The derivative of the function f(x) is:
[tex]f'(x)=-2x[/tex]
Step-by-step explanation:We are given a function f(x) as:
[tex]f(x)=5-x^2[/tex]
We have:
[tex]f(x+h)=5-(x+h)^2\\\\i.e.\\\\f(x+h)=5-(x^2+h^2+2xh)[/tex]
( Since,
[tex](a+b)^2=a^2+b^2+2ab[/tex] )
Hence, we get:
[tex]f(x+h)=5-x^2-h^2-2xh[/tex]
Also, by using the definition of f'(x) i.e.
[tex]f'(x)= \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}[/tex]
Hence, on putting the value in the formula:
[tex]f'(x)= \lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-(5-x^2)}{h}\\\\\\f'(x)=\lim_{h \to 0} \dfrac{5-x^2-h^2-2xh-5+x^2}{h}\\\\i.e.\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2-2xh}{h}\\\\f'(x)=\lim_{h \to 0} \dfrac{-h^2}{h}+\dfrac{-2xh}{h}\\\\f'(x)=\lim_{h \to 0} -h-2x\\\\i.e.\ on\ putting\ the\ limit\ we\ obtain:\\\\f'(x)=-2x[/tex]
Hence, the derivative of the function f(x) is:
[tex]f'(x)=-2x[/tex]
Answer:
The derivative of given function is -2x.
Step-by-step explanation:
The first principle of differentiation is
[tex]f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
The given function is
[tex]f(x)=5-x^2[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{5-(x+h)^2-(5-h^2}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{5-(x^2+2xh+h^2)-5+h^2}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{5-x^2-2xh-h^2-5+h^2}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-x^2-2xh}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-x^2}{h}-\frac{2xh}{h}[/tex]
[tex]f'(x)=lim_{h\rightarrow 0}\frac{-x^2}{h}-2x[/tex]
Apply limit.
[tex]f'(x)=\frac{-x^2}{0}-2x[/tex]
[tex]f'(x)=0-2x[/tex]
[tex]f'(x)=-2x[/tex]
Therefore, the derivative of given function is -2x.
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.Step 1 of 2 : Suppose a sample of 523 suspected criminals is drawn. Of these people, 172 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer: The required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.
Step-by-step explanation:
Since we have given that
Number of suspected criminals is drawn = 523
Number of criminals were captured = 172
We need to find the proportion of people who were caught after being on the 10 Most wanted list.
So, Proportion of people who were caught is given by
[tex]\dfrac{172}{523}\\\\=0.3288\\\\\approx 0.329[/tex]
Hence, the required proportion is [tex]\dfrac{172}{523}[/tex] in fraction and [tex]0.329[/tex] in decimals.
The estimated proportion of suspected criminals caught after being on the FBI's 10 Most Wanted list is 0.329, or 32.9%, based on a sample where 172 out of 523 individuals were captured.
Explanation:To estimate the proportion of people who were caught after being on the FBI's 10 Most Wanted list, we can use the sample data provided. In the sample, 523 suspected criminals were monitored and 172 were captured. The estimated proportion of individuals caught is calculated by dividing the number of people captured by the total number in the sample.
To find this proportion, we perform the following calculation:
Proportion = Number of people captured / Total number of suspected criminals
Proportion = 172 / 523
Proportion = 0.329 (rounded to three decimal places)
So, the estimated proportion of people who were caught after appearing on the list is approximately 0.329, or 32.9%.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk, C is the curve of intersection of the plane x + z = 8 and the cylinder x2 + y2 = 81.
