Answer:
$705.71
Step-by-step explanation:
Let's assume the regular price of the sofa is "x".
According to the problem statement, the sale price is 65% off the regular price, which means the sale price is equal to 35% of the regular price.
We can write this relationship as:
0.35x = $247
To find the value of "x", we need to solve for "x" in the above equation.
Dividing both sides by 0.35, we get:
x = $247 ÷ 0.35
x = $705.71
Therefore, the regular price of the sofa is $705.71.
Plot -2 1/6 and 11/6 on the number line below.
The number line where we plotting -2 1/6 and 11/6 is attached
Plotting -2 1/6 and 11/6 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-2 1/6 and 11/6
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-13/6 and 11/6
This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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A rectangle has a height of 4x and a width of 3x +1. Express the area of the entire rectangle. Expression should be expanded. Area =
Answer:
12[tex]x^{2}[/tex]+4x
Step-by-step explanation:
area = width * height
substitution: area = (3x+1)*4x
distributive property: area = (4x*3x)+(4x*1)
simplify: area = 12[tex]x^{2}[/tex]+4x
In a 300-m-tall building, the stairwells are no more than 20 stories high. A story is approximately 3 m high. What is the maximum pressure differential in a stairwell? What is the atmospheric pressure difference between the top of the building and street level? What is the difference in static water pressure between consecutive floors?
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
We have,
Assuming a standard atmospheric pressure of 101.3 kPa.
Maximum pressure differential in a stairwell:
Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:
= 20 x 3
= 60 m
Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(60 m)
= 58,860 Pa
The atmospheric pressure difference between the top of the building and street level:
The atmospheric pressure decreases with increasing altitude.
Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(300 m)
= 2,943,000 Pa
The difference in static water pressure between consecutive floors:
Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:
ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa
Therefore,
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
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The interest earned on rs15000 in 3 years at simple interest is rs5400 find the rate of interest per anunm
Answer:
12%
Step-by-step explanation:
Let the rate of interest be R%
r = R% as decimal =R/100
Simple interest earned for 3 years at rate r on ₹15,000 = ₹5,400
The formula for interest earned is given by
I = Prt
where P is the principal amount (15,000)
r = annual interest rate as a decimal (to be determined)
t = number of years
Plugging in known values we get
5400 = 15000 x r x 3
= 45000 x r
r = 5400/45000
r = 0.12
Rate of interest as a percentage = r x 100 = 0.12 x 100 = 12%
HELP FAST PLEASE
Question
Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
All choices that have numbers like a/b are fractions.
Choices:
A= (0.97)^t
y= 3.7 (0.2)^t
y= 9/11 (4)^t
P= 7/9 (5/4)^t
V= 0.8 (9)^t
P= 0.9 (8.3)^t
g(x)= 2.1(x)
The exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
If the base is larger than 1, it will be an exponential growth.
For example, [tex]3^2=9[/tex]
If the base is smaller than 1, it will be an exponential decay.
For example, [tex]0.5^2=0.25[/tex]
If the function does not have an exponent, that means there will be no exponential growth or decay.
Therefore the exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
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Pedrobuysawheelbarrowpricedat$86.Shippingandhandlingareanadditional30%oftheprice.HowmuchshippingandhandlingwillPedropay?
The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.
To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:
30% of $86 = 0.3 x $86 = $25.80
Therefore, Pedro will need to pay $25.80 for shipping and handling.
Cheese costs $4.40 per pound. Find the cost per kilogram. (1 kg ≈ 2.2 lb)
The cost per kilogram of cheese is found by dividing the cost per pound by the conversion factor 0.45359237 kilograms per pound. The result is $9.68 per kilogram.
Start with the given cost of cheese per pound: $4.40.
To convert from pounds to kilograms, we need to divide by the conversion factor 2.2 (since 1 kilogram is approximately equal to 2.2 pounds). So, we have
1 pound / 2.2 = 0.45359237 kilograms / 1 pound
Note that we can write this as a conversion factor with the pound unit cancelling out, leaving us with kilograms as the desired unit.
