If a population is normal with a variance of 99, the necessary sample size is 7 (Option B).
To find the necessary sample size for a given confidence level and margin of error, we can use the formula:
n = (Z² * σ²) / E²
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ² is the population variance, and E is the margin of error.
In this case, the population variance (σ²) is 99, the desired confidence level is 68.26%, and the margin of error (E) is 4 units. The Z-score corresponding to a 68.26% confidence level is approximately 1, as it is close to one standard deviation from the mean in a normal distribution.
Now, we can plug the values into the formula:
n = (1² * 99) / 4²
n = (1 * 99) / 16
n = 99 / 16
n ≈ 6.19
Since we cannot have a fraction of a sample, we round up to the nearest whole number, which is 7. So, the necessary sample size is 7 (Option B).
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Jack plus 1/3 pound of birdseed into his birthday. Every time he sells it how many times can jack sell his bird feeder with 4 lb of birdseed
Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :
Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.
Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:
1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.
Simplifying this equation, we get:
1/3 = 4/x
To solve for x, we can cross-multiply:
1x = 12
x = 12
Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.
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How much paint will you need to paint all sides of the box shown below? 4m 13m 4m 4m 11m
To paint all sides of the box, you would need approximately 344 square meters of paint.
To calculate the amount of paint needed to paint all sides of the box, we first need to find the total surface area of the box.
The box has five sides: top, bottom, front, back, and two sides.
Given the dimensions:
Top: 4m x 13m
Bottom: 4m x 13m
Front: 4m x 4m
Back: 4m x 4m
Sides (2): 4m x 11m.
To calculate the surface area, we sum the areas of all the sides:
Surface Area = (4m x 13m) + (4m x 13m) + (4m x 4m) + (4m x 4m) + (4m x 11m) + (4m x 11m)
Surface Area = 52m² + 52m² + 16m² + 16m² + 44m² + 44m²
Surface Area = 224m² + 32m² + 88m²
Surface Area = 344m²
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The width of the large size is 9.9 cm and its height is 19.8 cm.
The width of the small size bottle is 4.5 cm.
hcm
h =
4.5 cm
Calculate the height of the small bottle.
19.8 cm
9.9 cm
+
cm
Answer and Explanation:
The height of the small bottle can be calculated using the ratio of the width of the large and small bottles.
Ratio of width = Large bottle width / Small bottle width
Ratio of width = 9.9 cm / 4.5 cm
Ratio of width = 2.2
Therefore, the height of the small bottle can be calculated by multiplying the ratio of width with the height of the large bottle.
Height of small bottle = Ratio of width x Height of large bottle
Height of small bottle = 2.2 x 19.8 cm
Height of small bottle = 43.56 cm
Use similar triangles to calculate the height, h cm, of triangle ABE. 10 cm 36 cm D B 20 cm E Optional working I h = Answ cm Search
Answer:
h=24
Step-by-step explanation:
Since the traingles are similar we can calculate the scale factor
20/10 = 2
So the Linear Scale Factor is 2
We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20
We cans say that the ratio between DBC and ABE is 2:1
Using this we can see that the ratio of the height is split into 2:1 and the total is 3
Knowing this we can calculate the the heights of both triangles
36 / 3 = 12
Height of small traingle = 1*12 = 12
Height of large triangle = 2*12 = 24
Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?
If we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
The car wash costs $7, and the price per gallon of gas with the car wash is $3.19, while the price per gallon of gas without the car wash is $3.39. Let's assume that we buy x gallons of gas, then the total cost of buying gas with the car wash would be:
Total cost with car wash = 7 + 3.19x
The total cost of buying gas without the car wash would be:
Total cost without car wash = 3.39x
To determine when it is worth it to buy the car wash, we need to find when the total cost with the car wash is less than the total cost without the car wash:
7 + 3.19x < 3.39x
Solving for x:
7 < 0.2x
x > 35
This means that if we plan to buy more than 35 gallons of gas, it is worth it to buy the car wash.
Now, let's consider the scenario where the car wash costs $2. The total cost of buying gas with the car wash would be:
Total cost with car wash = 2 + 3.19x
To determine when it is worth it to buy the car wash in this scenario, we need to find when the total cost with the car wash is less than the total cost without the car wash:
2 + 3.19x < 3.39x
Solving for x:
2 < 0.2x
x > 10
This means that if we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
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how many times can 2 go into 1742? please its for my homework due tomorrow
BRAINLEST AND 40 POINTS!!
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water.
Enter an estimate for the land area on the planet. Round the answer to the nearest million.
An estimate for the land area on the planet is
mi?
