Answer:
y=p(1+R/100)^t
y=10000(1+1.5/100)¹=10000×1.015
=$10150a flagpole casts a shadow 17 feet long. at the same time, the shadow cast by a 33-inch-tall shrub is 66 inches long. find the height of the flagpole.
Answer: The flagpole is 32 feet high. hope this helps
Step-by-step explanation:
This is a Ratio and Proportion question.
The relationship between the height of the sign and its shadow is the same as the relationship between the flagpole and its shadow.
That relationship is 8:3.
That means that for every 8 feet tall an object is, its shadow is 3 feet long.
If some object is 16 object shadow=166=83
If some object is 4 feet tall, its shadow is 1.5 feet long.
object shadow=4 1.5=83
that works backwards too.
If the shadow is 9 feet long, the object is 24 feet tall.
object shadow=249=83
Keep the shadow in the denominator even it the problem names it feet tall, its shadow is 6 feet long.
In the problem, the ratio of object to shadow is 8:3 in both cases, even though only one object is exactly 8 feet tall. objectnshadow=83=x12
That means you can solve for x to find the height of the flagpole.
You can solve the pair of equal fractions by cross multiplying and then solving for x, already defined as "the height of the flagpole."
1) Cross multiply3x=8⋅12
2) Divide both sides by 3 to isolate x, already defined as "the height of the flagpole.
To weasel out of having to multiply 8⋅12, make the numbers small by first dividing by 3.
After you have divided both sides by 3, you will have this: x=8⋅4x=32
solve sin(5x)cos(8x) - cos(5x)sin(8x) = -0.3 for the smallest positive solution
We can use the trigonometric identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b) to rewrite the left-hand side of the equation as sin(5x - 8x). Therefore, we have:
sin(5x - 8x) = -0.3
Simplifying further, we get:
sin(-3x) = -0.3
Since sin(x) is an odd function, we can rewrite sin(-3x) as -sin(3x):
-sin(3x) = -0.3
Dividing both sides by -1, we get:
sin(3x) = 0.3
To find the smallest positive solution, we need to find the smallest value of x that satisfies this equation. The solutions to the equation sin(3x) = 0.3 can be found using the inverse sine function (sin^-1 or arcsin), which gives us:
3x = sin^-1(0.3) + 2πn or 3x = π - sin^-1(0.3) + 2πn
where n is an integer representing the number of complete cycles around the unit circle.
Solving for x, we get:
x = [sin^-1(0.3) + 2πn]/3 or x = [π - sin^-1(0.3) + 2πn]/3
Substituting n = 0 in each case to obtain the smallest positive solution, we get:
x = [sin^-1(0.3)]/3 or x = [π - sin^-1(0.3)]/3
Using a calculator, we can evaluate sin^-1(0.3) ≈ 0.3047 and substitute it into the two equations above to obtain:
x ≈ 0.1015 or x ≈ 1.0472
Therefore, the smallest positive solution to the equation sin(5x)cos(8x) - cos(5x)sin(8x) = -0.3 is approximately x ≈ 0.1015.
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Which expression means the same as "25 less than 5y"?
A. 5y - 25
B. 25 - 5y
C. 5y - 25
D. 25 = 5y
Answer:
a) 5y - 25
Step-by-step explanation:
2. Reason How is solving an absolute value equation similar to solving an
equation that does not involve absolute value? How is it different?
Answer: Absolute value will alwase be a positive number, while solving an equation that does not involve absolute value could be any number. Positive, negativ, you name it. They ae similer, because either way, you are trying to figure out a varible. -hope this helped! if i misunderstood anything, let me know! i love to improve :D
show that the dimensions of the largest area rectangle that can be inscribed into a circle of radius 4 is a square. then, show that this is true for any radius r.
Rectangle ABCD is a square.
Relation between rectangle and square?
Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.
Radius of circle R = 4cm
let sides of rectangle is a,b
let rectangle be ABCD in which AB =CD= a , AC=BD=b
ACD is right angled triangle on C.
