Given two points on a line, we can find its slope using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(7,0) \\ \Rightarrow slope=\frac{10-7}{3-0}=\frac{3}{3}=1 \end{gathered}[/tex]Thus, the slope is equal to 1.
The temperature in a town is 26.2F during the day and -11.2F during the night Find the difference in the temperatures.
what is the differience
The difference in the temperatures of the town is -37.4 degrees Fahrenheit.
What is the difference between the two values?The difference between two values refers to the result of a subtraction operation.
A subtraction operation has the following parts: minuend, subtrahend, and difference.
In this situation, the minuend is 26.2F while the subtrahend is -11.2F.
Thus, the difference results from subtracting -11.2F from 26.2F, which is -37.4F, showing that the temperature is reduced by -37.4F to reach -11.2F during the night.
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compute the mean median mode * 63.373 Point 486.81 05.21 28.4 101.5 94.7 + 116.9
Mean = Sum of points/ number of points
Median
The measure of a supplement of an angle is 35 more than twice the complement of the angle. Find the measures of the angle, its supplement, and its complement.
The measure of the angle is 35°. The complement is 55° and the supplement is 145°.
How to calculate the angle?Let's measure of the angle = x
Supplementary angle of x = 180° - x
Complementary angle of x = 90° - x
By the given condition
180° - x = 2(90° - x) + 35°
Find the measure of the angle
180° - x = 2(90° - x) + 35°
⇒ 180° - x = 180° - 2x + 35°
⇒ - x = - 2x + 35°
⇒ - x + 2x = 35°
⇒ x = 35°
The measure of the angle = 35
The complement will be:
= 90° - 35° = 55°
The supplement will be:
= 180° - 35° = 155°
The concept illustrates how angles are calculated.
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PLEASE HELP ASAP
The math counts club had a party at school. There were cookies and 40 slices pizza with nothing left pizza to be shared equally. Each students had the same number of whole cookies and the name number of slices of pizza with nothing left over. How many students How many students could have been at the party? (There is more than one answer. List as many as you can)
Answer:
There could have been 5, 10, or 20 students at the party.If there were 5, each student got 4 cookies and 8 slices of pizza if there were 10, each student got 2 cookies and 4 slices of pizza if there were 20, each student got 1 cookie and 2 slices of pizza
math is hard ok
attachments below
The measurement that does not represent the dimension of the triangle is 15, 30 and 45cm
The measurement that does represent the dimension of the triangle is 4, 8 and 10 cm.
What are the measurements?Two triangles are similar if the ratio of the side lengths of the triangle are equal.
The ratio of the length of the triangles are 6 cm : 12 cm : 15 cm
Express the ratio in its simplest form - 2 cm : 4 cm : 5 cm
Ratio of 12, 24 cm and 30cm in its simplest form - 2 : 4 : 5
Ratio of 10, 20 and 25cm in its simplest form - 2 : 4 : 5
Ratio of 18, 36, 45cm in its simplest form - 2 : 4 : 5
Ratio of 15, 30 and 45cm in its simplest form - 1 : 2 : 3
Ratio of 4, 8 and 10 in its simplest form - 2 : 4 : 5
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use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 4 0 ln(3 ex) dx, n
a. Trapezoidal Rule- 9.413607
b. Midpoint Rule-9.393861
c. Simpson's Rule -9.400407
a. We use n=8 for this integral, .Δt=4-0/8=0.5
Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]
#For the Trapezoidal Rule:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]
=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]
=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]
=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]
≈9.413607
Hence, the approximate integral value using Trapezoidal rule is 9.413607
b.For the Midpoint Rule, we calculate the integral as:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]
x1 is the midpoint of the ith interval.
From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are
[0.25,0.75,1.25,2.25,2.75,3.25,3.75]
We therefore have the integral value as:
=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]
Hence, the approximate integral value using the Midpoint Rule is 9.393861
c. For the Simpson's Rule, we calculate the integral rule as follows:
Hence, the approximate integral value using the Simpson's Rule is 9.400407
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f(x) = 6 - 1/(x-4)
Determine the value that the function f approaches as the magnitude of x increases. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
The value of the function as x increases comes closer to 6 and at limit x→∝ the value is 6.
In mathematics, a limit is the value that such a function (or sequence) gains as the input (or index) gets closer to a particular value.
Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.The concept of a limit of a series is further generalized to encompass the concept of such a limit of a topological net, in addition to being strongly related to limit and indirect limit in category theory.Several different converging ideas can be defined on function spaces. This sometimes relies on how frequently the area is set up. Two well-known examples of function spaces having a notion of convergence are Lp spaces and Sobolev space.Given the function is [tex]f(x) = 6-\frac{1}{x-4}[/tex]
Now we put the limit to the function as [tex]lim_{x\rightarrow \infty} f(x)[/tex]
Therefore :
[tex]lim_{x\rightarrow \infty} (6-\frac{1}{x-4})\\=lim_{x\rightarrow \infty} 6 - lim_{x\rightarrow \infty}\frac{1}{x-4}\\=6 - 0\\=6[/tex]
Hence the value of the function is 6.
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The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
The area of the circle is 67.1 cm² rounded to
1 decimal place.
The area of the square is 12.3 cm² truncated
to 1 decimal place.
Write the error interval for the area, a, of the
shaded region
The error interval of the area a of the shaded region
What is Error Interval?
Error intervals are the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated.
Given,
Area of the circle = 67.1cm²
Area of the square = 12.3cm²
According to the question:
The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
Putting the value of Area of circle and Area of square
= 67.1cm² - 12.3cm²
= 54.8cm²
The Error interval of area a = 54.8 + 0.5 and 54.8 - 0.5
= 54.85 and 54.75
Hence, Area of shaded region is 54.85< a < 54.75
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What is the avrage length finger nails will grow in 12 months
The average length by which finger nails will grow in 12 months will be 60mm, considering that they grow by an average of 5mm every month.
As per the question statement, there is no information provided about the average monthly growth of fingernails, and we required to calculate the average length by which finger nails will grow in 12 months.
To solve this question, we assumed that, the fingernails grow by an average of 5mm every month.
Now, using the unitary method, we can form a series of Mathematical statements to solve this question, which goes as follows:
If the average monthly growth of fingernails is 5mm,
It means that, fingernails grow in 1 month, by an average of 5mm.
Therefore, they will grow in 12 months, by an average of (5 * 12) = 60mm.
Average: In Mathematics and Statistics, the mean or average refers to a central tendency among a set of values in a sample or observation, calculated by the sum of all the values in the set, divided by the number of elements in that set.To learn more about Average, click on the link below.
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Use the graph to find the value of f (x) when x = 3 for the function f (x)=-x2-4.
Answer: (3,-13)
Step-by-step explanation:
[tex]f(x)=-x^2-4\\x=3[/tex]
using long division
helo me please show your complete ssolutions
Step-by-step explanation:
Make the facts and then you can get the answer easily
Find the value of k, if x – 1 is a factor of p(x)
i) (i) p(x) = x^2+x+k
Answer:
k = -2.
Step-by-step explanation:
By the Factor Theorem, if x - 1 is a factor then p(1) = 0.
So, p(1) = (1)^2 + 1 + k = 0
k = -1 - 1
k = -2.
Gale sells 16 bags of cherries at the farmers market. Each bag weighs 1.8 pounds. How many pounds of cherries does Gale sell in all?
Number of bags= 16
Bag weight= 1.8 pounds
Then, number of pounds is
= 16x 1.8 = 28.8 pounds of cherries
The radius of the wheel of a unicycle is 14 inches. What is the
distance, in inches, that the unicycle covers after 10 full
rotations of the wheel? Use 3.14 for pi
Step-by-step explanation:
We need to find the circumference of the equation.
One circle circumference is a circle full rotation.
[tex]c = \pi(d)[/tex]
[tex]d = 2r[/tex]
[tex]c = 2r\pi[/tex]
R is 14.
[tex]c = 28\pi[/tex]
We need a rotation 10times so
[tex]10 \times 28\pi = 280\pi[/tex]
The monthly sale (in thousands of units) for the t^th month after the introduction of a product in the market is given by S = 135t/(t^2 + 50). In which earliest month would the sale (S) have been 9?
Given the following equation:
[tex]\text{ S = }\frac{135t}{t^2\text{ + 50}}[/tex]Let's determine t at S = 9.
