The actual area of the reservoir in m² as required in the task content is; 0.5m².
Conversions using scale factors.It follows from the task content that the actual area of the reservoir is to be determined.
Hence, since it is given that the area of the reservoir on the map is 2cm² and the map has a scale of 1: 2500.
Hence, it follows from proportions that the area of the reservoir is; 2cm² × 2500 = 5000cm².
However, when expressed in m²; the actual area of the reservoir is; 5,000/10000 = 0.5m².
Ultimately, the area of the reservoir in m² is; 0.5m².
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Find the distance between the two points in simplest radical form.
(-6, 5) and (-3, 7)
Answer: [tex]\sqrt{13}[/tex]
Step-by-step explanation:
Using the distance formula,
[tex]\sqrt{(-6-(-3))^2 +(5-7)^2}=\sqrt{13}[/tex]
Some researchers developing a new Intelligence test are trying to decide how much time to allow to complete the test. The researchers have recorded the times(in minutes) for completion of 26 people who took the test for practice. The frequency distribution below summarizes the completion times recorded by theresearchers.Time for completion(in minutes)Frequency9 to 1112 to 14715 to 1785318 to 2021 to 233Based on the frequency distribution, using the midpoint of each data class, estimate the mean completion time of the people who took the test. For yourintermediate computations, use four or more decimal places, and round your answer to one decimal place.
To find the mean of grouped data, we need to use the next formula:
[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex]First, we need to find the midpoint of each interval:
The midpoint of interval = 1/2 (lower class limit + upper-class limit)
Then:
Time for competition (in minutes) ----- frequency ---- midpoint
9 -11 8 1/2(9+11) = 10
12 -14 7 1/2(12+14) = 13
15-17 5 1/2(15+17)= 16
18 - 20 3 1/2(18+20) = 19
21-23 3 1/2(21+23) = 22
Now, multiply the frequency of each interval by its midpoint:
10 * 8 = 80
13* 7 = 91
16 * 5 = 80
19 * 3 = 57
22 *3 = 66
Summ all the results 80 + 91 +80+57+66= 374
Then, sum all the frecuencys = 8 + 7 +5 +3 +3 = 26
Use the mean formula =
[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex][tex]Mean\text{ of a gruop data =}\frac{374}{26}=14.38461[/tex]The mean is given using five decimals.
Which value of X Satisfy 2(x +5.3) =4.2
SOLUTION
This question simply means we should find the value of x,
[tex]2\mleft(x+5.3\mright)=4.2[/tex]First we expand by using 2 to multiply the items in the bracket, we have
[tex]\begin{gathered} 2\times x+2\times5.3=4.2 \\ 2x+10.6=4.2 \\ 2x=4.2-10.6 \\ 2x=-6.4 \\ \text{dividing both sides by 2, we have } \\ \frac{2x}{2}=\frac{-6.4}{2} \\ x=-3.2 \end{gathered}[/tex]Hence the answer is -3.2
F(x) = 3 + 5x to the second power - x + 5, 2f(3-) - f(4) =
the given equation is
[tex]f(x)=3x^2-x+5[/tex]calculate f(-3) by putting x = -3
[tex]\begin{gathered} f(-3)=3(-3)^2-(-3)+5 \\ f(-3)=27+3+5=35 \\ \end{gathered}[/tex]now, f(4)
[tex]\begin{gathered} f(4)=3(4)^2-4+5 \\ f(4)=48+1=49 \end{gathered}[/tex]now the final calculation
[tex]\begin{gathered} 2f(-3)-f(4) \\ 2\times35-49 \\ 70-49 \end{gathered}[/tex]that is 70 -49 = 21
so the correct answer is 21
2f(-3) - f(4) = 21 .
The table shows information recorded about the location and speed of an airplane during an overseas flight.
a) Determine the altitude in miles.
b) Determine the ground speed in miles per hour.
c) Determine the headwind in miles per hour.
d) Determine the temperature in degrees Fahrenheit using the formula
F=9/5 C+32
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
Part a
The altitude = 9770 meters
To convert meter to miles, divide the length by 1609
Therefore,
9770 meters = 9770/1609
=6.07 miles
Part b
The ground speed = 707 km/hours
To convert km per hour to miles per hour, divide the speed value by 1.609
707 km/hour = 707/1.609
= 439.30 miles per hour
Part c
The head wind = 184 km/hour
To convert km per hour to miles per hour, divide the speed value by 1.609
184 km/hour = 184/1.609
= 114.35 miles per hour
Part d
The outside air temperature = -41 degree C
F = (9/5)C + 32
= (9/5)×-41+32
= -41.8 degrees Fahrenheit
Hence,
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
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True or false?
In centrally planned economies, the distribution of goods costs nothing to administer
The following statement "In centrally planned economies, the distribution of goods costs nothing to administer" is true.
