The limiting value of the population is 1000000, and it will take approximately 49.92 months for the population to be equal to one-half of this limiting value. The correct option is A.
To find the limiting value of the population and the time it will take the population to be equal to one-half of this limiting value, we need to solve the initial-value problem:
dp/dt = 0.1P(1 - P/1000000), P(0) = 10000
To find the limiting value of the population, we need to find the value of P as t approaches infinity. We can do this by finding the equilibrium solutions of the differential equation. An equilibrium solution is a constant population size that does not change over time. It is found by setting dp/dt = 0, and solving for P.
In this case, we have:
dp/dt = 0.1P(1 - P/1000000) = 0
Solving for P, we get:
P = 0 or P = 1000000
The population size cannot be zero, so the limiting value of the population is P = 1000000.
To find the time it will take the population to be equal to one-half of this limiting value, we need to solve for the value of t when P = 500000. Unfortunately, there is no algebraic solution for this equation, so we need to use numerical methods to estimate the value of t.
One way to do this is to use a numerical solver to solve the initial-value problem. Here, we can use a computer software or a graphing calculator to solve the differential equation and find the value of P for different values of t, until we find the time at which P = 500000.
Using a graphing calculator or a computer software, we can solve the differential equation to get:
P(t) = 1000000/(1 + 999e^(-0.1t))
Using this formula, we can find the time it takes for P to reach 500000 by solving for t when P = 500000:
500000 = 1000000/(1 + 999e^(-0.1t))
1 + 999e^(-0.1t) = 2
e^(-0.1t) = 1/999
-0.1t = ln(1/999)
t = -10 ln(1/999) ≈ 49.92
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Complete question is:
A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are
a. 1000,000, 49.92
b. 500,000, 58
C. 1000,000 42
d. 1000,000 46
f(x) = 2x - 7
g(x) = 3x² - 5x - 7
Find: f(g(x))
Express in standard form
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = 6x² - 10x - 21.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The function g(x) in this problem is given as follows:
g(x) = 3x² - 5x - 7.
Hence, for the composite function in this problem, the lone instance of x in f(x) is replaced by 3x² - 5x - 7, as follows:
f(g(x)) = f(3x² - 5x - 7) = 2(3x² - 5x - 7) - 7 = 6x² - 10x - 21.
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The measures of two angles of a triangle are in the ratio of 3:4. The measure of
the third angle is 20° more than the measure of the smaller of the first two
angles. Find the measure of each angle.
The measure of each of the angles in the triangle given is 48°, 64° and 68°.
What does a Ratio define?Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b, which means that a parts of a quantity is corresponding to b parts of another quantity.
Given that,
Ratio of measures of two angles of a triangle = 3 : 4
Let x be a number such that,
Measure of smaller angle =3x
Measure of second angle = 4x
Measure of third angle is 20° more than the measure of the smaller of the first two angles.
Measure of third angle = 3x + 20
We know that sum of interior angles of a triangle = 180°
3x + 4x + (3x + 20) = 180
10x + 20 = 180
10x = 160
x = 16
Measure of smaller angle = 3x = 48°
Measure of second angle = 4x = 64°
Measure of third angle = 3x + 20 = 68°
Hence the measures of each of the angle in triangle is 48°, 64° and 68°.
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The sum of the ages of a man and his son is equal to twice the difference of that ages, the product of their ages is 507. Find their ages?.
The solution is, their ages are 13 & 39 yrs., when the sum of the ages of a man and his son is equal to twice the difference of that ages, the product of their ages is 507.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
The sum of the ages of a man and his son is equal to twice the difference of that ages,
the product of their ages is 507.
let, their ages are, a &b
now, The sum of the ages of a man and his son is equal to twice the difference of that ages,
so, we get,
a+b = 2(a-b)...(1)
and, ab = 507....(2)
we get,
from (1) we get,
solving both side,
2a - a = b + 2b
or, a = 3b
now, putting the value of a in (2),
from (2) we get,
so, 3b^2 = 507
solving we get,
b = 13
a= 39
Hence, The solution is, their ages are 13 & 39 yrs.
