Answers
What you can say about 12th, 18th and the 21st child, depends if these numbers are multiples of 4 (every 4th child is wearing spectacles), 3 (every 3rd child is a girl) and 2 (every 2nd child is wearing a white shirt).
If a numer is multiple of another one, then the quotient between them is an integer number.
for 12th:
12/4 = 3
12/3 = 4
12/2 = 6
12 is multiple of 3, 4 and 6.
Then, 12th child is wearing spectacles, a white shirt and is a girl.
for 18th:
18/4 = 4.5
18/3 = 6
18/2 = 9
18 is multiple of 3 and 2.
Then, 18th child is a girl and is weraing a white shirt
for 21th:
21/4 = 5.25
21/3 = 7
21/2 = 11.5
21 is multiple of 3.
THen, 21st child is a girl.
Related Questions
10. The graph shows the scores of an exam. About what percent of students scored above 86%?Distribution of Exam Scores20Percent1078808286889084Score11%18%6.5%
Answers
Answer
Option B is correct.
Percent of students that scored above 86% = 18%
Explanation
To find the percentage of students that scored above 86%, we will need to add the percent of the bars for all the scores greater than 86%.
For 87%, the bar is 8%
For 88%, the bar is 5.8%
For 89%, the bar is 2.2%
For 90%, the bar is 2%
So,
Percent of students that scored above 86% = 8 + 5.8 + 2.2 + 2 = 18%
Hope this Helps!!!
write three things you used to do but don't do anymore
Answers
Answer:
Trusting peoples
Be happy
make friends
Prof. Glatt likes 2% milk (2% fat) for her cereal in the morning. Her parents only buy wholemilk (3.5% fat) and non-fat milk (0% fat). While she is visiting her parents, how much of eachtype of milk does she need to mix to get 3 cups of 2% milk. The answer can be rounded to thenearest tenth.linear systems solving algebraically
Answers
It is given that there are two types of milk.
One is 3.5% and one is 0%.
Let the number of cups of 3.5% milk be x and the number of cups of 0% milk used be y.
The total should be 3 cups so it follows:
[tex]x+y=3\ldots(i)[/tex]It is also known that the resulting milk is 2% so it follows:
[tex]\begin{gathered} \frac{3.5}{100}x+\frac{0}{100}y=\frac{2}{100}(x+y) \\ \frac{3.5}{100}x=\frac{2}{100}(x+y) \end{gathered}[/tex]Multiply by 100 on both sides to get:
[tex]\begin{gathered} 3.5x=2(x+y) \\ 3.5x=2x+2y \\ 1.5x=2y \\ x=\frac{2}{1.5}y \\ x=\frac{2\times2}{1.5\times2}y \\ x=\frac{4}{3}y \end{gathered}[/tex]Substitute the value of (ii) in (i) to get:
[tex]\begin{gathered} x+y=3 \\ \frac{4}{3}y+y=3 \\ \frac{4+3}{3}y=3 \\ \frac{7}{3}y=3 \\ \frac{3}{7}\times\frac{7}{3}y=\frac{3}{7}\times3 \\ y=\frac{9}{7} \end{gathered}[/tex]Hence the quantity of 0% milk is 9/7 cups.
The quantity of 3.5% milk is given by:
[tex]\begin{gathered} x=\frac{4}{3}y \\ x=\frac{4}{3}\times\frac{9}{7} \\ x=\frac{12}{7} \end{gathered}[/tex]Hence the quantity of 3.5% milk is 12/7 cups.
For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chumpkin hide
Answers
Let x and y be the number of holes dug by the chipmunk and the squirrel, respectively.
Therefore, the number of hidden acorns by each animal is given by the equations below
[tex]\begin{gathered} a_{chipmunk}=3x \\ a_{squirrel}=4y \end{gathered}[/tex]On the other hand, since the squirrel needed 4 fewer holes, and the number of hidden acorns is the same
[tex]\begin{gathered} y=x-4 \\ and \\ a_{chipmunk}=a_{squirrel} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3x=4y \\ \Rightarrow3x=4(x-4) \\ \Rightarrow3x=4x-16 \\ \Rightarrow x=16 \end{gathered}[/tex]Hence,
[tex]\Rightarrow16*3=48[/tex]The chipmunk hid 48 acorns.Alexa claims that the product of 2.3 and 10^2 is 0.23. Do you agree or disagree? Explain why or why not?
