$2,444.44 was invested in the 7.5% bond and $20,555.56 was invested in the 13% bond.
How the solution was obtainedLet x be the amount invested in the 7.5% bond
(23,000 - x) be the amount invested in the 13% bond.
The interest earned by 7.5% bond = (7.5/100) * x = 0.075x.
The interest earned by 13% bond = (13/100) * (23,000 - x) = 0.13 * (23,000 - x).
The total interest earned on both investments = 0.075x + 0.13 * (23,000 - x) = 2,880.
We can solve for x by substituting 0.075x + 0.13 * (23,000 - x) = 2,880 and solving for x.
0.075x + 0.13 * 23,000 - 0.13x = 2,880
0.045x = 2,880 - 0.13 * 23,000
0.045x = 2,880 - 2,990
0.045x = -110
x = -110 / 0.045 = 2,444.44 (rounded to two decimal places)
So, x = $2,444.44 was invested in the 7.5% bond and (23,000 - $2,444.44) = $20,555.56 was invested in the 13% bond.
Learn more on financial bonds here https://brainly.com/question/25965295
#SPJ1
what is the constant of proportonality in the equation 3y = 2x
The constant of proportionality in the equation 3y = 2x is 2/3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
if y is directly proportional to x, this is expressed as:
y ∝ x
y = kx .................... 1
k = y/x
Given the expression 3y = 2x
Divide both sides by 3
3y/3 = 2x/3
y = 2/3 x ................ 2
Compare equation 1 and 2 to find "k"
kx = 2/3 x
k = 2/3
Hence, the constant of proportionality in the equation 3y = 2x is 2/3.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
if mbdc = 3 (x – 5) and m arc bc = x 25, what is ma?
Ma = 3x - 15, since mbdc = 3(x - 5) and m arc bc = x 25. Therefore, ma = 3x - 15, which is the product of 3 times (x-5).
To solve for ma, we need to start with the given information. We are given that mdbc = 3(x - 5) and m arc bc = x 25. We can start by expanding mbdc. We know that mbdc = 3(x - 5). This can be expanded by multiplying each term in the parenthesis by 3. We get mbdc = 3x - 15. We can then use this information to solve for ma. We know that ma = mbdc - m arc bc. Plugging in the values we found for mdbc and m arc bc, we get ma = 3x - 15. This is the product of 3 times (x - 5). Therefore, ma = 3x - 15.
Learn more about arc here
https://brainly.com/question/20294211
#SPJ4
the oppertunity cost of earning an advanced college degree is that
The opportunity cost is that the person will earn less money during the years that you are in college.
What is opportunity cost?Opportunity cost is the potential-forgone profit from a missed opportunity as the result of choosing one alternative and forgoing another.
The advantages of opportunity cost :-
Opportunity cost has to do with one forgoes when one makes a different choice. For example, if there's a choice between going to school and playing football, and the person goes to school, the opportunity cost is the fun that one will have enjoyed while playing football.The opportunity cost of earning the advanced college degree will be that the person will earn less money during the years that you are in college. When the person is in college, the person won't be able to take up certain jobs that'll provide money to him or her.Hence, the correct option is the opportunity cost is that the person will earn less money during the years that you are in college.
Learn more on about opportunity cost, click:
https://brainly.com/question/13036997
#SPJ1
-1/4 + 1/12 - 1/8b + 13/24
The simplified expression is equal to 13/24 - 3/8b.
What do you mean by algebraic expression?It represents a value that can change, depending on the values of the variables.
For example, "2x + 3" is an algebraic expression. The variable x can take on any value, and the expression represents a value that is the result of adding 2 times x to 3. When x is equal to 5, the expression equals 2 * 5 + 3 = 13.
Algebraic expressions can be combined using the operations of addition, subtraction, multiplication, and division to form more complex expressions. They can also be simplified by combining like terms or using the distributive property.
Algebraic expressions are an important tool in mathematics, and are used in many areas including science, engineering, and economics. They can be used to model and understand complex systems, and to make predictions and analyze data.
The expression -1/4 + 1/12 - 1/8b + 13/24 can be simplified by finding the common denominators and adding the numerators:
-1/4 + 1/12 - 1/8b + 13/24 = (3 * -1/12) + (3 * 1/12) - (3 * 1/8b) + (3 * 13/72) = 3 * (-1/12 + 1/12 - 1/8b + 13/72) = 3 * (13/72 - 1/8b) = 13/24 - 3/8b.
