We know that the diameter of the wheel is 1215 inches
Since CD is a perpendicular bisector of AB, it means that CD passes through the center of the circle. Let O be the center of the circle. Then OD is the radius of the circle.
Since chord CE passes through the center O, it is a diameter of the circle. Therefore, CE = 2OD.
Let's use the intersecting chords theorem to find OD.
According to the intersecting chords theorem,
AC * CB = EC * CD
We know that AC = CB (since they are radii of the same circle) and CD = 4 inches. We also know that AB = 12 inches. Let's call the length of segment AE x. Then the length of segment EB is 12 - x.
So we have:
x * (12 - x) = EC * 4
Simplifying:
12x - x^2 = 4EC
Rearranging:
EC = 3x - x^2/4
Now let's use the intersecting chords theorem again, but this time for chords AB and CD:
AC * CB = AD * DB
We know that AC = CB and AB = 12 inches. Let's call the length of segment AD y. Then the length of segment DB is 12 - y.
So we have:
x^2 = y * (12 - y)
Simplifying:
y^2 - 12y + x^2 = 0
Using the quadratic formula:
y = (12 ± sqrt(144 - 4x^2))/2
We can discard the negative solution (since y is the length of a segment, it cannot be negative), so:
y = 6 + sqrt(36 - x^2)
Now let's use the fact that CD is a perpendicular bisector of AB to find x.
Since CD is a perpendicular bisector of AB, it divides AB into two segments of equal length. Therefore,
AD = DB = 6
Using the Pythagorean theorem in triangle ACD:
AC^2 + CD^2 = AD^2
Substituting the values we know:
x^2 + 4^2 = 6^2
Solving for x:
x = sqrt(20)
Now we can find EC:
EC = 3x - x^2/4
Substituting x:
EC = 3sqrt(20) - 5
Finally, we can find OD:
AC * CB = EC * CD
Substituting the values we know:
(2OD)^2 = (3sqrt(20) - 5) * 4
Simplifying:
OD^2 = 12sqrt(20) - 20
OD = sqrt(12sqrt(20) - 20)
We are asked to find the diameter of the circle, which is twice the radius:
Diameter = 2OD = 2sqrt(12sqrt(20) - 20)
This is approximately equal to 1215 inches.
So the answer is:
The diameter of the wheel is 1215 inches.
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Alex can stack exactly 16 cookies, each with a diameter of 5 cm inside a cylindrical container with the same diameter and a volume of 100% cm³. What is
the surface area of the container? Round your answer to the nearest square centimeter.
Answer:
Read
Step-by-step explanation:
If Alex can stack exactly 16 cookies with a diameter of 5 cm inside a cylindrical container with the same diameter, then the height of the cylinder will be equal to the height of 16 cookies stacked on top of each other, which is 16 multiplied by the height of one cookie.
The diameter of each cookie is 5 cm, so the radius is 2.5 cm. The volume of each cookie is πr²h, where r is the radius and h is the height, so the volume of one cookie is:
V1 = π(2.5 cm)²h
The volume of 16 cookies will be:
V16 = 16π(2.5 cm)²h
Since the volume of the cylindrical container is 100% cm³, we have:
V16 = Vcyl
where Vcyl is the volume of the cylindrical container. Therefore:
16π(2.5 cm)²h = Vcyl
The height of 16 cookies stacked on top of each other is 16 times the height of one cookie, so:
h = 16(1 cm) = 16 cm
Substituting this value into the equation above and solving for the radius, we get:
r = √(Vcyl / (16πh)) = √(100 cm³ / (16π(16 cm))) ≈ 1.03 cm
The surface area of the cylindrical container is given by the formula:
A = 2πr² + 2πrh
Substituting the values we found for r and h, we get:
A = 2π(1.03 cm)² + 2π(1.03 cm)(16 cm) ≈ 142 cm²
Therefore, the surface area of the container is approximately 142 square centimeters. Rounded to the nearest square centimeter, the answer is 142 square centimeters.
The surface area of the given cylindrical container is 290 cm².
What is the volume of a cylinder?The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We know that the volume of the cylindrical container is 100π cm³ and that it has the same diameter as the cookies, which is 5 cm.
Since the diameter of the container is 5 cm, its radius is 2.5 cm.
