SOLUTION:
Step 1:
In this question, we are given the following:
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s.
For example, the value of a particular rocking chair is well approximated by:
[tex]V=60(1.25)^t[/tex]where V is in dollars and t is the number of years since 1975.
Find the rate, in dollars per year, at which the price is increasing.
Step 2:
Next,
[tex]\begin{gathered} \text{Given,} \\ V=\text{ }60(1.25)^t \\ \text{Calculating the rate, } \\ we\text{ ne}ed\text{ to differentiate V with respect to t, we have that:} \\ \frac{dV}{\differentialDt t}=(1.25)^t\ln (1.25)\text{ 60} \end{gathered}[/tex]
Now, we need to evaluate:
[tex]\begin{gathered} \ln (1.25)60\text{ = 13. 38861308 }\approx\text{ 13. 3886} \\ \end{gathered}[/tex]Hence, the rate, in dollars per year since 1975, at which the price is increasing is:
[tex]\frac{dV}{\differentialDt t}=13.3886(1.25)^t[/tex]
The surface areas of the circular cylinder shown in the figure is given by S = 2π(25) + 2π(5h).
Find the heighth of the cylinder if the surface area is 942 square feet. Use 3.14 for 7t.
h =
The heighth of the cylinder if the surface area is 942 square feet is 25 feet.
How to calculate the height?From the information given, the S = 2π(25) + 2π(5h). We are to find the heighth of the cylinder if the surface area is 942 square feet.
This will be:
S = 2π(25) + 2π(5h).
2π(25) + 2π(5h) = 942
50π + 10πh = 942
(50 × 3.14) + (10 × 3.14 × h) = 942
157 + 31.4h = 942
Collect like terms
31.4h = 942 - 157
31.4h = 785
h = 785/31.4
h = 25
The height of the cylinder is 25 feet
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O POLYNOMIAL AND RATIONAL FUNCTIONSFinding the maximum or minimum of a quadratic function
Given
The function,
[tex]g(x)=x^2+4x[/tex]To find:
The maximum or minimum value of the function, and where does it occur.
Explanation:
It is given that,
[tex]g(x)=x^2+4x[/tex]That implies,
Set g(x)=y.
Then,
[tex]\begin{gathered} y=x^2+4x \\ y=(x+2)^2-4 \\ y+4=(x+2)^2 \end{gathered}[/tex]Here, a=1>0.
Then, the parabola opens up.
And, k is the minimum functional value, it occurs when x = h.
Therefore,
1) g(x) has a minimum value.
2) g(x)'s minimum value is -4.
3) And it occurs at x = -2.
Solve the equation p + 7 = −15 for p. −22 22 −8 8 need help
An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
p + 7 = -15
Subtract both sides by 7
p + 7 - 7 = -15 - 7
p + 0 = -22
p = -22
Hence "An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct".
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Which of (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to y = x + 2?
O(3, 5) and (4, 6)
O(4, 6) and (5, 7)
Onone
O all
All of them would be the answer.
What is the basic component of solving an equation?The left side and right side of every equation should be equal. It is essential that both parties are on an even playing field. An equation must contain the following elements: coefficients, variables, operators, constants, terms, expressions, and an equals sign. Any one, some, or all of these terms may circle the equal sign in an equation.
Rule of Thumb for Equation Solving:
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.Here, we will put the values of x and y coordinates in the equations:
5=3+2
6=4+2
7=5+2
8=6+2
Hence, the right and left side of the equation is equal.
Thus, all of them are correct answers. It would just be all of them.
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What is the concentration of hydrogen ions in a solution with a pH of 2?
When pH is 2, the hydrogen ion concentration in [tex]litre^{-1}[/tex] is [tex]10^{-2}[/tex]
What is pH?The pH value of water indicates how acidic or basic it is. The negative log of the hydrogen ion concentration is defined as pH. The pH scale starts from 0 and ends at 14. A pH of 7 is considered neutral because pure water has a pH of exactly 7. Acidic values are less than 7; basic or alkaline values are greater than 7.
