Answer:
a = 99
b = 51
Step-by-step explanation:
We can translate this problem into a linear equation. We know that:
2b - 3 = a
and
a + b = 150
We will start by minusing b from both sides in the second equation, giving us:
a = 150 - b
Then, we will substitute this into our second equation, giving us:
2b - 3 = 150 - b
We will add 3 and b to both sides, giving us:
3b = 153
Then we divide by 3:
b = 51
Now, we will substitute this into our second equation, giving us:
a + 51 = 150
Subtract 51 from both sides gives us:
a = 99
So, the a piece is 99 yards long, and the b piece is 51 yards long.
a = 99
b = 51
Hope this helped!
the equation y=ax describes the graph of a line.if the value of a is negative,the line
If the value of a is negative, the line is reflected across any of the axis
How to describe the line?The equation is given as:
y = ax
The new line is given as
y = -ax
The above implies that y = ax is transformed to y = -ax
The transformation can be any of:
reflection across the x-axisreflection across the y-axisHence, if the value of a is negative, the line is reflected across any of the axis
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A random sample of n D 225 and xN D 21 was drawn from a normal population with a known
standard deviation of 26:8: Calculate the 95% confidence interval of the population mean.
Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the other parameters are:
[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]
The interval is: (17.5, 24.5).
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1. Spring Time Manufacturers produces a single product and the
company is trying to determine the effectiveness of their
pricing decisions. As a consultant, you have been asked to
develop cost functions that will assist in arriving at the
optimal price that will enable the company to maximize
profits. During the year, you were provided with the following
demand and costs functions for the product:
P = 485-25Q, where P is the unit selling price and Q is quantity
of units in thousands.
TC = 5Q² +95Q + 200, where TC is total costs in thousands of
dollars.
Required:
(a) Find the output at which profit is maximized.
(b) Find the optimal price that maximizes profit.
(c) Determine the optimal sales revenue.
(d) Calculate the maximum profit.
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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Any ideas for this graph
order the decimales from leaste to gratest: 72.5, 73.943, 72.1, 73.77,
43.2 43.219 42.1 42.59
38.507 38.507 38.4 28.23 39.5
71.743 71.3 71.3 72.43 72.5
The decimals would be ordered as:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
How to Order Decimals?To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.
The decimals will be ordered as shown below:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
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Heights of men on a baseball team have a bell-shaped distribution with a mean of 176cm and a standard deviation of 5cm .Using the empirical rule,what is the approximate percentage of men between the following values?
% of the men are between 165cm and 186cm
95% men are between 165 cm and 186 cm.
What is the empirical rule?
The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.
z-score = (raw-score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean,
so, 95% men are between 165 cm and 186 cm.
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95% of men are between 165 cm and 186 cm.
What is the approximate percentage of men between the following values?Given:
The heights of men on a baseball team have a bell-shaped distribution a mean of 176cm and a standard deviation of 5cm.Find:
What is the approximate percentage of men between the following values?Solution:
The empirical rule is also referred to as the three sigma rule or the 68-95-99.7
Rule:
z - score = (raw - score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean.
So, 95% of men are between 165 cm and 186 cm.
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Which equation represents the vertex form of the equation y = x² + 2x - 6?
y = (x + 2)² -
y = (x + 1)2 - 6
y = (x + 2)²-7
y = (x + 1)²-7
Answer:
Step-by-step explanation:
Steps
1] On the right, put brackets around the 1st 2 terms.
y = (x^2 + 2x) - 6
2] Divide the second term's coefficient by 2 and square the result.
2/2 = 1
3] Square the result
1^2 = 1
4] Add that inside the brackets
y = (x^2 + 2x + 1) - 6
5] Subtract 1 outside the brackets. The original equation is still there.
y = (x^2 + 2x + 1) - 6 - 1
y = (x^2 + 2x + 1) - 7
6] What is inside the brackets is a perfect square.
y = (x + 1)^2 - 7
Answer D
Simplify. x^2+5x-/14 x²+8x+7
please send a picture of it
the equation seems a lil bit complicated
The magnitude, M, of an earthquake is represented by the equation M=2/3logE/E0 where E is the amount of energy released by the earthquake in joules and E0=10^4.4 is the assigned minimal measure released by an earthquake. Which shows a valid step in the process of calculating the magnitude of an earthquake releasing 2.5 • 10^15 joules of energy?
2.5•10^15 = 2/3logE/10^4.4
10^4.4=2/3logE/2.5•10^15
M=2/3log(9.95•10^9)
M=2/3log(2.55•10^10)
M=2/3log(9.95•10^10)
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
M = (2/3) * log (E/E₀)
Where M is the magnitude, E is the amount of energy and E₀ = 10^4..4
For E = 2.5 * 10¹⁵:
M = (2/3) * log (2.5 * 10¹⁵/10^4.4)
M = 7.33
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
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Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?