So, the simplified expression is equal to 13/24 - 3/8b.
To know more about expression visit:
https://brainly.com/question/24242989
#SPJ1
BRAINLIEST!!! CORRECT ANSWERS ONLY
-x+y=14
2x+y=-7
Solve both.
Answer:
see below
Step-by-step explanation:
-x+y=14 --> so x=y-14
2x+y=-7 put x in here
2(y-14)+y =-7
2y-28+y = -7
3y =21
y=7
x= y - 14 = -7
approximately how fast is a person located at the earth's equator traveling due to the rotation of the earth? hint: a person located at the equator will go once along the circumference of a circle with radius equal to the radius of the earth in a time interval equal to 24 hours. speed is equal to distance traveled divided by the time interval.
The speed of the person located at earth's equator traveling due to rotation is, 1670 km/hr.
The person at equator traveling due to it's rotation will cover one complete round of earth in 24 hours. Hence the distance travelled is the circumference of the earth.
The radius of the earth is, 6 378.1 kilometers.
The circumference can be calculated as, 2×π×R
Using R = 6 378.1 kilometers,
Circumference = 2×π×6 378.1 kilometers
Circumference = 40090.91 kilometers.
The distance traveled = 40090.91 kilometers.
Time taken is 24 hrs.
Hence speed = distance/time
Speed = 40090.91/24
Speed = 1670 km/hr
The speed of the person is 1670 km/hr.
To know more about the speed, here
brainly.com/question/29775794
#SPJ4
PLease guys I need help and I need to get my grade up!
This one shouldn't be too hard! :)
A diameter of a circle is just the total distance across the circle.
The two dots that stretch ALLLLL the way across the circle are dots R to S
Your answer is The third one RS
Hope this helps!
2) Find a then the measures of angle K and J: (3 marks)
H
G
(20a +30)
5aº
(17a+ 48)
K
From the given triangle JKL, measure angle K is 65 degrees.
What are the four different types of triangles?The length of the sides distinguishes triangles of the scalene, isosceles, and equilateral kinds. If the lengths of the three sides are all different, the triangle is a scalene triangle. A triangle that has equal lengths on each of its three sides is said to be isosceles.
The measure of angle j in the triangle JKL is 30 degrees less than the measure of angle K, while the measure of angle L is 80 degrees. measure the angle K.
Suppose angle K = x, at which point angle J = x-30 degrees, and angle L = 80 degrees.
The total of a triangle's three angles is 180 degrees, or K+L+J = 180.
The angles of the triangle are
since x+80+x-30
= 180 + 2x
= 180-80+30
= 130 and
x= 130/2 = 65 degrees.
K = 65 degrees,
L = 80 degrees, and
J = 35 degrees
To learn more about triangles from given link
https://brainly.com/question/28144202
#SPJ1
Complete question -
In triangle JKL,the measure of angle j is 30 degrees less than the measure of angle K and measure angle L=80. find measure angle K.
Match each feature of the graph with
the corresponding coordinate point.
If the feature does not exist, choose
"none".
none
(0,7)
Algebra Kantner/Selm-Spring23/Unit 4-Functions
(1.5, 2)
(4,16)
height (feet)
20
16
Choices
Il vertical intercept
II maximum
8
4
horizontal intercept
minimum
3 4 5 6 7
time (seconds)
Each feature of the graph should be matched with the corresponding coordinate point as follows:
Maximum ⇒ (4, 16).Minimum ⇒ (1.5, 2).Vertical intercept ⇒ (0, 7).Horizontal intercept ⇒ none.What is the vertical intercept?In Mathematics, the vertical intercept (y-intercept) of any graph such as a quadratic function or an exponential function, generally occur at the point where the value of "x" is equal to zero (x = 0).
By critically observing the graph which represents the function (see attachment), we can logically deduce that the vertical intercept (y-intercept) is equal to the ordered pair (0, 7).
Additionally, the maximum point of any graph is the point where the graph is at the highest point, which is equal to the ordered pair (4, 16) while the minimum point of any graph is the point where the graph is at the lowest point, which is equal to the ordered pair (1.5, 2).