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²
The surface area of a sphere is given by the formula:
S = 4πr²
where S is the surface area and r is the radius.
Substituting the given radius, we get:
S = 4π(2,812)²
S ≈ 99,392,252.4 mi²
Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:
Land area ≈ (1/3) x 99,392,252.4
Land area ≈ 33,130,750.8 mi²
Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.
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Find the area of triangle ABC given that AB= 8cm , AC = 6cm , ∠ = 55° ∠ = 35°.
a) 48cm*2 b) 12cm*2 c) 24cm*2 d) 5cm*2
Step-by-step explanation:
so like you use sine rule to find line BC and i got 7.3 the you have to split the triangle in half to get a right angle triangle then divide 7.3 by two to get 3.7 and then use .pythagoras theorem to find the height and then use the area of a triangle formula to get your answer as option (C)
find f(x) for the given function.
f(x) = 1/1-x
To find f(x) for the given function f(x) = 1/1-x, we simply replace the "x" in the equation with whatever input value we want to evaluate the function at.
For example, if we want to find f(2), we would replace x with 2 and get:
f(2) = 1/1-2
f(2) = -1
Similarly, if we want to find f(a), we would replace x with a and get:
f(a) = 1/1-a
Therefore, f(x) = 1/1-x, where x is any input value.
To find f(x) for the given function, simply rewrite the function as it is:
f(x) = 1 / (1 - x)
Here, f(x) represents the function value for any input x, and the expression on the right side indicates how to calculate it.
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Please answer 1-9, i really need help tysm
Answer:
the answer is 8
Step-by-step explanation:
it is because if you take your 9 fingers and remove 1 finger it will be 8
Which expression is equivalent to 3x – (2x + 4) + 5?
Responses
The expression that is equivalent to 3x – (2x + 4) + 5 is x+1 ( optionB)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example , 2a+6a is equivalent to 2a( 1+3) and they will surely have the same value when a value is replaced with a
3x – (2x + 4) + 5 = 3x-2x-4+5
= x-4+5
= x +1
therefore the equivalent of 3x – (2x + 4) + 5 is x+1
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sin^2(x) + sin(x) = 0
Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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please hurry A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled less than 8 pounds with entries a, c, e. Column 3 is labeled greater-than-or-equal-to 8 pounds with entries 50, d, 70. Column 4 is labeled Total with entries b, 96, 160.
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more.
a = 64, b = 14, c = 76, d = 20, e = 90
a = 14, b = 64, c = 90 d = 20, e = 76
a = 14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
Answer: the correct answer is:
a = 14, b = 64, c = 76, d = 20, e = 90
Step-by-step explanation: can i get brainliest :D
Solve the system of equations.
6x – y = 6
6x2 – y = 6
A (0, 6) and (0, –6)
B (1, 0) and (0, –6)
C (2, 6) and (1, –11)
D (3, 12) and (2, 19)
The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?
Answer: 32000
Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.
Select the statement that correctly describes the relationship for angles of an inscribed quadrilateral. (10pts pls help)
The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
What is the relationship between the angles of an inscribed quadrilateral, and how related to each other?An inscribed quadrilateral is a quadrilateral whose vertices all lie on a circle. Let's label the vertices of the quadrilateral as A, B, C, and D, in clockwise order.
Draw the circle that contains all four vertices, and label the center of the circle as O.
Now, draw chords AC and BD that cross at point P. Each chord divides the quadrilateral into two triangles. Notice that angle AOC and angle BOD are both central angles that subtend the same arc, CD.
Therefore, these angles have the same measure, and we can write:
angle AOC = angle BOD = x
Similarly, we can show that angle AOB = angle COD = y.
Now, consider the two triangles APC and BPD. These triangles share the side P D and have the same angle APD, which is equal to angle AOC + angle BOD, or 2x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APC = angle BPD = (180 - 2x)/2 = 90 - x
Similarly, consider the two triangles APB and CPD. These triangles share the side P C and have the same angle APC, which we just found to be 90 - x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APB = angle CPD = (180 - (90 - x))/2 = 90 + x/2
Finally, notice that angle APB + angle CPD = (90 + x/2) + (90 - x/2) = 180, so the opposite angles in the quadrilateral are indeed supplementary.
Therefore, the main answer is: The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
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If R is the unbounded region between the graph of [tex]y=\frac{1}{x(ln(x))^2}[/tex] and the x-axis for [tex]x\geq 3[/tex] then what is the area of R?
will give brainliest to answer with good explanation please i'm desperate
The area of the unbounded region R between the graph of y=1/(xln(x))² and the x-axis for x≥3 is 1/ln(3) square units. The integral was found by substitution and evaluated at the interval limits.
