Answer:
The postage per ounce would be of $2.02.
Step-by-step explanation:
Exponential model:
The postage, in t years after 1963, follows the following format:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial value and r is the growth rate, as a decimal.
In 1963, postage was 5 cents per ounce.
This means that [tex]P(0) = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 5(1+r)^t[/tex]
In 1981, postage was 18 cents per ounce.
This means that [tex]P(1981 - 1963) = P(18) = 18[/tex]. We use this to find r. So
[tex]P(t) = 5(1+r)^t[/tex]
[tex]18 = 5(1+r)^{18}[/tex]
[tex](1+r)^{18} = \frac{18}{5}[/tex]
[tex]\sqrt[18]{(1+r)^{18}} = \sqrt[18]{3.6}[/tex]
[tex]1 + r = (3.6)^{\frac{1}{18}}[/tex]
[tex]1 + r = 1.0738[/tex]
So
[tex]P(t) = 5(1.0738)^t[/tex]
If the trend had continued through to 2015, what would the postage per ounce be?
2015 - 1963 = 52, so this is P(52).
[tex]P(52) = 5(1.0738)^{52} = 202[/tex]
202 cents, so $2.02.
Graph the line that represents this equation:
y = -5.1 +2
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
PLEASE HELP
A spinner is divided into eight equal sections numbered 1-8. find the probability of not spinning a 5. write your answer as a fraction, percent and decimal.
Answer:
7/8, 87.5%, 0.875
Step-by-step explanation:
There is only 1 5 on the spinner. And there are 8 equal sections.
The probability of spinning a 5 is 1/8.
So, the probability of not spinning a 5 is 7/8
To find the Percent and Decimal form, divide 7 by 8.
You get 0.875-the decimal form
Move the decimal point 2 places to the right:
87.5
Add the percent symbol, and you're done!
I hope this helps!
Tell me if you need more explaining :)
Precision manufacturing: A process manufactures ball bearings with diameters that are normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter. Round the answers to at least four decimal places. (a) Find the 60th percentile of the diameters. (b) Find the 67th percentile of the diameters. (c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be
Answer:
a) The 60th percentile of the diameters is of 25.0177 millimeters.
b) The 67th percentile of the diameters is of 25.0308 millimeters.
c) The diameter of the hole should be of 24.8562 millimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter.
This means that [tex]\mu = 25, \sigma = 0.07[/tex]
(a) Find the 60th percentile of the diameters.
This is X when Z has a p-value of 0.6, so X when Z = 0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.253 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = 0.253*0.07[/tex]
[tex]X = 25.0177[/tex]
The 60th percentile of the diameters is of 25.0177 millimeters.
(b) Find the 67th percentile of the diameters.
This is X when Z has a p-value of 0.67, so X when Z = 0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.44 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = 0.44*0.07[/tex]
[tex]X = 25.0308[/tex]
The 67th percentile of the diameters is of 25.0308 millimeters.
(c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be.
This is the 2nd percentile, which is X when Z has a p-value of 0.08, so X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = -2.054*0.07[/tex]
[tex]X = 24.8562[/tex]
The diameter of the hole should be of 24.8562 millimeters.
Probabilityyyyyyyyyyyyyyy
Answer:
Reduce if needed, asked or necessary
Step-by-step explanation:
1. 4/10
2. 2/6
3. 4/10
4. more likely
Answer:
Since Probability Is Usually Written In Fraction Form OR Ratios
(Although It Really Doesn't Matter):
1. 4/10 (2/5)
2. 2/6 (1/3)
3. 6/10 (3/5)
(All Fraction Form)
Last Question:
I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.
Step-by-step explanation:
This is the basic fraction form : ____ / ____
Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!
Without third-party reimbursement, inclusive of private insurance carriers, healthcare finance and delivery systems that it supports would take on a very different complexion one that would not be sustainable. What does the author mean when she makes this statement?
