Required error is the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.
What is perimeter of a triangle?
The perimeter of a triangle is the total length of the three sides of the triangle. It is a fundamental geometric concept that is important in many applications, including architecture, engineering, and construction.
To calculate the perimeter of a triangle, you simply add up the lengths of its three sides. This is expressed by the following formula,
Perimeter = side a + side b + side c
where "a," "b," and "c" are the lengths of the three sides of the triangle.
Here Alfonso's error is that he added the three side lengths incorrectly. The correct way to find the perimeter of a triangle is to add up all three sides.
In this case, the three side lengths are 22 cm, 11 cm, and 27 cm. Adding them up, we get,
22 cm + 11 cm + 27 cm = 60 cm
Therefore, the perimeter of the triangle is 60 cm, not 66 cm as Alfonso said.
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Correct question is " There is a triangle whose sides are 22 cm, 11 cm and 27 cm.
Alfonso said that the perimeter of this
triangle is 66 centimeters. What was his error?"
The volume of a volleyball is approximately 113 in ^3. What is its diameter? Round your answer to the nearest whole number.
A. 13 in
B. 6 in
C. 2 in
D. 5 in
will give brainliest
If the volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.
The formula for the volume of a sphere is
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows
113 = (4/3)πr³
r³ = 113 / ((4/3)π)
r³ ≈ 21.50
r ≈ 2.8
To find the diameter, we double the radius:
d = 2r ≈ 5.6
Rounding this to the nearest whole number
d = 5 in
Therefore, the correct option is (D) 5 in
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WORTH 45!!!
Use division to show that (x+5) is a factor given y= 2x^3 - x^2 - 41x + 70
what is the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin?0.14260.13570.24610.0321
The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.
Option C is correct
The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:
P(X = k) = (n choose k) [tex]* p^k * (1-p)^(n-k)[/tex]
where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.
Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:
P(X = k) = (n choose k [tex]* 0.5^k * ()1-0.5)^(n-k)[/tex]
We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:
[tex]P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)[/tex]
Simplifying this expression, we get:
[tex]P(X = n/2) = (n choose n/2) * 0.5^n[/tex]
Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:
P(X = 5) = (10 choose 5) [tex]* 0.5^5 * (1-0.5)^(10-5)[/tex] = 0.2461
Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.
Option C is correct
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the probability that a student is a vegetarian is 0.21. you randomly select 12 students and ask each if they are vegetarians. find the probability that the number of students who say that they are vegetarians is exactly one. 0.1885 0.0591 0.9409 0.7524
the probability that exactly one student out of 12 says they are a vegetarian is 0.1885, which is option A.
To solve this problem, we need to use the binomial distribution formula:
[tex]P(X=k) = (^nc_k) * p^k * (1-p)^{n-k}[/tex]
where:
- X is the random variable representing the number of students who say they are vegetarians
- k is the number of students who say they are vegetarians (in this case, k=1)
- n is the total number of students selected (n=12)
- p is the probability that a student is a vegetarian (p=0.21)
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items and is calculated as: n! / (k! * (n-k)!)
Substituting the values given in the problem, we get:
[tex]P(X=1) = (12 choose 1) * 0.21^1 * (1-0.21)^{12-1}\\P(X=1) = 12 * 0.21 * 0.79^{11\\P(X=1) = 0.1885[/tex]
Therefore, the probability that exactly one student out of 12 says they are a vegetarian is 0.1885, which is option A.
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The probability that exactly one student out of 12 is a vegetarian is approximately 0.1885.
To find the probability that exactly one out of 12 randomly selected students is a vegetarian, given that the probability
of a student being a vegetarian is 0.21, you can use the binomial probability formula.
The binomial probability formula is:
[tex]P(x) = C(n, x) × p^x × (1-p)^(n-x)[/tex]
Where:
- P(x) is the probability of x successes (vegetarians) out of n trials (students)
- C(n, x) is the number of combinations of n items taken x at a time
- p is the probability of success (a student being a vegetarian, 0.21)
- n is the number of trials (12 students)
- x is the number of successes (1 vegetarian)
Using the formula, we get:
[tex]P(1) = C(12, 1) × 0.21^1 × (1-0.21)^(12-1)[/tex]
C(12, 1) = 12 (since there are 12 ways to choose 1 vegetarian out of 12 students)
[tex]P(1) = 12 × 0.21^1 × 0.79^11 ≈ 0.1885[/tex]
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a simple random sample of 100 8th graders at a large suburban middle school indicated that 86% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. a) (0.699, 0.941) b) (0.829, 0.834) c) (0.779, 0.941) d) (0.679, 0.891) e) (0.779, 0.741) f) none of the above
For a random sample of 100 students related to aftee school activity. The 98% confidence interval that estimates the proportion of students who are involved in an after school activity is equals to (0.779, 0.941). So, option (c) is right one.
