Answer: The composite function (g f)(x) is found by first applying the function f to x and then applying the function g to the result. In other words, (g f)(x) = g(f(x)).
So, for the given functions g(x) = x - 5 and f(x) = -x - 1, the composite function is:
(g f)(x) = g(-x - 1) = (-x - 1) - 5 = -x - 6
Evaluating the composite function at x = 7, we get:
(g f)(7) = -7 - 6 = -13
Step-by-step explanation:
Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?
Step-by-step explanation:
(x-2)(x-2)-4x
x²-2x-2x +4-4x
x²-4x-4x +4
x²-8x+4
Answer:
4x - (x - 2)² = 4x - x² + 4 = 3x + 4
Step-by-step explanation:
A boat has a top speed of 26 knots and a displacement of approximately 81,000 tons. Express the top speed in miles per hour and the displacement in metric tons. The boat has a top speed of approximately______mile(s) per hour. (Round to the nearest tenth as needed.)
The boat has a top speed of approximately 29.7 miles per hour and a displacement of approximately 73,934 metric tons.
Answer:
[tex]29.9[/tex] miles per hour
[tex]73482[/tex] metric tons
Step-by-step explanation:
We are given:
top speed of 26 knots
displacement of 81,000 tons
It is asking us to convert knots to miles per hour.
It is asking us to convert tons to metric tons.
We can use conversion factors to complete the unit conversions.
1 knot (kt) = 1.15077945 miles per hour (mph)
1 ton = 0.907185 metric tons
Numerical Evaluation
Lets convert our top speed.
We can set up an equation like this
[tex]\frac{1}{1.15077945} =\frac{26}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=26*1.15077945[/tex]
Evaluate [tex]26*1.15077945[/tex].
[tex]26*1.15077945 =29.9202657[/tex]
Round to the nearest tenth.
[tex]29.9[/tex] miles per hour
Lets convert our displacement.
We can set up an equation like this
[tex]\frac{1}{0.907185 } =\frac{81000}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=81000*0.907185[/tex]
Evaluate [tex]81000*0.907185[/tex].
[tex]81000*0.907185=73481.985[/tex]
Round to the nearest tenth.
[tex]73482[/tex] metric tons
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The figure below shows a rope that circles the Earth. The radius of the Earth is
6371
63716371 kilometers.
Assuming the rope makes a perfect circle, what is the length of this rope?
Give your answer in terms of pi.
Answer:
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the circle.
Plugging in the value for the radius of the Earth, we have:
Circumference = 2π(6371 km) = 12,742 km
So the length of the rope, assuming it makes a perfect circle around the Earth, would be 12,742 km = 2π(6371) kilometers.
Step-by-step explanation:
Solve for x. Round to the nearest tenth.
xº
54
12
The required measure of the angle x in the given right triangle is 12.38°.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
Since the question seems to be incomplete the complete question has been attached after the solution.
We have given a triangle where x° is the angle of the right triangle where the hypotenuse is 54 and one legs is 12. With the help of trig ratios
sin x = 12 / 54
x = sin⁻¹(12/54)
x = 12.38°
Thus, the required measure of the angle x in the given right triangle is 12.38°.
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Miguel was selling apples, plums, and peaches at the local farmer’s marker. He sold 18 more
pounds of apples than pounds of plums. He sold 9 pounds less of peaches than pounds of
plums. He sold a total of 69 pounds of fruit. How many pounds of each fruit did he sell?
Answer:
He sold 32 pounds of apples, 14 pounds of plums and 23 pounds of peaches.