By Stokes' theorem,
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]
where [tex]S[/tex] is the surface with [tex]C[/tex] as its boundary. The curl is
[tex]\nabla\times\vec F(x,y,z)=2\,\vec\imath-x\,\vec k[/tex]
Parameterize [tex]S[/tex] by
[tex]\vec\sigma(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(8-u\cos v)\,\vec k[/tex]
with [tex]0\le u\le9[/tex] and [tex]0\le v\le2\pi[/tex]. Then take the normal vector to [tex]S[/tex] to be
[tex]\vec\sigma_u\times\vec\sigma_v=u\,\vec\imath+u\,\vec k[/tex]
Then the line integral is equal to the surface integral,
[tex]\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9(2\,\vec\imath-u\cos v\,\vec k)\cdot(u\,\vec\imath+u\,\vec k)\,\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle=\int_0^{2\pi}\int_0^9(2u-u^2\cos v)\,\mathrm du\,\mathrm dv=\boxed{162\pi}[/tex]
If F(x,y) = x^2sin(xy), find Fyx.
Answer:
[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
Step-by-step explanation:
We need to find out the partial differential [tex]F_{yx}[/tex] of [tex]F(x,y)=x^{2}sin(xy)[/tex]
First, differentiate [tex]F(x,y)=x^{2}sin(xy)[/tex] both the sides with respect to 'y'
[tex]\frac{d}{dy}F(x,y)=\frac{d}{dy}x^{2}sin(xy)[/tex]
Since, [tex]\frac{d}{dt}\sin t =\cos t[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times \frac{d}{dy}(xy)[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{2}cos(xy)\times x[/tex]
[tex]\frac{d}{dy}F(x,y)=x^{3}cos(xy)[/tex]
so, [tex]F_y=x^{3}cos(xy)[/tex]
Now, differentiate above both the sides with respect to 'x'
[tex]F_{yx}=\frac{d}{dx}x^{3}cos(xy)[/tex]
Chain rule of differentiation: [tex]D(fg)=f'g + fg'[/tex]
[tex]F_{yx}=cos(xy) \frac{d}{dx}x^{3} + x^{3} \frac{d}{dx}cos(xy)[/tex]
Since, [tex] \frac{d}{dx}x^{m} =mx^{m-1}[/tex] and [tex] \frac{d}{dt} cost =-\sin t[/tex]
[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times \frac{d}{dx}(xy)[/tex]
[tex]F_{yx}=cos(xy)\times 3x^{2} - x^{3} sin(xy)\times y[/tex]
[tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
hence, [tex]F_{yx}=3x^{2} cos(xy)- yx^{3} sin(xy)[/tex]
The probability that a college student belongs to a health club is 0.3. The probability that a college student lives off-campus is 0.4. The probability that a college student belongs to a health club and lives off-campus is 0.12. Find the probability that a college student belongs to a health club OR lives off-campus. Tip: P(A or B) = P(A) + P(B) - P(A and B) 0.54 0.58 0.70 0.82
Answer:
The correct option is 2.
Step-by-step explanation:
Let A be the event that the college student belongs to a health club and B be the event that the college student lives off-campus.
The probability that a college student belongs to a health club is 0.3.
[tex]P(A)=0.3[/tex]
The probability that a college student lives off-campus is 0.4.
[tex]P(B)=0.4[/tex]
The probability that a college student belongs to a health club and lives off-campus is 0.12.
[tex]P(A\cap B)=0.12[/tex]
The probability that a college student belongs to a health club OR lives off-campus is
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(A\cup B)=0.3+0.4-0.12[/tex]
[tex]P(A\cup B)=0.58[/tex]
The probability that a college student belongs to a health club OR lives off-campus is 0.58. Therefore the correct option is 2.
Please need help in these 3 algebra questions !!!!
7. Add: (3s2 + 7s + 2) + (5s2 + 9s – 1)
A. 8s2 + 16s + 3
B. 8s4 + 16s + 1
C. 8s2 + 16s + 1
D. –2s2 – 2s + 1
8. (–3t2u3)(5t7u8) = _______.