A centrally planned economy, often known as a command economy, is an economic system in which a government agency makes economic choices affecting the production and distribution of products. Centrally planned economies vary from market economies in that these decisions are the outcome of hundreds of choices made by producers and consumers.
State-owned corporations provide goods and services in planned economies, however, independent firms may occasionally be brought into economic planning. Prices, salaries, and production schedules are often set by a centralized bureaucracy.
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Rewrite the following percents as decimals. i. 4% ii. 76% ii. 120% iv. 100% V. 32.5%
Answer
i) 4% = 0.04
ii) 76% = 0.76
iii) 120% = 1.20
iv) 100% = 1.00
v) 32.5% = 0.325
Explanation
The key to writing percents as decimals is to divide the percents by 100 to get the decimal equivalent.
i) 4% = (4/100) = 0.04
ii) 76% = (76/100) = 0.76
iii) 120% = (120/100) = 1.20
iv) 100% = (100/100) = 1.00
v) 32.5% = (32.5/100) = 0.325
Hope this Helps!!!
Veronika has 3 daughters. Today the eldest is 7 years older the the second who is 2 years older than the youngest. The sum of their ages 12 years from now will be 56. How old are they today?
We define the following variables:
• x = age (in years) of the eldest,
,• y = age (in years) of the second,
,• z = age (in years) of the youngest.
From the statement, we know that:
0. the eldest is 7 years older than the second → , x = 7 + y,,
,1. the second is 2 older than the youngest → ,y = 2 + z,,
,2. the sum of the ages 12 years from now will be 56 → x + y + z + 12 = 56 → ,x + y + z = 56 - 12 = 44,.
We have the following system of equations:
[tex]\begin{gathered} x=7+y, \\ y=2+z, \\ x+y+z=44. \end{gathered}[/tex]i) Replacing the second equation in the first one, we have:
[tex]x=7+y=7+(2+z)=9+z\text{.}[/tex]ii) Summing the ages of the three daughters, we have:
[tex]x+y+z=(9+z)+(2+z)+z=11+3z\text{.}[/tex]iii) Equalling the last equation with the third one, we have:
[tex]\begin{gathered} 11+3z=44, \\ 3z=44-11=33, \\ z=\frac{33}{3}=11. \end{gathered}[/tex]Replacing the value of z in the equation of x and y, we get:
[tex]\begin{gathered} x=9+11=20, \\ y=2+11=13. \end{gathered}[/tex]Answer
The ages of the daughters are 20, 13 and 11.
Mathematics. Sets Question. Answer Fast
Answer:
B
Step-by-step explanation:
the full domain is
(-∞,-7[ ∪ ]-7,+∞)
What can I do to decrease my bill by $25.00 per month?"
Employee: "Your bill is currently __________ per month, so we'll make a change to a less expensive option that will result in a 30% decrease in your monthly payment."
If he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
The percentage decrease in the monthly payment = 30%
The amount of decrease in the bill per month = $25
Consider the current bill amount as x
Then the equation will be
x × (30/100) = $25
Solve the equation
0.3x = $25
x = 25/0.3
x = $83.33
Hence, if he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33
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At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?
0.029
0.050
0.120
0.091
The standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
How to find the standard error for the sample mean?Let the value of mean be [tex]$P(\bar{X} < 0.95)$$[/tex]
Normal Distribution, [tex]$\mu=1, \sigma=0.1, n=12$[/tex]
[tex]$P(\bar{X} < 0.95)=$[/tex] Area to the left of 0.95
we convert this to standard normal using
[tex]$z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$[/tex]
[tex]$P(\bar{X}[/tex] < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)
P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex]
Therefore, the standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
The complete question is;
What is the probability that the sample mean will be below 0.95 centimeters?
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.
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Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.
The relationship between the discriminant of a quadratic polynomial and the number of real roots is that the discriminant let us know the number and type of the solutions.
Basically for a quadratic polynomial ax²+ bx + c = 0, the b² - 4ac is the discriminant.if the discriminant is greater than zero (b²- 4ac > 0), the graph intersects the abscissa twice which means it has two real solutions, whereas if the discriminant is equal to zero ( b² - 4ac = 0), then the graph intersects once the abscissa which means it has a single real solution and at last if less than zero (b² - 4ac < 0), then the graph doesn't at all intersect the abscissa which, it has imaginary solutions.
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Which of the following could be a cross-section of a triangular prism? circle o hexagon O octagon O rectangle
A triangular prism have two possible cross sections: A triangle and a rectangle
Pls help (give right answer)!!
seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf
What values complete each statement?Enter your answers in the boxes.(16−−√)2 = in simplest form.By the Power of Power rule, (16 1/2)2=16 2/2. So, 16 1/2 must equal in radical form.