We can rearrange the formula for volume to solve for
h = V/πr²
h = 100π/π(2.5)²
h = 16
So, the height of the container is 16 cm.
To find the surface area of the container, we can use the formula:
A = 2πrh + 2πr²
where r is the radius of the container and h is its height.
Substituting the values we have, we get:
A = 2π(2.5)(16)+2π(2.5)²
A = 92.5π
A ≈ 290.45
Rounding to the nearest square centimeter,
A = 290
Thus, the surface area of the container is 290 cm².
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The perimeter of the rectangle below is 16 cm. What is the value of k? 5 cm kcm Not to scale
Answer:
3 cm.
Step-by-step explanation:
Let's use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.In this case, we have:P = 16 cm (given)
l = k cm (given)
w = 5 cm (given)Substituting these values into the formula, we get:
16 cm = 2(k cm) + 2(5 cm)
Simplifying, we get:
16 cm = 2k cm + 10 cm
Subtracting 10 cm from both sides, we get:6 cm = 2k cm
Dividing both sides by 2, we get:
3 cm = k
Therefore, the value of k is 3 cm.
Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample.
n = 81, p = 0.5: p(x ≥ 46)
group of answer choices
0.1210
0.1335
0.8790
0.1446
We know that the indicated probability is approximately 0.1210.
To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:
np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10
Since both conditions are met, we can use the normal approximation to find the probability.
First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:
mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5
Next, we need to standardize the value of x:
z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22
Finally, we can use a standard normal table or calculator to find the probability:
P(z ≥ 1.22) = 0.1118
Therefore, the answer is approximately 0.1210.
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The spinner has 8 congurent sections it is spun 24 times what is a reasonable prediction for the number of times the spinner will land on the number 3.
A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.
1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.
2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24
3. Simplify the expression:
Expected number of times = 3
So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
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8. (02.03 mc)
costs of attendance
category
dollar amount
annual tuition and fees
$4,934.00
annual room and board
$1,424.00
annual cost of books and supplies $1,250.00
other one-time fee
$275.00
annual scholarship and grants
$5,250.00
using the information from the table, identify the equation in slope-intercept form that models the total cost of attendance. (1 point)
o y = 2,358x + 275
o y = 2,633x
o y = 7,608x + 275
o y = 7,883
The equation in slope-intercept form that models the total cost of attendance is: y = 2,633x + 275.
1. Add up the annual costs: tuition and fees ($4,934), room and board ($1,424), and cost of books and supplies ($1,250) to get the total annual cost: $4,934 + $1,424 + $1,250 = $7,608.
2. Subtract the annual scholarship and grants from the total annual cost: $7,608 - $5,250 = $2,358. This is the slope (x) of the equation, as it represents the cost per year.
3. The other one-time fee ($275) is the y-intercept of the equation, as it's a fixed cost that does not change with the number of years.
4. Put the slope and y-intercept into the slope-intercept form (y = mx + b) to get: y = 2,633x + 275.
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Find the following integral results a. So to dz b. C2+ IT x'sir. 'o 1+cos? dx A solid is obtained by rotating the shaded region about the specified line such as the x-axis or the y-axis. Find the volume of the solid
V = ∫2πx f(y) dy volume of the solid
a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:
∫ dz = z + C
b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:
∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'
where C' is the constant of integration.
c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.
If we rotate the region about the x-axis, we can use the formula:
V = ∫2πy f(x) dx
where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.
If we rotate the region about the y-axis, we can use the formula:
V = ∫2πx f(y) dy
where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.
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Curtis loves Pokémon! He went to school on Thursday and traded a bunch of cards to get new ones. He saw Dino and traded 3 of his cards for one of Dino's. Then a girl he liked, Tippi, wanted to trade cards. He was really nice to her because he liked her, so he traded 5 of his cards for 2 of hers. He then put his cards away. When he got home he noticed that 10 of his cards were missing. He was so upset that his mom bought him another pack of 12 cards. He hid half of his cards at home and took the rest to school the next day. He traded ¼ of the cards he brought to school to Dino again and got back 3 of Dino's cards. Curtis now has 9 cards at school. How many cards did he start with? How many cards total does he have now?
Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
How to find cards?To find how many card ,We see Curtis has 9 cards at school after trading with Dino again, which means he had 12 cards before the trade.