Confidence intervals represents the variation around a statistical estimate. A confidence interval is a range of interval of estimates for an unknown parameter.
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
where [tex]\hat p[/tex]-->sample proportion
n --> sample size
We have a simple random sample of 8ᵗʰ graders at a large suburban middle school. Sample size, n = 100
Sample proportion for students who involved with some type of school activity, [tex]\hat p[/tex] = 86% = 0.86
We have to calculate the 98% confidence interval that estimates the proportion of students sample.
Level of significance, α = 98%
= 0.98
Using the normal distribution table, value of z-score for 98% of confidence interval is 2.326 . Now, plug all known values in following confidence interval formula,
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 1 - 0.86)0.86}{100}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 0.14)0.86}{100}}[/tex]
[tex]= 0.86 ± 0.081 [/tex]
[tex]= (0.86 - 0.081 , 0.86 + 0.081) [/tex]
= (0.779, 0.941)
Hence, required value is (0.779, 0.941).
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Graph the function: f(x) = -2 for x< 1. Show a T-chart with all of your work. Determine a solution that is part of the
function for the given interval.
The graph of the given function f(x) = -2 is as attached .
How to graph a function?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
We are given the function as:
f(x) = -2
Thus, this means that the graph will be a straight horizontal line cutting across the point -2 on the y-axis which is indicated in the graph attached
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Calculate the lengths of the 2 unlabeled sides.
Leave your answer in exact form.
Answer:
BC=4
AC=[tex]4\sqrt{2}[/tex]
Using the graph, determine the coordinates of the vertex of the parabola.
Based on the information given, the vertex of the parabola can be found using the coordinates of the turning point (also known as the vertex).
What is the explanation for the above response?The vertex is located at (4,-4), which means that the value of x is 4 and the value of y is -4. Therefore, the coordinates of the vertex are (4,-4).
The fact that the curve is on the upper and lower quadrants of the right side of the cartesian coordinate system suggests that the parabola opens upwards.
Also, since the curve meets the x-axis at two points, this indicates that the parabola intersects the x-axis at those two points, which are (2,0) and (6,0).
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Help?
You are interested in studying the proportion of people 65 years or older that have an active Netflix subscription. You interview 65 random people that are 65 years or older that live in the United States. 23 of them claim to have an active Netflix subscription.
a) Define the parameter of interest.
b) State and check if the assumptions needed for constructing the appropriate CI for the parameter of interest are satisfied.
c) Find a 90% confidence interval for the parameter defined in part a). (Use the provided table, not the calculator to find the appropriate critical value. )
d) Write a sentence to interpret the CI computed in part c)
a) The parameter of interest is the proportion of people 65 years or older in the United States.
b) The assumptions include the sample is random, the sample size is large and observations are independent.
c) The 90% confidence interval lie in (0.198, 0.51).
d) We are 90% confident that the true proportion of people 65 years or older lies between 0.198 and 0.51.
a) The parameter of interest is the proportion of people 65 years or older in the United States who have an active Netflix subscription.
b) The assumptions needed for constructing the appropriate confidence interval for the proportion include: 1) the sample is random, 2) the sample size is sufficiently large (at least 10 times the number of successes and failures), and 3) the observations are independent.
To check these assumptions, we need to verify that the sample is indeed random, and that the sample size is large enough. Since the sample size is 65 and the number of successes (i.e., those with an active Netflix subscription) is 23, we can assume that the sample size is sufficiently large.
Additionally, we assume that each person in the sample has an independent probability of having an active Netflix subscription.
c) To find a 90% confidence interval for the proportion of people 65 years or older in the United States with an active Netflix subscription, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:
p' ± z*(√(p'(1-p'))/n)
where p' is the sample proportion (23/65), z* is the critical value from the standard normal distribution corresponding to a 90% confidence level (1.645), and n is the sample size (65).