Answer:
sorry dko alm hahahahahahahahajshaja
3p + 4q = 22
10p + 12 q = 68
What is p and what is q
(Similtaneous equations)
Answer:
q=4
p=2
Step-by-step explanation:
3p+2q=14
10p+6q=44
10(3p+2q=14)
3(10p+6q=44)
30p+20q=140-
30p+18q=132
2q=8
2q/2=8/2
q=4
3p+2*4=14
3p+8=14
3p=14-8
3p/3=6/3
p=2
hope this helps
Answer:
[tex]p=2\\q=4[/tex]
Step-by-step explanation:
One is given the following system of equations,
[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]
The fastest method to solve a system of equations is the method of elimination. This process is manipulating one of the equations, by multiplying or diving it by a value, such that one of the coefficients variables in the equation is the additive inverse of the like term in the other equation. That way, when one adds the equations, one of the variables cancels out. Then one can solve for the other term. Finally, one can back sovle by substituting the value of the solved variable into one of the equations and simplifying to find the value of the other variable.
[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]
Manipulate the first equation so that the variable (q) cancels
[tex](3p + 4q = 22) *(-3)\\\\10p + 12q = 68[/tex]
[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]
Add the equations,
[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]
[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]
Simplify,
[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]
[tex]p=2[/tex]
Backsovle for the variable (p). Substitute the values of (p) into one of the original equations. Then simplify and use inverse operations to solve for the variable (q).
[tex]3p+4q=22[/tex]
Substitute,
[tex]3(2)+4q=22[/tex]
Simplify,
[tex]3(2)+4q=22[/tex]
[tex]6+4q=22[/tex]
Inverse operations,
[tex]6+4q=22[/tex]
[tex]4q=16\\q=4[/tex]
Which statements apply to the expression
? Check all that apply.
3
The base is 5
The base is 3.
The exponent is 3.
3 3 3
The expanded form is 555.
3.3.3
The expanded form is
5
Answer:
A, C, D, F
Step-by-step explanation:
Given the expression : (3/5)³
Recall :
a^b where, a = base ; b = exponent
In ; (3/5)^3
Base = 3/5 ; exponent = 3
Similarly ;
a^b = a in b places
(3/5)^3 = (3/5) * (3/5) * (3/5)
(3/5) * (3/5) * (3/5) = (3*3*3) / (5*5*5) = 27/125
Hence, A, C, D and F are all correct
Two different types of injection-molding machines are used to form plastic parts. Two random samples, each of size 300, are selected. 15 defective parts are found in the sample from machine 1 and 8 defective parts are found in the sample from machine 2. Is it reasonable to assume that both machines have the same defective rate
Answer:
No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine
Hope This Helps!!!
What is the range of the function shown in the graph?
у
A
8
6
2
2
X
8
- 6
2
4
6
8
2
4
6
ce
I
OA. -5 < y < 0
OB -00
O c. - < y < -5
-
5
Answer:
-∞ <y<5
Step-by-step explanation:
The range of the graph is the values that y can take. The graph can go from negative infinity to 5
-∞ <y<5
√x²+2√3 +3 =0
[tex] \sqrt{x^{2} + 2 \sqrt{3} + 3} = 0[/tex]
solve x
Square both sides:
x^2+2sqrt3+3=0
x^2=-2sqrt(3)-3
x=sqrt(2sqrt(3)+3)i
or
x=-sqrt(2sqrt(3)+3)i
Show all the steps to solve the following
942.6 - 19.734
Answer:
922.868
Step-by-step explanation:
1. Thousandth place of 942.6002. Subtracting[tex]942.600-19.732=922.868[/tex]
Which method correctly solves the equation using the distributive property?
Negative 0.2 (x minus 4) = negative 1.7
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 4 = negative 1.7. Negative 0.2 x = 2.3. x = negative 11.5.
Negative 0.2 (x minus 4) = negative 1.7. x minus 4 = 0.34. x = 4.34.
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x + 0.8 = negative 1.7. Negative 0.2 x = negative 2.5. x = 12.5.
Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 0.8 = negative 1.7. Negative 0.2 x = negative 0.9. x = 4.5.
9514 1404 393
Answer:
(c) x = 12.5
Step-by-step explanation:
-0.2(x -4) = -1.7
-0.2x +0.8 = -1.7 . . . eliminate parentheses using the distributive property
-0.2x = -2.5 . . . . . . subtract 0.8
x = 12.5 . . . . . . . . divide by -0.2
A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it takes to go 6 km upstream. What is the speed of the river?