Step-by-step explanation:
Let:
x = Mass of Apples (pounds)
y = Mass of plums (pounds)
z = Mass of peaches (pounds)
He sold 18 more pounds of apple than pounds of plums: [tex]x = 18 + y[/tex]
He sold 9 less pounds of peaches than pounds of plums: [tex]z - 9 = y[/tex]
He sold a total of 69 pounds of fruit: [tex]x + y + z = 69[/tex]
We have 3 unknown variables, therefore a system of 3 linear simultaneous equations:
[tex]x = 18 + y[/tex] ——- (equation i)
[tex]z - 9 = y[/tex]
∴ [tex]z = 9 + y[/tex] ——— (equation ii)
[tex]x + y + z = 69[/tex] ——- (equation iii)
The above linear simultaneous equations can be solved by Substitution Method:
Substitute (equation i) and (equation ii) into (equation iii) to solve for y. Expand the parenthesis and bring all the like terms together. y has to be made the subject of the equation:
[tex](18 + y) + y + (y + 9) = 69[/tex]
= [tex]18 + y + y + y + 9 = 69[/tex]
= [tex]y + y + y = 69 - 18 - 9[/tex]
= [tex]3y = 42[/tex]
= [tex]y = \frac{42}{3}[/tex]
∴ y = Mass of plums = 14 pounds
Substitute the calculated value of y into the other two equations to solve for x and for z:
[tex]x = 18 + (14)[/tex]
∴ x = Mass of apples = 32 pounds
[tex]z = 9 + (14)[/tex]
∴z = Mass of peaches = 23 pounds
The diagram below shows the rectangle PLUMP
Find the area of rectangle PLUMP
If entering your answer as a decimal, round your final answer to the nearest hundredth.
PLS show work.
Step-by-step explanation:
we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :
1. Pythagoras
a² + b² = c²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
2. geometric mean theorem
height = sqrt(p×q)
with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.
so, to get the length of the rectangle (PL) we use Pythagoras :
PL² = 6² + 8² = 36 + 64 = 100
PL = 10 units
to get PM we first need to get ML. and for that we need to get MA.
6 = sqrt(MA × 8)
36 = MA × 8
MA = 36/8 = 4.5 units
that means ML = 8 + 4.5 = 12.5 units
and again Pythagoras
ML² = PL² + PM²
12.5² = 10² + PM²
156.25 = 100 + PM²
56.25 = PM²
PM = 7.5 = 7.5 units
so, the area of the rectangle is
10 × 7.5 = 75 = 75.00 units²
to "round" to the nearest hundredth.
The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 feet, what are the lengths of the three sides?
Answer:
the solution is done in the given picture..
thank you
18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
In the critical value method, we find the area in the tail end and compare it to alpha to determine whether to reject or fail to reject the null hypothesis.
The critical value strategy entails deciding whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true in order to determine whether something is "likely" or "unlikely."
How do you determine the rejection zone and the crucial value?
The rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .
To execute any hypothesis test, the critical value technique entails four specific phases, which are as follows:
The null and alternative hypotheses should be specified.Calculate using the sample data and the null hypothesis as the default. the test statistic's value Using the t-statistic t=m−μ÷s/√n which follows a t-distribution with n - 1 degrees of freedom, we may test the population mean hypothesis.By determining the value of the known distribution of the test statistic such that the likelihood of making a Type I mistake is low, also known as the "significance level of the test," or (greek letter "alpha"), the crucial value can be found (typically 0.01, 0.05, or 0.10).Assess the critical value against the test statistic. Reject the null hypothesis in favor of the alternative hypothesis if the test statistic is more extreme in the alternative direction than the crucial value. When the test statistic falls inside the acceptable range,To know more about critical value method visit:
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Select the correct answer.
A right angle triangle where ABC angle is 90° and angle ACB is 45°.
Which trigonometric ratio will not have the same value as sin A?
A.
cos A
B.
sin C
C.
tan C
D.
cos C
Reset Next
Trigonometric Ratios: Mastery Test
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Trigonometric ratio in option (c) tan C will not have the same value as sin A.
What are Trigonometric Functions?Trigonometric functions are defined as the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given a right angled triangle ABC given below.
ABC angle is 90° and angle ACB is 45°.
Then angle BAC = 180° - (90° + 45°) = 45°
Since two angles are equal, it is an isosceles triangles.
So opposite sides to the equal angles are equal.
AB = BC
AC is the hypotenuse.