To find the area of the region R, we need to integrate the function y = 1/(x ln(x))² with respect to x over the interval x≥3.
Let's first find the indefinite integral
∫ 1/(x ln(x))₂ dx = ∫ u₂ du [where u = ln(x)]
= - u⁻¹ + C
= - ln(x)⁻¹ + C
Now, to find the definite integral, we need to evaluate this expression at the upper and lower bounds of the interval x≥3
[tex]\int\limits^ \infty} _3[/tex]1/(x ln(x))² dx = [- ln(x)⁻¹[tex]]^ \infty} _3[/tex]
= [- ln(∞)⁻¹] - [- ln(3)⁻¹]
= 0 - (-1/ln(3))
= 1/ln(3)
Therefore, the area of the region R is 1/ln(3) square units.
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Can anyone help? i need to solve these using the completing the square method
Using the completing the square method, the quadratic equation x²-5x=9 can be simplified to (x-2.5)²=15.25, and the solutions are x=2.5+√15.25 and x=2.5-√15.25.
To solve this quadratic equation using the completing the square method. Here are the steps
Move the constant term (in this case, 9) to the right-hand side of the equation
x² - 5x = 9 becomes x² - 5x - 9 = 0
To complete the square, we need to add and subtract a constant term inside the parentheses. The constant term we add is half of the coefficient of the x-term, squared. In this case, the coefficient of the x-term is -5, so we need to add and subtract (5/2)² = 6.25.
x² - 5x - 9 + 6.25 - 6.25 = 0
Rearrange the terms inside the parentheses to group the perfect square with the x-term
(x² - 5x + 6.25) - 15.25 = 0
Factor the perfect square trinomial inside the parentheses
(x - 2.5)² - 15.25 = 0
Add 15.25 to both sides of the equation
(x - 2.5)² = 15.25
Take the square root of both sides
x - 2.5 = ±√15.25
Add 2.5 to both sides
x = 2.5 ±√15.25
So the solutions to the equation x² - 5x = 9, using the completing the square method, are x = 2.5 + √15.25 and x = 2.5 - √15.25.
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--The given question is incomplete, the complete question is given
"Can anyone help? i need to solve these using the completing the square method
x²-5x = 9"--
Fish enter a lake at a rate modeled by the function E given by E(t) = 20+15sin(pi*t/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4+20.1*t^2. Both E(t) and L(t) are measured in fish per hour and 't' is measured in hours since midnight (t=0).a.) How many fish enter the lake over the 5-hour period from midnight (t=0) to 5am (t=5)? Give your answer to the nearest whole number.b.) What is the average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5)?c.) At what time, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify.d.) Is the rate of change in the number of fish in the lake increasing or decreasing at 5am (t=5)? Explain your reasoning.
Answer: a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
Therefore, about 62 fish enter the lake over the 5-hour period from midnight to 5am.
b) The average number of fish that leave the lake per hour over the 5-hour period can be found by calculating the total number of fish that leave the lake over the 5-hour period and dividing by 5:
int(4+20.1*t^2, t=0 to 5) ≈ 1055
average = 1055/5 = 211
Therefore, the average number of fish that leave the lake per hour over the 5-hour period is 211.
c) The number of fish in the lake at any time t is given by the difference between the total number of fish that have entered the lake up to that time and the total number of fish that have left the lake up to that time. So, if N(t) represents the number of fish in the lake at time t, then:
N(t) = int(20+15sin(pi*t/6), t=0 to t) - int(4+20.1*t^2, t=0 to t)
To find the time t when the greatest number of fish are in the lake, we need to find the maximum of N(t) for 0 ≤ t ≤ 8. We can do this by taking the derivative of N(t) and setting it equal to zero:
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
0 = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
Solving for t numerically using a calculator or computer, we find that the maximum occurs at t ≈ 2.34 hours. Therefore, the greatest number of fish in the lake occurs at 2.34 hours after midnight.
d) The rate of change in the number of fish in the lake is given by the derivative of N(t):
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
To determine whether the rate of change is increasing or decreasing at t=5, we need to find the second derivative:
d^2N(t)/dt^2 = -5.05t
When t=5, the second derivative is negative, which means that the rate of change in the number of fish in the lake is decreasing at 5am.
a. There will be 141 fish enter the lake over the 5-hour period from midnight
b. The average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5) is 101.
c. At 3.25 hour, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake
d. The rate of change in the number of fish in the lake is decreasing at 5am.
