Answer: [tex]5\frac{1}{4}[/tex] gallons are left
Step-by-step explanation:
convert to mixed number...
[tex]8\frac{3}{4} = \frac{35}{4}[/tex]
[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]
[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]
[tex]\frac{21}{4} =5\frac{1}{4}[/tex]
therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank
Answer:
5 1/4 gallons are left... correct
Another quick geometry question! Thanks!
Which of the following terms describes the measure indicated by the black
arrow below?
4
A. Median
B. Range
C. Mean
D. Minimum
Answer:
the answer is A
Step-by-step explanation:
The line is the middle point of the graph/ the middle number of all therefore it's the median.
ary
S
Homework: Homework Chapter
7 Section C
h
In a large casino, the house wins on its blackjack tables with a probability of 50.4%. All bets at blackjack are 1 to 1, which means that if you win, you gain the amount
you bet, and if you lose, you lose the amount you bet
a. If you bet $1 on each hand, what is the expected value to you of a single game? What is the house edge?
a. The expected value to you of a single game is $ -0.008
(Type an integer or a decimal)
The house edge is $ 0.008
(Type an integer or a decimal)
b. If you played 150 games of blackjack in an evening, betting $1 on each hand, how much should you expect to win or lose?
c. If you played 150 games of blackjack in an evening, betting $5 on each hand, how much should you expect to win or lose?
d. If patrons bet $4,000,000 on blackjack in one evening, how much should the casino expect to earn?
b. You should expect to lose $1.2
(Type an integer or a decimal)
c. You should expect to lose $6.00
(Type an integer or a decimal.)
d. The casino should expect to earn $ 32,000
ere to search
Help me solve this View an example Get more help -
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Question 3, 7.C.31
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Answer:
the answer is D
Step-by-step explanation:
What is the sum?
2/x^2+4/x^2
Answer:
6/x2
Step-by-step explanation:
Answer:
[tex]\mathsf {\frac{6}{x^{2}}}[/tex]
Step-by-step explanation:
[tex]\mathsf {\frac{2}{x^{2}} + \frac{4}{x^{2}} }[/tex]
[tex]\mathsf {\frac{2+4}{x^{2}}}[/tex]
[tex]\mathsf {\frac{6}{x^{2}}}[/tex]
A trapezoid is a quadrilateral with one or more pairs of parallel sides.
O A. True
OB. False
least common denominator of 1
[tex] \frac{1}{6} \: and \: \frac{7}{9} [/tex]
can someone help me asap :)
Answer:
Option 2 - TU is perpendicular to MN and MN is parallel to PQangle M = angle P ( 90°)
so MN is parallel to pq
MN makes 90° with UT so it is perpendicular
What are m and b in the linear equation y=16+6x
Answer: B=16 and m=6
Step-by-step explanation:
in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.
Which standard form of the equation of the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y equals plus or minus five twelfths times x question mark
y squared over 25 minus x squared over 144 equals 1
y squared over 144 minus x squared over 25 equals 1
x squared over 25 minus y squared over 144 equals 1
x squared over 144 minus y squared over 25 equals 1
The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have:
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(5/12)x
The equations we have:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
From the equation first:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
The value of a and b are:
a = 12
b = 5
Vertices of the hyperbola = (0, b) and (0, -b)
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(b/a)x
Asymptotes: y = ±(5/12)x
Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
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Answer:
A
Step-by-step explanation:
PLS HELP!!
The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
O Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B
The correct answer are as follows:
A. False
B. True
C. False
D. False
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
False, it is the y-intercept of the function that indicates the amount at the start of the experiment.
B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
True, the y-intercept is given when x = 0, indicating the initial value of the function.
C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
False, because the maximum value of each table is given in different times, and also the initial value of each table is different.
D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
False, the growth rate is not given by the initial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.
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Find the value of d.
Answer:
Step-by-step explanation:
Comment
The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.
Givens
Arc 1 = 94
Arc2 = d
interior angle = 75
Formula
(d + 94)/2 = interior angle/1
Solution
(d + 94)/2 = interior angle/1 Cross Multiply
1*(d + 94) = 75 *2 Combine
d + 94 = 150 Subtract 94 from both sides
d + 94 - 94 = 150 - 94 Combine
d = 56
Answer: d = 56
a straight line passes through points A(-2,6) and B(4,2). M is the midpoint of line AB.Find the coordinates of M
Answer:
(1,4)
Step-by-step explanation:
If x=3 y=4 z=6 then 4x+8yz+3y equals
Answer:
216
Step-by-step explanation:
4x+8yz+3y
Let x=3 y=4 z=6
Substitute the values into the expression
4(3)+8(4)(6)+3(4)
Multiply first
12+192+12
Then add
216
Use the point-slope formula to write an equation of the line that passes through (4,10) and has a slope of m= 3. Write the
answer in slope-intercept form (if possible).
The equation of the line is
Please help me with this hard problem
Part 1: Finding [tex](g\circ h)(x)[/tex]
Note that [tex](g\circ h)(x)=g(h(x))[/tex]
In this case, it is [tex]g(\sqrt{x+4})=(\sqrt{x+4})^{2}-3=x+4-3=\boxed{x+1}[/tex]
Part 2: Domain
For the domain, we need to make sure the radicand of h(x) is greater than or equal to 0, so we get [tex]x+4 \geq 0 \longrightarrow \boxed{x \geq -4}[/tex]
The composition (g ο h) = x+ 1 and the domain of the composition (g ο h) is = (-∞ , ∞).
