which of the following is a mathematical representation of a function that provides detailed information but can become unwieldy?
Answer:
C. Equation
Step-by-step explanation:
An equation generally provides the most specific information about a function. However, it cannot always be used for certain purposes—such as finding a specific inverse function value.
In the case of equations that are infinite series, even evaluating the function can become difficult when the series converges slowly.
Rotation
The triangle DEF with vertices D (-4, 4), E (-1, 2), F (-3, 1). Graph the figure and its image after a 90 ° clockwise rotation about its origin.
Answer:
Step-by-step explanation:
The vertices of the already rotated triangle are:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Answer:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Step-by-step explanation:
An Article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family’s financial situation, 37% would like to talk about school, and 30%would like to talk about religion. These and other sampling were based on 522 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. Express the answer in the form P hat+- E
Answer:
The estimate is [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is [tex]\r p__{hat}} = 0.37[/tex]
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]
Generally the margin of error can be mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]
=> [tex]E = 0.0348[/tex]
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is
[tex]P__{hat}} \pm E[/tex]
substituting values
[tex]0.37 \pm 0.0348[/tex]
The _________ measures the strength and direction of the linear relationship between the dependent and the independent variable.
Answer:
Correlation Coefficient
Step-by-step explanation:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet
The volume of a square pyramid is found by multiplying the area of the base by the height divided by 3.
32 = 4^2 x h/3
32 = 16 x h/3
Multiply both sides by 3
96 = 16 x h
Divide both sides by 16
H = 96/16
H = 6
The height is 6 feet
Answer:
6 ft
Step-by-step explanation:
Volume of the pyramid:
V= lwh/3, where l- base length, w- base width, h- heightGiven
V= 32 ft³l=w= 4 fth=?Then, as per formula, we can solve it for h:
32= 4×4×h/3h= 32×3/16h= 6 ftHeight of the pyramid is 6 ft
Richard is buying a subscription for video game rentals. The plan he has chosen has an
initial fee of $20 plus $2 per video game rented. This plan can be represented by the
function f(x) = 2x + 20. How much money will Richard pay this month if he rents 5 video
games?
Answer:
Richard will pay $30.
Step-by-step explanation:
Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!
6th-grade math, fill out the table! :)
Answer:
21 wins, table is attached.
Step-by-step explanation:
The ratio of 7 wins to 2 losses is 7:2. A ratio is just saying that every time one value is increased by 7, the other is increased by 2.
So we can fill out the table, in every iteration wins increases by 7 and losses increases by 2.
When we fill this out, we find that when losses is 6, wins is 21, so when you have 2 losses you have 21 wins.
Hope this helped!
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent y values? Select both in the
list
Answer:
14 and 9
Step-by-step explanation:
Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.
please help Find: ∠x ∠a ∠b
Answer:
x = 22
<a = 88°
<b = 92°
Step-by-step explanation:
To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.
To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:
[tex] (5x - 18) + (3x + 22) = 180 [/tex]
Solve for x
[tex] 5x - 18 + 3x + 22 = 180 [/tex]
[tex] 5x + 3x - 18 + 22 = 180 [/tex]
[tex] 8x + 4 = 180 [/tex]
Subtract 4 from both sides:
[tex] 8x + 4 - 4 = 180 - 4 [/tex]
[tex] 8x = 176 [/tex]
Divide both sides by 8
[tex] \frac{8x}{8} = \frac{176}{8} [/tex]
[tex] x = 22 [/tex]
=>Find <a:
According to the properties of parallel lines, alternate interior angles are equal. Therefore:
<a = 3x + 22
Plug in the value of x
<a = 3(22) + 22 = 66 + 22
<a = 88°
=>Find <b:
According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,
<b = 5x - 18
Plug in the value of x to find <b
<b = 5(22) - 18
<b = 110 - 18 = 92°
Half of a quarter of a number is 3/4 .Find the number.
Answer:
[tex]\huge\boxed{6}[/tex]
Step-by-step explanation:
[tex]half=\dfrac{1}{2}\\\\quarter=\dfrac{1}{4}\\\\half\ of\ a\ quarter=\dfrac{1}{2}\cdot\dfrac{1}{4}=\dfrac{1\cdot1}{2\cdot4}=\dfrac{1}{8}\\\\\text{Let}\ n-\text{number}\\\\\text{The equation:}\\\\\dfrac{1}{8}n=\dfrac{3}{4}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{1}{8\!\!\!\!\diagup}n=8\cdot\dfrac{3}{4}\\\\n=\dfrac{24}{4}\\\\n=6[/tex]
Need answer now in 10 min!!!
Answer:
40 deg
Step-by-step explanation:
The vertical sides of the rectangle are parallel, so the triangle is a right triangle.
The triangle is a right triangle, so the acute angles are complementary.
The bottom right angle of the triangle measures 90 - 50 = 40 deg.
