The equation of the line in slope-intercept form is y = -11x + 29.
What is the formula to calculate the slope?To find the slope of given points we are using the slope-intercept formulae
The line passing through the point are (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
m is the slope of the line.
Putting all values in the above equation, we get:
m = (-15 - (-4)) / (4 - 3) = -11
So the slope of the line is -11
To write the equation of line the point-slope form of the equation we can use
y - y1 = m(x - x1)
Put all values into the equation
y - (-4) = -11(x - 3)
Simplifying, we get:
y + 4 = -11x + 33
Subtracting 4 from both sides, we get:
y = -11x + 29
So the equation of the line in slope-intercept form is y = -11x + 29.
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Select all expressions that are equal to 6^-10
Answers:
Step-by-step explanation:
(1/6²)⁵ = 1/6¹⁰ = 6^-10
because in the case of exponent of an exponent the exponents are multiplied with each other.
and 1/n = n^-1
(6^-5)² = 6^-10
because as above the exponents are multiplied with each other.
6^-3 / 6⁷ = 6^(-3 - 7) = 6^-10
a^n × a^m = a^(n+m)
a^n / a^m = a^(n-m)
the others are not 6^-10 :
6^-5 × 6² = 6^(-5 + 2) = 6^-3
6⁵×6^-3 / 6^-8 = 6^(5 - 3 - -8) = 6^(5 ‐ 3 + 8) = 6¹⁰
I just need an explanation and answer on both plsssss
Since the total amount of kids who participated in the survey is 150, 100% of the pie is equal to 150 kids.
We know that 46% of the 150 kids like video games so the number of kids that like video games is 0.46 * 150 = 69.
Similarly, 14 + 16 = 30% of 150 kids like reading and art so the number of kids that like reading and art is 0.3 * 150 = 45.
Your second question is quite hard to understand. But you know that 120 kids like video games and those kids make up 40% of the total so mathematically you can say,
40% * number of total students = 120
number of total students = 120/40% = 300
mr balewa works at a bakery every Monday he uses 4 1/2 cups of flour to make six dozen cookies every Friday he makes 12 dozen cookies
In the proportion, Mr.Balewa needs 9 cups to makes 12 dozen cookies.
What is proportion?A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here
He uses 4 1/2 cups of flour to make six dozen cookies then to makes 12 dozen cookies the x cups of flour .
Now using proportion,
= (4 1/2) / 6 = x / 12
= (9/2) / 6 = x/12
x = (9*12)/(2*6) = 9
= 9 cups.
Hence Mr. Balewa needs 9 cups to makes 12 dozen cookies.
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I need to know the missing angle if u can help I’ll give u a lot of points if u keep helping me
Answer:
?=45 degrees
Step-by-step explanation:
All of the angles are congruent.
So the equation is:45+90+?=180
?=45 degrees
Answer: 45 degrees
Step-by-step explanation:
a laboratory scale is known to have a standard deviation of 0.005 in repeated weightings. scale readings in repeated weightings are normally distributed, with the mean of all possible measurements equal to the true weight of the specimen. a specimen weighted 4 times on this scale. the average weight is 4.53 grams. suppose that we needed a 95% confidence interval for this specimen using this data. what would the margin of error be?
The margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
To find the margin of error for a 95% confidence interval, we need to determine the standard error of the mean. The standard error of the mean formula can be written as:
SE = σ/√n
where:
SE = standard error of the mean,
σ = the standard deviation of the population
n = the sample size.
the standard deviation of the laboratory = 0.005
sample size = 4.
calculating the standard error of the mean:
SE = 0.005/√4
= 0.0025
Next, we need to find the critical value for a 95% confidence interval. the sample size is small (n < 30), then we need to use a t-distribution.
Critical value = 3.182.
The formula for calculating the margin of error is:
ME = t*SE
where :
ME = margin of error
t = critical value = 3.182.
SE = standard error of the mean = 0.0025
By substuting the values, we get:
ME = t*SE
= 3.182*0.0025
= 0.008 grams
Therefore, the margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
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how to solve 132/8 answer should be in whole numbers
Answer:
use long divison ike this
16
-------
8 | 132
8
-----
52
48
-----
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
132/8 = 16 with 4 leftover
32 divided by 8 is 4, 96 divided by 8 is 12, the
extra 4 left over
) the average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. a lot contains 200 of these vehicles, brand new. (a) how many of the 200 would you expect to fail in their first 2 years? (b) what is the approximate probability that 50 or more of them fail in their first 2 years? (c) if you have learned that 30 vehicles have already failed in under 2 years, what is the approximate probability that no more than 10 of the rest of them fail in their first 2 years?
a) We would expect approximately 0.2325 × 200 = 46.5 vehicles
to fail in their first 2 years. Since we cannot have a fraction of a vehicle
failing, we would expect around 46 or 47 vehicles to fail in their first 2
years.
b) The approximate probability that 50 or more vehicles fail in
the first 2 years is 0.0004.
c) The approximate probability that no more than 10 of the remaining
vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.
a) The average lifespan of the vehicle is 8 years, and it follows an
exponential distribution, which has a probability density function of
[tex]f(x) = (1/θ) \times e^(-x/θ)[/tex],
where θ is the mean of the distribution. Thus, θ = 8.