Now, we can multiply the cost per pound by the conversion factor to get the cost per kilogram
Cost per kilogram = Cost per pound * (1 pound / 0.45359237 kilograms)
= $4.40 * (1 / 0.45359237)
Evaluating this expression using a calculator gives us
Cost per kilogram = $9.68
So the cost of cheese per kilogram is approximately $9.68.
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The product of two numbers is 1296. If one number is16 times the other, find the number.
your aanswer is 9 ⚡
The value of numbers are,
⇒ 9 and 16
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The product of two numbers is 1296.
And, one number is 16 times the other,
Let first number = x
Hence, Second number is, 16x
So, We get;
⇒ 16x × x = 1296
⇒ 16x² = 1296
⇒ x² = 81
⇒ x = 9
Hence, first number = 9
And, Second number is,
= 16x
= 16 x 9
= 144
Thus, The value of numbers are,
⇒ 9 and 16
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A statistics student believes that black cars are less likely to receive tickets for moving violations. Black cars make up 19% of all cars manufactured. The student randomly selects 70 moving violation records and finds that 10 of them involved black cars. The P-value for the test of the hypotheses, H 0: p = 0.19 and H alpha: p less-than 0.19, is 0.24. What is the correct interpretation of this value?
There is a 24% chance of a black car receiving a moving violation.
Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the null hypothesis is true.
Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.
Assuming the true proportion of black cars that receive moving violations is less than 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone.
The correct interpretation of the P-value in this context is: Assuming the true proportion of black cars that receive moving violations is 0.19, there is a 24% probability that the sample proportion would be 0.15 or less by chance alone. So, the correct answer is C).
In other words, the P-value is the probability of obtaining a sample proportion of 0.15 or less (which corresponds to 10 black cars out of 70 total) if the true proportion of black cars that receive moving violations is actually 0.19.
Since the P-value is relatively high (larger than the significance level of 0.05), we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that black cars are less likely to receive tickets for moving violations.
So, the correct answer is C).
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Question
Which of the following key characteristics is NOT true of a linear function?
Responses
Domain is all real numbers.
Maximum number of vertices is one.
Rate of change is constant.
There is exactly 1 y -intercept.
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
Flexible
Budge
Actual
Sales (7,000 pools)
$265,000 $265,000
Variable expenses:
Variable cost of goods sold*
79,240
97,525
Variable selling expenses
19,000
19,000
Total variable expenses
98,240
116,525
Contribution margin
166,760
148,475
Fixed expenses:
Manufacturing overhead
Selling and administrative
Total fixed expenses
Net operating income (loss)
67,000
67,000
85,000
85,000
152,000
152,000
$ 14,760 $ (3,525)
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to "get things under control. Upon reviewing the plant's income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
Direct materials
Direct labor
Variable manufacturing overhead
Total standard cost per unit
Standard
Quantity or
Hours
3.5 pounds
0.4 hours
0.3 hours
Standard Price or Rate
§ 2.10 per pound
$ 7.60 per hour
$ 3.10 per hour
Standard
Cost
$ 7.35
3.04
0.93
$ 11.32
During June, the plant produced 7,000 pools and incurred the following costs:
a. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.
b. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
c. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.
d. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.
It is the company's policy to close all variances to cost of goods sold on a monthly basis
Required:
1. Compute the following variances for June:
a. Materials price and quantity variances
b. Labor rate and efficiency variances.
c. Variable overhead rate and efficiency variances.
2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.
ANSWER THIS FIRST GET BRAINLESS W EXPLANATION!
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
To solve this equation by combining terms, the answer will be: (c) -4a + 22b.
How to solve the equationTo solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:
12a -16a + 26b -4b.
= -4a + 22b
When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.
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Hi can i convert the binary number 1000000 to a hexadecimal number?
Answer: yes, the hex of the number 1,000,000 would be 40.
