Answer:
[tex](x,y) = (-3,2)[/tex] is a solution
Step-by-step explanation:
Given
[tex]y \le -4x + 3[/tex]
[tex]x + 8y \ge 7[/tex]
Required
Determine if [tex](x,y) = (-3,2)[/tex] is a solution
[tex]y \le -4x + 3[/tex] becomes
[tex]2 \le -4 * -3 + 3[/tex]
[tex]2 \le 15[/tex] --- this is true
[tex]x + 8y \ge 7[/tex]
[tex]-3+ 8 * 2 \ge 7[/tex]
[tex]13 \ge 7[/tex] --- this is also true
Hence,
[tex](x,y) = (-3,2)[/tex] is a solution
The table gives estimates of the world population, in millions, from 1750 to 2000. (Round your answers to the nearest million.)
Year Population
1750 790
1800 980
1850 1260
1900 1650
1950 2560
2000 6080
(a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950 1900 1950 million people million people
(b) Use the exponential model and the population figures for 1800 and 1850 to predict the world population in 1950 million people
(c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000 million people
Answer:
A.) 1508 ; 1870
B.) 2083
C.) 3972
Step-by-step explanation:
General form of an exponential model :
A = A0e^rt
A0 = initial population
A = final population
r = growth rate ; t = time
1)
Using the year 1750 and 1800
Time, t = 1800 - 1750 = 50 years
Initial population = 790
Final population = 980
Let's obtain the growth rate :
980 = 790e^50r
980/790 = e^50r
Take the In of both sides
In(980/790) = 50r
0.2155196 = 50r
r = 0.2155196/50
r = 0.0043103
Using this rate, let predict the population in 1900
t = 1900 - 1750 = 150 years
A = 790e^150*0.0043103
A = 790e^0.6465588
A = 1508.0788 ; 1508 million people
In 1950;
t = 1950 - 1750 = 200
A = 790e^200*0.0043103
A = 790e^0.86206
A = 1870.7467 ; 1870 million people
2.)
Exponential model. For 1800 and 1850
Initial, 1800 = 980
Final, 1850 = 1260
t = 1850 - 1800 = 50
Using the exponential format ; we can obtain the rate :
1260 = 980e^50r
1260/980 = e^50r
Take the In of both sides
In(1260/980) = 50r
0.2513144 = 50r
r = 0.2513144/50
r = 0.0050262
Using the model ; The predicted population in 1950;
In 1950;
t = 1950 - 1800 = 150
A = 980e^150*0.0050262
A = 980e^0.7539432
A = 2082.8571 ; 2083 million people
3.)
1900 1650
1950 2560
t = 1900 - 1950 = 50
Using the exponential format ; we can obtain the rate :
2560 = 1650e^50r
2560/1650 = e^50r
Take the In of both sides
In(2560/1650) = 50r
0.4392319 = 50r
r = 0.4392319/50
r = 0.0087846
Using the model ; The predicted population in 2000;
In 2000;
t = 2000 - 1900 = 100
A = 1650e^100*0.0087846
A = 1650e^0.8784639
A = 3971.8787 ; 3972 million people
In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3. Consider 1980 as the starting point (time zero) for this problem. Create an explicit exponential formula for the median age of the U.S. population t years after 1980, assuming the median age has exponential growth.
Answer: [tex]30e^{0.00813x}[/tex]
Step-by-step explanation:
Given
Median age in 1980 is [tex]30[/tex]
It is [tex]35.3[/tex] in year 2000
Suppose the median age follows the function [tex]ae^{bx}[/tex]. Consider 1980 as starting year. Write the equation for year 1980
[tex]\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a[/tex]
For year 2000
[tex]\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813[/tex]
After t years of 1980
[tex]\Rightarrow 30e^{0.00813x}[/tex]
Need help on the last problem please.
Answer:
6 of x and 5 of y
Step-by-step explanation:
x = number of closets of the first type
y = number of closets of the second type
1200 = 100x + 120y
100 = 10x + 8y
10x = 100 - 8y
10x(100 - 8y) + 120y = 1200
1000 - 80y + 120y = 1200
40y = 200
y = 5
100 = 10x + 8×5 = 10x + 40
60 = 10x
x = 6
20x + 24y = max
20×6 + 24×5 = 120 + 120 = 240
You and Michael have a total of $19.75. If Michael has $8.25, how much
money do you have?
$27.00
$28.00
$11.50
$12.00
Answer:
You have a total of $11.50
Step-by-step explanation:
We first subtract $19.75 by $8.25 and the result will be $11.50
Answer:
11.50
Step-by-step explanation:
19.75-8.35= 11.50
May I have the brainiest?