Plugging in the values, we get:
0.354 ± 1.645*(√(0.354*(1-0.354))/65)
This simplifies to:
(0.198, 0.51)
d) We are 90% confident that the true proportion of people 65 years or older in the United States with an active Netflix subscription lies between 0.198 and 0.51. This means that if we were to repeat this study many times and construct a 90% confidence interval for each study, we would expect that 90% of these intervals would contain the true proportion.
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A colored pencil is a wood hexagonal prism with a column of colored lead running through its center. The typical length of the usable lead is 19 centimeters, and the lead core has a diameter of 3 millimeters. A cross section of the pencil has an area of 89.25 square millimeters. What percentage of a colored pencil is wood?
Answer:
i guess 97 %
Step-by-step explanation: see fist of all
most colour pencils ARE made of wood so yeah sorry dont know im still in 6th
The diameter of a semicircle is 4 feet. What is the semicircle's perimeter?
need urgent help pls
99 pts
Answer:
.22222 or [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]2(\frac{1}{3^{2} })\\\\2(\frac{1}{9})\\\\= .22222 \\[/tex] or [tex]\frac{2}{9}[/tex]
4 out of 7 questions. PLEASE help me.
A tangent line is line GJ.
A secant line is line HF.
A chord is line GF.
What is the chord of a circle?In Mathematics and Geometry, the chord of a circle can be defined as a line segment that typically join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two (2) separate points on a circle such as line GF.
What is a secant line?In Mathematics and Geometry, a secant line can be defined as a type of line that intersects the edge of a circle twice i.e it goes through the interior of the circle twice and intersects its boundary twice such as line HF.
In conclusion, a tangent line is a type of line that lies outside of a circle and intersects the edge of a circle exactly once i.e it touches the outside of the circle only once such as line GJ.
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Find the Length of the Arc ^PQ and round your answer to the nearest Hundredth place.
Please help
The length of an arc is PQ is 9.42 units.
How to find the length of an arc?The length of an arc is PQ can be found as follows:
length of an arc = ∅ / 360 ×2πr
where
∅ = central angler = radius of the circleTherefore,
∅ = 60 degrees
r = 9 units
length of the arc = 60 / 360 × 2 × 3.14 × 9
length of the arc = 1 / 6 × 56.52
length of the arc = 56.52 / 6
length of the arc = 9.42 units
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a prescription for ear drops specifies that the patient put 2 drops in each ear twice a day for 9 days. approx how many millilitres of medication would be needed for this prescription? ( dosage×frequency×day supply )
approximately 3.6 milliliters of medication would be needed for this prescription.
To calculate the total milliliters of medication needed for this prescription, we will use the formula dosage × frequency × day supply.
In this case, the dosage is 2 drops per ear, the frequency is twice a day, and the day supply is 9 days.
First, let's find out how many drops are needed per day:
2 drops/ear × 2 ears = 4 drops
Since the frequency is twice a day, multiply this number by 2:
4 drops × 2 = 8 drops per day
Now, multiply the number of drops per day by the day supply (9 days):
8 drops/day × 9 days = 72 drops
Typically, 1 drop is approximately 0.05 millilitres. To find out how many millilitres of medication are needed, multiply the total number of drops by the volume of one drop:
72 drops × 0.05 mL/drop = 3.6 mL
So, approximately 3.6 millilitres of medication would be needed for this prescription.
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Approximately 1.8 milliliters of medication would be needed for this prescription.
To calculate how many milliliters of medication would be needed for this prescription, we need to use the following formula:
dosage × frequency × day supply.
The dosage is 2 drops, the frequency is twice a day, and the day supply is 9 days.
First, we need to convert drops to milliliters.
One drop is equal to approximately 0.05 milliliters.
2 drops would be equal to 0.1 milliliters.
Next, we can plug in the values into the formula:
[tex]0.1 milliliters/drop \times 2 drops/twice a day \times 9 days = 1.8 milliliters. [/tex]
The patient will be using exactly 2 drops in each ear for each dose, and that there will be no waste or spillage of the medication.
To determine how many milliliters of medicine would be required for this prescription:
dose frequency day supply.
