The height corresponding to the given side is 18cm
How to determine the heightSome of the properties of a parallelogram are given below as;
The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are congruent or equal.The measure of the sum of the interior angles are 360 degrees.The interior alternating angles are supplementary, that is, their sum is 180 degrees.The formula for calculating the area of a parallelogram is expressed as;
Area = bh
Given that;
b is the base side of the parallelogram and h is the height
Substitute the values
540 = 30h
Divide by the coefficient of h
h = 18 cm
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Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
Answer: Let's assume that the speed of the plane in still air is represented by p and the speed of the wind is represented by w.
When the plane is flying with the tailwind, its speed relative to the ground is the sum of its speed in still air and the speed of the wind, or (p + w). Similarly, when the plane is flying against the wind, its speed relative to the ground is the difference between its speed in still air and the speed of the wind, or (p - w).
We can set up two equations based on the given information:
(p + w) = 158 (1) (when flying with the tailwind)
(p - w) = 112 (2) (when flying against the wind)
To solve for p and w, we can add equations (1) and (2):
2p = 270
p = 135
So the speed of the plane in still air is 135 km/h.
We can then substitute this value of p into equation (1) to solve for w:
(p + w) = 158
(135 + w) = 158
w = 23
So the speed of the wind is 23 km/h.
Therefore, the plane flies at 135 km/h in still air and the wind blows at 23 km/h.
Step-by-step explanation:
True
The following table is a function.
X
y
1
5
-3 2
7 2 6 3
7
-4 5
9
8 4 1
7
1 0
True
False
Given statement: Here's the table with the values organized:
X | Y
-----
1 | 5
-3 | 2
7 | 2
6 | 3
7 | -4
5 | 9
8 | 4
1 | 7
1 | 0
This statement is False.
Because, The table provided is not a function because it does not have a clear and unique output value for each input value.
Since the X values 1 and 7 have multiple Y values, the given table is not a function.
In a function, each input value (X) must have a unique output value (y). However, in the given table, there are some input values, such as X = 7 and X = 1, that have multiple output values. For example, when X = 7, the table provides two output values, 2 and -4. Similarly, when X = 1, the table provides two output values, 5 and 0.
A function is a mathematical relationship between the input and output values, where each input value produces only one unique output value. Functions are used to represent many real-world scenarios, including calculating distances, temperatures, and profits. Therefore, it is crucial to ensure that the provided table represents a function by ensuring that each input value has a unique output value.
In conclusion, the table provided is not a function as it violates the one-to-one mapping between input and output values.
A function must have a clear and unique output value for each input value.
To determine if the given table represents a function, we need to make sure that each input (X value) corresponds to only one output (Y value).
Now let's check for any repeating X values with different Y values:
1 corresponds to both 5 and 7
7 corresponds to both 2 and -4.
False.
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The retail price at the department store is calculated by increasing the wholesale price by 40%. That is, the retail price is calculated by adding 40% of the selling price to the selling price as well. a) What is the retail price of a piece of clothing if its wholesale price is $300? b) What is the selling price of a pair of jeans if its retail price is $77?
Using the given information, we calculated the following prices:
a) The retail price is $420
b) The wholesale price is $55
What are retail and wholesale prices?
The processes of wholesale and retail are essentially distinct from one another because they entail the transfer of commodities from manufacturing to distribution. Purchasing products and selling them to clients constitute retail.
Retailers pay wholesale pricing to producers or distributors. Then, the shop charges customers a higher price—the retail price—for the identical product. Wholesale pricing is what you charge retailers who buy things in large amounts. With wholesale pricing, products are sold for more money than it costs to produce them in order to generate a profit.
The final selling price that retailers decide to charge customers is known as the retail price. In retail pricing, the customer is everything.
Let,
The retail price = x
The wholesale price = y
Then,
x = y + 0.4y = 1.4y
a) When y = $300
x = 1.4 * 300 = $420
b) When x = $77
77 = 1.4y
y = 77/1.4 = $55
Therefore using the given information, we calculated the following prices:
a) The retail price is $420
b) The wholesale price is $55
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Suppose that buses are scheduled to arrive at a bus stop at noon but are always X minutes late, where X is an exponential random variable with mean of 4 minutes. Suppose that you arrive at the bus stop precisely at noon. Compute the probability that you have to wait for more than five minutes for the bus to arrive.
