Paul has a collection of nickels and
dimes that has
a total value of
& 12.50. He Has 150 coins in all. How
many dimes does paul have?
Answers
Answer:
#nickels = 50
#dimes = 100
Step-by-step explanation:
system of equations:
n + d = 150
.05n + .10d = 12.50
let n = '150 - d' and substitute this into the second equation
.05(150-d) + .10d = 12.5
7.5 - .05d + .10d = 12.5
.05d = 5
d = 5/.05
d = 100
n = 50
Related Questions
The number line below shows information about a variable, m.
Select all of the following values that m could take:
-2, 4, -3.5, 0, -5, -7
Answers
Answer: -3.5, -5, and -7
Step-by-step explanation:
all u have to do is find the numbers that are in the line and the line is continues into the negatives so -7 would be included
is 12/200 and 9/150 proportional
Answers
if there are 26 students in each third grade class and 3 third grade classes in the school , how many students will attend an assembly for third grafers if a total of 4 students absent.
Answers
Answer:
74 students would attend the assembly for third graders
Step-by-step explanation:
26 × 3 = 78
78 - 4 = 74
On a survey of 40 students, 25% said they liked winter sports. How many students said they like winter sports?
Answers
Which number is greatest?6. 23 times 10 superscript 126. 23 times 10 superscript 86. 23 times 10 superscript negative 66. 23 times 10 superscript 3.
Answers
From the given numbers, the greatest number is 23 × 10^126
The first number = 23 × 10^126
The second number = 23 × 10^86
The third number = 23 × 10^66
The fourth number = 23 × 10^3
The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten
Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10
The number with largest power of 10 = 23 × 10^126
Hence, the greatest number is 23 × 10^126
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A baseball bat strikes a ball with an average force of 2.0 x 104 Newtons. if the bat stays in contact with the ball for a distance of 5.0 x 10-3 meter, what kinetic energy will the ball acquire from the bat?
1.0 x 102 J
2.0 x 102 J
2.5 x 101 J
4.0 x 102 J
Answers
The kinetic energy will the ball acquire from the bat is 2× 10² J
According to the question
Bat stays in contact for 5.0 X 10⁻³ and the ball travels at a speed of 2.0 X 10⁴.
An object's kinetic energy is the power it has as a result of motion. It is explained as the amount of effort required to move a mass-based body from rest to the indicated velocity.
The body keeps its kinetic energy, which it acquired during acceleration, unless its speed changes.
A mass m object moving at a speed v has kinetic energy 1/2 mv² according to classical mechanics.
Favg= -1/2 MV²
K= -1 2 ( 5.0 x 10⁻³)²
K = - 1/2 ×25 × 10⁻⁶
K = 2× 10² J
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Help me with this pls i dont understand
Answers
Answer:
Slope is 6 and Y intercept is 4.. You can look the image above.
To find the x intercept you set y=0 and solve for x. So 0=-1/2x+2. x=4. So the x intercept is (4,0) the y intercept is 2
please help me its on the image please
Answers
Answer: I don’t know if you want the area or just y but anyways, y= 9
Step-by-step explanation:
The question requires a scale factor (since both triangles have similar sides (an equal ratio is a good way to think about it) the 10cm side of the large triangle is proportionate to the same side of the smaller triangle.
In other words to get that scale factor (how much one shape is bigger than the other) we need to divide the 10 by 4 (you need to use the same side you can’t do 10/6 because they are completely different sides) 10/4 = 2.5
Now we know the larger triangle is 2.5 times bigger than the smaller triangle. This means the smaller triangle is 2.5 times smaller than the big triangle. So to find the base of the larger triangle we use a similar method we used to find the scale factor (but not divide multiply because when you want to find the bigger you multiply when you want to find scale factor/ smaller you divide) so 6* 2.5= 15 and since y is not the entire base only a part of it, we can do 15(which is the entire length of the big triangle base) - 6 = 9
Therefore y=9
Determine whether the equation has One Solution, No Solution, or Infinitely Many Solutions. −3+3x=3x−1−3
Answers
Answer:
No solutions (Maybe)
Step-by-step explanation:
If you input 0 into the equation you get -3=-4, which means it has no solutions.
i need help with number seven with a full explanation please
Answers
The value of x would be 32.
