Answer:
44%
Step-by-step explanation:
33 first-year teachers
42 experienced teachers
What % of the teachers in the meeting were Trst-year teachers?
33/(33+42)= 44%
A savings account pays interest at a rate of R% per year.
Nick invests £8 500 in the account for one year.
At the end of the year, Nick pays tax on the interest at a rate of 30%.
After paying tax, he gets £166.60
Work out the value of R.
Answer:
The Value of R is 20%.
Step-by-step explanation:
Let R be the interest rate (in percentage) per year. The interest earned after one year would be R% of £8,500, which is (R/100) * £8,500 = £(R * 85)/100.
After paying tax, the amount Nick receives would be (R * 85)/100 * (100 - 30)/100 = £(R * 85 * 70)/10000.
Since Nick receives £166.60 after paying tax, we have:
£(R * 85 * 70)/10000 = 166.60
Solving for R, we get:
R = (10000 * 166.60) / (85 * 70) = 20.0.
Therefore, the interest rate R is 20%.
3x-y=18
-2y=-6x-120
solve the system of equations!
show your work!! :)
The system is inconsistent.
The two lines are parallel and never intersect.
====================================================
Work Shown:
Solving the 1st equation for y.
3x-y=18
-y=18-3x
y = -(18-3x)
y = -18+3x
y = 3x-18
Plugging that into the other equation to solve for x.
-2y=-6x-120
-2(y)=-6x-120
-2(3x-18)=-6x-120
-6x+36=-6x-120
-6x+6x=-120-36
0x = -156
0 = -156
We arrive at a false statement.
Therefore, this system has no solutions
The system is inconsistent.
If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.
suppose that you randomly draw one card from a standard deck of 52 cards. after writing down which card was drawn, you replace the card, and draw another card. you repeat this process until you have drawn 15 cards in all. what is the probability of drawing at least 7 clubs?
The probability of drawing at least 7 clubs in 15 draws from a standard deck of 52 cards is approximately 0.496.
The number of ways to draw 7 or more clubs in 15 draws can be found by using the cumulative distribution function for the binomial distribution. This distribution models the number of successful outcomes (clubs) in n independent trials (card draws), each with the same probability of success (drawing a club). The cumulative distribution function gives the probability of getting a certain number of successful outcomes or fewer.
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The probability of a high school basketball team winning any game is 58%. This team is in a six-game tournament,
and the games are played independently of one another. Let X represent the number of games the team might win
in this tournament. What are the mean and standard deviation of X?
The mean (expected value) of X is 3.48, and the standard deviation of X is 1.27.
Basketball Game Win StatsMean (Expected Value) of X:The mean or expected value of X, representing the number of games the team might win, can be calculated using the formula:
E(X) = n * p
where:
n = number of games (6)
p = probability of winning each game (0.58)
So, E(X) = 6 * 0.58 = 3.48
Standard Deviation of X:The standard deviation of X, representing the spread of the distribution, can be calculated using the formula:
SD(X) = √(n * p * (1 - p))
where:
n = number of games (6)
p = probability of winning each game (0.58)
So, SD(X) = √(6 * 0.58 * (1 - 0.58)) = 1.27
Therefore, the mean of X is 3.48, and the standard deviation of X is 1.27.
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Alex the electrician needs 34 yards of electrical wire to complete his job. He has a coil of wiring in his workshop. The coiled wire is 18 inches in diameter and is made up of 21 circles of wire. Will this coil be enough to complete the job? Let Pi be 3. 14
Alex will not be able to complete his job. According to the measurement given for the coil, the electrician will not be able to complete the job.
The circumference of the coil of wiring can be calculated with
C= 2πr
where r is the radius and π= 3.14
The radius can be calculated by dividing the diameter by 2. Then:
r= 18 inches ÷ 2
r= 9 inches
Convert 9 inches to yards (1 yard= 36 inches)
(9 inches)(1 yard ÷ 36 inches) = 0.25 yard
Substitute this radius into the formula:
C= 2(3.14)(0.25 Yard)
C= 1.57 Yard
Since there are 21 circles of wire, we need to multiply C= 1.57 yards by 21
C = (1.57 Yard)(21) = 32.97 Yard
The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.
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What iS the ratio for cos b?
Answer:
12/37
Step-by-step explanation:
Given right triangle ABC with sides AB=37, BC=12, and CA=35, you want the cosine of angle B.
CosineThe cosine of an angle in a right triangle is ...
Cos = Adjacent/Hypotenuse
The leg adjacent to angle B is BC=12. The hypotenuse is AB=37.