–2
–1
1
2
The value for x that is a double root of this function is x = -1
How to determine the double root?The function is given as:
f(x) = x^3 - 3x - 2
From the graph of the above function (see attachment), we have the following highlights:
The curve crosses the x-axis at x = 2The curve touches the x-axis at x = -1The point that it touches the x-axis is the double root point
Hence, the value for x that is a double root of this function is x = -1
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16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions
Answer:
Step-by-step explanation:
2x+3y=15
multiply by 2
4x+6y=30 ...(1)
6y=-4x+12
4x+6y=12 ...(2)
(1) and (2) represent parallel lines.
Hence no solution.
24g ____ 1,679mg?
Complete the inequality statement
Answer:
24g > 1,679mgWhat is the volume of this prism if a scale factor of 1.25 is applied to its dimensions?
A. 17.00 cubic units
B. 33.20 cubic units
C. 21.25 cubic units
D. 13.60 cubic units
Answer: B
Step-by-step explanation:
1: 5 × 1.25 = 6.25
2 × 1.25 = 2.5
1.7 × 1.25 = 2.125
2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic
Evaluate bh for b = 12 and h = 2. Type a numerical answer in the space provided.
The value of bh for b =12 and h = 2 is 24
How to evaluate the expression?The expression is given as:
bh
Where
b = 12 and h = 2
So, we have:
bh = 12 * 2
Evaluate
bh = 24
Hence, the value of bh for b =12 and h = 2 is 24
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PreCalc work, Need help writing piecewise functions with graphs. Giving brainliest
Answer:
f(x) = 2 for x < -2
f(x) = -2x + 11 for x > 3
Marina has a pattern to make bows that requires 1/4 yard of ribbon for each bow. Part A: Fill in the table to show how many bows she can make from a given length of ribbon.
the table complete is:
x y
1 4
2 8
3 12
4 16
Where x is the ribbon length in yards and y is the number of bows she can make.
How to complete the table?We know that Marina needs 1/4 yards of ribbon for each bow.
Then, with one yard of ribbon, she can make 4 bows, then the relation between y, the number of bows she can make, and x, the yards of ribbon that she has, is:
y = 4*x
Now we want to complete the table:
x y
1
2
3
4
To do so, we just need to evaluate the above function.
when x = 1.
y = 4*1 = 4
When x = 2:
y = 4*2 = 8
when x = 3
y = 4*3 = 12
when x = 4
y = 4*4 = 16
Then the table complete is:
x y
1 4
2 8
3 12
4 16
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The two-way table shows the number of students in a class who like mathematics and/or science. Like Mathematics Do Not Like Mathematics Total Like Science 18 ? 38 Do Not Like Science 16 6 32 Total 34 26 70
The missing number is 20.
What is the missing number?Subtraction is the mathematical operation that is used to find the difference between two or more numbers.
In order to find the missing number, subtract the total number of people who like science and mathematics from the total number of people who like science
38 - 18 = 20
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ION 10
answered
out of 1.00
Flag
n
What is the likelihood of Jada investing with Bank JNC if the following holds under the following conditions?
..
there is a 75% chance Jada will invest if the economic conditions remain stable;
there is a 25% chance investing if economic conditions suffer a decline;
there is a 55% chance of investing if the economic conditions improve.
the chance the economic conditions remaining stable (S), declining (D) and improving (1) are 0.20, 0.40
and 0.40, respectively.
Select one:
O.a. 0.135
O b. 0.103
OC. 0.400
O d. 0.470
Answer:
a
Step-by-step explanation:
look at the picture
Answer:
C
Step-by-step explanation:
x²-9x<-8
x²-9x+(-9/2)²<-8+(-9/2)²
(x-9/2)²<-8+81/4
(x-9/2)²<(-32+81)/4
(x-9/2)²<49/4
|x-9/2|<7/2
-7/2<x-9/2<7/2
add 9/2
9/2-7/2<x-9/2+9/2<7/2+9/2
2/2<x<16/2
1<x<8
The graph of the discrete probability to the right represents
the number of live births by a mother 40 to 44 years old
who had a live birth in 2015. Complete parts (a) through (d)
below.
0.30-
0.25-
0.20
0.15
0.10
0.05
0.00
0
0.235
1
0.270
2
0784
113 0101
-4426-0004 0.045
3
6
Number of Live Births
(a) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth live birth in that year?
(Type an integer or a decimal)
(b) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year?
(Type an integer or a decimal.)
(c) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year?
(Type an integer or a decimal)
(d) If a 40-to 44-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had?