Box 1 )
[tex](\sqrt[]{16})^2=16[/tex]Box 2 )
[tex]16^{\frac{1}{2}}=\sqrt[]{16}[/tex]Ubicar las siguientes fracciones en la recta numérica: 3/9
The most appropriate choice for Number line will be given by -
The number line has been shown in the figure attached.
What is a number line?
A visual representation of the real numbers can be shown on a diagrammatic representation of graduated straight lines. The visual representation of the real numbers is known as the number line. Number line can be used for addition or subtraction of two numbers.
Here,
The number line has been attached
[tex]\frac{3}{9}[/tex] lies between 0 and 1
So the space between 0 and 1 is divided into 9 equal parts as the denominator of the given fraction is 9
Now the third small line is the required value i.e [tex]\frac{3}{9}[/tex] as 3 is in the numerator of the given fraction
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3 9/13 to a improper fraction
Answer:
48/13
Step-by-step explanation:
To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction
3 * 13/13 = 39/13
Then add it to the rest of the fraction
39/13 + 9/13
= 48/13
Answer: 48/13
Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.
You are 37 years old have accumulated 150000 in your savings account. You intend to add a fixed amount each month for twenty years. For first 5 years you add 100 at the end of each month.
The recommended dosage of a drug for pediatric patients is 200 mg per kilogram of a patient's weight. If Janine weighs 102 lb, how much of the drug should she receive? Use the fact that 1 lb = 0.45 kg
Janine should receive about ____ milligrams of the drug.
(Round to the nearest milligram as needed.)
Answer: 9180 mg
Step-by-step explanation:
First we must convert the patients weight from lb to kg.
102lb x [tex]\frac{0.45kg}{1lb}[/tex] = 102 x 0.45 kg = 45.9 kg
Now to calculate the amount of the drug she should receive.
45.9 kg x [tex]\frac{200mg}{kg}[/tex] = 9180 mg
A triangle has angle measurements of 72, 34 and 74 . what kind of triangle is it?
We can give two classifications to that triangle
It's a scalene triangle, because all the sides are different (because all the angles are different). Also, it's a acute triangle because all the angles are less than 90°
The mode of data 33, 22, 10, 0, 33, 40, 33 is _____
What is the sign of 37+(-37)? Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero
Simplify the expression. Write your answer as a power.(-8.3)8 (-8.3)4(-8.3)? (-8.3)3The simplified expression is
This will be simplified with this law of indices
[tex]\frac{a^e}{a^y}=a^{e-y}[/tex][tex]\begin{gathered} \text{Therefore the initial question becomes:} \\ ((-8.3)^{8-7})\text{ }\cdot\text{ (}(-8.3)^{4-3}) \end{gathered}[/tex][tex]\begin{gathered} (-8.3)^1\cdot(-8.3)^1 \\ (-8.3)^{1+1} \\ (-8.3)^2 \\ \end{gathered}[/tex]Going further, we can simplify to:
[tex]\begin{gathered} (-8.3)\times(-8.3) \\ =68.89 \end{gathered}[/tex]For the following, find f(2.1) and f(4).
Answer:
A
Step-by-step explanation:
Comment
The tricky part is f(4)
Log part
That is defined by log_2 which means that the base used for the log is 2.
We don't have log_2 on our calculators so you have to create it.
Substitute 4 for x
log_2 (4) = log_10(4)/ log_10 (2) Which your calculator can handle
log_2 (4) = Log(4)/ log(2) = 2
f(x) = 1/2 x^2
x = 2.1
Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2
1/2 2.1^2 = 1/2 4.41 = 2.205
Answer
A
Answer:
(a) f(2.1) = 2.205 and f(4) = 2
Step-by-step explanation:
You want to evaluate a piecewise-defined function to find f(2.1) and f(4).
DomainThe first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.
for f(2.1), you want to use the definition for the domain 2 < x < 4for f(4), you want to use the definition for the domain 4 ≤ x < 8Function evaluationOnce you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.
f(2.1) = 1/2(2.1)² = 1/2(4.41) = 2.205f(4) = log₂(4) = log₂(2²) = 2The desired function values are f(2.1) = 2.205 and f(4) = 2.
