Answer:
mother age 37
sons age 12
The pH of a fruit juice is 5.6. Find the hydronium ion concentration, [H3O+], of the juice. Use the formula pH=-log[H3O+].
The hydronium ion concentrate H 30 plus as approximately? moles per liter
The hydroxonium ion concentration of the fruit juice whose pH as given in the task content is; 5.6 can be evaluated as; [H3O+] = 2.51 × 10^-6.
What is the hydroxonium ion concentration of the fruit juice whose pH is 5.6?Since the given pH of the fruit juice is 5.6, the hydroxonium ion concentration of the fruit juice can be evaluated by means of the formula as follows;
pH=-log[H3O+].
5.6 = -log[H3O+].
-5.6 = log[H3O+].
[H3O+] = antilogarithm (-5.6)
[H3O+] = 2.51 × 10^-6.
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simplify (2+3)2 + 8/2
Answer
[tex]2 \times 2 + 6 \times 2 + \frac{8}{2 } [/tex]
[tex]4 + 12 + 4[/tex]
[tex]16 + 4[/tex]
[tex]20[/tex]
19
Select the correct answer.
Which exponential function has the greatest average rate of change over the interval [0, 2]?
OA j(x) = 3(1.6)²
OB. An exponential function, f, with a y-intercept of 1.5 and a common ratio of 2.
OC.
OD.
g(x)
k(x)
The function with the greatest average rate of change is the function k(x)
How to determine the function?The average rate of change is calculated as
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
The interval is [0,2].
So, we have
[tex]m = \frac{y_2 - y_1}{2 -0}[/tex]
[tex]m = \frac{y_2 - y_1}{2}[/tex]
For function j(x), we have
j(2) = 3 * 1.6^2 = 7.68
j(2) = 3 * 1.6^0 = 3
So, we have
[tex]m_j = \frac{7.68 - 3}{2}[/tex]
[tex]m_j = 2.34[/tex]
For function g(x), we have
g(2) = 25/2
g(0) = 8
So, we have
[tex]m_g = \frac{25/2 - 8}{2}[/tex]
[tex]m_g = 2.25[/tex]
For function k(x), we have
k(2) = 9
k(0) = 4
So, we have
[tex]m_k = \frac{9 - 4}{2}[/tex]
[tex]m_k = 2.5[/tex]
For function f(x), we have
f(2) = 1.5 * 2^2 = 6
f(0) = 1.5
So, we have
[tex]m_f = \frac{6 - 1.5}{2}[/tex]
[tex]m_f = 2.25[/tex]
The function with the greatest average rate of change is the function k(x) with a rate of 2.5
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Consider these two functions:
F(x) = 2cos(πx)
G(x) = 1/2cos(2x)
What are the amplitudes and periods of the two functions?
Answer:
[tex]\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}[/tex] for [tex]\mathrm{HCl}[/tex] \& [tex]\mathrm{ClOH}[/tex]
Answer:
f(x): Amplitude = 2, Period = 2
g(x): Amplitude = ¹/₂, Period = π
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftFunction f(x)
[tex]f(x)=2 \cos (\pi x)[/tex]
Comparing this with the standard form of a cosine function:
Amplitude = 2[tex]\sf Period = \dfrac{2 \pi}{\pi}=2[/tex]Function g(x)
[tex]g(x)=\dfrac{1}{2} \cos (2x)[/tex]
Comparing this with the standard form of a cosine function:
[tex]\sf Amplitude=\dfrac{1}{2}[/tex][tex]\sf Period = \dfrac{2 \pi}{2}=\pi[/tex]Learn more about the cosine graph here:
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which equation is represented by the graph below a. y=1/8ex b.y=1/2ex c.y=2ex. d.y=8ex
The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. (-3, 1)
The information given illustrates that the graph of the function decreasing.
How to illustrate the information?We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.
Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.
So according to the given graph on the interval (-3, 1) the graph is decreasing.
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they’re 25 student’s 14 female and 11 male two students are selected at random to participate in a probability experiment. compute that
b) a male is selected then a female
c) a female selected then a male
d) two females are selected
e) no males are selected
The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%
How to find the Probability of Selection?The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)
= 25*24/2
= 300
(A) Probability of selecting 1 male and 1 female:
[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))
= 51.33%
(B) Probability of selecting 1 female and 1 male:
[(14C1) * (11C1)]/300 = 51.33%
(C) Probability that 2 females are selected is;
(14C2)/300 = 30.33%
D) Probability that no males are selected is;
P(no males) = (11C0 * 14C2 )/300 = 30.33%
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True or False - All whole numbers are integers but not all integers are whole numbers
Answer:
false
correct me if i'm wrong :]
Answer:
True
Step-by-step explanation:
the picture is the explanation and pretty much sus everything up about integers
help please I really need it
any answer is better than mine. need help asap
From the line bisected with the given midpoints, we have been able to prove that; BC = CE by substitution property of Equality
How to prove bisection of a Line?We are given that;
C is the midpoint of BD
D is the midpoint of CE
1) Thus, BC = CD because of definition of Midpoint.
2) Similarly, by definition of midpoint we know that CD = DE.
3) We can say that BC = DE because of substitution property of equality.
4) We can say that BC + CD = BD because of segment addition postulate.
5) Similarly, by segment addition postulate, we can say that CD + DE = CE.
6) Finally we can say that BC = CE by substitution property of Equality
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Prove that (- 1 + i)^7 = -8(1 + i)
Convert [tex]-1+i[/tex] to polar form.
[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]
By de Moivre's theorem,
[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]
QED
Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
Answer:
The constant of variation is 4
Step-by-step explanation:
We are looking for the constant of variation when t varies directly as the square of s
t = k s^2 where k is the constant of variation
t = 64 and s = 4
64 = k 4^2
64 = k * 16
Divide each side by 16
64/16 = k * 16/16
4 = k
The constant of variation is 4
At what points does the curve r(t) = t i + (4t − t2) k intersect the paraboloid z = x^2 + y^2?
(smaller t-value) (x, y, z) = ?
(larger t-value) (x, y, z) = ?
The points are known to intersect the curve at
(smaller t-value) (x, y, z) = 0, 0, 0(larger t-value) (x, y, z) = 2, 0, 4How to find the pointsWe have our equation as: r(t)=ti+(4t-t2)k (4t - t2)k
From r(t)
We have x to be t, y to be 0 and z=4t-t2
The given paraboloid can be defined to be
z=x^2+y^2
We are to put the values in the equation
4t-t²=t²+0
2t²=4t
Then t wuld be 2 or 0
Hence we have to conclude that ours points of intersection are at (0,0,0) and (2,0,4).
The 0,0,0) and (2,0,4) points is where the intersection of the paraboloid take place.
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What is the value of tan M?
15
15
17
L
∞ ∞01 200
8
17
8
15
15
K 8
8
M
Answer:
The value of tan M = 15/8
Step-by-step explanation:
[tex]tan \: m \: = \frac{p}{b} \\ tan \: m \: = \frac{15}{8} [/tex]
Complete the solution of the equation. Find
the value of y when x equals 4.
-3x + 9y = -57
Answer: -5
Step-by-step explanation:
-3x+9y=-57 x=4
-3(4)+9y=-57
-12+9y=-57
+12
9y=-45
9y
y=-5
A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed: JOB TIMES (minutes) A B C D E Workstation A 27 18 70 26 15 Workstation B 45 33 30 24 10 Click here for the Excel Data File a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B.
1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.
2. The determination of the amount of idle time for Workstation B is 37 minutes.
Johnson's Sequencing Rule:According to Johnson's sequencing rule, start listing jobs with minimum completion time first.
If the job occurs at Workstation A, list it on the left side. If the job occurs at Workstation B, list it on the right side, as below:
Data and Calculations:JOB TIMES (minutes) A B C D E
Workstation A 27 18 70 26 15
Workstation B 45 33 30 24 10
The first job with a minimum completion time is Job E at Workstation B.
The second job with a minimum completion time after Job E is Job B at Workstation A.
The third job with a minimum completion time after Job B is Job D at Workstation B.
The fourth job with a minimum completion time after Job D is Job A at Workstation A.
The last job is Job C at Workstation B.
The sequence that minimizes total completion time is as follows:
B A C D E
A B
Calculation of Idle Time at Workstation B:Job Workstation A Workstation B Idle Time
In Out In Out Workstation B
B 0 0+18 = 18 18 18+33 = 51 18
A 18 18+27 = 45 51 51+45 = 96 19
C 45 45+70 = 115 115 115+30 = 145 0
D 115 115+26 = 141 145 145+24 = 169 0
E 141 141+15 = 156 169 169+10 = 179 0
Total Idle Time at Workstation B = 37 (18 + 19)
Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.
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Question Completion with Answer Options:1. A-B-C-D-E
2. E-D-B-C-A
3. D-C-B-A-E
4. B-A-C-D-E
5. C-A-B-D-E
A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.
1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x − d)] + c.
-
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.
A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3. Here, amplitude of the graph is 5, value of k is π/40, d is π/2 and c is 3.
Developing the Equation of a Cosine Graph
The given information constitutes the following,
Diameter = 10 m
⇒ Radius, r = 5 m
Time, t = 80 s
Height above the ground, h = 2 m
Thus, we can infer that,
Amplitude, A = 5 m
Period, T = 80 s
Minimum height = 2 m
The cosine function is given as,
a cos [k(x − d)] + c
Here, A is amplitude
B is cycles from 0 to 2π and thus period = 2π/k
d is horizontal shift
c is vertical shift (displacement)
Now, 2π/k = 80
⇒ k = 2π/80 = π/40
The value of c is given as,
c = Amplitude - Minimum height
c = 5 - 2
c = 3
For a shift to the left by π/2 gives, we have,
d = π/2
Thus, the desired equation of the drawn cosine graph is,
y = 5 cos [( π/40)(x - (π/2))] + 3
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Teacher increases spatial awareness for children as they use position words and provide experience through mapping and manipulating shapes.
a. True
b. False
It is true teachers can increase spatial awareness as they use position words or implement mapping and shape manipulation.
Whatis spatial awareness?This refers to the ability to understand the position of one's body in relation to space and other objects as well as understanding how location and movement work.
How can spatial awareness be increased in children?In children spatial awareness can be increased through:
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Type the correct answer in each box. If necessary, round your answer(s) to the nearest hu The vertices of AABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of AABC is
Answer:
22.81
Step-by-step explanation:
The distance formula can be used to find the distances between pairs of vertices. The perimeter is the sum of those distances.
Side lengthsThe distance formula is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Using this formula the triangle side lengths are ...
AB = √((6 -(-2))^2 +(2 -2)^2) = √(8^2) = 8
BC = √((0 -6)^2 +(8 -2)^2) = √(6^2 +6^2) = 6√2
CA = √((-2 -0)^2 +(2 -8)^2) = √(4 +36) = √40
The perimeter of the triangle is the sum of these lengths:
P = 8 +6√2 +2√10 ≈ 22.8098
The perimeter is about 22.81 units.
Find function then simplify tje answer
Answer:
a)(x+h+2)²=x²+2xh+h²+4x+4h+2
b)(x+h+2)²–(x+2)²=2xh+h²+4h
c)2x+4+h
Step-by-step explanation:
f(x)=x²+4x+2
Aight so for part a you have to replace x with x+h
a)f(x+h)=(x+h)²+4(x+h)+2=x²+2xh+h²+4x+4h+2
and then for part b you need to subtract f(x) from part a:
b)f(x+h)–f(x)=x²+2xh+h²+4x+4h+2–x²–4x–2===>
2xh+h²+4h
and for part c divide the answer by h:
c)
[tex] \frac{f(x + h) - f(x)}{h} = = = > \\ \frac{2xh + 4h + {h}^{2} }{h} = = = > \\ 2x + 4 + h[/tex]
and if you limit h by 0 you'll get the derivative of f(x)
Find AC if EC = 9, ED = 12, and BD = 20. Round to the nearest tenth.
The value of AC = 23
According to the statement
Here we have given the values of tangent from the diagram
EC = 9, ED = 12, and BD = 20.
and we have to find the value of AC.
We know that the according to the given diagram the tangent
BE is always equal to the Tangent AE.
So, we generate a equation to find the AC then
BE = AE
Convert this into parts like
BD +DE = AC+CE
Substitute the values in it which are given in the statement
20+12 = AC + 9
32 = AC + 9
32 -9 = AC
AC = 23
So, The value of AC = 23
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Write these decimals in order from smallest to largest: 0.507, 0.75, 0.5, 0.078
Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?