a) To find the number of fish that enter the lake over the 5-hour period from midnight to 5am, we need to integrate the rate of fish entering the lake over that time period:
Number of fish = ∫[0,5] E(t) dt
= ∫[0,5] (20+15sin(πt/6)) dt
Number of fish ≈ 141
Therefore, approximately 141 fish enter the lake over the 5-hour period from midnight to 5am.
b. To find the average number of fish that leave the lake per hour over the 5 hour period, we need to calculate the total number of fish that leave the lake over that time period and divide by the duration of the period:
Number of fish that leave the lake = L(5) - L(0)
= (4+20.1*5^2) - (4+20.1*0^2)
= 505.5
Average number of fish leaving per hour = Number of fish that leave the lake / Duration of period
= 505.5 / 5
= 101.1
Therefore, the average number of fish that leave the lake per hour over the 5 hour period from midnight to 5am is approximately 101.
c. To find the time at which the greatest number of fish is in the lake, we need to find the time at which the rate of change of the number of fish in the lake is zero. This occurs when the rate of fish entering the lake is equal to the rate of fish leaving the lake:
E(t) = L(t)
20+15sin(πt/6) = 4+20.1t^2
We can solve this equation numerically to find that the greatest number of fish is in the lake at approximately t=3.25 hours (rounded to two decimal places).
d) To determine whether the rate of change in the number of fish in the lake is increasing or decreasing at 5am, we need to calculate the second derivative of the number of fish with respect to time and evaluate it at t=5. If the second derivative is positive, the rate of change is increasing. If it is negative, the rate of change is decreasing.
d²/dt² (number of fish) = d/dt E(t) - d/dt L(t)
= (15π/6)cos(πt/6) - 40.2t
d²/dt² (number of fish) ≈ -44.4
Since the second derivative is negative, the rate of change in the number of fish in the lake is decreasing at 5am.
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Guided practice
it's not letter c. -2.6
state what number you would subtract from each side of the inequality to solve the inequality.
5.7 ≥ k + 3.1
a.
3.1
b.
5.7
c.
–2.6
The value of k that is less than or equal to 2.6
To solve the inequality 5.7 ≥ k + 3.1, you should subtract 3.1 from each side of the inequality.
To isolate the variable k, we need to perform the same operation on both sides of the inequality. In this case, we need to subtract 3.1 from each side:
5.7 - 3.1 ≥ k + 3.1 - 3.1
This simplifies to:
2.6 ≥ k
Therefore, the correct answer is:
k ≤ 2.6
We subtracted 3.1 from each side to isolate the variable k, resulting in the inequality k ≤ 2.6. This means that any value of k that is less than or equal to 2.6 will satisfy the original inequality 5.7 ≥ k + 3.1.
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1. Mrs. Zimmerman is interested in learning about how much time seventh grade students at our school spend outdoors on a typical school day.
Select all the samples that are a part of the population. Justify your reasoning.
. The 20 students in a seventh grade math class.
B. The first 20 students to arrive at school on a particular day.
C. The seventh grade students participating in a science fair put on by the four middle schools in a school district.
D. The 10 seventh graders on the school soccer team.
E. The students on the school debate team.
A, c, D
Step-by-step explanation:
A) we can sample these 7th graders as we are looking to study 7th graders.
b) The first 20 students could be from any grade and so this option wouldn't work.
c) Involves 7th graders.
d) involves 7th graders
E) The students could be any grade level on the debate team so, this option wouldn't work.
whats the answer!???????
Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
The standard deviation of the sampling distribution is 2.53. It would not be appropriate to use a normal distribution to model the sampling distribution.
(a) When dealing with a sampling distribution, the mean of the sampling distribution (μ_x) is equal to the mean of the population (μ). In this case, the mean of the population is 65. Therefore, the mean of the sampling distribution is also 65.
To calculate the standard deviation of the sampling distribution (σ_x), you will use the following formula: σ_x = σ / √n, where σ is the standard deviation of the population and n is the sample size. In this case, the standard deviation of the population is 8 and the sample size is 10. So the standard deviation of the sampling distribution is:
σ_x = 8 / √10 ≈ 2.53
(b) The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided that the population is not heavily skewed or has extreme outliers. Since the scores are extremely skewed left and the sample size is only 10, it would not be appropriate to use a normal distribution to model the sampling distribution. A larger sample size would be needed to use a normal distribution model.
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A basket contains a red, a yellow, and a green apple. A second basket contains an orange, a lemon, and a peach. Use an organized list to show all the outcomes in sample space
There are 9 different outcomes in the sample space when selecting one fruit from each basket.
