Answer:
a) 19/15 b) 1/3
Step-by-step explanation:
in both the question I reduced the numbers with 5
What would you have to calculate to prove the figure below is a SQUARE?
O None of these choices are correct.
O use the distance formula to show that the opposite sides are supplementary
the sides all have the same slopes
O diagonals are ½ the length of the midpoint
slopes are perpendicular where the sides meet
The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet
How to Prove a quadrilateral is a Square?We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.
Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.
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A bacteria culture grows with constant relative growth rate. The bacteria count was 1,920 after 4 hours and 1,966,080 after 12 hours.
(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)
(b) What was the initial size of the culture?
(c)Find an expression for the exact number of bacteria after t hours, y(t).
(d) Find the number of bacteria after 9.5 hours. (Round your answer to the nearest whole number.)
(e) Find the rate of growth (in bacteria per hour) after 9.5 hours. (Round your answer to the nearest whole number.)
(f) How many hours did it take for the population to reach 72,000? (Round your answer to two decimal places.)
From the calculation, the growth rate is 0.88.
What is the growth rate?To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
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I need help ASAP please
Answer:
8.1
Step-by-step explanation:
[tex]\sqrt{(-1-0)^2 + (5-(-3))^2}=\sqrt{65} \approx 8.1[/tex]
In the diagram the origin is at the center of a cube that has edges 6 units long. The x-,y-, and z-axes are perpendicular to the faces of the cube give the coordinates of the corner at point A.
Answer:
the third answer (-3, -3, 3)
Step-by-step explanation:
the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.
so, we know that A is the left-back-upper corner of the cube.
the x-axis goes front-back. front is positive.
the y-axis goes left-right. right is positive.
the z-axis goes up-down. up is positive.
since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.
as we said : left-back-upper corner.
left means negative y.
back means negative x.
upper means positive z.
so, the coordinates of A are
(-3, -3, 3)
Use the data in the table to describe how the population in a town is changing. Then identify a function that
models the data. Use your function to predict the population after 6 years.
Population in a Town
Year
0
1
2
3
Population
600
1200
2400
4800
O There is a constant ratio 2
y = 600(2)*
38,400
O There is a constant ratio 2
y = 600 + 2x
5412
O There is a constant ratio 4
y = 600(2x)
7200
www
There is a constant ratio 4
y = 600 + 2x
664
D
The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400
How to compute the ratio?The ratio based on the information given will be:
= 1200/600
= 2
Therefore, the constant ratio is 2.
In 6 years, the population will be:
= 600 × 2^6
= 600 × 64
= 38400
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A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Because this answer involves an expression that is more complex than a whole number times n , remember to type in multiplication symbols *. For example, if you wanted to enter 12n , type this in as (1/2)*n.
The value P price they charges for shirts is (-0.008n) + 38
According to the statement
we have given that the 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 .
And we have to find the linear equation.So,
Let p = price
n = number of shirts
m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)
b = y intercept
And they gives us the two points like here (1000, $30) and (3000, $14) which have to be on our line.
To find the slope m, you use m = (p₁-p₂)/(n₁-n₂)
Filling in from our points m = (30-14)/(1000-3000)
m = 16/-2000
m = -0.008
Now that we have the slope and a point, we can find our equation
p-p₁=m(n-n₁)
p-30=(-.008)(n-1000)
p-30= (-.008n) + 8
p=(-.008n) + 38
So, The value P price they charges for shirts is (-0.008n) + 38
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m∠ __ +m∠BPD=180∘
what is the blank for Linear Pairs
The blank space to form a linear pair with m∠BPD is m∠APD.
What are linear pair angles?Linear pair of angles are formed when two lines intersect each other at a single point.
Linear pair angles are adjacent to each other.
Therefore, the sum of a linear pair angles is equals to 180 degrees.
This means linear pair angles are supplementary.
Hence,
m∠APD + m∠BPD = 180°
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look at the pictures
Answer:
A
Step-by-step explanation:
9|x-8|<36
|x-8|<4
-4<x-8<4
add 8
-4+8<x-8+8<4+8
4<x<12
A group of researchers wants to develop an experiment to determine whether a new drug effectively treats high blood pressure. The researchers want to inject the drug in monkeys first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find that blood pressure levels return to normal, and they declare the drug is the cause of the change. Is this a good assumption? Explain. (5 points)
The ethical issues about testing with animals is it resulting in suffering and they have the right to live without human interference.
What is Experiment?This is defined as a procedure which is carried in order to support or refute a hypothesis.
The blood pressure returning to normal when the drugs were used on the animals is a good assumption as most parts of the animal and human body work similarly.
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer:
a: Angle EBD
b: Can't really phrase this well, a semicircle that is to the left or right of diameter BD
c: Arc EDC
d: 80 degrees
e: 180
Step-by-step explanation:
An inscribed angle is an angle with all 3 points on the circumference of a circle.
A semicircle is half a circle
A major arc is an arc greater than 180 degrees
The inner angle is 80 degrees
Arc BCD is half a circle so its 360/2=180 degrees
1. Determine the
square units of the
figure below.
