Answer:
Variability expected among these Proportions is given by Standard deviation = 0.125
Step-by-step explanation:
The probability of tossing heads is the same for a fair coin as the probability of tossing tails.
The probability of tossing heads is then 1 chance out of 2
P = 1/2 = 0.5
The standard deviation of the sample distribution of the sample proportion = √Pq/n
Standard deviation = √p(1-p)/n
= √0.5(1-0.5)/16
Standard deviation = 0.125
The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.
Explanation:The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.
In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.
The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.
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"One baseball game has 9innings. During the season there are 45 innings that are at home and 45 innings that are away. If 36 of the innings for the season have been played how many games remain?
Answer:
6 baseball games remain in the season.
Step-by-step explanation:
Let the number of baseball games remaining be 'x'.
Given:
Number of innings in 1 baseball game = 9
Number of innings to be played at home = 45
Number of innings to be played away from home = 45
Total number of innings played in the given season = 36
Now, total number of innings to be played in a season is equal to the sum of the innings played at home and away from home.
So, Total number of innings = 45 + 45 = 90 innings.
Now, out of 90 innings, 36 innings are already played.
So, the number of innings that remain is given as:
Innings remaining = Total innings - Innings already over
Innings remaining = 90 - 36 = 54
Now, 9 innings is equivalent to 1 baseball game.
So, 54 innings is equivalent to 'x' baseball games.
Setting up a proportion and solving by cross multiplication, we get:
[tex]\frac{9}{1}=\frac{54}{x}\\\\9x=54\\\\x=\frac{54}{9}=6[/tex]
Therefore, 6 baseball games remain in the season.
△CDE maps to △STU with the transformations (x, y) arrowright (x − 2, y − 2) arrowright (3x, 3y) arrowright (x, −y). If CD = a + 1, DE = 2a − 1, ST = 2b + 3 and TU = b + 6, find the values of a and b. The value of a is and the value of b is .
Answer: The value of a is 2 and the value of b is 3.
Step-by-step explanation:
Given : △CDE maps to △STU with the transformations (x, y) → (x − 2, y − 2) →(3x, 3y)
The first transformation is a translation ,so there will be no change in the length of the sides ∵ translation is a rigid motion.
The second transformation is a dilation ,so there will be a change in the length of the sides by scale factor of 3. ∵ dilation is not a rigid motion.
Basically , by combining both transformation:
Length of Side in △STU = 3 x (Corresponding side in △CDE )
⇒ ST = 3CD and TU = 3 DE
If CD = a + 1, DE = 2a − 1, ST = 2b + 3 and TU = b + 6 , then
2b + 3=3(a + 1) and b + 6 = 3(2a − 1)
⇒ 2b + 3=3a+3 and b + 6 = 6a-3
⇒ 3a-2b=0 (i) and b = 6a-9 (ii)
Put value of b from (ii) in (i) , we get
3a-2(6a-9)=0
⇒ 3a-12a+18=0
⇒ -9a=-18
⇒ a= 2
Put value of a in (ii) , we get
b= 6(2)-9
=12-9=3
Hence, the value of a is 2 and the value of b is 3.
Answer:
a = 4 , b = 6
Step-by-step explanation: I did the same question
chandra and simone have 152 baseball cards together. chandra's collection has 42 more baseball cards in it than simone's collection. how many baseball cards does chandra have
Answer:
Chandra have 97 baseball cards.
Step-by-step explanation:
Given:
Chandra and Simone have 152 baseball cards together. Chandra's collection has 42 more baseball cards in it than Simone's collection.
Now, to find baseball cards Chandra have.
Let the baseball cards Simone's have be [tex]x.[/tex]
As, given Chandra's collection has 42 more baseball cards in it than Simone's collection.
So. Chandra's collection of cards is [tex]x+42.[/tex]
Together Chandra and Simone have baseball cards = 152.
According to question:
[tex]x+(x+42)=152[/tex]
[tex]x+x+42=152[/tex]
[tex]2x+42=152[/tex]
Subtracting both sides by 42 we get:
[tex]2x=110[/tex]
Dividing both sides by 2 we get:
[tex]x=55.[/tex]
Thus, Simone's collection of cards = 55.
