The total cost of fencing a square park at rupees 20 per meter are rupees
2880. Find the side of the square park.
Answers
The side of square park, whose fencing costed Rs 2880 is 36m.
What is a square?
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about a square's characteristics, mathematics, and design.
We know perimeter of a square of side 'a' is 4a
Therefore, the cost of fencing a square park at Rs 20/meter would be equal to
= Rs(20*4a)
= Rs 80a
Given, the cost of fencing = Rs 2880
Thus, 80a = 2880
⇒ a = 2880/80
⇒ a = 36
Thus, the side of square park, whose fencing costed Rs 2880 is 36m
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Related Questions
The management of a restaurant has been studying whether or not new customers return within a month. The collected data reveal that 60% of the new customers have returned. If 90 new customers dine at the restaurant this month, what is the probability that at least 60 will return next month? Use Normal approximation to Binomial distribution.
Answers
Using the normal approximation to the binomial, it is found that there is a 0.119 = 11.9% probability that at least 60 will return next month.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).In this problem, we have that:
60% of the new customers have returned, hence p = 0.6.90 new customers dine at the restaurant this month, hence n = 90.Thus, the mean and the standard error for the approximation are given as follows:
\(\mu = np = 90(0.6) = 54\)\(\sigma = \sqrt{np(1-p)} = \sqrt{90(0.6)(0.4)} = 4.6476\)Using continuity correction, the probability that at least 60 will return next month is P(X > 60 - 0.5) = P(X > 59.5), which is 1 subtracted by the p-value of Z when X = 59.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{59.5 - 54}{4.6476}\)
Z = 1.18
Z = 1.18 has a p-value of 0.881.
1 - 0.881 = 0.119.
0.119 = 11.9% probability that at least 60 will return next month.
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Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.The numerator is AnswerThe denominator is Answer
Answers
Explanation
\(\begin{gathered} \frac{\left(q^2-9\right)}{\left(q^2+6q+9\right)}\div\frac{\left(q^2-2q-3\right)}{\left(q^2+2q-3\right)} \\ \end{gathered}\)Step 1
factorize:
remember those cases:
\(\begin{gathered} (a^2-b^2)=(a+b)(a-b) \\ (a^2+2ab+b^2)=(a+b)^2 \\ \end{gathered}\)so
\(\begin{gathered} (q^2-9) \\ (q^2-9)=(q^2-3^2)=(q+3)(q-3) \\ \text{and} \\ (q^2+6q+9)=(q^2+(2\cdot q\cdot3)+3^2)=(q+3)^2 \\ \text{also} \\ (q^2-2q-3)=(q+1)(q-3),\text{ because 1-3= -2 and, 1}\cdot-3=-3 \\ so \\ (q^2-2q-3)=(q+1)(q-3) \\ \text{ finally } \\ (q^2+2q-3)=(q-1)(q+3),because\text{ -1+3=}2,\text{ and -1}\cdot3=-3 \\ (q^2+2q-3)=(q-1)(q+3) \end{gathered}\)Step 2
replace
\(\begin{gathered} \frac{(q^2-9)}{(q^2+6q+9)}\div\frac{(q^2-2q-3)}{(q^2+2q-3)} \\ \frac{(q+3)(q-3)}{(q+3)^2}\div\frac{(q+1)(q-3)}{(q-1)(q+3)} \\ \text{ reduce} \\ \frac{(q-3)}{(q+3)^{}}\div\frac{(q+1)(q-3)}{(q-1)(q+3)} \\ \frac{\frac{(q-3)}{(q+3)^{}}}{\frac{(q+1)(q-3)}{(q-1)(q+3)}}=\frac{(q-3)(q-1)(q+3)}{(q+3)(q+1)(q-3)} \\ \frac{(q-3)(q-1)(q+3)}{(q+3)(q+1)(q-3)}=\frac{(q-1)}{(q+1)} \\ \frac{(q-1)}{(q+1)} \end{gathered}\)therefore the answer is
numerator : q-1
denominator: q+1
I hope this helps you
help me plsss <333333333333 and tyyyyyy <33333 :)
Answers
Value of variable x in the equation is 2.
Define equationIn mathematics, an equation is a statement that two expressions are equivalent. It comprises of two sides with a phrase on each, usually divided by an equal symbol (=). An equation declares that for some or all of the values of the variables in the equation, the two expressions have the same value. Equations can include one or more variables and can be either linear or nonlinear. Finding the values of the variables that make the equation true is the first step in solving an equation.
Given equation
3(x+6)=24
Dividing the terms by 3, we get
x+6=8
x=8-6
x=2
Hence, value of variable x in the equation is 2.