What are a congruent quadrilaterals?
In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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By analyzing the figure, The value of x would be 32.
What are a congruent quadrilaterals?In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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registered voters are classified as democrat, republican, or independent. suppose that the percentage of voters registered as democrat and republican is 35% and 40%, respectively. (a) what percent of the registered voters are independent?
Answers
We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.
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My son needs help on finding percents. example. what is 53% of 80?
Answers
According to the information given in the exercise, you know that the 100% is 80.
Let be "x" the number that is the 53% of 80.
By definition, you can write 53% as a Decimal number by dividing it by 100. Then, this is:
\(\frac{53}{100}=0.53\)You can write 100% as a Decimal number:
\(\frac{100}{100}=1\)Knowing the above, you can set up the following proportion:
\(\frac{80}{1}=\frac{x}{0.53}\)Now you must solve for "x":
\(\begin{gathered} (0.53)(80)=x \\ x=42.4 \end{gathered}\)The answer is:
\(42.4\)Darin receives a $3,000 commission for the first 10 cars he sells and 450 for each additional car he sells. Which of the following expresses the commission C, in dollars, Darin receives if he sells x cars in a month, where x > 10 ?
A. C= 450x + 3, 000
B. C= 450x-1,500
C. C = 350x - 1, 50c
D. C = 450x + 1, 500
Answers
Answer:
A C= 450x + 3,000
Step-by-step explanation:
if Darin sells more than 10 cars, you have to multiplicate 450 * x (number bigger than 10) plus 3000
The power, P(watts), of a car engine is proportional to the square of its speed, s(m/s).
When s=45 P=2200.
Work out the speed (to 1 DP) when the power is 1890 watts
Answers
The speed of the car is 41.7 m/s when the power is 1890 watts.
What is Proportion?Proportion is defined as an equation on which two or more ratios are made to be equal to each other.
It is given that the power, P is proportional to square of the Speed,s.
If P ∝ s², then P = k s², for some constant k.
When s = 45 m/s, P = 2200 watts
k = P / s² = 2200 / 45² = 1.086
∴ when P = 1890 watts,
1890 = 1.086 × s²
s² = 1740.331
s = 41.717 ≈ 41.7 m/s
Hence, if power is proportional to the square of the speed, then, the speed of the car engine is 41.7 m/s if the power is 1890 watts.
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A researcher has conducted a survey using a simple random sample of 225 elementary teachers to create a confidence interval to estimate the proportion of elementary teachers favoring the addition of a soda machine to the cafeteria. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 25 teachers instead of 225 elementary teachers. Which of the following statements best describes how the confidence interval is affected by this change? The width of the new interval is about the same width as the original interval. The width of the new interval is about twice the width of the original interval. The width of the new interval is about one half the width of the original interval. The width of the new interval is about one third the width of the original interval. The width of the new interval is about three times the width of the original interval.
Answers
The width of the new interval is about three times the width of the original interval. As the sample size decreases, the standard error of the estimate increases, resulting in a wider confidence interval. In fact, the width of a confidence interval is inversely proportional to the square root of the sample size.
The width of a confidence interval is affected by three factors: the sample size, the level of confidence, and the variability of the data. In this case, the sample size has decreased from 225 to 25, while the level of confidence and the variability of the data have remained constant.
As the sample size decreases, the standard error of the estimate increases, resulting in a wider confidence interval. In fact, the width of a confidence interval is inversely proportional to the square root of the sample size.
To be more specific, the formula for the width of a confidence interval for a population proportion is:
Width = 2 × zα/2 × SE
where zα/2 is the critical value of the standard normal distribution corresponding to the desired level of confidence, SE is the standard error of the estimate, and the factor of 2 is used to account for the two-sided nature of the interval.