The prοbability that we have tο wait fοr mοre than 5 minutes fοr the bus tο arrive, given that we arrived precisely at nοοn, is 1. In οther wοrds, we will always have tο wait fοr mοre than 5 minutes, οn average, fοr the bus tο arrive.
We are given that X, the amοunt οf time the bus is late, is an expοnential randοm variable with mean οf 4 minutes. This means that the prοbability density functiοn οf X is:
f(x) = (1/4) * [tex]e^{(-x/4)[/tex], fοr x >= 0
We want tο find the prοbability that we have tο wait fοr mοre than 5 minutes fοr the bus tο arrive, given that we arrived at nοοn. Let Y be the tοtal amοunt οf time we have tο wait, which is the sum οf X and 5 minutes. Then:
Y = X + 5
The prοbability that we have tο wait fοr mοre than 5 minutes is:
P(Y > 5) = P(X + 5 > 5)
= P(X > 0)
Since X is an expοnential randοm variable with parameter 1/4, we can calculate this prοbability as:
P(X > 0) = ∫(0 tο ∞) f(x) dx
= ∫(0 tο ∞) (1/4) *[tex]e^{(-x/4)} dx[/tex]
[tex]= [-e^{(-x/4)}][/tex](0 tο ∞)
= 1
Therefοre, the prοbability that we have tο wait fοr mοre than 5 minutes fοr the bus tο arrive, given that we arrived precisely at nοοn, is 1. In οther wοrds, we will always have tο wait fοr mοre than 5 minutes, οn average, fοr the bus tο arrive.
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Women from 10 different countries have won the annual Greentree Marathon, a 26.2-mile race. For the marathon's 13-year history, the median women's winning time is about 146 minutes, or 2 hours 26 minutes, and the interquartile range is about 7 minutes.
Answer: The median women's winning time of 146 minutes means that half of the winning times were below 146 minutes and half were above. This is a measure of the central tendency of the data.
The interquartile range (IQR) of 7 minutes gives us a measure of the spread of the data. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. It represents the middle 50% of the data.
In this case, we don't know the actual values of Q1 and Q3, but we can say that the IQR is about 7 minutes. This means that the difference between the winning times of the 75th percentile and the 25th percentile is about 7 minutes.
Overall, these statistics tell us that the winning times for women in the Greentree Marathon have a relatively narrow range, with most of the winning times falling within a 7-minute range around the median. However, we don't know anything about the distribution of the data beyond this range, such as whether there are any outliers or whether the data is symmetric or skewed.
Step-by-step explanation:
Jim's favorite hockey player can shoot a hockey puck at a speed of 108 mph what is the speed of the puck in feet per second
Answer:
158.4 ft/sec
Step-by-step explanation:
multiply the speed value by approximately 1.467
please help i’m struggling
The vertices of the image of triangle ABC under the transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 are A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).
What is transformation?Transformation in maths is the process of changing the position, size, orientation or shape of a figure or shape. It involves various techniques such as translation, rotation, reflection and scaling.
The transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 is a combination of a translation and a dilation. A translation is a transformation that moves the shape without changing its size or orientation. In this case, the translation moves the triangle 3 units to the left and 1 unit up. A dilation is a transformation that enlarges or reduces a shape. In this case, the dilation uses a scale factor of 2, so the triangle will be twice as big as it was before.
The vertices of the original triangle ABC are (A(x1,y1), B(x2,y2), C(x3,y3)). After the translation, the vertices will be (A(x1-3,y1+1), B(x2-3,y2+1), C(x3-3,y3+1)). After the dilation, the vertices will be (A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).
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Determine a series of transformations that would map polygon ABCDE onto polygon
A'B'C'D'E'?
The sequence of transformations is:
Reflection over the x-axis.Reflection over the y-axis.Translation of 3 units to the right.How to find the series of transformations?Let's only follow the coordinates of one of the vertices to identify the transformations, we clearly have a reflection over a vertical line and a reflection over a horizontal line, so first let's apply thes two.
Vertex A starts at (1, -4)
First a reflection over the x-axis will change the sign of the y-component, then we get:
A₁ = (1, 4)
Then a reflection over the y-axis changes the sign of the x-component to:
A₂ = (-1, 4)
Finally we have a translation, we can see that:
A' = (2, 4).
