Answer:
a^2 + 4a/b + 4/b^2
Step-by-step explanation:
Which of the following is equivalent to (a + b/2) ^2?
The expression (a + b/2)² is equivalent to (a² + b²/4 + ab).
What is algebraic expression?In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.
Given is the algebraic expression as -
(a + b/2)²
We can write -
(a + b/2)² = a² + (b/2)² + 2 × a × b/2
(a + b/2)² = a² + (b/2)² + ab
(a + b/2)² = a² + b²/4 + ab
Therefore, the expression (a + b/2)² is equivalent to (a² + b²/4 + ab).
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Find the derivative of the function using the definition of derivative.
State the domain of the function and the domain of its derivative.
f(x) = 1/10x-1/3
Answer:
(i) The derivative of the function is [tex]f' = \frac{1}{10}[/tex].
(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex]
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
[tex]Dom\{f'\} = \mathbb{R}[/tex]
Step-by-step explanation:
(i) Find the derivative of the function using the definition of derivative:
The derivative is defined by the following limit:
[tex]f' = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)
If we know that [tex]f(x) = \frac{1}{10}\cdot x - \frac{1}{3}[/tex], then the definition of derivative is expanded:
[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot (x+h) - \frac{1}{3}-\frac{1}{10}\cdot x +\frac{1}{3}}{h}[/tex]
[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot h }{h}[/tex]
[tex]f' = \lim_{h \to 0} \frac{1}{10}[/tex]
[tex]f' = \frac{1}{10}[/tex]
The derivative of the function is [tex]f' = \frac{1}{10}[/tex].
(ii) State the domain of the function and the domain of its derivative:
The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex]
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
[tex]Dom\{f'\} = \mathbb{R}[/tex]
help help help help help
Answer:
The maximum value is (2,9) I can't really see the question well btw
The relationship between the height of a tree and the time snice the tree was planted?
Answer:
Answer: It´s correlated. Step-by-step explanation: The graph shows that the height of the tree increases as time passes, meaning that the more time that a three has been planted the more height it has, so there´s a direct correlation between the time passing and the height of the tree.
3 |a| +5 |b| if a = −2; b = −1
WILL AWARD BRAINLIEST
Answer:
-11
Step-by-step explanation:
[tex]3( - 2) + 5( - 1)[/tex]
[tex] - 6 + ( - 5)[/tex]
[tex] - 11[/tex]
16 is the sum of a number and 2.
What is the equation?
Answer:
14
Step-by-step explanation:
[tex]x + 2 = 16 \\ x = 16 - 2 \\ x = 14[/tex]
Like this ？？？
Answer:
16 = 2 + 14
Step-by-step explanation:
Sum means to add to numbers, so we are finding x + 2 = 16.
x + 2 - 2 = 16 - 2
x = 14
Find the missing value(s) in this ratio table. Pens: 3 6 ? Pencils: 4 ? 12
Pen is 3 x 2 = 6
Pencils s 4 x 3 = 12
Please help me quick
Answer: 20 inches
Step-by-step explanation:
using pythagorean theorem according to which hypotebous ^2=altitude ^2+base^2
c^2=a^2+b^2
c^=(12)^2+(16)^2
c^2=144+256
c^2=400
c=20
What is the value of xwhen ik o h)(r)
-1?
OA.
2
OB.
-3
O C. 1
OD.
4
I NEED HELP ASAP
Answer:
4
Step-by-step explanation:
It is desired to compare the hourly rate of an entry-level job in two fast-food chains. Eight locations for each chain are randomly selected throughout the country, the selections for each chain being independent. The following hourly rates are recorded:
Chain A 4.25 4.75 3.80 4.50 3.90 5.00 4.00 3.80
Chain B 4.60 4.65 3.85 4.00 4.80 4.00 4.50 3.65
Under the assumption of normality and equal variances, can it be concluded at the 5% significance level that chain A pays more than chain B for the job under consideration?
Answer:
It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration
Step by Step Solution:
The given data are;
Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80
Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65
Using the functions of Microsoft Excel, we get;
The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25
The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478
The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625
The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649
The significance level, α = 5%
The null hypothesis, H₀: [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]
The alternative hypothesis, Hₐ: [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]
The pooled variance, [tex]S_p^2[/tex], is given as follows;
[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]
Therefore, we have;
[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]
The test statistic is given as follows;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]
The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14
At 5% significance level, the critical t = 2.145
Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration
CAN AYONE PLEASE HELP ME WITH MY HOMEWORK ILL MARK BAINLYIST
Answer: v-(kx8)
Step-by-step explanation: plz mark me brainliest
A 2p coin has a radius of 1.3 cm
A 1p coin has a diameter of 1.8 cm
Which coin has the greater area?
