Hello!
The common denominator is 100.
~Sophia
Snow is falling at a rate of r(t)=2e-0.1t inches per hour, where t is the time in hours since the beginning of the snowfall. Which of the following expressions gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours?
2e-0.5 - 2
Answer A: 2e -0.5 - 2
A
0.2 - 0.2e-0.5
Answer B: 0.2 - 0.2e -0.5
B
4 - 4e-0.5
Answer C: 4 - 4e -0.5
C
20 - 20e-0.5
The amount of snow that falls from time t = 0 to time t = 5 hours is 20(1-e^(-0.5)) inches.
What is integration ?
Integration is the process of finding an antiderivative of a function. An antiderivative of a function is a function whose derivative is equal to the original function. In other words, integration is the reverse process of differentiation. The process of integration can be thought of as the summing of an infinite number of infinitesimal "slices" of the function being integrated, over a given interval. The symbol ∫ is used to denote integration.
The amount of snow that falls between time t = 0 and time t = 5 hours can be found by evaluating the definite integral of the rate of snowfall with respect to time over the interval [0, 5].
∫[0,5] 2e^(-0.1t) dt
The antiderivative of 2e^(-0.1t) with respect to t is -20e^(-0.1t)
Therefore, the definite integral is
-20e^(-0.15) - (-20e^(-0.10))
= -20e^(-0.5) + 20 = 20(1-e^(-0.5))
Therefore, the amount of snow that falls from time t = 0 to time t = 5 hours is 20(1-e^(-0.5)) inches.
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Can someone verify this for me?
Answer:
It looks correct.
Step-by-step explanation:
The other answer choices don't make sense.
This chart summarizes the gender of each student in a class as well as whether they own a dog or cat. If we randomly choose a pet from this group what is the probability that the pet is a dog owned by a boy?
Answer:
Step-by-step explanation:
2. Determine the lateral and total surface area of the pyramid. 6.9 cm 8 cm Lateral Surface Area Total Surface Area
Answer:
Step-by-step explanation:
Step 1: Calculate the slant height of the pyramid.
Slant Height = √(6.9^2 + 8^2) = 10.1 cm
Step 2: Calculate the lateral surface area of the pyramid.
Lateral Surface Area = 4 * (1/2 * 6.9 * 10.1) = 176.5 cm^2
Step 3: Calculate the total surface area of the pyramid.
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 176.5 cm^2 + (1/2 * 6.9 * 8) = 227.7 cm^2
What’s 1x+6y=8 graphed?
Answer: y = -1/6x + 1 1/3
Step-by-step explanation:
PLEASE HELP!!!!!
Isa's family uses sap to make maple syrup. The table shows the temperature of the sap as it heats up. Find the slope and y-intercept then write the equation in slope intercept form. Interpret the meaning of this equation.
Time (h)
Temp (°F)
Chart:
0 1 2 3 4
38 83 128 173 218
The tallest tree in the United States is the coast redwood and your deer Smith State Park in California. It is 321 feet tall suppose you are 5‘,8“ tall and cast a shadow that is 2 feet at a certain time of day about how long is the trees shadow at the same time of day convert five point 5‘8“ to feet
The tree's shadow at the same time of day was 113.29 foot long.
What is foot?Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures (typically 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.
The metre, the fundamental linear unit in the metric system, has largely replaced the foot, with its multiples and subdivisions, in most nations and in all scientific applications. In the United States, the definition of a foot as exactly 30.48 cm went into effect in 1959.
We know that
1 feet = 12 inches
So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet
Now, lets find the shadow of tree
5[tex]\frac{2}{3}[/tex]/2 = 321/x
x = 113[tex]\frac{5}{11}[/tex]
x = 113.29
Thus, the tree's shadow at the same time of day was 113.29 foot long
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Assuming that 13.2% of pennies in circulation are pre-1982 copper pennies, is it surprising to randomly select 50 pennies for which 11/50 = 22% or greater? Justify your answer.
It is surprising to some extent when the probability of getting pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.
What is probability?As with "point" and "time," which we can't exactly define, the concept of "the probability of something" is one of those concepts that is still useful. The ideas in the paragraphs that follow should help you grasp the idea.
Typically, events are the "somethings" for which we consider the probabilities. We might discuss the likelihood that someone in a particular group will develop a specific disease within the next five years, the probability that the number on a die we rolled is 5, the likelihood that it will rain tomorrow, etc.