Now, to get the baseball cards Chandra have we substitute the value of [tex]x[/tex]:
[tex]x+42\\=55+42\\=97.[/tex]
Therefore, Chandra have 97 baseball cards.
Yo sup??
total number of cards that Chandra and Simone have =152
let number of cards that Simone have be x
then chandra will have 42+x
from the statement given to us we can say that
x+x+42=152
2x=110
x=55
therefore Simone has 55 cards and chandra has 97 cards
Hope this helps
Lindsay brought x watermelon slices to a party. Caroline brought y watermelon slices. The 7 people at the party each ate the same number of watermelon slices. If Lindsay brought 12 watermelon slices and Caroline brought 9 watermelon slices, how many slices did each person eat?
Answer: each person ate 3 slices of watermelon.
Step-by-step explanation:
The total number of people at the party was 7.
Total number of watermelon slices that Lindsay brought to the party is 12. Total number of watermelon slices that Caroline brought to the party is 9. Total number of slices that that both of them brought to the party would be
12 + 9 = 21 slices
The 7 people at the party each ate the same number of watermelon slices. It means that the number of slices that each person ate would be
21/7 = 3
Answer:
3. I checked.
Step-by-step explanation:
Which is the correct written form of the scientific name that uses the rules of binomial nomenclature?Felis domesticus Felis Domesticus Felis domesticus felis domesticus
Answer:
Step-by-step explanation:
The correct written form of the scientific name that uses the rules of binomial nomenclature is "Felis domesticus." Each binomial nomenclature identifies each species by a scientific name of two Latin words. The first name is capitalized, the second is not.
The correct written form of the scientific name using binomial nomenclature is 'Felis domesticus'. Developed by Carolus Linnaeus, the system assigns every organism a unique two-part name, made up of genus and species.
Explanation:The correct written form of the scientific name, using the rules of binomial nomenclature, is Felis domesticus. Binomial nomenclature is a system developed by Swedish botanist Carolus Linnaeus that gives every organism a unique, two-part scientific name. This two-part name consists of the genus name first (capitalized) and the species name second (lowercase). Both parts of the name are italicized in print to differentiate them.
For instance, the scientific name for humans is Homo sapiens with 'Homo' representing the genus and 'sapiens' the species. Similarly, in the case of Felis domesticus, 'Felis' is the genus and 'domesticus' is the species describing a domestic cat.
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Evaluate the expression. 8!-6!
8! - 6!
Evaluate the factorials.
40320 - 720
Subtract.
39600.
The expression (8!) - (6!) is equal to 39600.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
After the expression has been evaluated, looking at the main value of 8! − 6!, it becomes 39,600. Therefore 8! − 6! = 39,600.
How do we evaluate the expression?To evaluate the expression 8!−6!, we first need to determine the value of 8! and the value of 6!, and then subtract the two results.
8! (read as "8 factorial") means:
8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320
6! (read as "6 factorial") means:
6 × 5 × 4 × 3 × 2 × 1 = 720
subtract 6! from 8!:
8!−6! = 40,320 − 720 = 39,600
Therefore 8! − 6! = 39,600.
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Paul is building a rectangular pen for his goat. The length of the pen will be 5feet more than twice as long as the width of the pen. The cost of the pen will be $7.50 per foot of fencing. If x represents the width of the oen, c(x) in terms of c to represent the cost of the fencing if x represents the width the pen, write a function
Answer:
[tex]C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]
Step-by-step explanation:
We are given the following in the question:
The length of the pen will be 5 feet more than twice as long as the width of the pen.
Let y be the length and x be the width. Thus, we can write:
[tex]y = 2x +5[/tex]
Fencing = Perimeter of rectangular pen
[tex]\text{Perimeter of rectangle} = 2(\text{length} + \text{width})\\ P = 2(y+x)\\P=2(2x+5+x)\\P= 2(3x+5)\\P = (6x + 10)\text{ feet}[/tex]
The cost of the pen will be $7.50 per foot of fencing.
Total Cost of fencing =
[tex]\text{Cost of fencing}\times \text{Perimeter}\\C(x) = 7.50\times (6x+10)\\C(x) = 45x + 75\\\text{where x is the width of rectangular pen}[/tex]
is the required cost function.