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-x < - 29 solve for x
Answers
Answer:
x<29
Step-by-step explanation:
divide both sides by -1 since x cannot be negative
The perimeter and area of a rectangle are 22 cm
and 30 cm² respectively. Find the length and
breadth of the rectangle
Answers
The perimeter and area of a rectangle are (5,6) and (6,5).
The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.
A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.
The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.
The perimeter of the rectangle:
P=2l+2w=22
divide 2 into both sides
l+w=11 -------------> (1)
w=11-l
Area of the rectangle:
l*w=30
l(11-l)=30
11l-l^2-30=0
l^2-11l+30=0
By factor method,
(l-5)(l-6)=0
l=5,6.
Substitute this value in w,
l=5 implies w=6
l=6 implies w=5
There we have two solutions.
The length and breadth of the rectangle is
(5,6) and (6,5).
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there are how many distinct website graphics to be created?
Answers
According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
What is website?A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.
Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:
n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
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uporządkuj jednomian
a) 2x*x*(-x)
b)3/4 ab * (-a) * (-b) *4
c) (-a) * (-a) * (-a)* (-a)
pls daje naj a
Answers
93,83,65,59,88,76,86,93,48,73,54,79
What is the percentage of these test scores that are less than 88?
Answers
32) Find the cost of linoleum flooring for a floor that is 15 feet by 10 feet if it costs $9.00 to cover 12 square feet.
O a.) $110.50
Ob.) $132.50
Oc.) $122.50
Od.) $112.50
Answers
Answer:
d.) $112.50
Step-by-step explanation:
Area of floor:
15 ft × 10 ft = 150 ft²
150 ft² is how many times 12 ft²?
It is 150 ft² / 12 ft² = 12.5.
150 ft² is 12.5 times 12 ft².
12 ft² cost $9.00, so 12.5 times 12 ft² costs 12.5 times $9.00.
12.5 × $9.00 = $112.5
Answer: d.) $112.50
The Square foot flooring is calculated by doing 15ft x 10ft = 150ft^2. Since it cost $9.00 to cover 12ft^2, you would do 150ft^2/12ft^2 to find out how many times you have to pay 9 dollars. This gives you 12.5 times you have to pay 9 dollars. Therefore, you do $9.00x12.5 which gives you $112.50
Evaluate the following expression.
(-3)0
Answer here
Answers
The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0
Evaluating the expression (-3)0From the question, we have the following parameters that can be used in our computation:
(-3)0
The above statement is a product expression that multiplies the values of -3 and 0
Also, there is no need to check if there are like terms in the expression or not
This is because we are multiplying the factors
So, we have
(-3)0 = 0
This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0
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The angles of a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measure of all three angles.
Answers
Answer:
20, 40, 120
Step-by-step explanation:
Smallest angle = x
Second angle = x + 100
Third angle = 2x
4x + 100 = 180
4x = 80
x = 20
20, 120, 40
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20.
Answers
The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).
How to explain the relationshipIn the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.
To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).
If we subtract each value in column 1 from the corresponding value in column 2, we find that:
11 - 1 = 10
22 - 2 = 20
33 - 3 = 30
44 - 4 = 40
By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.
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In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:
Disk: 269.0, 249.3, 255.2, 252.7, 247.0, 261.6
Oval: 268.8, 260.0, 273.5, 253.9, 278.5, 289.4, 261.6, 280.2 Can you conclude that the mean dissolve times differ between the two shapes? Conduct a hypothesis test at the
α = 5% level.
a. State the appropriate null and alternative hypotheses.
b. Compute the test statistic.
c. Compute the P-value.
d. State the conclusion of the test in the context of this setting.
Answers
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.
The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.
We would set up the hypothesis.
a) The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
For disk shaped,
Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8
Standard deviation = √(summation(x - mean)²/n
n1 = 6
Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54
Standard deviation, s1 = √(337.54/6) = 7.5
For oval shaped,
Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375
n2 = 8
Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875
Standard deviation, s2 = √(991.75875/8) = 11.1
b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
Therefore,
t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)
t = - 3
c) The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46
df = 12
We would determine the probability value from the t test calculator. It becomes
p value = 0.011
d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes
The Punjab Highway department is studying traffic pattern on G.T. Road near Lahore. As part of previous study, population standard deviation is 680 number of vehicles per day. A random sample of 64 days gives mean of 5410 cars. Find a 90 percent confidence interval for population Mean (the average number of vehicles per day).
Answers
Answer:
for this we need 90 percent 5410
so we multiply 5410*0.9=4869
Hope This Helps!!!
