The rate of change of S for the weekly sales is :
-250 000e⁻°·⁵t
Given:
the sales of the product is :
S = 500,000e^-0.5t
where S is the weekly sales in the dollars and t is the number of weeks since end of the campaign.
we are asked to find the rate of sales dS/dt = ?
that is the rate of sales of delay.
Given:
S = 500,000e^-0.5t
dS/dt =(500,000)e^-0.5t + 500,00 (e^-0.5t)
= 0 + 500,00 (e^-0.5t)
= - 250 000 e^0.5t
therefore, dS/dt = - 250 000 e^0.5t
Hence we get the required answer.
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You buy the following at Target:
1 bottle of lotion for $5, 1 t-shirt for $12, 1 birthday card for $3
What is the subtotal: $
You use your Target RedCard and save 5%, what is your savings:
New Subtotal: $
Sales tax is 6%: $
Total: $
4
The subtotal is $20, Savings is $ 1, New Subtotal is $19, Sales tax is $1.14 and the Total is $20.14
How to determine the subtotal?
A sales discount is a reduced price offered by a business on a product or service
Given:
1 bottle of lotion = $5
1 t-shirt = $12
1 birthday card = $3
Subtotal = $5 + $12 + $3 = $20
If you use your Target RedCard and save 5%, savings will be:
Savings = 5% of Subtotal
Savings = 5/100 × $20 = $1
New Subtotal: $20 - $1 = $19
Sales tax is 6%: 6/100 × $19 = $1.14
Total: New Subtotal + Sales tax = $19 + $1.14 =$20.14
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7(3x+5)-11x simply the expression
Answer:
10x + 35
Step-by-step explanation:
7(3x+5)-11x
21x + 35 - 11x
10x + 35
Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for
The circumference of the circle is 25.12 inches
How to determine the circumference?From the question, we have the following parameters that can be used in our computation:
Radius = 4 inches
The circumference of a circle can be calculated using
C = 2πr
Substitute the known values in the above equation, so, we have the following representation
C = 2 * 3.14 * 4
Evaluate
C = 25.12
Hence, the circumference is 25.12 inches
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3x + 5 < 2x - 8 is:
all values more than -13.
all values less than -13. all values less than 3. all values less than -3.
Answer:
all values less than -13
Step-by-step explanation:
3x + 5 < 2x - 8
3x + 5 - 5 = 2x - 8 - 5 ==> isolate x by subtracting 5 on both sides
3x < 2x - 13 ==> simplify
3x - 2x < 2x - 2x - 13 ==> subtract 2x from both sides to move x to the left
side of the inequality
x < -13 ==> simplify
Hence, the answer is all values less than -13.
8.
For which set of data is the median greater than the mean?
A.
B.
C.
D.
{8, 12, 14, 14, 20}
{8, 12, 14, 14, 22}
{9, 13, 14, 15, 19}
(9, 13, 14, 15, 20}
Answer:
B
Step-by-step explanation:
For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.
Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.
Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.
Anil completes the 72km journey between Bristol and Cardiff in 48 minutes. He then drives 69km from Cardiff to Swansea at an average speed of 60km/h
Work out Anil's average speed (in km/h) for his total journey from Bristol to Swansea.
(with working out pls)
Answer:
75 km/h
Step-by-step explanation:
48 minutes = 48/60
(48 : 12)/(60:12)
4/5
0.8 hours
average speed between Bristol and Cardiff = 72/0.8 = 90 km/h
average speed of the journey = (60 + 90)/2 = 150/2 = 75 km/h
Jeremy's mother deposited $1,200 into a
savings account as a college fund when he
was born. How much will Jeremy have in
this account after 18 years at a yearly
simple interest rate of 4.25%?
A) $51.00
C) $918.00
B) $10,380.00
D) $2,118.00
Answer: D) $2,118.00
Step-by-step explanation:
1 year = 4.25% interest rate
18 years = 76.5% interest rate
76.5% = 0.765
Take 1200 times 0.765 = $918.00
$918.00 is the interest money he will receive after 18 years. We have to add both numbers to find the total.