Final answer:
The cost function for fencing a rectangular pen, given the width x and a cost of $7.50 per foot, is c(x) = 45x + 75, representing the total cost as a function of the width x.
Explanation:
The student is asking for a function that represents the cost of fencing a rectangular pen when the width is given. Let x be the width of the pen. The length of the pen, according to the problem, is 5 feet more than twice the width, so it can be expressed as 2x + 5 feet.
The cost of the fencing is $7.50 per foot. To find the total cost of the pen, we have to calculate the perimeter of the rectangular pen, which is 2 times the width plus 2 times the length. Hence, the perimeter P(x) can be represented as P(x) = 2x + 2(2x+5).
Multiplying through and simplifying gives us the cost function c(x) = 7.50 * P(x). Therefore, c(x) = 7.50 * (2x + 2(2x + 5)) = 7.50 * (6x + 10) = 45x + 75. This function represents the cost of fencing the pen as a function of its width x.
On Monday billy spent 4 1/4 hours studying.On Tuesday he spent another 3 5/9 hours studying what is the combined time he spent studying answer as a mixed number
Answer:
[tex]7\frac{29}{36}\ hours[/tex]
Step-by-step explanation:
Given:
Time spent on Monday (M) = [tex]4\frac{1}{4}\ hours[/tex]
Time spent on Tuesday (T) = [tex]3\frac{5}{9}\ hours[/tex]
Now, the total combined time spent on study is equal to the sum of the times spent on Monday and Tuesday.
So, we need to add both the times to get the combined time spent on studying.
The combined study time is given as:
Total time spent = Time spent on Monday + Time spent on Tuesday
[tex]Total\ time=4\frac{1}{4}+3\frac{5}{9}\\\\Total\ time = \frac{4\times 4+1}{4}+\frac{3\times 9+5}{9}\\\\Total\ time = \frac{17}{4}+\frac{32}{9}\\\\\textrm{Taking LCD of 9 and 4 as 36, we get:}\\\\Total\ time = \frac{17\times 9}{4\times 9}+\frac{32\times 4}{9\times 4}\\\\Total\ time = \frac{153}{36}+\frac{128}{36}\\\\\textrm{Since the denominators are same, we add the numerators.}\\\\Total\ time = \frac{153+128}{36}\\\\Total\ time = \frac{281}{36}\ hours[/tex]
Divide 281 by 36. The quotient is the whole number part, the remainder is the numerator part and the denominator remains the same.
So, on dividing, we get 7 as quotient and 29 as remainder. So, converting to mixed fractions, we get:
[tex]Total\ time = 7\frac{29}{36}\ hours[/tex]
Therefore, the the combined time he spent studying is [tex]7\frac{29}{36}\ hours[/tex]
A machinist produced 22 items during a shift. Three of the 22 items were defective and the rest were not defective. In how many different orders can the 22 items be arranged if all the defective items are considered identical and all the nondefective items are identical of a different class?
Answer: There are 1540 different orders.
Step-by-step explanation:
The number of ways to arrange n things where 'a' things are alike and 'b' things are a like and so on...[tex]\dfrac{n!}{a!\ b!\ ....}[/tex]
Given : Total items = 22
Defective items = 3
Not defective items = 22-3 = 19
Then, the number of different orders can the 22 items be arranged if all the defective items are considered identical and all the non-defective items are identical of a different class :
[tex]\dfrac{22!}{3!\times19!}\\\\=\dfrac{22\times21\times20\times19!}{6\times19!}=1540[/tex]
Hence, there are 1540 different orders.
NEED HELP! I ALREADY DID HALF, BUT STILL CONFUSED!
Find CU. If necessary, round answers to 4 decimal places Show all your work for full credit. Hint: Use the Pythagorean Theorem first.
Answer:
Step-by-step explanation:
Triangle BCZ is a right angle triangle. Triangle BCU is also a right angle triangle. Side BU is common to both triangles.
To determine m∠ZBC, we would apply the tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan B = 8/6 = 1.33
m∠ZBC = Tan^-1(1.33) = 53.06
m∠UBC = m∠ZBC/2 = 26.53
To determine CU, we would apply
the tangent trigonometric ratio.