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Hi. Please help. each container will be made from material that costs $0.0015 per square inch. Explain how to determine the costs of each container. Then find the cost of container B. Round to the nearest cent.
PICTURES OF CONTAINER B:
The cost of each container is $0.18.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given figure we get,
container's length = 6in
width = 2.5in
height = 8in
volume of the container =120 in^3
each container will be made from material that costs $0.0015 per cubic inch.
so, the costs of each container = $0.0015* 120
= $0.18
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square root of 76 simplifying radicals
Answer:
76 can be written as the product of 2 and 38. It is given as: √ 76 = √ (2 × 38) 2 is not a perfect square. Hence, it stays within the root sign. 38 can be shown as 2 × 19. The simplified radical form of the square root of 76 is 2 √ 19.
For the piecewise function, find the values h(-6), h(0), h(1), and h(7).
- 4x-20, for x < -6
h(x) = { 1,
x + 5,
for-6≤x<1
for x ≥ 1
h(-6)= (Simplify your answer.)
...
Since x is less than -6, we use the first equation to calculate h(-6):
h(-6) = 4(-6) - 20 = -24
What do you mean by function?A function is a mathematical concept that assigns to each input value (or "argument") exactly one output value (or "image"). In other words, a function is a rule that assigns a unique output for each input value. The set of input values is called the domain of the function, and the set of output values is called the range. A function can be represented graphically as a curve, or analytically as a formula. Functions play a central role in many areas of mathematics, science, and engineering.
For x < -6, h(x) = -4x - 20. So, h(-6) = -4(-6) - 20 = 24 - 20 = 4.
For -6 ≤ x < 1, h(x) = x + 5. So, h(0) = 0 + 5 = 5.
For x ≥ 1, h(x) = 1. So, h(1) = h(7) = 1.
So, the values are:
h(-6) = 4, h(0) = 5, h(1) = h(7) = 1.
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Enrique can spend at most $2240 to renovate his home. One roll of wallpaper costs $32, and one can of paint costs $28. He needs at least 30 rolls of wallpaper and at least 20 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.
The possible combinations made by Enrique are mentioned below:
What is the combination?In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.
Formula for selection of a objects from the n objects,
N = ⁿCₐ
The graph shows a scatter plot of points and does not have the feasible region shaded to show the combinations of wallpaper and paint that Enrique can buy.
In order to graph the feasible region, the budget constraint and minimum requirements constraint need to be plotted as lines on the same graph, and the feasible region would be the region that lies between these lines and below them.
Two possible combinations that Enrique can buy are (30, 100) and (40, 80).
These points represent 30 rolls of wallpaper and 100 cans of paint, or 40 rolls of wallpaper and 80 cans of paint, respectively.
These points lie on the feasible region and satisfy both the budget constraint and the minimum requirements constraint.
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A box contains cards, number 1 to 90. A card is drawn at random from the box. Find the
probability that the selected card bears a:
(i) Two-digit number.
(ii) Perfect square number
Probability that the selected card bears a Perfect square is 1/10 and the probability that the selected card bears a two digit number is 81/90.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that a box contains cards, number 1 to 90.
A card is drawn at random from the box.
We have to find the the probability that the selected card bears a two-digit number.
In 90 cards, from 1 to 9 are single digit numbers which are 9 in number.
The remaining 81 are two-digit numbers (10 to 90). So the probability of selecting a two-digit number is
81/90
(ii) There are 9 perfect squares between 1 and 90, namely 1, 4, 9, 16, 25, 36, 49, 64, and 81.
So the probability of selecting a perfect square number is:
P(Perfect square) = 9/90 = 1/10
Hence, the probability that the selected card bears a two digit number is 81/90 and probability that the selected card bears a Perfect square is 1/10.