Then,
\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)
Area of rectangle = Area of ΔACD + ΔABD
= \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)
Area of rectangle = a×b
by eqn (1)
Area = \(a\times (\sqrt{64-a^{2} } )\)
For maximum area
\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)
\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)
So, a=b
Means Rectangle ABCD is a square.
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a rectangle has a length of 14 meters and a width of 200 centimeters. What is the area of the rectangle in meters?
Answer:
a=28m^2
Step-by-step explanation:
Given:
l=14m
w=200cm
Required
a=?
w in meters
Formula:
1m=100cm
b=200cm---criss cross it
b*100cm/100cm=1m*200cm/100cm
b=2m
a=l*w
a=14m*2m
a=28m^2
ali and jake went on a cross country trip they took a train part of the way and a bus the rest of the way they traveled a total of 1050 kilometers riding on the train 200 more kilometers than in the bus how many kilo meters did they travel by
Answer:
1900 km
Step-by-step explanation:
train = 1050km
bus = 200 less than train or 1050-200 = 850
1050+850=1900
Answer:
625, just got it right
Step-by-step explanation:
HELP PLEASE. I DONT KNOW IF ITS 30 OR 180
Answer:
Step-by-step explanation:
6\(\sqrt{5\\\)
\(\sqrt{5*36}\)
\(\sqrt{180}\)
If you think about it logically, how can you take 6 out? So there was a number 36 under the root, and because of that there is a possibility to take it out, because 6 squared is 36
Please help me with this question
Answer:
D, D
Step-by-step explanation:
3x - 2 = -2x + 3
5x = 5
x = 1
Simplify the expression:
3x + 5x + 6x – 4
Answer:
14x-4
Step-by-step explanation:
So you know 3x +5x = 8x so then you add 6x and put -4
Answer:
14x - 4
Step-by-step explanation:
simplifying this kind of given expression just means to put the variables all together and the numbers all together to get a shorter and more simplified version of the equation.
first do:
3x+5x+6x=
14x
and than you just have one number so your final simplified equation would be:
14x-4
Evaluate the expression w² - v + 1 for w = -2 and v = -8.
Answer:
13
Step-by-step explanation:
-2(-2) - (-8) + 1
4 + 8 + 1 = 13
Answer:
13
Step-by-step explanation:
cause i did it and it was right
Don jacinto tiene 230 libretas y 300 borradores en cada una. Para saber cuantos borradores tiene en total don jacinto multiplico 12 por 300. Sin borrar lo que esta en la calculadora pregunta que operacion debe hacer don jacinto para saber la cantidad de borradores que ahi en 4 cajas ayuda plis dime la operacion y resultado
Hay 1200 gomas de borrar en total en las 4 cajas.
Para saber la cantidad de gomas de borrar que hay en 4 cajas, Don Jacinto necesita multiplicar la cantidad de gomas de borrar en cada caja (300) por la cantidad de cajas (4).
La operación que debe hacer es:
300 * 4
El resultado de esta multiplicación es:
300 * 4 = 1200
Es importante notar que en el escenario dado, la información inicial acerca de que Don Jacinto tiene 230 cuadernos no es relevante para encontrar el número de borradores en las 4 cajas. Solo necesitamos considerar el número de gomas de borrar en cada cuadro (300) y el número de cajas (4) para realizar la multiplicación y calcular el número total de gomas.
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3 subtracted from a number x – 3 is?
suppose we have 3 groups of linearly related bivariate data with the following values of r: group 1
Compare the values of r for all three groups to determine which group has the strongest linear relationship.
Calculate the values of r for each group of linearly related bivariate data and compare them to determine the strongest linear relationship. The explanation step-wise involves calculating the correlation coefficient for each group.
In the first group, the bivariate data has a linear relationship. we need to determine the value of r for each group. The explanation step-wise is as follows:
1. For group 1, the value of r is missing. To find it, calculate the correlation coefficient using the given data points.
2. Repeat the same process for group 2 and group 3 to find their respective values of r.
3. Compare the values of r for all three groups to determine which group has the strongest linear relationship.
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use the drop-down menus to indicate whether each statement describes a traditional use of computers or a new use.
