Work Shown:
A = P*(1+r/n)^(n*t) .... compound interest formula
A = 200(1+0.07/1)^(1*5) .... plug in given info
A = 200*(1.07)^5
A = 200*1.4025517307
A = 280.51034614
A = 280.51
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
helppppppppp pleaseeeeeee
Answer:
Going from up to down
Box #1=0
Box #2=3
Box #3=5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Going from up to down
Box #1=0
Box #2=3
Box #3=5
Find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 7.
Answer:
The height of the right circular cylinder is 14/√3 and its radius is 7√6/3.
Step-by-step explanation:
Check the attachment for the diagram.
The volume of a right circular cylinder = πr²h
r is the radius of the cylinder
h is the height of the cylinder
V = πr²h... 1
From the diagram, we can use Pythagoras theorem on the right angled triangle to get r². From the triangle P² = r²+(h/2)²
P is the radius of the sphere.
P = 7
7² = r²+(h/2)²
r² = 49-(h/2)²... 2
Substituting equation 2 into 1:
V = π(49-(h/2)²)h
V = π(49h-h³/4)...3
To get the height h of the cylinder, we need to differentiate the volume of the cylinder with respect to h and equate to zero. i.e dV/dh = 0 since it's the maximum volume.
dV/dh = π(49-3h²/4)
0 = π(49-3h²/4)
Dividing both sides by π
0/π = π(49-3h²/4)/π
49-3h²/4 = 0
49 = 3h²/4
3h² = 49×4
3h² = 196
h² = 196/3
h = √196/√3
h = 14/√3
To get the radius of the cylinder, we will substitute h = 14/√3 into equation 2
r² = 49-(h/2)²
r² = 49-{(14/√3)/2}²
r² = 49-{14/2√3}²
r² = 49-(7/√3)²
r² = 49 - 49/3
r² = (147-49)/3
r² = 98/3
r = √98/√3
r = √49× √2/√3
r = 7√2/√3
r = 7√2/√3 × √3/√3
r = 7√6/3
The height of the right circular cylinders is 14/√3 and its radius is 7√6/3.
Mary is 2 times older than Bob and Bob is 5 years older than Sally. Sally is 10 years old how old is Bob
Answer:
Bob is 15 years old.
Step-by-step explanation:
If Sally is 10 years old and Bob is five years older than Sally then we just need to add 10+5=15.
Hope this helps!!
From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?
Answer: 0.18
Step-by-step explanation:
P(1 unit is defective)= C2 1* P^1*Q^1
C2 1= 2!/(1!*(2-1)!)=2
P=0.1 - probability that items from a production line are defective
Q=1-0.1=0.9 - probability that items from a production line are functional.
P(1 unit is defective)= 2*0.1*0.9=0.18
[URGENT] (25 points) Ryan randomly drew a marble out of a bag of marbles, then put it back. He did
this 25 times. Of the 25 times he drew a red marble 6 times. He concluded
that the probability of drawing a red marble was
6/25
Answer:
Unpredictable
Step-by-step explanation:
Cuz if u look at it it is also random and u cant predict a random thing, so its quite simply unpredictable
Question 1
A 16-ounce bag of sugar is supposed to weigh 16 ounces, but it is acceptable for the weight of the bag to vary as much as 0.4 ounce. Which absolute value inequality can be used to find X, the acceptable
weight of a bag of sugar?
Answer: I x - 16ozI ≤ 0.4oz
Step-by-step explanation:
The weight is supposed to be exactly 16 oz.
But we can accept a maximum error of 0.4oz.
Now, if x is the weight of the sugar bag, the error can be calculated as:
E = x - 16oz
if x is larger than 16oz, we have E positive, which means that we have more sugar than 16oz
if x is smaller than 16 oz, we have E negative, which means that we are a little bit short of sugar in the bag.
Now, we know that the maximum error acceptable is 0.4 oz (negative or positive)
So we can write:
-0.4oz ≤ E ≤ 0.4oz
-0.4 ≤ x - 16oz ≤ 0.4oz
Now, if we apply absolute value to the error, we get:
I x - 16ozI ≤ 0.4oz
So the correct option is the fourth one (or the bottom one)
Answer:
D.) |x−16|≤0.4
Step-by-step explanation:
144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9
What is 24-(-6) because in confused
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x)= 6x +sinx
Answer:
[tex]f(x) = x^3 -sinx +Cx+D[/tex]
Step-by-step explanation:
Given that:
[tex]f ''(x)= 6x +sinx[/tex]
We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.
We will have to integrate it twice to find the value of f(x).
Let us have a look at the basic formula of integration that we will use in the solution:
[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]
[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]
Now, integrating it again to find f(x):
[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]
h(x)=-4+16 find x when h(x)=48 Plz don't say it is incomplete
Answer:
x = -8
Step-by-step explanation:
When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!