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Jane was shopping for oranges, which were listed $0.75 each. She brought seven oranges to the checkout lane, where she learned that there was a sale on oranges. With the discount , she was charged $ 4.30 before tax. What was the percent discount on each orange?
The percentage discount is 95 percent
What is percentage discountA percentage discount is a reduction in price that is expressed as a percentage of the original price. Percentage discounts are commonly used in retail sales and promotions to incentivize customers to make purchases.
To determine the percentage discount of the orange, we can find the original price.
0.75 * 7 = 5.25
This is the cost of orange
The total amount charged = 4.30
The discount = 5.25 - 4.30 = 0.95
The percentage discount will be;
percentage discount = 0.95 * 100 = 95%
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Julie wants to invest $3,000 into a mutual fund that pays 7% interest for 10 years. Suppose the interest were compounded monthly instead of annually. How much would the future value of the investment increase?
In a transshipment problem, which of the following statements is a correct representation of the balance-of-flow rule if Total supply < total demand
Inflow-Outflow >= S or D
I + O >= S or D
I - O <= S or D
I + O <= S or D
In a transshipment problem (c) I - O <= S or D. here s is supply and D is demand,
A model that falls within the category of transportation issues is the transshipment model. Transshipment issues come in two different flavors.
Using transient (i.e. intermediate) nodes as sources and destinations
between the sources and the destination with a few temporary nodes
In a transportation issue, the shipment may move from S1 to D1, S1 to D2, S1 to D3, S2 to D1, S2 to D2, and so forth, from one specific source to another specific destination.
In this approach, the shipment travels via one or more intermediary nodes before arriving at the final location. With this technique, the shipment can move back and forth between sources and destinations before arriving at the intended location.
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Region Ris the base of solid. For the solid, each cross section perpendicular to the y-axis is rectangle whose height is twice the length of its base in region R: Find the volume of the solid.
the volume of the solid is x²/2R.
Let x be the length of the base of the rectangle.
The volume of the solid is given by:
V = ∫R 2x dx
= 2∫R x dx
= 2[x²/2]∫R dx
= x²/2 ∫R dx
= x²/2 (R - 0)
= x²/2 R
The volume of the solid is given by the integral of the cross sectional area of the solid. The cross sectional area is a rectangle whose base is x and the height is twice the length of the base. Therefore, the area of the cross section is 2x. The volume of the solid is calculated by integrating the area over the range of the variable, which in this case is R. The integral of 2x over the range R is 2x times R (2x*R). This can be simplified to x squared over two times R (x^2/2*R). Therefore, the volume of the solid is x squared over two times R.
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The heights of a certain type of tree are approximately normally distributed with a mean height Mu = 5 ft and a standard deviation Sigma = 0.4 ft. Which statement must be true?
A tree with a height of 6.2 ft exists 3 standard deviations above the mean.
What is meant by normally distributed?The normal distribution represents a symmetrical display of data around its mean value, with the standard deviation serving as the determinant of the curve's breadth. The "bell curve" is used to visually represent it.
The normal distribution, sometimes referred to as the Gaussian distribution, is a probability distribution that is symmetric about the mean and demonstrates that data that exists closer to the mean exists more likely to even than data that exists farther from the mean. The normal distribution is depicted graphically as a "bell curve."
The majority of data points in a continuous probability distribution known as a "normal distribution" cluster around the middle of the range, while the remaining data points taper off symmetrically toward either extreme. The mean of the distribution is another name for the center of the range.