Answer:
10
Step-by-step explanation:
Need help I don’t understand what it means
Answer:
b) - 10
Step-by-step explanation:
Average rate of change:To find the average rate of change, we have divide the change in y of f(x) , by the change in x(input).
[tex]\sf \boxed{\text{\bf Average rate of change = $\dfrac{f(b)-f(a)}{b-a}$}}[/tex]
a = 4 ; f(a) = -17
b = 6 ; f(b) = -37
[tex]\sf Average \ rate \ of \ change = \dfrac{-37-[-17]}{6-4}[/tex]
[tex]\sf =\dfrac{-37+17}{2}\\\\=\dfrac{-20}{2}\\\\=-10[/tex]
Read Solar Basics and answer the question. When solar energy is converted to thermal energy, how is the thermal energy used? Check all that apply.
Thermal energy can be used in the heating systems either at home or in the industries
However, when solar energy is converted to thermal energy, the radiant energy from the sunlight is converted into heat which can then be used as space and hot water heating, power generation and industrial process heat
What is energy?Energy simply refers to the capacity of doing work. Some forms of energy are:
Solar energyNuclear energyElectrical energyThermal energyKinetic energyPotential energyMechanical energySo therefore, thermal energy can be used in the heating systems either at home or in the industries.
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Find the measure of D, and the perimeter and area of parallelogram ABCD.
A
16cm
30⁰
25cm
8cm
OLD = 150°, P = 82 centimeters, A = 200 square centimeters
O D = 60°, P = 41 centimeters, A = 200 square centimeters
O D = 160°, P = 82 centimeters, A = 400 square centimeters
OLD = 60°, P = 41 centimeters, A = 400 square centimeters
The measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A
How to determine the area and perimeter
For the parallelogram ABCD, it can be deduced that
Line AB and CD are parallel and AD is a transversal so the angles A and D is co-interior , Co-interior angles are said to be supplementary whose sum is 180 degrees
A + D = 180°
30° + D = 180°
D = 180° - 30°
D = 150°
Perimeter = 2 ( a + b)
a = 16cm, b = 25cm
Perimeter = 2 ( 16 + 25) = 2 ( 41)
Perimeter = 82 cm
Area = b × h
base = 25cm , h = 8cm
Area = 25 × 8
Area = 200 square centimeters
Thus, the measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A
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Find the slope between the two points given. Then, use the slope and one of the points to write the
equation of the line in Slope-Intercept form. State the slope and y-intercept.
Answer:
The slope is -2
y =-2x - 1
Step-by-step explanation:
The slope is -2 or -2/1.
The slope is the change in y over the change in x. The ordered pair is written in the form (x,y) The first number is the x coordinate and the second number is the y coordinate.
(1, -3) (0, -1) The -1 and the -3 are the y coordinates. We subtract these.
-1 -(-3) is the same as
- 1 + 3 which is 2.
(1, -3) (0, 1,) the 1 and the 0 are the x coordinates. We subtract these
0 - 1 is -1
The change in y is 2 and the change in x is -1, so our slope is -2/1 which is the same as -2.
To write the equation we need the slope and the y intercept. We have the slope now. We need to find the y-intercept. We will use the slope and one of the points to find the y-intercept. It does not matter which of the two points (1,-3) or (0,-1). I will use (0,-1)
y = mx + b The b is the y-intercept which is what we are looking for
-1 = -2(0) + b
-1 = 0 + b
-1 = b
y = -2x -1
The lifespans of meerkats in a particular zoo are normally distributed. The average
meerkat lives 10.4 years; the standard deviation is 1.9 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a meerkat
living less than 16.1 years.
The probability of a meerkat living smaller than 16.1 years exists at 99.85%.
How to estimate the probability of a meerkat living less than 16.1 years by using empirical rule?
The empirical rule notes that for a normal distribution most of the data lose within three standard deviations (σ) of the mean (µ). That exists 68% of the data lose within the first standard deviation (µ ± σ), 95% loses within the first two standard deviations (µ ± 2σ), and 99.7% declines within the first three standard deviations (µ ± 3σ).
68% declines within (10.4 ± 1.9). 68% declines within 8.5 years to 12.3 years.
95% declines within (10.4 ± 2[tex]*[/tex]1.9). 95% declines within 6.6 years to 14.2 years.
99.7% declines within (10.4 ± 3 [tex]*[/tex]1.9). 68% declines within 4.7 years to 16.1 years.
Probability of a meerkat living less than 16.1 years
= 100% - (100% - 99.7%)/2
= 100% - 0.15%
= 99.85%
Therefore, the probability of a meerkat living less than 16.1 years exists at 99.85%.
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half a number is 21 less than double the number find the number.
Answer:
14
Step-by-step explanation:
let the number be x
2x is larger than half of x by 21: 2x = 0.5+21
Solve:
2x = 0.5+21
1.5x = 21
x = 14
8 to the second power to the -4 power is equivalent to
Answer:
1.138789 is equivalent to 8 to the second power to the -4 power.
Hope this helps :)
Raymond’s gas tank is 1/3 full. After he buys 11 gallons of gas, it is 5/6 full. How many gallons can Raymond’s tank hold?