Work out m and c for the line:
y – 37 = 5
Answer:
first thing is y - 35 = 5
then y = 35 + 5 because when = come here - will be + and
then we should do+ y=40 answer
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
A Professor at a Nigerian University sent his phone number in a disorderly manner to his students. The disordered phone number was 82002273285.To know his real phone number, he gave the student the following conditions:(1) Eight (8) must come between two zeros (0's). (2)The first number after the first condition is met must not be an odd number and it must be greater than 5. (3)The seventh number must be 1. (4) The fifth and sixth numbers must be two numbers whose difference is 1 and the bigger number must come first.(5)The fifth and sixth numbers are greater than 2.(6)The ninth and tenth numbers are the same.(7)The eighth number is greater than the last number (8) The phone number must be 11 digits. What is the Professor's real phone number?
Answer:
I think you have a type.. "the seventh number must be a 1"
there are no 1's in the original set of numbers
Step-by-step explanation:
What fraction of the total number of students are boys?
Step-by-step explanation:
total number of students are :4x 3 = 12
Fraction that's boys are : 3÷12
help me pleaseeeeeeeeeeeeeeeeee………….
Answer:
d
Step-by-step explanation:
because u did the math for you
The park is 18 miles east of my home. The library is 12 miles north of the park. How far is my home from the library?
35 miles
21.6 miles
8.2 miles
18.6 miles
Answer:
21.6 miles
Step-by-step explanation:
If you draw, it'll be a right triangle with legs 12 miles and 18 miles, we need to find the hypotenuse.
So,
[tex] \sqrt{ {12}^{2} + 18^{2} } [/tex]
[tex] = \sqrt{144 + 324} [/tex]
[tex] = \sqrt{468} [/tex]
[tex] = 6\sqrt{13} [/tex]
6√13 ≈ 21.6
Answered by GAUTHMATH
I'm not sure if this will be easy for some of you I really need help
find the place value of 1 in 382619.
Answer:
Place value of 1 = 1 × 10 = 10
Step-by-step explanation:
In 382619,
Place of 1 = Tens
Place value of 1 = 1 × 10 = 10
Use the image to complete the equation below. Do not include any spaces in your answer
Linear pair of angles are supplementary (180°).
So,
(3q) + (15q + 18) = 180°.
Which statement explains how to correct the error that was made?
The subtraction property of equality should have been applied to move m to the other side of the equation.
The multiplication property of equality should have been applied before the division property of equality.
The division property of equality should have been applied to move the fraction to the other side of the equation.
O The square root property should have been applied to both complete sides of the equation instead of to select
variables.
Answer:
The square root property should have been applied to both complete sides of the equation instead of to select
variables.
A sample of students was asked what political party do they belong. which of the following types of graphical display would be appropriate for the sample?
A. Stemplot.
B. Pie chart.
C. Scatterplot.
D. All of the above.
Answer:
B. Pie chart.
Step-by-step explanation:
In this question, the students are asked what political party they belong. The best display format would be one in which the graph can be divided into parts, or percents, according to the percentage of students belonging to each political party. The graph that best describes this, distributing a group into parts, is a pie chart, and thus, the correct answer is given by option b.
Scatterplot is used when two variables correlate together, that is, there is a relationship between them, which we don't have between the number, or proportion of students belonging to each political party. Stemplot are used when there is a high number of quantitative data, which we do not have here.
If $100 is interested at 6% compounded:
a-Annually
b-Monthly
What is the amount after 4 years? How much interest is earned?
To find the simple interest we'll plug it into one of the two available formulas. I will use both formulas so you can determine which is easiest for you, for future problems.
r = I/Pt or I = Prt
(the / represents division)
Let's define and plug.
r = the rate (we'll be solving for r)
I = the total interest earned within the time frame ($2)
P= the principal amount ($100)
t = the total time the principal accrued interest. (6 months/ .5years)
**Because this is in a monthly basis, lets change it into a year to make it easier**
we'll just divide 6 months by 12 months.
6 ÷ 12 = 0.5 years
============================================================
Let's use the first formula first. r = I / Pt
r = 2 / 100 (0.5)
100 x 0.5 = 50
We're now left with: r = 2 / 50
Divide what we have left.
2 ÷ 50 = 0.04
This is our simple interest but we have to convert it into a percentage. To convert the decimal to the percentage, we'll move the decimal two places to the right to make 4.0.
Therefore, our simple interest would be 4%
==========================================================
let's set up the second formula: I = Prt
2 = 100 (r) (0.5)
2 = 50 (r)
2 ÷ 50 = 0.04
0.04 in percentage = 4%
The lengths of pregnancies are normally distributed with a mean of days and a standard deviation of days. a. Find the probability of a pregnancy lasting days or longer. b. If the length of pregnancy is in the lowest %, then the baby is premature. Find the length that separates premature babies from those who are not premature.
Answer:
a) The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
b) We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
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.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
a. Find the probability of a pregnancy lasting X days or longer.
The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
b. If the length of pregnancy is in the lowest a%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
Math help please ………….