The recommended dosage is 2 drops, twice day, with a 9-day supply.
We must first convert droplets to milliliters.
A drop is around 0.05 milliliters in volume. As a result, 2 drops are equivalent to 0.1 milliliters.
The values may then be entered into the formula as follows:
0.1 milliliters each drop times twice daily for nine days equals 1.8 milliliters.
As a result, this prescription would require about 1.8 milliliters of medicine.
It's crucial to note that this estimate is predicated on the patient applying precisely 2 drops to each ear for each dose.
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what is x to the problem 45x+225=1060
Answer:
To solve for x in the equation 45x+225=1060, we can use algebraic manipulation.
First, we can subtract 225 from both sides of the equation to isolate the variable term on the left side:
45x + 225 - 225 = 1060 - 225
Simplifying both sides:
45x = 835
Finally, we can solve for x by dividing both sides of the equation by 45:
45x/45 = 835/45
Simplifying:
x = 18.56
Therefore, the value of x is approximately 18.56 when rounded to two decimal places.
Step-by-step explanation:
An electronic book device had a value of t dollars before a holiday. The value decreased by 15% after the holiday. Which expressions show the value of the electronic book device after the holiday? Select all the expressions that apply.
A. 1.15
B. 0.85
C. −0.15
D. 1−0.15
E. −0.85
F. (1−0.15)
The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
Which expressions show the value of the electronic book device after the holiday?The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.
Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.
In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
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Write down the equations of six lines that increase in steepness
Answer:
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target
The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.
The probability of missing all 4 shots is (0.75)^4 = 0.3164.
Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:
1 - 0.3164 = 0.6836 or 68.36%.
So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.
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Please help me find the answer to this
The average rate of the function is -3.
What is function?In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (also referred to as the codomain), where each input has precisely one output and the output can be linked to its input.
To find the average rate of the function h(x) = -x² + 8x + 20 over the interval 0 ≤ x ≤ 5, we need to calculate the total change in the function over the interval and divide it by the length of the interval.
First, we find the value of h(x) at x = 0 and x = 5:
h(0) = -0² + 8(0) + 20 = 20
h(5) = -5² + 8(5) + 20 = 5
The total change in the function over the interval is the difference between the two values:
h(5) - h(0) = 5 - 20 = -15
The length of the interval is 5 - 0 = 5.
Therefore, the average rate of the function h(x) over the interval 0 ≤ x ≤ 5 is:
average rate = (change in function) / (length of interval)
= (-15) / (5)
= -3
So, the average rate of the function is -3.
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3. Which of the following is not true about the
number line below?
A
A)
B)
C)
-2
ţ
0
+
2
The absolute value of point A is positive
The opposite of point A is positive
The additive inverse of point A is -1
The statement that is not true about point A on the number line is none of the above. All of the given statements are true.
How to determine the following that is not true about the number lineOn the number line provided, point A is located at -1, which means it is one unit to the left of 0.
A) The absolute value of point A is the distance between A and 0 on the number line, which is 1 unit. Since the absolute value of any number is always positive, it is true that the absolute value of point A is positive.
B) The opposite of a number is its reflection across 0 on the number line. The opposite of -1 is 1, which is positive. Therefore, it is true that the opposite of point A is positive.
C) The additive inverse of a number is the number that when added to it gives a sum of 0. The additive inverse of -1 is 1, which means -1 + 1 = 0. Therefore, it is true that the additive inverse of point A is -1.
Therefore, the statement that is not true about point A on the number line is none of the above. All of the given statements are true.
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On Wednesday, it rained 2 1/2 inches. This was 3/4 of an inch more than how much it rained the week before. What was the rainfall amount the week before?
Therefore , the solution of the given problem of fraction comes out to be the previous week's rainfall total was 7/4 inches.
A fraction is what?Any combination of sections of the same size can be used to represent the whole. Quantity is described as "a portion" under a particular measurement in Standard English. 8, 3/4. Fractions are included in wholes. These act as the ratio divisor, which is a pair of integers in mathematical words. Here are a couple of examples showing how to change straightforward halves into entire numbers.
Here,
Let's refer to the amount of rain that fell the previous week as x inches.
