The values associated to the exponential function are listed below:
g(- 1.75) = 3.572 × 10⁻⁶g(- 1) = 7.716 × 10⁻⁴g(- 0.25) = 0.167g(0) = 1g(0.25) = 6g(0.50) = 36g(0.75) = 216g(1) = 1 296How to evaluate an exponential function
Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.
g(- 1.75) = 3.572 × 10⁻⁶
g(- 1) = 7.716 × 10⁻⁴
g(- 0.25) = 0.167
g(0) = 1
g(0.25) = 6
g(0.50) = 36
g(0.75) = 216
g(1) = 1 296
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i don’t understand graphs
Answer:
y ≤ 2.5x + 5
Step-by-step explanation:
first step is to obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = 2.5x + 5 ← equation of line
since the line is solid then inequality will be ≤
the solution to the inequality is the blue region below the line , then
y ≤ 2.5x + 5 ← inequality represented by graph
What is the exponent of x in in the expression -4x^3y^2 + 6
Answer:
3
Step-by-step explanation:
- 4x³y² + 6
the x is raised to the power of 3 , that is exponent of x is 3
Suppose you invested $1000 every 3 months over a 15 year period. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period. How much is the interest earned? Show all your calculations
Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.
What is the future value formula?The future value formula is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
In which:
P is the periodic payment.i is the equivalent yearly interest rate.n is the number of periods.For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:
P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.
Hence the amount available is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]
F = $100,336.67
The amount deposited was:
15 x 4 x $1000 = $60,000.
Hence the amount earned in interest was:
$100,336.67 - $60,000 = $40,336.67
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What error did zacharias make? the –5 should be 5. the 52 should be –52. the 2 in the numerator should be –2. the 2 in the denominator should be –2.
The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
Quadratic equationThere are four methods of solving quadratic equation. Namely;
Factorization methodCompleting the square methodGraphical methodFormula method0 = -2x² + 5x - 3
Using quadratic formulax = -b ± √b² - 4ac / 2a
where,
a = -2b = 5c = -3x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
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Circle X is shown. Line segments W X and Y X are radii. Tangents W Z and Y Z intersect at point Z outside of the circle. Arc W Y is 109 degrees.
What is the measure of angle WZY?
54.5°
71°
125.5°
180°
From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°
How to find the angle from a circle tangent?The lines ZY and ZW are tangents to the attached circle which is centered at x.
From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.
From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.
Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;
∠WZY = 360° - (90° + 90° + 109°)
∠WZY = 360° - 289°
∠WZY = 71°
Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°
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Answer: B. 71°
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
I got it right!
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of the halfpipe is Option A , (0, 20); Y equals one over eighty times x squared plus 20.
The equation of the halfpipe is Y = X²/80 +20.
What is parabola ?
A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola.The equation of parabola is given by
(X-h)² = 4p(Y-k)²
In this case h = 0
So we get
Y = X²/4P +k
Focus point is (h, p+k) , (p+k) = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X²/80 +20
Therefore, the equation of the halfpipe is Y = X²/80 +20
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The complete question is -
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. How many ounces of concentrate were in the original container before any juice was made? PLEASE HELP ME
TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
Number of ouncesA. Let assume the two are linear relationship
Let y represent juice made
Let x represent the concentrate remaining
Hence:
Slope=600-200/200-280
Slope=400/-80
Slope=-5
y=-5x+b
Where:
x=200
y=-5(200)+b=600
y=-1000+b=600
b=1600
Thus,
y=-5x+1600
y=0. -5x+1600=0
-5x=-1600
divide both side by 5x
x=-1600/-5
x=320 ounces
B. x=0
y=1600 ounces
Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
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Consider the quadratic equation x² 20x + 13 = 0.
-
Completing the square leads to the equivalent equation (x-
—)² = —
The analogous equation for the square will be; (x-10)²=87.
What is Equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations.
Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;
Using the original equation as a starting point as;
-20x+ x² + 13 = 0
Now x² - 20x = -13.