Therefore,
Tan 26.53 = CU/6
CU = 6Tan26.53
CU = 6 × 0.4992
CU = 2.9952
Sara got a 70%, 64%, and 83% on her first three tests. What must she get on her 4th test if she wants to get a final average of 75%?
Show your work, please.
We set up the equation (70+64+83+x)/4=75
Multiply by 4 on both sides: 70+64+83+x=300
Combine like terms on left side: 217+x=300
Subtract 217 from both sides: x=83
So Sara must get at least an 83% in order to maintain a final average of 75%
Hope this helped!
Answer: she must score 83% on her 4th test if she wants to get a final average of 75%
Step-by-step explanation:
The formula for determining average is expressed as.
Average = sum of the score/ number of tests.
Sara got a 70%, 64%, and 83% on her first three tests. Her former average would be
(70 + 64 + 83) 217/3 = 72.3℅
Let x represent the score that she needs to get on her 4th test if she wants to get a final average of 75%.
Therefore,
(x + 217)/4 = 75
Cross multiplying by 4, it becomes
x + 217 = 300
x = 300 - 217
x = 83%
Jim received a $2000 loan from his bank. The loan accrues 3% interest every 3 months. How much will Jim owe the bank after 4 years? Round to the nearest cent
Answer:
$2253.98
Step-by-step explanation:
Jim received a $2000 loan from his bank. The loan accrues 3% interest every 3 months.
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P=2000
r= 3%=0.03 and t= 4 years
interest every 3 months so n= 4
[tex]A=2000(1+\frac{.03}{4} )^{4 \cdot 4}[/tex]
[tex]A=2000(1+\frac{.03}{4} )^{16}\\A=2000(1.0075)^{16}\\\\A=2253.98[/tex]
Compound interest is the addition of interest. The interest that is needed to be paid by Jim in the 4 years of tenure is $2253.98.
What is compound interest?Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
We know that the Principal amount received by Jim is $2000, while the interest that Jim needs to pay is 3% quarterly, therefore, he needs to pay the interest 4 times a year. Thus, the value of n is 4.
Now, we know all the values therefore, substitute the values in the formula of compound interest,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
[tex]A = 2000(1+ \dfrac{3}{4})^{4 \times 4}\\\\A = \$2,253.98[/tex]
Hence, the interest that is needed to be paid by Jim in the 4 years of tenure is $2253.98.
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PLEASE HELP I NEEED ANSWER.. ASAP
Answer:
Step-by-step explanation:
Triangle IGH is a right angle triangle.
From the given right angle triangle
GI represents the hypotenuse of the right angle triangle.
With m∠I as the reference angle,
HI represents the adjacent side of the right angle triangle.
GH represents the opposite side of the right angle triangle.
To determine Hl, we would apply the tangent trigonometric ratio
Tan θ = opposite side/adjacent side. Therefore,
Tan 42 = 11/HI
0.9HI = 11
HI = 11/0.9
HI = 12.22
On tax free weekend, Alyssa bought 3 pairs of blue jeans for $92.31. The cost of the jeans is proportional to the number of pairs of jeans bought. What is the constant of proportionality in terms of dollars per pair of jeans?
The constant of proportionality, which is the cost per pair of jeans, is found by dividing the total cost by the number of pairs. For Alyssa's purchase of 3 pairs of jeans for $92.31, the constant of proportionality is $30.77 per pair.
Explanation:To determine the constant of proportionality for the jeans Alyssa bought, we need to divide the total cost by the number of pairs of jeans she purchased. Since Alyssa bought 3 pairs of jeans for $92.31, we calculate the constant of proportionality as follows:
Therefore, the constant of proportionality is $30.77 per pair of jeans.
Final answer:
The constant of proportionality, or the cost per pair of blue jeans, is $30.77 calculated by dividing the total cost of $92.31 by the number of blue jeans, which is 3.
Explanation:
The student has asked how to find the constant of proportionality, which in this context is the cost per pair of blue jeans when buying multiple pairs. If Alyssa bought 3 pairs of blue jeans for a total of $92.31 on tax free weekend, we can calculate the cost per pair by dividing the total cost by the number of pairs. The constant of proportionality would be: $92.31 / 3 = $30.77 per pair of jeans.