Sin A = Opposite side / Hypotenuse = BC / AC
(a) Cos A = Adjacent side / Hypotenuse = AB / AC = BC / AC
(b) Sin C = AB / AC = BC / AC
(c) Tan C = Opposite side / Adjacent side = AB / BC = BC / BC = 1, not equal to Sin A
(d) Cos C = BC / AC
Hence the option (c) is not equal to sin A.
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Find the complex number given arg(z+1) =pi/6 and arg(z-1)=(2*pi)/3
Answer:
Therefore, z = 1 + i.
Step-by-step explanation:
Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.
Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).
Using the argument values given, we have:
arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.
arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.
From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:
a = (z + 1 + z - 1)/2 = 1
b = (z + 1 - z - 1)/2 = 1
Therefore, z = 1 + i.
the answer to this question
Answer is B.
y= 2x -3 y= -2x + 1
step by step
First I found the y intercepts at (red line) -3 and (green line) +1.
There is only one answer that shows these two y intercept values.
To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.
Slope was found on the graph finding rise over run and compared to the number next to x in the equations.
See attached graph.
Astronomers believe that the radius of a variable star increases and decreases with the brightness of the star. Suppose a variable star has an average radius of 20 million miles and changes by a maximum of 1.6 million miles from this average during a single pulsation, and that the time between periods of maximum brightness is 5.2 days. Find an equation that describes the radius of this star as a function of time. (Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing.) R(t) =
Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then R(t) = 20 + 1.6sin(2πt/5.2).
The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.
In this case, the amplitude is 1.6.
Since the radius changes by a maximum of 1.6 million miles.
The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)
The phase shift is 0, since when t = 0 the radius is increasing.
The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)
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2x+3y=102, x, plus, 3, y, equals, 10
In the xyx, y-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
Any line of the form:
y = (3/2)x + b
Is perpendicular to the given line.
Which equation is perpendicular to the given one?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the product between the slopes is -1.
Here we want to find a line perpendicular to:
2x + 3y = 10
We can rewrite this as:
3y = 10 - 2x
y = (10/3) - (2/3)*x
Then the slope of the perpendicular line must be such that:
a*(-2/3) = -1
a = 3/2
Then any line of the form:
y = (3/2)*x + b
Is perpendicular to the given line.
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On a road trip to central Florida, you average 35 miles per hour while driving within city
borders and 60 miles per hour while driving on the highway (not in the city.) The trip was 995 miles long. You were in city borders for 4 hours longer than on the highway. Let C be the time, in hours, you spent driving in the city. Let H be the time, in hours, you spent driving on the highway. Find the sum C + H
The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
What is distance?Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.
Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.
Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation
Distance = Speed × Time
to solve for the time spent in both city and highway.
For time spent in city:
35 mph × C = 995 miles
C = 995 miles/35 mph = 28.43 hours
For time spent in highway:
60 mph × H = 995 miles
H = 995 miles/60 mph = 16.58 hours
Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.
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Solve for x in the equation −6x+18=−6. Place the steps for solving this equations in order.
Answer:
x=4
Step-by-step explanation:
-6x = -6-18
-6x = -24
-6x/-6 = -24/-6
x =4
Examine the right triangle below. Let a = 15, b = 20, and c = 25. What is the
sin B=, rounded to the nearest hundredth?
The value of sin B rounded to the nearest hundredth is 0.80.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
The right triangle represented in the question is given below.
We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.
In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.
Sin B = AC / AB
Sin B = b / c
Sin B = 20 / 25
Sin B = 0.8
Hence the value of sine of B is 0.8.
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Find the values of p for which the equation (p+1)x² + 4px +9=0 has equal roots.
The values of p for which the equation (p+1)x² + 4px +9=0 has equal roots:
p = (36 ± 59.8)/32
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The quadratic equation,
(p+1)x² + 4px +9=0
So, for equal roots, we have:
(4p)² - 4 x (p + 1) x 9 = 0
Solving for p, we get:
16p² - 36 p -36 = 0
This is a quadratic equation, and we can find the roots using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Where a = 16, b = -36, and c = -36.
