A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]
B. Using the function, the population will be 11 million by 2059.
What is the exponential growth function for the population?The function is given by:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the population in 2000.k is the exponential growth rate, as a decimal.t is the number of years after 2000.Item a:
We have that:
A(0) = 5.89, A(50) = 10.
We use this to find k, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]10 = 5.89e^{50k}[/tex]
[tex]e^{50k} = \frac{10}{5.89}[/tex]
[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]
[tex]50k = \ln{\frac{10}{5.89}}[/tex]
[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]
k = 0.0106.
Hence the equation is:
[tex]A(t) = 5.89{0.0106t}[/tex]
Item b:
We have to solve for t when A(t) = 11, hence:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]11 = 5.89e^{0.0106t}[/tex]
[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]
[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]
[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]
[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]
t = 58.9
Rounding up, the population will be of 11 million in 2059.
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To mix weed killer with water correctly, it is necessary to mix 30 teaspoons of weed killer with 5 gallons of water. Find how many gallons of water are needed to mix
with the entire box if it contains 36 teaspoons of weed killer.
gallons of water are needed to mix with the entire box of weed killer.
What is the measure of z?
4
y
N
9
z = 3√ [?]
3₁
Answer:
z = 3[tex]\sqrt{13}[/tex]
Step-by-step explanation:
According to Euclidian theorem we can find the measure of z using the following equation:
z^2 = 9*(9+4)
z^2 = 9*13 multiply
z^2 = 117 find the root of both sides
z = 3[tex]\sqrt{13}[/tex]
Which expression represents a rational number?
StartFraction 5 Over 9 EndFraction + StartRoot 18 EndRoot
Pi + StartRoot 16 EndRoot
StartFraction 2 Over 7 EndFraction + StartRoot 121 EndRoot
StartFraction 3 Over 10 EndFraction + StartRoot 11 EndRoot
The rational number among all the answer choices is; Pi + √16.
What is a Rational number?A rational number by definition, is one that can be represented as the quotient a/b of two integers in which case b ≠ 0.
On this note, it follows that since the constant pi is; 22/7, the number pi + √16 can be represented as a rational number as follows;
22/7 + 4 = 50/7.
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Answer:
The answer is b.
Step-by-step explanation:
goodluck
Which shows an equation in point-slope form of the line shown?
y−4=43(x−2)
y−2=34(x+6)
y−4=34(x−2)
y+2=43(x+6)
Number graph ranging from negative ten to ten on the x and y axes. A line passes through the labeled points (negative six, negative two) and (two, four).
Answer: Option (3)
Step-by-step explanation:
The slope of the given line is
[tex]\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}[/tex]
Thus, the answer must be Option (3)
Solve x2 – 5x – 24 = 0 by completing the square
A)
x = –6 and x = –4
B)
x = 6 and x = –4
C)
x = 3 and x = –8
D)
x = –3 and x = 8
The solutions of the equation x² – 5x – 24 = 0 will be 8 and -3. Then the correct option is D.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The quadratic equation is given below.
x² – 5x – 24 = 0
Then the factor of the equation will be
x² – 5x – 24 = 0
x² – 8x + 3x – 24 = 0
x(x – 8) + 3(x – 8) = 0
(x – 8)(x + 3) = 0
x = 8, -3
Then the correct option is D.
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PLEASE SEE THE ABOVE PICTURE.
Solve this part please fast
Give the right answers
Step-by-step explanation:
believe it or not, the area of any triangle is
baseline × height / 2
we have here 2 triangles, both with the same baseline (8 cm), but with 2 different heights : 6.5 cm and 4.6 cm.
so, their areas are
8 × 6.5 / 2 = 4 × 6.5 = 26 cm²
8 × 4.6 / 2 = 4 × 4.6 = 18.4 cm²
so, in total, the shaded region is
26 + 18.4 = 44.4 cm²
A restaurant records the number of tables served each night, and the results have the values: minimum = 3, lowe
quartile = 14, median = 23, upper quartile = 29, and maximum = 40.