You're playing the slots and "win" twenty-five bucks! You're stoked. During the past ten weeks, you've won another fifty bucks. But you've dropped two bucks in the slot machines every day for ten weeks. What are we talking about here?
Answer: You loss is 65bucks.
Step-by-step explanation:
First, you win 25 bucks.
Next, the past 10 weeks 50 bucks.
For 10 weeks, you lost 2 bucks everyday:
10 × 7= 70days × 2= 140bucks.
In total you won) 25 + 50= 75 bucks.
You dropped 140bucks in total.
140- 75= 65 bucks.
Therefore, You lost 65bucks.
This question deals with Mathematics, specifically the concept of profit and loss. Despite winning a total of $75 over 10 weeks at the slots, you lose $2 everyday, totaling to $140 in losses over the ten weeks. Hence, you end up with a net loss of $65.
Explanation:The subject of this question is related to Mathematics and more specifically on the concept of profit and loss. Here you have won a total of $75 over 10 weeks, but each day you play slot machines you lose $2. Given that a week has 7 days, you’ve lost $2 * 7 days/week * 10 weeks = $140 over the course of 10 weeks. So, despite seeming to 'win' at the slot machine, when we subtract the total loss from total gain, $75 - $140, we find that you've actually ended up with a net loss of $65.
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What is the value of 7 ^−3 ^ −1 for = −2 and = 4?
a. −224
b. 7/4096
c. 7(−8)^−4
d. −7/32
Answer:
d. −7/32
Step-by-step explanation:
The expression that we have to evaluate in this problem is:
[tex]7x^{-3}y^{-1}[/tex]
We have to evaluate this expression for:
x = -2
y = 4
We start by rewriting the expression by rewriting it using the following:
[tex]a^{-n}=\frac{1}{a^n}[/tex]
So the expression can be rewritten as
[tex]7x^{-3}y^{-1}=\frac{7}{x^3 y}[/tex]
Now we observe that:
[tex](-2)^3=(-2)(-2)(-2)=-8[/tex]
Therefore, by substituting x = -2 and y = 4 into the expression, we find:
[tex]\frac{7}{(-2)^3\cdot 4}=\frac{7}{-8\cdot 4}=-\frac{7}{32}[/tex]
Miami, Florida has a latitude of 26° N. Where would the North Star (north celestial pole) appear in Miami?
Answer: Polaris would appear at [tex]26\°[/tex] latitude
Step-by-step explanation:
Let's begin by explaining that Latitude is the angular distance between the Earth's equator, and a specific point on the planet. It is measured in degrees and is represented according to the hemisphere in which the point is located, which can be north or south latitude.
In this sense, latitude [tex]0\°[/tex] refers to the equatorial line that divides the Earth in two hemispheres (North and South), and Miami's latitude [tex]26\°[/tex] refers to the Northern hemisphere.
On the other hand, talking about the North Star (also known as Polaris); if we were just in the North Pole (latitude [tex]90\°[/tex]), Polaris would by exactly over our heads or the zenith ([tex]90\°[/tex] over the horizon), but as we go until latitude [tex]26\°[/tex], Polaris altitude will be approximately at that same angle over the horizon.
Hence, from an observer located in Miami, Polaris would appear at [tex]26\°[/tex] N.
In Miami, with a latitude of 26° N, the North Star appears at an altitude of 26° above the horizon. As you move southward, it appears lower; when you travel north, it appears higher. Precise navigation also considers the slight angular difference between Polaris and the true celestial pole.
In Miami, Florida, which has a latitude of 26° N, the North Star, or north celestial pole, would appear at an altitude of 26° above the northern horizon. This is because the altitude of the North Star above the horizon is roughly equivalent to the latitude of the observer's location in the Northern Hemisphere. Therefore, as one drives southward from Miami to a city at a lower latitude, the North Star would appear lower in the sky. Conversely, driving northward would make the North Star appear higher.
It's important to note that due to the Earth's curvature, as you move southward from Miami, both the North Star and the southern sky would appear to sink, while the opposite would occur as you move northward. If you were to reach the equator, the North Star would align with the northern horizon, and it would not be visible from latitudes south of the equator. For precision in navigation or astronomy, one must also account for the small angular distance between Polaris and the true north celestial pole.