If HK and GJ are congruent, what is the measure of GOJ?
125 ° 80°
Answer:
80°
Step-by-step explanation:
Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.
How many ways can three different numbers be selected from 10 numbers to open a keypad lock?
A. 324 B. 260 C. 648 D. 720
There are 720 ways through which 3 numbers can be selected from 10 numbers to open a keypad lock.
Given that there are 10 numbers are 3 numbers are required to open a keypad lock.
Permutations are the number of ways in which objects can be selected without replacements to form subsets.
It is expressed as n[tex]P_{r}[/tex]=n!/(n-r)!.
Factorial of a number is the product of consecutive numbers less than the number.
Total numbers available=10
Numbers to be selected=3
Number of ways can be found by using permutations.
Number of ways =10[tex]P_{3}[/tex]
=10!/(10-3)!
=10!/7!
=10*9*8*7!/7!
=10*9*8
=720 ways.
Hence there are 720 ways through which 3 numbers can be selected from 10 numbers.
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What’s the volume of a rectangle solid with the given dimensions: length 20, width 23, height 26
The volume of the rectangular solid is: 11,960 units³.
How to Find the Volume of a Rectangular Solid?The formula to find the volume of a rectangular solid is: (length)(width)(height).
Given the dimensions as:
Length = 20 unitsWidth = 23 unitsHeight = 26 unitsVolume = (20)(23)(26)
Volume of the rectangular solid = 11,960 units³.
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please solve this
Solve by completing the square. 4x2+8x−3=0
Step-by-step explanation:
4x2+8x−3=0
For this equation: a=4, b=8, c=-3
4x2+8x+−3=0
Step 1: Use quadratic formula with a=4, b=8, c=-3.
x=
−b±√b2−4ac
2a
x= −(8)±√(8)2−4(4)(−3)
2(4)
x= −8±√112
8 x=−1+
1 2 √7 or x=−1+
−1 2 √7
Answer: x=−1+
1 2√7 or x=−1+
−1 2 √7
giving brainliest!!!!!!!!!!!!!!!!!!!!!
Answer:
The function has 4 roots.
Step-by-step explanation:
Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).
Answer:
4 roots, two real and two complex.
Step-by-step explanation:
The degree of the polynomial indicates the number of solutions
Hope this helps
One serving of vegetables is 1/2 cup. You want to make 2 1/2 servings of vegetables. How many cups of vegetables is that? Make a math drawing and write and annotate an equation for this problem.
Answer: 1 1/4 cups
Step-by-step explanation:
1 serving is half a cup so 2 servings would be 1 cup
and half of a serving would be 1/4 of a cup
for a drawing you could do something like this
The mean length of 3 childrens' index finger is 9.9cm.
The mean length of 3 adults' index finger is 13.2cm.
What is the mean length (rounded to 2 DP) of these 6 people's index finger?
The mean length of the 6 people's index finger is 11.55
How to determine the mean length?The given parameters are:
Mean length of 3 children = 9.9 cmMean length of 3 adults = 13.2 cmThe mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{3 * 9.9 + 3 * 13.2}{3 + 3}[/tex]
Evaluate
[tex]\bar x = \frac{69.3}{6}[/tex]
Divide
[tex]\bar x = 11.55[/tex]
Hence. the mean length of the 6 people's index finger is 11.55
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Simplify the expression completely if possible.
x^{3}-8x^{2}}{x^2-64}
The simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex]
Factor the numerator
[tex]\frac{x^{2}(x-8)}{x^2-64}[/tex]
Express the denominator as a difference of two squares
[tex]\frac{x^{2}(x-8)}{(x-8)(x + 8)}[/tex]
Cancel out the common factor
[tex]\frac{x^2}{x + 8}[/tex]
Hence, the simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]
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DOK= (0, 2) (0, 6)
The scale factor is:
00
O 1/3
D 3
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: scale \: \: factor = \cfrac{new \: \: measure}{original \: measure} [/tex]
[tex]\qquad \sf \dashrightarrow \: s = \dfrac{6}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: s = 3[/tex]
so, correct choice is D
Results from a survey conducted in a certain grocery store showed that 3 out of 5 people preferred crispy-flakes cereal to crunchy-flakes cereal. Based on this survey, if a total of 2,500 customers bought one of these two cereals, how many most likely purchased crunchy-flakes cereal?
The number of people who how many most likely purchased crunchy-flakes cereal is 1000 customers.
How many most likely purchased crunchy-flakes cereal?
Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).
The first step is to determine the ratio of people who preferred crunchy-flakes cereal:
Ratio of people who preferred crunchy-flakes cereal : 5 - 3 = 2
Now, multiply the ratio of those who prefer crunchy-flakes cereal by the total number of customers: (2/5) x 2500 = 1000 customers.
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PLEASE IF ANYONE CAN HELP
ME SOLVE THESE ILL GIVE YOU BRAINLEAEST THANK YOU
Answer:
You must graph the two equations and find the point of intersection (x,y)
Point of intersection: (-4, -3)
Step-by-step explanation:
I can not provide a picture, but if you know how to graph these linear functions on the graph properly, you will find a point where the linear functions intersect at (x,y).