The pre-1982 copper pennies are 13.2%
That is for every 100 pennies randomly selected there will 13.2 pre-1982 copper pennies,
And for 50 pennies there will be 13.2/2 pre-1982 copper pennies
= 6.6
So the probability of getting a pre-1982 copper pennies from random 50 pennies are 6.6.
Therefore, it is surprising to some extent when the probability of getting pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of acts on a certain object, the acceleration of the object is . If the acceleration of the object becomes , what is the force?
If the acceleration of the object becomes 9m/s², the force will be 24N
How to calculate the force?From the information, the moving object, the force acting on the object varies directly with the object's acceleration. When a force of 36N acts on a certain object, the acceleration of the object is 6m/s². The constant will be:
y = k/x
y = force.
x = acceleration
k = constant of proportionality.
k = 36 × 6
k = 216
If the acceleration of the object becomes 9m/s², the force will be:
= 216 / 9
= 24
The force is 24N.
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1 Gavin's mother poured 1 cups of milk in his
3
5
glass. If Gavin drinks cup of the milk, what
fraction of the milk will remain in the glass?
A
11
20
B
7
20
C
9
20
D
13
20 which should I choose
Answer:
choice B ( 7/20) is the right answer.
Step-by-step explanation:
If Gavin's mother poured 1 cup of milk in the glass and Gavin drinks 1/5 of the milk, the fraction of the milk that will remain in the glass is (4/5) of 1 cup.
So, B ( 7/20) is the right answer.
Solve for b.
7+b=a
I need this for a quiz review
Answer:
b = a - 7
Step-by-step explanation:
subtract 7 from both sides of the equation
Which number makes the equation true?
Answer:
7/28 = 1/4
This is because:
7/28 = 0.25
0.25 = 1/4
Step-by-step explanation:
Hope it helps! =D
Answer:
a) 7
Step-by-step explanation:
Given problem,
→ [ ] ÷ 28 = 1/4
Let us assume that,
→ missing number = x
Forming the equation,
→ x ÷ 28 = 1/4
→ x = (1/4) × 28
→ x = 28/4
→ [ x = 7 ]
Hence, the answer is 7.
Write a system of linear equations in two variables that has a solution of (4.2, -2.5)
The system of linear equations y = x - 6.7 and y = - x + 1.7 have solution at point (x, y) = (4.2, - 2.5).
How to derive a system of two linear equations
In this problem we need to construct a system of two linear equations whose solution is point (x, y) = (4.2, - 2.5). Linear equations are algebraic equations of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableThe procedure is shown below. First, obtain the intercept of the first equation:
b = y - m · x
(x = 4.2, y = - 2.5, m = 1)
b = - 2.5 - 4.2
b = - 6.7
Second, write the first linear equation:
y = x - 6.7
Third, find the intercept of the second equation:
b = y - m · x
(x = 4.2, y = - 2.5, m = - 1)
b = - 2.5 - (- 1) · (4.2)
b = - 2.5 + 4.2
b = 1.7
Fourth, write the second linear equation:
y = - x + 1.7
Please see the image attached below for a representation of the system of linear equations.
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Please help with 1 or 2!!!
In the ΔWXY, with the incenter of the triangle being Z.
1. The measure of m∠WYZ = 43°.
2. The measure of m∠WXY = 66°.
3. The measure of m∠YWX = 28°.
4. The measure of m∠ZWX = 14°.
What is an incenter?
The intersection of the triangle's three interior angle bisectors forms the triangle's incenter. Due to the junction point of the central axis being the centre of the triangle's inscribed circle, this point is equally spaced from the sides of a triangle.
In ΔWXY, the incenter of the triangle is Z.
This means that ∠W, ∠Y and ∠X are equally bisected angles.
It is given that the measurement of ∠WYX = 86° and ∠WXZ = 33°
1. The measure of angle ∠WYZ.
The angle ∠WYX is bisected by the line segment YZ.
It forms two angles ∠WYZ and ∠XYZ.
So, the measurement of ∠WYZ = ∠WYX/2
∠WYZ = 86°/2
∠WYZ = 43°
Therefore, the measurement of ∠WYZ = 43°.
2. The measure of angle ∠WXY.
The angle ∠WXY is bisected by the line segment XZ.
It forms two angles ∠WXZ and ∠ZXY.
The measurement of angle ∠WXZ = 33°.