Gordon has two jobs. He earns $10 per hour babysitting his neighbors children and he earns $12 per hour. Write an inequality to represent the number of hours, x , babysitting and the number of hours ,y , Gordon will need to work to earn a minimum of $120
Answer:
Step-by-step explanation:
Let x represent the number of hours that he works. babysitting his neighbors children.
Let y represent the number of hours that he works at the other job.
He earns $10 per hour babysitting his neighbors children. This means that the amount that he earns, babysitting his neighbors children for x hours would be
10x
He earns $12 per hour working at the other job. This means that the amount that he earns, working at the other job for y hours would be
12y
Therefore, the inequality that represent the number of hours that he needs to work at both jobs to earn a minimum of $120 is
10x + 12y ≥ 120
Find the mean of the data summarized in the given frequency distribution. The highway speeds (in mph) of a random sample of cars are summarized in the frequency distribution below. Find the mean speed. Round your answer to one decimal place.
Answer:
Mean speed is 55.7 mph.
Step-by-step explanation:
The provided frequency distribution is:
Speed Cars
30-39 4
40-49 19
50-59 50
60-69 15
70-79 12
The formula to compute the mean for the grouped data is:
[tex]\bar{X} =\frac{\sum(mf)}{\sum(f)}[/tex]
Here, m is mid point and f is frequency.
The mean speed can be computed as:
Thus, the mean speed is 55.7 mph.
To find the mean of data from a frequency table, multiply each speed by its frequency, sum those products, and then divide by the total number of items. This produces a weighted average that reflects the frequency of each speed value in the dataset.
Explanation:To calculate the mean from a frequency table, we should multiply each speed by its frequency to get the 'combined speed' for each group. Add those combined speeds together, then divide by the total number of cars (or the sum of the frequencies).
For example, suppose we had 5 cars with a speed of 60 mph and 10 cars with a speed of 70 mph. We multiply each speed by its frequency (5*60 + 10*70), then sum these values to get the total combined speed. Divide this total combined speed by the total number of cars (5 + 10) to get the mean speed.
This method averages out the impact of each speed, weighted by how frequently each occurs in the dataset.
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What is the area of this polygon? 28.5 units² 34.5 units² 37.5 units² 40.5 units² 6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)
Answer:
Option B.
Step-by-step explanation:
The given vertices of the polygon are (-6,-2),(-5,1),(-1,4),(1,1),(5,3),(1,-2).
We need to find the area of the polygon.
Plot the given vertices and on a coordinate plane and draw the polygon. Divide the polygon in 4 parts as shown below.
Area of rectangle is
[tex]A=length\times width[/tex]
Area of triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
Area of each figure is
[tex]A_1=\dfrac{1}{2}\times 1\times 3=1.5[/tex]
[tex]A_2=\dfrac{1}{2}\times 6\times 3=9[/tex]
[tex]A_3=\dfrac{1}{2}\times 4\times 3=6[/tex]
[tex]A_4=6\times 3=18[/tex]
Area of polygon is
[tex]A=A_1+A_2+A_3+A_4[/tex]
[tex]A=1.5+9+6+18=34.5[/tex]
The area of polygon is 34.5 units².
Therefore, the correct option is B.
George weighed 160 pounds when he started college. If he gains just 0.25 pounds each month for four years of college, how much will he weigh? Suppose he doesn't change his habits after graduation, and continues that modest sounding waking weight gain for the next 10 years after college. How much will he weigh for his 10 college reunion?
Final answer:
George will weigh 172 pounds after four years of college, gaining 0.25 pounds per month. If he continues this trend for 10 more years, he will weigh 202 pounds at his 10-year college reunion.
Explanation:
To calculate the weight gain of George after college and for the next 10 years, we can use simple arithmetic. George starts at 160 pounds and gains 0.25 pounds each month.
Weight After College
Four years of college is equivalent to 4 years × 12 months/year = 48 months. If he gains 0.25 pounds each month, then over 48 months he will have gained:
0.25 pounds/month × 48 months = 12 pounds.
So, after college, his weight will be:
160 pounds + 12 pounds = 172 pounds.