A. –15t14u24
B. 2t9u11
C. –15t–5u–5
D. –15t9u11
11. The square of a number is equal to 6 more than the number. Find all such numbers.
A. –4; –3
B. –2
C. 3; –2
D. –3
Answer:
[tex]\large\boxed{7.\ B.\ 8s^2+16s+1}\\\\\boxed{8.\ D.\ -15t^9u^{11}}\\\\\boxed{11.\ C.\ 3,\ -2}[/tex]
Step-by-step explanation:
[tex]7.\\(3s^2+7s+2)+(5s^2+9s-1)=3s^2+7s+2+5s^2+9s-1\\\\\text{combine like terms}\\\\=(3s^2+5s^2)+(7s+9s)+(2-1)\\\\=8s^2+16s+1[/tex]
[tex]8.\\(-3t^2u^3)(5t^7u^8)=(-3\cdot5)(t^2t^7)(u^3u^8)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=-15t^{2+7}u^{3+8}=-15t^9u^{11}[/tex]
[tex]11.\\n-the\ number\\\\n^2=n+6\qquad\text{subtract}\ n\ \text{and}\ 6\ \text{from both sides}\\\\n^2-n-6=0\\\\n^2+2n-3n-6=0\\\\n(n+2)-3(n+2)=0\\\\(n+2)(n-3)=0\iff n+2=0\ \vee\ n-3=0\\\\n+2=0\qquad\text{subtract 2 from both sides}\\n=-2\\\\n-3=0\qquad\text{add 3 to both sides}\\n=3[/tex]
In a college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 59.3%. The difference between the number of cars and the number of SUVs is 16. Find the number of SUVs in the lot.
Answer:
27 SUVs
Step-by-step explanation:
Let number of ordinary cars be x and SUVs be y
We can write 2 equations and use substitution to solve for the number of SUVs.
"The number of ordinary cars is larger than the number of sport utility vehicles by 59.3%"-
This means that 1.593 times more is ordinary cars (x) than SUVs (y), so we can write:
x = 1.593y
"The difference between the number of cars and the number of SUVs is 16" -
Since we know ordinary cars are "more", we can say x - y = 16
We can now plug in 1.593 y into x of the 2nd equation and solve for y:
x - y = 16
1.593y - y = 16
0.593y = 16
y = 27 (rounded)
Hence, there are 27 SUVs
A psychologist wishes to conduct a study on the effects of music deprivation on high school students. A high school class consists of the 30 students numbered in the list below. The researcher establishes a treatment group of 15 students who will have their portable music players replaced by experimental players that present the sound of water running. The control group of 15 students will all get regular portable music players, stuffed full of their favorite songs. 00 Aaron 01 Buffy 02 Chandler 03 Cindy 04 Drusilla 05 Eric 06 Fallon 07 Graham 08 heather 09 Hsin-chi 10 Ismail 11 Jasmine 12 Kiefer 13 Lucia 14 Monte 15 Naomi 16 Otis 17 Polly 18 Quincy 19 Rachael 20 Sarah 21 Stacy 22 Tasha 23 Tuan 24 Ukiah 25 Valerie 26 Wahib 27 Xavier 28 Yolanda 29 Zachary Use the line of random numbers below to select the first 5 students to receive the treatment. What is the name of the fifth student selected? 59784 44312 15954 09233 00046 74318 02610 57396 16843 38454.
Answer:
Quincy
Step-by-step explanation:
Each student is assigned a two digit number, so let's split the random number line into two digit numbers:
59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54
Now let's identify the numbers between 00 and 29.
59, 78, 44, 43, 12, 15, 95, 40, 92, 33, 00, 04, 67, 43, 18, 02, 61, 05, 73, 96, 16, 84, 33, 84, 54
So the fifth student in the list is #18, or Quincy.
Answer:
Quincy is the answer
Step-by-step explanation:
In a batch of 8,000 clock radios 7% are defective. A sample of 1313 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected
Answer: Probability that the entire batch will be rejected is 0.611.
Step-by-step explanation:
Since we have given that
Number of clock radios in a batch = 8000
Probability of defective clock radio = 7%
According to question, we have mentioned that A sample of 13 clock radios is randomly selected without replacement from the 8,000 and tested.