We need to take the "x" term's coefficient, or b, to complete the square.
Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,
B = -20
b/2 = -10
(b/2)² = 100
x² - 20x +100 = -13 + 100
On the left side,
LHS: (x + b/2)² = (x-10)2
RHS: -13 + 100 = 87
(x-10)² = 87
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Solve this equation. Make sure your answer is
fully reduced.
7/8 + x = 1/4
The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.
How a linear equation is solved?A linear equation is represented by ax + b = 0. The solution for this equation is
ax + b = 0
⇒ ax = -b
⇒ x = -b/a
Calculation:The given equation is
7/8 + x = 1/4
On simplifying,
x = 1/4 - 7/8
⇒ x = -5/8
Therefore, the solution of the given equation is -5/8.
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Graph the equation:
Y = 1/3x + 2
Please help!!
please explain in a way a middle schooler would understand!!
ty!
Geometry: complete this proof, ASAP!!!!!!!!
Answer:
1. Given
2. Definition of Congruent Angles
3. Triangle Interior Angle Sum Theorem
4. Transitive Property of Equality
5. Substitution Property of Equality
6. Definition of Congruent Angles
What number could be added to 0.40 ml for the level of precision to be 0.01 ml? check all that apply 0.2 ml 0.154 ml 6 ml 2.02 ml 8.8331 ml
The following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.
What is the amount of liquid to be added to sample according to a given precision?
If the measuring has a level of precision of 0.01 ml, this means that the measured quantities are only sensible to the smallest hundreths. Any change less than 0.01 ml and any decimal less than a hundreths are "invisible" for measuring processes.
Hence, the following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.
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Answer:
B,D,E
Step-by-step explanation:
What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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________ If an arc has measure 7π/4 radians, what is its measure in degrees?
________ What is 60° in radians?
If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
Given that arc has measure of 7π/4.
We are required to convert the measure from radian to degree measure.
Converting means chaning of units from one to another.
To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.
7π/4=7*180/4
=7*45
=315 degrees
Now we have to convert 60 degrees into radians.
60 degrees=60*π/180
=π/3
Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
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A small manufacturer constructs refrigerators. the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator. the average cost function to produce x refrigerators is represented by: what is the horizontal asymptote of c(x)? y =
Horizontal asymptote of c(x) is 450.
What is Horizontal asymptote?A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.
According to the information:Since we have given that
Cost to produce one refrigerator = $450
Fixed monthly cost = $200,000
Thus, the following formula represents the average cost to produce x refrigerators:
C(x) = (200000 + 450x)/x
Horizontal asymptote of c(x) would be
= 450x/x
= 450
Hence, Horizontal asymptote of c(x) is 450
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Find the general solution of the given second-order differential equation. 12y'' − 5y' − 3y = 0
The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
The probability that the person is over 40 and prefers cola exists at 1.3725.
What is probability?The probability of an event exists in the ratio of the size of the event space to the size of the sample space.
The size of the sample space exists the entire number of possible outcomes.
The event space exists the number of outcomes in the event you exists interested in.
So, P = size of the event space/size of the sample space
To estimate the probability that the person exists over 40 years.
Size of the sample size = 255
Size of the event space = 85
P = 85/255
P = 1/3
To estimate the probability that they drink cola.
Size of the sample size = 255
Size of the event space = 95
P = 95/255
P = 19/51
To estimate the probability that the person exists over 40 years of age or that they drink cola
So, P = (1/3) + (19/51)
[tex]$P = (51*3+3*19)/153[/tex]
P = 1.3725
Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.
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Helpppppp show your work
Answer:
-5/3
Step-by-step explanation:
Do PEMDAS
8 - 11 = -3
-3 ^ 3 = -27
-(-27) = 27
I-14I = 14
3 x 14 = 42
27 - 42 = -15
2^4 = 16
16 - 7 = 9
-15/9 = -5/3
2- (ITA-2007) Dentre 4 moças e 5 rapazes deve-se formar uma comissão de 5 pessoas com, pelo menos , 1 moça e 1 rapaz. De quantas formas distintas tal comissão poderá ser formada?