It exists said that an X value exists found Z standard deviations from the mean if:
[tex]$\frac{X-\mu}{\sigma}=Z$$[/tex]
Given:
[tex]$$\begin{aligned}& \mu=5 \mathrm{ft} \\& \sigma=0.4 \mathrm{ft}\end{aligned}$$[/tex]
We have four different values of X and we must calculate the Z-score for each
For X = 5.4 ft
[tex]$& Z=\frac{X-\mu}{\sigma} \\[/tex]
substitute the values in the above equation, we get
[tex]$ Z=\frac{5.4-5}{0.4}=1\end{aligned}$$[/tex]
A tree with a height of 5.4 ft exists 1 standard deviation above the mean
First Option: False
For X = 4.6 ft
[tex]$Z=\frac{4.6-5}{0.4}=-1\end{aligned}$$[/tex]
A tree with a height of 4.6ft exists 1 standard deviation below the mean
Second Option: False
For X = 5.8 ft
[tex]$Z=\frac{5.8-5}{0.4}=2\end{aligned}$$[/tex]
A tree with a height of 5.8 ft exists 2 standard deviation above the mean
Third Option: False
For X = 6.2 ft
[tex]$ Z=\frac{6.2-5}{0.4}=3\end{aligned}$$[/tex]
A tree with a height of 6.2 ft exists 3 standard deviations above the mean.
Therefore, the correct answer is option d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.
The complete question is;
The heights of a certain type of tree are approximately normally distributed with a mean height y = 5 ft and a standard deviation = 0.4 ft. Which statement must be true?
a) A tree with a height of 5.4 ft is 1 standard deviation below the mean
b) A tree with a height of 4.6 ft is 1 standard deviation above the mean.
c) A tree with a height of 5.8 ft is 2.5 standard deviations above the mean
d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.
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For each function x given below, find a single expression for x (i.e., an expression that does not involve multiple cases). Group similar unit-step function terms together in the expression for x. (c) x(t) = 4t +4 -1 St<-Ź 412 -
Thus, a single expression for x(t) that does not involve multiple cases is:
x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)
Using the properties of the unit step function,
we can write:
x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)
Breaking it down:
For t < 2, the unit step function u(t-2) is 0,
so it does not affect the expression for x(t).
For 2 ≤ t < 4, u(t-2) = 1 and u(t-4) = 0,
so the expression becomes:
x(t) = 4t + 4 - 1 = 4t + 3
For 4 ≤ t < 12, u(t-2) = u(t-4) = 1,
so the expression becomes:
x(t) = 4t + 4 - 2 = 4t + 2
For t ≥ 12, u(t-2) = u(t-4) = 1, and u(t-12) = 1,
so the expression becomes:
x(t) = 4t + 4 - 1 - 2 + 12 = 4t + 13
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Nancy collected 7 times as many bags of can if her friend collected 5/6 of a bag how many bags did Nancy collect
Nancy collected 5 5/6 cans of bags which is 7 times more than her friend.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Nancy collected 7 times as many bags of can and her friend collected 5/6 of a bag.
Therefore, The amount of bags of cans Nancy collected can be obtained by multiplying 7 by the number of bags of can collected by her friend which is,
= (5/6)×7 bags.
= 35/6 bags.
= 5 5/6 can of bags.
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Draw a number line from 0 to 2. Then write each of the following numbers in
its correct place on the number line.
Answer: draw a number line and plot the 0, 1 , and 2
Explanation:
hello! can i get help with this asap
Answer:
x=41,y=15
Step-by-step explanation:
The given system of equations is:
x = 41
x + 2y = 71
We can use substitution to solve for y.
Starting with the first equation:
x = 41
We can substitute the value of x into the second equation:
x + 2y = 71
41 + 2y = 71
2y = 71 - 41
2y = 30
Finally, we can solve for y by dividing both sides of the equation by 2:
y = 30 / 2
y = 15
x=41,y=15.