In conclusion, there is no horizontal intercept (x-intercept) on this graph.
Read more on y-intercept here: brainly.com/question/6240745
#SPJ1
The table shows ordered pairs of the function . What is the value of y when ?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12.
–20
–8
8
48
The value of y when x = -12 is given as follows:
y = 32.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y when x = 0.From the table, when x increases by 2, y decays by 4, hence the slope m is obtained as follows:
m = -4/2
m = -2.
Hence:
y = -2x + b.
When x = -3, y = 14, hence the intercept b is obtained as follows:
14 = -2(-3) + b
b = 8.
Hence the function is:
y = -2x + 8.
When x = -12, the value of y is given as follows:
y = -2(-12) + 8
y = 24 + 8
y = 32.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Please help me figure out what the last one is and how to get the answer
Tysm!
A triangle can be formed.
Value that goes in the box is [tex]31\frac{3}{4}[/tex]
It's the same as the first angle mentioned. The value doesn't change.
=====================================================
Explanation:
3/4 = 0.75
1/2 = 0.50
The three given angles in decimal form are:
31.7553.5094.75If these angles add to 180 degrees, then a triangle can be formed.
31.75+53.50+94.75
85.25+94.75
180
So, 31.75+53.50+94.75 = 180 is definitely the case.
Therefore, a triangle can be formed.
You'll type the mixed number [tex]31\frac{3}{4}[/tex] into the box which was that first angle mentioned.
a particle is oscillating in one dimension, with a position given by =cos(2) . how many seconds elapse between turning points? give your answer to the nearest hundredth.
After finding the time period of particle, time elapsed between turning points is 1.57 seconds.
A particle is oscillating in one dimension, with a position by x=cos(2t).
The general equation of simple harmonic equation is
x = Acos(ωt)
At t = 0 the particle is at x =1.
On comparing ω = 2
Time period of the particle = 2π/ω
Now putting the value
Time period of the particle = 2π/2
Time period of the particle = π seconds
Thus, the particle takes half the time to get from one extreme to another, which is a turning point.
So, Time elapsed = π/2 seconds
Time elapsed = 3.14/2 seconds
Time elapsed = 1.57 seconds
To learn more about simple harmonic motion link is here
brainly.com/question/2195012
#SPJ4
The complete question is:
A particle is oscillating in one dimension, with a position given by x=cos(2t). How many seconds elapse between turning points?
the olympic games logo (above, left) is usually seen as being made of 5 interlocking circles. however, while it we can clearly see it as circles, it is not necessarily the only way you can group the lines. instead, you could have a series of strange shapes that intersect in just the right spots (e.g. the shapes shown above on the right, where each color represents a different shape). what makes us see them as circles as opposed to any other combination of complex shapes?
The perception of the Olympic logo as interlocking circles is due to the human brain's tendency to simplify and organize visual information.
This is known as "gestalt psychology," where our brain perceives objects as a whole rather than individual elements. The circles provide a clear and recognizable shape that is easy for our brain to process, whereas a series of complex shapes might be harder to understand and remember.
The circles are a consistent and repeated shape in the design, further emphasizing their perception as the main element. In conclusion, it's the brain's innate pattern recognition ability and our cultural familiarity with the design that lead us to see the Olympic logo as interlocking circles.
Learn more about Olympic logo here: brainly.com/question/6285660
#SPJ4
A line intersects the points (7, 6) and (11, -6) what is the slope of the line in simplest form?
The slope of line is -3.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
A line intersects the points (7, 6) and (11, -6).
So, the slope is
= [tex](y_2 - y_1)/ (x_2 - x_1)[/tex]
= (-6 - 6) / (11 - 7)
= -12 / 4
= -3
Hence, the slope is -3.
Learn more about Slope here:
https://brainly.com/question/3605446
#SPJ1
dr. hart is interested in the role of relationships in preventing heart disease. as her patients come into her office in bluebell, alabama, she asks them two questions: are you a in a relationship? have you experienced any heart problems in the last 8 years? based on her findings, she concludes that relationships cause cardiovascular (heart) problems. one issue with her methodology is that the results are not generalizable. what does this mean?
This means that Dr. Hart result may be not true for the entire population.