Plugging in the values into the formula, we get:
p = (36 ± 59.8)/32
Thus, the values of p for which the equation (p + 1)x² + 4px + 9 = 0 have equal roots are (36 ± 59.8)/32.
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The triangles are similar. What is the missing length?
8
18
72
16
The answer is B. 18
When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.
33/44 = x/24
Once finished solving the proportion, you are left with 18
The missing length of triangle is 18.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.Equilateral Triangle - A triangle has three sides that are of the same length.A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.Triangle with a Right Angle - A triangle with one of its angles equal to 90°.Now,
As these triangles are similar that means
we can find the proportion of sides from given sides and
from that find x.
So, here AC/AM=AL/AB
44/33=24/x
AL=24*33/44
AL=18
Hence,
The missing length AL of triangle is 18.
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Please see attached photo thanks
The single payment 2 years from now will be of $13,287.26
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.
To calculate investments or debts with compound interests.
Where:
V(n) is the value of the debt after n years,
R is the annual interest rate,
t is the number of times the debt is going to be compounded annually,
n is the number of years the debt is going to be compounded,
P is the principal amount being owed.
we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.
Then you have that t = 4, because the debt is compounded quarterly.
We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.
And finally we have that R = 7.74.
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 2,370 / (1 + 7.74/365)(365)^(2)
P = $13,287.26
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Last year Kristen had $ 20 , 000 to invest. She invested some of it in the first account that paid 7 % simple interest per year, and she invested the rest of it in a second account that paid 8 % simple interest per year. After one year, she received a total of $ 1 , 540 in interest. How much did she invest in each account?
The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 20,000 equation 1
0.07a + 0.08b = 1540 equation 2
Where:
a = amount invested in the account that earns 7% interest
b = amount invested in the account that earns 8% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.07
0.07a + 0.07b = 1,400 equation 3
Subtract equation 3 from equation 2
0.01b = 140
Divide both sides of the equation by 0.01
b = 140/ 0.01
b = 14,000
Substitute for b in equation 1:
a + 14,000 = 20,000
a = 20,000 - 14,000
a = 6,000
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Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X.
X 0 1 2 3 4 or more
Probability 0. 58 0. 23 0. 11 0. 05 0. 03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0. 40 and 0. 66, respectively. The fat quarters sell for $5. 00 each, but are discounted by $1. 50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company G?
Answer:
(a) To determine the mean and standard deviation of Y, we need to find the expected value and standard deviation of the number of defects that can be sold by Company F. Since the number of defects that can be sold is equal to X if X is less than or equal to 2, and equal to 2 if X is greater than 2, we can use the following formula to find the expected value of Y:
E(Y) = P(X = 0) × 0 + P(X = 1) × 1 + P(X = 2) × 2 + P(X > 2) × 2
E(Y) = 0.58 × 0 + 0.23 × 1 + 0.11 × 2 + 0.03 × 2
E(Y) = 0.23 + 0.22 + 0.03
E(Y) = 0.48
To find the standard deviation of Y, we can use the following formula:
Var(Y) = P(X = 0) × (0 - E(Y))^2 + P(X = 1) × (1 - E(Y))^2 + P(X = 2) × (2 - E(Y))^2 + P(X > 2) × (2 - E(Y))^2
Var(Y) = 0.58 × (0 - 0.48)^2 + 0.23 × (1 - 0.48)^2 + 0.11 × (2 - 0.48)^2 + 0.03 × (2 - 0.48)^2
Var(Y) = 0.58 × 0.2304 + 0.23 × 0.1024 + 0.11 × 0.0304 + 0.03 × 0.0304
Var(Y) = 0.1333
The standard deviation of Y is the square root of the variance:
StdDev(Y) = √Var(Y)
StdDev(Y) = √0.1333
StdDev(Y) = 0.3663
So, the mean and standard deviation of Y are 0.48 and 0.3663, respectively.