1. Communicating via e-mail is a traditional use of computers.
2. Creating advertisements and paying someone to publicize them is a traditional use of computers.
3. Communicating via social networking websites is a new use of computers.
4. Collaborating as a virtual team is a new use of computers.
5. Manually managing financial, inventory, and scheduling records is a traditional use of computers.
1. Communicating via e-mail is a use of computers:
This is a traditional use of computers. Computers have long been used for sending and receiving emails, which allows for efficient and instant communication between individuals and organizations.
2. Creating advertisements and paying someone to publicize them is a use of computers:
This statement can be considered both a traditional and a new use of computers. While the act of creating advertisements can involve traditional methods like graphic design software on computers, the mention of paying someone to publicize them suggests a more modern approach, potentially involving digital marketing platforms and online advertising.
3. Communicating via social networking websites is a use of computers:
This is a new use of computers. Social networking websites have become popular platforms for communication and connecting with others. Computers and internet access are essential for engaging in social networking activities.
4. Collaborating as a virtual team is a use of computers:
This is a new use of computers. With advancements in technology, virtual teams can collaborate remotely using computers and various online collaboration tools. This allows team members to work together, share documents, communicate, and coordinate their efforts, regardless of their physical location.
5. Manually managing financial, inventory, and scheduling records is a use of computers:
This is a traditional use of computers. Computers have been widely used for managing and organizing various records, such as financial transactions, inventory management, and scheduling. This digital approach provides more efficient data storage, retrieval, and analysis compared to manual record-keeping methods.
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Complete Question:
Use the drop-down menus to indicate whether each statement describes a traditional use of computers or a new use.
Communicating via e-mail is a use of computers.Creating advertisements and paying someone to publicize them is a use of computers.Communicating via social networking websites is a use of computers.Collaborating as a virtual team is a use of computers.Manually managing financial, inventory, and scheduling records is a use of computers.4350 g = how many kilograms
Answer:
4.35
Step-by-step explanation:
Answer:
4.35 kilo
Step-by-step explanation:
In the coordinate plane, the directed line segment from K to N has endpoints at K(–6, –2) and N(8, 3). Point L partitions the directed line segment from K to N in a ratio of 1:2. Point M partitions the directed line segment from L to N in a ratio of 3:1. What are the coordinates of point M? Round to the nearest tenth, if necessary. (–1.3, –0.3) (2.5, 1) (5.7, 2.2) (7, 2.5)
Answer:
I believe it's (5.7, 2.2)
I hope it's correct :)
c
Step-by-step explanation:
for the lazy people like me its c
Find the next three terms in the pattern 6, 4, 2, 0, −2, .... and complete the description of the pattern.
to get to the next term. The next three terms are
Answer: -4, -6, and -8, respectively. You must multiply each phrase by -2 to get to the next term (or remove it by 2). The next three terms would be -4, -6, and -8 as a result.
Which expressions are equivalent to 2^5 2^4? CHECK ALL THAT APPLY!!!
2^20
2.2^9
2^10 • 2²
2^-2 2^11
(2.2.2.2.2).(2.2.2.2)
Answer:
last option is correct
...................................
Work out the area of this trapezium.
15m
6m
10m
Answer:
105m²
Step-by-step explanation:
15+6=21
21÷2=10.5
10.5x10=105
Which of the following methods of agriculture is the most reliant upon technology and automation? a. rangeland grazing b. American agriculture c. traditional rice cultivation d. Dutch agriculture Please select the best answer from the choices provided A B C D
please hurry :(
sorry it says math
Answer: D
Step-by-step explanation:
Answer:
D: Dutch
Step-by-step explanation:
if the demand curve shifts to the left, what happens to price and quantity?
Answer:
A lower price and quantity would result.