The inverse variation equation that relates x and y is x = 4032 / y.
What is the equation that relates x and y?if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
The equation that represents inverse proportion : x = b/y
where b = constant of proportionality
112 = b /36
b = 36 x 112 = 4032
The equation : x = 4032 / y
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If B is the midpoint of AC, which of the following equations is correct?
AB + AC = B
OBA + BC = AC
O None of these choices are correct.
O
AB = AC
Answer:
BA + BC = AC
Step-by-step explanation:
B is the midpoint of AC
Then
BA = AC/2 and BC = AC/2
Then
BA + BC = AC/2 + AC/2 = AC
Answer:a
Step-by-step explanation:
Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x)).
f(h(x)) = 2x - 7
f(h(x)) = 2x - 4
f(h(x)) = 3x - 4
f(h(x)) = 3x - 7
Answer:
2nd option
Step-by-step explanation:
to find f(h(x)) substitute x = h(x) into f(x) , that is
f(h(x))
= f(2x + 3)
= 2x + 3 - 7
= 2x - 4
Find the solution(s) to the system of equations represented in the graph. (5 points)
Answer:
(0, -2) and (2, 0)
Step-by-step explanation:
The solution to a systems of equations is when the x and y values are equal for two equations. This can also been seen as when the two equations intersect. So by looking at the graph you see the line and the circle intersect at the point (2, 0) and (0, -2) which are going to be the two solutions to the systems of equations.
The following contingency table gives the results of a sample survey of Sowetan male and female respondents regarding their preferred mobile phone service provider.
What is the probability of selecting a respondent who does not prefer Cell C?
a.
0.2250
b.
0.50
c.
0.3750
d.
0.65
e.
0.7750
The probability of selecting a respondent who does not prefer Cell C is 0.775
How to determine the probability?The complete question is in the attached image
From the attachment, we have
Prefer cell C = 90
Total = 400
So, the number of respondents that do not prefer cell C is
Do not = 400 - 90
Do not = 310
The probability is then calculated as:
P = 310/400
Evaluate
P = 0.775
Hence, the probability of selecting a respondent who does not prefer Cell C is 0.775
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In a one tail hypothesis where you only in the lower tail, what is the p-value if
P-Value becomes 0.8599 when (z < 1.08).
According to the statement
We have given that the Z-stat value is 1.08 and we have to find the P value with the help of Z-stat value.
So,
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
and we know that
The P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.
So, If the z-stat is 1.08, the p-value for a left-tail test is the probability that (z < 1.08), which is 0.8599.
So, P-Value becomes 0.8599 when (z < 1.08).
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Which of these is equal to ⅔ × ¾ × ⅗?
Answer:
3/10
Step-by-step explanation:
Just multiply all of the numerators (top numbers) and then multiple all of the denominators (bottom numbers)
2/3x3/4x3/5 would be 18/60 Then take any number that is a factor to both 18 and 60 and divide both numbers by that factor. I could use 2 or 3 or 6 because both 18 and 60 is divisible by any of these numbers. I will choose 3. I will divide the top and bottom of 18/60 by 3 to get 6/20, now I will divide the top and bottom of that number by 2 to get 3/10
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{3}{5}}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{2\times3\times3}{3\times4\times5}}[/tex]
[tex]\mathsf{= \dfrac{6\times3}{12\times5}}[/tex]
[tex]\mathsf{= \dfrac{18}{60}}[/tex]
[tex]\mathsf{= \dfrac{18\div3}{60\div 3}}[/tex]
[tex]\mathsf{= \dfrac{6}{20}}[/tex]
[tex]\mathsf{= \dfrac{6\div2}{20\div2}}[/tex]
[tex]\mathsf{= \dfrac{3}{10}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{3}{10}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Which of the following graphs represents a function?
The third graph represents a function.
In a function, every input (x value) has exactly one output (y value). If even a single input has zero or two outputs, the graph does not represent a function.
A good way of testing this is using a vertical line. As you move a vertical line from left to right across a graph, it should always be touching exactly one point on the graphed line.
In this case, every graph fails this vertical line test except for the third graph, so the third graph represents a function.