So, the measurement of ∠WXY = ∠WXZ × 2
∠WXY = 33° × 2
∠WXY = 66°
Therefore, the measurement of ∠WXY = 66°.
3. The measure of angle ∠YWX.
According to the properties of the triangle, the sum of three angles of triangle is 180°.
So, the equation will be -
∠YWX + ∠WXY + ∠XYW = 180°
∠YWX + 66° + 86° = 180°
∠YWX + 152° = 180°
∠YWX = 180° - 152°
∠YWX = 28°
Therefore, the measurement of ∠YWX = 28°.
4. The measure of angle ∠ZWX.
The angle ∠YWX is bisected by the line segment WZ.
It forms two angles ∠YWZ and ∠ZWX.
So, the measurement of ∠ZWX = ∠YWX/2
∠ZWX = 28°/2
∠ZWX = 14°
Therefore, the measurement of ∠ZWX = 14°.
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Which statement is true for rows A, C, and E?
r → (р^q)
Or-(pvq)
(q^r)-p
(qvr)-p
The truth of the table here is r → (р ∨ q). Option b
How to solve the tableFor rows A and E, we must now choose which of the following statements is true:
We must utilize the P -> Q table shown in the figure to ascertain that.
We are aware that only P -> Q will be true if both of P and Q's hypotheses are true. As a result of utilizing that method, we can see that the final solutions only include the transformations q->r and r->q.
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ACTIVITY: Writing an Inequality
Work with a partner. In 3 years, your friend will still not be old enough
to apply for a driver's license.
a. Which of the following represents your friend's situation?
What does x represent? Explain your reasoning.
x + 3 < 16
x + 3 ≤ 16
x + 3 > 16
ling
x+3≥ 16
Answer:
The first one, x+3<16
Step-by-step explanation:
The first one is correct. X represents your friend. In three years, your friend will still not be able to get a license.
Thus, your friend now + three years is STILL LESS THAN SIXTEEN.
X + 3 < 16
That is what that conveys.
In Exercises 5-8, use the graph which shows the right-hand and left-hand behavior of a polynomial function f.
The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is
f(x₁) < 0 and f(x₂) > 0
What is intermediate value theorem?The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).
The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value
Using the graph
f(x₁) is less than 0 which shows negative values f(x₂) is greater than 0 which shows positive valuesAt the point of change of sign is the required zero
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Simple interest easy pleas ehelp due please pls
Answer:
Part A - Option B $382.50
Part B - 11 years
Step-by-step explanation:
The formula for simple interest is
[tex]A=P(1+rt)[/tex]
[tex]A[/tex] is the final amount
[tex]P[/tex] is the initial amount
[tex]r[/tex] is the interest rate as a decimal
[tex]t[/tex] is the time
We are given
[tex]P=3000\\r=0.0425[/tex]
Part A
To evaluate the amount of interest we need to use this equation
[tex]I=Prt[/tex]
[tex]I=3000*0.0425*3[/tex]
[tex]I=382.5[/tex]
Part B
We can start with this equation, but we need to solve for [tex]t[/tex].
[tex]A=P(1+rt)[/tex]
Lets solve for [tex]t[/tex].
Divide both sides of the equation by [tex]P[/tex].
[tex]\frac{A}{P} =1+rt[/tex]
Subtract 1 from both sides of the equation.
[tex]\frac{A}{P}-1 =rt[/tex]
Divide both sides of the equation by [tex]r[/tex].
[tex]\frac{\frac{A}{P}}{r}-\frac{1}{r}=t[/tex]
Simplify the first term by multiplying the numerator by the reciprocal of the denominator.
[tex]\frac{A}{Pr} -\frac{1}{r}=t[/tex]
[tex]t=\frac{A}{Pr} -\frac{1}{r}[/tex]
Now we have an equation for time.
Substituting our values into the equation gives us
[tex]t=\frac{4402.50}{3000*0.0425} -\frac{1}{0.0425}[/tex]
[tex]t=11[/tex]
The original price of a toaster is $20.00. If Horace uses a coupon and the price is decreased 10%, what is the price Horace will pay?
Answer:
18 dollars
Step-by-step explanation:
The easiest way of calculating discount is, in this case, to multiply the normal price $20 by 10 then divide it by one hundred. So, the discount is equal to $2. To calculate the sales price, simply deduct the discount of $2 from the original price $20 then get $18 as the sales price.