K
The reading speed of second grade students in a large city is approximately normal, with a mean of 88 words per
minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).
(a) What is the probability a randomly selected student in the city will read more than 94 words per minute?
The probability is 0.2743.
(Round to four decimal places as needed.).
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
OA. If 100 different students were chosen from this population, we would expect
per minute.
OB. If 100 different students were chosen from this population, we would expect
minute.
OC. If 100 different students were chosen from this population, we would expect
per minute.
to read more than 94 words
to read exactly 94 words per
to read less than 94 words
If 100 different students were chosen from this population, we would expect approximately 27 of them to read more than 94 words per minute. Therefore, the correct choice is (A).
How to explain the probabilityThe probability that a randomly selected student in the city will read more than 94 words per minute is 0.2743.
z-score = (x - μ) / σ = (94 - 88) / 10 = 0.6
Therefore, the probability of a z-score being greater than 0.6 is:
P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 = 0.2743
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a. Find angle x
b. What kind of angle is angle x ?
Answer: if the first angle is 61° then the angle x is 119°
but if the first angle is 67 then the angle x is 113°
Step-by-step explanation:
Line is 180° that means our formula will look like that 67 or 61 + x = 180 in that case we have to calculate x ⇒ 180 - 61 or 67 = x
TrianglePQR is shown.
A. What are the missing side lengths in TrianglePQR
B. Explain how you arrived at your answer.
The length of the two unknown sides of the triangle are: 12√2
How to find the missing lengths of the triangle?There are different methods of finding the missing sides of triangles such as:
Pythagoras Theorem
Law of sines or sine rule
Law of cosines or cosine rule
Now, we are given an Isosceles triangle with a base length and two equal base angles.
Thus, the two unknown sides will have equal side lengths.
∠D = 90°
Thus, using sine rule:
12/sin 90 = QR/sin 45
QR = 12 * 1/√2
Rationalizing the denominator gives:
QR = 12√2
Since the two unknown sides of the triangle are equal, then we say that:
PQ = 12√2
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For each triangle, calculate the ratio of the opposite side to the adiacent side to two decimal places. How do they compare?
Answer:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
Choice C: The ratio is the same for both triangles
Step-by-step explanation:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
So both ratios are the same. This is also because the ratios represent the tan of the angle that the adjacent side makes with the hypotenuse and this angle of 22° is same in both triangles
help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither
The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;
Points 1, 3, and 5 are relative maximum points
Points 2 and 4 are relative minimum points
Point 5 is an absolute maximum point
Point 2 is an absolute minimum point
What is a relative maximum point?A relative maximum is a point in which the maximum with regards to the immediate surrounding points.
Therefore, the relative maximum points are;
The points 1, 3, and 5
The relative minimum points are points that are the minimum points, when compared with the surrounding points
The relative minimum are the points 2 and 4
The absolute maximum is the point which is at the highest point on the graph
The absolute maximum on the graph is therefore, the [oint 5
The absolute minimum on the graph is the point which is the minimum point compared to all other points
Therefore, the absolute minimum point is the point 2
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Find the value of x. Round to the nearest degree.
The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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In the diagram shown, Δ ABC is equilateral. AD is an altitude.
10). ∠ ABD = ______.
11). ∠ ADB = ______.
12). ∠ BAD = _____.
13). ∠ CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of Δ ABC
The missing sides of the triangle are
10). ∠ ABD = 60 degrees
11). ∠ ADB = 90 degrees
12). ∠ BAD = 30 degrees
13). ∠ CAD = 30 degrees
How to find the missing sides in the triangle14. BD is half of the length = BC / 2 = 6/2 = 3
15. AD is the height this is solved using Pythagoras theorem as below
AD^2 = AB^2 - BD^2
AD^2 = 6^2 - 3^2
AD^2 = 36 - 9
AD = sqrt (27)
16. Area of Δ ABC
= 1/2 * base * height
= 1/2 * 6 * sqrt (27)
= 9 sqrt (3)
= 15.59 square units
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Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find μ. Round to one decimal place. Answer
Answer:
The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).