Then we have a translation (a, b) such that:
(-1 + a, 4 + b) = (2, 4)
So we can see that a = 3 and b = 0, then we have a translation of 3 units to the right.
That is the sequence of transformations.
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Suppose you borrow $5000 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $325 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$5000
$4520.84
Question Help: Video
1.75% Interest
on Prior Balance
S
$74.81
Monthly Payment
$325
$325
$325
$325
Ending Balance
$
S
$5000
$4520.84
Answer:
Step-by-step explanation:
To fill in the table, we can use the following steps:
Calculate the interest for each month, which is the prior balance multiplied by the monthly interest rate (1.75%).
Subtract the monthly interest from the prior balance to get the new balance before the monthly payment.
Subtract the monthly payment from the new balance to get the ending balance.
Month Prior 1.75% Interest on Monthly Ending
Balance Prior Balance Payment Balance
1 $5000 $87.50 $325 $4762.50
2 $4762.50 $83.39 $325 $4520.84
3 $4520.84 $79.06 $325 $4276.90
4 $4276.90 $74.50 $325 $4029.23
5 $4029.23 $69.69 $325 $3777.87
Therefore, after 5 months of making $325 payments, the remaining balance on the loan is $3777.87.
In a Gallup poll conducted nationwide in July 2020, it was found that 63% of a sample of female
adults supported a ban on public smoking.
a) Describe the population parameter of interest in this study.
The population parameter of interest in this study is the proportion or percentage of all female adults in the entire population who support a ban on public smoking. The Gallup poll was conducted to estimate this proportion or percentage by collecting data from a sample of female adults. By using statistical inference methods, the researchers can use the sample data to make inferences about the population parameter with a certain level of confidence.
A Bakery allows customers to design and order special cupcakes. There is a single fee of $4 to create the new design and then each special cupcake ordered costs $3.
thy be c matey truth me ARG!!??
Answer:7$
Step-by-step explanation:$4+3$=7$
I’M STUCK! BRAINLIEST TO WHOEVER CAN GET THIS QUESTION CORRECT!
The two column proof that shows that ΔADC ~ ΔDBC is as shown below.
How to complete the two column proof?A two-column proof is defined as a geometric proof that is said to consist of a list of statements, and the reasons for which those statements are true. The statements are thus listed in a column on the left, with the reasons for which the specific statements can be made are now listed in the right column.
The complete two column proof is expressed as:
Statement 1: ∠ADC is a right angle
Reason 1: Given
Statement 2: DB is perpendicular to AC
Reason 2: Given
Statement 3: ∠DBC is a right angle
Reason 3: Definition of Perpendicular
Statement 4: ∠ADC ≅ ∠DBC
Reason 4: All right angles are congruent
Statement 5: ∠C ≅ ∠C
Reason 5: Reflexive Property of Congruence
Statement 6: ΔADC ~ ΔDBC
Reason 6: AA Similarity
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The sum of the first two terms of a G.P is 5/2 , and the sum of the first four terms is 65/18. Find the G.P if r>0
Answer:
Common ratio r = [tex]\dfrac{2}{3}[/tex]
Sequence is described by
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
Step-by-step explanation:
[tex]S_n = \dfrac{a_1(1-r^n)}{1-r}[/tex]
where
r = common ratio
a₁ = first term
Sum of first two terms
[tex]S_2 = \dfrac{a_1(1-r^2)}{1-r}[/tex]
Sum of first four terms:
[tex]S_4 = \dfrac{a_1(1-r^4)}{1-r}[/tex]
[tex]\dfrac{S_4}{S_2} = a_1 \cdot \dfrac{1-r^4}{1-r} \div a_1 \cdot \dfrac{1-r^2}{1-r}\\[/tex]
