A sine function that has an amplitude of 2, a midline of 4 and a period of 2/3 is write as:
y = 2 sin 3πx + 4How to write the sine functionThe sine function is written considering the general formula in the form
sine function, y = A sin wx + b
where
A = amplitude
w = 2π / period
b = midline
In the problem the values available are
A = 2
b = 4
period = 2/3
substituting the known values
sine function, y = A sin wx + b
sine function, y = 2 sin (2π / 2/3) x + 4
sine function, y = 2 sin (3π) x + 4
sine function, y = 2 sin 3πx + 4
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3. Mr. Black's pay increased by 15% when he got a raise, bringing his new salary to $184. What was Mr. Black's original pay?
Answer:
$160
Step-by-step explanation:
115% = $184
100% = X
let X be the original salary
(X is unknown)
115% = $184
100% = X
cross mutiply
115 x X = 100 x 184
115X = 18400
X = 18400 divided by 115
X = $160
therefore,Mr Black's original salary before increased by 15% was $160
hope am helpful.
Nathan shares out 12 sweets he gives yasmin 1 sweet for 3 sweets he buys how many sweets does nathan get
Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.
How many sweets does Nathan gets?Given that, Nathan shares out 12 sweets, he gives Yasmin 1 sweet for 3 sweets he buys.
Let the sweet be represented by x
For each x sweet for Yasmin, Nathan gets 3x sweets
Hence
x + 3x = 12
We solve for x
4x = 12
x = 12/4
x = 3
Hence;
Yasmin gets x sweet = 3
Nathan gets 3x sweets = 3 × 3 = 9
Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.
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The number of marriage licenses issued by Clark County Nevada, the county where Las Vegas is located, has been
decreasing since the year 2000:
According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.
You must find the linear regression equation first.
The number of marriage licenses were issued in 2003 is 21586.
According to the statement
we have to find the number of marriage licenses were issued in 2003
and the given equation is y=3.405x^2-17674x+21533000
And in this equation x represent the time
And Y represent the number of marriage certificate issued.
So, in given equation
y=3.405x^2-17674x+21533000
we fill the value of X and find the value of Y means tne number of marriage license is issued in 2003
We know that X = 3 from 2000 to 2003
Then put X=3 in the given equation.
Then
This is the equation (1) represent the change
y=3.405(3)^2-17674(3)+21533000 -(1)
y = 30.645+53022+21533000
y = 21586052.645
On nearest hundred the value becomes 21586.
So, The number of marriage licenses were issued in 2003 is 21586.
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DISCLAIMER: The question was incomplete. please find the full content below.
QUESTION:
According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.
The number of marriage licenses issued by Clark county Nevada, the county where Las Vegas is located, has been decreasing since the year 2000. This can be modeled by y=3.405x^2-17674x+21533000 where x is the year and y is the number of marriage licenses issued.
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Answer: A. 137,000
Step-by-step explanation: I did the quiz.
Select the correct answer. A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot. Ο Α. 71 feet OB. 89 feet OC. OD. 45 feet 141 feet
From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.
How do you determine the maximum side length?We are given the following details are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b²
The total surface area is calculated using:
T = L + b²
So, we have:
T = 10b² + b²
Evaluate the sum
T = 11b²
Recall that the maximum surface area is 50,000 square feet
So, we have:
11b² = 50000
Divide both sides by 11
b² = 50000/11
Taking the square root of both sides, we have
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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The diameter of an electric cable is normally distributed, with a mean of 0.9 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.92 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.)
The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841
What is probability?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The given parameters are:
Mean = 0.9
Standard deviation = 0.2
Calculate the z-score at x = 0.92 using
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
z = (0.92 - 0.9)/0.02
Evaluate the numerator; subtract 0.9 from 0.92
z = 0.02/0.02
Divide 0.02 by 0.02. This gives
z = 1
The probability is then represented as:
P(x > 0.92) = P(z > 1)
Next, we look up the value of the z table of probabilities
From the z table of probabilities, we have:
P(x > 0.92) = 0.841
Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841
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The image of the point (-7, 8) under a translation is (-11, 6). Find the coordinates
of the image of the point (8, -3) under the same translation.
Answer:
(4,-5)
Step-by-step explanation:
Solve the quadratic equation by graphing it. Select all possible answers.