Answer:
Speed of the river = [tex]\frac{4}{3}[/tex] km per hour
Step-by-step explanation:
Speed of the boat in still water = 4 km per hour
Let the speed of the river = v km per hour
Speed of the boat upstream = (4 - v) km per hour
Time taken to cover 6 km = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]
= [tex]\frac{6}{4-v}[/tex] hours
Speed of the boat downstream = (4 + v) km per hour
Time taken to cover 12 km = [tex]\frac{12}{4+v}[/tex] hours
Since, time taken by the boat in both the cases is same,
[tex]\frac{6}{4-v}= \frac{12}{4+v}[/tex]
6(4 + v) = 12(4 - v)
24 + 6v = 48 - 12v
12v + 6v = 48 - 24
18v = 24
v = [tex]\frac{24}{18}[/tex]
v = [tex]\frac{4}{3}[/tex] km per hour
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?
In the figure below. JLM is similar to JKN if JM=14 inches what is the length of JN
Answer:
Hello good evening friend
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 23 feet, and the length of the other base is 50 feet. The height is 20 feet. What is the area of this section of the deck?
The area for the section of the deck is ____ ft
Answer:
Area of a trapezoid= (big base+small base)/2 x height
A=(67+54)/2 x 18
A=60.5 x 18
A=1089
Wrap your foot by plastic cover. B. Directions: Read the sentences carefully. Write TRUE if the statement is True and FALSE if not. 16. Rain and dull clouds, windy blue skies, cold snow, and sticky heat are very different conditions, yet they are all weather. 17. A weather instrument is any type of measurement device that gives information about the weather. 18. Weather is the mix of events that happen each day in our atmosphere. 19. Weather is different in different parts of the world and changes over minutes, hours, days and weeks. 20. The four letters EW, SW, NE, SN represent the four directions: East West, South West, North East, and South North.
Answer:
16. false
17. True
18. True
19. True
20. false
Step-by-step explanation:
16. all terms are expressions of weather - except for cold snow. "snowfall" would be the weather condition. "snow" itself is the accumulated mass of snowflakes on the ground.
17. that is simply true. there is nothing really to explain.
18. the same as 17. that is the definition of weather.
19. yes, that is part of the explanation of the difference between weather and climate.
20. South North is NOT a direction. it kind of contradicts itself. and what is between South and North ? East and West. so, even from that perspective it is not clear.
overall, what kind of math question is that ? that is more for geography, Earth science, or meteorology or something like this.
solve it
[tex]4 \frac{1}{3} \times (3 \frac{1}{3} \times 3 \frac{1}{2} ) \ {}^{7} \div 9 \frac{3}{4} [/tex]
solve it fast
Answer:
[tex]\frac{257357187500}{19683}[/tex]
Step-by-step explanation:
We can convert these mixed fractions to ordinary fractions.
[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]
[tex]3(1/3)=\frac{10}{3}[/tex]
[tex]3(1/2)=\frac{7}{2}[/tex]
[tex]9(3/4)=\frac{39}{4}[/tex]
Then we have:
[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]
[tex]\frac{257357187500}{19683}[/tex]
I hope it helps you!
One of the lengths of a leg of a right angled triangle is 15 feet. The length of the hypotenuse is 17 feet. Find the length of the other leg.
4 feet
6 feet
8 feet
10 feet
Answer:
8ft
Step-by-step explanation:
We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,
[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]
Lara says that she can use this picture to show that two pairs of congruent angles and
one pair of corresponding congruent sides is enough information to prove that two
triangles are congruent. Is Lara correct?
Answer:
Bottom left
Step-by-step explanation:
Mark brainliest please
Yes, Lara is correct.
Congruent triangleTwo triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measureTriangles are congruent when they have exactly the same three sides and exactly the same three angles.How to solve this problem?The steps are as follow:
Since there is a series of rigid motions that will match the triangles up exactly.Also, Lara is correct only if the corresponding congruent side is in between the two anglesThis would be "ASA" triangle congruceny which means Angle Side Angle congrucenySo Lara is correct
Learn more about Congruent triangle here:
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For which equation is (4, 3) a solution?
y=x+3
y=3 x-4
y= 2 x-5
y= 2 x-1
please say how you got your answer
Answer:
y = 2x - 5
Step-by-step explanation:
We can use trial and error to solve this.