We will use "Binomial distribution":
here, n = 13 and
p (probability of success) = 7% = 0.07
so, we need to find that
P(the entire batch will be rejected) = P(at least one of those test is defected)
So, it becomes,
P(at least one of those tested is defective) = 1 - P(none are defective)
So, P(none are defective ) is given by
[tex](1-0.07)^{13}\\\\=0.93^{13}\\\\=0.389[/tex]
So, P(at least one of those tested is defective) = 1 - P(none are defective)
= 1 - 0.389
= 0.611
Hence, Probability that the entire batch will be rejected is 0.611.
Find the interest rate needed for an investment of $10,000 to grow to an amount of $11,000 in 4 years if interest is compounded quarterly. (Round your answer to the nearest hundredth of a percent.) %
Answer:
[tex]2.39\%[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=4\ years\\ P=\$10,000\\A=\$11,000\\ r=?\\n=4[/tex]
substitute in the formula above
[tex]11,000=10,000(1+\frac{r}{4})^{4*4}[/tex]
[tex]1.1=(1+\frac{r}{4})^{16}[/tex]
Elevated both sides to (1/16)
[tex]1.005975=(1+\frac{r}{4})[/tex]
[tex]0.005975=\frac{r}{4}[/tex]
[tex]r=0.005975*4=0.0239[/tex]
Convert to percent
[tex]0.0239*100=2.39\%[/tex]
The sun has a radius of about 695,000 km. What is the volume of the sun (in scientific notation, using 3 decimal places in the mantissa)?
Answer:
1.406×[tex]10^{[tex]10^{18}km cubed
Step-by-step explanation:
The volume of a sphere is
[tex]V=\frac{4}{3}\pi r^3[/tex]
Filling in our formula:
[tex]V=\frac{4}{3}\pi (695,000)^3[/tex]
Cubing first gives us:
[tex]V=\frac{4}{3}\pi (3.35702[/tex]×[tex]10^{17}[/tex]
Do the multiplication and division of those numbers, multiply in the value of pi on your calculator, and you'll get 1.406×[tex]10^{18}[/tex]
To determine the volume of the Sun with a radius of about 695,000 km, we first convert the radius to centimeters and then apply the formula V = (4/3)πr³. After performing the calculations, the volume of the Sun is approximately 1.401 x 10³³ cm³in scientific notation with three decimal places in the mantissa.
Explanation:The student has asked what the volume of the Sun is, given its radius of about 695,000 km. To find the volume of a sphere, the formula to use is V = (4/3)πr³, where V represents the volume and r is the radius.
First, we need to convert the radius from kilometers to centimeters because the standard unit for volume in scientific notation often involves cubic centimeters. There are 100,000 centimeters in a kilometer, so the radius in centimeters is 695,000 km × 100,000 cm/km = 6.95 x 10¹⁰cm.
Now, we can calculate the volume using the formula:
V = (4/3)π(6.95 x 10¹⁰ cm)³
V = (4/3)π(6.95^3 x 10³⁰) cm³
V = (4/3)π(334.14 x 10³⁰) cm³
V = (4/3)π(3.3414 x 10³²) cm³
V ≈ 4.1888 x 3.3414 x 10³² cm³
V ≈ 1.401 x 10^33 cm³
Therefore, the volume of the Sun in scientific notation, using three decimal places in the mantissa, is approximately 1.401 x 10³³ cm³.
Learn more about Volume of the Sun here:https://brainly.com/question/12053350
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5x=k-14 solve for x (literal equation)
Answer:
[tex]\large\boxed{x=\dfrac{k-14}{5}}[/tex]
Step-by-step explanation:
[tex]5x=k-14\qquad\text{divide both sides by 5}\\\\\dfrac{\not5x}{\not5}=\dfrac{k-14}{5}\\\\x=\dfrac{k-14}{5}[/tex]
Answer:
[tex]5x = k - 14 \\ \frac{5x}{5} = \frac{k - 14}{5} \\ x = \frac{k - 14}{5} [/tex]
Help ASAP!! See screenshot below.