Answer:
Step-by-step explanation:
A painter needs to measure the height from the ground to the base of a 2nd story window. He props his ladder against the base of the window. He finds the height from one rung of the ladder to the point on the ground below it, and the distance from that point to the base of the ladder. This is shown in the figure.
If XY = 8 inches, WY = 24 inches, and XZ = 48 inches, the height from the ground to the base of the window is inches.
The height from the ground to the base of the window is 16 inches.
What is the height from the ground to the base of the window is inches?The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.
In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.
XY / XZ = WY / VZ
(8 / 24) = WY / 48
WY = (8 X 48) / 24 = 16 inches
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A binary operation * is defined on the set of Real numbers,R by m*n=(√m +√n) (√m-√n).Find the values of P,if P*3=1
The value of P such that P*3=1 is 4
How to solve for P in the set?The set of Real numbers, R is given as
m*n=(√m +√n) (√m-√n).
The values of P, if P*3=1 is represented as:
P * 3=(√P +√3) (√P-√3).
The result of this operation is 1.
So, we have:
(√P +√3) (√P-√3) = 1
Apply the difference of two squares
P - 3 = 1
Add 3 to both sides
P = 4
Hence, the value of P such that P*3=1 is 4
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Explain this diagram.
The shape that we have here is sued to show the infinite geometric progression.
What is geometric progression?This is the sequence of numbers that has all the other values in the sequence gotten by the multiplication of a certain factor
In this question or the shape we can see that the triangle is made up of smaller other triangles embedded in it.
The area of the traingle that is in the red color is seen to have been made up of 1/3 of the total triangles that we have in the shape. This can be seen to be similar as the triangles that are represented by the green and the blue color.
Putting a lot of triangles inside one big triangle gives up a pictorial diagram on how to add infinite amount of things up.
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help pls i will give brainleast no links
Answer: 100 square cm
Step-by-step explanation: the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.
Answer: 104
Step-by-step explanation:
area of trangle =33 because 6*11/2=33
area of rectangle 9*7=63
area of rectangle 2*2=4
33+63+4=100^2
help me pls like srsly
The time it will take the thermometer to hit the ground is 22 seconds
Calculating TimeFrom the question, we are to determine the how long it would take the thermometer to hit the ground
From the given information,
The equation for the height as a function of time is
h(t) = -16t² + initial height
From the given information,
The thermometer falls from a weather balloon at a height of 7744 ft
∴ Initial height = 7744 ft
When the thermometer hits the ground, h(t) = 0
Thus, we get
0 = -16t² + 7744
16t² = 7744
t² = 7744/16
t² = 484
t = √484
t = 22 seconds
Hence, the time it will take the thermometer to hit the ground is 22 seconds
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For Exercises 11-15, sketch the locus of points in a plane that satisfy the
given conditions.
14. equidistant from both points
A and B and points C and D
B C
A
O
D
15. equidistant from the sides of
LJKL and on OC
L
A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.
Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.
A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).
An equidistant locus is one that is at the same distance to a reference point or a line.
In question 14, the required locus should be at the same distance to points A, B, C, and D.
In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.
The required construction is herewith attached to this answer.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
numbers
Step-by-step explanation:
numbers
Expand and simplify (2+√3)² - (2-√3)²
Answer:
8√3
I hope this helps you
A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years
Answer:
1/2^6 = 1/64
Step-by-step explanation:
Half life = 10 years
Time = 60 years
No of half life = T/t
= 60 / 10 = 6
Remaining fraction = 1/2^(no of half life)
= 1/2^6
= 1/64
16. a) In the given figure, OB bisects ABC and OC bisects ACB, prove that BOC - BAC = ABO+ACO.
Answer:
Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.
Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.
m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB
m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO
m<ABO + m<ACO = m<BOC - m<BAC
A computer chip factory produces 520 chips in 13 minutes. at this rate, how many chips does it produce in 1 hour?