Whole numbers to make 2.8 in three different ways
Answers
Answer:
28/10
14/5
3 - 1/5
Step-by-step explanation:
28/10
14/5
3 - 1/5
The whole numbers to make 2.8 in three different ways are 28/10,14/5, 3 - 1/5.
What is a whole number?An entire quantity is an absolutely any high-quality wide variety that does not encompass a fractional or decimal component. because of this, as an example, the numbers 0, 1, 2, three, 4, 5, 6, and 7 are all whole numbers. Numbers that include -three, 2.7, or 3 ½ aren't whole numbers.
The complete numbers are a set of real numbers that consist of 0 and all superb counting numbers. while, excludes fractions, negative integers, fractions, and decimals. when you consider that, 1 is a positive integer and is a counting number. therefore, it is taken into consideration to be a whole wide variety.
sure, 0 is a rational variety. because we understand, a rational number may be expressed as p/q, in which p and q are integers and q isn't equal to 0. for this reason, we will explicit zero as p/q, wherein p is identical to zero and q is an integer.
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HURRY I GOT 30 MINS
A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. The balls are then placed in a bag and shaken. A golf pro then selects a ball and hits it. The distance the ball travels is then measured. The bag is shaken again, and the golf pro selects another ball to hit. She continues this procedure until all 80 of the golf balls are hit.
Has the principle of comparison been addressed in this experimental design?
A Yes, because the balls are randomly selected, the distances of the new ball can be compared to the distances of the original ball.
B Yes, because the original ball type is included in this experiment, the distances the different balls travel can be accurately compared.
C No, because a placebo ball was not used, a comparison cannot be made to determine if the new ball travels significantly farther.
D No, because all of the new type of balls are not hit first, the distances they travel cannot be compared to the distances of the original ball.
Answers
Answer:
B
Step-by-step explanation:
Edge
Can someone help with this? Thank you!
Answers
The value of x is 24 and different angles of hexagon will be -
A = 160
B = 142
C = 120
D = 156
E = 31
F = 111
Describe angle.An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.
We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).
Given the figure is hexagon,
the sum of angles of a hexagon is 720,
Upon adding the given angles,
mA = (7x-8)°
mB (4x+46)°
mC = (5x)
mD = (6x+12)°
mE = (x+7)°
mF = (5x-9)°
⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720
⇒ 28x + 48 = 720
⇒ 28x = 672
⇒ x = 24
Therefore, the angles will be -
A = 160
B = 142
C = 120
D = 156
E = 31
F = 111
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The volume of a cylinder is 402 cubic units. The radius of the cylinder is 4 units.
Find the height, and enter the value of the height rounded to the nearest whole number.
Answers
Answer:
h=12
Step-by-step explanation:
you would plug in the formula for volume and get h=a/2 pie r-r and then you plug in 4 for r and 402 for the a
The height of the cylinder is 8 units.
Given that, the volume of a cylinder= 402 cubic units and the radius of the cylinder= 4 units.
We need to find the height of the cylinder.
What is the formula to find the volume of a cylinder?The formula to find the volume of a cylinder is πr²h.
Now, the volume of a cylinder=3.14×4²×h
⇒402=3.14×16×h
⇒402=50.24×h
⇒h=8.001≈8 units
Therefore, the height of the cylinder is 8 units.
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The table shows
the temperatures of the water in
14 different beakers. What is the average
temperature, rounded to the nearest tenth
of a degree?
Answers
Answer:54
Step-by-step explanation:
the sum of two numbers is 39 .one is 2 times as large as the other. what are the numbers ?
larger number
smaller number
Answers
The smaller number would be 13.
They add up to 39, and 13 times 2 is 26.
The larger number is 26 and the smaller number is 13.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The two numbers be 'a' and 'b'.
Therefore, a + b = 39 and a = 2b.
So, a + b = 39.
2b + b = 39.
3b = 39.
b = 39/3.
b = 13.
Hence, a = 26.
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9. Find the range, mean, median, and mode of the following data set. 5, 17, 21, 21, 7, 13, 1, 3 a. Range 20 Mean 11 Median 10 Mode 21 c. Range 20 Mean 10 Median 10 Mode 21 b. Range 24 Mean 11 Median 10 Mode 21 d. Range 20 Mean 11 Median 21 Mode 21
Answers
Mean: 11
Median: 10
Mode: 21
if f(a)=a²-1 find f(5)
Answers
Answer: 24
Step-by-step explanation:
A=5 so F(x)=5^2-1
F(x)=24
3. A water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. Find this minimum length of pipe. B 6.00 mi CH P 12.0 mi A 10.0 mi D
Answers
The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.
We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.
The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).
Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).
From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).
After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.
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Math Homework: Unit 3 Assignment
Answers
What is the CIRCUMFERENCE of this pie?