Answer:
hello! As I think it is 2p coin but not sure
Chin noticed 1/4 of the watches he bought needed repairs. He also noticed that 1/2 of the good watches had gold bands. If 48 of the good watches had gold bands how many watches did chin buy.
so 48 have gold and 48 is half of the good watches then there is 96 good watches and that's 3/4 of all the watches so the answer would be
128 watches in total
The nutritional chart on the side of a box of a cereal states that there are 87 calories in a 3/4 cup serving. How many calories are in 8 cups of the cereal?
Answer:
Total calories in 8 cup = 928 calories
Step-by-step explanation:
Given:
Calories in 3/4 cup of cereal = 87 calories
Find:
Total calories in 8 cup
Computation:
Total calories in 8 cup = 8 x 87 x [4/3]
Total calories in 8 cup = 928 calories
Given quadrilateral QRST - quadrilateral HIJK, QR = 10, QT = 6, and HI = 8, find KH.
Answer:
B. 24/5
Step-by-step explanation:
QR = 10
QT = 6
HI = 8
Quadrilateral QRST ~ quadrilateral HIJK, therefore, their corresponding side lengths would be proportional to each other.
This:
QR/HI = QT/HK
Plug in the values
10/8 = 6/HI
Cross multiply
10*HI = 8*6
10*HI = 48
Divide both sides by 10
HI = 48/10
HI = 24/5
Answer:
B. 24/5
Step-by-step explanation:
Hope this helps
What is the value of y in the equation 3(3y-12)=0
Answer:
y = 4
Step-by-step explanation:
use the distributive property
9y - 36 = 0
+36 +36
9y = 36
divide by 9
y = 4
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
In ΔQRS, r = 89 inches, s = 32 inches and ∠Q=116°. Find ∠R, to the nearest degree.
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
tinyurl.com/wpazsebu
In 2012 the NYC misdemeanor crimes totaled 374,364, in 2013 the total was 359,350. What was the percent change?
Answer:
-4%
Step-by-step explanation:
final value - initial value / initial value
359350 - 374364 / 374364
= -15014 / 374364
= -0.04010535201
-0.04010535201 x 100 = -4.01053520103
The value of percent change is -4%.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
In 2012, the NYC misdemeanor crimes totaled 374,364.
And, In 2013, the total was 359,350.
Now.
The percent change = ( Final value - Initial value / Initial value ) x 100
=( 359,350 - 374,364 / 374,364 ) x 100
= (-15014 / 374364) x 100
= -0.04 x 100
= - 4%
Thus, The value of percent change is -4%.
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After traveling 70 m in its dive, the submarine is at a depth of 25 m. What will the submarine’s depth be if it continues its dive for another 110 m? (NOTE: The total length of the dive is MORE than 110m!)
Answer:
Total Depth: 64.28m
Step-by-step explanation:
Assuming that the submarine is travelling at a constant rate, then we can use the information provided and apply a Rule of Three since it is basically a ratio problem. In this rule, you simply need to multiply the diagonal values of the ratio and divide by the last value to get the variable, which would be the depth after 110m
70min <=======> 25 m
110min <=======> x m
(110 * 25) / 70 = x
2750 / 70 = x
39.28 = x
We can see that at 110min the depth would be 39.28 m but since this is an additional period of time that the submarine travelled we need to add this distance to the initial 25 m to get the total depth of the submarine.
39.28m + 25m = 64.28m
Find the area of the shape shown below.
Answer:
6
Step-by-step explanation:
Area of sq:
A = bh
A = (2)(2)
A = 4
Area of triangle:
A = 1/2bh
A = 1/2(2)(2)
A = 2
Combined:
4 + 2 = 6
A circular table has an area of 75.5, what is the radius and diameter?
Answer:
r = 4.90228481 in
d = 9.80456963 in
Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)
b) What is the vertex of the parabola? (1 point)
c) What is the focus of the parabola? (2 points)
d) What is the directrix of the parabola? (2 points)
e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point
Answer:
a) The axis of symmetry is the line, y = 2
b) The vertex of a parabola is (-3, 2)
c) The focus of the parabola is (0, 2)
d) The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola
Step-by-step explanation:
a) The function for the parabola can be expressed as follows;
12·(x + 3) = (y - 2)²
The general form of the equation of the parabola is x = a·(y - k)² + h
The axis of symmetry is the line, y = k
By comparison, with the given equation of the parabola, we have;
12·(x + 3) = (y - 2)²
x = (1/12)·(y - 2)² - 3
Therefore;
a = (1/12), k = 2, h = -3
The axis of symmetry is y = k
∴ The axis of symmetry is the line, y = 2
b) The vertex of a parabola = (h, k)
∴ The vertex of a parabola = (-3, 2)
c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)
The focus of the parabola = (0, 2)
d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]
[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]
The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel
The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
It is given that the parabola equation is [tex]\rm 12(x+3)=(y-2)^2[/tex]
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We know the standard form of a parabola is:
[tex]\rm x= a(y-k)^2+h[/tex] .........(1)
We have the equation of parabola:
[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)
a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.
