Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
I NEED HELP WITH THIS PLEASE HELP ME
Answer:
156 minutes
Step-by-step explanation:
So we need to create an equation to represent how Frank's phone company bills him
I will denote "y" as the total for his billI will denote "x" as the number of minutes Frank usesSo the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"
They then charge $0.06 for every minute he talks, this will be our "slope"
Combining everything into an equation, we have: y = 0.06x + 8
Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value
y = 0.06x + 8 → y - 8 = 0.06x → [tex]x=\frac{y-8}{0.06}[/tex] Then plugging in our y value we get [tex]x=\frac{17.36-8}{0.06}=\frac{9.36}{0.06}= 156[/tex]Frank used up a total of 156 minutes
Which of the functions below could have created this graph?
Answer:
i don't know if this is right or not i did to much work to put it all down but i pretty sure it's C.
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
(Bonus) A rectangular box has its edges changing length as time passes. At a par-ticular instant, the sides have lengthsa= 150 feet,b= 80 feet, andc= 50 feet.At that instant,ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec. Determine if the volume of the box is increasing, decreasing,or not changing at all, at that instant.
Answer:
the volume of the box is increasing
dV = +310,000 ft^3/s
Step-by-step explanation:
Volume of a rectangular box with side a,b and c can be expressed as;
V = abc
The change in volume dV can be expressed as;
dV = d(abc)/da + d(abc)/db + d(abc)/dc
dV = bc.da + ac.db + ab.dc ......1
Given:
a= 150 feet,
b= 80 feet, and
c= 50 feet
ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec
da = +100 feet/s
db = -20 feet/s
dc = +5 feet/s
Substituting the values into the equation 1;
dV = (80×50×+100) + (150×50×-20) + (150×80×+5)
dV = +400000 - 150000 + 60000 ft^3/s
dV = +310,000 ft^3/s
Since dV is positive, the volume of the box is increasing at that instant.
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
Simplify this equation x2-5x-36
Answer:
[tex]=\left(x+4\right)\left(x-9\right)[/tex]
Step-by-step explanation:
[tex]x^2-5x-36\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+4x\right)+\left(-9x-36\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9x-36\mathrm{:\quad }-9\left(x+4\right)\\=x\left(x+4\right)-9\left(x+4\right)\\\mathrm{Factor\:out\:common\:term\:}x+4\\=\left(x+4\right)\left(x-9\right)[/tex]
Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? A: x^2 + 8x – 308 = 0 B: x^2 – 8x + 308 = 0 C: x^2 + 8x + 308 = 0 D: x^2 − 8x − 308 = 0
Answer:
A
Step-by-step explanation:
The smaller negative integer is x.
The larger one is x+8, since they are 8 units apart.
The equation would be:
x*(x+8)=308
Let's simplify it by distributing.
x^2+8x=308
Subtract 308 from both sides.
x^2+8x-308=0
Therefore, the answer would be A.
Please answer this question for me thank you !! 20 Points !! Will give brainliest !!
Answer:
b
Step-by-step explanation:
In a parralel graph, the slopes would always be the same. The intercept in the answer is 2, showing that the coordinate points are (0,2)
Hope this helps!:)
Answer:
B) y = 2x + 2
Step-by-step explanation:
Firstly, you have to know that parallel lines have congruent slopes. That means that the slope of this line will be 2.
Next, make a point slope form of the equation:
y - y1 = m(x - x1)
y - 2 = 2(x - 0)
y - 2 = 2x - 0
Now, we can make it into slope intercept form.
y - 2 = 2x
y = 2x + 2
Hope this helps :)
Please answer this question !! 20 points and brainliest !!
Answer:
yes, they are parallel; the general form equation differs only in the constant.
Step-by-step explanation:
Subtract y from the first equation and multiply by 2.
y -y = 1/2x -y +3
0 = x -2y +6
x -2y +6 = 0 . . . . . put in general form
Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.
This means the lines are parallel.
A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
What is 80,000,000,000,000 in standard form (80 billion)
Answer:
8x10^13
Step-by-step explanation:
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
For a super soaker water gun, a pump handle is moved back and forth to build up pressure in the water reservoir. The water is released by pulling a trigger and shooting the water a significant distance. Assuming that you can create an absolute pressure of 8 atm in the reservoir:
a) What is the velocity at which the water leaves the gun?
b) If the water exits the gun through a hole with a radius of 1-mm, what is the volume rate of flow in m3/s?
c) If the water gun is fired horizontally and held 1.2 meters above the ground, where does the water hit the ground? Pressure 8 cm water
Answer:
a) The velocity at which the water leaves the gun = 37.66 m/s
b) The volume rate of flow = (1.183 × 10⁻⁴) m³/s
c) The water hits the ground 18.64 m from the point where the water gun was shot.
Step-by-step explanation:
a) Using Bernoulli's equation, an equation that is based on the conservation of energy.
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
The two levels we are considering is just inside the water reservoir and just outside it.