Which box plot represents the data?
The box plot that represents the data is the first box plot.
What is a box plot?A box plot is graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the values of the whiskers gives the range of the dataset.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the upper quartile and the lower quartile is the interquartile range.
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Answer:
The box plot that represents the data is the first box plot.
Step-by-step explanation:
PLEASE HELP!!!
There are many different kinds of numbers (whole numbers, fractions, etc.). Name some different types of numbers. Do you know how to do operations with different types of numbers? What operations do you know how to perform with the different types of numbers?
Answer:
Types of numbers
Natural Numbers - Common counting numbers.
Prime Number - A natural number greater than 1 which has only 1 and itself as factors.
Composite Number - A natural number greater than 1 which has more factors than 1 and itself.
Whole Numbers - The set of Natural Numbers with the number 0 adjoined.
Integers - Whole Numbers with their opposites (negative numbers) adjoined.
Rational Numbers - All numbers which can be written as fractions.
Irrational Numbers - All numbers which cannot be written as fractions.
Real Numbers - The set of Rational Numbers with the set of Irrational Numbers adjoined.
Complex Number - A number which can be written in the form a + bi where a and b are real numbers and i is the square root of -1.
Step-by-step explanation:
What is the value of p if the two side are 140 and 90
The value of P is 50 degree , Option D is the correct answer.
What is the property of Exterior Angle of a Triangle ?According to the exterior angle property the measure of exterior angle is equal to the sum of opposite interior angles.
In the given figure it can be seen that one of the exterior angle is 90 degree ,
which is making a supplementary angle with the interior angle corresponding to it , angle B in the figure
Therefore the interior angle B is 90 degree ,
The value of angle C = p degree
To determine the value of angle C
The exterior angle next to angle A = 140 degree
By the exterior angle property
140 = 90 +p
p = 50 degree
The value of P is 50 degree , Option D is the correct answer.
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Simplify the following by removing parentheses and combining terms
-(2q+6)+3(2q+4)-2q
Answer:
2q+6
Step-by-step explanation:
So basically, you would do this.
-2q-6+6q+12-2q
Next
-4q+6q = 2q
12-6=6
2q+6
Answer:
2q + 6
Step-by-step explanation:
To simplify, we will use the distributive property.
-(2q + 6) simplifies to -2q - 6 (In this case we are distributing the - sign or -1)
3(2q + 4) simplifies to 6q + 12
So if we recombine: -2q - 6 + 6q + 12 - 2q
Let's combine like terms (q's with q's, numbers with numbers)
-2q + -2q + 6q = 2q
-6 + 12 = 6
So if we recombine: 2q + 6
One number is 2 more than another. The difference between their squares is 24. What are the numbers?
Answer:
5 and 7Step-by-step explanation:
One number is 2 more than another. The difference between their squares is 24. What are the numbers?
(x + 2)² - x² = 24
x² + 4x + 4 - x² = 24
4x + 4 = 24
4x = 20
x = 20 : 4
x = 5
----------------------
5 + 2 = 7
check
(5 + 2)² - 5² = 24
49 - 25 = 24
24 = 24
the answer is good
A graduate student believes that people consider faces with more contrast between eye color and skin tone as more feminine. She identifies the null and alternative hypotheses as:
H₀: The level of contrast between eye color and skin tone does not affect how feminine a face is considered.
H₁: The level of contrast between eye color and skin tone affects how feminine a face is considered.
She chooses a significance level of 0.01. After she collects the data and computes the sample statistics, it is time for her to make a decision about H₀.
Check the two possible decisions that the graduate student can make given her choices of H₀ and H₁. Check all that apply.
There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.
What decision should the graduate student make if the test statistic is not inside the critical region?
A. The graduate student should reject the alternative hypothesis.
B. The graduate student should reject the null hypothesis.
C. The graduate student cannot reject the null hypothesis.
Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is ____ the critical region. Therefore, the graduate student _____ reject the null hypothesis, and she _____ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.