Given that,
pH = 2 for HCl acid
We know that,
The relation between concentration of acid and pH is,
pH = -log[[tex]H^{+}[/tex]]
2 = -log[[tex]H^{+}[/tex]]
[tex][H^{+} ][/tex] = [tex]10^{-2}[/tex]
Hence, the hydrogen ion concentration in a solution with a pH of 2 is [tex]10^{-2}[/tex].
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Find the total surface area of the following cone. leave your answers in terms of PI
Given
height of cone = 4cm
Base radius of cone = 3cm
Find
TSA of cone
Explanation
[tex]l=\sqrt{4^2+3^2}=\sqrt{16+9}=5[/tex]We know that TSA of cone is
[tex]\begin{gathered} TSA=\pi r(r+l) \\ =\pi(3)(3+5) \\ =\pi(3)(8) \\ =24\pi cm^2 \end{gathered}[/tex]Final Answer
[tex]TSA=24\pi cm^2[/tex]A coffee shop collected the following information regarding purchases from 110 of its customers. 67 purchased coffee. 41 purchased donuts. 19 purchased coffee and donuts. Complete parts a) through c) . a) Of those surveyed, how many purchased only coffee? (Type a whole number.)
We have the next information
Let X be the number of customer purchased coffee
Let Y be the number of customer pwho urchased donuts
X∩Y Then is the number of customers who purchased both coffee and donuts
X∪Y is the number of customers who purchased both coffee or donuts
The number of customers who purchase only coffee is
[tex]67-19=48[/tex]48 customers purchased only coffee
The number of customers who purchase only donuts is
[tex]41-19=22[/tex]22 customers purchased only donuts
In order to know how many customers did not purchase either of these items
First we will calculate the customers that purchase something
[tex]67+41-19=89[/tex]then we know that the total number of customers is 110
[tex]110-89=21[/tex]21 customers did not purchase either of these items
Can anyone put on these on a table
y=4x-7 and y + x =6
Answer:
4x_7+x=6 4x_x=7+6 3x=13 x=13÷3
(a) Rewrite as a logarithmic equation.e^y=2(b) Rewrite as an exponential equation.In x=9
Let's rewrite it the first one
[tex]e^y=2[/tex][tex]\begin{gathered} \log _ee^y=\log _e2 \\ y=\log _e2 \end{gathered}[/tex]When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.
Rewriting the second one:
[tex]\begin{gathered} \ln (x)=9 \\ \log _ex=9 \\ x=e^9 \end{gathered}[/tex]Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9
is when you multiply with any number with a negative or possitive the asnwer is also suppossd to also have a negative and possitive . Also will i get the answer wrong if i dont put any of the sighn ?
If we mutiply a positive number with a positive or negative sign we get the answer as number with sign.
[tex]eg\colon5\times(+1)=5,5\times(-1)=-5[/tex]If we mutiply a negative number with sign the answer will be,
[tex]eg\colon(-5)\times(+1)=-5,)-5\times(-1)=5_{}[/tex]Thus, if we mutiply a negative to a positive number the sign gets reversed.
Determine the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
SOLUTIONS
The parallel line will be of form
[tex]m_1=m_2[/tex]the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
[tex]\begin{gathered} -4y-3x=-3 \\ -4y=3x-3 \\ y=\frac{3x}{-4}-\frac{3}{-4} \\ y=-\frac{3}{4}x+\frac{3}{4} \\ y=mx+c \\ m_1=-\frac{3}{4} \end{gathered}[/tex]The equation of the line parallel to point(1/7 , 1)
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=\frac{1}{7},y_1=1 \\ y-1=-\frac{3}{4}(x-\frac{1}{7}) \\ y-1=-\frac{3}{4}x+\frac{3}{28} \\ y=-\frac{3}{4}x+\frac{3}{28}+1 \\ multiply\text{ through by 28} \\ 28y=-21x+3+28 \\ 28y=-21x+31 \end{gathered}[/tex]15. In circle A, SQ = 12 and AT = 8. Find AR.AR =AR
We have to find the length of AR.