GEOMETRY The combined volume of a cube and a cylinder is 1000 cubic inches. If the height of the cylinder is
twice the radius and the side of the cube is four times the radius, find the radius of the cylinder to the nearest tenth
of an inch
The radius of the cylinder with a combined volume of 1000 cubic inches is 2.4 inch
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let r represent the radius of the cylinder/cone.
For the cylinder:
Volume = π * radius² * height
but height is twice the radius, height = 2r, hence:
Volume = π * r² * 2r = 2πr³
For the cube:
Volume = side³
but side is four times the radius, side = 4r, hence:
Volume = (4r)³ = 64r³
The combined volume of a cube and a cylinder is 1000 cubic inches, hence:
1000 = 2πr³ + 64r³
r³(2π + 64) = 1000
r³ = 1000/(2π + 64)
r³ = 14.228
r = 2.4 inch
The radius is 2.4 inch
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Pls I need help!!! Can someone help me solve all this pls!!!
In a coordinate plane, a transformation is a function that maps pre-image points (inputs) to image points (outputs).
What is transformation rule?In (x,y) → (-y,x)
When you reflect a point across the line y = x, the x- and y-coordinates swap positions. When you reflect over the line y = -x, the x- and y-coordinates swap places and are negated (the signs are changed). This is a reflection across the y-axis.In (x,y) → (x + 4, y - 2)
The following are the coordinate plane rules such as : (x, y) = (x ± h, y ± k)In(x,y) → (x,-y)
The x-coordinate remains unchanged while the y-coordinate is the inverse of the original point, where h and k are the horizontal and vertical shifts. In general, this can be stated as x-axis reflection.To learn more about transformation rule refer to :
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The drama club earned $1040 from a production. A total of 64 adult tickets and 132 student tickets were sold. An adult ticket costs twice as much as a student ticket. What is the price of each type of ticket sold? Use x for adult tickets and y for student tickets.
Answer: $8
Step-by-step explanation:
one adult ticket costs twice as much as one student ticket so
cost of 1 student ticket=x
cost of one adult ticket=2x
total money made=1040
adults+students=1040 so
64(2x)+132(x)=1040
128x+132x=1040
260x=1040
divide both sides by 260
x=4
1 student ticket=$4
1 adult ticket=2x=2(4)=$8
Ike- I went geek sorry..
Graph the solution or the following inequality on the number line
(X+3)(x-4)<0
_
Treat the,, >, or sign as a = sign when graphing an inequality.
How do you graph the solution of an inequality on a number line?Draw a circle over the number to begin plotting an inequality on a number line, such as x>3 (e.g., 3). The circle should be filled in if the sign also includes equal to (or). Leave the circle blank if the sign doesn't contain the equal to symbol (> or ).
By treating the,, >, or sign as a = sign, the inequality can be shown graphically. Make a dotted line graph of the equation if the inequality is either or. Make a solid line out of the equation if the inequality is either or.
Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers. The value is not included, as indicated by the open circle. The value is included, as indicated by the closed circle.
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Anyone able to assist with the last question
The graph of the equation x^2-x-2=3 is a parabola which opens downward.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions separated by an equals sign (=). Equations are used to express relationships between unknowns, knowns, and constants. Equations are used to solve problems and describe the behavior of systems.
The graph intersects the x-axis at two points, x=1 and x=3.
Therefore, the solutions to the equation are x=1 and x=3.
To find an estimate of the solution, we can draw a straight line from the x-axis to the point of intersection on the parabola.
The line intersects the x-axis at a point slightly higher than x=1, so the estimated solution is x=1.5.
This is an approximate solution and is only an estimate. To find the exact solution, the quadratic formula must be used.
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A manufacturing company is shipping a certain number of orders that need to weigh between 183
and 184
pounds in order to ship. Use the dot plot below to answer the following questions.
1) Orders between 186 and 187 is zero
2) Common order weight is 183.8.
3) Average is 183.6625
How to interpret Dot Plots?A dot plot is defined as a simple plot that displays data values as dots above a number line. Dot plots show the frequency with which a specific item shows in a data set. Dot plots simply show the distribution of the data.
A manufacturing company is shipping a certain number of orders that need to weigh between 184 and 184 pounds in order to ship.