The two possible decisions that the graduate student is that:
There is not enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.What decision should the graduate student make if the test statistic is not inside the critical region?If the test is not inside the critical region, the graduate student cannot reject the null hypothesis.
Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is outside the critical region. So:
The test statistic is not in the critical region.
2. Therefore, the graduate student cannot reject the null hyopthesis,
3. and she cannot conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.
Note that a failure to reject the null hypothesis in any kind of significance test does not imply that the null hypothesis holds true. It only imply that the person was not able to give enough evidence for the alternative hypothesis.
See options for the last question
Options for the last section...
1. The test statistic is ____not in/in_____ the critical region.
2. Therefore, the graduate student _____can/cannot_____ reject the null hyopthesis,
3. and she ______can/cannot_______ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered
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Question 7 of 12, Step 1 of 2
6/19
Correct
If you throw exactly one head in two tosses of a coin you win $9. If not, you pay me $15.
Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Answer
Step-by-step explanation:
the expected value is calculated by multiplying each of the possible outcomes by their probability, and then summing up all these results.
tossing a coin 2 times gives us 4 possible different outcomes (all with the same probability of 0.25) :
head - tail
head - head
tail - head
tail - tail
to have exactly one head is 2 out of these 4 possible outcomes, and the probability is 0.5.
everything else is also 2 out of these 4 possible outcomes, and the probability for that is therefore 0.5 too.
the expected value (from your point of view) is
9×0.5 - 15×0.5 = -$3.00
A small startup company wishes to know how many hours, per week, that it's employees spend commuting to and from work. The number of hours for each employee are shown below. Construct a frequency table for grouped data using four classes.
1,2,18,4,13,18,12,3,17,10,3,12,15,2 15,8,5,17,18,18
The frequency table for grouped data using four classes is shown in the picture.
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
We have:
A small startup company wishes to know how many hours, per week.
The number of hours for each employee are shown below:
1,2,18,4,13,18,12,3,17,10,3,12,15,2 15,8,5,17,18,18
Make the group of 1-5, 6-10, 11-15, and 16-20
And count the numbers lies between the interval.
Thus, the frequency table for grouped data using four classes is shown in the picture.
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Find the domain and range of the following function.
Answer:
Domain : [-5,5]
Range : [-3,4}
Step-by-step explanation:
By definition:
Domain is the set of all inputs for which the given function is defined
Graphically we can visualize it as the shadow of the graph on the x axis, and the shadow is formed above and below the x axis.In this graph, the shadow starts at -5 and ends at 5 , hence domain is [-5,5]Range is the set of all outputs
Graphically it is the shadow of the graph on the y axis from both sidesIn this graph, the shadow on y axis starts at -3 and ends at 4, hence range is [-3,4}On that question regarding adding up different amounts of time you came to the conclusion the answer was 7.825. How much time is .825?
The time 0.825 is 49.5 minutes based on the conclusion that the sum of the different amounts of time was 7.825 hours.
What is the proportion in time?Proportion in time refers to the relationship between two or more ratios or quantities expressed in time measurements.
Data and Calculations:One hour = 60 minutes
One minute = 60 seconds
0.825 of an hour = 49.5 minutes (0.825 x 60 minutes)
0.5 minutes = 30 seconds (0.5 x 60)
Thus, we can conclude that the total time involved is 7 hours, 49 minutes, and 30 seconds.
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A bike store marks up the wholesale cost of all bikes they sell by 30%. Calvin wants to buy a bike that has a price tag of 123.50. What was the wholesale cost of this bike?
Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues.
{[tex]\frac{-10}{4}[/tex], [tex]\frac{12}{16}[/tex], [tex]\frac{-14}{64}[/tex], [tex]\frac{16}{256}[/tex],...}
Thank you
Answer:
ans : general term = (2n +8)/(4^n) * (-1)^n
find x and y !!!!
pls pls help
Answer:
x = 59°, y = 31°
Explanation:
Angles (x) and (x - 28) sum ups to 90° on a straight line.