HELPP
Lacey was looking at some data on World Cup soccer matches. She noticed a negative linear relationship
between the number of fans attending a match and the number of total goals scored in that match. Here is
computer output from a least-squares regression analysis for using attendance (in thousands of fans) to predict
the total number of goals scored:
Predictor
Coef
SE Coef
T
P
Constant
3.260
0.145
22.535
0.000
Attendance (thousands)
-0.009
0.003
-3.330
0.001
Use this model to predict the total number of goals scored in a match with 90 thousand fans in attendance.
You may round your answer to the nearest whole number of goals.
goals
Answer:
the answer is 2
Step-by-step explanation:
this was a question on my test on khan academy :D
11. Twelve contestants are competing to be 15.
on American Idol. The judges will keep either way
three or four of the contestants. How many
more groups would be formed if the judges
pick four instead of three?
A) 275
B) 715
C) 792
D) 10,560
Answer:
Option A
Step-by-step explanation:
Out of 12 contestants, the judges will select either 3 or 4 contestant.
Number of groups that can be formed when judges pick three contestants
\(^{12}C_3\)
\(220\)
Number of groups that can be formed when judges pick three contestants
\(^{12}C_4\\495\)
Number of more groups that can be formed if the judges pick four instead of three
\(= 495-220 = 275\)
Hence, option A is correct
Help me on this I have no idea how to do this
Answer:
i also don't have the idea
the boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. some summary statistics are also provided. the extreme outlier is an electric car whose electricity usage is equivalent to 112 miles per gallon. if that electric car is removed from the data set, how will the standard deviation be affected? the iqr?
Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.
The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.
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Select the FALSE statement about completely random design. a.) Subjects are randomly assigned to treatments. b.) Any number of treatments may be addressed. c.) The additional variables affect different control groups differently. d.) It minimizes the effects of confounding variables.
Answer:
your answer is A.
Step-by-step explanation:
The false statement about completely random designs is this: c.) The additional variables affect different control groups differently.
What is the false statement?The false statement about completely random designs is that additional variables affect different control groups differently. It is however true that in completely random esigns, the subjects are randomly assigned to treatments and any number of treatments may be addressed.
Also, the goal of this type of design is to reduce the effects of confounding variables. So, the correct option number that describes the false statement is C.
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uppose a batch of steel rods produced at a steel plant have a mean length of 170 millimeters, and a standard deviation of 10 millimeters. if 299 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.7 millimeters? round your answer to four decimal places.
The probability that the mean length of a sample of 299 steel rods would differ from the population mean by less than 0.7 millimeters is 0.9992, rounded to four decimal places.
The mean of a sample of steel rods can be considered as a random variable, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the mean of the sample of 299 rods would have a mean of 170mm and a standard deviation of 10mm divided by the square root of 299, which is approximately 0.577 mm.
To find the probability that the mean length of the sample rods would differ from the population mean by less than 0.7 mm, we need to find the probability that the standardized sample mean falls within a range of plus or minus 0.7 mm from the population mean. We can calculate this probability using the standard normal distribution, by calculating the z-score for the lower and upper limits of this range and then finding the area under the curve between these z-scores.
The z-score for a deviation of 0.7 mm from the mean is (0.7 - 0) / 0.577 = 1.2127. Therefore, the probability that the sample mean would differ from the population mean by less than 0.7 millimeters is the area under the standard normal curve between -1.2127 and 1.2127, which can be found using a standard normal distribution table or calculator. This probability is 0.9992, rounded to four decimal places. Therefore, we can conclude that it is highly likely that a sample of 299 rods would have a mean length that is very close to the population mean.
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Find the number that makes the ratio equivalent to 7:3.
84:?
Answer:
36
Step-by-step explanation:
Divide 84 by 7
84 ÷ 7 = 12
Now multiply 3 by 12
3 × 12 = 36
Then
7 : 3 = 84 : 36
An internet company reported that its earnings will be less than the 24 cents per share that was predicted
Answer:
p < 0.24
Step-by-step explanation:
If earning is 24% less Than predicted, this means that the we can represent the predicted earning with a variable, p
If the predicted earning = p
Then, the actual earning can be represented by the inequality ; p < 24%
p < 0.24