$1,200 + $918.00 = $2118.00
Use the image below to answer the identify the following: One pair of vertical angles: One pair of adjacent angles: One pair of supplementary angles:
A pair of vertical angles is; Angle 1 and Angle 4
A pair of supplementary angles are; Angle 2 and angle 1
How to identify angle properties?Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.
Two angles are defined as adjacent angles when they share the common vertex and side.
Two angles are defined as supplementary angles if they sum up to 180 degrees.
By those definitions above, we can say that;
Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.
We can also say that;
Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.
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Work out the base of a square with area,
A
= 64cm2.
Answer: 8cm
Step-by-step explanation:
Square root 64 to get 8
Answer:
8cm
Step-by-step explanation:
A base is either the length or the width of the square (doesn't matter because square has 4 equal lengthed sides). To find the area from the base, square it. To find the base from the area, square root it (inverse operations.)
[tex]\sqrt{64cm^2}[/tex]
8cm
Hassan buys an apartment for $78 000.
After one year the value decreases by 5%.
Work out the new value of Hassan’s apartment.
Answer:
3900 is decreased.$74100 is new value
Step-by-step explanation:
5% of 78000 subtracted by 78000...
dose the following relation represen a function {(-21,-4),(-4,-17),(-12,-21),(4,-12),(23,-17)}
Answer:
yes
Step-by-step explanation:
for a relation to be a function then each value of x can only map to one unique value of y.
This is the case here, then the relation is a function
Caroline drinks 2 cups of milk per day. She buys 4 quarts of milk. How many days will her 4 quarts of milk last?
Answer:
4 quarts of milk will last her 8 days.
We can solve this by finding how many cups are in a quart.
1 quart=4 cups
4 quarts= 16 cups
Since Caroline drinks 2 cups a day, divide 16 by 2.
16/2=8
4 quarts will last her 8 days.
Hope this helps! :D
Step-by-step explanation:
John spread 45 minutes after school reviewing his notes before taking a 15 minute break for a snack. After that snack, he continues reading his notes for the other 30 minutes. What would you add to find the total time that John studied?
Answer:
its A
Step-by-step explanation:
Ben
Write the following as an algebraic expression. Then
simplify.
The perimeter of a triangle whose sides are of
lengths 6x, 6x + 6, and x.
Answer:
[tex]6x + 6x + 6 + x = 13x + 6[/tex]
Ticket to a baketball game can be ordered online for a et price per ticket plu a $5. 50 ervice fee. The total cot in dollar for ordering 5 ticket i $108. 0. Which linear function repreent c, the total cot, when x ticket are ordered? (A ervice fee i a ingle fee applied to the total, no matter the number of ticket purchaed). C(x) = 5. 50 20. 50x
c(x) = 5. 50x 20. 50
c(x) = 5. 50 21. 60x
c(x) = 5. 50x 21. 60
The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
The total cost for ordering 5 tickets is $108.00. This means that each ticket costs $20.50 plus a service fee of $5.50.
Therefore, we can create a linear function that represents the total cost when x tickets are ordered. The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
When x = 5, then c(x) = 5.50 + 21.60x = 5.50 + 21.60(5) = 108.00, which matches the given total cost.
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sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.
The equation x²/3 + y²/3 = 4 represents an ellipse in the shown graph below and the length of the given ellipse is 8 units.
The equation x²/3 + y²/3 = 4 represents an ellipse centered at the origin with a major axis along the x-axis and a minor axis along the y-axis.
The equation can be rewritten as x²/4 + y²/12 = 1 to highlight the lengths of the semi-major and semi-minor axes.
The semi-major axis length is given by the square root of the denominator of the x-term, which is 4, so the semi-major axis length is 2.
The semi-minor axis length is given by the square root of the denominator of the y-term, which is 12, so the semi-minor axis length is 2√3.