To divide, flip the divisor and multiply
[tex]\dfrac{S_4}{S_2} =\dfrac{a_1(1-r^4)}{1-r} \times \dfrac{1-r}{a_1(1-r^2)}[/tex]
The a₁ and (1-r) terms cancel out from numerator and denominator leaving
[tex]\dfrac{S_4}{S_2} =\dfrac{1-r^4}{1-r^2} \cdots [1][/tex]
Using the identity
[tex]a^2 - b^2 = (a- b)(a+b)[/tex]
[tex]1- r^4 = 1^4 - r^4 = (1^2 - r^2)(1^2+r^2) = (1-r^2)(1+r^2)[/tex]
Plugging this into equation 1 we get
[tex]\dfrac{S_4}{S_2} =\dfrac{(1-r^{2})(1+r^{2})}{1-r^{2}}[/tex]
The [tex]1- r^2[/tex] terms cancel out leaving:
[tex]\dfrac{S_4}{S_2} =1 + r^2[/tex]
We are given
[tex]S_4 =\dfrac{65}{18}\\\\S_2 = \dfrac{5}{2}[/tex]
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \div \dfrac{5}{2}[/tex]
To divide, flip the denominator [tex]\dfrac{5}{2}[/tex] and multiply
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \times \dfrac{2}{5}\\\\= \dfrac{13}{9}[/tex]
Therefore
[tex]1 + r^2 = \dfrac{13}{9}\\\\r^2 = \dfrac{13}{9} - 1\\\\= \dfrac{13}{9} - \dfrac{9}{9}\\\\= \dfrac{4}{9}[/tex]
[tex]r = \sqrt{\dfrac{4}{9}}\\\\= \dfrac{\sqrt{4}}{\sqrt{9}}\\\\= \dfrac{2}{3}[/tex]
So the common ratio
[tex]r = \dfrac{2}{3}[/tex]
To find the first term we have sum of first two terms = 5/2
[tex]S_2 = \dfrac{a_1(1-r^2)}{(1-r)} = a_1 (1+ r)[/tex]
Plugging in knowns
[tex]\dfrac{5}{2} = a_1(1+\dfrac{2}{3})\\\\= a_1 \cdot \dfrac{5}{3}[/tex]
Multiply both sides by 3/5 to get
[tex]a_1 = \dfrac{5}{2} \times \dfrac{3}{5}\\\\a_1 = \dfrac{3}{2}[/tex]
The nth term of a GP is
[tex]a_n = a_1 \cdot r^{n-1}\\[/tex]
Plugging in the values obtained
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
Gaby logra duplicar su dinero y pagar 70,000 que debía;le queda. 90,000 cuánto dinero tenía Gaby al inicio
Answer:
logra =70000
queda=90000
Step-by-step explanation:
additional
total income 70000+90000=160000
division by 2
160000/2
=$80.000
Find the length of BC
bc=√{ac²-ab²}
bc=√{16²-11²}
bc=√{256-121}
bc=√{135}
bc=11.62
Find the value of x in the isosceles triangle. Round to the nearest tenth if necessary.
The value of x is 15 inches, we find this by Pythagoras theorem and property of isosceles triangle.
What is Pythagoras Theorem?Pythagoras theorem states that sum of square of base and square of perpendicular is equal to square of hypotenuses.
So , it can be formula is given below ,
[tex]perpendicular^{2} + base^{2} = hypotenuse^{2}[/tex]
And In ab isosceles triangle two equal side vertex divide base in two equal parts.
So, here base = 40.
Therefore it is divided in 20-20 inches,
Now putting the formula of Pythagoras theorem, we get
[tex]20^{2} + x^{2} = 25^{2}[/tex]
[tex]x^{2} = 25^{2} - 20^{2}[/tex]
[tex]x^{2} = 225[/tex]
So we get, x = 15 inches.
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Therefore , the solution of the given problem of area comes out to be the rectangle's dimensions are 6.5 yards and 10 yards, respectively.
What is an area exactly?By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.
Here,
Let w represent the rectangle's breadth.
In light of the issue statement, the rectangle's length is 2w - 3.
Since the rectangle's area is 65, we can construct the following equation:
=> w(2w - 3) = 65
By enlarging and condensing the left half, we obtain:
=>2w² - 3w - 65 = 0
Now that we have the quadratic formula, we can answer this quadratic equation:
=> w = (-b √(b² - 4ac)) / 2a.
where c = -65, b = 3, and a = 2. By replacing these numbers, we obtain:
=> w = (-(-3) ± √(-3)² - 4(2)(-65))) / 2(2)
=> w = (3 + √(529)) / 4
=> w = (3 ± 23) / 4
=> w = (3 + 23) / 4 = 6.5
=> l = 2w - 3 = 2(6.5) - 3 = 10
The rectangle's dimensions are 6.5 yards and 10 yards, respectively.