Before his mom bought him another pack of 12 cards, he had 10 missing, so he must have had 24 cards in total (12 + 12).
He hid half of his cards at home, so he has 12 cards at home.
He traded ¼ of the cards he brought to school to Dino and got back 3 of Dino's cards. Let's call the number of cards he brought to school "x".
So, he traded x/4 cards to Dino, and got back 3 cards, which means he now has (x/4) - 3 cards.
We know that he now has 9 cards at school, so we can set up an equation:
(x/4) - 3 = 9
Solving for x, we get:
x/4 = 12
x = 48
So, Curtis brought 48 cards to school, which means he started with 24 + 12 + 48 = 84 cards in total.
Therefore, Curtis started with 84 cards and now has 12 cards at home and 9 cards at school, for a total of 21 cards.
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find an expression which represents the difference when
(7x−10) is subtracted from (−5x+6) in simplest terms.
Answer: -12x + 16
Step-by-step explanation:
To find the difference between (−5x+6) and (7x−10), we need to subtract the second expression from the first. So we have:
(−5x+6) - (7x−10)
To subtract the second expression, we can distribute the negative sign to all the terms inside the parentheses:
-5x + 6 - 7x + 10
Then we can combine the like terms:
-12x + 16
Therefore, the difference between (−5x+6) and (7x−10) is -12x + 16.
The music industry has steadily moved from selling music in a physical format such as records, eight tracks, cassettes, and CDs telling music in digital formats. In 2001, the music industry sold $26.5
billion of music in the physical format. Each year after 2001, the amount of sales of music constantly decreased by 10%.
Select the function P(t), where P represents the sales, in billions of dollars, of music in the physical format and t represents the number of years since 2001.
P(0) 26 5/0 1
Answer:
P(t)=26.5 (0.1)^t
Step-by-step explanation:
If p = (-4,7), find:
ry-axis (p)
([?], []).
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
We have,
To find the reflection of a point P in the y-axis, negate the x-coordinate of the point while keeping the y-coordinate unchanged.
Given that P = (-4, 7),
The reflection of P in the y-axis, denoted as [tex]R_{y-axis}(P),[/tex] can be found by negating the x-coordinate:
[tex]R_{y-axis}(P) = (4, 7)[/tex]
Thus,
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
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The complete question:
If p = (-4, 7)
R_{y-axis} (P) = ?
Please help and solve this! Have a blessed day!
Answer: 8
Step-by-step explanation:
CF looks like the radius of the circle.
ED looks like the diameter.
.: ED = 2 x CF = 2 x 4 = 8
.: ED = 8
Answer:
The length of ED, or the diameter, is 8
Step-by-step explanation:
As the other person explained, CF is the radius, as the radius is from the centermost point to the edge. I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point. Therefore, since the diameter is double the radius, we can solve this with the following equation:
2 * r = d, where r is radius and d is diameter.
2 * 4 = d
8 = d
A bag contains seven tiles labeled A B C D E F and G wich
One tile will be randomly picked.
What is the probability of picking a letter that is not a vowel
Two liters of the Gatorade cost $3.98. How much do 8 liters cost?
Answer:
$15.92
Step-by-step explanation:
We Know
2 liters of Gatorade cost $3.98
How much do 8 liters cost?
We take
3.98 x 4 = $15.92
So, 8 liters cost $15.92
Frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be? credit card balance apr a $2,380 19% b $4,500 15% c $1,580 17.50% d $900 21% a. $390.00 b. $462.91 c. $467.29 d. $52.00 please select the best answer from the choices provided a b c d
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
Option C is the correct answer.
We have,
To calculate the monthly credit card payment for consolidating Frank's credit cards, we can use the formula for the monthly payment on a loan:
[tex]M = P (r (1 + r)^n) / ((1 + r)^n - 1),[/tex]
where M is the monthly payment, P is the total loan amount (sum of all credit card balances), r is the monthly interest rate, and n is the number of months.
First, let's calculate the total loan amount:
Total loan amount = $2,380 + $4,500 + $1,580 + $900 = $9,360.
Next, let's calculate the monthly interest rate:
Monthly interest rate = APR / 12 = 18% / 12 = 1.5%.