It will be the same as the length of AS, as they are both radius of the circle:
[tex]AR=AS[/tex]AS is the hypotenuse of a right triangle with legs AT and TS.
Also, TS has half the length of SQ, so we have:
[tex]TS=\frac{1}{2}SQ=\frac{1}{2}\cdot12=6[/tex]We then can calculate AS as:
[tex]\begin{gathered} AS^2=TS^2+AT^2 \\ AS^2=6^2+8^2 \\ AS^2=36+64 \\ AS^2=100 \\ AS=\sqrt[]{100} \\ AS=10 \\ \Rightarrow AR=10 \end{gathered}[/tex]Answer: AR = 10
The next nine births at a hospital all being girls
Answer:
There is a chance it could happen. Rare occurrence though.
Step-by-step explanation:
how do I solve 9-2x=35
In order to solve the expression:
[tex]9-2x=35[/tex]We operate inn such a manner that x is left alone, that is:
[tex]9-2x=35\Rightarrow9=35+2x\Rightarrow9-35=2x[/tex][tex]\Rightarrow-26=2x\Rightarrow-13=x[/tex]We have our expression 9 - 2x = 35.
In order to solve for x, we try and leave x alone, that is, we sustract 9 from both sides of the operation:
9 - 9 - 2x = 35 -9 => -2x =26
Now that we have this, we proceed to eliminate -2 from the side of x, for that we divide both sides by -2, that is:
(-2/-2)x=(26/-2) => x = -13
The angel pitch of a roof is safest when measuring between 18 - 27. According to these guidelines, is the roof pictured in the image safe? I cannot figure out where to start with this question nor how to solve it.
we know that
YZ=RV+VQ ----> by addition segments postulate
substitute given values
30=RV+15
so
RV=30-15=15 ft
that means
Point V is the midpoint of the segment RQ
triangle RPQ is an isosceles triangle
mFind out the value of angle x
tan(x)=4/15 ------> by TOA
x=tan^-1(4/15)
x=14.93 degrees
The angle x is not between 18 - 27
therefore
The roof Is not safe2. Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day.
I NEED HELP .How fast in inches per minute can this weed grow? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
Invasive weed grows at a rate of 0.0011 ft per minute a day
In the above question, it is given as
Invasive weed grows really fast and the rate of its growth is being provided as follows
The rate at which the weed is growing a day is = 1.65 ft
We need to find the, rate at which this weed is growing per minute
So, to do this, we'll find the growth in 1 min
In 24 hours growth is = 1.65 ft
Conversion factors
We know, 1 hour = 60 minutes
In 1 min growth is = [tex]\frac{1.65}{24 . 60}[/tex]
Here, we have multiplied with 60 in the denominator to convert hours into minutes
After solving the fraction we'll get
Growth in 1 min of the weed = 0.0011 ft
Hence, Invasive weed grows at a rate of 0.0011 ft per minute a day
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Y-Intercept: x-intercept: y 소 4 3+ 2+ 1- HX 1 2 3 4 -2+ -3 -47 -1413121110-9-8-7-6-5-4-3-2 -61 - 77 -8+ -9+ -10 -11+ -12+ -13+ -141
Input data
Graph
Procedure
y-intercept
Y-Intercept of a Straight Line. Where a line crosses the y-axis of a graph.
(0, -6)
x-intercept
The x-intercept is the point where a line crosses the x-axis
(-8,0)
For each system choose the best description of a solution if applicable give the solution
ANSWER
The system has no solution
EXPLANATION
We want to find the solution to the system of equations given:
[tex]\begin{gathered} x+4y-4=0 \\ -x-4y=4 \end{gathered}[/tex]From the first equation, make x the subject of the formula:
[tex]x=4-4y[/tex]Substitute that into the second equation and simplify:
[tex]\begin{gathered} -(4-4y)-4y=4 \\ -4+4y-4y=4 \\ \Rightarrow4y-4y=4+4 \\ 0=8 \end{gathered}[/tex]As we can see, the two sides of the equality sign have two different values.