Answers
Answer:
disagree
Step-by-step explanation:
product = 2.3 * 10²
= 2.3 * 100
= 230
thus, the answer is different from the one acclaimed by Alexa.
choose which group of sets the following number belongs to. Be sure to account for ALL sets. 2/7
Answers
A. Real numbers, rational numbers
Explanations:Note:
Real numbers are numbers that can be found on the number line. They include all rational and irrational numbers
Natural numbers are counting numbers. They include 0 and all whole numbers (1, 2, 3, ....)
Rational numbers are numbers that can be expressed as fractions of two integers. eg 2/3, 5/4, etc
Irrational numbers are numbers that cannot be expressed a s fractions of two integers. eg √7, π, etc
2/7 is a real number because it can be found on the number line, and is continuous
Also, 2/7 is a rational number because it is expressed as a fraction of two integers (2 and 7)
If it costs $1.50 for a pack of Starbursts at ShopRite, how much will 5 packs cost?
Answers
Answer : $7.5
1 pack of starbursts cost $1.50 at shoprite.
How much will 5 packs cost
Let the cost in dollars of 5 packs of starbursts be x
1 pack will cost $1.50
5 packs will cost $x
Mathematically,
1 pack ---------------- $1.50
5 packs -------------= $x
Cross multiply
1 * x = 5 x 1.50
x = $7.5
Hence, 5 packs of starbursts would cost $7.5
The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?
Answers
As given by the question
There are given that area of rectangle and width of a rectangle
[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]Now,
From the formula of area of a rectangle:
[tex]\text{Area}=\text{length}\times width[/tex]Then,
Put the value of an area and width into the above formula
So,
[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]Then,
[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]Hence, the value of length is ( b + 6 ).
A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?
5
36
35
36
cakes/week
cakes/week
1
1 cakes/week
35
01. cakes/week
4
Answers
Answer:
11.2 Slices / Week
Step-by-step explanation:
We know that Jake has eaten 5 slices of cake in 3 days. You can divide 5 / 3 to get an average of 1.6 slices of cake being eaten per day. The question asks what the weekly rate or eating the cake will be, do you need to multiple 1.6 x 7 for the total amount of cake eaten per week, which is 11.2 slices!
Answer:
11.6
explanation
we have 7 days.
7days-3days =4
in 3 days he has eaten 5 slices
again 4-3 days=1
so in 6 days he has eaten 10 slices
we have 1 day left.so if he eats 5 slices in 3 day,how many he eat slices in 1 day?5/3=1.6
10+1.6=11.6
Jenny borrowed $8000 at a rate of 9%, compounded semiannually. Assuming she makes no payments, how much will she owe after 10Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
SOLUTION
We will use the formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where\text{ } \\ A=amount\text{ after 10 years = ?} \\ P=money\text{ borrowed = \$8,000} \\ r=9\%=\frac{9}{100}=0.09 \\ t=time\text{ in years = 10} \\ n=compounding=semi-annualy=2 \end{gathered}[/tex]plugging in, we have
[tex]\begin{gathered} A=8,000(1+\frac{0.09}{2})^{2\times10} \\ A=8,000(1.045)^{20} \\ A=8,000\times2.4117140 \\ A=19,293.7121986 \end{gathered}[/tex]Hence the answer is $19,293.71
22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale
Answers
SOL
Step 1 :
In this question, we are meant to find the value of
the hypotenuse in the right angle below:
Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Step 2 :
From the above theorem, we can see that that the two adjacent sides are :
14 inches and 48 inches.
From the principle of Pythagoras' Theorem,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]
CONCLUSION :
The value of the hypotenuse in the Right angle, c = 50 inches.
many solutions can be found for the system of linear equations represented on the graph?A. no solution B. one solution C. two solution D. Infinity many solutions
Answers
The lines are not intersecting. The system of linear equations has a solution only if the lines corresponding to the equations intersect.
The general linear equation is,
y=mx+c, where m is the slope.
The slopes of lines m=2.
Since the graphs are parallel or have the same slope and will never intersect, the system of linear equations have no solution.
Which function has the greatest average rate of change on the interval [1,5]
Answers
Answer:
Explanation:
Given: interval [1,5]
Based on the given functions, we start by computing the function values at each endpoint of the interval.
For:
[tex]\begin{gathered} y=4x^2 \\ f(1)=4(1)^2 \\ =4 \\ f(5)=4(5)^2 \\ =100 \\ \end{gathered}[/tex]Now we compute the average rate of change.
[tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{100-4}{5-1} \\ \text{Calculate} \\ =24 \end{gathered}[/tex]For:
[tex]\begin{gathered} y=4x^3 \\ f(1)=4(1)^3 \\ =4 \\ f(5)=4(5)^3 \\ =500 \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{500-4}{5-1} \\ =124 \end{gathered}[/tex]For:
[tex]\begin{gathered} y=4^x \\ f(1)=4^1 \\ =4 \\ f(5)=4^5 \\ =1024 \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{1024-4}{5-1} \\ =255 \end{gathered}[/tex]For:
[tex]\begin{gathered} y=4\sqrt[]{x} \\ f(1)=4\sqrt[]{1} \\ =4 \\ f(5)\text{ = 4}\sqrt[]{5} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{(4\sqrt[]{5\text{ }})\text{ -4}}{5-1}\text{ } \\ =1.24 \end{gathered}[/tex]Therefore, the function that has the greatest average rate is
[tex]y=4^x[/tex]Miguel has 225 base ball cards. He plans to keep 75 cards and give the rest to his friends.Can Miguel give an equal number of cards to 6 friends? Explain.
Answers
We know what Miguel has 225 baseball cards, and he plans on keeping 75, while giving them the rest of them to his friends. We want to know if he can give an equal number to 6 of his friends.
For this objective, we know what he will have to give to his friends an amount of:
[tex]undefined[/tex]A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.
Answers
part A. We are given that a hiker will increase the distance covered by 10% each day. Let "S" be the distance, then on the first day the distance is:
[tex]S_1[/tex]On the second day, we must add 10% of the first day, we get:
[tex]S_1=S_1+\frac{10}{100}S_1[/tex]Simplifying we get:
[tex]S_2=S_1+0.1S_1=1.1S_1[/tex]On the third day, we add 10% of the second day, we get:
[tex]S_3=S_2+0.1S_2=1.1S_2=(1.1)(1.1)S_1=(1.1)^2S_1[/tex]On the fourth day, we add 10% of the third day, we get:
[tex]S_4=S_3+0.1S_3=1.1S_3=(1.1)^3S_1[/tex]If we continue this pattern and we set "n" as the number of days, then a formula for the distance after "n" days is:
[tex]S_n=(1.1)^{n-1}S_1[/tex]Now, we are given that for n = 7 the distance is 75897, therefore, we substitute n = 7 in the formula:
[tex]S_7=(1.1)^{7-1}S_1[/tex]Substituting the value of the distance:
[tex]75897=(1.1)^{7-1}S_1[/tex]Now we can solve for S1, we do that by dividing both sides by 1.1 together with its
exponent:
[tex]\frac{75897}{(1.1)^{7-1}}=S_1[/tex]Now we solve the operations:
[tex]\frac{75897}{(1.1)^6}=S_1[/tex]Solving the operations:
[tex]42842=S_1[/tex]Therefore, the distance the first day was 42842 miles.
part B. The formula for Sn is the given previously but we replace the known value of S1:
[tex]S_n=42842(1.1)^{n-1}[/tex]Part C. To determine the distance after 10 days, we substitute the value n = 10 in the formula, we get:
[tex]S_{10}=42842(1.1)^{10-1}[/tex]Solving the operations we get:
[tex]S_{10}=101019.19[/tex]Therefore, the distance after 10 days is 101019.19 miles.
hello i am haveing some trouble with ineqalles and can you help with this create a word problem that leads to an inequality by filling in the blanks with your corresponding answer.Twenty subtracted from the product of seven and a number exceeds one hundred.
Answers
Step 1
To change word problem to an inequality, you must take the word problem step by step and translate it into an inequality.
Step 2
Take the word problem step by step
[tex]\begin{gathered} \text{Twenty refers to the number }^{\prime}20^{\prime} \\ \text{Twenty subtracted from means 20 was removed from something.} \\ i.e\text{ say x-20} \end{gathered}[/tex][tex]\begin{gathered} \text{Twenty subtract}ed\text{ from the product of seven and a number } \\ \text{Product of seven and a number first} \\ Let\text{ the number be x} \\ so\text{ it now} \\ \text{Product of seven and x=7x } \end{gathered}[/tex][tex]\text{Twenty subtract}ed\text{ from the product of seven and a number}=7x-20[/tex]Multiply. Write your answer in decimal form: (8 x 10^2)(4 x 10^2)
Answers
Answer:
32×10⁴
Step-by-step explanation:
open the bracket
8×4×10^(2+2)
32×10⁴
hope it helps
please mark brainliest
I have a calculus question about related rates, pic included
Answers
ANSWER
40807 cm³/min
EXPLANATION
The tank has the shape of a cone, with a total height of 9 meters and a diameter of 3.5 m - so the radius, which is half the diameter, is 1.75 m. As we can see, the relationship between the height of the cone and the radius is,
[tex]\frac{r}{h}=\frac{1.75m}{9m}=\frac{7}{36}\Rightarrow r=\frac{7}{36}h[/tex]So the volume of water will be given by,
[tex]V(h)=\frac{1}{3}(\pi r^2)h=\frac{1}{3}\cdot\pi\cdot\frac{7^2}{36^2}h^2\cdot h=\frac{49\pi}{3888}h^3[/tex]Where h is the height of the water (not the tank).