Think of it like saying y = -4x + 16, y = 48.
48 = - 4x + 16
32 = - 4x
8 = -x
Divide by -1 both sides.
-8 = x
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below. -2(bx-5) = 16 the value of x in terms of b is. The value of x when b is 3 is.
The value of x in terms of b is x = [tex]\frac{-3}{b}[/tex]. Therefore the value of x when b = 3 is x = [tex]\frac{-3}{3}[/tex] = -1.
We can find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
- 10
-2bx = 6
÷ -2
bx = -3
÷ b
x = -3/b, which is the answer to the first part.
To get the second answer, we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
I hope this helps!
The value of x in terms of b is x = -3/b. Therefore, the value of x when b = 3 is x = -1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We need to find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
-2bx = 6
bx = -3
x = -3/b,
Now we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
The value of x in terms of b is x = -3/b.
Therefore, the value of x when b = 3 is x = -1.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ5
A population is increasing according to the exponential function defined by y = 3e^.04x, where y is in millions and x is the number of years. Which of the following should be done in order to answer the question "When will the population reach 4 million?"
A. Solve 3e^.04x=12
B. Evaluate y = 3e^.04x(4).
C. Evaluate y = 3e^.04x(1/4)
D. Solve 3e^.04x= 4.
Answer:
D. Solve 3e^0.04x= 4.Step-by-step explanation:
Given the population increasing according to the exponential function defined by y = 3e^0.04x, where y is in millions and x is the number of years, to determine when the population will reach 4 million, the following steps must be carried out.
Since y is in millions, we will first substitute y = 4 into the modeled equation as shown;
4 = 3e^0.04x
Therefore to calculate x, we need to solve the expression 3e^0.04x = 4 for the value of x and this is arrived at by simply substituting y = 4 into the given equation.
To get x;
3e^0.04x = 4
e^0.04x = 4/3
taking the ln of both sides
lne^0.04x = ln1.333
0.04x = 0.287
x = 0.287/0.04
x≈ 3.59 years
Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects.The mean and standard deviation of the reaction times (in seconds) for the fifty adult male subjects were 1.82 seconds and 0.28 seconds respectively. Previous psychological studies have shown that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived adult males is longer than that of non-sleep-deprived adult males.
A. H0:μ=1.82;Ha:μ<1.82
B. H0:μ=1.70;Ha:μ<1.70
C. H0:μ=1.82;Ha:μ>1.82
D. H0:μ=1.70;Ha:μ>1.70
E. None of the above
Answer:
D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
Find the Slope of the line
-4
1
1/4
4
Answer:
Hey there!
The slope is rise over run, or 1/-4.
This gives us the slope, which is -1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
( i mean i think it is - 1/4 but that isn't an answer choice- )
Slope (m) =
ΔY overΔX= -1 over 4 = -0.25
subtract x^1 and x^2 also y^1 and y^2
and put the answer of y' s over the answer of x 's
divide and you got your answer!
If 3 is added to the absolute value of the product of a number and –9, the result is 4.
Answer:
± (1 ÷ 9)
Step-by-step explanation:
Data provided in the question
Since 3 is added to the absolute value and -9
The result is 4
Now this information should be transformed in a mathematical equation
Let us assume be x so the product of the number and -9 be -9x
Fo rthe absolute value we use the mode. Thus the required expression is:
3 + |-9x|
Given that the result is 4
So, it would be
3 + |-9x| = 4
Now Solving the above equation which is given below:
|-9x| = 4-3
|-9x| = 1
here we will remove the mode by introducing ± sign which is shown below:
-9x = ± 1
-9x = 1 or -9x = -1
x = -1/9
or
x = [tex]\frac{1}{9}[/tex]
Therefore, the value of x is ± (1 ÷ 9).
67.805 what is the value of the 0 help please asap!
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)
assume the carrying capacity of the earth is 21 billion. use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2% per year?
Answer:
current population growth rate would be -3.1%
Step-by-step explanation:
We have to:
Growth rate = r * (1 - population / carrying capacity)
for 1960,
we have carrying capacity = 21 billion
population = 3 billion
r = Growth rate 1960 / (1 - population / carrying capacity)
replacing:
r = 0.021 / (1 - 3/21)
r = 0.0245
that is to say r = 2.45%
Now the current population would be:
= 0.0245 * (1 - carrying population / carrying capacity)
we replace:
= 0.0245 * (1 - 6.8 / 3)
= -0.031
current population growth rate would be -3.1%
The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.
Given :
Assume the carrying capacity of the earth is 21 billion. Use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion.The growth rate is given by the formula:
[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]
Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).