ABOUT HEART DISEASEHeart disease is a condition when the heart is disturbed. Several types of heart disease, including:
Coronary heart disease, is a heart disease that occurs due to narrowing of the blood vessels in the heart. Congenital heart disease, is a heart problem found since infancy, the most common of which is a leaky heart valve. Heart infection (endocarditis), is an infection of the inner lining of the heart. Heart failure, is a failure of the heart muscle to adequately pump blood throughout the body. Arrhythmia is a heart rhythm disorder that causes an abnormal heart rate.Learn more about heart disease at
https://brainly.com/question/1347334.
#SPJ4
9. Triangles ACD and BCD are isosceles. Angle DBC has a measure of 110 degrees and angle BDA has a measure of 22 degrees. Find the measure of angle BAC.
In an isosceles triangle, if Angle DBC has a measure of 110 degrees and angle BDA has a measure of 22 degrees, then the measure of angle BAC is 48 degrees.
What is an isosceles triangle?A triangle with two equivalent sides and angles with equal measures on opposing sides is said to be isosceles.
Triangle BAC's angles should be labelled as follows:
Angle BAC = x
Angle ABC = y
Angle BCA = z
Because a triangle's angles sum up to 180 degrees,
x + y + z = 180
As ACD and BCD are isosceles triangles,
angle DBC = angle DCB = 110 degrees
Because BDA and DBC are a pair of linear angles,
angle BDA + angle DBC = 180 degrees
Using values for angles DBC and BDA and substituting them,
22 + 110 = 180
By finding y,
y = 180 - 22 - 110
When the value of y is substituted in the equation x + y + z = 180,
x + (180 - 22 - 110) + z = 180
Solving for x,
x = 180 - (180 - 22 - 110) - z
Substituting the value of z = 180 - (22 + 110),
x = 180 - (180 - 22 - 110) - (180 - 22 - 110)
To know more about isosceles triangle, visit
brainly.com/question/2456591
#SPJ1
*please answer fast*
2. [tex]\angle 1 \cong \angle 2[/tex]
3. [tex]\overline{AC} \cong \overline{AC}[/tex]
4. [tex]\triangle ABC \cong \triangle CDA[/tex]
Kim has health insurance with a deductible of $500 and an 80/20 coinsurance. How much will she pay if she incurs a loss of $1,500?
a.$200
b.$500
c.$700
d.$1,300
If Kim has health insurance with a deductible of $500 and 80/20 coinsurance then amount she pay if she incurs a loss of $1500 is (c)$700 .
In an 80/20 coinsurance, the insurance company pays 80% of covered expenses after the deductible has been met, and the policyholder is responsible for paying the remaining 20%.
So , if Kim incurs a loss of $1500, she first needs to pay the $500 deductible before her insurance kicks in. After that, she will pay for 20% of the remaining $1000 in covered expenses:
⇒ 20% of $1,000 = $200
So, in total, Kim will pay $500 for the deductible plus $200 in coinsurance, for a total of:
⇒ $500 + $200 = $700
Therefore, If Kim will pay (c) $700.
Learn more about Coinsurance here
https://brainly.com/question/28463232
#SPJ4
You can make only four different cuboids with 16 cubes. Complete the table to show the dimensions. Put the answers in order of size from left to right
The dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.
What is a cuboid?
A closed three-dimensional geometric shape called a cuboid is surrounded by six rectangular plane sections.
Given that, the dimensions of the first two cuboids are 1,1,16 and 1,2,8.
Note that the volume of each cuboid is the same, therefore, the multiplication of the dimensions should be the same for each cuboid.
Therefore, the dimensions of cuboid C and Cuboid D are:
Cuboid C: 1,4,4 Since 1 ×4×4=16.
Cuboid D: 2,4,2 as 2×4×2 = 16
Hence, the dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.
Situation:
A 9 gram sample of a substance that's
used for drug research has a k-value of
0.1459.
N = -kt
Noe
No initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
The given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.
What is amount?Amount is a numerical quantity that is used to measure the size or magnitude of something. It is typically expressed in terms of a unit of measure such as a dollar, pound, or other currency.