μ = 20 x 0.08
μ = 1.6
Rounded to one decimal place, μ is 1.6.
Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days long. (Round your answers to the nearest cent.)
$500 balance, 16%, $50 payment
(a) previous balance method $
(b) adjusted balance method $
(c) average daily balance method
Interest charge for the month = 51.69 rounded to the nearest penny.
Here, we have,
The particular month in question is 30 days long.
Your balance at the start of the month is 3,000.
Annual interest rate = 21%.
Payment = 150.00.
When the payment is made in the month, it reflects on the tax amount you pay on both the average day balance.
YOU SEND THE PAYMENT IN ON THE FIRST DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 11TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 10 (10 days)
Average daily balance is 2850 from day 11 until day 30 (20 days)
Average daily balance for the month = 10 * 3000 + 20 * 2850
= 87000 / 30
= 2900
Interest charge for the month = 0.21 * 2900 * 30 / 365
Interest charge for the month = 50.05 rounded to the nearest penny
YOU SEND THE PAYMENT IN ON THE TWENTIETH DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 30TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 29 (29 days)
Average daily balance is 2850 from day 30 until day 30 (1 day)
Average daily balance for the month = 3000 * 29 + 1 * 2850
= 89850 / 30
= 2995
Interest charge for the month = 0.21 * 2995 * 30 / 365
Interest charge for the month = 51.69 rounded to the nearest penny
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Complete Question:
Calculate the monthly finance charge for the following credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Round your answer to the nearest cent.
3,000 balance, 21% rate, 150 payment, average daily method
Using the parallel lines below determine the measure of the smaller angle.
-
x+114
x+72
▸
The measure of the smaller angle of the co-interior angles is 69°
What the measure of the smaller angle?Co-interior angles are simply angles that occur in between two parallel lines when they are intersected by a transversal.
The two angles add up to 180º as they occur on the same side of the transversal always.
From the image, the two co-interior angles are:
x + 114
x + 72
Since the two angles add up to 180º.
x + 114 + x + 72 = 180
Solve for x
2x + 186 = 180
2x = 180 - 186
2x = -6
x = -6/2
x = -3
Hence, the measure of the two angles are:
x + 114 = -3 + 114 = 111°
x + 72 = -3 + 72 = 69°
Therefore, the smallest angle is 69 degree.
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The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. Which plot represents a stemplot of the data? * Height of eruption (in.) 66 32 50 900 50 40 70 70 59 61 60 88 80 50 63 54 62 73 70 49
The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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Please help me show work
1.) m<A = 51°
AB = 17.5
BC = 13.6
How to calculate the missing side and angles of the given triangle?To calculate the missing part of the triangle, m <A ;
The sum of the interior triangle = 180°
That is , 180° = 90°+ 39° + m
make m the subject of formula;
m = 180 - 129
m <A = 51°
Using the formula from SOHCAHTOA;
Sin 39° = 11/AB
make AB the subject of formula;
AB = 11/0.629320391
= 17.5
Using the Pythagorean formula;
C² = a² + b²
C² = 17.5
a² = 11
b² = BC = ?
17.5² = 11² + b²
make b² the subject of formula;
b² = 17.5²-11²
b² = 306.25 - 121
b² = 185.25
b = √185.25
b = 13.60
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what is the formula for finding the surface of a cone
Answer:
Formula for finding the surface area of a cone is shown below
[tex]\pi \: r {}^{2} + \pi \: rl \\ or \\ \pi(r + l)r[/tex]
The formula for finding the surface area of a cone is:
Surface area = πr² + πrl
Where:
π is the mathematical constant pi (approximately 3.14159) r is the radius of the base of the conel is the slant height of the cone, which can be calculated using the Pythagorean theorem (l² = r² + h²), where h is the height of the coneBrainly pls help me with this
Answer:
38.part A) 3p = 25.47
partB) $8.49
Step-by-step explanation:
38) to get the price of a game ,$25.47 will be divided by
25.47÷3=$8.49
the price of 1 game =&8.49
to get the price of 1 game , the equation will be
3p=25.47
p=25.47÷3
p=$8.49
A rectangle has perimeter 70 inches, and its area is 286 sq-inches. Find the dimensions of this
rectangle. (For purposes of this problem only, the width is shorter than the length.)
length =
width=
inches
inches
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.