The composition (g ο h) means that the function g(x) composes of h(x) that is g(h(x)). So we have to put the the values of h(x) in the function g(x).
Now here it is given that
g(x) = [tex]x^{2} -3[/tex] and h(x) = [tex]\sqrt[2]{x + 4}[/tex]
so to get (g ο h) we have to replace the x with the value of h(x)
That gives :
g(h(x)) = [tex]\sqrt[2]{x+4} ^{2} - 3[/tex]
g(h(x)) = x + 4 - 3 = x +1
So the composition (g ο h) = x+ 1
The domain of the function is the values of x for which the function is defined.
so the domain of the composition (g ο h) is :
g(h(x)) = x+ 1
This function is undefined for no value of x .
So its domain is (-∞ , ∞).
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solve for a
(log(a-1))^2 =log10
A function assigns the values. The value a is 11.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given logarithmic function can be solved as shown below.
[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]
Hence, the value a is 11.
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n studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean of each of them. Consider the following: Personal phone calls received in the last three days by a new employee were 2, 4, and 7. Assume that samples of size 2 are randomly selected with replacement from this population of three values. What different samples could be chosen? What would be their sample means?
The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
What is Mean ?Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.
On the basis of given data
The number given is 2,4,7
Size of the sample = 2 with replacement
The Total outcome with replacement will be given by
3² = 9
Possible outcome can be
2,2 2,4 2,7 4,4 4,2 4,7 7,7 7,2 7,4
The sample mean can be calculated as
(a+b)/2
(2+2)/2 = 2
similarly the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
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Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is t ≥ 0
The greatest concentration of the medication is 5mg/L
Given that:
C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t ≥ 0
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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which law would you use to simplify the expression...
Answer:
Power of a quotient
Find the degree of a polynomial.
Answer:
What is Poly in gender. Gender is Gender "Female" "Non-binary" "Male". Poly is Triangle gender which means random gender.
Answer: Explanation: To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
Step-by-step explanation:
Need number 8 please!!
Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are given as follows:
f(x) = x².g(x) = f(x) - 2 = x² - 2.Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.
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50% of 42 students are girls. How many of the students are girl's
Answer:
21 girls.
Step-by-step explanation:
50% of 42 students are girls.
So 42/2 = 21.
Therefore 21 of the students are girls.
Hope I helped
The following table shows the probability distribution for a discrete random
variable.
13
16
17
21
23
25
26
31
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08
What is the mean of this discrete random variable? (That is, what is E(X), the
expected value of X?)
A. 21.5
B. 22
) C. 21
D. 20.42
find the area for this pls
Answer:
3,36 in^2
Step-by-step explanation:
The geometric shape shown in image is called a trapezoid
to calculate the area of a trapezoid we use the following formula:
1/2*(a+b)*h (a and b are bases, h: height)
bases are 1.3 and 3.5 and height is 1.4
1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is
3,36 in^2
only 1st main ,please do solve this asap
Answer:
(i) 8b-32
(ii) 7z^3+12z^2-20z
(iii) –q+p
(iv) a+ab
(v) 8x^2y+8xy^2-4x^2-7y^2
(vi) 4y^2-3y
Step-by-step explanation:
segment CD has endpoints at C(0, 3) and D(0, 7). If the segment is dilated by a factor of 3 about point C, what is the length of the image of segment CD question mark (1 point)
The length of CD is 7-3=4.
Therefore, if we dilate by a scale factor of 3, the length is 4(3) = 12
Answer:
b) 12
Step-by-step explanation:
the length of the image is 12. i just know. trust me.
The following confidence interval is'obtained for a population proportion p: 0.87 < p < 0.93 What is the margin error E. The following confidence interval is'obtained for a population proportion p : 0.87 < p < 0.93 What is the margin error E.
The margin error of the confidence interval 0.87<p<0.93 is 0.03.
Given confidence interval 0.87<p<0.93.
We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.
Confidence interval is 0.87<p<0.93.
Width of the interval= 0.93-0.87
=0.06
=0.03
Hence the margin of error is equal to 0.03.
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A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 3600 ft2 (including the margins).
If x denotes the left-right width (in feet) of the billboard, determine the value of x that maximizes the area of the printed region of the billboard.
An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,
The total area of the billboard, A= x·y
The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]
Given in problem that the area of the billboard is 3600 ft².
x·y = 3600
y = (3600)/x
Substituting the value of y in the equation of the total printed area of the billboard,
[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]
Now, the value of x is needed to be minimum, therefore, differentiating the given function,
[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]
Equate the differentiated function with 0,
[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]
Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
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Find dy/dx if y =x^3+5x+2/x²-1
How would I go about finding this? I would appreciate if you could be as detailed as possible!
Differentiate using the Quotient Rule –
[tex]\qquad[/tex][tex]\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\[/tex]
According to the given question, we have –
f(x) = x^3+5x+2 g(x) = x^2-1Let's solve it!
[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2) \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5) - ( x^3+5x+2) 2x}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex] \pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\[/tex]
[tex]\qquad[/tex][tex]\pink{\therefore \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}} = \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\[/tex]
what figure was rotated
Answer: Rectangles
Step-by-step explanation:
Whenever rectangles are rotated about an axis, a cylinder is formed.
