100 POINTS HELP EXPERTS PLEAASE!
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 2 multiplied by 0.85 to the power of x. The straight line f of x joins ordered pairs minus 7, 3 and minus 3, minus 2 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 1 and minus 3, minus 2 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (4 points)
Part B: Write any two solutions for f(x). (4 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (6 points)
Answers
Answer:
A) (-3, -2)
B) (-7, 3) and (-3, -2)
C) (4.074, 1.032)
Step-by-step explanation:
An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.
Part A.The function p(x) is defined to pass through points (4, 1) and (-3, -2).
The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
These function definitions have point (-3, -2) in common.
(-3, -2) is the solution to the equation p(x) = f(x).
Part B.The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
Two solutions to f(x) are (-7, 3) and (-3, -2).
We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.
Part C.The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...
(4.07369423957, 1.03158324553)
Answer:
A) (-3, -2)
B) (1, -7) and (5, -12)
C) (4, 1) to the nearest whole number
Step-by-step explanation:
Function g(x):
[tex]g(x)=2(0.85)^x[/tex]
Function f(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (-7, 3)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]
[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
Function p(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (4, 1)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]
[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
Part AWe have been given two ordered pairs for function f(x) and function p(x).
One of those ordered pairs is the same for both functions.
The solution to a pair of equations is their point(s) of intersection.
Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.
Part BThe solutions for f(x) are any points on the line of the function f(x).
To find any two points, substitute values of x into the found equation for f(x):
[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]
[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]
Therefore, two solutions are (1, -7) and (5, -12).
Part C
The solution to p(x) = g(x) is where the two graphs intersect. From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).
Therefore, the approximate solution to p(x) = g(x) is (4, 1).
To prove this, substitute x = 4 into the equations for p(x) and g(x):
[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]
[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]
The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.
Related Questions
help ASAP!!!!!!!!!!!!!!!
Answers
Answer: 4.0 * 10^0 kg = 4.0 kg essentially
Step-by-step explanation:
No need to convert these to numbers...
Weight of 1 bee: 1 * 10^-4 = (0.0001 kg)
Number of bees: 4 * 10^4 = (40000 bees)
(1 * 10^-4) * (4 * 10^4) =
(1 * 4) * (10^-4 * 10^4) =
(10^0 because when multiply exponential numbers, you add the exponents)
4 * 10^0 =
4 * 1 = 4 kg
A rhombus is a four-sided figure with all sides the same length.
Points F(22, 22), G(22, 3), and H(2, 6) are three vertices of
rhombus FGHJ. Vertex J is directly below vertex H.
a. Graph rhombus FGHJ. Label J with its coordinates.
b. What is the perimeter of the rhombus? Show your work.
Answers
The perimeter of the rhombus FGHJ is 20 units
How to graph the rhombusThe coordinates are given as:
F = (-2, -2)
G = (-2, 3)
H = (2, 6)
From the question, we understand that vertex J is directly below vertex H.
This means that vertices H and J have the same x coordinate.
So, we have
J = (2, y)
The distance between F and G is 5 units,
So, we have
J = (2, y - 5)
Where
y = 6 i.e. the y coordinate of H
This gives
J = (2, 6 - 5)
Evaluate
J = (2, 1)
See attachment for the graph of the rhombus
The perimeterIn (a), we have:
The distance between F and G is 5 units,
This means that
FG = 5
The side lengths of a rhombus are equal.
So, the perimeter is
P = 4 * FG
This gives
P =4 * 5
Evaluate
P = 20
Hence, the perimeter of the rhombus is 20 units
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A sequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence?
Answers
1/2 value can be used as the common ratio in an explicit formula that represents the sequence.
Definition of sequence -
The following of one thing after another; succession. order of succession: a list of books in alphabetical sequence. A continuous or connected series: a sonnet sequence. something that follows; a subsequent event; result; consequence.A sequence that progresses geometrically has the first term as 12.
Each number is the previous number divided by 2.
so the sequence will be 12, 6, 3, 1.5...........
Explicit formula of a geometric sequence is given by
[tex]T_{n} = ar^{n-1}[/tex]
Where [tex]T_{n}[/tex] = nth term of the sequence
a = first term
r = common ratio
and n = number of term
In this sequence common ratio = [tex]\frac{Successive term }{previous term}[/tex]
= 6/12
= 1/2
Therefore, common ratio will be 1/2.
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What is the probability that a five-card poker hand contains the two of diamonds and the three of spades?.
Answers
Answer:
1/311875200.
There is exactly 1 way to have all 5 of these cards. For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:
(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.
Step-by-step explanation:
In 4 weeks, Mark earns an average of $400 per
week. If, after working another 2 weeks at a
constalat salary, his average carnings per week
are $500, how much did he earn in the last 3
weeks?
Answers
400 + 2y = 500
2y = 100
y = 50 weeks 5-6
Last three weeks
Week 4 100
Week 5 50
Week 6 50
He earned about $200
What is 63% of 35. Please tell me how to do it not just answer please!
Answers
Answer:
22.05
Step-by-step explanation:
First, convert 63% into a decimal.
To do this, divide it by 100.
[tex] \frac{63}{100} = 0.63[/tex]
Multiply 0.63 by 35.
[tex]35 \times (0.63) = 22.05[/tex]
Answer:
Step-by-step explanation:
.63(35)= 22.05
Multiply .63(35)
If 12 oz. of sausage contains 300 calories, how many calories w ould 7 oz, contain? how would i write a formula
Answers
Answer:
175 cal
Step-by-step explanation:
if 12oz = 300 cal
then, 7 oz = ?
cross multiplication
12×?= 7×300
? = 2100/12
? = 175 cal
NB: you can replace the question mark with any variable.
what is 155x60cm into square inches
Answers
Answer:
1441.503 square inches
Step-by-step explanation:
155×60cm=9300square centimeter
9300 divide 6.452 to change to square inches.
Ans=1441.503
Answer:
64.58 sq.in
Step-by-step explanation:
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answers
The summary of the given data is are as follows :-
Minimum: 11
Lower quartile:11
Median:24
Upper quartile:34
Maximum:45
Interquartile range:23
Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45
Minimum = The smallest number of data
Thus Minimum = 11
Maximum = The largest number of data
Thus Maximum = 45
Median = The middle number of the data if data consists of odd number of elements
Thus Median = 45
Lower quartile = The median of the lower half of data
Thus Lower quartile = 11
Upper quartile = The median of the upper half of data
Thus Upper Quartile = 34
Interquartile range = The difference of upper and lower quartiles,
Thus Interquartile range = 34 -11 = 23
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Construc t a 95% confidence interval for the population standard deviation σ of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 13.5 pounds. assume the population is normally distributed
Answers
The 95% confidence interval for the population standard deviation will be,
[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]
simplifying the equation, we get
[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]
The 95% confidence interval exists (9.887, 21.288).
What is the 95% of confidence interval?
A random sample of 15 men exists selected. The mean weight exists at $165.2 pounds and the standard deviation exists at $13.5 pounds. The population exists normally distributed.
So, [tex]$n=15, \bar{X}=165.2, s=13.5$[/tex]
where n exists the sample size, [tex]$\bar{X}$[/tex] exists the sample size
s exists the sample standard deviation.
The degrees of freedom will be n - 1 i.e.15 - 1 = 14.
For a 95% confidence interval, the level of significance will be [tex]$\alpha=0.05$[/tex].
The 95% confidence interval for the population standard deviation will be,
[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]
substitute the values in the above equation, we get
[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi^{2}} 0.05} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0}^{2}}} \\[/tex]
[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.975}^{2}}} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.025}^{2}}} \\[/tex]
simplifying the above equation, we get
[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]
The 95% confidence interval exists (9.887, 21.288).
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Practice another write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 4 0, t ≥ 4
Answers
Using the Laplace transform to solve the given integral equation f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is [tex]\frac{4(1-2e^-5s)/}{s}[/tex]
explanation is given in the image below:
Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.
The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.
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If takes 3/4 hour to paint 12by 12 room how long does it take to paint 15by 16 room
Answers
How would you solve this? Please give an explanation.
Answers
The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)
How to generate values from a recursive function
In this question we have a kind of recursive function known as Fibonacci's function, where a value of the series is generated from at least immediately previous elements. In this case, we need to find the first three elements from the fifth and fourth elements of the series:
[tex]a_{n-2} = a_{n-1} - a_{n} + 4[/tex]
a₄ = a₅ - a₆ + 4
a₄ = - 2 - 0 + 4
a₄ = 2
a₃ = a₄ - a₅ + 4
a₃ = 2 - (- 2) + 4
a₃ = 8
a₂ = a₃ - a₄ + 4
a₂ = 8 - 2 + 4
a₂ = 10
a₁ = a₂ - a₃ + 4
a₁ = 10 - 8 + 4
a₁ = 6
The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)
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WS=
Help me please thanks so much :) I appreciate it
Answers
Answer:
Step-by-step explanation:
3 units
Answer:
3 units.
Step-by-step explanation:
Opposite sides of a parallelogram are equal in length,
So side OD = side WS.
We see from the diagram that OD is 3 units long so
WS = 3 also.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
[tex]y = 2x {}^{2} - 4x - 16 \\ \delta = b {}^{2} - 4ac \\ \delta = ( - 4) {}^{2} - 4(2)( - 16) \\ \delta = 16 + 128 \\ \delta = 144 > 0 [/tex]
[tex]x = \frac{ - b + \sqrt{ \delta} }{2a} = \frac{4 + 12}{2 \times 2} = \frac{16}{4} = 4[/tex]
[tex]x = \frac{ - b - \sqrt{ \delta} }{2a} = \frac{4 - 12}{2 \times 2} \frac{ - 8}{4} = - 2[/tex]
[tex]x = 4 \: \: \: \: \: or \: \: \: \: x = - 2 \\ (x - 4) = 0 \: \: \: \: \: or \: \: \: \: \: (x + 2) = 0[/tex]
[tex]f(x) = \alpha (x - 4)(x + 2) \\ f(x) = \alpha x { }^{2} + 2 \alpha x - 4 \alpha x - 8 \alpha \\ f(x) = \alpha x {}^{2} - 2 \alpha x - 8 \alpha \\ by \: comparison \\ \alpha = 2[/tex]Factors are:1) 22) x - 43) x + 2If f(x)=x²-3x - 4 and g(x) = x² + x, what is (f + g)(x)?
Answers
Answer: (f+g)(x)=2(x-2)(x+1).
Step-by-step explanation:
[tex]f(x)=x^2-3x-4\ \ \ \ \ g(x)=x^2+x\\(f+g)(x)=(x^2-3x-4)+(x^2+x)\\(f+g)(x)=x^2-3x-4+x^2+x\\(f+g)(x)=2x^2-2x-4\\(f+g)(x)=2*(x^2-x-2)\\(f+g)(x)=2*(x^2-2x+x-2)\\(f+g)(x)=2*(x*(x-2)+(x-2))\\(f+g)(x)=2*(x-2)*(x+1).[/tex]
Select the correct answer from each drop-down menu. B For circle O, m In the figure, 2 C CD T - 125° and m2ABC= 55°. and 2 have measures equal to 35°.
Answers
Answer:
Step-by-step explanation:
The relevant relations here are ...
the sum of arc measures in a semicircle is 180°the sum of angles in a triangle is 180°Arc measuresThe given arc CD is part of the semicircular arc CDA. The remaining arc, DA, is the supplement of CD:
arc DA = 180° -CD = 180° -125° = 55°
Central angle AOD has the same measure, 55°. That is one of the acute angles in right triangle AOB, so the other one is the complement of 55°.
∠ABO = 90° -∠AOB = 90° -55°
∠ABO = 35°
Triangle anglesIn right triangle ABC, angle ABC is given as 55°. The other acute angle, ACB, will be the complement of this.
∠ACB = 90° -∠ABC = 90° -55°
∠ACB = 35°
In the figure, angles ABO and ACB have measures of 35°.
What is the slope of the line that passes through the points (2, -4) and
(5,2)? Write your answer in simplest form.
Answers
Answer:
2
Step-by-step explanation:
Your slope is your change in y over your change in x. The ordered pair is in the form of (x,y), so you subtract the y's and put that in your numerator (top)and subtract your x's and put that in your denominators (bottom).
2 - (-4) would be your top number. To subtract a negative number is the same as adding a positive, so 2 - (-4) is the same as 2 +4, so your top number is 6.
Now, to find the bottom number, you subtract the x's.
5-2 which is 3.
We now have the top and the bottom number
6/3 which is the same as 2.
Find an equation of the line perpendicular to y = − 7 8 x + 2 and containing the point (14, − 3)
Answers
Answer:
[tex]y=\frac{-x}{78} -\frac{220}{78}[/tex]
Step-by-step explanation:
Remember to create a line perpendicular to one another the slope has to be the reverse reciprocal of the first line.
Given the current slope is [tex]\frac{-78}{1}[/tex] the new slope would be [tex]\frac{1}{78}[/tex].
To find the line that passes through a point with a given slope we must use point slope form, remember the default equation of point slope form:
[tex]y-y1=m(x-x1)[/tex]
Where y1 is the y value of the point, m is the slope, and x1 is the x value of the point.
Lets substitute in our values
[tex]y-(-3)=\frac{-1}{78} (x-14)[/tex]
Simplify the equation
[tex]y+3=-\frac{1}{78}\left(x-14\right)\\y+3=\frac{-x}{78}+\frac{14}{78}\\y=\frac{-x}{78}-\frac{220}{78}\\[/tex]
A blueprint is 1 in: 12ft. Then width of a building is 48ft. What is the width of the building on the blueprint?
Answers
The width on the blueprint is 4 inches.
What is the width of the building on the blueprint?
The blueprint is a scale drawing of the building. A scale drawing is a reduced form in terms of dimensions of an original image / building / object
The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 inch 12 feet. This scale means that 1 inch of the blueprint represents 12 feet of the building.
Width of the building on the blueprint = 48 / 12 = 4 inches
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A plank of wood is 4.6 meters long.
These two lengths of wood are cut from the plank - 88cm and 1630mm
What is the length of the wood left
Answers
Step-by-step explanation:
1 meter = 100 centimeter = 1000 millimeter
therefore, 1 cm = 10 mm
4.6 m = 4.6 × 1000 = 4600 mm
88 cm = 880 mm
and so, they cut off
880 mm + 1630 mm = 2510 mm
that means
4600 - 2510 = 2090 mm = 2.09 m
are left.
Consider the function f(x) = 1/3(6)*. What is the value of the growth factor of the function?
1/3
2
6
18.
Answers
Answer:
6
Step-by-step explanation:
The growth factor is the same as the base of the exponential factor.
The value of the function [tex]$f(x)=(1/3)(6)^x[/tex] growth factor exists 6.
How to estimate the value of the growth factor of thefunction [tex]$f(x)=(1/3)(6)^x[/tex]?
Given: [tex]$f(x)=(1/3)(6)^x[/tex]
For any equation [tex]$ f(x)=ab^x[/tex]
Let, 'a' exists the initial value
b exists the growth or decay factor.
When the value of b exists greater than 1 then its growth factor
when the value of b exists between 0 and 1 then it exists a decay factor
Let x exists the number of years
Given function, [tex]$ f(x)=(1/3)(6)^x[/tex]
The value of b exists 6.
So the growth factor exists 6.
Therefore, the correct answer is option c. 6.
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h(x)=
8
1
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?h(x)=
8
1
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?