→ x + (x - 28) = 90
→ 2x - 28 = 90
→ 2x = 90 + 28
→ 2x = 118
→ x = 59°
Then find value of y
Angle y, x, 90° lies on a straight line which sum ups to 180°
→ x + y + 90° = 180°
→ 59 + y + 90° = 180°
→ y = 180° - 149°
→ y = 31°
A circle in the xyxyx, y-plane has a center at \left(\dfrac{3}{4\,},\dfrac{1}{2}\right)(
4
3
,
2
1
)left parenthesis, start fraction, 3, divided by, 4, end fraction, comma, start fraction, 1, divided by, 2, end fraction, right parenthesis and a radius that is \dfrac{3}{5}
5
3
start fraction, 3, divided by, 5, end fraction units long. Which of the following is an equation of the circle
The equation of the circle will be (x – 3/4)² + (y – 1/2)² = 9/25. Then the correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x – h)² + (y – k)² = r²
We have
(h, k) = (3/4, 1/2)
r = 3 / 5
Then the equation of circle will be
(x – 3/4)² + (y – 1/2)² = (3/5)²
(x – 3/4)² + (y – 1/2)² = 9/25
Then the correct option is A.
The missing options are given below.
A. (x – 3/4)² + (y – 1/2)² = 9 / 25
B. x² + y² = 9/25
C. (x – 3/4)² + (y – 1/2)² = 25 / 9
D. (x – 1/2)² + (y – 3/4)² = 9/25
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ten selected students took a. altitude test out of the total score of 100 these students scored 60,50,50,70,40,80,65,55,50 and 90 respectively calculate the mean and the mode and the median for the given set of data
Answer:
• mean = 61
• mode = 50
• median = 57.5
Step-by-step explanation:
• The mean is calculated by adding all the values together, and dividing the result by the number of values.
∴ mean = [tex]\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}[/tex]
⇒ mean = [tex]\frac{610}{10}[/tex]
⇒ mean = 61
• The mode of a set of values is the value that is the most common (has highest frequency) among them.
50 is the most common value.
∴ mode = 50
• The median is the middle-value of a set of ordered values.
∴ We have to first rearrange the set:
⇒ 40, 50, 50, 50, 55, 60, 65, 70, 80, 90
Now we need to find the middlemost value:
Since we have 10 values, which is an even number, we have to use the formula:
median = [tex]\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}[/tex]
where n is the number of values.
∴ median = [tex]\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}[/tex]
⇒ median = [tex]\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}[/tex]
The 5th and 6th terms in our ordered series are 55 and 60 respectively.
∴ median = [tex]\frac{55 + 60}{2}[/tex]
⇒ median = 57.5
Please see attached photo please
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-b + 8c}[/tex]
[tex]\huge\textbf{Simplifying: }[/tex]
[tex]\mathsf{-b + 8c}[/tex]
[tex]\mathsf{= -2 + 8(-2)}[/tex]
[tex]\mathsf{= -2 - 16}[/tex]
[tex]\mathsf{= -18}[/tex]
[tex]\huge\textbf{Therefore, the answer should be: }[/tex]
[tex]\huge\boxed{\frak{-18}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
given g(x)=3x+6 on what interval is the function negative
Step-by-step explanation:
A number that is negative is less than 0, so
[tex]3x + 6 < 0[/tex]
[tex]3x < - 6[/tex]
[tex]x < - 2[/tex]
So this function is negative, when x is less than -2
Hi !
[tex]3x+6\leq 0\\3x\leq -6\\x\leq \frac{-6}{3} =-2[/tex]
g(x)≤0 for x∈ ]-∞;-2]
Have a nice day
what is the value of F(6) in the functions below
F(x)-2^x
The value of the exponential function when x = 2 is 64
Exponential functionsThe standard form of exponential equation is expressed as y = ab^x
Given the exponential function expressed as:
f(x) = 2^x
For the value f(6)
f(6) = 2^x
f(6) = 2^6
f(6) = 64
Hence the value of the exponential function when x = 2 is 64
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Heads, Heads
15
Heads, Tails
11
Tails, Heads
17
Tails, Tails
7
Total
50
Based on your data, what is the experimental probability that the family has two dogs or two cats?