[tex]y=x^2+8x+12\\x=?[/tex]
Possible answers:
-6
6
-8
2
-2
8
No real solutions
The solutions to the given quadratic equation are x = -6 and x = -2
Quadratic equationsFrom the question, we are to solve the given quadratic equation
The given equation is
y = x² + 8x + 12
To solve the equation, we will set it equal to 0
That is,
x² + 8x + 12 = 0
Solving
x² + 8x + 12 = 0
x² + 2x + 6x + 12 = 0
x(x +2) +6(x + 2) = 0
(x +6)(x + 2) = 0
x +6 = 0 OR x +2 = 0
x = -6 OR x = -2
Hence, the solutions to the given quadratic equation are x = -6 and x = -2
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22. Chris bought a new car for $12,500. He made a $3,000 down payment and financed the rest at an annual interest rate of 14.5% for 36 months (3 years). How much less would his total interest be for the same loan for 24 months (2 years)? A. $1,387.50 B. $1,377.50 C. $1,367.50 D. $1,357.50
Answer:
Step-by-step explanation:
Purchase price (A) : $12,500
Down Payment (B): $3,000
Loan Taken (C = A - B): $9500
D : Interest calculation for $9,500 for 3 years P(1 + rt)
= 9500(1 + (14.5/100) * 3)
= 9500(1 + 0.145 * 3)
= 9500 * 1.435
= $13632.5
E : Interest calculation for $9,500 for 2 years P(1 + rt)
= 9500(1 + (14.5/100) * 2)
= 9500(1 + 0.145 * 2)
= 9500 * 1.29
= $12,255
Difference between D - E
= $13632.5 - $12,255
= $1377.5
Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years
find the square root of 9_4√2
[tex]\begin{gathered} 9 - 4\sqrt{5} \\ \\ = 4 + 5 - 4\sqrt{5} \\ \\ = (- 2)^2 + (\sqrt{5})^2 + (2 \times - 2 \times \sqrt{5}) \\ \\ = (- 2 + \sqrt{5})^2 \\ \\ = (\sqrt{5} - 2)^2 \\ \\ \\ \therefore \sqrt{9 - 4\sqrt{5}} = \sqrt{5} - 2 \end{gathered}[/tex]
Hope this may be helpful.
Which statement describes the graph of y + 2 ≥ –4(x – 3)2? a parabola opening up, with shading above the vertex a parabola opening up, with shading below the vertex a parabola opening down, with shading above the vertex a parabola opening down, with shading below the vertex
Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.
How to describe the shape of the parabola.To do this you have to create a graph of the equation as seen in the attachment.
From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.
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Use the Associative Property to find the value of the variable.
(8 x 15) x s = 8 x (15 x 11)
Answer:
hey its me again so the answer is 11.
I'm sure because I did this.
A candy company designs a package to hold chocolates. The height of the container is 13 inches and the diameter of its bottom is 9 inches. Diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. Which shape best models the package, and what is the approximate surface area of the package? The best model for the package is a . The approximate surface area is square inches.
The best model for the package is a cone and the approximate surface area is 258 square inches.
How to illustrate the information?From the information given, it was stated that the diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches.
In this case, the information given about the diagram shows that it's a cone.
Also, given the information, the total surface area of the cone that has a slant height and diameter is given as:
= π(d/2)(d/2 + l)
In such a situation, it should be noted that d represents the diameter in the question. The surface area is the total area that's covered by its surface.
Therefore, the best model for the package is a cone and the approximate surface area is 258 square inches.
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Solve p/-1+ 17 = 13 for p.
Answer: 208
Step-by-step explanation:
[tex]\frac{p}{-1+17} =13[/tex]
[tex]\frac{p}{16} =13[/tex]
[tex](16)\frac{p}{16} =13(16)[/tex]
[tex]p=13*16[/tex]
[tex]p=208[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{p}{-1}+17=13 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply \ the \ properties \ of \ fractions: \frac{a}{-b}=-\frac{a}{b}. } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\frac{P}{1} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply\:the\:rule \:\frac{a}{1}=a} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-P} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P+17=13} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Subtract \ 17 \ from \ both \ sides. } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P+17-17=13-17} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P=-4} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Divide\:both\:sides\:by\:-1} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{-p}{1}=\frac{-4}{-1} } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P=4} \end{gathered}$}}[/tex]Triangle L N M is shown. Angle L N M is 90 degrees and angle N M L is 20 degrees. The length of L N is 21.