ANSWER
The relation is not a function.
EXPLANATION
The relation is not a function because we have an x-coordinate mapping on to more than one y-coordinate.
This occurs at x=1.
The ordered pairs (1,1) and (1,3) disqualify the relation from being a function.
Hence the relation is not a function.
Suppose that 3 cards from a standard deck of 52 playing cards are successively drawn at random without replacement (a) Find the probability that all 3 are queens (b) Find the probability that all 3 are spades (a) The probability that all 3 are queens is (Type an integer a simplified fraction) or (b) The probability that all 3 are spades is (Type integer simplified fraction) an or a
[tex]|\Omega|=52\cdot51\cdot50=132600[/tex]
a)
[tex]|A|=4\cdot3\cdot2=24\\P(A)=\dfrac{24}{132600}=\dfrac{1}{5525}[/tex]
b)
[tex]|A|=13\cdot12\cdot11=1716\\P(A)=\dfrac{1716}{132600}=\dfrac{11}{850}[/tex]
a. Probability of all 3 cards being queens:
Number of ways to choose 3 queens from 4: 4C3 = 4.Number of ways to choose 3 cards from 52: 52C3 = 22100.Probability = 4/22100 = 1/5525.b. Probability of all 3 cards being spades:
Number of ways to choose 3 spades from 13: 13C3 = 286.Number of ways to choose 3 cards from 52: 52C3 = 22100.Probability = 286/22100 = 13/1001.If an increase in one variable causes a decrease in another variable, there is A. a negative relationship. B. a dependent relationship. C. a direct relationship. D. an independent relationship.
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given a situation that
If an increase in one variable causes a decrease in another variable,
Then, there is inverse relationship.
When one variable is increased whereas other variable falls.
There will be inverse relationship.
Since inverse relation has negative relation.
Then, there is a negative relationship.
Hence, Option 'A' is correct.
An increase in one variable causing a decrease in another indicates a negative relationship between the two variables, characterized by opposite directional movements and graphically represented by a line with a negative slope.
Explanation:When discussing the correlation between two variables, it is important to consider the direction and type of relationship they share. If an increase in one variable causes a decrease in the other variable, this is defined as a negative relationship. In a negative relationship, the two variables move in opposite directions, meaning that as one variable increases, the other decreases and vice versa.
The relationship is depicted graphically as a line with a negative slope on a graph, where the line descends as it moves from left to right. This situation should not be confused with dependent, direct, or independent relationships, which describe different aspects of variable interaction.
Which number is rational?
Answer:
5.(3)
Step-by-step explanation:
5.(3)=16/3
Answer:
d
Step-by-step explanation:
Peter kim wanted to buy a new car.To help finance the purchase he decided to sell his organic markets bond in the secondary market.Peters bond had a par value of $ 10,000 and a coupon of 6 percent.Current interests were 3 percent.What would peters bond sell for?
Which zero pair could be added to the function fon) = x2 + 12x + 6 so that the function can be written in vertex form?
03.-3
0 6.6
03-3
O 36,-36
ANSWER
36,-36
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} + 12x + 6[/tex]
To write this function in vertex form;
We need to add and subtract the square of half the coefficient of x.
The coefficient of x is 12.
Half of it is 6.
The square of 6 is 36.
Therefore we add and subtract 36.
Hence the zero pair is:
36, -36.
The correct answer is D.
Answer:
Last option: 36,-36
Step-by-step explanation:
The vertex form of the function of a parabola is:
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
To write the given function in vertex form, we need to Complete the square.
Given the Standard form:
[tex]y=ax^2+bx+c[/tex]
We need to add and subtract [tex](\frac{b}{2})^2[/tex] on one side in order to complete the square.