Answer:
if the terms are approaching zero then it is convergent.
Therefore the stated series is convergent
Step-by-step explanation:
3х + 2 + (-5) in simplest form, thanks!
Answer:
3x-3
Step-by-step explanation:
3x has a variable attach, because no other numbers have a variable attached leave it alone.
2+(-5) are like terms so combine these two. 2+(-5)=-3
now put back in the equation
3x-3
The figure shows trapezoid ABCD on a coordinate plane.
Which of the following represents the area of this figure, rounded to the nearest square unit?
99
121
198
231
Answer:
121 unit^2.
Step-by-step explanation:
The area = height/2 * ( sum of the opposite parallel lines)
= h/2(BC + AD
h = BF = 14 - 3 = 11 units.
BC = 13 - 5 = 8 units.
AD = 16 - 2 = 14 units.
Area = (11/2)(8 + 14)
= 5.5 * 22
= 121 unit^2.
Answer:
121
Step-by-step explanation:
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.06. If 235 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.04
Answer:
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose the true proportion is 0.06.
This means that [tex]p = 0.06[/tex]
235 are sampled
This means that [tex]n = 235[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.06[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.06*0.94}{235}} = 0.0155[/tex]
What is the probability that the sample proportion will differ from the population proportion by greater than 0.04?
Proportion below 0.06 - 0.04 = 0.02 or above 0.06 + 0.04 = 0.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.
Probability the proportion is below 0.02.
p-value of Z when X = 0.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.06}{0.0155}[/tex]
[tex]Z = -2.58[/tex]
[tex]Z = -2.58[/tex] has a p-value of 0.0049.
2*0.0049 = 0.0098
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
For what value of the variable : is the value of 9-y twice as much as the value of y?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = 3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{"The value of 9-y twice as much as the value of y" can be written as:}}\\\\9-y = 2y[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'y'...}}\\\\9-y=2y\\------------\\\rightarrow 9 -y + y = 2y + y\\\\\rightarrow 9 = 3y\\\\\rightarrow \frac{9=3y}{3}\\\\\rightarrow 3 = y\\\\\rightarrow \boxed{y = 3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
In this diagram, ABAC – AEDF. If the
area of ABAC = 6 in?, what is the
area of AEDF?
Answer:
2.7 in²
Step-by-step explanation:
similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.
so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.
in other words
EF = BC × 2/3
2 = 3 × 2/3
correct
how do we calculate the area of a triangle ?
Area = baseline × height / 2
from BAC we know
Area = 6
baseline = 3
height = ?
6 = 3 × height / 2
12 = 3 × height
height = 4
aha !
now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3
so, for EDF we know
Area = ?
baseline = 2
height = 4 × 2/3 = 8/3
therefore, the area is
Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7
the shirt answer would be :
we know from the 2 baselines that the scaling factor for each distance is 2/3.
for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.
2/3 × 2/3 = 4/9
=>
Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7
Find the length of side AB.
Give your answer to 1 decimal place.
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, scalene, equilateral, acute, obtuse and right angled triangle. A right angle triangle is a triangle with one angle being 90°.
Trigonometric ratios is used to show the relationship between the angles and sides of a right angled triangle. Examples are:
sinΘ = opposite/hypotenuse; cosΘ = adjacent/hypotenuse; tanΘ = opposite/adjacent
From the question:
cos(62) = AB/12
AB = 12 * cos(62)
AB = 5.6 cm
Jeremy bought 3 pairs of pants that cost
The same amount of money. He had a
$10 off coupon for the pants. Using the
coupon, Jeremy spent $35. Write an
equation that can be used to find the cost
of the pants before the coupon was
applied
(use p as your variable)
Help fasttt
Answer:
3p - 10 =35
Step-by-step explanation
You want to cancel out everything, besides the p, on the left side.
then add the ten to 35 to cancel it out
divide 3 by 45 to cancel it out
p equals 15
The answer is 15
Problem is in the picture below
Answer:
68.1
Step-by-step explanation:
If those angles are congruent, then all side lengths follow the same ratio.
So the smaller triangle side length of 9 over the small side length of the bigger triangle 21.5, is the ratio for all the sides.
9/21.5 = unknown side / 48
unknown side = 48 * 9/21.5
So to find the length of CD, multiply 48 by our ratio to get ~ 20.1
Add that to our 48 and we get 68.1
PLEASE HELP!!! Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
Answer:
is it going to be 10.5
Step-by-step explanation:
I do not have any explanation
Answer: 0 (zero)
Step-by-step explanation:
Start Learning & start growing! edge2023
*DROPS THE MIC*
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
A population has mean j = 18 and standard deviation o = 20. Find I, and oz for samples of size n = 100, Round your answers to
one decimal place if needed,
Answer:
))
Step-by-step explanation:
just place your decimal once to the left I think
Please help NO LINKS
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