Data is given below;
Arranged in ascending order this would be
183.2, 183.2, 183.3, 183.3, 183.7, 183.7, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.9, 183.9
Min is 183.2 and max is 183.9
1) Orders between 186 and 187 is nil
2) Common order weight is one which is maximum repeated and in this case, the common order weight is 183.8.
3) Average = sum/16
Average = 183.2 + 183.2 + 183.3 + 183.3 + 183.7 + 183.7 + 183.8 + 183.8 + 183.8 + 183.8 + 183.8 + 183.8 + 183.8 + 183.8 + 183.9 + 183.9
Average = 2,938.6/16
Average = 183.6625
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A person charges $100 to a credit card with a 24% nominal annual interest rate.
Assuming no other charges or payments are made, what is the balance on the card, in dollars, after 1 year if interest is calculated:
1. Annually: $
2. Every 6 months: $
3. Every 3 months: $
The balance (future value) on the card after 1 year if interest is calculated:
1. Annually: $124.00
2. Every 6 months: $125.44
3. Every 3 months: $126.25.
What is the future value?The future value represents the present value compounded at an interest rate into the future, using the principle of the time value of money.
The future value can be computed using an online finance calculator.
1. Interest Calculation Annually:
N (# of periods) = 1 year
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $124.00
Total Interest = $24.00
2. Interest Calculation Every 6 months:
N (# of periods) = 2 semi periods (1 year x 2)
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $125.44
Total Interest = $25.44
3. Interest Calculation Every 3 months:
N (# of periods) = 4 quarters (1 year x 4)
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $126.25
Total Interest = $26.25
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parallelograms are ___ rectangles
Parallelograms are all rectangles because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal.
What is parallelogram?Parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
There are five important properties of parallelograms such as:
Opposite sides are congruent (AB = DC)Opposite angels are congruent (D = B)Consecutive angles are supplementary (A + D = 180°)If one angle is right, then all angles are rightThe diagonals of a parallelogram bisect each otherTherefore all rectangles are parallelograms because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal. It abides by all the properties of a parallelogram.
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If the ratio of A2 to A1 was 100, what force would be required to lift a 10,000 N car?
Therefore ,As a result, the answer to the provided problem of force is (-26.46i-52.92k) Nm.
What is a force?It is capable of both pulling and pushing. Unbalanced forces are what lead to acceleration. A force is represented by the Newton (abbreviation is N). One Newton of force is required to change a weight of one kilogram's mobility by one meters per seconds (m/s) per sec. It goes like this: 1 N = 1 kg m/s2 (kg metre / second squared)
Here,
Given: There is a force F occurring at a size of F = 165 N along the parallelepiped's diagonal in this situation.
In order to calculate the force moment F around point A.
MA=rBXF
={(-600) (-88.2i+132.3j+44.1k)}
=(-52920k - 26460i) Nm
=(-26.46i-52.92k) Nm
Therefore , the solution to the given problem of force comes out to be (-26.46i-52.92k) Nm.
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#6
Write an equation in slope-intercept form of the line that passes through the given points.
The line y=—x-2 can be seen on the right-hand graph. the expression for m=273. A slope intercept form is one that offers both a gradient and an intercept.
What exactly is a slope-intercept form?The slope intercept format can be used once you are aware that Y = mx + b. The point-slope form is a way to express an equation for a line by utilizing just a specific point just on line and its slope. You can use the slope intercept equation, y = mx + b, to get the slope, which is defined as the rise over run and represented by the point form (x,y) (0, b). The point-slope form is a way to expression an equation for a line by utilizing just a specific point on the linear and its slope.
Here,
Given:
The line y = 3x - 1 undergoes dilation with such a scale factor of 2.
The lines y = 3x is enlarged and centered by a factor of two (scaling factor).
The chart on the right displays the equation m=273 and the line y=—x-2.
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7 Hafiz poured of the water in a tank into a basin and the rest into a pail. He then poured 1 litres of water from the basin into the pail. Both the basin and the pail had an equal amount of water in the end. How much water was poured into the basin at first? Express your answer as a mixed number in its simplest form.
Answer:
x = bottles
y = pail
So, originally the pail had 3.68L from the finished bottle
x+3.68L=y
Then the second equation is after Bill spills 1.2L from the pail, the contents are 3 times that of the bottle
y-1.2L=3x
then played first
so
x-y = -3.68
-3x+y= 1,2
__________+
-2x= -2.48
x=1.24L
So the volume of the bottle is 1.24 L
Pail volume: 1.24+3.68= 4.92L