Using these values, the cosine of B is ...
cos(B) = BC/BA
cos(B) = 12/37
solve the following systems of linear equations using substitution
6x - y = -7 and 5x + y = -4
Answer:
(-1,1)
Step-by-step explanation:
1. Rearrange either equation to isolate one of the variables. Lets use 6x - y = -7 :
6x - y = -7
-y = -7 - 6x
y = 7+6x
2. Now use this definition of x in the second equation:
5x + y = -4
5x + (7+6x) = -4
11x = -11
x = -1
3. Now use x = -1 in either equation to find y:
6x - y = -7
6 (-1) - y = -7
-y = -1
y = 1
The solution is (-1,1)
See the attached graph.
A shop sells bagels for $5 per dozen. You can use the table to answer the questions. Explain your reasoning.
number of bagels price in dollars
12 5
How many bagels can you buy for $50?
The number of bagels when you buy for $50 will be 120 bagels.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A shop sells bagels for $5 per dozen.
Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,
y / x = 5 / 12
12y = 5x
The number of bagels when you buy for $50 will be given as,
12(50) = 5x
600 = 5x
5x = 600
x = 120
The number of bagels when you buy for $50 will be 120 bagels.
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Your friend determines whether x and y are proportional. Is your friend correct? Explain
Answer: How can you tell whether X and Y are proportional?
Step-by-step explanation: How can you tell whether X and Y are proportional?
To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional. please select brainiest if right
A small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years. in the first year of the agreement, the country will keep its emissions at 115,000 kilotons and the emissions will decrease by 1.6% in each successive year. how many total kilotons of carbon dioxide would the country emit over the course of the 11 year period, to the nearest whole number?
The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be 2.23 x 10 ⁻¹⁵ kilotons.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years.
The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be calculated as:-
Amount = 115000 x ( 0.016)¹¹
Amount = 2.23 x 10 ⁻¹⁵ kilotons.
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3. the table below shows world population size from different points in history. create a function to model this data. what type of model best fits the data? what would the expected world population be in 2017? research and compare your prediction with the known value.
A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value.
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.
To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.
Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.
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The complete question is
I need help on this hmh assignment
The diagram shows the graph of y = x² - 4x + 6, with a tangent drawn to the
curve at x = 3.
Use the tangent to estimate the gradient of the curve at
=
3.
What is the geometric number between 16 and 64.
Hi there, here's your answer:
Geometric mean between 2 numbers a and b: [tex]\sqrt{ab}[/tex]
Therefore, the geometric mean between 16 and 64 will be
[tex]\sqrt{16*64}[/tex] = [tex]\sqrt{1024}[/tex] = 32.
Hope it helps!
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Solve for x
80°
45°
11x
Given two parallel lines. Solve for x.
The value of x, given the parallel lines and the angles involved, can be found to be 12. 3 .
How to find the value of x ?The angles on the parallel lines are drawn such that 11 x and 45 degrees are supplementary angles .
This means that they add up to 180 degrees .
The value of x can therefore be found to be :
11 x + 45 = 180
11 x = 180 - 45
11 x = 135
x = 135 / 11
x = 12. 3
In conclusion, the value of x is 12. 3 .
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Is (x − 2) a factor of f(x) = x3 − 2x2 + 2x + 3? Use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
(x - 2) is not a factor of f(x)
Step-by-step explanation:
We can use the Remainder Theorem to check if (x - 2) is a factor of f(x) = x^3 - 2x^2 + 2x + 3.
The Remainder Theorem states that if we evaluate a polynomial at a specific value and the result is zero, then that value must be a root of the polynomial and therefore the polynomial can be divided by the corresponding linear factor.
So, if we plug in x = 2 into f(x), we get:
f(2) = 2^3 - 2 * 2^2 + 2 * 2 + 3
= 8 - 8 + 4 + 3
= 7
Since f(2) is not equal to zero, it follows that (x - 2) is not a factor of f(x).
Alternatively, we could use the Factor Theorem, which states that a polynomial is divisible by (x - a) if and only if f(a) = 0. Since f(2) is not equal to zero, (x - 2) is not a factor of f(x).
Algebra 1
Write an exponential function that is in the family of
f(x) = 2x with a vertical shrink and translation down 5?
Image attached
The exponential function of the family f(x) = 2^x with a vertical shrink and a translation down 5 units is given as follows:
A. f(x) = 0.5(2)^x - 5.
How to define the function?The parent function is defined as follows:
f(x) = 2^x.
For the vertical shrink, the function is multiplied by a constant that has an absolute value less than one, hence:
f(x) = 0.5(2)^x.
For the translation down 5 units, the number 5 is subtracted from the definition of the function, hence:
A. f(x) = 0.5(2)^x - 5.
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suppose that the length of a certain rectangle is two centimeters more than three times its width. if the area of the rectangle is 33 square centimeters, find its length and width.