Explain about the rectangle:An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
Let the length of rectangle be 'l'
Let the width be 'w'.
Then,
Perimeter = 2(l + w)
70 = 2(l + w)
35 = l + w
l = 35 - w ...eq 1
Now,
Area = length * width
286 = l*w ...eq 2
Put eq 1 in eq 2
286 = (35 - w)*w
286 = 35w - w²
w² - 35w + 286 = 0
Solving the quadratic equation:
w² - 22w - 13w + 22*13 = 0
w(w - 22) - 13(w - 22)= 0
(w - 22)(w - 13) = 0
w = 22 and w = 13
As, length is greater than width-
width w = 13 inch
Length l = 35 - 13 = 22 inches.
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the day before Valentine's Day a store has 400 red roses and 200 boxes of chocolate. After the store opens at 9 a.m. half of the available roses are bought every 2 hours. 15% of the boxes are bought every hour. a. Find a formula that represents the number of red roses left t hours before the store opens. b. Find a formula that represents the number of box chocolates left t hours after the store opens. c. At what time will the number of roses be equal to the number of boxes of chocolates. d. How many boxes of chocolate are left at 12:30 in the afternoon? Round your answer to make sense in this context of the problem. e. Suppose you want to buy that special someone 36 red roses at the store. What is the latest you can arrive to successfully make your purchase?
Answer:
Step-by-step explanation:
a. The number of red roses left t hours before the store opens can be represented by the formula:
N(t) = 400 * (1/2)^(t/2)
Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.
b. The number of box chocolates left t hours after the store opens can be represented by the formula:
M(t) = 200 * (0.85)^t
Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.
c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:
400 * (1/2)^(t/2) = 200 * (0.85)^t
Dividing both sides by 200:
2 * (1/2)^(t/2) = 0.85^t
Taking the logarithm of both sides:
log(2) - (t/2) * log(2) = t * log(0.85)
Simplifying:
t * (log(0.85) + (log(2)/2)) = log(2)
t = log(2) / (log(0.85) + (log(2)/2))
Using a calculator, we get:
t ≈ 11.9 hours
Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.
d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:
M(3.5) = 200 * (0.85)^3.5
M(3.5) ≈ 97.4
Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.
e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:
400 * (1/2)^(t/2) = 36
Dividing both sides by 400:
(1/2)^(t/2) = 0.09
Taking the logarithm of both sides:
t/2 * log(1/2) = log(0.09)
Simplifying:
t ≈ 5.2 hours
Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.
Please answer question
The equation of line perpendicular to the tangent is found to be -
y = -2x + 7.
Give an explanation of the slope-intercept form:The equation for a line should be written in the slope-intercept form so that the y-intercept (where its line crosses a vertical y-axis) and slope (steepness) are immediately visible. The y = mx + b form is a common name for this form.
Given condition of digression line:
Comparing with the standard form: y = 1/2 x + 7 y = mx + c
m is the slant and c is the y block:
m = 1/2
Let the incline of the line opposite to the digression be M.
Then, at that point, connection between the inclines of opposite lines:
m. M = -1 equation of line perpendicular to the tangent.
y - 3 = M(x - 2)
y - 3 = -2(x - 2)
y = -2x + 4 + 3
y = -2x + 7
Thus, the equation of line perpendicular to the tangent is found to be -
y = -2x + 7.
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Complete question:The circle has the centre at (2,3). The equation of the tangent of the line on the circle : y = 1/2 x + 7. What is equation of line perpendicular to the tangent.