(c) To find the mean and standard deviation of the selling price for the fat quarters sold by Company G, we need to find the expected value and standard deviation of the price, taking into account the discount for each defect. We can use the following formula to find the expected value of the price:
E(Price) = $5.00 - $1.50 × E(Defects)
E(Price) = $5.00 - $1.50 × 0.40
E(Price) = $5.00 - $0.60
E(Price) = $4.40
To find the standard deviation of the price, we can use the following formula:
StdDev(Price) = $1.50 × StdDev(Defects)
StdDev(Price) = $1.50 × 0.66
StdDev(Price) = $0.99
So, the mean and standard deviation of the selling price for the fat quarters sold by Company G are $4.40 and $0.99, respectively.
PLEASE PLEASE PLEASE HELP DONT IGNORE
Answer: the first box is does not the 2st box does i hope this helps
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-2, 3) (2, -1)
(-1 - 3)/(2 + 2)= -4/4 = -1
m = -1
does
does not
y - 3 = -1(x + 2)
y - 3 = -x - 2
y = -x + 1
Option 1
which coordinate plane has the graph of y=2/5x—4
The required graph has been attached below which represents the given linear equation y = (2/5)x - 4.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To plot the graph of y = (2/5)x - 4, you can follow these steps:
Choose a range of values for x that you want to plot. For example, you can choose x values from -10 to 10.
Substitute the x values into the equation to find the corresponding y values. For example, if x = -10, then y = (2/5)(-10) - 4 = -8.
Plot the ordered pairs (x, y) on a coordinate plane. For example, if x = -10 and y = -8, plot the point (-10, -8) on the plane.
Repeat this process for several x values to plot additional points.
Connect the points with a straight line to obtain the graph of the equation y = (2/5)x - 4.
Note that the graph should be a straight line with a slope of 2/5 and a y-intercept of -4.
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The question seems incomplete, the correct question would be as:
How to plot the graph of y = (2/5)x — 4?
Isaac Newton sat under an apple tree to drink some tea and think. While he was thinking, an apple fell off a branch of the tree. The equation v=(19.8d)12
can be used to find the velocity, in meters per second, of the apple after dropping a distance , in meters. If the apple was connected to a branch 9 meters above the ground, what was the velocity of the apple, to the nearest hundredth, when it hit the ground?
The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
How to determine the velocity of the apple?From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:
Velocity = (19.8d)^{1/2}
Where:
d represents the distance in meters.
Velocity = (19.8 × 9)^{1/2}
Velocity = (178.2)^{1/2}
Velocity = 13.35 meters per seconds.
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4x - 3 = 17
-2x - 7y = 11
My question is in the picture below
The proportional relationship used to find the distance that the train will travel after m minutes is given as follows:
d = 0.12m.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Considering that when the input is of 5, the output is of 0.6, the constant of the relationship in this problem is given as follows:
k = 0.6/5
k = 0.12.
Hence the equation is given as follows:
d = 0.12m.
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You place one grain of rice on the first square of a chess board. You then put two on the second,
four on the third, eight on the fourth, and so on until you've reached the sixty-fourth square.
If Scrooge McDuck bought five-pound bags of enriched white rice from Walmart, could he afford
to buy all the rice needed for the previous paragraph?
Answer:
yes
Step-by-step explanation:
Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares.
The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units
The radius of the base = 4 units
The length of the side of the square = 2x
The area of the square = a^2
Where a is side of the square
The area of the square = (2x)^2
= 4x^2
The equation of the circle is
x^2 + y^2 = 16
x^2 = 16 - y^2
The area = 4(16 - y^2 )
= 64 - 4y^2
The volume of the square
V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]
= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]
= 64×4 - 4×(4^3/3)
= 256 - 256/3
= 512/3 cubic units
Therefore, the volume of the solid is 512/3 cubic units
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Carole is paid a monthly salary of $2011.10. Her regular workweek is 35 hours.
(a) What is Carole's hourly rate of pay?
(b) What is Carole's gross pay for May if she worked 73/4 hours overtime during
the month at time-and-a-half regular pay?