Now, let's calculate the monthly payment using the formula:
[tex]M = $9,360 \times (0.015 (1 + 0.015)^{24}) / ((1 + 0.015)^{24} - 1).[/tex]
Using a calculator, we can compute the value of M:
M ≈ $467.286.
Rounding to the nearest cent,
Frank's monthly credit card payment for consolidating his credit cards will be $467.29.
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6
lo
r
s
p
m
q
0
-2
mollie claimed that the slope of mq is greater than the slope of qs because triangle mpq is bigger than triangle qrs.
explain the error in mollie's claim and calculate the slope for both mq and qs show all your work.
enter your work and explanation in the space provided.
Size of triangles doesn't determine slope, mq slope=-2, qs slope=-0.5
How to explain Mollie's incorrect slope claim?Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. The slope is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. Therefore, we need to find two points on the lines mq and qs to calculate their slopes.
Let's start by finding the slope of mq. We can identify two points on the line, (0,6) and (2,2). Using these points, we can calculate the slope as:
slope of mq = (change in y-coordinates) / (change in x-coordinates)
slope of mq = (2 - 6) / (2 - 0)
slope of mq = -4 / 2
slope of mq = -2
Now let's find the slope of qs. We can identify two points on the line, (2,2) and (6,0). Using these points, we can calculate the slope as:
slope of qs = (change in y-coordinates) / (change in x-coordinates)
slope of qs = (0 - 2) / (6 - 2)
slope of qs = -2 / 4
slope of qs = -0.5
Therefore, the slope of mq is -2 and the slope of qs is -0.5.
In summary, Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. We calculated the slopes of lines mq and qs by finding two points on each line and using the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. The slope of mq is -2, and the slope of qs is -0.5.
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Find the slope of the line represented by the data below
Answer:
m = -3
Step-by-step explanation:
We Know
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,15) (2,9)
We see the y decrease by 6, and the x increase by 2, so the slope is
m = -6/2 = -3
So, the slope of the line representing the data is -3.
A tailor charges set amounts for alterations on dresses and suits.
One customer has
2
dresses and
1
suit altered for a total of
$
80
.
Another customer has
1
dress and
3
suits altered for a total of
$
115
The cost to alter each dress is $25 and each suit is $30 based on the given set of relations.
Let us represent the dresses as x and suit as y. Forming the equation for both customers.
Cost of one dress × number of dress +
Cost of one suit × number of suit = total cost
2x + y = 80 : equation 1
x + 3y = 115 : equation 2
Multiply equation with 1
6x + 3y = 240 : equation 3
Subtract equation 2 from equation 3
6x + 3y = 240
- x + 3y = 115
5x = 125
x = 125/5
x = $25
Keep the value of x in equation 2 to find the value of y
25 + 3y = 115
3y = 115 - 25
3y = 90
y = 90/3
y = $30
Hence, the altering cost of each is $25 and $30.
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The complete question is -
A tailor charges set amounts for alterations on dresses and suits. One customer has 2 dresses and 1 suit altered for a total of $80. Another customer has 1 dress and 3 suits altered for a total of $115. How much does it cost to alter each dress?
help pls rlly fast i will give good points
Answer: less than
Step-by-step explanation:
The area of a rectangle is 72.8cm? if one side of the length is 6.52cm. find the length of the other two to two decimal places
Answer:
11.17, my answer needs to be 20+ characters soooooooo
A group of friends wants to go to the amusement park. They have $100. 25 to spend
on parking and admission. Parking is $17. 75, and tickets cost $13. 75 per person,
including tax. Which equation could be used to determine p, the number of people
who can go to the amusement park?
100. 25 = 13. 75p + 17. 75
Op=
100. 25-13. 75
17. 75
Submit Answer
13. 75(p+17. 75) = 100. 25
O p =
17. 75-100. 25
13. 75
The correct equation to determine the number of people (p) who can go to the amusement park is: 100.25 = 13.75p + 17.75.