The bottom line and the top side of the rectangle are parallel, so corresponding angles are congruent. x and the 40-deg angle are corresponding angles, so they are congruent.
x = 40 deg.
What does 20 * 1 * 2 equal?
Answer:
40
Step-by-step explanation:
20 * 1
= 20
20 * 2
= 40
Answer:
40
Step-by-step explanation:
The first step is to multiply 20 by 1. Whenever you multiply something by 1, it will always stay the same no matter what.
20*1=20
The next step is to multiply by 2. When multiplying anything by two, it is the same as adding the same number to itself. so
20*2=40 or 20+20=40
Hope this helps. Feel free to ask any follow-up questions if you are still confused
Have a great day! :)
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas and in increasing order.d
When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].
Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.
* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.
A factory manufactures chairs and tables, each requiring the use of three operations: cutting, assembly, and finishing. The first operation can use at most 40 hours; the second at most 42 hours; and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 for a table, what is the maximum revenue? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.
Answer:
z(max) = 650 $
x₁ = 10 units
x₂ = 15 units
Step-by-step explanation:
That is a linear programming problem, we will use a simplex method to solve it
Formulation:
Let´s call x₁ number of chairs and x₂ number of tables then :
Item (in hours) cutting assembly finishing Profit ($)
Chairs (x₁) 1 2 1 20
Tables (x₂) 2 1 1 30
Availability 40 42 25
Objective Function
z = 20*x₁ + 30x₂ ( to maximize) subject to:
x₁ + 2x₂ ≤ 40
2x₁ + x₂ ≤ 42
x₁ + x₂ ≤ 25
x₁ , x₂ >= 0
Using excel or any other software we find:
z(max) = 650
x₁ = 10
x₂ = 15
The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674
Let x represent chairs, and y represent tables
So, the given parameters are:
Cutting:
Chairs: 1 hourTable: 2 hoursHour available: 40So, the constraint is:
[tex]\mathbf{x + 2y \le 40}[/tex]
Assembly:
Chairs: 2 hoursTable: 1 hourHour available: 42So, the constraint is:
[tex]\mathbf{2x + y \le 42}[/tex]
Finishing:
Chairs: 1 hourTable: 1 hourHour available: 25So, the constraint is:
[tex]\mathbf{x + y \le 25}[/tex]
The unit profit on the items are:
Chairs: $20Table: $30So, the objective function to maximize is:
[tex]\mathbf{Max\ z = 20x + 30y}[/tex]
And the constraints are:
[tex]\mathbf{x + 2y \le 40}[/tex]
[tex]\mathbf{2x + y \le 42}[/tex]
[tex]\mathbf{x + y \le 25}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Using graphical method (see attachment for graph), we have the following feasible points:
[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]
Calculate the objective function using the feasible points.
[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]
[tex]\mathbf{z = 650}[/tex]
[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]
[tex]\mathbf{z = 580}[/tex]
[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]
[tex]\mathbf{z = 673.5}[/tex]
Approximate
[tex]\mathbf{z = 674}[/tex]
Hence, the maximum revenue is 674
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Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function? 0.02 0.98 1.02 1.98
Step-by-step explanation:
Hal is expected to use 0.98, the reason is that 2% of $10,000 will give $200
i.e (2/100)*10,000= $200.
therefore 10,000-200= $9800.
Since the money is decreasing by 2%, we have 100-2= 98% = 0.98
hence when 10,000 is multiplied by 0.98 we have $200 which is 2% of $10,000
Answer:
It's B.
Step-by-step explanation:
I just took the test.
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answer: 0.06x
Step-by-step explanation:
An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.The given statement: A number is 30% of 20% of the number x.
The required algebraic expression would be:
30% of 20% of x
[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex] [we divide a percentage by 100 to convert it into decimal]
[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]
Hence, the required algebraic expression would be :
0.06x
Please help with this question ASAP!
You are studying for the SAT and start the first week spending 2 hours studying. You plan to increase the amount you study by 10% each week. How many hours do you study in the 8th week?
Answer:
8w : 3.8974342 ≈ 3.9 or 4 (hope it help)
Step-by-step explanation:
1w : 2
2w : 2 + 10% = 2.2
3w : 2.2 + 10% = 2.42
4w : 2.42 + 10% = 2.662
5w : 2.662 + 10% = 2.9282
6w : 2.9282 + 10% = 3.22102
7w : 3.22102 + 10% = 3.543122
8w : 3.543122 + 10% = 3.8974342
3.8974342 ≈ 3.9 or 4
Please Help!!!
Family Size. You selected a random sample of n = 31 families in your neighborhood and found the mean family size for the sample equal to 3.1, the standard deviation for the sample is 1.42? What is the 90% confidence interval for the estimate?
Step to step explanation:
Confidence interval for mean, when population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom
We assume the family size is normal distributed.