This implies that the system of equations has no solution.
please break down 145 + 216 with the hundreds tens and ones.
Step 1:
Sum the numbers
[tex]145+216=361[/tex]Step 2:
Express the number in Hundreds, Tens, and Ones
3 has a value of 300
6 has a value of 60
1 has a value of 1
Therefore, to express 361 in hundreds, tens and ones
Which of the following represent(s) the commutative law of addition?1.6 X 5 = 5 x62.6 + 5 = 5 + 63.6–5 = 5-64.2 and 33 only1 and 42 only
Given:
Commutative law of addition.
[tex]6+5=5+6[/tex]2 only is the correct answer.
Balloon A is released 5 feet above the ground. Balloon B is released at ground level. Both balloons rise at a constant rate. Which situation can you represent using an equation of the form y = kx? Explain.
Table for Balloon A shows that the balloon reaches 9ft in 1s, 13ft in 2s, 17ft in 3s. Table for Balloon B shows that the balloon reaches 4ft in 1s, 8ft in 2s and 12ft in 3s.
Answer: Balloon B
Step-by-step explanation:
The distance, in feet, is always four times the time, in seconds.
-r + 23 = -7r+ 3(2r + 8)
Ned help solving….Please help
The equation has no solution.
How to find the solution of the given equation?
-r + 23 = -7r + 3(2r + 8)
Applying distributive property A(B+C) = AB+AC
⇒ -r + 23 = -7r + 6r + 24
Combining like terms,
⇒ 7r - 6r -r = 24 - 23
⇒ 7r - 7 r = 1
⇒ 0 = 1
L.H.S ≠ R.H.S
Since the two sides are unequal , there is no solution.
What is the distributive property ?
In mathematics, the rule governing addition and multiplication operations is known as distributive law or distributive property.It is shown as A(B+C) = AB+AC.This law makes it simple to demonstrate that multiplying a sum of numbers by a certain number after adding multiple numbers has the same result as multiplying each number by the same amount independently before adding the results. It claims that multiplying a collection of significant two or three digit numbers will produce the same result as partitioning, multiplying, and adding the numbers individually.To learn more about distributive property, refer:
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Help me to find the measure of angles 1 2 and 3!
Given:
Given the diagram
Required: The measure of angles 1, 2 and 3.
Explanation:
The sum of interior angles of a triangle is 180 degrees. So,
[tex]\begin{gathered} x+55^o+70^o=180^o \\ x=180^o-55^o-70^o \\ =55\degree \end{gathered}[/tex]The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.
[tex]\begin{gathered} x+m\angle1=180\degree \\ 55\degree+m\angle1=180\degree \\ m\angle1=180\degree-55\degree \\ =125\degree \end{gathered}[/tex]The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,
[tex]m\angle2=55\degree[/tex]Angle y and 150 degrees are supplementary angles. So,
[tex]\begin{gathered} y+150\degree=180\degree \\ y=180\degree-150\degree \\ =30\degree \end{gathered}[/tex]The sum of the interior angles of a triangle equals 180 degrees.
[tex]\begin{gathered} m\angle2+m\angle3+y=180\degree \\ 55\degree+m\angle3+30\degree=180\degree \\ m\angle3=180\degree-55\degree-30\degree \\ =95\degree \end{gathered}[/tex]Final Answer:
[tex]m\angle1=125\degree,m\angle2=55\degree,m\angle3=95\degree[/tex]- The simple interest equation is I = Prt, where I is the interest
-
earned, P is the principal investment, and t is the amount of time
(in years).
Use the formula to solve the problem: If a $5,000 investment earns
$1,57 interest over 18 years, what is the annual interest rate?
% (enter your answer as a percent and do not round)
T=
The rate of the given amount 0.001744%
What is Simple Interest?