Then, given [tex]y=x^2+12x+6[/tex], we know that:
[tex](\frac{12}{2})^2=6^2=36[/tex]
Then, completing the square, we get:
[tex]y=x^2+12x+(36)+6-(36)[/tex]
[tex]y=(x+6)^2-30[/tex] (Vertex form)
Therefore, the answer is: 36,-36
Write the standard equation of a circle that passes through (-5 5) with center (-10 -5) brainly
Answer:
The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
Step-by-step explanation:
* lets study the standard form of the equation of a circle
- If the coordinates of the center of the circle are(h , k) and its radius
is r, then the standard equation of the circle is:
(x - h)² + (y - k)² = r²
* Now lets solve the problem
∵ The coordinates of the center of the circle are (-10 , -5)
∵ The standard form of the equation is (x - h)² + (y - k)² = r²
∵ h , k are the coordinates of the center
∴ h = -10 , k = -5
∴ The equation of the circle = (x - -10)² + (y - -5)² = r²
∴ The equation of the circle = (x + 10)² + (y + 5)² = r²
- To find the value of the radius lets use the point (-5 , 5) to
substitute their coordinate instead of x and y in the equation
∵ The circle passes through point (-5 , 5)
∵ (x + 10)² + (y + 5)² = r²
- Use x = -5 and y = 5
∴ (-5 + 10)² + (5 + 5)² = r² ⇒ simplify
∴ (5)² + (10)² = r²
∴ 25 + 100 = r²
∴ r² = 125
* Now lets write the equation in standard form
∴ (x + 10)² + (y + 5)² = 125
* The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form
A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given value and use the z-score to determine whether the value is significant. Consider a score to be significant if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A. -1.6; not significant B.-17.6; significant C. -1.6, significant D. 1.6; not significant
Answer:
A. -1.6; not significant
Step-by-step explanation:
The z-score of a data set that is normally distributed with a mean of [tex]\bar x[/tex] and a standard deviation of [tex]\sigma[/tex], is given by:
[tex]z=\frac{x-\bar x}{\sigma}[/tex].
From the question, the test score is: [tex]x=48.4[/tex], the mean is [tex]\bar x=66[/tex], and the standard deviation is [tex]\sigma =11[/tex].
We just have to plug these values into the above formula to obtain:
[tex]z=\frac{48.4-66}{11}[/tex].
This simplifies to: [tex]z=\frac{-17.6}{11}[/tex].
[tex]z=-1.6[/tex].
We can see that the z-score falls within two standard deviations of the mean.
Since [tex]-2\le-1.6\le2[/tex] the value is not significant.
The correct answer is A. -1.6; not significant
For f(x) = 2|x+3| – 5, name the type of function and describe each of the three transformations from the parent function f(x) = |x|.
Answer:
Type of function: Absolute Value
Transformations: 1) elongated by a stretch factor of 2; 2) shifted left 3; 3) shifted down 5
Answer:
Shifted 5 units downShifted 3 units to the leftVertically streched by a scale of 2.Step-by-step explanation:
The parent function is
[tex]f(x)=|x|[/tex]
The transformed function is
[tex]g(x)=2|x+3|-5[/tex]
You can deduct by comparison, that the function was shifted 5 units down, 3 units to the left, and vertically streched by a scale of 2.
We deduct this transfromations based on the following rules.
[tex]f(x)-u[/tex] indicates a movement downside [tex]u[/tex] units.
[tex]f(x+u)[/tex] indicates a movement leftside [tex]u[/tex] units.
[tex]uf(x)[/tex] indicates a vertical stretch for [tex]u>1[/tex].
A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure antifreeze. In order to obtain 30 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
First brand of antifreeze: 21 gallons
Second brand of antifreeze: 9 gallons
Step-by-step explanation:
Let's call A the amount of first brand of antifreeze. 20% pure antifreeze
Let's call B the amount of second brand of antifreeze. 70% pure antifreeze
The resulting mixture should have 35% pure antifreeze, and 30 gallons.