If we derive this equation, we will find the rate at which the volume of water is changing with time,
[tex]\frac{dV}{dt}=\frac{49\pi}{3888}\cdot3h^{3-1}=\frac{49\pi}{3888}\cdot3h^2=\frac{49\pi}{1296}h^2[/tex]We want to know what is the change of volume with respect to time, and this is,
[tex]\frac{dV}{dt}=\frac{dV}{dt}\cdot\frac{dh}{dt}[/tex]Because the height also changes with time. We know that this change is 24 cm per minute when the height of the water in the tank is 1 meter (or 100 cm), so we have,
[tex]\frac{dV}{dt}=\frac{49\pi}{1296}h^2\cdot\frac{dh}{dt}=\frac{49\pi}{1296}\cdot100^2cm^2\cdot\frac{24cm}{1min}\approx28507cm^3/min[/tex]This is the rate at which the water is increasing in the tank. However, we know that there is a leak at a rate of 12300 cm³/min, which means that in fact the water is being pumped into the tank at a rate of,
[tex]28507cm^3/min+12300cm^3/min=40807cm^3/min[/tex]Hence, the water is being pumped into the tank at a rate of 40807 cm³/min, rounded to the nearest whole cm³/min.
help meeeeeeeeee pleaseee !!!!!
Answers
Because x is continuous, we should use interval notation, the domain is:
D: [1, ∞)
How to find the domain?For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).
To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.
There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:
D: x ≥ 1
We know that the value x =1 belongs because there is a closed dot there.
The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:
D: [1, ∞)
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The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?
Answers
We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:
[tex]d(t)=20\sin (\frac{\pi}{30}t)+10[/tex]If we consider the position of the person at t = 0, which is:
[tex]d(0)=20\sin (\frac{\pi}{30}\cdot0)+10=20\cdot0+10=10[/tex]This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:
[tex]\begin{gathered} \sin (\frac{\pi}{30}t)=\sin (2\pi) \\ \frac{\pi}{30}\cdot t=2\pi \\ t=2\pi\cdot\frac{30}{\pi} \\ t=60 \end{gathered}[/tex]Then, the wheel will repeat its position after t = 60 seconds.
Answer: 60 seconds.
6 eggs weigh 3/4 of a pound. How much does each egg weigh? 1/4 pounds1/6 pounds1/8 pounds2/3 pounds
Answers
consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?
Answers
Problem: consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?.
Solution:
Let the function f(x) whose second derivative is:
[tex]f^{\prime\prime}(x)\text{ = 4x+4sin(x)}[/tex]Now, the antiderivative (integral) of the above function would be:
EQUATION 1:
[tex]f^{\prime}(x)=\int f^{\prime\prime}(x)\text{ }dx\text{= }2x^2-4\cos (x)\text{ +C1}[/tex]where C1 is a constant because we have an indefinite integral. Now the antiderivative (integral) of the above function f´(x) is:
[tex]f(x)=\int f^{\prime}(x)\text{ }dx\text{=}\int \text{ (}2x^2-4\cos (x)\text{ +C1)}dx\text{ }[/tex]that is:
EQUATION 2:
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+C1x+\text{ C2}[/tex]where C2 is a constant because we have an indefinite integral.
Now using the previous equation, if f(0)= 3 then:
[tex]3=\text{ C2}[/tex]Now, using equation 1 and the fact that f ´(0) = 4, then we have:
[tex]4=f^{\prime}(0)\text{= }^{}-4\text{ +C1}[/tex]That is:
[tex]4=\text{ }^{}-4\text{ +C1}[/tex]Solve for C1:
[tex]8=\text{ }^{}\text{C1}[/tex]Now, replacing the constants C1 and C2 in equation 2, we have an expression for f(x):
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+8x+3[/tex]Then f(5) would be:
[tex]f(5)=\text{ }\frac{2(5)^3}{3}-4\sin (5)+40+3=\text{ }125.98[/tex]
then the correct answer is:
[tex]f(5)=\text{ }125.98[/tex]Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs.
a. Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.