Assuming a 95% level of confidence and a sample proportion of 0.5, the standard error of the estimate for the original sample size of 225 is:
SE = sqrt[(0.5 × 0.5) / 225] = 0.033
The critical value of zα/2 for a 95% level of confidence is approximately 1.96. Therefore, the width of the original confidence interval is:
Width = 2 × 1.96 × 0.033 = 0.13
For a new sample size of 25, the standard error of the estimate becomes:
SE = sqrt[(0.5 × 0.5) / 25] = 0.1
Using the same critical value of zα/2, the width of the new confidence interval is:
Width = 2 × 1.96 × 0.1 = 0.39
Therefore, the width of the new interval is about three times the width of the original interval.
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|x|=6
pls help its for homework and I forget
Answers
Answer:
x=-6, x=6
Step-by-step explanation:
|x| means the distance that x is from zero, so there are only two real possibilities. The only two numbers are +-6.
the fox population in a certain region has a continuous growth rate of 6 percent per year. it is estimated that the population in the year 2000 was 21700.
Answers
Answer:
In 2022 the population will be 78196
Step-by-step explanation:
Nf - number of foxes = ?
No - number of foxes in 2000 = 21700
p - growth rate = 6%
n - numebr of years = 22
\(N_{f}=N_{o} * (1+\frac{p}{100})^{n}\)
\(N_{f}=21700 * (1+\frac{6}{100})^{22}\)
\(N_{f} = 78196 foxes\)
Assume a general Cobb-Douglas production function, y=Ax
1
h
1
x
2
b
2
. i) Prove that the above production function is negatively sloped and convex to the origin ii) What signs should the parameters be for the function to be well-behaved? Show your work. iii) Find the equation of the isocline defined by RTS=1, where RTS is the marginal rate of technical substitution.
Answers
i) The Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin. ii) These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative. iii) This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.
i) To prove that the Cobb-Douglas production function y = Ax^1h^1x^2b^2 is negatively sloped and convex to the origin, we need to show that the partial derivatives with respect to x1 and x2 are positive, and the second-order partial derivatives are non-negative.
Partial derivatives:
∂y/∂x1 = A *\((1 * x^1 * h^1 * x^2b^2) / x1 = A * h^1 * x^2b^2\)
∂y/∂x2 = A *\((1 * x^1 * h^1 * x^2b^2) / x2 = A * x^1 * h^1 * b^2 * x2(b^2-1)\)
The partial derivatives are positive since A, h^1, and x^1 are assumed to be positive parameters.
Second-order partial derivatives:
∂^2y/∂x\(1^2\) = \(A * h^1 * x^2b^2 > 0\)
∂^2y/∂x\(2^2\) = \(A * x^1 * h^1 * b^2 * (b^2-1) * x2(b^2-2) > 0\)
The second-order partial derivatives are non-negative since A, \(h^1,\) and \(b^2\) are assumed to be positive parameters.
Therefore, the Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin.
ii) For the function to be well-behaved, the parameters A, \(h^1,\) and \(b^2\) should have the following signs:
- A should be positive, as it represents the overall productivity level of the production function.
-\(h^1\) should be positive, as it represents the elasticity of output with respect to the input factor x1.
- \(b^2\) should be positive, as it represents the elasticity of output with respect to the input factor x2.
These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative, leading to a well-behaved and meaningful production function.
iii) The marginal rate of technical substitution (RTS) for a Cobb-Douglas production function is defined as the ratio of the marginal product of one input to the marginal product of the other input:
RTS = (∂y/∂x1) / (∂y/∂x2)
From the partial derivatives calculated earlier, we have:
RTS = \((A * h^1 * x^2b^2) / (A * x^1 * h^1 * b^2 * x2(b^2-1))\)
=\((x^2b^2) / (x^1 * b^2 * x2(b^2-1))\)
= \((x^2b^2) / (x^1 * x2(b^2-1))\)
To find the isocline defined by RTS = 1, we set RTS equal to 1:
1 =\((x^2b^2) / (x^1 * x2(b^2-1))\)
Simplifying, we get:
\(x2(b^2-1) = x^1 * x^2b^2\)
This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.