Then we know that the total amount of mixture will be:
[tex]A + B = 30[/tex]
Then the total amount of pure antifreeze in the mixture will be:
[tex]0.2A + 0.7B = 0.35 * 30[/tex]
[tex]0.2A + 0.7B = 10.5[/tex]
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:
[tex]-0.7A -0.7B = -0.7*30[/tex]
[tex]-0.7A -0.7B = -21[/tex]
[tex]-0.7A -0.7B = -21[/tex]
+
[tex]0.2A + 0.7B = 10.5[/tex]
--------------------------------------
[tex]-0.5A = -10.5[/tex]
[tex]A = \frac{-10.5}{-0.5}[/tex]
[tex]A = 21\ gallons[/tex]
We substitute the value of A into one of the two equations and solve for B.
[tex]21 + B = 30[/tex]
[tex]B = 9\ gallons[/tex]
please help!!! What is the decimal equivalent of this fraction?
Answer:
[tex]\bullet\ \ 0.\overline{15}[/tex]
Step-by-step explanation:
5/33 = (5·3)/(33·3) = 15/99 = 0.151515151515...
_____
You may recall that 1/9 = 0.11111...(repeating indefinitely). That is, a multiple of 1/9 is a single-digit repeating decimal.
Likewise, 1/99 = 0.01010101...(repeating indefinitely). This means when a 2-digit numerator has 99 as the denominator, the decimal equivalent is that number repeated indefinitely. Any fraction with 999 as the denominator is a 3-digit repeat in decimal; 9999 as the denominator gives a 4-digit repeat, and so on.
Harry operates a coffee shop. One of her customers wants to buy two kinds of beans. Arabian mocha and Columbian decaf. If she wants twice as much Arabian mocha as Columbian decaf how much of each can she buy for a total of $181.50?
The customer can buy ____ lbs of arabian mocha
And ______ lbs of Columbian decaf
Answer:
11 lbs of Arabian Mocha5.5 lbs of Columbian DecafStep-by-step explanation:
Since we want twice as much Mocha as Decaf, we can create a "bag" that contains 2 lbs of Mocha (at 11.50 each) and 1 lb of Decaf (at 10). The value of this "bag" is then 2×11.50 +10.00 = 33.00. For 181.50, we can buy ...
181.50/33.00 = 5.5
"bags". This amount is ...
11 lbs of Arabian Mocha and 5.5 lbs of Columbian Decaf
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight equals negative 5.33 plus 0.1926 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?
The residual for the newborn is -0.9148 kg, indicating he is lighter than what the model predicts for his length.
To calculate the residual for the newborn's weight, we first use the least squares regression line equation, which is weight = -5.33 + 0.1926 * length. We then input the newborn's length of 48 cm into the equation to predict the weight.
Predicted weight = -5.33 + (0.1926 * 48) = -5.33 + 9.2448 = 3.9148 kg
The residual is the difference between the actual weight and the predicted weight, so for this newborn, the residual = actual weight - predicted weight = 3 kg - 3.9148 kg = -0.9148 kg.
The negative residual indicates that the newborn weighs less than what the regression model predicts for a boy of 48 cm in length. This could suggest that the child is lighter than average for his length
Find the probability of the given event. A bag contains 7 red marbles, 2 blue marbles, and 3 green marbles. A randomly drawn marble is blue.
Answer: [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
The given event : A randomly drawn marble is blue.