Here's the step-by-step explanation:
1. The total amount they have to spend is $100.25.
2. The cost of parking is $17.75, which is a one-time expense.
3. The cost of admission per person is $13.75.
To find out how many people can go, you need to account for both the parking cost and the cost of tickets for each person. Therefore, the equation is:
100.25 (total amount) = 13.75p (cost per person times the number of people) + 17.75 (cost of parking)
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An investment of $4000 is deposited into an account in which interest is compounded continuously. complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (round your answers to the nearest cent.)
t = 4 years
The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)
Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
Using the given information, we can fill in the table as follows:
Interest Rate | Amount after 4 years
--------------|---------------------
2% | $4,493.29
3% | $4,558.56
4% | $4,625.05
5% | $4,692.79
6% | $4,761.81
To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:
2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81
Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
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Let X be the number of screws delivered to a box by an automatic filling device.
Assume = 1000 and
2 = 25. There are problems with too many screws going
into the box or too few screws going into the box.
a. How many units to the right of is 1009? (5 marks)
b. What X value is 2. 6 units to the left of ? (4 marks
There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box. When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To answer this question, we need to use the normal distribution formula.
a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:
z = (X - μ) / σ
where X = 1009, μ = 1000, and σ = 25.
z = (1009 - 1000) / 25 = 0.36
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.
To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):
units to the right = 0.5 - 0.3520 = 0.1480
Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.
b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:
X = μ - zσ
where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.
X = 1000 - (-2.6) * 25 = 1065
Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
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Find the area of the following shape. You must show all work to recive credit.
this is a writting question
The total area of the given figure is 12 units²
In the given figure, we have 3 shapes. One is rectangle and the other two are triangles. We can find areas of all three shapes and add to find the total area.
Finding area of the triangle ABC,
base of the triangle ABC = 4 units
height of the triangle ABC = 4 units
Area of the triangle ABC = 1/2 x base x height = 1/2 x 4 x 4 = 8 units²
Finding area of the triangle CDE,
base of the triangle CDE = 2 units
height of the triangle CDE = 2 units
Area of the triangle CDE = 1/2 x base x height = 1/2 x 2 x 2 = 2 units²
Finding area of the rectangle,
length of the rectangle = 2 units
breadth of the rectangle = 1 unit
Area of the rectangle = length x breadth = 2 x 1 = 2 units²
So, total area of the given figure = 8 units² + 2 units² + 2 units² = 12 units²
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BRAIN-COMPATIBLE
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
Write your answer in your activity notebook.
1. If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
Problem
Solution
2. I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
Problem:
Solution:
3 What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a. M. And arrived station Y ay 9:30 a. M.
The correct arrangement of problem is explained below and their solution are as follows:
(1) Zaira will arrive at her grandmother's house at 9:00 am.
(2) The total distance covered by bus is 207.5 km.
(3) The average-speed of the train was 28 km/h.
Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?
Solution:
Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.
So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.
Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?
Solution:
The distance covered by the bus in the morning can be calculated as:
Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,
The distance covered in the afternoon can be calculated as:
Distance = Speed × Time = 55 kph × 2 hours = 110 km
So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.
Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was average speed of train?
Solution:
The time taken by the train to cover the distance of 14 km can be calculated as:
Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours
The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;
Therefore, the average speed of the train was 28 km/h.
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The given question is incomplete, the complete question is
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
(1) If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
(2) I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
(3) What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m.
Two cars start together and travel in the same direction.
One car goes twice as fast as the other. After five
hours, they are 225 kilometers apart.
How fast is each car traveling?
Faster car's speed:
Slower car's speed:
The speed of the faster car is 90 kph and the speed of the slower car is 45 kph.
We are given that two cars are starting together and they travel in the same direction. Let one car be car A and the other car B. Speed of car B is twice the speed of car A. Let r be the rate of speed of car A and 2r be the rate of speed of car B.
We know that these two cars are 225 km apart. We will use the formula distance = speed * time. Let the distance car A travels after 5 hours be 5r. So, the distance traveled by car B after 5 hours will be 5(2r) = 10r.
Since car B is faster, it will have traveled farther after 5 hours. Therefore,
Distance traveled by car B - distance traveled by car A = 225
10r - 5r = 225
5r = 225
r = 45 kph
and
2r = 90 kph
Therefore, car A is traveling at 45 kph and car B is traveling at 90 kph.
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25) When (x + 1)2 is divided by x - 2, the quotient is 16 and the remainder is x - 3. Find the possible values of x.
Answer:
x = 3 or x = 12
Step-by-step explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expressionThe given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
ApplicationHere, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
__
Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).