Give an approximate answer by using 3.14 for π.
SHOW YOUR WORK!
Answers
Steps:
Circumference = 2πr
r = radius
8.1/2 = 4.05
2π(4.05) = 25.434 in
A radioactive substance is decaying according to the functionQ(t) = 36e^-0.061where Q(t) is the amount of the substance (in grams) and t is the time (inhours).a.) How many grams of the substance will there be after one day (t = 24hours)? Round to the nearest tenth.b.) How long will it take until only 1 gram of the substance is left? Round tothe nearest whole number.c.) how fast is the amount of the substance changing when t =10 hours round to the nearest tenth
Answers
We have the next function
\(Q(t)=36e^{-0.06t}\)a)
For answer this section we need to find the value of Q when t=24
\(Q(24)=36e^{-0.06(24)}=8.52=8.5\text{grams}\)b)
In order to know how long will take until 1 gram of substance left we need to isolate t of the formula and Q=1
\(1=36e^{-0.06t}\)then we isolate t
\(\begin{gathered} \ln (1)=\ln (36e^{-0.06t}) \\ \ln (1)=\ln (36)+\ln (e^{-0.06t}) \\ \ln (1)=\ln (36)+\ln (e^{-0.06t}) \\ \ln (1)-\ln (36)=-0.06t \\ t=\frac{\ln (1)-\ln (36)}{-0.06}=59.72=59.7\text{ hours} \end{gathered}\)c)
We have the initial amount that is when t=0
\(Q(0)=36e^{-0.06(0)}=36\)when t=10
\(Q(10)=36e^{-0.06(10)}=19.75\)Then we calculate
\(\frac{19.75-36}{10-0}=-1.625=-1.6\text{ grams/hour}\)Because the result is negative it is decreasing
Which expression is equivalent to (3+4i)(2−3i)
Answers
The expression that is equivalent to the given value would be = 18-i . That is option C.
What is an equivalent expression?An equivalent expression is defined as the type of expression that is similar to a given value when simplified.
The given expression = ( 3 + 4i) ( 2 - 3i)
Expand the given expression by removing the brackets as follows:
= =2(3+4i)−3i(3+4i)
=(6+8i)−(9i−12)
= (6+12)+i(8−9)
=18−i.
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please please help last text then finals l give brainliest
Answers
1. The x - intercepts of the parabola are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex of the parabola is at (5, 80).
What is a parabola?A parabola is a curved shape
1. Given the parabola above, to find the x - intercepts, we proceed as follows.
The x-intercepts are the points at which the graph cuts the x-axis.
They are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.
The plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex is the maximum point on the graph.
So, we see that the vertex is at x = 5 s and y = 80 ft
So, the vertex is at (5, 80).
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Suppose you have a jar with 380 marbles that are either red or green. You want to estimate how may marbles in the jar are red without counting all of them. You take four random samples of 16 marbles. After each sample, the marbles are returned to the jar. Choose the best conclusion you can make.
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Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole
Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.
It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.
To calculate the proportion of red marbles in each sample
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What value of x would make KM ∥ JN?
Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.
Complete the statements to solve for x.
By the converse of the side-splitter theorem, if JK/KL =
, then KM ∥ JN.
Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.
Cross-multiply: (x – 5)(
) = x(x – 3).
Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).
Multiply and simplify: x2 – x –
= x2 – 3x.
Solve for x: x =
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To solve for the value of x that would make KM ∥ JN, we can use the converse of the side-splitter theorem.
What value of x would make KM ∥ JN?This theorem states that if the ratio of the lengths of any two sides of a triangle are equal to the ratio of any two corresponding sides of another triangle, then the two triangles are similar.This means that if we determine the ratio of JK/KL, then this ratio must be equal to the ratio of LM/MN for KM to be parallel to JN. To find the ratio of JK/KL, we must first substitute the given expressions into the proportion: JK/KL = (x – 5)/x. We can then cross-multiply to get (x – 5)(x) = x(x – 3).We can then distribute and simplify to get x2 – x – 20 = x2 – 3x. Solving for x, we get x = 20. Thus, the value of x that would make KM ∥ JN is 20.To solve for x, both sides of the equation x2 – x – 20 = x2 – 3x can be set equal to zero. This yields a quadratic equation of the form ax2 + bx + c = 0, where a = 1, b = -1, and c = -20.To solve this equation, one can use the quadratic formula, which states that the solutions to a quadratic equation of the form ax2 + bx + c = 0 are given by x = (-b ± √(b2 - 4ac)) / (2a). In this case, the solutions are x = 21 and x = -1. This problem is called solving a quadratic equation.To learn more about the side-splitter theorem refer to:
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