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find the median for the given data
Answers
Answer: ytdfyikf
Step-by-step explanation's r 8r 86v086v 8rp
What are the steps for using a compass and straightedge to construct the bisector of ∠g? two rays share a common endpoint labeled g, forming an obtuse angle. one ray is horizontal and points right. the second ray is inclined to horizontal in upward-left direction. drag the steps and drop them in order from start to finish. arrange responses in the correct order to answer the question. select a response, navigate to the desired position and insert response at that position. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can be moved using the up and down arrow keys or by dragging with a mouse.
Answers
The steps for using a compass and straightedge to construct the bisector will be:
1. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G.
2.Label the points of intersection as points H and J.
3. Place the point of the compass on point H and draw an arc in the interior of the angle.
4. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.
5.Label the intersection of the arcs in the interior of the angle as point K.
6. Use the straightedge to draw GK.
What is bisection?Bisection in geometry is the division of something into two equal or congruent portions, usually by a line, which is then known as a bisector. The segment bisector and the angle bisector are the most commonly used forms of bisectors.
To bisect anything implies to divide it into two equal sections. A bisector is a line that divides anything into two equal pieces. Bisectors include segment bisectors, angle bisectors, and shape bisectors. A segment bisector is a line that runs across the center of a particular segment.
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Suppose that f(x)=x^2 and g(x)=-2/3 x^2 which statement best compares the graph of g)x) with the graph of f(x)?
Answers
The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.
The correct option is C.
We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.
The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.
The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is stretched vertically and reflects over x axis(option c).
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Find the second derivative of the below function. Simplify your answer.
f(x) = (5x^4 + 3x^2) * In(x^2)
Answers
The second derivative of f(x) is f''(x) = -5x² + 92x² + 6x.
The function is f(x) = (5x⁴ + 3x²) * ln(x²) We are to find the second derivative of the function f(x).
Let's start by taking the first derivative using the product rule as follows: f(x) = u(x) * v(x)where u(x) = 5x⁴ + 3x² and v(x) = ln(x²)u'(x) = 20x³ + 6xand v'(x) = 1 / x
Now, f'(x) = u'(x) * v(x) + u(x) * v'(x) = (20x³ + 6x) * ln(x²) + (5x⁴ + 3x²) * (1 / x)
Next, we find the second derivative by using the product rule again:
f'(x) = u(x) * v'(x) + u'(x) * v(x) + u'(x) * v'(x) where u(x) = 5x⁴ + 3x² and v(x) = ln(x²)u'(x) = 20x³ + 6xand v'(x) = 1 / xThus, f''(x) = u(x) * v''(x) + 2 * u'(x) * v'(x) + u''(x) * v(x) + u'(x) * v'(x)²= (5x⁴ + 3x²) * (-1 / x²) + 2 * (20x³ + 6x) * (1 / x) + 0 + 20x³ + 6x= -5x² + 92x² + 6x
Hence, the second derivative of f(x) is f''(x) = -5x² + 92x² + 6x.
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find the multiplier for the rate of exponential growth or decay.
1) 1% growth
Answers
1% growth has a multiplier 1+0.01=1.01
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
The exponential function which models the exponential growth has a form
\(y= C(1+r)^x\)
where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1+r is a multiplier.
The exponential function which models the exponential decay has a form
\(y= C(1-r)^x\)
where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1-r is a multiplier.
Thus,
1. 1% growth has a multiplier 1+0.01=1.01;
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About how many times greater was change in price per gallon in 2007 than 2000? Show your work or explain how u determind your answer.
Answers
The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b
Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b
Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.
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you volunteered to help set up water stations for a marathon. the first station is 3.58 mi from the starting point. the second station is 5.7 mi from the first station. the third station is 3.96 mi from the second station. the last station is 7 mi from the third station. what is the distance of the last station to the finish line if a marathon is approximately 26.2 mi long?
Answers
The distance from the last water station to the finish line is approximately 5.56 miles.
To calculate the distance from the last water station to the finish line, we need to add up the distances between each consecutive water station.
The given distances are:
3.58 miles, 5.7 miles, 3.96 miles, and 7 miles.