The number of blue marbles in the bag = 2
The total number of marbles in the bag = [tex]2+7+3=12[/tex]
Now, the probability of drawing a blue marble is given by :-
[tex]\text{P(Blue)}=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}\\\\\Rightarrow\text{P(Blue)}=\dfrac{2}{12}=\dfrac{1}{6}[/tex]
Hence, the probability of the given event event = [tex]\dfrac{1}{6}[/tex]
Simplify 16m^2/m^2+5/4m/3m^2+15
Answer:
12m
Step-by-step explanation:
We are given the following expression where a fraction is divided by another fraction:
[tex]\frac{\frac{16m^2}{m^2+5} }{\frac{4m}{3m^2+15} }[/tex]
To change this division into multiplication, we will take reciprocal of the fraction in the denominator and then solve:
[tex] \frac { 1 6 m ^ 2 } { m^2+5} } \times \frac{3m^2+15}{4m}[/tex]
Factorizing the terms to simplify:
[tex] \frac { 4 m ( 4m ) } { m ^ 2 + 5 } \times \frac { 3 ( m ^ 2 + 5 ) } { 4 m } [/tex]
Cancelling the like terms to get:
12m
Answer: [tex]12m[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{\frac{16m^2}{m+5}}{\frac{4m}{3m^2+15}}[/tex], we can rewrite it in this form:
[tex](\frac{16m^2}{m+5})(\frac{3m^2+15}{4m})[/tex]
Now we must multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:
[tex]=\frac{(16m^2)(3m^2+15)}{(m^2+5)(4m)}}[/tex]
According to the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
And the Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then, simplifying, we get:
[tex]=\frac{3(m^2+5)(4m)(4m)}{(m^2+5)(4m)}}\\\\=3(4m)\\\\=12m[/tex]
Find the distance from the point to the line. (-1,-2,1);x=4+4t, y=3+t, z=6-t .The distance is ____ Typn exact answer, using radicals as needed.)
Answer:
The distance is 4.726
Step-by-step explanation:
we need to find the distance from the point to the line
Given:- point (-1,-2,1) and line ; x=4+4t, y=3+t, z=6-t .
used formula [tex]d=\frac{|a\times b|}{|a|}[/tex]
Let point P be (-1,-2,1)
using value t=0 and t=1
The point Q (4 , 3, 6) and R ( 8, 4, 5)
Let a be the vector from Q to R : a = < 8 - 4, 4 - 3, 5 - 6 > = < 4, 1, -1 >
Let b be the vector from Q to P: b = < -1 - 4, -2 - 3, 1 - 6> = < -5, -5, -5 >
The cross product of a and b is:
[tex]a \times b= \begin{vmatrix} i & j & k\\ 4 &1&-1\\-5 &-5&-5\\ \end{vmatrix}[/tex]
= -6i+15j-15k
The distance is : [tex]d=\frac{\sqrt{(-6)^{2}+(15)^{2}+(-15)^{2}}}{\sqrt{(4)^{2}+(1)^{2}+(-1)^{2}}}[/tex]
[tex]=\frac{\sqrt{36+225+225}}{\sqrt{16+1+1}}[/tex]
[tex]=\frac{\sqrt{36+225+225}}{\sqrt{16+1+1}}[/tex]
[tex]d=\frac{\sqrt{486}}{\sqrt{18}}[/tex]
≈4.726
Therefore, the distance is 4.726
Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 53 and, in a separate drawing, you must also select the correct single number between 1 and 45. Find the probability of winning the jackpot.
[tex]|\Omega|={_{53}C_3}\cdot 45=\dfrac{53!}{3!50!}\cdot45=\dfrac{51\cdot52\cdot53}{2\cdot3}\cdot45=1054170\\|A|=1\\\\P(A)=\dfrac{1}{1054170}\approx0.00000095\%[/tex]
if f(x)=2x-1+3 and g(x)=5x-9, what is (f-g)(x)?
Answer:
[tex]\large\boxed{(f-g)(x)=-3x+11}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x-1+3=2x+2\\g(x)=5x-9\\\\\text{Substitute:}\\\\(f-g)(x)=(2x+2)-(5x-9)\\\\=2x+2-5x-(-9)\\\\=2x+2-5x+9\qquad\text{combine like terms}\\\\=(2x-5x)+(2+9)\\\\=-3x+11[/tex]
The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
Answer:
3x -4y = 2
Step-by-step explanation:
A plot of the points makes it clear that the longest diagonal is BD. The 2-point form of the line through those points can be found by filling in ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-2))/(6 -(-2))(x -(-2)) +(-2) . . . . . fill in points B and D
y = (6/8)(x +2) -2
4y = 3(x +2) -8 . . . . . . multiply by 4
3x -4y = 2 . . . . . . . . . . add 2-4y