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Find the directional derivative, Duf, of the function at the given point in the direction of vector v. f(x, y) = 2 ln(x2 + y2), (2, 1), v = −1, 2
The directiοnal derivative οf [tex]f(x,y) = 2ln(x^2 + y^2)[/tex] at the pοint (2,1) in the directiοn οf the vectοr v = (-1,2) is 0.
Directiοnal derivative and gradient: what are they?A directiοnal derivative shοws hοw quickly a functiοn changes in any directiοn. A fοrmula that incοrpοrates the gradient can be used tο determine the directiοnal derivative. The gradient οf a functiοn οf mοre than οne variable shοws the directiοn οf greatest change.
We must cοmpute the dοt prοduct οf the gradient οf f at (2,1) with the unit vectοr in the directiοn οf v in οrder tο determine the directiοnal derivative οf the functiοn [tex]f(x,y) = 2ln(x2, + y2)[/tex] at the pοsitiοn (2,1) in the directiοn οf the vectοr v = (-1,2).
Then, we determine f's gradient:
Grad(f) is equal tο [tex](f/x, f/y) = (4x/(x2+y2), 4y/(x2+y2)[/tex]
Hence, the gradient at lοcatiοn (2,1) is as fοllοws:
grad [tex](f)(2,1) = (4(2)/(2^2+1^2), 4(1)/(2^2+1^2)) = (8/5, 4/5)[/tex]
The unit vectοr in the directiοn οf v is then lοcated:
||v|| = √((-1)²+ 2²) = √5\su = v/||v|| = (-1/√5, 2/√5)
We calculate the directiοnal derivative last.
Def = grad(f) (2,1) · u\s= (8/5)(-1/√5) + (4/5)(2/√5)\s= -8/5√5 + 8/5√5\s= 0
Hence, at pοint (2,1) in the directiοn οf the vectοr v = (-1,2), the directiοnal derivative οf f(x,y) = 2ln(x², + y²) is equal tο 0.
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Solve the system
0.2x+y=1.3
2(0.5x-y)=4.6
Answer:
x = 36/7 (or approximately 5.143); y = 19/70 (or approximately 0.271)
Step-by-step explanation:
First, we can distribute the 2 to have both equations look similar:
[tex]2(0.5x-y)=4.6\\x-2y=4.6[/tex]
Now, we can eliminate the ys by multiplying the entire first equation by 2. This will allow us to solve for x.
[tex]2(0.2x+y=1.3)\\\\0.4x+2y=2.6\\x-2y=4.6\\\\1.4x=7.2\\x=\frac{36}{7}\\ x=5.142857143[/tex]
Now, we can plug in 36/7 for x in any of the two equations:
[tex]0.2(\frac{36}{7})+y=1.3\\ \frac{36}{35}+y=1.3\\ y=\frac{19}{70}\\ y=0.2714285714[/tex]
If you use the decimal answers, you can round as much as you need.
The grain required to produce 100 L of ethanol can feed a person for a year, Around 49 billion liters more ethanol was produced in US from corn in 2018 than in 2001, how many people could this have fed?
Step-by-step explanation:
Assuming that the grain required to produce 100 liters of ethanol could feed one person for a year, we can calculate the number of people that could have been fed by the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018.
First, we need to determine the amount of grain required to produce 1 liter of ethanol. This can vary depending on a number of factors, including the type of grain and the production method, but a commonly cited estimate is that it takes around 1.4 kilograms of corn to produce 1 liter of ethanol.
Therefore, to produce 49 billion liters of ethanol, we would need:
49,000,000,000 liters x 1.4 kg of corn per liter = 68,600,000,000 kg of corn
To convert this to the amount of grain required to feed people, we need to divide by the amount of grain needed to feed one person for a year. Again, this can vary depending on the person's age, sex, and level of activity, but a commonly cited estimate is that an adult needs around 700 kilograms of grain per year.
Therefore, the amount of grain required to feed the number of people who could have been fed by the grain used to produce the additional ethanol is:
68,600,000,000 kg of corn / 700 kg of corn per person per year = 98,000,000 people
So the additional 49 billion liters of ethanol produced in the US from corn between 2001 and 2018 could have fed around 98 million people for a year.