Answers
The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2
How to determine the average rate of change?The function is given as:
[tex]h(x) = \frac 18x^3 - x^2[/tex]
The interval is given as:
−2 ≤ x ≤ 2
Calculate h(2) and h(-2)
[tex]h(2) = \frac 18 * 2^3 - (2)^2[/tex]
h(2) = -3
[tex]h(-2) = \frac 18 * (-2)^3 - (-2)^2[/tex]
h(-2) = -5
The average rate of change is then calculated as:
[tex]m = \frac{h(-2) - h(2)}{-2-2}[/tex]
This gives
[tex]m = \frac{-5 + 3}{-4}[/tex]
Evaluate
m = 1/2
Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2
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Complete question
[tex]h(x) = \frac 18x^3 - x^2[/tex]
What is the average rate of change of h over the interval −2 ≤ x ≤ 2
When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodness-of-fit test, can you tell exactly how the distribution of observed values over the specified categories differs from the expected distribution? explain your answer.
Answers
No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.
What is a null hypothesis?The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.
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5. Elias has 1/2 of a candy bar. He shares 1/4 of it with his best friend. How much of the candy bar did his best friend receive?
Answers
Answer:
1/8
Step-by-step explanation:
say the bar has 20 pieces. he has 10 pieces. and he gave away 1/4 of those 10
1/4 x 10 = 2.5
20 / 2.5 = 8
So his friend recieved 1/8
you could also just do 1/2 x 1/4 which is 1/8
Answer:
1/8 of the candy bar.
Step-by-step explanation:
Elias has 1/2 of a candy bar.
He gave 1/4 of 1/2 to his friend.
[tex]\sf Friend's s\ share = \dfrac{1}{4} \ of \ \dfrac{1}{2}[/tex]
[tex]\sf =\dfrac{1}{4}*\dfrac{1}{2}\\\\=\dfrac{1}{8}[/tex]
In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are different. What is the mode?
Answers
The mode of the set of 10 observations is 2.
What is the mode?
Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.
According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.
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Solve for all values of xx by factoring.
x^{2}+5x-3= −4x−3
Answers
Answer:
x=0, x= -9
Step-by-step explanation:
First we simplify the equation into the form
ax^{2}+bx+c=0
By adding 4x+3 on both sides, we form the equation
x^{2}+9x=0
Now, we factor out the common factor: x.
x(x+9)=0
The only values that allow x(x+9) to be equal to 0 are:
x=0 or
x+9=0
The solutions are x=0 or x= -9
A system of linear equations is shown below, where A and B are real numbers.
3x + 4y = A
Bx – 6y = 15
What values could A and B be for this system to have no solutions?
Answers
Answer:
A = 0; B = -9/2
Step-by-step explanation:
To have no solutions, you need parallel lines with equal slopes and different y-intercepts.
3x + 4y = A Eq. 1
Bx - 6y = 15 Eq. 2
In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.
We must have the same ratio for the coefficients in Eq. 2.
B/(-6) = 3/4
4B = -6(3)
4B = -18
B = -9/2
Now we have
3x + 4y = A Eq. 1
-9/2 x - 6y = 15 Eq. 2
How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2
To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.
If we divide 15 by -3/2 we get -10.
The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.
To have no equations, the y-intercepts must be different, so A can be any number other that -10.
Answer: A = 0; B = -9/2
Find the value of z.
Answers
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.
Applying the angle of intersecting chords theorem, let's find x first:
73 = 1/2(96 + x)
Multiply both sides by 2
2 × (73) = 1/2(96 + x) × 2
146 = 96 + x
Subtract both sides by 96
146 - 96 = 96 + x - 96
50 = x
x = 50°
Therefore:
x + z + 96 + 114 = 360° [full circle measure]
Plug in the value of x
50 + z + 96 + 114 = 360
z + 260 = 360
Subtract both sides by 260
z + 260 - 260 = 360 - 260
z = 100°
The answer is: D. 100°.
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If x is the first of two consecutive odd integers, and the sum of the two integers is 72, what is the smaller of the two integers?
Answers
Answer:
x = 35.
Step-by-step explanation:
since they are odd, the second number isn't x + 1, it is x + 2.
x + x + 2 = 72
2x + 2 = 72
2x = 70
x = 35