Given, n= 31 , [tex]\overline{x}=3.1[/tex], s= 1.42 ,
[tex]\alpha=1-0.9=0.10[/tex]
Critical t value for [tex]\alpha/2=0.05[/tex] and degree of 30 freedom
[tex]t_{\alpha/2}[/tex] = 1.697 [By t-table]
The required confidence interval:
[tex]3.1\pm ( 1.697)\dfrac{1.42}{\sqrt{31}}\\\\=3.1\pm0.4328\\\\=(3.1-0.4328,\ 3.1+0.4328)=(2.6672,\ 3.5328)\approx(2.67,\ 3.53)[/tex]
Hence, the 90% confidence interval for the estimate = (2.67, 3.53)
A 6-ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.
Answer:
25
Step-by-step explanation:
150/6
The Unit rate of calories per ounce will be 25 calories per ounce.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Weight of the Greek yogurt container = 6 ounce
Calories per container = 150 calories
The Unit rate of calories per ounce = 150 / 6 = 25
Therefore, the unit rate of calories per ounce will be 25 calories per ounce.
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Algebra 1 worksheet inequalities
Answer:
see explanation
Step-by-step explanation:
(1)
2x - 3 ≤ 3 ( add 3 to both sides )
2x ≤ 6 ( divide both sides by 2 )
x ≤ 3
(2)
2 - 3y > 16 ( subtract 2 from both sides )
- 3y > 16
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.
y < - [tex]\frac{14}{3}[/tex]
Which one doesn’t belong? Why? Explain.
Answer:
THE M ONE
Step-by-step explanation:
IT HAS A DIFFERENT VARIABLE
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
The length, width and height are consecutive whole numbers. The volume is 120 cubic inches.
Answer:
4, 5 and 6
Step-by-step explanation:
Consecutive means right next to each other.
4 x 5 x 6 = 120 cubic inches.
4 X 5 = 20
20 X 6 = 120
The values of the consecutive numbers will be 4, 5, and 6.
Let the numbers be represented by a, a+1, and a+2.
Therefore, a(a+1)(a+2) = 120
a³ + 3a² + 2a = 120
a = 4
Therefore, a + 1 = 4+1 = 5
a + 2 = 4 + 2 = 6
Therefore, the values will be 4, 5, and 6.
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A certain variety of pine tree has a mean trunk diameter of y = 150 cm and a
standard deviation of o = 30 cm.
A certain section of a forest has 500 of these trees.
Approximately how many of these trees have a diameter smaller than 120 cm?
Answer:
80 trees have a diameter smaller than 120cm
Step-by-step explanation:
Step 1
To solve this question, we would make use of the Z score formula.
z = x - μ/σ
Where
z = z score
x = Raw score = 120cm
μ = Population mean = 150cm
σ = Population standard deviation = 30cm
Hence,
z =120 - 150/30
z = -1
The z score = -1
Step 2
We find the Probability of the calculated z score using the z score table.
P(z) = P(z = -1) = P(x<120) = 0.15866
Approximately to the nearest hundredth = 0.16
Converting to percentage = 0.16 × 100 = 16%
The percentage of trees with a diameter smaller than 120cm = 16%
Therefore, the number of trees with a diameter smaller than 120cm
= 16% × 500 trees = 80trees
What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
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, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
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Solve for x 2x^2-5=13 lesser and greater
Answer:
I got x=3,-3
Step-by-step explanation:
Squares are the results of multiplying a value by itself. The value of x in the given equation 2x² - 5 = 13 is -3 and 3.
What is square root?Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.
The value of x for the given equation 2x²-5=13, can be solved as shown below.
2x² - 5 = 13
Add 5 on both the sides of the equation,
2x² - 5 + 5 = 13 + 5
2x² = 18
Divide both the sides of the equation by 2,
2x² / 2 = 18 / 2
x² = 9
Taking the square root on both the sides of the equation,
√x² = √9
x = ±3
x = -3, 3
Hence, the value of x in the given equation 2x² - 5 = 13 is -3 and 3.
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What is the square root of -16?
Answer:-8
Step-by-step explanation:
Use Newton's method with initial approximation x1 = −1 to find x2, the second approximation to the root of the equation x3 + x + 8 = 0. (Round your answer to four decimal places.) x2 =
Answer:
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Step-by-step explanation:
The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:
[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where:
[tex]x_{i}[/tex] - i-th approximation, dimensionless.
[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.
[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.
[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.
The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:
[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]
If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]
[tex]x_{2} = -1.5000[/tex]
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Answer:
-2.5000
Step-by-step explanation:
The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224
Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
[tex]S \sim N ( 1200,60)[/tex]
the probability that the sample mean will be larger than 1224 will now be:
[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]
[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]
[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . Use 3.14 for π as necessary. - - - no lengthy explanation needed! all I need is the answer! first answer gets brainliest!
Answer:
810.66 ft²
Step-by-step explanation:
Short answer:
Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =14*20 + 530.66 = 810.66 ft²Answer: 810.66 ft²
I agree.