Adding these distances together, we get:
3.58 + 5.7 + 3.96 + 7 = 20.24 miles.
This represents the total distance covered from the starting point to the last water station.
To find the remaining distance from the last water station to the finish line, we subtract the total distance covered from the marathon's total distance:
26.2 - 20.24 = 5.96 miles.
Therefore, the distance from the last water station to the finish line is approximately 5.56 miles. This indicates the remaining distance that participants need to cover after passing the last water station to reach the finish line of the marathon.
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Kayla's father throws Kayla a graduation party that costs $775. He pays the DJ $250, $75 for the cake, and $5 per party guest for food. How many people were at the party?
Answers
Answer:
90 people
Step-by-step explanation:
775= 250+75+5x and solve for x
775= 325 + 5x
450 = 5x
90 = x
Answer:
90 people were at the party.
Step-by-step explanation:
250 plus 75 is 325 and 5 times 90 is 450 and 450 plus 325 is 775.
Hello what is the answer to this and the domain
Answers
We are given the following functions:
\(\begin{gathered} f(x)=7\sqrt[]{x}+6 \\ g(x)=x+6 \end{gathered}\)We are asked to determine the composite function:
\((f\circ g)(x)\)The composition of functions is equivalent to:
\((f\circ g)(x)=f(g(x))\)Therefore, we replace the value of "x" in function "f" for the function "g", therefore, we get:
\((f\circ g)(x)=f(g(x))=7\sqrt[]{x+6}+6\)Since we can't simplify any further this is the composition.
Now we are asked to determine the domain of this function. Since we have a square root, the domain must be the values of "x" where the term inside the radical is greater or equal to zero, therefore, we have:
\(x+6\ge0\)Now we solve for "x" by subtracting 6 from both sides:
\(x\ge-6\)Therefore, the domain is:
\(\lbrack-6,\infty)\)a water tank is emptied at a constant rate. at the end of the first hour it has 36000 gallons left and at the end of the sixth hour there is 21000 gallons left. how much water was there at the end of the fourth hour
Answers
There is 24000 gallons of water in the tank at the end of the fourth hour.
To determine the amount of water in the tank at the end of the fourth hour, we can calculate the rate at which the water is being emptied.
In the first hour, the tank lost 36000 gallons.
In the sixth hour, the tank lost 21000 gallons.
The difference between the gallons lost in the first and sixth hours is 36000 - 21000 = 15000 gallons.
Since the rate of water loss is constant, we can assume that the tank loses the same amount of water each hour. Therefore, the amount of water lost in each hour is 15000 / 5 = 3000 gallons.
To find the amount of water in the tank at the end of the fourth hour, we subtract the amount lost in the first four hours from the initial amount.
Initial amount - (Rate of loss × Number of hours)
36000 - (3000 × 4)
36000 - 12000
24000 gallons
Therefore, there is 24000 gallons of water in the tank at the end of the fourth hour.
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The quadratic function h(t) = 16t2 models the height (in feet) at time t (in seconds). A person drops an egg off the roof of a building from a height of 92 feet.
a) How long does it take the egg to pass by a window at a height of 20 feet?
Answers
The time it take the egg to pass by a window at a height of 20 feet is 2.18 secs
What are quadratic equations?Given the quadratic equation that models the height as h(t) = 16t^2If a person drops an egg off the roof of a building from a height of 92 feet, then;
96 - 20= 16t^2
t^2 = 76/16
t = 2.18secs
Hence the time it takes the egg to pass by a window at a height of 20 feet is 2.18 secs
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an experiment of study times versus test scores found a correlation coefficient of r = 0.49. how would you describe this relationship?
Answers
The correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores. This suggests that as study times increase, there is a tendency for test scores to also increase. However, the relationship is not extremely strong.
The correlation coefficient, denoted by 'r', ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. In this case, the correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores.
It's important to note that the correlation coefficient of 0.49 falls between 0 and 1, closer to 1. This suggests that there is a tendency for test scores to increase as study times increase, but the relationship is not extremely strong. Other factors may also influence test scores, and the correlation coefficient does not imply causation.
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