The information provided indicates that it rained 2 1/2 inches on Wednesday, which is 3/4 of an inch more than the quantity that fell the previous week. This knowledge can be expressed as an equation:
=> 2 1/2 = x + 3/4
=> 2 1/2 - 3/4 = x
=> 2 1/2 = 5/2
=> 3/4 = 3/4
=> 5/2 - 3/4 = x
In this instance, 2 and 4 have a common denominator of 4, which is 4. So, using 4 as the common denominator, we can rewrite the fractions as follows:
=> 5/2 - 3/4 = x
=> (5/2) × (2/2) - 3/4 = x
=> 10/4 - 3/4 = x
=> 7/4 = x
Therefore, the previous week's rainfall total was 7/4 inches.
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1. How far away (in kilometers) is South Florida from Washington, DC? Show how
you found this answer.
The distance between South Florida from Washington , DC is 816 miles in kilometer it is 1313.225 kilometers.
What about distance?
In mathematics, distance refers to the numerical value that measures the separation between two points, objects, or locations in a given space. Distance is a fundamental concept in geometry and is typically measured in units such as meters, kilometers, feet, or miles.
In Euclidean geometry, which is the study of flat or two-dimensional space, the distance between two points is calculated using the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. By applying this theorem, the distance between two points in a plane can be calculated using their coordinates.
According to the given information:
The distance between South Florida from Washington , DC is 816 miles in kilometer it is 1313.225 kilometers.
When we convert it into kilometers,
816 miles = 816 x 1.609
= 1313.225 kilometer
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Rick is building a sandbox for his cousins in the shape of a parallelogram. When drawn on a coordinate plane, the sandbox has vertices at (-4,0), (-2,6), (4,0), and (2,-6). If every unit represents a foot, what area does the sandbox cover?
~a.) 24ft²
~b.) 36ft²
~c.) 48ft²
~d.) 64ft²
The area of the sandbox of parallelogram shape is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal in length and parallel to each other. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure).
According to the given informationWe can choose any side of the parallelogram as the base, and the distance from that side to the opposite side as the height. Let's choose the side between (-4,0) and (-2,6) as the base. The length of this side is the distance between these two points:
√[(-2-(-4))² + (6-0)²] = √40 = 2√10
The height of the parallelogram is the distance between the line containing (-2,6) and (4,0) and the point (2,-6). We can find the equation of the line containing (-2,6) and (4,0) by finding the slope and y-intercept:
Slope: (0-6)/(4-(-2)) = -6/6 = -1
Y-intercept: y = mx + b -> 0 = (-1)(4) + b -> b = 4
Therefore, the equation of the line is y = -x + 4. We can find the distance between this line and the point (2,-6) by substituting x = 2 into the equation and finding the corresponding y-value:
y = -x + 4 = -2
The distance between the line and the point (2,-6) is the absolute value of the difference between the y-coordinate of the point and the y-coordinate of the line:
|(-6) - (-2)| = 4
Therefore, the height of the parallelogram is 4 feet.
The area of the parallelogram is then:
A = base x height = (2√10) x 4 = 8√10
Rationalizing the denominator, we get:
A = 8√10 x √10/√10 = 80/√10 = 80√10/10 = 8√10
Therefore, the area of the sandbox is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².
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Jody's team scored 26, 25, 34, 28, and 32 points at the last five basketball games.
What does the mean number of points Jody's team scored represent?
Responses:
A mean of 29 means that the data values are relatively close together and Jody's team scored around 29 points each game.
A mean of 29 points means that the data is very spread out.
A mean of 29 points means that Jody's team scored exactly 29 points in each of the last 5 games.
Answer: A
Step-by-step explanation:
jackie converted the fallowing decimals to fractions.
explain plisssss
Answer:
Step-by-step explanation:
To convert a fraction to a decimal, you divide the numerator by the denominator. The line in the middle of a fraction is essentially a large division sign.
Let's check Jackie's work
1/200 = 0.005
3/10 = 0.3
7/8 = 0.875
4/5 = 0.8
Jackie listed 7/8 as 0.625, which is incorrect. 7/8 is 0.875
So, 0.625 is your answer.
Calculate the area of each of the polygons with the following dimensions.
1. Triangles
B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)
H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.
3. Rectangle (L = length) and (w = width)
rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)
rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)
b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?