In one classroom homework is worth 25% of the final grade, each of the three projects is worth 10%, and the final exam is worth 45%. If student has an 87 on a homework average and a 94 on the first project, what is the students grade at this point if that same student from part a gets a 71 on the second project and a 78 on the third project what is the lowest grade the student can get on the final exam to get an 80 over on the course
Answer
• a) 30.9
,• b) 76
Explanation
Given
• Homework: 25%
,• Project: 10% (each)
,• Final exam: 45%
A student has:
Part A
• Homework: 86
,• First project: 94
Part B
• Second project: 71
,• Third project: 78
,• Total grade: 80
Procedure
• a)
To know the student's grade at the point where he has an 86 homework average and 94 on the first project. We have to multiply the ponderation of each category times the grade to find the final grade (TG), meaning:
[tex]TG=86(0.25)+94(0.10)[/tex]Simplifying:
[tex]TG=21.5+9.4[/tex][tex]TG=30.9[/tex]• b)
Following the same procedure, now we have to multiply the ponderations of the new grades, as follows:
[tex]TG=FE+30.9+71\cdot(0.1)+78\cdot(0.1)[/tex][tex]TG=FE+30.9+7.1+7.8[/tex][tex]TG=FE+45.8[/tex]Next, as we are asked to find the calculations of the grade of the exam to get a final grade of 80, we have to consider the latter and the ponderation for the exam:
[tex]80=x\cdot0.45+45.8[/tex]where x is the grade of the exam.
Solving for x:
[tex]x=\frac{80-45.8}{0.45}[/tex][tex]x=76[/tex]
> Question 1
In 2 to the 4th power = 16 number 2 is called what?
and number 4 is called what?
The most appropriate choice for exponents will be given by-
In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.
What is exponent?
Exponent of a number is the number of times a number is multiplied by itself.
For example: [tex]3^5 = 3 \times 3 \times 3 \times 3 \times 3[/tex], 3 is multiplied by itself 5 times
If [tex]a^m = a \times a \times a \times a .....[/tex](m times)
a is called the base and m is called the power or index,
Here,
In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.
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In January 1, Juan weighed 247 pounds and decided to diet and exercise. Kn June 30, Juan weighed 221 pounds. Determine the percent decrease in Juans weight from January 1 to June 30.
Given the initial value, w1, and the final value, w2, the percent decrease can be calculated as:
[tex]P=\frac{w_1-w_2}{w_1}\times100\%[/tex]The initial value is 247 and the final one is 221, so:
[tex]\begin{gathered} P=\frac{247-221}{247}\times100\% \\ P=\frac{26}{247}\times100\% \\ P=0.10526\ldots\times100\% \\ P\approx10.53\% \end{gathered}[/tex]So, the percent decrease is approximately 10.53%.
I just need to quickly know if my answers are correct thank you!
1) All of these questions are about evaluating those functions for each input.
9) So, let's check them out evaluating each one.
[tex]\begin{gathered} f(4)\Rightarrow f(x)=(\frac{1}{2}x)+13 \\ f(4)=(\frac{1}{2}\cdot4)+13 \\ f(4)=2+13\Rightarrow f(4)=15 \\ D \end{gathered}[/tex]10)
[tex]\begin{gathered} f(x)=\frac{3}{5}x-10 \\ f(5)=\frac{3}{5}(5)-10 \\ f(5)=3-10 \\ f(5)=-7 \end{gathered}[/tex]11)
[tex]\begin{gathered} f(x)=x^2+7 \\ f(-1)=(-1)^2+7\Rightarrow f(-1)=1+7\Rightarrow f(-1)=8 \end{gathered}[/tex]12)
[tex]\begin{gathered} f(x)=3x^3-12x^2 \\ f(2)=3(2)^3-12(2)^2 \\ f(2)=24-48 \\ f(2)=-24 \end{gathered}[/tex]Mr. Anderson grows fruit which hesells at a farmers' market.- His truck has a total payloadcapacity (total weight ofpassengers and cargo) of1,200 pounds.- Mr. Anderson weighs 190 pounds.- The table he sells his fruit onweighs 10 pounds.- He transports his fruit in crates.Each crate weighs 3 pounds.- A crate can hold up to 22 poundsof fruit.Write and solve an equation to findC, the greatest number of fullcrates of fruit that Mr. Anderson cancarry in his truck along with himself and the table
We will have that the expression that represents the problem is:
[tex]1200>(3+22)C+190\Rightarrow1200>25C+190[/tex][tex]\Rightarrow1010>25C\Rightarrow C<40.4[/tex]So, at most he will be able to carry 40 crates with him.
A stack of one dozen cookies of diameter 2.5 in. exactly fits in a cylindrical container of volume 29.452 in3. Which is the thickness of each cooke?
The volume of a cylinder is given by:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=29.452in^3_{} \\ r=\frac{d}{2}=\frac{2.5}{2}=1.25 \end{gathered}[/tex]solve for h:
[tex]\begin{gathered} 29.452=\pi\cdot(1.25)^2\cdot h \\ h=\frac{29.452}{\pi(1.25)^2} \\ h=5.999912171 \end{gathered}[/tex]divide the height by 12:
[tex]\frac{h}{12}=0.499992681in[/tex]The thickness of each cookie is 0.499992681in or approximately 0.5in