By comparing the equation (1) and (2), we get:
Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.
b) Vertex of the parabola = (h,k): (-3, 2)
c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],
[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]
∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]
The focus of the parabola is (0, 2)
d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]
[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]
The directrix of a is x = -6
e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry
Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
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Hey guys I think I know the answer but I cant afford to get it wrong-
Answer: $1.50 per ticket
Step-by-step explanation:
Divide 7.50 by 5 (You can do any of them. Like, 10.50/7 or 13.50/9 but you'll get the same answer.)
Once you divide them, you'll get 1.5.
$1.50 per ticket.
Not that bad
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
15
12
Answer:
x = 9
Step-by-step explanation:
[tex]a^{2} = c^{2} - b^{2}[/tex]
[tex]a^{2} = 15^{2} - 12^{2}[/tex]
[tex]a^{2} = 225 - 144[/tex]
[tex]a^{2} = 81[/tex]
[tex]\sqrt{a^2} = \sqrt{81}[/tex]
[tex]a = 9[/tex]
Solve for the length of BA and BC, round your answer to 1 decimal place
Answer:
[tex]BA = 6.0[/tex]
[tex]BC = 13.4[/tex]
Step-by-step explanation:
Given
The attached triangle
Solving (a) BA
Considering the tangent of angle C, we have:
[tex]tan\ C = \frac{BA}{AC}\\[/tex]
This gives:
[tex]tan\ 25 = \frac{BA}{12}[/tex]
Make BA the subject
[tex]BA = 12 * tan\ 25[/tex]
[tex]BA = 12 * 0.4663[/tex]
[tex]BA = 6.0[/tex] --- approximated
Solving (a) BC
Using Pythagoras theorem
[tex]BC^2 = BA^2 + AC^2[/tex]
[tex]BC^2 = 6.0^2 + 12^2[/tex]
[tex]BC^2 = 180[/tex]
Square root of both sides
[tex]BC = \sqrt{180[/tex]
[tex]BC = 13.4[/tex]
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level. What would be the appropriate alternative hypothesis if he wanted to substantiate his suspicion
Answer:
The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]
Step-by-step explanation:
At the null hypothesis, we test that the mean is equal to a certain value.
At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 238[/tex]
A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu > 238[/tex]
A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution : X~Exp (0.2)
Find the quartile 3. Round to the nearest tenth.
Answer:
The quartile 3 is 0.3
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
X~Exp (0.2)
This means that [tex]m= 0.2, \mu = \frac{1}{0.2} = 5[/tex]
Find the quartile 3.
The 3rd quartile is the 75th percentile, for which [tex]P(X \leq x) = 0.75[/tex], or [tex]P(X > x) = 1 - 0.75 = 0.25[/tex]
Since
[tex]P(X > x) = e^{-\mu x}[/tex]
[tex]e^{-5x} = 0.25[/tex]
[tex]\ln{e^{-5x}} = \ln{0.25}[/tex]
[tex]-5x = \ln{0.25}[/tex]
[tex]x = -\frac{\ln{0.25}}{5}[/tex]
[tex]x = 0.277[/tex]
Rounding to the nearest tenth, the quartile 3 is 0.3.
A line has a slope of 2 and y-intercept of -3/4 . Which if the following is an equation of the line ?
Answer: y = 2x - 3/4
Step-by-step explanation:
y = mx + b where m is the slope, and b is the y-intercept.
y = 2x - 3/4
Forty people used a popular weight loss program. The mean weight loss was 3.0 lb and the standard deviation was 4.9 lb. Use a 0.01 significance level to test the claim that the mean weight loss is greater than o lb. Use Table A-3 to find the range of values for the P-value.
Answer:
P-value < 0.005
Step-by-step explanation:
just took it
Yolanda created a scatter plot of the relationship between the number of times she visited different friends each month, y, and the distance in miles of the friends from her home, x. She calculated the equation of the trend line to be y = −3.5x + 20. Use this information to predict the number of times in one month Yolanda would visit a friend who is 4 miles from her home.
Answer:
6 times
Step-by-step explanation:
y = −3.5x + 20 ; x = 4
y = -3.5(4) + 20
y = -14 + 20
y = 6
The sum of three consecutive positive numbers is 147. Find the product of the greatest and the
smallest number.
Answer:
2400
Step-by-step explanation:
x+y+z=147
x+(x+1)+(x+2)=147
3x+3=147
3x=144
x=48
The three consecutive positive numbers are 48, 49, and 50.
48 • 50 = 2400
Answer:
2400 just believe me I’m correct