ρgh is an extension of potential energy and since the two levels are at the same height,
ρgh₁ = ρgh₂
Bernoulli's equation becomes
P₁ + ½ρv₁² = P₂ + ½ρv₂²
P₁ = Pressure inside the water reservoir = 8 atm = 8 × 101325 = 810,600 Pa
ρ = density of water = 1000 kg/m³
v₁ = velocity iof f water in the reservoir = 0 m/s
P₂ = Pressure outside the water reservoir = atmospheric pressure = 1 atm = 1 × 101325 = 101,325 Pa
v₂ = velocity outside the reservoir = ?
810,600 + 0 = 101,325 + 0.5×1000×v₂²
500v₂² = 810,600 - 101,325 = 709,275
v₂² = (709,275/500) = 1,418.55
v₂ = √(1418.55) = 37.66 m/s
b) Volumetric flowrate is given as
Q = Av
A = Cross sectional Area of the channel of flow = πr² = π×(0.001)² = 0.0000031416 m²
v = velocity = 37.66 m/s
Q = 0.0000031416 × 37.66 = 0.0001183123 m³/s = (1.183 × 10⁻⁴) m³/s
c) If the height of gun above the ground is 1.2 m. Where does the water hit the ground?
The range of trajectory motion is given as
R = vT
v = horizontal component of the velocity = 37.66 m/s
T = time of flight = ?
But time of flight is given as
T = √(2H/g) (Since the initial vertical component of the velocity = 0 m/s
H = 1.2 m
g = acceleration due to gravity = 9.8 m/s²
T = √(2×1.2/9.8) = 0.495 s
Range = vT = 37.66 × 0.495 = 18.64 m
Hope this Helps!!!
Each limit represents the derivative of some function f at some number a. State such an f and a in each case.
lim √9 + h - 3 / h
h-->0
Answer:
a = 0f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]limit of the function is 1/6Step-by-step explanation:
The general form representing limit of a function is expressed as shown below;
[tex]\lim_{h \to a} f(h)[/tex] where a is the value that h will take and use in the function f(h). It can be expressed in words as limit of function f as h tends to a. Comparing the genaral form of the limit to the limit given in question [tex]\lim_{h \to 0} \frac{\sqrt{9+h} - 3}{h}[/tex], it can be seen that a = 0 and f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]
Taking the limit of the function
[tex]\lim_{h \to 0} \frac{\sqrt{9+h} -3}{h}\\= \frac{\sqrt{9+0}-3 }{0}\\= \frac{0}{0}(indeterminate)[/tex]
Applying l'hopital rule
[tex]\lim_{h \to 0} \frac{\frac{d}{dh} (\sqrt{9+h} - 3)} {\frac{d}{dh} (h)}\\= \lim_{h \to 0} \frac{1}{2} (9+h)^{-1/2} /1\\=\frac{1}{2} (9+0)^{-1/2}\\= \frac{1}{2} * \frac{1}{\sqrt{9} } \\= 1/2 * 1/3\\= 1/6[/tex]
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
A cognitive psychologist would like to evaluate the claim that the omega-3 fatty acids can help improve memory in normal adult humans. One group of participants is given a large dose of fish extract containing the Omega-3 (500 mg), and a second group is given a placebo containing no Omega-3 (0 mg). The researcher asks each participant to read the front page of a local newspaper thoroughly every morning and to take their prescribed dosage (of either Omega-3 or placebo) immediately afterwards. The researcher gives each participant a memory test at the end of two weeks and records how many news items each participant remembers from the past three weeks of news. Answer the following:
A) What names would you give the independent and dependent variables;
B) Is the dependent variable discrete or continuous?
C) What scale of measurement (nominal, ordinal, interval or ratio; and continuous or discrete) is used to measure the independent variable?
D) What research method is being used (experimental or observational)? Explain why you conclude that the research method is one or the other.
Answer:
(a)
Independent Variable- Dosage of Omega-3 Fatty AcidsDependent Variable - Number of news item remembered(b)Discrete
(c)Ratio Scale and Discrete Variable
(d) Experimental Method
Step-by-step explanation:
The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.
(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).
The memory test involves measuring the number of items each participant remembers from the past three weeks of news.
Therefore:
Independent Variable- Dosage of Omega-3Dependent Variable - Number of news item remembered(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.
(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.
Since the dosage is given in multiples of 50mg, it is a discrete variable.
(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
A research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years. When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years
a) What is the population of interest in this situation?
b) How many samples were described?
c) Is the average age of 37 years a parameter or a statistic?
d) Tell whether this information represents a quantitative or qualitative variable? - age of the visitor - whether the visitor has a season pass
e) What possible explanation is there for the large difference in age between the two samples?
Answer:
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic.
(d) The above information represents a quantitative variable.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
Step-by-step explanation:
We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.
When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. [tex]\bar X_1[/tex] = 37 years.
(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is AnswerWhich of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph