Answer:
log(10)
Step-by-step explanation:
We can use the product property for logarithms:
log(a)+log(b)=log(ab)
In our case, a=5 and b=2. We can multiply a and b now to get the new number we're taking the logarithm of.
log(2)+log(5)=log(2×5)=log(10)
PLEASE HELP 50 POINTS
To check if a solution is correct for a system of equations, we substitute the values of the solution into both equations and see if they are true.
Let's assume that the solution for the system of equations is (x,y) = (1,-1).
To check if this solution is correct for the first equation y = 2x - 3, we substitute x = 1 and y = -1:
-1 = 2(1) - 3
-1 = -1
Since -1 = -1, the solution (1,-1) satisfies the first equation.
To check if this solution is correct for the second equation y = -1/2x + 2, we substitute x = 1 and y = -1:
-1 = -1/2(1) + 2
-1 = 1
Since -1 is not equal to 1, the solution (1,-1) does not satisfy the second equation.
Therefore, the solution (1,-1) is not a solution for the system of equations y = 2x - 3 and y = -1/2x + 2.
Sophia wishes to retire at age 65
with $1,600,000
in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
compounded monthly. What is the monthly deposit that Sophia must make in order to reach her goal? Round your answer to the nearest cent, if necessary
Answer:
To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)
P = monthly deposit
r = annual interest rate (which is 9%)
n = number of times interest is compounded per year (which is 12 for monthly compounding)
t = number of years until retirement (which is 65 - 28 = 37)
Substituting the given values, we get:
1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)
Simplifying and solving for P, we get:
P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)
P ≈ $524.79
Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.
Step-by-step explanation:
The perimeter of a rectangle is 120 meters and the length is 40 meters longer than the width. Find the dimensions of the rectangle. Let x= the length and y= the width. The corresponding modeling system is {2x+2y=120x−y=40 . Solve the system graphically.
The dimension of the rectangle is 50 meters by 10 meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]
If the length is 40 meters longer than the width, then:
[tex]\text{l} = 40 + \text{w}[/tex]
Substitute
[tex]120 = 2(40+2\text{w})[/tex]
[tex]60 = 40 + 2\text{w}[/tex]
[tex]30 = 20+ \text{w}[/tex]
[tex]\bold{w = 10 \ meters}[/tex]
Since [tex]\text{l} =40 + \text{w}[/tex]
[tex]\text{l} =40 +10[/tex]
[tex]\bold{l=50 \ meters}[/tex]
Hence the dimension of the rectangle is 50 meters by 10 meters
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Classify the function type of f(x) = x+2−−−−−√3
x
+
2
3
A. square root
B. cube root
C. quadratic
D. exponential
The function type of f(x) = √3x + 2 is A. square root
Classifying the function type of f(x)From the question, we have the following parameters that can be used in our computation:
f(x) = √3x + 2
In the above function, we have the notation √
The notation √ is a square root notation
This means that the function type of f(x) is A. square root
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The mass of a bowling ball is 9ibs and the volume is 135 in³. How many lbs per cubic inch is its density? Round to the nearest hundreth
Answer:
9 pounds/135 cubic inches
= 1 pound/15 cubic inches
= .07 pounds/cubic inch
I am confused on this question. "George is building flower boxes to sell as gifts. Draw and label a net to represent a flower box. Then find the amount of material George needs for each box. Explain why you drew the net the way you did." There is also a picture that goes with it down below.
Answer:
To answer the question, you first need to understand what a net is. A net is a two-dimensional diagram that can be folded to form a three-dimensional object. In the context of this question, a net represents the unfolded and flattened-out shape of a flower box before it is assembled.
To draw a net that represents a flower box, you need to imagine what the box would look like if it were flattened out and unfolded. You can start by drawing a rectangle for the bottom of the box. Then draw four rectangles that represent the sides of the box. Each of the side rectangles should be the same length as the length of the bottom rectangle, and the width of each side rectangle should be the same as the height of the box.
Next, you need to label the net to indicate which sides will be connected to form the box. Label the edges of the rectangles with the corresponding letter to show how the box will be assembled. For example, label the top edge of the bottom rectangle as "A" and the bottom edge of one of the side rectangles as "B". Then, label the side edges of the side rectangle as "C" and "D".
To find the amount of material George needs for each box, you need to calculate the total surface area of the net. The surface area represents the amount of material needed to cover the entire box. You can find the surface area by calculating the area of each rectangle and adding them together.
In this case, the bottom rectangle has an area of 16 square inches, and each of the four side rectangles has an area of 8 square inches. Therefore, the total surface area of the net is:
16 + 4(8) = 48 square inches
This means that George needs 48 square inches of material to make one flower box.
You drew the net the way you did because it represents the flattened-out and unfolded shape of the flower box before it is assembled. Labeling the edges and rectangles helps to visualize how the box will be assembled and allows you to calculate the surface area needed to cover the entire box.
have a good day and stay safe
If sin 0 = 3/4 and angle 0 is in quadrant I, what is the exact value of tan20 in simplest radical form?
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Analyze a CSR capital investment proposal for Ganon Inc.
Ganon Inc. is evaluating a proposal to replace its HID (high intensity discharge) lighting with LED (light emitting diode) lighting throughout its warehouse. LED lighting consumes less power and lasts longer than HID lighting for similar performance. The following information was developed:
Line Item Description Value
HID watt hour consumption per fixture 500 watts per hr.
LED watt hour consumption per fixture 300 watts per hr.
Number of fixtures 800
Lifetime investment cost (in present value terms)
to replace each HID fixture with LED $300
Operating hours per day 10
Operating days per year 300
Metered utility rate per kilowatt-hour (kwh)* $0.12
*Note: A kilowatt-hour is equal to 1,000 watts per hour.
a. Determine the investment cost for replacing the 800 fixtures.
$240,000
b. Determine the annual utility cost savings from employing the new energy solution.
c. Should the proposal be accepted?
Yes
Evaluate the proposal using net present value, assuming a 15-year life and 8% minimum rate of return. (Click here to view Present Value of Ordinary Annuity.)
a)
The investment cost for replacing the 800 fixtures is $240,000.
b)
Annual utility cost savings is $57,600/year.
c)
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
We have,
a.
The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:
Total Investment Cost = Number of fixtures x Investment cost per fixture
Total Investment Cost = 800 x $300
Total Investment Cost = $240,000
b.
To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:
Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption
Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr
Energy consumption savings per fixture per hour = 200 watts/hr
Total energy consumption savings per hour for 800 fixtures:
= Energy consumption savings per fixture per hour x Number of fixtures
Total energy consumption savings per hour for 800 fixtures.
= 200 watts/hr x 800
Total energy consumption savings per hour for 800 fixtures.
= 160,000 watts/hr
Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year
Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year
Total energy consumption savings per year = 480,000,000 watt-hours/year
Total energy consumption savings per year in kilowatt-hours (kWh):
= Total energy consumption savings per year / 1,000
Total energy consumption savings per year in kWh = 480,000,000 / 1,000
Total energy consumption savings per year in kWh = 480,000 kWh/year
Annual utility cost savings:
= Total energy consumption savings per year in kWh x Metered utility rate per kWh
Annual utility cost savings = 480,000 kWh/year x $0.12/kWh
Annual utility cost savings = $57,600/year
c.
To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.
Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:
PV of Investment Cost = -$240,000 (negative because it's a cash outflow)
PV of Annual Utility Cost Savings = $514,883.81
NPV = PV of Annual Utility Cost Savings - PV of Investment Cost
NPV = $514,883.81 - (-$240,000)
NPV = $754,883.81
Therefore,
The investment cost for replacing the 800 fixtures is $240,000.
Annual utility cost savings is $57,600/year.
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
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Hurry pls Time limit
Tell me the domain and the range
Tell me whether the graph is a function or not
The answer choices are below
Answer:
its not a function
Step-by-step explanation:
Does anyone know the answer to this question
Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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Solve the following for θ, in radians, where 0≤θ<2π.
6sin2(θ)−3sin(θ)−8=0
Select all that apply:
0.6
0.16
2.68
5.08
4.34
0.27
Answer:5.08
4.34 are correct
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
6u^2 - 3u - 8 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 6, b = -3, and c = -8. Substituting these values, we get:
u = (3 ± sqrt(9 + 192)) / 12
u = (3 ± sqrt(201)) / 12
Therefore, either:
A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is an even number.
The probability that the sum of the numbers is even is,
⇒ P = 0.47
Since, We know that;
To have this kind of event you can have the following events, where
(d₁ ,d₂), d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:
(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)
And, the total number of events is 36 since every dice have 6 numbers.
The probability is:
P(Event)=P(sum is even)/Total number of events
P = 17/36
P = 0.47
Thus, The probability that the sum of the numbers is even is,
⇒ P = 0.47
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The area of a square table top can be represented by (9x^2-30x+25) square feet. The perimeter of the table top is 34 feet. What is the value of x? Explain ow you solved this problem.
The requried value of x that satisfies the problem is 4.5,
Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:
Area = 9x² - 30x + 25
Side length = √(Area) = √(9x² - 30x + 25)
To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:
Perimeter = 4 * Side length
34 = 4 * √(9x² - 30x + 25)
8.5 = √(9x² - 30x + 25)
9x² - 30x - 47.25 = 0
We can solve this quadratic equation by using the quadratic formula gives,
x = 4.5 and -1.16
Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.
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Let GH be the directed line segment beginning at point G(4,4) and ending at point H(-7,-1). Find the point P on the line segment that partitions the line segment into the segments GP and PH at a ratio of 5:6.
The coordinates of point P are (-1, 1 8/11).
We have,
G(4, 4) and H(-7, 1)
m :n = 5:6
Using Section formula
x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)
Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1
So, x = (5(-7) + 6(4))/ 11 and y = (5(-1) + 6(4))/ 11
x = -35+24/11 and y = -5 + 24/11
x = -11/11 and y = -19/11
x = -1 and y = 1 8/11
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clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in
The painted area of the sign is approximately 324 square inches. This was calculated by finding the area of the pole, square signboard, and triangle portion of the signboard and adding them together.
To find the painted area, we need to find the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard.
Area of pole
The pole is a rectangular prism with height 60in and width 4in. Therefore, the area of the pole is:
60in x 4in = 240 sq. in.
Area of square signboard
The square signboard has a side length of 8in. Therefore, the area of the square signboard is:
8in x 8in = 64 sq. in.
Area of triangular portion of the signboard
The triangular portion of the signboard has a base of 8in and a height of 5in. Therefore, the area of the triangular portion of the signboard is:
(1/2) x 8in x 5in = 20 sq. in.
Total painted area
The total painted area is the sum of the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard. Therefore, the painted area is:
240 sq. in. + 64 sq. in. + 20 sq. in. = 324 sq. in.
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--The given question is incomplete, the complete question is given
" clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in "--
14. Describe a pattern in the numbers.
9, 12, 15, 18, 21, 24
(a + 2)/(1 + a + a ^ 2) - (a - 2)/(1 - a + a ^ 2) - (2a ^ 2)/(1 + a ^ 2 + a ^ 4)
What are the angles of △ABC with side lengths a=12, b=21, and c=14?
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c
Step-by-step explanation:
To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.
According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given side lengths:
14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)
196 = 144 + 441 - 504 * cos(C)
504 * cos(C) = 389
cos(C) = 389 / 504
C = arccos(389 / 504)
Using a calculator to find the approximate value of C, we get C ≈ 43.5°.
The parent function for the graph to the right is of the form y = ab*. Write the parent function. Then write a function for the
translation indicated.
translation: left 6 units, down 7 units
The parent function is [tex]y = ab^x[/tex]
A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;
[tex]y = ab^x[/tex]
[tex]y = ab^{x+6} - 7[/tex]
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer: C. V ≈ 635.2 cm^3.
Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).
Using the given values, we have:
V = (1/3)π(4.25 cm)^2(12 cm)
V ≈ 635.2 cm^3 (rounded to the nearest tenth)
Therefore, the answer is C. V ≈ 635.2 cm^3.
Verify Euler’s theorem: (, ) =
3
+
3
.