When two linear transformations are performed one after another, the combined effect may not always be a linear transformation. Choose the correct sin q) cos q) answer below. 0 A. True. When different types of transformations are combined, such as a rotation and a skew, the transformation is not linear except for a few special 0 B. False. A transformation is linear if T(u + v)=T(u) + T(v) and T(cu)= cT(u) for all vectors u, v, and scalars c. The first transformation results in some cases vector u, so the properties of a linear transformation must still apply when two transformations are applied True. When one transformation is applied after another, the property of a linear transformation which reads T(u + v)= T(u) +T(v) for vectors u and v will not be true. In these cases, T(u +v) instead equals T(u)T(v). C. 0 D. False. The combined effect of two linear transformations is always linear because multiplying two linear functions together will result in a function which is also linear.
D. False. The combined effect of two linear transformations is always linear because multiplying two linear functions together will result in a function which is also linear.
The statement says when two linear transformations are performed one after another, the combined effect may not always be a linear transformation.
This is false, the combined effect of two linear transformations is always linear because multiplying two linear functions together will result in a function which is also linear.
A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map.
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Dual questions for number 6 please help me out.
Step-by-step explanation:
arrange ff fraction 5/6,8/9,23
Which of the following are sources of sampling error and which are sources of nonsampling error? Explain your answers.
a. The subject lies about past illegal drug use.
b. A typing error is made in recording the data.
c. Data are gathered by asking people to go to a website and answer questions online.
a. The subject lies about past illegal drug use: This is a source of nonsampling error, as it is not related to the process of selecting a sample from a population. Rather, it is an error that arises from the behavior or characteristics of the individual being sampled.
b. A typing error is made in recording the data: This is a source of nonsampling error, as it is a mistake that occurs during the process of recording or processing the data, and is not related to the sample selection process.
c. Data are gathered by asking people to go to a website and answer questions online: This is a source of sampling error, as it can potentially lead to a biased sample. Only people who have access to the internet and are willing to answer questions online will be included in the sample, which may not be representative of the population as a whole. This type of bias is known as "self-selection bias" and is a common problem with online surveys.
Carmen reads of a page in her library book in
12
minutes. At this rate, how many minutes does
it take her to read the whole book if it has 140
pages?
Answer:
djsushf sjsushsjd sjdusbs
Step-by-step explanation:
iahsjsidjdjdudjdbdjdid
Each month, Morse budgets $2,117 for fixed expenses, $ 489 for living expenses, and $475 for annual expenses. His annual net income is $ 49,397. Describe his monthly budget by using a positive number to show how much of a surplus there is, a negative number to show how much of a deficient there is, or zero if it is a balance budget. Round answer to the nearest whole number.
Morse's monthly budget has a surplus of $3,860 (rounded to the nearest whole number).
Calculating monthly budgetFrom the we are to calculate Morse's monthly budget.
To determine Morse's monthly budget, we need to first calculate his total annual expenses:
Total Annual Expenses = Fixed Expenses + Living Expenses + Annual Expenses
= $2,117 + $489 + $475
= $3,081
Then, we can calculate his monthly budget by dividing his annual net income by 12:
Monthly Budget = Annual Net Income / 12
= $49,397 / 12
= $4,116.42
Now, we can determine Morse's monthly budget by subtracting his total monthly expenses from his monthly net income:
Monthly Budget = Monthly Net Income - Monthly Expenses
Monthly Net Income = Annual Net Income / 12 = $49,397 / 12 = $4,116.42 (rounded to the nearest cent)
Monthly Expenses = Total Annual Expenses / 12 = $3,081 / 12 = $256.75 (rounded to the nearest cent)
Monthly Budget = $4,116.42 - $256.75 = $3,859.67
Hence, Morse's monthly budget has a surplus of $3,860
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A map of a highway has a scale of 2 inchesequals33 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new map?
The distance between the rests in the new map is 0.825 inches.
How far apart are the rest stops on the new map?We know that the original scale is:
2 in = 33mi
or:
1 in = (33mi)/2
1in = 16.5 mi
And on a highway, there are 7 rests in 9 inches.