The additional ethanol production from corn in 2018 could have potentially fed 49 billion people
To determine how many people could have been fed with the additional 49 billion liters of ethanol produced in the US from corn in 2018 compared to 2001, we need to calculate the amount of grain saved by producing ethanol instead of using it for direct consumption.
According to the information given, the grain required to produce 100 liters of ethanol can feed a person for a year. Therefore, for each liter of ethanol produced, the grain equivalent can sustain one person for a year.
To find the number of people fed, we can multiply the additional 49 billion liters of ethanol produced by the grain equivalent for each liter:
49 billion liters * 1 person/year per liter = 49 billion people
Hence, the additional ethanol production from corn in 2018 could have potentially fed 49 billion people based on the assumption that the grain used to produce ethanol would have been used for direct consumption instead.
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temperature inside a building is
22°C. The temperature outside
the building is 22°F. Is your friend's
statement correct? Explain.
The temperature inside the building
is the same as the temperature
outside the building.
Yοur friend's statement is nοt cοrrect.
What is the basic mathematical οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Nο, yοur friend's statement is nοt cοrrect.
The reasοn is that the twο temperatures are measured using different scales. The temperature inside the building is given in Celsius (°C), while the temperature οutside is given in Fahrenheit (°F). These are twο different scales, and a temperature οf 22°C is nοt equal tο a temperature οf 22°F.
Tο cοmpare the twο temperatures, we need tο cοnvert οne οf them tο the οther scale. One way tο dο this is tο use the cοnversiοn fοrmula:
°F = (°C × 9/5) + 32
Using this fοrmula, we can cοnvert the temperature inside the building frοm Celsius tο Fahrenheit:
°F = (22°C × 9/5) + 32 = 71.6°F
Nοw we can see that the temperature inside the building is much higher than the temperature οutside the building.
Hence, yοur friend's statement is nοt cοrrect.
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A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone that is parallel to the base and 3 inches from the vertex?
A circular cross section is marked near the vertex of a cone, parallel to the base.
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is square inches.
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches
Calculating the area of the cross section of a coneFrom the question, we are to determine the area of the cross-section of the cone
To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.
Let the radius of the cross-section be x and radius of the base of the be r.
The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches
By similar triangle theorem, we can write that
8/r = 3/x
x = (3r)/8
From the given information,
The area of the base is 24 square inches
Thus,
πr² = 24
Therefore, r² = 24/π
The area of the cross-section will be
A = πx²
But, x = (3r)/8
Thus,
A = π [(3r)/8]²
A = π × 3²/8² × r²
A = π × 9/64 × 24/π
A = 27/8 square inches
Hence, the area is 27/8 square inches or 3 3/8 square inches
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Look at the picture below if you have any questions comment
Answer:
95.522
Step-by-step explanation:
First, we have to find the area of the triangle...
We know that the equation for the area of a triangle is: [tex]\frac{1}{2} lw[/tex]This means that our solution would be: [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × [tex]6[/tex] = [tex]24[/tex]Next, we have to find the area of the sector...
We know that the equation for the area of a circle is: πr²This means that our solution would be: π × 10² = 314As the sector is only 82° so we have to do: 360 ÷ 82 = 4.39024390244So we have to do 314 ÷ 4.39024390244 = 71.5222...(recurring)Now we have to add our results together...
71.5222...(recurring) + 24 = 95.5222...(recurring)Rounded to the nearest hundredth: 95.522Hope this helps, have a lovely day! :)
Suppose you invest $25,000 in a one-year certificate of deposit (CD) that pays simple interest at 4.25% annually. The CD is cashable at any time, with interest payable on a prorated basis. If you cashed the CD after seven months, how much would you earn in interest?
A $556.25
B $656.25
C $612.50
D $468.75
The amount of simple interest earned after 7 months is given as follows:
C $612.50
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The interest accrued over the period is modeled as follows:
I(t) = Prt.
The parameter values for this problem are given as follows:
P = 25000.r = 0.0425.t = 7/12 -> as the time is measured in one year, hence 7 months = 7/12 of an year.Then the accumulated interest is given as follows:
I = 25000 x 0.0425 x 7/12
I = $612.50.
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Given the similar hexagon-based prisms pictured below, if prism 2 has a surface area of 324 space cm squared, what is the surface area of prism 1?