Use the diagram to complete the statements.
The measure of angle L is
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
Angle L: 70°
The trigonometric ratio used to solve for NM is the tangent ratio.
NM = 57.7 [nearest tenth]
How to Apply the Trigonometric Ratios?Using the triangle sum theorem, find angle L.
Angle L = 180 - 90 - 20 = 70°
Using the tangent ratio, we can use ∠M and LN to solve for NM
Tan 20 = 21/NM [tan ∅ = opposite/adjacent]
NM = 21/tan 20
NM = 57.7 [nearest tenth]
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Answer:
70, tangent, 57.7
Step-by-step explanation:
A sphere has a radius of 5.4 yards. Find its a. volume and b. surface area. Use 3.14 for π. Round the answers to the nearest hundredth.
Answer:
sorry the drawing is messy, not used to drawing with just a finger haha! hope this helps<<3
Please draw the number line and show me if possible:)
The solution to the given inequality expression is expressed as x ≥ 6
Solving inequalitiesGiven the inequality expression shown below;
5x-9/7≥3
Cross multiply
(5x -9)≥7(3)
Expand
5x-9≥21
Add 9 to both sides
5x ≥ 21 + 9
5x ≥ 30
x ≥6
The solution to the given inequality expression is expressed as x ≥ 6
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Calculate the perimeter and area of this shape.
Perimeter =
Area =
7.5 cm
6 cm
2 cm
3 cm
2 cm
area = 25.5 cm²
Step-by-step explanation:
i have shown in the image you have to rotate it to see how i worked the area out
i am very sorry i cant work the perimeter out since i have no idea what the length of the two sides of the triangle are . if you need help on understanding how i worked out the area please let me know .
hopefully i was able to help you in half of the question i am sorry for not helping on the perimeter :)
Answer:
Step-by-step explanation:
Perimeter=25
Use the list method to write "the perfect square integers between 1 and 80 inclusive".
Answer:
Step-by-step explanation:
1 Answer
1=12.
4=22.
9=32.
16=42.
25=52.
36=62.
49=72.
64=82 .
Please help quick!!!
Reflect over the y axis then translate
The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)
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a. How many bushels of corn, if any, will the United States export or import at the prices below?
At $1, it will (import, export, or neither import or export )
___bushels.
b. How many bushels of corn, if any, will the United States export or import at the prices below?
At $2, it will (import, export, or neither import or export )
____bushels.
c. How many bushels of corn, if any, will the United States export or import at the prices below?
At $3, it will (import, export, or neither import or export )
____ bushels.
d. How many bushels of corn, if any, will the United States export or import at the prices below?
At $4, it will (import, export, or neither import or export )
____ bushels.
e. How many bushels of corn, if any, will the United States export or import at the prices below?
At $5, it will (import, export, or neither import or export )
____ bushels.
2.
a. Use this information to construct the U.S export supply curve and import demand curve for corn
b. Suppose that the only other corn-producing nations is France, where the domestic price is $4. Which country will export corn and which country will import it
The United Stated will import corn France will export it
The United States will export corn and France will import it
Neither country will import or export corn.
Based on the graph which depicts the United States domestic market for corn at different prices, we can logically deduce the following information:
At $1, the United States will import 15,000 bushels of corn.At $2, the United States will import 7,000 bushels of corn.At $3, the United States will neither import nor export any bushels of corn.At $4, the United States will export 6,000 bushels of corn.At $5, the United States will export 10,000 bushels of corn.Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.
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3 + b/d
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Fractions are mathematical expressions that relate two numbers as a quotient. Thus the answer to this question is: [tex]\frac{3d + b}{d}[/tex]
Fractions are expressions in a form of a quotient that relates one number to another number. The two numbers can be classified as either the numerator or the denominator. The number above the division line is the numerator, while that below the line is the denominator. Some types of fractions are proper fractions, improper fractions, and mixed fractions.
A given fraction can undergo basic arithmetic operations when two or more are involved. Also, a fraction can be added to one another, or subtracted from a whole number.
The given expression in the question involves the addition of a whole number (3), to a fraction (b/d).