First, we transform these 9 inches to miles
9 in = 9*(16.5 mi) = 148.5 mi
If the 7 rests are evenly divided in that distance, the distance between each rest is:
148.5mi/6 = 24.75mi
(we divide by 6 because one rest is at each end, so there are 6 even spaces between the two ends)
Now, in the new map the scale is:
1 inch = 30mi
Then the distance between the rests in the new map is:
d = 24.75/30 inches
d = 0.825 inches.
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Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral 4 + Squareroot x + x/x dx
The answer of this queation :∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C
where C = C1 + C2 + C3 is the constant of integration for the entire expression.
eparate integrals:
∫ 4 dx + ∫√x dx + ∫ x/x dx
The first two integrals can be easily integrated as follows:
∫ 4 dx = 4x + C1, where C1 is a constant of integration.
∫√x dx = 2/3 x^(3/2) + C2, where C2 is a constant of integration.
For the third integral, note that x/x simplifies to 1 for all nonzero x.
∫ x/x dx = ∫ 1 dx = x + C3, where C3 is a constant of integration.
Putting it all together, we have:
∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C
where the integration constant for the entire statement is C = C1 + C2 + C3.
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Definition: If r and s are statements, r unless s means if ∼s then r. Consider the following statement. This door will not open unless a security code is entered. Which of the following expresses the statement in if-then form? If a security code is entered, then the door will not open. If the door will not open, then a security code was entered. If a security code is not entered, then the door will open. If the door will open, then a security code was not entered. If a security code is not entered, then the door will not open.
The statement "This door will not open unless a security code is entered" can be expressed in if-then form as "If a security code is not entered, then the door will not open."
This is because the statement "unless" indicates a necessary condition. In other words, the security code must be entered in order for the door to open, and if the security code is not entered, then the door will not open. Therefore, the correct option is: If a security code is not entered, then the door will not open.
The capacity to use numerical data to recognise patterns, solve problems without a pre-existing formula, understand graphs, and reach reasonable conclusions when faced with numerical evidence is known as mathematical reasoning.
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how did I write: The sum of X and one third is three fourths
In numbers aka algebraic equation
The statement as an algebrai equation is x + 1/3 = 3/4
How to dettermine the expressionFrom the question, we have the following parameters that can be used in our computation:
The sum of X and one third is three fourths
In mathematics and algebra, we have
One third = 1/3
Three fourths = 3/4
So, the statement becomes
The sum of X and 1/3 is 3/4
Express as a summation equation
This gives
x + 1/3 = 3/4
Hence, the equation is x + 1/3 = 3/4
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Brett's fish tank can hold up to 10.5 gallons of water before it overflows. Brett has poured 9 gallons of water into his fish tank so far.
Let x represent how many more gallons of water Brett can pour into his fish tank. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
Brett can pour at most
more gallons of water into his fish tank.
Answer:
x ≤ 1.5
Step-by-step explanation:
Brett can pour at most 1.5 more gallons of water into his fish tank. This is because the fish tank can only hold 10.5 gallons of water and Brett has already poured 9 gallons into the tank. So, the maximum amount of water he can pour is the remaining 1.5 gallons.
Find the missing side of each right triangle. Round answers to the nearest tenth. Match the question number with the answers below. Color the heart on the back accordingly.
The missing sides of the triangles are given below.
What is length?Length is defined as the measurement of distance of an object from one end to the other.
To find the missing sides of the given triangles.
Question 1 :
In the triangle, consider sin 90° = [tex]\frac{opposite side}{hypotenuse side}[/tex]
1 = [tex]\frac{13}{x}[/tex]
⇒ x = 13
Which is the length of the missing side of the triangle.
Question 2:
In this triangle, consider degree 63° we have to find the length of hypotenuse side, then,
sin 63° =[tex]\frac{opposite side }{hypotenuse side}[/tex] = [tex]\frac{18}{x}[/tex]
0.89 x = 18
⇒ x = 18/0.22 = 20.22.
Length of the hypotenuse side is 20.22 cm.