The rectangle measures 6 centimetres in width and 18 centimetres in length.
The rectangle's length is two millimetres longer than its width. As a result, the length (L) is equal to 3(W) + 2, where W is the rectangle's width. Additionally, we are aware that the rectangle (A) has a 33 square centimetre area. In order to find W, we can apply the formula A = L x W. 33 = 3W2 + 2W because it is (3(W) + 2) x W. The quadratic equation can be used to find W, which equals 6. This indicates that the rectangle has a width of 6 centimetres and a length of 3(6)+2=18 cm.
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Using the credit card from question 13,(you have a credit card that has a balance of $3,589.90 and a credit limit of $5,000.) if you have a good credit rating, how much must you pay at the end of the month to get the balance to the acceptable debt ratio percentage
You must pay $2,089.90 at the end of the month to bring the balance to the acceptable debt ratio percentage.
How to determine the amount to payFrom the question, we have the following parameters that can be used in our computation:
Balance = $3589.90
Credit limit = $5000
To determine the acceptable debt ratio percentage, we make use of 30% minimum credit utilization rate.
So, the acceptable balance on the credit card is:
Balance = $5,000 * 30% = $1,500.
Since the current balance is $3,589.90, we have
Payment = $3,589.90 - $1,500
Payment = $2089.9
So, you must pay $2,089.90
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why does the solution of c(r) in 3d spherical coordinates behave differently than the solution of c(x) in 1d coordinates from problem 2? discuss in 1-2 sentences.
The solution of c(r) in 3D spherical coordinates behaves differently because in 3D, there are radial and angular dimensions.
What do you mean 3D coordinates?3D coordinates refers to the system of three-dimensional spatial representation of an object, where each point in 3D space is represented by a set of three values, also known as coordinates. These coordinates are typically written in the form (x, y, z), where x, y, and z represent the values along the three axes of a three-dimensional coordinate system.
3D coordinates are commonly used in computer graphics, engineering, and mathematics to describe the positions and orientations of objects in 3D space. In computer graphics, for example, objects are often represented using 3D coordinates to specify their position, orientation, and size in the virtual world. In engineering and mathematics, 3D coordinates are used to describe the positions of points in three-dimensional space and to perform transformations, such as rotations and translations, on these points.
The 3D coordinate system is a fundamental tool for visualizing, analyzing, and manipulating objects in three-dimensional space, and it provides a powerful way to describe complex 3D shapes, geometric relationships, and physical interactions.
The solution of c(r) in 3D spherical coordinates behaves differently than the solution of c(x) in 1D coordinates because in 3D, there are radial and angular dimensions to consider, which can affect the overall behavior of the solution. Additionally, the spherical coordinates take into account the spherical symmetry of the problem, while the 1D coordinates do not.
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Please help
Find CD.
1.) 4.5
2.) 5.3
3.) 5.5
4.) 6.3
Answer:
CD = 6.3
Step-by-step explanation:
triangles CFG and CDE are similar, so their side lengths are proportional
this means CD/CF = CE/CG
since we don't know CF, we need to first solve for CF in order to find CD
luckily, we know CD = CF + FD, and FD is given:
CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG
multiply both sides by CF to get CF + FD = CE * CF / CG
move the terms with CF to one side, and the constants to the other side:
CF - CF(CE/CG) = -FD
solve for CF:
CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5
Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3
Evaluate each expression if a = 9, b = 3
15b + a^2
Answer:
126
Step-by-step explanation:
a=9
b=3
we have
15b+a^2
just substitute the value
15*3+9*9
45+81
126
Answer:
126 is your answer!
Step-by-step explanation:
15 x 3=45
9^2=81
45+81=126
Drag each expression to show whether the expression is equivalent to 24x−48 24 x - 48 , 36x+12 36 x + 12 , or neither.
The equivalent expression 36x + 12 is the same as 24x - 48. Because the statement is identical to itself, the label 24x - 48 fits it.
This equation denotes the result of multiplying 24 by x and then subtracting 48.
The phrase is referred to as "36x + 12" since it is a duplicate of itself. This formula denotes the result of multiplying 36 by x and then adding 12.
The formulations in the two scenarios cannot be compared since they use different coefficients for x and different constant terms. The word "neither" does not apply to either phrase because they are both equal to one another.
Therefore, 36x + 12 is equal to the formula 24x - 48.
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Here is a clock face. For each time given, name the number the second hand points at.
1. 15 seconds after 1:00.
2. 30 seconds after 1:00.
3. 1 minute after 1:00.
4. 5 minutes after 1:00.