Answers
Using the normal distribution and the central limit theorem, the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is:
[tex]P(3.5 \leq \bar{X} \leq 4.25) = 0.7482[/tex]
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of each review are given as follows:
[tex]\mu = 4, \sigma = 1.2[/tex]
For the sampling distribution of sample means of size 16, the standard error is given as follows:
[tex]s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is the p-value of Z when X = 4.25 subtracted by the p-value of Z when X = 3.5, hence:
X = 4.25:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.25 - 4)/0.3
Z = 0.83.
Z = 0.83 has a p-value of 0.7967.
X = 3.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (3.5 - 4)/0.3
Z = -1.67.
Z = -1.67 has a p-value of 0.0475.
Hence the probability is:
0.7967 - 0.0485 = 0.7482.
The statement is:
[tex]P(3.5 \leq \bar{X} \leq 4.25)[/tex]
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Identify the domain and range of the relation. Is the relation a function? Why or why not?
{(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Answers
Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
What is a function?A relation is a function if it has only one y-value for each x-value.
The given relation is {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
The domain is the set of all the first numbers of the ordered pairs.
In other words, the domain is all of the x-values.
Domain={-3, 0, 1, 2}
The Range is the set of all the second numbers of the ordered pairs.
In other words, the range is all of the y-values.
Range={1,2,5,4}
The given relation is not a function because there are two values of y for one value of x. It means 4 and 1 are values of 2.
Hence Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
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A regular hexagon has sides 2 feet long. What is the exact area of the hexagon? What is the approximate area of the hexagon?
Answers
The formula for the area of a hexagon is
[tex]A=\frac{3\sqrt[]{3}}{2}s^2[/tex]where 's' is the length of one side of the regular hexagon.
The side of our regular hexagon is 2 feet, therefore, its area is
[tex]\begin{gathered} A=\frac{3\sqrt[]{3}}{2}\cdot(2)^2=6\sqrt[]{3} \\ 6\sqrt[]{3}=10.3923048454\ldots\approx10 \end{gathered}[/tex]The exact area of the hexagon is 6√3 ft², which is approximately 10 ft².
Which is a way to model 9485 with base ten blocks
Answers
The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
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use the figure at the right . if JK=5x+23 and NO=29, what is the value of x?
Answers
From the triangle midpoint theroem,
[tex]\begin{gathered} NO=\frac{1}{2}JK \\ 29=\frac{1}{2}(5x+23) \\ 58=5x+23 \\ 58-23=5x \\ 35=5x \\ x=7 \end{gathered}[/tex]can you solve for x and y y=4x-11=x+13
Answers
x = 8, y = 21
Explanations:The given equation is:
y = 4x - 11 = x + 13
This can be splitted into two equations as:
y = 4x - 11..........(1)
y = x + 13..........(2)
Substitute equation (1) into equation (2)
4x - 11 = x + 13
4x - x = 13 + 11
3x = 24
x = 24/3
x = 8
Substitute the value of x into equation (1)
y = 4x - 11
y = 4(8) - 11
y = 32 - 11
y = 21
x = 8, y = 21
$75 dinner, 6.25% tax, 18% tip please show work.You have to find the total cost
Answers
According the the information given in the exercise, you know that the cost of the dinner was:
[tex]d=_{}$75$[/tex]Where "d" is the cost of the dinner in dollars.
Convert from percentages to decimal numbers by dividing them by 100:
1. 6.25% tax in decimal for:
[tex]\begin{gathered} tax=\frac{6.25}{100} \\ tax=0.0625 \\ \end{gathered}[/tex]2. 18% tip in decimal form:
[tex]\begin{gathered} tip=\frac{18}{100} \\ \\ tip=0.18 \end{gathered}[/tex]To find the amount in dollars of the tax and the the amount in dollars of the tip, multiply "d" by the decimals found above.
Knowing the above, let be "t" the total cost in dollars.
This is:
[tex]\begin{gathered} t=d+0.0625d+0.18d \\ t=75+(0.0625)(75)+(0.18)(75) \\ t=93.1875 \end{gathered}[/tex]Therefore the answer is: The total cost is $93.1875
What is the volume of a hemisphere with a radius of 6.5 in, rounded to the nearesttenth of a cubic inch?
Answers
To calculate the volum of a hemisphere
We use the formula;
V = (2/3)πr³
where r = radius
π is a constant equal 3.14
r= 6.5 in and π = 3.14
Substituting into the formula
V = (2/3) x 3.14 x (6.5)³
Evauluate
V = (2/3) x 3.14 x 274.625
V = (2/3) x 862.3225
V=574.8816666666667
V= 574.89 in³ to the nearest tenth of a cubic inch.