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
How could you change the simulation to generate data for three pets?
The probability that the family has two dogs or two cats will be 0.5.
How to calculate the probability?From the information, the head represents cats and rte tails represent dogs.
The experimental probability that the family has two dogs or two cats will be:
= (1/2 × 1/2) + (1/2 × 1/2)
= 1/4 + 1/4
= 1/2
= 0.5
Also, the theoretical probability that they have three dogs or three cats is 0.5.
The simulation to generate data for three pets will be to add a new coin and category for the new pet.
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Which best describes the relationship between the line that passes through the points (-9, -7) and (-12, -2) and the line
that passes through the points (1, 9) and (6, 6)?
A. neither perpendicular nor parallel
B. perpendicular
C. same line
OD. parallel
Answer:
A
Step-by-step explanation:
The equation of the line that passes through the points (-9,-7) and (-12,-2) is
y = -5/3x-22
and
equation of the line that passes through the points (1, 9) and (6, 6) is
y = -3/5x+48/5
clearly it is not the same line,
[tex]\frac{-5}{3}.\frac{-3}{5} \neq -1[/tex] (lines are not perpendicular)
[tex]\frac{-5}{3}\neq \frac{-3}{5}[/tex] (not parallel)
Write 7/24 as an equivalent fraction with a denominator of 96
Answer: [tex]\frac{28}{96}[/tex]
Step-by-step explanation:
We will figure out what needs to happen to the denominator to get to 96, then we will do the same to the numerator.
[tex]\displaystyle \frac{7}{24}=\frac{?*x}{24*x=96} =\frac{7*4}{24*4}=\frac{28}{96}\\\\ \\\text \\\;\;\;\;\;\; \frac{28}{96}[/tex]
Answer:
28/96
Step-by-step explanation:
Equalize the equivalent fractions according to the desired denominator and solve for the numerator "x"
[tex]\frac{7}{24} =\frac{x}{96}[/tex]
[tex]x=\frac{(96)(7)}{24} =\frac{672}{24} =28[/tex]
The equivalent fraction is
[tex]\frac{28}{96}[/tex]
Hope this helps
Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel, given the following points. Show all work!!! HELP PLEASEE
The prove that the angle ABCD is said to be a parallelogram that shows both pairs of opposite sides as parallel figure is given below.
What is the parallelogram about?The four points in the shape above are : A, B, C, D.
Where
A = (-2,-4)
B = (1,2)
C = (2,10)
D = (-1,4)
We place or sit vector AB with vector DC and vector AD with vector BC
and so we find and place their coordinates.
vector AB (1-(-2), 2-(-4))
vector DC (2-(-1),10-4)
vector AD (-1-(-2), 4-(-4))
vector BC (2-1,10-2)
So we obtained:
vector AB (3,6)
vector DC (3,6)
vector AD (1,8)
vector BC (1,8)
Next step is to calculate for the lengths :
AB= [tex]\sqrt{3^{2} + 6^{2} }[/tex] DC= [tex]\sqrt{3^{2} + 6^{2} }[/tex]
Thus, AB = DC
AD = [tex]\sqrt{1^{2} + 8^{2} }[/tex] BC =[tex]\sqrt{1^{2} + 8^{2} }[/tex]
Hence one can say that AD is equal to BC.
Therefore, angle ABCD IS known to be a parallelogram .
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find the measure of the indicated angle to the neareat degree. show your equation, use proper trig function, and clearly mark your answer.
Step-by-step explanation:
for 1st triangle on the left
sin(x) = 24/38
x = inverse sin(24/38)
x = 39.1667 deg
for triangle 2
cos(x) = 20/52
x = inverse cos (20/52)
x = 67.38 deg
Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to sol
for x?
3x+5x-4
3x+4-5x
3x-4+5x
O3x-4-5x
Answer: 3x+4-5x
Step-by-step explanation:
3x+4=5x
3x+4-5x=0