> multiply 1/2 and 218.5
Area = 109.25 × sin(85)
==> multiply sin(85) and 109.25
Area = 108.8yd²
Note: When the triangle is not a right triangle ( when there is no 90° angle ) we have to use a special formula in order to find the area. Here this is given a side an angle and a side, when given a side an angle and another side you can solve using the formula Area = 1/2 ( a × b ) × sin(c)
If you were graphing y < -3x + 5, would you need a solid or broken line?
solid
broken
Answer:
broken
Step-by-step explanation:
when there isn’t an equals sign the line will always be broken
Peter weighs is 105 kg. His wants to lose 500 g per week. How many weeks will it take for him to have a mass of 90 kg
Answer:
30
Step-by-step explanation:
500 g = 1/2 kg => 2 weeks he loses 1 kg
105 - 90 = 15 kg
So he needs to take 30 weeks in total. ( 15 * 2)
Let weeks be x
So
105-0.5x=900.5x=105-900.5x=15x=15/0.5x=30weeksThe sum of two numbers is equal to 272. When the numbers are divided, the quotient is 3 and the remainder is 52. Find the difference of the numbers.
Answer:
the difference of the numbers are 217 and 55.
Step-by-step explanation:
a+b=272
a/b=3…52
a=3b+52
4b+52=272
4b=220
b=55
a=272-55=217
What is the rate of change and y intercept
Answer:
5
Step-by-step explanation:
In PQR, P = 90°, Q = 40° and PR =9cm. Find the length of QR .
Answer:
QR = 14.00 cm to the neatest hundredth.
Step-by-step explanation:
This is a right triangle with < P = 90.
So QR is the hypotenuse.
< Q is the angle opposite to the line PR.
sin Q = opposite/hypotenuse = PR/QR
sin 40 = 9/QR
QR = 9/sin40
= 14.002 cm.
please help me!
What is the molarity of a solution composed of 5.85g of K dissolved in 0.125L of Water? Molar Mass for Ki= 166.1g/mol.
a. .282M
b. .182M
c. .0028M
d. 3.28M
Answer:butt no ayes
Step-by-step explanation:10 is a yes is no
Name the decimal illustrated by this model.
Answer:
1.97
Step-by-step explanation:
1 whole square is filled so that would equal 1
97 out of 100 squares in the second is filled so it would be = 0.97
combine them:
0.97+1=1.97
Jason's summer job allowed him to save $1200
to use as spending money throughout the
upcoming school year. To make sure he has
enough money, Jason plans to spend the same
amount each month and not run out of money
until the end of the school year in 10 months.
120x + y = 1200
Answer:Slope=-240.000/2.000=-120.000
Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
120*x+y-(1200)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve 120x+y-1200 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
Don't Send links, don't Write random things and get the points for free.
Answer:
Option D, [tex]2010\ cm^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of a single cylinder
[tex]V=\pi r^2h[/tex]
[tex]V=\pi *(4\ cm)^2 * 10\ cm[/tex]
[tex]V = 3.14 * 16\ cm^2 * 10\ cm[/tex]
[tex]V = 502.4\ cm^3[/tex]
Step 2: Determine the total volume
[tex]502.4\ cm^3 * 4[/tex]
[tex]2,009.6\ cm^3[/tex]
Answer: Option D, [tex]2010\ cm^3[/tex]
Answer:
The last one :)
Step-by-step explanation:
I hoped this helped have a good day! <3
Solve the system of equations using elimination: -5x - 8y = -8 and
6x +9y = 12. Please help and explain how to solve
Find the surface area please!!! Ignore my writing
Answer:
240m2 (square metre)
Step-by-step explanation:
Just too smart.
What is the solution to 8x - 3(2x - 4) = 3(x - 6)? 6 2 30 No solution
Answer:
The correct answer would be C) 30
i need help ................
Answer:
The answer is B) 40 yards for $45.00
Step-by-step explanation:
Options:
A) 20 yards per $30.00
B) 40 yards per $45.00
C) 50 yards per $70.00
C) 65 yards per $85.00
Think if buying something at the lowest cost which gives more.
1 yard per $1.00, sounds like a good deal.
20 yards per $30.00 which mean $10.00 more.
40 yeards per $45.00 which mean $5.00 more.
50 yards per $70.00 which mean $20.00 more.
65 yeards per $85.00 which mean $25.00 more.
Does Anyone know #19?
[tex]\text{Endpoints of diameter,}~~ A(4,6)~ \text{and}~ B(-3,-1)\\\\\text{Diameter,}~AB = \sqrt{(4+3)^2+(6+1)^2}\\\\~~~~~~~~~~~~~~~~~~~=\sqrt{7^2+7^2}\\\\~~~~~~~~~~~~~~~~~~~=7\sqrt2\\\\\text{So , radius}~ = \dfrac{AB}2 = \dfrac{7\sqrt 2}2 =4.9~\text{units.}\\\\\text{Hence the answer is B.}[/tex]
PLS HELP AND HURRY!!
Answer:
The answer should be: -2, 0, -8, -18
HELPPPPPPPPPpppp med
Step-by-step explanation:
Using the formula:
Sin☆=Perpendicular ÷ Hypotenus
Sin☆ = 35 ÷ 48
Sin☆ = 0.7291666667
☆ = Sin^-1 (0.7291666667)
☆ =46.8165782066
where ☆= Degree.
Hence final answer is 46.816
I hope this is right.....
4.
1
Х
4
3.4
X
67°
432
599
Can I please get help with these two !!!
Answer:
acdfe
Step-by-step explanation
right
Work out the missing value in the calculation below
Answer:
5
Step-by-step explanation:
[tex]\frac{2}{3} +\frac{1}{6}= \frac{ }{6} \\[/tex]
Here LCM will be 6. (We made the denominator same)
so, now the equation will be :
[tex]\frac{2}{3}+\frac{1}{6} \\\\ =\frac{4}{6} + \frac{1}{6}[/tex]
= 5/6
So, the value in the red box is 5.
Hope it helps!
Six different names were put into a hat. A name is chosen 125 times and the name Grace is chosen 17 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Question content area bottom
The experimental probability of choosing the name Grace is __
(Type an integer or a simplified fraction.)
Answer:
Step-by-step explanation:
The experimental probability of choosing Grace is 13.6% (17/125*100)
The theoretical probability of choosing Grace is 16.67% (1/6)
Each probability would change because they depend on the data set so if the data set changes, that means the probability will also change depending on the amount it changes.