Simple interest is a quick and easy way to calculate interest on a loan. Simple interest is the daily interest rate multiplied by the principal multiplied by the number of days until the next payment.
Given,
Principal = $5000
Interest = $157
Time = 18years
The formula for simple interest:
I = P x R x T
157 = 5000 x R x 18
R = 157 / 5000 x 18
R =0.001744%
Hence, the annual rate of interest is 0.001744%
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Find the numerical value if x=4 and y=34x2(squared)+7y=?
To find the numerical value of the expression, we have to replace the variables for their given values. This way:
[tex]\begin{gathered} 4x^2+7y \\ 4(4)^2+7(3) \\ 4\cdot16+21 \\ 64+21 \\ 85 \end{gathered}[/tex]The numerical value of the expression is 85.
M) Point K is the midpoint of JL. JK = 6x + 9 andKL = 5x + 12. Find JK.1) 272) 303) 18
Answer:
The right option is 1) 27
Explanation:
According to the given data we have the following:
K is the midpoint of JL.
JK = 6x + 9
KL = 5x + 12
K is the midpoint of JL, hence, JL=JK+KL
So, to find JK we would equal JK with KL
So, 6x + 9=5x + 12
6x-5x=12-9
x=3
Therefore, JK=6(3)+9
JK=18+9
JK=27
Therefore, the right option is 1) 27
Please help me!! The question is in the attachment!!
Using it's concept, the probabilities are given as follows:
b) P(B|C) = 0.1429.
c) P(not A|B) = 0.8.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item b, the conditional probability can be written as follows:
P(B|C) = P(B and C)/P(C).
From the diagram, we have that:
P(B and C) = P(5) = 0.05.P(C) = P(5) + P(6) = 0.05 + 0.3 = 0.35.Hence:
P(B|C) = 0.05/0.35 = 0.1429.
For item c, the conditional probability is:
P(not A|B) = P(not A and B)/P(B).
From the diagram, these probabilities are:
P(not A and B) = P(4) + P(5) = 0.15 + 0.05 = 0.20.P(B) = P(3) + P(4) + P(5) = 0.05 + 0.15 + 0.05 = 0.25.Hence:
P(not A|B) = 0.20/0.25 = 0.8.
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A cyclist rides his bike at the speed of 11 ft per second what is the speed in miles per hour how many miles will the cyclist travel in 5 hours in your computations use the fact that one mile is equal to 5280 ft do not round your answers
The speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
According to the question,
We have the following information:
A cyclist rides his bike at the speed of 11 ft per second.
Now, it is given that we have to use 1 mile = 5280 ft.
So, we have:
1 ft = 1/5280 miles
We know that there 3600 seconds in 1 hour.
1 seconds = 1/3600 hour
So, we have the speed in miles per hour:
11*(1/5280)/(1/3600)
(11*3600)/5280
7.5 miles per hour
Time taken = 5 hours
Speed = 7.5 miles per hour
Distance = speed*time
Distance = 7.5*5
Distance = 30 miles
Hence, the speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
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A man walked 5 miles right and read a sign that said "20 miles north to Atlanta". How far is Atlanta from the starting point?
ANSWER
Atlanta is 20.62 miles away from the starting point
EXPLANATION
This is a diagram of this problem
We're looking for the hypotenuse of this right triangle. Using the Pythagorean theorem:
[tex]\begin{gathered} d^2=5^2+20^2 \\ d=\sqrt[]{25+400} \\ d=\sqrt[]{425} \\ d\approx20.62\text{ miles} \end{gathered}[/tex]f(x)=4x^{2}-8x-5 f(x)=4x 2 −8x−5 \text{Find }f(-7) Find f(−7)
The value of given quadratic equation at -7 is 247.
What is quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
given ,f(x) = [tex]4x^{2} -8x-5[/tex] to find f(-7)
f(-7)= 4(49)-8(-7)-5
=196+56-5
=247
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