We get,
[tex]\text{ 9 = }\frac{135t}{t^2\text{ + 50}}[/tex][tex]\frac{9(t^2+50\rparen}{9}\text{= }\frac{135t}{9}[/tex][tex]\text{ t}^2\text{ + 50 = 15t}[/tex][tex]\text{ t}^2\text{ -15t + 50}[/tex]a = 1, b = -15 and c = 50
Apply the quadratic formula:
[tex]\text{ t = x = }\frac{-\text{b }\pm\text{ }\sqrt{\text{b}^2\text{ - 4ac}}}{\text{ 2a}}[/tex][tex]\text{ = }\frac{\text{ -\lparen-15\rparen }\pm\text{ }\sqrt{(-15)^2\text{ - 4\lparen1\rparen\lparen50\rparen }}}{\text{ 2\lparen1\rparen}}[/tex][tex]=\text{ }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{ 225 - 200}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{25}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ 5}}{\text{ 2}}[/tex][tex]\text{ x}_1\text{ = }\frac{\text{ 15 + 5}}{\text{ 2}}\text{ = }\frac{20}{2}\text{ = 10th month}[/tex][tex]\text{ x}_2\text{ = }\frac{\text{ 15 - 5}}{\text{ 2}}\text{ = }\frac{\text{ 10}}{\text{ 2}}\text{ = 5th month}[/tex]Therefore, the earliest month will be either the 5th or 10th month.
Among the given choices, only the 10th month is in the choices.
Therefore, the answer is CHOICE B : 10th
A train travels 16 miles in 20 minutes . At this rate ٫ how many minutes will it take to travel 12 miles
We will establish simple proportions. If [tex]16[/tex] miles takes [tex]20[/tex] minutes, how many minutes for [tex]12[/tex] miles?
[tex]16miles/20min[/tex][tex]0.8miles/min[/tex]That makes [tex]12[/tex] miles in [tex]15[/tex] minutes.
[tex]0.8(12)=12miles/?min[/tex][tex]?=15min[/tex]Question
The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000.
Find the revenue function R when x pencils are manufactured.
Answer:C(x) = 2000+ 0.05 x
Step-by-step explanation: Cost (C) = fixed cost + (cost per pencil x number of pencils)
Since:
Fixed cost: $2000
Cost per pencil : $0.05
Replacing with the values given:
C(x) = 2000+ 0.05 x
Where x is the number of pencils manufactured.
Feel free to ask for more if needed or if you did not understand something.
Please use graph provided.
Graph the line with the slope of 4/3 and goes through the point (1,3)
The graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted
The slope of the line = 4/3
The line is passing through the point = (1,3)
Here we have to use the point slope form the line
The point slope form of the line = [tex](y-y_{1} )= m(x-x_{1})[/tex]
Where m is the slope of the line
[tex](x_{1},y_{1} )[/tex] is the coordinate of the point
Substitute the values in the equation
(y-3) = 4/3 (x-1)
y-3 = (4/3)x - 4/3
y = (4/3)x - 4/3 + 3
y = (4/3)x + 5/3
We got the slope intercept of the line.
Plot the graph using the slope intercept form of the line
Hence, the graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted
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helppppppp meeee plsssssWhich construction could this be?Inscribed SquareInscribed HexagonInscribed RectangleInscribed Octagon
1) Judging by the picture, which resembles a construction done with a compass with the same distance, therefore we can tell a regular polygon.
2) We can also trace some line segments then we'll have a:
[tex]Inscribed\:Hexagon[/tex]
what is (tan x + cot x) sin x * cos x ?
pls helppp
(tan x + cot x) sin x * cos x is 1
(tan x + cot x) sin x * cos x
= (tan x + 1 / tan x) sin x * cos x because cot x = 1 / tan x
= (((tan x) ^2 + 1) / tan x) sin x * cos x because (tan x) ^2 +1= (sec x) ^2
= (sin x / cos x) tan x
= tan x / tan x
= 1
A blank is a whole number that has more than two factors
Answer:
A composite number is a whole number greater than 1 with more than two factors.
Step-by-step explanation:
Is the shape a polygon?
Answer:
Yes
Step-by-step explanation:
Because a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
What is 2 1/2 ÷ 2 5/8
Answer: THE ANSWER IS 20/21
Step-by-step explanaTion:
Answer:
[tex]5\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]=\frac{5}{2} +\frac{21}{8}[/tex]
[tex]=\frac{40+42}{16}[/tex]
[tex]=\frac{82}{16}[/tex]
[tex]=\frac{41}{8}[/tex]
[tex]=5\frac{1}{8}[/tex]
Hope this helps
The sales tax rate is 5%. If Abdul buys a wheelbarrow priced at $79, how much tax will he
pay?
Answer:
$3.95Step-by-step explanation:
GivenPrice = $79,Sales tax = 5%.SolutionFind 5% of $79:
79 * 5/100 = 395/100 = 3.95Answer:
Abdul must pay $ 3.95.