A: 777.6 cm²
B: 67.81 cm²
C: 56.25 cm²
D: 135 cm²
The surface area of the prism 1 is 56.25( optionC)
What are similar shapes?Similar shapes are shapes with thesame shape but not necessarily thesame side.
The ratio of the corresponding sides of prism 1 to prism 2 = 5/12
therefore 5/12 is the linear scale factor.
The area factor is the square of linear scale factor .
Therefore area factor = (5/12 )² = 25/144
To find the area of prism 1, we use the area factor.
Represent the area of prism 1 by x
25/144 = x/ 324
144x = 324 × 25
144x = 8100
divide both sides by 144
x = 8100/144
x = 56.25
therefore the area of prism 1 is 56.25
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How do people express laughter on Reddit? Researchers studied millions of posts on Reddit and isolated comments that used a
textual form of laughter such as "lol" or "haha" (emojis weren't included). Of the comments with a textual form of laughter,
55.8% used some form of "lol". Randomly select 300 comments on Reddit that use a textual form of laughter and let X = the
number of comments that use a variation of "lol."
(a) Show that the probability distribution of X is approximately normal.
and n(1-p)=
np=
The probability distribution of X is approximately normal because np and n(1-p) are both
(b) Calculate the mean of the appropriate normal distribution.
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Based on Probability laws the answers are: (a) n(1-p) = 167.4 and (b) mean = 167.4
(a) To demonstrate that the probability distribution of X is roughly normal, we must determine if np and n(1-p), where n is the sample size and p is the chance of success, are both higher than or equal to 10. (using a variation of "lol").
If 55.8% of comments containing a textual form of laughter use some version of "lol," the numbers in this case are n = 300 and p = 0.558. Therefore:
[tex]n(1-p) = 300 * 0.442 = 132.6 np = 300 * 0.558 = 167.4[/tex]
The probability distribution of X is roughly normal since np and n(1-p) are both bigger than or equal to 10.
(b) The formula for the mean of the suitable normal distribution is: = np = 300 x 0.558 = 167.4.
Hence, 167.4 is the normal distribution's mean.
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Please help! I need the answer to the whole of the question!
A coffe costs x pence. A teas costs 20pence less than coffe.
a) write an expression in term of x ___pence
b) write an expression in the terms of x, for the total cost of 3 coffees and 2 teas
Answer:
x+3+3
Step-by-step explanation:
So bassicly you have to add everything up ad then divide by 1
find the inradius and circumradius of the triangle
Circumradius of the isosceles triangle = 20 units
What is an isosceles triangle?A triangle with two sides that have the same length is said to be isosceles. Let's carry out a quick exercise to better comprehend this. Fold the corners of a rectangular piece of paper in half. From the top folded corner to the bottom border, draw a line. O, D, and C should be noted as the triangle's vertices.
Now quantify the OD and OC. Use several measures to perform this exercise again and look for patterns. It is evident that OD and OC are consistently isosceles triangle. An isosceles triangle is a triangle with equal-lengths on both sides.
Now here circumradius, r = abc/√ [(a+b+c)(a+b-c)(a+c-b)(b+c-a)]
r = 29× 29 × 40/ √ (98×18×40×40)
= 29×29/42
≈20.02
=20
Hence the circumradius of the given triangle is 20 units.
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A triangle has sides with lengths of 19 feet, 59 feet, and 69 feet. Is it a right triangle?
Triangle GHI is similar to triangle JKL. Find LJ. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
Therefore , the solution of the given problem of triangle comes out to be LJ rounded to the closest tenth, is about 7.5
What is a triangle exactly?A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
The respective sides of the triangles CHI and JKL are proportional because of their similarity. Using the matching sides, we can construct a proportion:
=> JK / CI = LJ / CH
The values JK = 15 and CI = 8 are provided. Using the data shown in the picture, we must locate CH and LJ.
We can see from the picture that HI = 4 and KL = 20. By taking HI away from CI, we can discover CH:
=> HI = 8 - 4 = 4 CH = CI =
We can now solve for LJ by substituting the numbers we already know into our proportion:
=> LJ / 4 = 15 / 8
=> LJ = 4 * 15 / 8
=> LJ = 7.5
LJ, rounded to the closest tenth, is about 7.5.
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