Based on the symmetry of the ellipse, we can determine that it is symmetric with respect to both the x-axis and the y-axis.
This means that the length of the entire ellipse can be found by multiplying the semi-major axis length by 4, since there are 4 identical sections due to symmetry.
Length of the ellipse = 4 * semi-major axis length
= 4 * 2
= 8.
Therefore, the length of the given ellipse is 8 units.
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The correct question is as follows:
Sketch the curve with the equation x²/3 + y²/3 = 4 and use symmetry to find its length.
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for 7, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
Area :153.86 m
Circumference: 43.96 m
Step-by-step explanation:
Area: 3.14 x r^2
or, A= 3.14 x 7^2
Therefore, A= 153.86m
Circumference: 2 x 3.14 x r
or, C= 2 x 3.14 x 7
Therefore, C= 43.96 m
Hope this helps:)
(btw I put so much time and effort in this answer as it is hard to type mathematical problems in mobile, so I hope I can get marked as brainliest, I have written all the answer that needs to be written in an exam. Anyone can copy it and their work is done.)
5. The first five terms of a sequence are -7.7, -7.4, -7.1, -6.8, -6.5.
a. Find an expression for the nth term.
The expression of the nth term of the given sequence is
-7.7 + (n - 1)0.3
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-7.7, -7.4, -7.1, -6.8, -6.5
This is an arithmetic sequence.
Now,
a = -7.7
d = -7.4 + 7.7 = 0.3
The nth term of an arithmetic sequence.
= a + (n - a)d
Now,
a + (n - a)d
= -7.7 + (n - 1)0.3
Thus,
The nth term is -7.7 + (n - 1)0.3.
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One week, 100 tudent purchaed item from the tudent tore and the tore made a profit of $500. The next week, when 80 tudent purchaed item, the profit wa $460. Write a linear equation relating profit, to the number of tudent,
A linear equation relating profit, to the number of student is shown below.
y = 2x + 500
Linear equation is used to present the elements in mathematic. A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write a linear equation relating profit to the number of students, we need to find the slope and the y-intercept of the line.
The slope of the line can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
In this case, we can use the two data points given to find the slope:
slope = (460 - 500) / (80 - 100) = -40/ -20 = 2
The y-intercept of the line is the point where the line crosses the y-axis, which is the profit when the number of students is 0. In this case, the y-intercept is 500, since that is the profit when 100 students purchase items.
Using these values, we can write the linear equation in slope-intercept form:
y = 2x + 500
This equation can be interpreted as follows: the profit (y) is equal to 2 times the number of students (x) plus 500.
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(4.8)/(2z+15)=(0.2)/(5) PLS HELP! SHOW STEPS TOO IF POSSIBLE!
Answer:
z = 52.5
Step-by-step explanation:
You want the solution for (4.8)/(2z+15)=(0.2)/(5).
Cross multiplyMultiplying by 5(2z +15) we have ...
5(4.8) = 0.2(2z +15)
24 = 0.4z +3 . . . . . . . . . . simplify
21 = 0.4z . . . . . . . . . . . . subtract 3
z = 21/0.4 = 52.5 . . . . divide by the coefficient of z
The value of z is 52.5.
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4
The volume of a spherical balloon (V=4/3pir^3) is increasing at a constant rate of 0.78 inches per minute. At the instant when the radius is 3.20 inches, the radius is
increasing at a rate of…
The rate at which the radius is increasing is; 0.006 in/min
How to find the rate of increase of radius?We are given that the formula for the volume of a spherical balloon is;
V = ⁴/₃πr³
where r is the radius
The volume is increasing at the constant rate of 0.78 inches per minute. Thus;
dV/dt = 0.78
Now, differentiating with respect to t gives;
dV/dt = ⁴/₃(3πr²)(dr/dt)
At radius of 3.2 inches, we have;
0.78 = 4π * 3.2² * dr/dt
dr/dt = 0.78/(4π * 3.2²)
dr/dt = 0.006 in/min
This is therefore the rate at which the radius is increasing.