4 = x and 3 = y
y = x + 3: 4 + 3 = 7 ≠ 3 (not what we want)
y = 3x + 4: (3 x 4) - 4 = 8 ≠ 3 (not what we want)
y = 2x - 5: (2 x 4) - 5 = 3 (what we want)
y = 2x - 1: (2 x 4) - 1 = 7 ≠ 3 (not what we want)
The answer is y = 2x - 5
Mark looked at the statistics for his favorite baseball player, Jose Bautista. Mark looked at seasons
when Bautista played 100 or more games and found that Bautista's probability of hitting a home run
in a game is 0.173
If Mark uses the normal approximation of the binomial distribution, what will be the variance of
the number of home runs Bautista is projected to hit in 100 games? Answer choices are rounded
to the tenths place.
O 0.8
O 14.3
0 3.8
O 17.3
⭕ 17.3
#CARRYONLEARNING
[tex]{hope it helps}}[/tex]
For the problem I tried dividing but my answers were not correct. How can I solve this problem then? Can someone help me out here please?
Answer:
nsnndjdjejke
dl,dmfkfkkio4krm
Step-by-step explanation:
irikrkrkfmfmmfmfmmfmg
The lengths of nails produced in a factory are normally distributed with a mean of 6.13 centimeters and a standard deviation of 0.06 centimeters. Find the two lengths that separate the top 7% and the bottom 7%. These lengths could serve as limits used to identify which nails should be rejected.
Answer:
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 6.13 centimeters and a standard deviation of 0.06 centimeters.
This means that [tex]\mu = 6.13, \sigma = 0.06[/tex]
Value that separated the top 7%:
The 100 - 7 = 93rd percentile, which is X when Z has a p-value of 0.93, so X when Z = 1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = 1.475*0.06[/tex]
[tex]X = 6.2185[/tex]
Value that separates the bottom 7%:
The 7th percentile, which is X when Z has a p-value of 0.07, so X when Z = -1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.475 = \frac{X - 6.13}{0.06}[/tex]
[tex]X - 6.13 = -1.475*0.06[/tex]
[tex]X = 6.0415[/tex]
A value of 6.0415 centimeters separates the bottom 7%, while a value of 6.2185 centimeters separates the top 7%.
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
help me pleaseeeeeeeeeeeeeeeeee………….
Answer:
d
Step-by-step explanation:
because u did the math for you
Translate this sentence into an equation.
The difference of Malik's height and 11 is 44
Use the variable m to represent Malik's height.
Answer:
m - 11 = 44
Step-by-step explanation:
Breaking the phrase down...
"The difference of Malik's height and 11" - this indicates subtraction.
m - 11
"is 44" - this indicates that the value of the diffrence would be '44'.
'= 44'
The equation should be:
m - 11 = 44
Hope this helps.
A small college has 1200 students and 80 professors. The college is planning to increase enrollment to 1450 students next year. How many new professors should be hired to keep the ratio of students to professors the same
The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
Given,
A small college has 1200 students and 80 professors.
The college is planning to increase enrollment to 1450 students next year.
We need to find how many new professors should be hired to keep the
ratio of students to professors the same.
What is meant by proportion?If the two ratios are the same then we called it that they are in proportion.
Example:
4/6 = 10/15
2/3 = 2/3
Find the ratio between the students and professors before the increase in enrollment.
= Number of students / Number of professors
= 1200 / 80
Dividing by 8
= 150 / 10
= 15 / 1
This means one professor for 15 students.
Find the number of students after the increase in enrollment.
= 1450
Find the number of new students enrolled.
= 1450 - 1200
= 250
Since the ratio between the students and professor is 15 students for one professor.
For 250 new students, the number of new professors we need is:
= 250 ÷ 15
= 16.66
This means we need around 16.66 new professors.
Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
Learn more about finding the number of students in a college with students and professors relation is given here:
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Find the area of the region that is enclosed between the curves y = x2 and
y = x + 6.
Integrate:
[tex]\displaystyle\int_{-2}^3((x+6)-x^2)\,\mathrm dx = \int_{-2}^3(6+x-x^2)\,\mathrm dx[/tex]
[tex]=\left(6x+\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{-2}^3[/tex]
[tex]=\left(18+\dfrac92-9\right) - \left(-12+2+\dfrac83\right)[/tex]
[tex]=\boxed{\dfrac{125}6}[/tex]