Weight After Next 10 Years
To calculate his weight after the next 10 years, which is 10 years × 12 months/year = 120 additional months, we do the following calculation:
0.25 pounds/month × 120 months = 30 pounds gain.
Adding this to his weight after college:
172 pounds + 30 pounds = 202 pounds.
Therefore, for his 10-year college reunion, George will weigh 202 pounds.
Brian has an unlimited number of cents (pennies), nickels, and dimes. in how many different ways can he pay 1414cents¢ for a chocolate mint?
Answer:
The answer is 470 191 764
Step-by-step explanation:
Let's see how we got the figure. First, we need to check our data, or the information supplied.
Data:
There are unlimited pennies, nickels, and dimes. Therefore, it means that Brian can use any one of those to buy his chocolate. Second, there is 1414 coins. These coins come in three different forms mentioned in the first point: pennies, nickels, and dimes.Thus, we have 3 types of coins.We need to use a number of combinations so that none of the combinations is repeated. A formula for n distinct objects taken at different times will be: nCr = C(n,r) = n!/r!(n-r)!n = 1414 coins, r is the types of coins = 3Therefore, the formula will be:nCr = 1414!/ 3! (1414-3)!
= 470 191 764
It therefore means that Brian can combine all the 1414 coins in 470 191 764 ways. This makes sense as reflected by the large number of coins he has.
The width of a box is two inches less than twice the height. The length is 4 inches less than three times the height. The volume is 2240 cubic inches. What are the dimensions of the box
Answer:
Dimensions are 8 Inches by 14 inches by 20 inches
Step-by-step explanation:
The volume of the box is 2240. This means:
lbh = 2240
Where b is the width.
Width is two inches less than twice the height
b = 2h - 2
length is 4 inches less than 3 times the height
l = 3h - 4
Substituting these parameters into the lbh equation will yield the following:
h * (3h - 4) * (2h - 2) = 2240
h[6h^2-14h+8] = 2240
6h^3 -14h^2 + 8h - 2240= 0
Solving this cubic equation will yield one of the values to be 8. The other two values are complex numbers.
b = 2h - 2
l = 3h - 4
b = 2(8) - 2 = 14
l = 3(8) - 4 = 20
To determine the number of trout in a lake, a conservationist catches 450 trout, tags them, and releases them. Later 90 trout are caught, and it is found that 45 of them are tagged. Assuming that the proportion of tagged trout in the second sample was the same as the proportion of tagged trout in the total population, estimate the number of trout in the lake.
Answer:
595 Trout
Step-by-step explanation:
90 - 45 = 45
450 + 45 = 495
The estimated number of trout in the lake is 495 trouts.
How to the total number of trouts in the lake?The total number of trouts in the lakes that were initially tagged is added with the number of untagged trout that are caught afterward to find the total number of trout in the lake.
We can find the total number of trout in the lake as follows:It is given that 450 trout were initially caught and tagged by a conservationist and were later released into the lake.
Therefore the total number of tagged trout = 450
Later, when the trout are caught again, we notice that 90 are caught and of those 90 trout, 45 have been tagged. This means that there are 45 untagged trout.
Therefore, total number of untagged trout = 90 - 45
= 45
Therefore, the total number of trout in the lake = 450 + 45
= 495
Thus, we have found that the estimated number of trout in the lake is 495 trouts.
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What is the 6th value in the sequence with the explicit formula an=−2n−14?
The 6th value in a sequence is -26.
Step-by-step explanation:
The formula for nth term is a sequence ⇒ an = -2n-14To find 6th value in a sequence, substitute n=6 in the formula.an = -2n-14
⇒ a6 = -2(6)-14
⇒ a6 = -12-14
⇒ a6 = -26
∴ The 6th value in a sequence is -26.
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTUR
Answer:
[tex] \frac{24}{26} = \frac{12}{13} \\ [/tex]
Answer:
A
Step-by-step explanation:
Sin(C) = opposite/hypotenuse
Hypotenuse is the length opposite to the right angle, AC for this triangle
Opposite is the length opposite to the angle, AB in this case
Sin(C) = AB/AC
= 24/26 = 12/13
David and Karen are building a treehouse in the shape of a rectangular prism for their daughter.If the treehouse is going to 5 feet tall 8 feet wide and 7.5 feet long How much space will there be inside? How much space will they have to paint on the outside?