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A line passes through the point (9,
- 4) and has a slope of 3/4
Write an equation in slope-intercept form for this line.
Kayla works at a trampoline gym that hosts birthday parties. Parties are priced at $75 plus $12.50 per guest. Kayla rang up a customer who paid $200 for a party. How many guests were at the party?
Write and solve an equation to find the answer
Answer:
10 Guests
Step-by-step explanation:
200 - 75 = 125 (We need to find a number that will spend 125 dollars)
125 / 12.50 = 10
12.50 x 10 = 125
So the answer is 10
please answer I have limited time!!!!
Answer:
First second and third
Step-by-step explanation:
A function can only have one output for every input
Answer:
2, 3, 4
Step-by-step explanation:
an input can only have 1 output
Lee i packing a truck with mall and large filing cabinet. The large cabinet weigh 30 pound, and the mall cabinet weight 20 pound. To optimize the load, the total load weight hould be 1550 pound from a total of 65 cabinet. How many of each ize of cabinet hould Lee pack in the truck?
The number of cabinets of large size Lee should pack is equal to 40 and that of small size is equal to 25.
To determine how many of each size of cabinet Lee should pack in the truck, you can set up a system of equations. Let X be the number of large cabinets and Y be the number of small cabinets.
The total weight of the large cabinets is 30X pounds, and the total weight of the small cabinets is 20Y pounds. The total weight of all the cabinets is 1550 pounds, so the equation to represent this is:
30X + 20Y = 1550
The total number of cabinets is the sum of the number of large cabinets and the number of small cabinets, so the equation to represent this is:
X + Y = 65
To solve this system of equations, you can use the substitution method. First, solve for X in the second equation by substituting 65 - Y for X:
X = 65 - Y
Then, substitute 65 - Y for X in the first equation:
30(65 - Y) + 20Y = 1550
Solving this equation for Y, you get:
Y = 25
Substituting this value for Y in the second equation, you get:
X = 65 - 25 = 40
So, Lee should pack 40 large cabinets and 25 small cabinets in the truck.
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Explain three of seven phases of the impulse purchase cycle
Three of the seven phases of the impulse purchase cycle. The other phases include antecedent, search, and selection.
The impulse purchase cycle is a model that describes the process of making an impulsive purchase. It is typically divided into seven phases:
Antecedent: This phase is characterized by a need or desire for something. It can be triggered by a variety of factors, such as boredom, hunger, or a sudden craving for a particular product.
Search: In this phase, the consumer begins to actively search for a product that will satisfy their need or desire. They may search online or in physical stores, and they may consider various options before deciding on a product.
Selection: In this phase, the consumer narrows down their options and selects a specific product that they want to purchase. They may consider factors such as price, quality, and convenience when making their decision.
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A parabola is the set of all points in the plane that are equidistant from a fixed point called the ____ and a fixed line called the ____ of the parabola.
when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
Write a system of equations and then solve by the method of your choice: substitution or elimination
There are 30 questions for 2 points and 10 questions for 4 point.
What is elimination method?
The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
Given that, the total number of equations is 40. Total point on the paper is 100 points.
There are two types questions, one type question contains 2 points and other type question contains 4 points.
Assume that, there are x questions for 2 points and y questions for 4 points.
The total number of questions is x + y.
The total point is 2x + 4y.
Therefore,
x + y = 40 ......(i)
2x + 4y = 100 .....(ii)
Multiply 2 with equation (i)
2x + 2y = 80
2x + 4y = 100
___________
-2y = -20
Divide both sides by -2:
y = 10
Putting y = 10 in equation (i)
x + 10 = 40
x = 30
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Need help with this question
The figure S is translatation and then followed by rotation to map it into
figure T.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The figure S is translated (moved a fixed amount from the preimage)
and then followed by rotation(the preimage is rotated to create the final image) to map it into figure T.
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