The total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Triangles:
a) Area of triangle = 1/2 * base * height = 1/2 * 4in * 5in = 10in²
b) Area of triangle = 1/2 * base * height = 1/2 * 6ft * 10ft = 30ft²
c) Area of triangle = 1/2 * base * height = 1/2 * 12m * 15m = 90m²
Total area of two triangle tablecloths for one table = 2 * 1/2 * 2ft * 4ft = 8ft²
Parallelogram:
a) Area of parallelogram = base * height = 6in * 9in = 54in²
b) Area of parallelogram = base * height = 2ft * 5ft = 10ft²
c) Area of parallelogram = base * height = 3yds * 7yds = 21yds²
height = Area/base = 78mm²/13mm = 6mm
Rectangle:
a) Area of rectangle = length * width = 8ft * 6ft = 48ft²
b) Area of rectangle = length * width = 13ft * 5ft = 65ft²
Total area of the den = (2 * 9ft * 15ft) + (2 * 8ft * 10ft) = 270ft²+ 160ft² = 430ft². Charles has enough paint because one gallon of paint will cover 440 square feet of wall space.
Rhombus:
a) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 12yds * 12yds = 72yds²
b) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 10ft * 25ft = 125ft²
c) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 16in * 22in = 176in²
height of the rhombus = 2(area/diagonal1) = 2(72ft²/12ft) = 12ft
Trapezoid:
a) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (6ft + 7ft) * 10ft = 65ft²
b) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (5yds + 8yds) * 4yds = 26yds²
c) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (9in + 11in) * 13in = 130.5in²
d) Height of trapezoid = 2(area/(base1 + base2)) = 2(32km²/16km) = 4km
Hence, the total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
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The set B = {1 + t2, t + t2, 1 + 2t + t2} is a basis for P2.
Find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to B
The coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
To find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2}, we need to express p(t) as a linear combination of the basis vectors and then write down the coefficients as a column vector.
We have:
p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2)
Expanding this out, we get:
p(t) = (a + c) + (b + 2c)t + (a + b + c)t2
Comparing coefficients with the polynomial 1 + 4t + 7t2, we get the following system of equations:
a + c = 1
b + 2c = 4
a + b + c = 7
Solving this system, we find:
a = -1
b = 2
c = 2
Therefore, the coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
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Which property was used to simplify the expression? 3c+ 9 + 4c = 3c + 4c + 9
The property used to simplify the expression is the Commutative Property of Addition, which states that changing the order of addends does not change the sum.
What is Commutative Property?The Commutative Property is a property of operations that states that the order in which two numbers are added or multiplied does not affect the result. In other words, the property says that changing the order of the terms being added or multiplied will not change the final answer.
According to given information:The property that was used to simplify the expression is the Commutative Property of Addition. This property states that the order in which we add two numbers does not affect the result. In other words, if we have two numbers a and b, then a + b is equal to b + a.
In the given expression, we have two terms, 3c and 4c, that are being added together. By applying the Commutative Property of Addition, we can rearrange the terms to get 4c + 3c. This gives us the simplified expression 7c + 9.
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A curved ladder that children can climb on can be modeled by the equation y=-1/20x^2+x where x and y are measured in feet. Make a table of values that shows the height of the ladder for x = 0, 5, 10 , 15, and 20 feet from the left end
The values of x and y of a curved ladder in feet given by the equation y=-1/20x^2+x are as follows in tabular form,
Values of x (in feet) Values of y (in feet)
0 0
5 3.75
10 5
15 3.75
20 0
A curved ladder that children can climb on is modeled by the system of equations as,
y=-(1/20)x^2+x
where, x and y are measured in feet.
Putting x= 0 in the above equation y=-(1/20)x^2+x , we get,
y = - (1/20) (0^2) + (0) = 0
Putting x= 5 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(5^2)+(5) = -5/4 + 5 = 15/4 = 3.75
Putting x= 10 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(10^2)+(10) =-5 +10 = 5
Putting x= 15 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(15^2)+(15) = -45/4 +15= 3.75
Putting x= 20 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(20^2)+(20) = -20 +20 = 0
Hence, when x= 0 feet, y = 0 feet ; x= 5 feet, y = 3.75 feet ; x = 10 feet, y = 5 feet ; x =15 feet , y =03.75 feet ;and x = 20feet, y = 0 feet from the solving the given equation.
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