The given k-value of 0.1459 corresponds to the rate of decay of the 9 gram sample of the substance over time. The equation for determining the amount of the sample left after a certain amount of time (t) is: N = -kt, where N is the amount of the sample left after the given amount of time, k is a positive constant that depends on the substance itself and on the units used to measure time, and t is the amount of time in days.
N = N0 e^(-kt)
for half life N/N0 = 1/2 and k = 0.1459
1/2 = e^(-0.1459t)
=> -0.1459 t = ln(0.5)
t = - ln(0.5) /0.1459
= 4.8 days
Therefore, with the given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.
To learn more about amount visit:
brainly.com/question/25296782
#SPJ1
Complete question is:
A 9 gram sample of a substance that's used for drug research has a K value of 0.1459
Find the substances half-life in days, and round answer to the nearest ten. ( exponential decay )
URGENT URGENT!!!
What is the area and perimeters of the composite figure? Round to the nearest tenth
3.1b | Checking for Understanding
1. State the domain and the range for the following relation
{(a, g), (t, c), (s, g), (k, w), (j, k), (p, p)}
The domain and the range for the relation is {a, t, s, k, j, p} and {g, c, g, w, k, p} respectively.
What is domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it may take as input. The values in this set
Hence, once we input an x value, the function returns. The y values are those.
The domain is the input values or the x-coordinates. Hence the domain for the given relation is:
{a, t, s, k, j, p}
The range is the output value or the y-coordinate. Hence, the range of for the given relation is:
{g, c, g, w, k, p}
Hence, the domain and the range for the relation is {a, t, s, k, j, p} and {g, c, g, w, k, p} respectively.
Learn more about domain here:
https://brainly.com/question/28135761
#SPJ1
Each inch of Lenox, your scale drawing represents 1/2 foot of the actual triangle face what is a perimeter in feet of the actual triangle feet of the stone
The actual perimeter of the triangular face will be B. 18 1/2 feet.
How to calculate the perimeterThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
PQ + QR + PR
= 12 + 15 + 10
= 37 inches
Therefore, the actual perimeter of the triangular face will be:
= 37 / 2
= 18.5
The correct option is B.
Learn more about perimeter on:
brainly.com/question/19819849
#SPJ1
Which ratios have a unit rate greater than 17 Choose ALL that apply.
1
4 miles: 3 hours
miles: hour
6
915
miles: 3 hours
miles: 3 hours
3
7 miles:-hour
4
S
mile: 2 hours
8
Answer:
4 miles: 3 hours has a unit rate of 4/3 = 1.33 miles/hour which is greater than 17
7 miles: 1 hour has a unit rate of 7 miles/hour which is greater than 17.
4 glue sticks cost \$7.76.
Which equation would help determine the cost of 13 glue sticks?
Answer:
x = $20.40
Step-by-step explanation:
x = cost of 13 glue sticks
4 glue sticks cost $7.76, so to find the cost of 13 glue sticks, you would use the equation:
x = (13/4) * $7.76
or
x = $20.40
a bin of 50 parts contains 5 that are defective. a sample of 10 parts is selected without replacement. how many samples contain at least 4 defective parts?
A bin of 50 parts contains 5 that are defective and a sample of 10 parts is selected without replacement, then total 40,753,713 samples contain at least 4 defective parts.
A bin of 50 parts contains 5 that are defective.
A sample of 10 parts is selected without replacement.
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = Samples with precisely 4 defectives + samples with precisely 5 defects
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]^{5}C_{4}\cdot ^{45}C_{6}+ ^{5}C_{5}\cdot^{45}C_{5}[/tex]
Using the formula [tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5!}{4!(5-4)!}\cdot\frac{45!}{6!(45-6)!}+\frac{5!}{5!(5-5)!}\cdot\frac{45!}{5!(45-5)!}[/tex]
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5!}{4!1!}\cdot\frac{45!}{6!39!}+\frac{5!}{5!0!}\cdot\frac{45!}{5!40!}[/tex]
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5\times4!}{4!\times1}\cdot\frac{45\times44\times43\times42\times41\times40\times39!}{6\times5\times4\times3\times2\times1\times39!}+1\cdot\frac{45\times44\times43\times42\times41\times40!}{5\times4\times3\times2\times1\times40!}[/tex]
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 5 × 15 × 44 × 43 × 7 × 41 + 1 × 9 × 11 × 7 × 41
Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 40,753,713
To learn more about sample link is here
brainly.com/question/13287171
#SPJ4
the proportion of women in the sample who do not smoke while pregnant is about .85. does this help reconcile your finding from part (iii)?