Step-by-step explanation:
Now we have to,
→ find the amount of tax he must pay.
Then the amount will be,
→ (79/100) × 5
→ 0.79 × 5 = $ 3.95
Hence, he must pay $ 3.95.
45 divided by 3 to the power of 2 minus 37
Answer:
-32
Step-by-step explanation:
Answer:
-32
Step-by-step explanation:
45:3=15:3=5-37=-32
hope it helps
have a nice night with apples))
The function g(x) = (x + 2)2 + 4 is a transformation of the parent function f(x) = x2. Which of the following statements are true? Select all that apply.
A. Function g is the result of f being translated right 2 units and down 4 units.
B. Function g is the result of f being translated left 2 units and up 4 units.
C. The graph of function f opens upward.
D. The graph of function f opens downward.
E. The graph of function f is compressed by a factor of 2.
Answer: B. Function g is the result of f being translated left 2 units and up 4 units. and C. The graph of function f opens upward.
Step-by-step explanation:
It is translated 2 units to the left and 4 units up because in the function of a(x-h)^2k, h represents the function going left of right and k representing the function going up and down. a represents it stretching if it is greater than 1 and compressing if less than 1 and if it is negative it reflects over the x axis however here nothing changed for the a so it did not stretch nor compress nor reflect over the x axis
Use the scatter plot to answer the question.
A scatter plot with points at (negative 16, negative 7), (negative 9, negative 5), (negative 3, negative 3), (1, 2), (5, 4), (8, 3) & (14, 6).
Which function best fits the data in the scatter plot?
f(x)=2x−3f of x is equal to 2 x minus 3
f(x)=2x+1f of x is equal to 2 x plus 1
f(x)=12x−3f of x is equal to 1 half x minus 3
f(x)=12x+1
Using linear regression, the function that best fits the data in the scatter-plot is given by:
f(x) = 1/2x + 1.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the context of the problem.
The scatter-plot in this problem contains these following points:
(-16, -7), (-9, -5), (-3, -3), (1, 2), (5, 4), (8, 3) and (14,6).
Inserting these points into a calculator, the equation is given by:
f(x) = 0.46835x + 1.
Approximating the slope to 1/2 considering the given options, the function is given by:
f(x) = 1/2x + 1.
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This is question 13 from the book, on p. 436. The numbers are probably no longer accurate, but don't worry about that.) Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The mean age of Senators in the 209th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α = 0.05, is there sufficient evidence that state senators are on average younger than 60.35 (the average age Senators in Washington)?
Answer:
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
Step-by-step explanation:
Given a simple random sample, the size is 40 senators.
Since the relevant statistic is the sample mean, 60.35 years.
Calculate t as:
[tex]t=\frac{\bar{x}-\mu_{\bar{x}}}{\frac{s}{\sqrt[]{n}}}[/tex]*Significance level is 0.05.
[tex]\begin{gathered} t=\frac{60.35-55.4}{\frac{6.5}{\sqrt[]{40}}} \\ t=4.82 \end{gathered}[/tex]Area of 0.05, one-tail yields t=1.685.
Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
find the sum or difference 6 3/5 - (-2 1/5)
A. -4 2/5
B. 8 4/5
C. -8 2/5
D. 4 2/5
Answer:
B
Step-by-step explanation:
Fraction subtraction:
[tex]\sf 6 \dfrac{3}{5}-(-2\dfrac{1}{5})=6\dfrac{3}{5}+2\dfrac{1}{5}[/tex]
Convert mixed fraction to improper fraction,
[tex]\sf = \dfrac{33}{5}+\dfrac{11}{5}[/tex]
Now, add.
[tex]\sf = \dfrac{33+11}{5}\\\\=\dfrac{44}{5}[/tex]
Covert improper fraction to mixed fraction.
[tex]\sf = 8\dfrac{4}{5}[/tex]
Find the mystery number. If you multiply it by 1, then add 5, and finally subtract 2 you get 3. What is the mystery number?
The mystery number is y = 0.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), operations, variables, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Let's assume the mystery number to be y.
When we multiply it by 1, add 5, and finally subtract by 2 we obtain 3.
Using the statement we obtain the expression,
y × 1 + 5 - 2 = 3
y + 5 - 2 = 3
y + 3 = 3
Subtracting 3 from each side of the equation,
y + 3 - 3 = 3 - 3
y = 0
Hence the mystery number is 0.
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