[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]
[tex]0.021=r\times \dfrac{18}{21}[/tex]
0.0245 = r
So, r = 2.45%.
Now, the growth rate of the current population is:
[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]
[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]
0.031 = Growth Rate
So, the growth rate is -3.1%.
For more information, refer to the link given below:
https://brainly.com/question/2096984
Construct the cumulative frequency distribution for the given data.
Age (years) of Best Actress when award was won Frequency
20-29 28
30-39 37
40-49 14
50-59 3
60-69 4
70-79 1
80-89 1
Age (years) of Best Actress when award was won Cumulative Frequency
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80
Less than 90
Answer:
Age Frequency Cumulative Frequency
Less than 30 28 28
Less than 40 37 28 + 37 = 65
Less than 50 1 4 65 + 14 = 79
Less than 60 3 79 + 3 = 82
Less than 70 4 82 + 4 = 86
Less than 80 1 86 + 1 = 87
Less than 90 1 87 + 1 = 88
Step-by-step explanation:
Given:
The Frequency Distribution table of ages of best actresses when award was won
To find:
Construct the cumulative frequency distribution
Solution:
In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40 is 37 and the previous frequency (less than 30) is 28 so in order to calculate cumulative frequency 28 i.e. previous frequency is added to 37 (frequency of less than 30) and the cumulative frequency is 65. The complete table is given above.
Which graph is defined by the function given below ? y=(x-3)(x-3)
Answer:
Graph B
Step-by-step explanation:
We are looking for a graph with a double root at x=3. In such cases, the function will "touch' the x-axis at x=3. The graph that shows such behavior is Graph B.
Answer:B
X intercepts (3,0) Y intercepts (0,9)
A manufacturer makes plastic wrap used in food packaging and aims to have a minimum breaking strength of 0.5 kg. If the mean breaking strength of a sample drops below a critical value, the production process is halted and the machinery is inspected. Which of the following is a Type 1 error in context?
A) Halting the production process when too many rubber bands break.
B) Halting the production process when the true breaking strength is below the desired level.
C) Halting the production process when the true breaking strength is within specifications.
D) Allowing the production process to continue when the true breaking strength is below specifications.
E) Allowing the production process to continue when the true breaking strength is within specifications
Answer:
Option D
Step-by-step explanation:
A type I error occurs when you reject the null hypothesis when it is actually true.
The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.
A type one error would be allowing the production process to continue when the true breaking strength is below specifications.
Select the correct solution set.
x + 17 ≤ -3
A.{x | x ≤ 14}
B.{x | x ≤ -20}
C.{x | x ≥ -20}
if sqrt((2GM)/r) = 11 km/h, what does sqrt(((8G)(M/81))/r) equal?
Answer:
((23GM)
Step-by-step explanation:
it goes for this because 23gm = 40pm
One integer is
5 less than another. The sum of their squares is
157. Find the integers.
Answer:
[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's note a and b the two numbers.
a = b - 5
[tex]a^2+b^2=157[/tex]
We replace a in the second equation and we solve it
[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]
It means that the sum of the two roots is 5 and the product is -66.
because
[tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]
And we can notice that 66 = 6 * 11 and 11 - 6 = 5
So let's factorise it !
[tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]
It means that the solutions are
(6,11) and (-6,-11)
I guess we are after positive numbers though.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The graph of an exponential function has a y-intercept of 4 and contains the point (3,500). Construct the exponential function that describes the graph.
Answer:
The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:
500 = 4 * b³
125 = b³
b = 5 so the answer is f(x) = 4 · 5ˣ.
Answer:
f(x)=4(5)x
Step-by-step explanation:
An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
A random sample of 64 observations produced a mean value of 86 and standard deviation of 4.5. The 95% confidence interval for the population mean μ is between:_________.
Answer: (84.876, 87.124)
Step-by-step explanation:
Confidence interval for population mean if population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}(\dfrac{s}{\sqrt{n}})[/tex]
, where n= sample size
s= sample standard deviation
[tex]\overline{x}[/tex] = sample mean
[tex]\alpha=[/tex] significance level
[tex]t_{\alpha/2}[/tex] = critical-t value
Given: n= 64
Degree of freedom = n-1 = 63
s= 4.5
[tex]\overline{x}[/tex] = 86
[tex]\alpha=[/tex] 0.05
[tex]t_{\alpha/2}[/tex] = 1.9983
Now, the required 95% confidence interval would be:
[tex]86\pm (1.9983)(\dfrac{4.5}{\sqrt{64}})\\\\=86\pm (1.9983)(\dfrac{4.5}{8})\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)[/tex]
The 95% confidence interval for the population mean μ is between: (84.876, 87.124)