Yes, it does reconcile my finding from part iii.
The finding that the number of cigarettes smoked being -10 to predict a birth weight of 125 ounces is unrealistic could be due to the fact that the model doesn't take into account other factors that could impact the weight of the child. The high proportion (85%) of women in the sample who don't smoke during pregnancy supports this conclusion, as it suggests that there may be other factors contributing to the weight of the child.
Key points:
Birth weight prediction: Birth weight is a crucial factor in determining the health and well-being of a newborn baby. It is important to accurately predict birth weight so that medical professionals can prepare for potential complications.Factors influencing birth weight: There are several factors that can impact birth weight, including maternal health, genetics, maternal age, and lifestyle factors such as smoking, alcohol consumption, and diet.The role of smoking: Smoking during pregnancy has been linked to a reduction in birth weight. This is because chemicals from tobacco smoke can cross the placenta and harm the developing fetus.Model limitations: The model used to predict birth weight may not take into account all the factors that could impact birth weight, such as the presence of other health conditions or genetics. In addition, the sample size used to train the model may not be representative of the general population, leading to biases in the predictions.Importance of considering other factors: To obtain accurate predictions of birth weight, it is important to consider not just smoking but all the factors that could impact birth weight. This includes maternal health, genetics, and lifestyle factors, among others.Learn more about Birth weight prediction here:
https://brainly.com/question/29009821
The complete question is:
(iii) According to the model, in order to predict a birth weight of 125 ounces, the number of cigarettes smoked would have to be -10. This is not realistic as the model describes that the average birth weight of the child when the mother is not a smoker is only 119.77 ounces. This could be because the model doesn't take into account the influence of other factors in predicting the weight of the child.
The proportion of women in the sample who do not smoke while pregnant is about 85%. Does this reconcile your finding from part iii?
#SPJ4
which is the graph of y=^x-5-1?
Answer: its D
Step-by-step explanation: js trust mee :)
The number of students enrolled at a college is 16,000and grows 6% each year. Complete parts (a) through (e).
The growth of the population after .t. years would be [tex]y_t = 16000^{(1.06t)}[/tex].
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex].
Given, The number of students enrolled at a college is 16,000 and grows 6% each year.
Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.
The initial amount is 16000.
So, After t number of years, the population would be, [tex]y_t = 16000^{(1.06t)}[/tex].
learn more about exponential growth here :
https://brainly.com/question/1340582
#SPJ1
Are attitudes toward digital books changing? Sample surveys show that more people are open to reading books digitally now than in the past. A recent survey asked a random sample of 2500 U.S. adults if they agreed or disagreed with the statement, “I prefer digital books to paper books.” In this survey, 1350 agreed. A local bookstore owner claims that only 50% of all U.S. adults would say “Agree” if asked the same question.
(a) What is the sample proportion of U.S. adults who agreed with the statement?
(b) If the Kindle employee’s claim is true, what is the probability that the proportion in a random sample of 2500 U.S. adults is at least as far above 0.50 as the results of this survey?
(c) Based on your answer in part (b), do you have reason to doubt the bookstore owner’s claim?
The probability that the proportion in a random sample is 0.99997.
What is Standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
For this case we have a random sample of 2500 people, this value represent n.
We know that in the sample selected the number of people who say that prefer shop online rather than in a store are 1575.
For this case we can calculate the sample proportion with this formula:
h(p) = x/n
= 1350/ 2500
= 0.54
Now, [tex]\mu_p =[/tex] 0.54
and, [tex]\sigma_p[/tex] = √0.54 (1- 0.54)/2500
= 0.00996
and, we want to calculate the following probability:
P(p>0.50)
= 1- P(p< 0.50)
= 1 - P(z < (0.5 - 0.54)/ 0.00996)
= 1 - P(z< -4.016)
= 1- 0.00003
= 0.99997
c) For this case since the probability is very high we can conclude that the manager is correct since is very improbable that the true proportion would be lower than 0.5.
Learn more about Standard deviation here:
https://brainly.com/question/23907081
#SPJ1