Question 4:
In this triangle, consider cos function.
sin 18°= [tex]\frac{opposite side}{hypotenuse}[/tex] = x/11
0.3090*11 = x
x = 3.399 = 3.4 inches.
Question 5:
consider sin angle.
sin 90° = [tex]\frac{opposite side}{hypotenuse}[/tex] = x/21
⇒x = 21 yard.
Question: 6
For this triangle we consider, tan functions.
tan 43° = [tex]\frac{opposite side}{adjacent side}[/tex] = x/23
⇒ x =21.4 mm.
Question 7:
For this triangle , we consider sin function.
sin 33° = 9/x
⇒0.5446 *x=9/0.5446
⇒x = 16.5km
Question 8:
For this triangle we have to choose tan function,
tan67 ° = opposite side/ adjacent side
= 17/x
⇒x = 7m
Question 9:
For this triangle, we take sin function.
sin 90°= opposite side/hypotenuse
1 = x/19
⇒x = 19m
Question 10:
For this triangle we consider sin function,
sin 90°= 26/x
⇒x = 26 feet.
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-4z^2-3z+5=0
How many solutions does your quadratic have based on the discriminant?
Pick TWO ways to find the specific solutions or show that there is no solution:
Quadratic Formula
Graphing
Factoring
Square Root Property
Completing the Square
The solution to the parts of the question with regards to the quadratic equation are;
The discriminant indicates that the quadratic equation has two real solutionsThe solutions of the quadratic equation -4·z² - 3·z + 5 = 0, obtained using the quadratic formula, and the completing the square method are; z = 0.804 and z = -1.55What is a quadratic equation?A quadratic equation is an equation of the form f(x) = a·x² + b·x + c
The discriminant, D, of a quadratic equation, f(x) = a·x² + b·x + c, can be obtained using the expression;
D = b² - 4 × a × c
The specified quadratic function is; -4·z² - 3·z + 5 = 0
The discriminant, D of the above quadratic expression is therefore;
D = (-3)² - 4 × (-4) × 5 = 89
The discriminant is larger than zero, therefore, the quadratic expression has two solutions.
The two method to be used to find the specific solution are;
Quadratic FormulaCompleting the squareQuadratic Formula;
The solutions of the quadratic equation based on the quadratic formula are;
z = (-(-3) ± √((-4)² - 4 × (-4) × 5))/(2 × (-4))
z = (3 ± √(89))/(-8)
z ≈ -1.55 and z ≈ 0.804Completing the Square
The completing the square method can be used as follows;
-4·z² - 3·z + 5 = 0
z² + (3/4)·z - 5/4 = 0
z² + (3/4)·z = 5/4
z² + (3/4)·z + ((3/4)/2)² = 5/4 + ((3/4)/2)²
z² + (3/4)·z + (3/8)² = 5/4 + (3/8)²
(z + (3/8))² = 5/4 + (3/8)²
z + (3/8) = ±√((5/4) + (3/8)²)
z = ±√(5/4 + (3/8)²) - (3/8)
z = √(5/4 + (3/8)²) - (3/8) ≈ 0.804 and z = -√(5/4 + (3/8)²) - (3/8) ≈ -1.55Learn more on the quadratic formula here: https://brainly.com/question/24419456
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a number (n) is increased by 10 and the result is doubled. If this result is 5 less than three times the original number (n) , what is the value of (n)
Answer:
the value of the original number (n) is 25.
Step-by-step explanation:
Let's use algebra to solve the problem.
We are told that a number (n) is increased by 10 and the result is doubled, which gives:
2(n + 10)
We are also told that this result is 5 less than three times the original number (n), which gives:
2(n + 10) = 3n - 5
Expanding the left side of the equation:
2n + 20 = 3n - 5
Subtracting 2n from both sides:
20 = n - 5
Adding 5 to both sides:
25 = n
Therefore, the value of the original number (n) is 25.