Various doses of an experimental drug, in milligrams, were injected into a patient. The patient's
change in blood pressure, in millimeters of mercury, was recorded in the table below.
40 50
Dose (mg)
Change in Blood Pressure
(mmHg)
10
2
20
9
30
12
14 16
Use the model to find the expected change in blood pressure for a 100 mg dose.
10
Using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions, one on the left side and one on the right side, which are connected by an equals sign (=). Equations are fundamental to mathematics, and are used to solve many problems. In addition, equations can also be used to describe physical laws, such as Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model suggests that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg. This can be seen by using the linear equation 10 + 2x + 3x + 4x. Here, the first coefficient of 10 represents the change in blood pressure for a 10 mg dose, the second coefficient of 2 represents the change in blood pressure for each additional 10 mg dose, the third coefficient of 3 represents the change in blood pressure for each additional 20 mg dose, and the fourth coefficient of 4 represents the change in blood pressure for each additional 30 mg dose.
For example, if the patient was given a 40 mg dose, the equation would be 10 + 2(20) + 3(30), which would yield a change in blood pressure of 140 mmHg. Similarly, if the patient was given a 50 mg dose, the equation would be 10 + 2(20) + 3(30) + 4(10), which would yield a change in blood pressure of 190 mmHg.
Therefore, using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
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The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
What is equation?A mathematical statement that expresses the equality of two expressions is known as an equation. It comprises of two expressions that are joined together by the equals sign (=), one on the left side and one on the right. Equations are essential to mathematics and are frequently used to resolve issues. Moreover, equations can be utilised to explain natural laws like Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
Using the linear equation 10 + 2x + 3x + 4x, this may be observed. In this case, the first coefficient of 10 denotes the change in blood pressure for a dose of 10 mg, the second coefficient of 2, the change for each additional dose of 10 mg, the third coefficient of 3, the change for each additional dose of 20 mg, and the fourth coefficient, the change for each additional dose of 30 mg.
For instance, if the patient received a dose of 40 mg, the equation would be 10 + 2(20) + 3(30), resulting in a 140 mmHg change in blood pressure. The calculation would be 10 + 2(20) + 3(30) + 4(10) if the patient received a 50 mg dose, which would result in a 190 mmHg change in blood pressure.
As a result, we can infer from the linear model that a 100 mg dose of the experimental medication would result in a 540 mmHg change in the patient's blood pressure.
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Suppose the horses in a large stable have a mean weight of 807lbs, and a variance of 5776. what is the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the stable?
The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.
Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.
Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).
Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51
Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.
Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)
Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310
So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
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Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 39 pound mass suspended on a spring scale stretches the spring 10 inches, how far will a 48 pound mass stretch the spring? Round your answer to one decimal place if necessary
48 pound mass will stretch the spring approximately 12.31 inches.
To solve this problemIf the spring's force is directly proportional to how far it is stretched, we can express this relationship mathematically as follows:
F = kx
Where
F is the force exerted by the springx is the distance that the spring is stretchedk is the proportionality constantWe can use the first value of the spring scale to determine k:
39 = k(10)
k = 3.9
Now, using this value of k, we can calculate how far the spring is stretched when a 48-pound mass is applied:
F = kx
48 = 3.9x
x = 48/3.9
x = 12.31
Therefore, a 48 pound mass will stretch the spring approximately 12.31 inches.
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12. Julie is buying a house for $225,000. She obtains a mortgage in the amount of $156,000 at a
4. 5% fixed rate. The bank offers a 4. 25% interest rate if julie pays 2. 25 points. What is the cost
of points for this mortgage rounded to the nearest dollar?
$3,510
$5,063
$6,630
$7,020
The cost of points for this mortgage is $3,510 rounded to the nearest dollar if Julie pays 2.25 points.
Cost of house = $225,000.
Mortgage amount = $156,000
Fixed-rate = 4.5%
Bank offer rate = 4.25%
Points to pay = 2.25 points
If we assume that one point is equal to 1%, then 2.25 points are equal to 2.25% of the loan amount.
The cost of points for the mortgage can be calculated by the product of the loan amount by 2.25%.
Cost of points = 0.0225 × $156,000
Cost of points = $3,510
Therefore, we can conclude that the cost of points for this mortgage is $3,510 rounded to the nearest dollar.
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