The values of the probabilities are
The probabilities are 0.109, 0.202, 0.106The expected number of births is 3How to determine the probabilities?The image that completes the question is added as an attachment
The probability of having her fourth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
Hence, the probability is 0.109
The probability of having a live birth in her fourth or fifth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
P(x) = 0.093 when x = 5
So, we have:
P(4 or 5) = 0.109 + 0.093
Evaluate
P(4 or 5) = 0.202
Hence, the probability is 0.202
The probability of having a live birth in her sixth or more live birth in that year?This is represented as:
P(x >= 6)
From the attached graph, we have:
P(x) = 0.022 when x = 6
P(x) = 0.036 when x = 7
P(x) = 0.048 when x = 8
So, we have:
P(x >= 6) = 0.022 + 0.036 + 0.048
Evaluate
P(x >= 6) = 0.106
Hence, the probability is 0.106
How many live births would you expect the mother to have had?This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8
Evaluate
E(x) = 2.986
Approximate
E(x) = 3
Hence, the expected number of births is 3
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Please Please Please help with this math problem
Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.
Mathematically, the revenue can be calculated by using the following expression:
R(x) = x × P(x)
Revenue, R(x) = x(-1/20(x) + 920)
Revenue, R(x) = x(-x/20 + 920)
Revenue, R(x) = -x²/20 + 920x.
Expressing the profit as a function of x, we have:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = -x²/20 + 920x - (80x + 6000)
P(x) = -x²/20 + 840x - 6000.
For the value of x which maximizes profit, we would differentiate the profit function with respect to x:
P(x) = -x²/20 + 840x - 6000
P'(x) = -x/10 + 840
x/10 = 840
x = 840 × 10
x = 8,400.
For the maximum profit, we have:
P(x) = -x²/20 + 840x - 6000
P(8400) = -(8400)²/20 + 840(8400) - 6000
P(8400) = -3,528,000 + 7,056,000 - 6000
P(8400) = $3,522,000.
Lastly, we would calculate the price to be charged in order to maximize profit is given by:
P(x) = -1/20(x) + 920
P(x) = -1/20(8400) + 920
P(x) = -420 + 920
P(x) = $500.
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lim
x →1+. 1- x/x² - 1
Answer: [tex]\displaystyle \boldsymbol{-\frac{1}{2}}[/tex]
================================================
Work Shown:
[tex]\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = \frac{-1}{1+1}\\\\\\\displaystyle L = -\frac{1}{2}\\\\\\[/tex]
In the second step, I used the difference of squares rule to factor.
The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.
Will mark brainliest
Find an equation of the tangent line to the function
y = 3x2
at the point P(1, 3).
Solution
We will be able to find an equation of the tangent line ℓ as soon as we know its slope m. The difficulty is that we know only one point, P, on ℓ, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point
Q(x, 3x2)
on the parabola (as in the figure below) and computing the slope mPQ of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
How to determine the equation of a line tangent to a quadratic equation by algebraic methods
Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:
m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]
m = 3 · [(x + Δx)² - x²] / Δx
m = 3 · (x² + 2 · x · Δx + Δx ² - x²) / Δx
m = 3 · (2 · x + Δ x)
If Δx = 0, then the equation of the slope of the tangent line is:
m = 6 · x
If we know that x = 1, then the slope of the tangent line is:
m = 6 · 1
m = 6
Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6
b = y - m · x
b = 3 - 6 · 1
b = - 3
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
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20) Chester bought a new car with a sticker price of $18,675. He paid 25% of the cost as a down payment. What
amount did he finance?
O a.) $14,016.25
Ob.) $14,126.25
O c.) $14,006.25
Od.) $14,106.25
Answer:
B is correct
Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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Solve. −4 3/4=x−1 1/5 What is the solution to the equation? Enter your answer as a simplified mixed number in the box.
plssssss helppp
Answer: x= -3 11/20 Decimal form: x=-3.55
Step-by-step explanation:
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.
Using the t-distribution, the critical value needed is: t = 2.2622.
How to find the critical value for the t-distribution?The critical value is found using a calculator, with two parameters:
The confidence level.The number of degrees of freedom, which is one less than the sample size.For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.
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Evaluate function expressions
Answer:
Your answer is -24.
Step-by-step explanation:
Given information.
The graph of f(x) and g(x)
Solving for
-6 * f(3) - 6 * g(-1) = ?
think of f(x) = y as x is the input and y is the output.
Input a value of x into f(x) or g(x) gets us a y value.
Looking at the graph of f(3) = -2 and the graph of g(-1) = 6
Now substitute that and solve.
-6 * -2 -6 * 6 = 12 - 36 = -24
Answer: -24
Step-by-step explanation:
We should first find the outputs to the functions f and g with inputs 3 and -1 respectively. We can do this by looking at the graph and finding the y value for each desired x value.
Thus, we can see that f(3) = -2 and g(-1) is 6.
We can replace these into the expression to get
[tex]-6*-2-6*6[/tex]
We should first multiply, so we get
[tex]12 -36[/tex]
[tex]-24[/tex]
Hence, the answer is -24.
root of polynomial function f(x)=(x-3)^4(x+6)^2