Given: 3 + b/d
The LCM is d, thus;
3 + b/d = [tex]\frac{3d + b}{d}[/tex]
Therefore, the required answer is: [tex]\frac{3d + b}{d}[/tex]
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Find the difference between Simple interest and compound interest on 1200 for one year at 10% per annum
Answer:
the difference between them is zero cause on first year simple interest and compound interest are equal
Attached as an image below.
The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years
Growth constant
The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor
it is also called the logarithmic return, compounded return, or the force of interest.
Note that the general formula for growth rate is given as;
[tex]P(t) = P0 e^k^t[/tex]
Where,
Po = Initial value = 400 squirrels
r = Rate of growth
k = constant of proportionality = 0. 5 per year
t = time = 1 year
The function P(t) is given as;
P(t) = 400 e^0.5t
Note that the formula for doubling time is given as;
[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]
r = 4
t = 1
substitute into the formula
[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]
Doubling time = 1 × 17. 68
Doubling time = 17. 68 years
Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years
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1/2x + 1/4y = 3 solve for y
Answer:
y=-2x+12
Step-by-step explanation:
First, subtract 1/2 from each side
1/4y = -1/2x + 3 --> multiply each side by 4
y = -2x + 12 is your final answer
On 1st January 2014, Rs1,000,000 was invested and on 1st January of each
successive year Rs500,000 was added to it. What sum will be accumulated by
31st December 2018 if interest is compounded each year at 10% per annum?
The sum accumulated by 31st December 2018 is Rs 4,163,060.00
What is future value?
Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.
Note in this case that Rs500,000 would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)
We can determine the future value of each investment using the future value formula shown below:
FV=PV*(1+r)^N
PV=amount invested
r=interest=10%
N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)
Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1
Total FV=Rs 4,163,060.00
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Find the missing side of the triangle. pythagorean 4 A. 337‾‾‾‾√ km B. 5‾√ km C. 193‾‾‾‾√ km D. 112‾√ km
The missing side in the given triangle is x = √193 km
Pythagoras theoremThe Pythagoras theorem is expressed as;
x^2 = a^2 + b^2
where
x is the longest side
Substitute the given side
x^2 = 12^2 + 7^2
x^2 = 144 + 49
x = √193 km
Hence the missing side in the given triangle is x = √193 km
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Using the tree diagram below, what is the probability of getting tails and an even number?
Answer:
1/4
Step-by-step explanation:
Chances of getting tails out of all the numbers (including heads)
Totals numbers (including heads & tails): 12
Tails & Even Number: 3
3/12 simplified to 1/4
What is the name of the green segment in the hyperbola below?
A. Minor axis
OB. Transverse axis
OC. Major axis
OD. Directrix
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k.
The vertex form of the equation is y = 3(x + 2)^2 - 5
How to complete the square?The equation is given as:
y = 3x^2 + 12x + 7
Set to 0
3x^2 + 12x + 7 = 0
Subtract 7 from both sides
3x^2 + 12x = -7
Divide through by 3
x^2 + 4x = -7/3
-------------------------------------------------------------------
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)^2 = 4
-------------------------------------------------------------------
So, we add 4 to both sides of x^2 + 4x = -7/3
x^2 + 4x + 4 = -7/3 + 4
Express as perfect square
(x + 2)^2 = -7/3 + 4
Multiply through by 3
3(x + 2)^2 = -7 + 12
Evaluate
3(x + 2)^2 = 5
Subtract 5 from both sides
3(x + 2)^2 - 5 = 0
Rewrite as
y = 3(x + 2)^2 - 5
Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5
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Darcy read her thermometer in the morning and the
temperature was -2° C. In the afternoon the same
thermometer showed a temperature of -5° C.
Which of the following is true?
The temperature was 3 degrees warmer in the afternoon.
The temperature was 3 degrees colder in the afternoon.
The temperature was 7 degrees colder in the afternoon.
The temperature was 7 degrees warmer in the afternoon.
Answer:
The temperature was 3 degrees colder in the afternoon
Step-by-step explanation:
numbers on the left of zero on the number line are arranged in decreasing order and as such -2 is greater than -5.
The true statement is The temperature was 3 degrees colder in the afternoon.
What is temperature?Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Given that, Darcy read her thermometer in the morning and the temperature was -2° C. In the afternoon, the same thermometer showed a temperature of -5° C.
-2-3 = -5
We see, that, the temperature is falling from -2 to -5, that means, there was a fall in temperature from morning to afternoon.
Hence, the temperature was 3 degrees colder in the afternoon.
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