The space left inside the tree is 300 cubic feet.
David and Karen have to paint 275 square feet on the outside.
Explanation:
It is given that the length of the tree house is 7.5 feet
The width of the tree house is 8 feet
The height of the tree house is 5 feet
The tree house is in the shape of a rectangular prism.
The volume of the rectangular prism is given by
[tex]\text {Volume}=\text {length } \times \text {width} \times \text {height}[/tex]
Substituting the values, we have,
[tex]Volume$=7.5 \times 8 \times 5$\\Volume $=300$[/tex]
Thus, the volume of the rectangular prism is 300 cubic feet
Hence, the space left inside the tree is 300 cubic feet.
The area they have to paint on the outside can be determined using the formula for surface area of the prism .
[tex]Area=2(w l+h l+h w)[/tex]
Substituting the values, we get,
[tex]Area=2[(8*7.5)+(5*7.5)+(5*8)][/tex]
Multiplying the terms within the bracket, we get,
[tex]Area=2(60+37.5+40)[/tex]
Adding the terms, we have,
[tex]Area=2 \times 137.5[/tex]
Multiplying, we get,
[tex]Area =275[/tex]
Thus, David and Karen have to paint 275 square feet on the outside.
V= L x W x H
Leight x with x height = V
5 x 8 x 7.5= V
=300feet2
Step-by-step explanation:
Hope it helps
Explain and show how to find the square root of 50 to the nearest tenth
Answer:
[tex]\sqrt{50}=7.1[/tex]
Step-by-step explanation:
We want to find the square root of 50;
We need to first rewrite 50 as a prime factorization.
[tex]\sqrt{50}=\sqrt{25\times 2}[/tex]
We now split the square root to get:
[tex]\sqrt{50}=\sqrt{25}\times \sqrt{2}[/tex]
Take square root to get:
[tex]\sqrt{50}=5 \sqrt{2}[/tex]
[tex]\sqrt{50}=5(1.414)=7.07[/tex]
To the nearest tenth we have [tex]\sqrt{50}=7.1[/tex]
The Garcia family is driving from San Diego, California, to bar harbor, Maine. In 5 day,they have traveled 2,045 miles. At this rate,how long will it take them to travel from San Diego to bar harbor?
By first calculating the Garcia family's travel rate of 409 miles per day, we can estimate it will take them approximately 9 days to travel from San Diego, California to Bar Harbor, Maine.
Explanation:The subject of this question is Mathematics, and it involves understanding and applying the concept of rate – the speed at which something happens over a particular period of time. In this case, we have the Garcia family traveling from San Diego, California, to Bar Harbor, Maine. They have traveled 2,045 miles in 5 days.
To find out how long it will take them to travel the entire way, we first need to calculate the rate at which they are traveling. We do that by dividing the total distance they have traveled by the total number of days it took them to travel that distance: 2045 miles / 5 days = 409 miles per day.
The distance from San Diego to Bar Harbor is about 3,305 miles. So, if they continue to travel at a rate of 409 miles per day: 3305 miles / 409 miles per day = about 8.08 days. Since they can't travel a fraction of a day, we'll round that up to 9 days. So it will take them approximately 9 days to travel from San Diego to Bar Harbor at their current rate.
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A flat, square roof needs a square patch in the corner to seal a leak. The side length of the roof is (x 1 12) ft and the side length of the patch is x ft. What is theareaofthegoodpartoftheroof?
Answer:
Area of good part of roof =
[tex]A(x) = (24x + 144)~ft[/tex]
Step-by-step explanation:
We are given the following in the question:
Length of square roof =
[tex](x+12)~ft[/tex]
Length of square patch =
[tex]x~ft[/tex]
Area of square =
[tex]A = (\text{Side})^2[/tex]
We have to find the area of good part of roof.
Area of good part of roof =
Area of roof - Area of patch
[tex]A(x) = (x+12)^2 - (x)^2 \\A(x) = (x+12+x)(x+12-x)\\A(x) = (2x+12)12\\A(x) = (24x + 144)~ft[/tex]
is the required area of roof.