Using an organized list, we can represent all the possible outcomes in the sample space for the two baskets of fruit:
1. Red Apple, Orange
2. Red Apple, Lemon
3. Red Apple, Peach
4. Yellow Apple, Orange
5. Yellow Apple, Lemon
6. Yellow Apple, Peach
7. Green Apple, Orange
8. Green Apple, Lemon
9. Green Apple, Peach
In total, there are 9 different outcomes in the sample space when selecting one fruit from each basket.
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Help!! Will give out brainliest answer :)
Leslie paid $13 for 4 children’s tickets and 1 adult ticket.
Antonio paid $14 for 3 adult’s tickets and 2 children’s tickets.
Write and solve a system of equations to find the unit price for a child ticket and an adult ticket. Explain your steps and show all your work
The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.
To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.
From the first sentence, we know that:
4x + y = 13 ...(1)
From the second sentence, we know that:
3y + 2x = 14 ...(2)
Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.
Multiplying equation (1) by 3, we get:
12x + 3y = 39 ...(3)
Subtracting equation (2) from equation (3), we get:
10x = 25
x = 2.50
Substituting x = 2.50 into equation (1), we get:
4(2.50) + y = 13
y = 3
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A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the house, the base is moving away at the rate of 24 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
The rate of change of the height of the top of the ladder is -144/h ft/sec when the base of the ladder is 6 ft from the house.
The area of the triangle formed by the ladder, wall, and ground is decreasing at a rate of 163.2 ft^2/sec when the base of the ladder is 6 ft from the house.
The angle between the ladder and the ground is decreasing at a rate of 1/8 rad/sec when the base of the ladder is 6 ft from the house.
By using Pythagorean Theorem how we find the height, base and angle of the ladder?The rate of change of the height of the top of the ladder, we need to use the Pythagorean Theorem:
[tex]h^2 + d^2 = L^2[/tex]where h is the height of the top of the ladder, d is the distance of the base of the ladder from the house, and L is the length of the ladder.
Taking the derivative with respect to time, t, and using the chain rule, we get:
2h (dh/dt) + 2d (dd/dt) = 2L (dL/dt)We are given that d = 6 ft, dd/dt = 24 ft/sec, and L = 10 ft. We need to find dh/dt when d = 6 ft.
Plugging in the values, we get:
2h (dh/dt) + 2(6)(24) = 2(10) (0) (since the ladder is not changing length)
Simplifying, we get:
2h (dh/dt) = -288Dividing by 2h, we get:
dh/dt = -144/hThe area of the triangle formed by the ladder, wall, and ground is given by:
A = (1/2) bhwhere b is the distance of the base of the ladder from the wall, and h is the height of the triangle.
Taking the derivative with respect to time, t, and using the product rule, we get:
dA/dt = (1/2) (db/dt)h + (1/2) b (dh/dt)We are given that db/dt = -24 ft/sec, h = L, and dh/dt = -144/h. We need to find dA/dt when d = 6 ft.
Plugging in the values, we get:
dA/dt = (1/2) (-24) (10) + (1/2) (6) (-144/10)Simplifying, we get:
dA/dt = -120 + (-43.2)dA/dt = -163.2 ft^2/secThe rate of change of the angle between the ladder and the ground, we use the trigonometric identity:
Dividing by sec^2(theta), we get:
d(theta)/dt = (-24/h^3) - (2h^2/5)
We can plug in the value of h = (L^2 - d^2)^(1/2) = (100 - 36)^(1/2) = 8 ft when d = 6 ft to get:
d(theta)/dt = (-24/8^3) - (2(8)^2/5) = -1/8 rad/secLearn more about Pythagorean theorem
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In a game of chance players spin the pointer of a spinner with six equal sized sections Anna 1 John 4 Carrie 4 Steve 1 Ethan 2 Liz 4 Jane 1 which outcome has a frequency closest to its expected frequency A (1) B (2) C (3) D (4)
The outcome with a frequency closest to its expected frequency is C (3).
Which outcome in a spinner game has a frequency closest to its expected frequency?In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.
To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.
Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.
Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.
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Need help asap. (See photo below)
Angles Formed by Chords, Tangents, Secants
The value of m∠MGA between the tangent and the diameter is 90 degrees.
How to find the angle between tangent?A line that touches the circle at one point is known as a tangent to a circle.
Therefore, MU is tangent to the circle O at the point G. The diameter of the
circle is GA.
Therefore, let's find the angle m∠MGA in the circle.
If a tangent and a diameter meet at the point of tangency, then they are perpendicular to one another. Therefore, the point where they meets form a right angle(90 degrees).
Hence,
m∠MGA = 90 degrees
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