Based on the given time; the number the second hand points at are;
1. 15 seconds after 1:00 - The seconds hand points at 32. 30 seconds after 1:00 - The seconds hand points at 63. 1 minute after 1:00 - The seconds hand points at 124. 5 minutes after 1:00 - The seconds hand points at 12Which number is the second hand pointing at?There are a total of 12 numbers on a clock starting from 1 and ending at 12
There are 60 strokes or lines with equal spaces on a clock
Each stroke or line represents a second
60 seconds = 1 minutes
1. 15 seconds after 1:00.
= The seconds hand points at 3
2. 30 seconds after 1:00.
The seconds hand points at 6
3. 1 minute after 1:00.
1 minutes = 60 seconds
The seconds hand points at 12
4. 5 minutes after 1:00
5 minutes = 300 seconds
The seconds hand points at 12
Therefore, the seconds hand of the given time points at 3, 6, 12 and 12 respectively.
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What expression represents the value of y?
Answer:
Second choice:
[tex]\mbox{\large y = \sqrt{wz}}[/tex]
Step-by-step explanation:
Consider the right triangle ABC
By the Pythagorean theorem,
AB² = BC² + AC²
BC = x, AC = (w + x) and AB = v
Plug in above values
(w + z)² = v² + x² (1)
In right triangle BCD,
BC² = BD² + CD²
Plugging in values we get
x² = w² + y² (2)
In right triangle ABD
AB² = BD² + AD²
v² = y² + z² (3)
Plug in values of x² from eq (2) and v² from eq 3 into equation (1) to get
(w + z)² = y² + z² +w² + y²
Left side (w + z)² = w² + 2wz + z²
==> w² + 2wz + z² = y² + z² +w² + y²
w² and z² cancel out since they are on both sides of the equation with same sign
=> 2wz = y²+y²
2wz = 2y²
Divide by 2:
wz = y²
Switch sides:
y² = wz
[tex]\mbox{\large y = \sqrt{wz}}[/tex]
Suppose you know that ∠S and ∠Y are complementary and that m∠S = 2(m∠Y) − 30°. Find m∠Y.
Answer:
Step-by-step explanation:
Since ∠S and ∠Y are complementary, we have:
∠S + ∠Y = 90°
We also know that:
m∠S = 2(m∠Y) − 30°
Substituting the second equation into the first equation, we get:
2(m∠Y) − 30° + ∠Y = 90°
Combining like terms:
3(m∠Y) = 120°
Dividing both sides by 3:
m∠Y = 40°
Therefore, m∠Y is 40 degrees.
fwam took a taxi from his house to the airport. the taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip. write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05 and the number of miles is 13.
Finding the number of miles:Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'
Here we have
The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.
Let 'x' be the number of miles in the taxi ride
Total cost to travel 'x' mile = 3.80 + 2.25(x)
From the given data, the total fare was $33.05
=> 3.80 + 2.25(x) = 33.05
=> 2.25x = 33.05 - 3.80
=> 2.25x = 29.25
=> x = 29.25/2.25
=> x = 13
Therefore,
The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05 and the number of miles is 13.
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Resolve ax/a+x into an infinite series. Write the first 5 terms. Consider x as the variable. Then, use summation notation to create a formula for the infinite series
The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:
[tex]Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5[/tex]
The infinite series can be expressed using summation notation as:
[tex]∑_(n=1)^∞ (ax)^n / (a+x)^n[/tex]
Using the formula for a geometric series, the sum of the infinite series can be calculated as:
[tex]S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x[/tex]
Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.
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Which of the contexts below represents exponential decline or decay?
Snow was melting at a rate of 2.5 inches per hour.
O A radioactive compound decays at a rate of 19% per hour.
O A town's population grows at a rate of 9.2% every year.
Money invested in a savings account grows at an annual rate of 4.2%.
Answer:
B. A radioactive compound decays at a rate of 19% per hour.
Step-by-step explanation:
We can eliminate C. (A town's population grows at a rate of 9.2% every year.) and D. (Money invested in a savings account grows at an annual rate of 4.2%.) since both of the options show growth, not decay. That leaves us with A. and B. The problem speaks of exponential, not linear, so B. would be the answer. If they asked for the linear decline or decay, A. would be the answer.
The contexts that represents exponential decline or decay is A radioactive compound decays at a rate of 19% per hour.
About exponential decayExponential Decay is a reduction or decrease in the value of the quantity compared to the value of the previous quantity. Examples of phenomena that are classified as decay are a decrease in the price of goods and the decay of radioactive substances.
Based on the question above, option C and Option D Both options increase, It shows no decrease, so it can be ruled out.
While option B: the problem is exponential rather than linear.
If ask about linear decay, the answer is A.
A. radioactive compound decays at a rate of 19% per hour.
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How do I solve this, thx!
Answer:
Step-by-step explanation: y=22.5