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.
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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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.
Phyllis invested $11,000, a portion earning a simple interest rate of
2 1/2% per year and the rest earning a rate of 2% per year. After one year the total interest earned on these investments was $255.00. How much money did she invest at each rate?
She invest money at each rate
First = 1000
Second = 10,000
What is simple interest?Simple interest is a method of calculating the interest charge. The interest can be calculated as the product of principal amount, rate and time peroid.
We are given that Phyllis invested $11,000, a portion earning a simple interest rate of 2 1/2% per year and the rest earning a rate of 2% per year.
Given the following :
Amount invested = $11,000
A portion earns 2 and 1/2 % interest per year
The rest earns a rate of 2% per year
The Total Interst earned after a year = $255
Amount invested at each rate;
Let amount invested at 2 1/2% = a
Amount invested at 2% is; 11,000 - a
Simple interest = principal x rate x time
First investment :
a x 5/2% x 1
Second :
(11000 - a) x 2%
Firat investment + second = $225
a x 0.025 + (11000 - a) x 0.02 = 225
0.025a + 220 - 0.02a = 225
0.005a = 225 - 220
0.005a = 5
a = 5 / 0.005
a = 1000
Amount in first investment = 1000
Second investment = 11000 - 1000 = 10,000
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Suppose A is nxn and the equation Ax-b has a solution for each b in R" Explain why A must be invertible. [Hint Is A row equivalent to n] Choose the correct answer below. O A. If the equation Ax-b has a solution for each b in R, then A has one pivot pasition It fallows that A is row equivalent ton Therefore, A is invertible O B f the equation Ax-b has a solution for each b ın Rn nen A has a prot position n each row. Srce 4 s s ae he p os mus be on e da ona of A t o lo s hat s :There re s nven ble O C. If the equation Ax-b has a solution for each b in R" then A has a pivot position in each row Since A is square, the pivots must be on the diagonal of A. It follows that A is row equivalent to In Therefore, A is invertble O D. the equation Ax -b has a solution for each b in IR", then A does not have a pivot position in each row Since A is square, and In is square, A is row equvalent to In Therefore, A is invertible
The right response is C. A has a pivot location in each row if the equation Ax-b has a solution for each b in [tex]R^n[/tex].
The pivots must be on A's diagonal since A is square. Hence, A is a row that is identical to In. A is hence invertible.
If there is an answer to the equation Ax-b for each b in [tex]R^n[/tex], then there is an answer to the equation Ax = b for each b. This indicates that A has complete rank since the column space of A is all of [tex]R^n[/tex].
A must-have n pivot points (one in each row), and the pivots must be on the diagonal of A since A is a square matrix with complete rank.
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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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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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in a scientific study there are 10 guinea pigs,4 of which are pregnant. if are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to decimal places.
The probability that all the guinea pigs selected randomly are pregnant is 1/30 or 0.033
Given, we have 10 guinea pigs out of which 4 are pregnant. We know that probability of an event ⇒ P(E) = (No of favorable outcomes)/(No of all outcomes) . So, The probability of selecting pigs that are pregnant is :
⇒ 4/10
Now, 3 selections are made randomly. The probability that the 1st selected guinea pig will be pregnant = 4/10
The probability that the 2nd selected guinea pig will be pregnant = 3/9
The probability that the 3rd selected guinea pig will be pregnant = 2/8
Therefore, the probability of all the 3 selected guinea pigs being pregnant will be :
⇒ (4/10) x (3/9) x (2/8)
⇒ 1/30
Therefore, The probability of all the selections of pigs being pregnant without replacement rounded to 3 decimal places is 0.033 or 1/30
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The complete question will be :
In a scientific study there are 10 guinea pigs,4 of which are pregnant. if 3are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to 3 decimal places.
Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span.
S = {(1, −2, 0), (0, 0, 1), (−1, 2, 0)}
The set S spans R₃ if and only if for any vector (a, b, c) in R₃, there exist scalars x, y, and z such that z is not zero and z/2 is nonzero. This is true for all vectors in R₃, so we conclude that S spans R₃.
To determine if the set S spans R₃, we need to see if any vector in R₃ can be written as a linear combination of the vectors in S.
Let (a, b, c) be an arbitrary vector in R₃. Then we want to see if there exist scalars x, y, and z such that:
x(1, -2, 0) + y(0, 0, 1) + z(-1, 2, 0) = (a, b, c)
This is equivalent to the system of equations:
x - z = a
-2x + 2z = b
y = c
Solving for x, y, and z, we get:
x = (a - z)/2
y = c
z = (b + 2x)/2 = (b + a - z)/2
Substituting these values into the equation for the linear combination, we get:
[(a - z)/2](1, -2, 0) + c(0, 0, 1) + [(b + a - z)/2](-1, 2, 0)
= ((a - z)/2 - (b + a - z)/2, -2(a - z)/2 + 2(b + a - z)/2, 0)
= (-b/2, (3a - b)/2, z/2)
Geometrically, the set S consists of two nonparallel vectors and a vector orthogonal to the xy-plane. Thus, the subspace spanned by S is a plane in R₃ passing through the origin.