I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
The mistake is when you try to divide by X - 1, because you can't divide by zero.
Where is the problem in this procedure?Here we start by defining:
X = 1
The second step makes sense, we are adding the same value in both sides:
X + X = X + 1
2X = X + 1
Now subtract 2 in both sides:
2X - 2 = X + 1 - 2
2X - 2 = X - 1
Here is the mistake, you divide both sides by X - 1
But we already defined that X = 1
Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
The magnitude of the speed of the particle is determined as √ (17), m/s.
option A.
What is the particle's speed?The speed of a particle is defined as the rate of change of the particle's displacement with time.
Mathematically, the formula for the speed of the a particle is given as;
v = dx/dt
where;
dx is the change in the particle's displacementdt is the change in the time of motion of the particleThe speed of the particle is calculated as;
v = u + at
where;
u is the initial speeda is the accelerationat time, t = 0, the equation for the speed of the particle becomes;
v = u
v = i + 4j
The magnitude of the speed is calculated as follows;
v = √ (1² + 4²)
v = √ (17), m/s
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Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
The most expensive car loan that Cindy can afford is $14,534.
What is the most expensive car loan?The most expensive car loan is calculated by applying the following formula.
M.P = (Pr) / (1 - (1 + r)^(-n))
Where;
P is the principalr is the monthly interest rate = 21%/12 = 0.175%n is the number of months = 6yrs x 12 = 72 monts215 = (P x 0.00175) / (1 - (1 + 0.00175)^(-72))
215 = (P x 0.00175)/0.1183
(P x 0.00175) = 215 x 0.1183
P x 0.00175 = 25.44
P = $14,534
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There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is 5: 7. Is Lonnie correct? Show why or why not.
Answer:
Step-by-step explanation:No, Lonnie is not correct. Step-by-step explanation: Because if we put 35 and 42 in rational form we can write it to its simple form by dividing it and after dividing we get the answer as 5 : 6. so that means Lonnie in incorrect.D
Just look at the picture
Answer:
perimeter = 84 feet
Step-by-step explanation:
using Pythagoras' identity in the right triangle to find a
a² + 35² = 37²
a² + 1225 = 1369 ( subtract 1225 from both sides )
a² = 144 ( take square root of both sides )
a = [tex]\sqrt{144}[/tex] = 12
then
perimeter = 35 + 37 + 12 = 84 feet
the sum of three numbers is 56. the difference of the larges and smallest is 44 and the sum of the two smaller numbers is 16. what are the numbers?
The three numbers are -2, 42 and 16 these we obtained by solving the equations
Let the three numbers x, y, and z. We know that:
x + y + z = 56 (Equation 1)
z - x = 44 (Equation 2)
x + y = 16 (Equation 3)
From Equation 3, we can solve for one of the variables in terms of the other:
y = 16 - x
Substituting this into Equation 1, we get:
x + (16 - x) + z = 56
Simplifying this equation, we get:
z = 40 - x (Equation 4)
Substituting Equation 4 into Equation 2, we get:
(40 - x) - x = 44
Simplifying this equation, we get:
40 - 2x = 44
Subtracting 40 from both sides, we get:
-2x = 4
Dividing both sides by -2, we get:
x = -2
z = 40 - (-2) = 42
Finally, using Equation 1, we can solve for y:
-2 + y + 42 = 56
y=16
Hence, the three numbers are -2, 42 and 16
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Find the missing angle
A
B
C
D
Answer:
53
Step-by-step explanation:
20+8=28
90-28=62
62-9=53
90 angle!
Find the missing angle
The measure of the missing angle is 20 degrees.
What is the measure of the missing angle?The figure in the image is a right triangle.
Missing angle θ = ?Opposite to angle θ = 8Adjacent to angle θ = 20To solve for the missing angle. we use trigonometric ratio.
Note: Tangent = Opposite / Adjacent
Plug in the values and solve for the angles:
tanθ = 8/20
Take the tan inverse
θ = tan⁻¹( 8/20 )
θ = 21.8°
θ ≈ 20°
Therefore, the angle is 20 degrees.
Option B)20° is the correct answer.
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