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What is the value of a?
[tex]k=\sqrt{f+f}\\f=a^2\\a=?[/tex]
In linear equation, √2a² is the value of a .
What are examples of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
k = √f + f
f = a²
k = √a² + a²
= √2a²
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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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By conversion of the markup formula, solve the following.
Note: Round your answer to the nearest whole percent.
Percent markup on cost: ?
Percent markup on selling price: 25%
Markup on cost price is 75%
Percent markup on selling price: 25%
Percent markup on cost: ?
Markup is the total profit on a particular commodity or service. It is represented as a percentage over a cost price.
Percent markup on selling price is 25% which means that a product is sold out with 25% profit,
Percent markup on cost price =100-markup on selling price
= 100-25
=75
Hence, markup on cost price is 75%
The value of Percent markup on cost nearest to the whole number is,
⇒ 75%.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The value of Percent markup on selling price is,
⇒ 25%
Hence, The value of Percent markup on cost is,
⇒ 100% - selling price
⇒ 100% - 25%
⇒ 75%
Thus, We get;
The value of Percent markup on cost is,
⇒ 75%
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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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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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Government saving equals
Select one:
a.
taxes less government expenditures.
b.
government purchases of goods and services less taxes.
c.
taxes.
d.
government purchases of goods and services plus transfer payments less taxes.
e.
transfer payments.
Government saving equals: a. taxes less government expenditures.
What is government expenditure?Government expenditure can be defined as those expenses that government has incurred and this occur when government spent on goods and services.
Government saving tend to equals taxes less government expenditure which is option A was the correct option.
Therefore we can conclude that the correct option is A.
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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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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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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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Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-8-7-6-5-4-3-2
298 165 +3
12
11
10
2
3
-8
-9
-10
-11
-12
1 2 3 4 5 6 7 8 9 10 11 12
An equation of the line in fully simplified slope-intercept form is y = -13x - 22.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data points (-2, 4), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4 = (10 - (-3))/(-3 - (-2))(x - (-2))
y - 4 = -13(x + 2)
y = -13x - 26 + 4
y = -13x - 22
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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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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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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.
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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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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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.
Benjamin considers purchasing a car for $35,000. He has been approved for a 6-
year loan for $30,000 with an interest rate of 5.25%. He also has the option to lease the car for $600 per month for 6 years with a $2,500 down payment.
Using the loan amortization formula, how much money does Benjamin save over the 6 years if he purchases the car? Do not consider the future value of the car in your answer.
Answer: Benjamin would save $11,720.48 over 6 years if he purchases the car instead of leasing it.
Step-by-step explanation:
To calculate the cost of the car if Benjamin purchases it, we can use the loan amortization formula. The formula for calculating the monthly payment of a loan is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = the monthly payment
r = the monthly interest rate (which is the annual interest rate divided by 12)
A = the loan amount
n = the total number of payments
For Benjamin's loan, the loan amount is $30,000, the interest rate is 5.25%, and the loan is for 6 years, or 72 months. Plugging these values into the formula, we get:
r = 0.0525 / 12 = 0.004375
A = $30,000
n = 72
P = (0.004375 * $30,000) / (1 - (1 + 0.004375)^(-72)) = $484.64
Therefore, Benjamin's monthly payment for the car loan is $484.64.
If Benjamin chooses to lease the car instead, he will pay $600 per month for 72 months, plus a $2,500 down payment. Therefore, the total cost of leasing the car is:
Total cost = ($600 * 72) + $2,500 = $45,700
To calculate how much money Benjamin saves by purchasing the car instead of leasing it, we can subtract the total cost of the car loan from the total cost of the lease:
Savings = Total cost of lease - Total cost of car loan
Savings = $45,700 - ($484.64 * 72)
Savings = $11,720.48
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.
95. A basketball team has won 60 games out of 80 played. It has 40 games still to play. How many of these must the team win to make its record for the season 80%?
F) 20
G) 22
H) 25
J) 30
K). none of these
Help 30 points !!!
Answer:
K. none of these (36 wins needed)
Step-by-step explanation:
1st way
80 + 40 = 120
80% of 120 = 96
96 - 60 = 36
2nd way
80 played + 40 left = 120 total
80% season record times 120 total =
12 times 8 is 96 = 80% win record
60 won 20 lost out of 80 total
120 total - 96 wins = 24 losses
96 wins 24 losses 120 total
96 wins - 60 wins = 36 wins out of 40 total
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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In 2016 the average NBA ticket for the finals was $1444. In 2017, the price increased by 20%. If this trend continues, what will be the price in 2020? Round to the nearest dollar
Answer:
Step-by-step explanation:
To find the price of the NBA ticket in 2017, we need to add 20% to the 2016 price:
Price in 2017 = $1444 + 0.20 x $1444 = $1732.80
To find the price of the NBA ticket in 2020, we need to increase the 2017 price by 20%:
Price in 2020 = $1732.80 + 0.20 x $1732.80 = $2079.36
Rounding this to the nearest dollar, we get:
Price in 2020 = $2079