The probability that a vehicle fails in the first 2 years can be found by
integrating the exponential probability density function from 0 to 2:
P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx
Using a calculator or a table of integrals, we can find this probability to
be approximately 0.2325.
b) The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.
The probability that 50 or more vehicles fail in the first 2 years can be
found using the Poisson distribution with parameter λ = 46.5:
P(X ≥ 50) = 1 - P(X < 50)
Using a Poisson distribution table or a calculator, we can find that P(X <
50) is approximately 0.9996.
Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).
c) Given that 30 vehicles have already failed in under 2 years, we need
to find the probability that no more than 10 of the remaining 170 vehicles
fail in their first 2 years.
The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525
(rounded to 40).
Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable
with parameter λ = 40.
Using a Poisson distribution table or a calculator, we can find that P(Y ≤
10) is approximately 0.0002.
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5.
Each table represents a proportional relationship. For each table:
Fill in the missing parts of the table.
Draw a circle around the constant of proportionality.
a.
b.
X
2
7
1
y
10
15
a.(Constant of proportionality: 5)
b.(Constant of proportionality: 5)
Hi! I'm happy to help you with your question. Let's analyze each table and fill in the missing parts.
a.
X | 2
Y | 10
To find the constant of proportionality, divide Y by X:
10 / 2 = 5 (Constant of proportionality)
Now, let's fill in the missing parts for X=7 and X=1 using the constant of proportionality:
For X=7:
Y = 5 * 7 = 35
For X=1:
Y = 5 * 1 = 5
So, the completed table for (a) is:
X | 2 | 7 | 1
Y | 10 | 35 | 5
(Constant of proportionality: 5)
b.
X | 1
Y | 15
To find the constant of proportionality, divide Y by X:
15 / 1 = 15 (Constant of proportionality)
As there are no other values in table (b), we can't fill in any more parts. The constant of proportionality is 15.
Your answer:
a.
X | 2 | 7 | 1
Y | 10 | 35 | 5
b.
X | 1
Y | 15
(Constant of proportionality: 15)
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Explain how to solve the given equation for "x".
we can solve the given equation by taking log to get answer as x = log₈(25)
what is an equation ?
An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.
In the given question,
Taking the logarithm of both sides with base 8, we get:
log₈(8ˣ) = log₈(25)
Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:
x log₈(8) = log₈(25)
Since log₈(8) = 1, we have:
x = log₈(25)
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What is the factored form of the polynomial x2 - 9x + 20?
A. x(x - 9) + 20
B. (x-4)(x + 5)
C. (x - 4)(x - 5)
D. (x2 - 4)(x2 - 5)
The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 105 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of a the tower to be 29.2°. Find the length of the tower to the nearest meter.
the tower leans 5.6° from the vertical, so we can draw a line perpendicular to the ground from the top of the tower to find the height. Let's call the height "h". the length of the tower is approximately [tex]57 meters[/tex] (rounded to the nearest meter).
What is the angle of elevation?We know that the angle of elevation from the tourist to the top of the tower is [tex]29.2^\circ[/tex] , so we can label that angle as 29.2°. We also know that the angle between the perpendicular line and the ground is 5.6°, so we can label that angle as 5.6°.
Using trigonometry, we can find the value of h:
[tex]tan(29.2^\circ) = h/105[/tex]
[tex]h = 105^\circ tan(29.2^\circ)[/tex]
[tex]h \approx 55.05[/tex]
So the height of the tower is approximately [tex]55.05[/tex] meters.
To find the length of the tower, we can use the Pythagorean theorem:
[tex]h^2 + x^2 = (105/cos(5.6^\circ))^2[/tex]
[tex]x^2 = (105/cos(5.6^\circ))^2 - h^2[/tex]
[tex]x \approx 56.67[/tex]
So the length of the tower is approximately [tex]56.67[/tex] meters.
Therefore, the length of the tower is approximately [tex]57[/tex] meters (rounded to the nearest meter).
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you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable estimate for the population proportion. you would like to be 99.5% confident that your estimate is within 4% of the true population proportion. how large of a sample size is required?
The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.
To determine the sample size required, we can use the formula:
n = (Z² * p * q) / E²
where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).
Plugging in these values, we get:
n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381
Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.
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the radius of a disk is given as with a maximum error of . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.
We have, a disk with radius of 15 cm.
Maximum error = 0.25
We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)
here, r = 15 cm , dr = 0.25
Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)
=> dA = 2πr dr
Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25
=> dA = 7.50 × π = 23.55
So, absoulte error in area = 22.55
Original value of area = π(15)² = 706.5 cm²
Now, relative error % = (∆A/A)×100
= (22.55/706.5)×100
= 0.031917 × 100
= 3.1917 ~ 3.192 %
Hence, required value is 3.192%.
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Complete question:
the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
The area of the trapezoid is 42square kilometers. What is the trapezoid's height, h?
the height of the trapezoid is 8.4 kilometers. To find the height, h, of a trapezoid when given the area, A, we need to use the formula:
A = ([tex]b_{1} + b_{2}[/tex])h/2
where b1 and b2 are the lengths of the two parallel bases of the trapezoid.
Given that the area of the trapezoid is 42 square kilometers, we can write:
42 = ([tex]b_{1} + b_{2}[/tex])h/2
We can simplify this equation by multiplying both sides by 2:
84 = ([tex]b_{1} + b_{2}[/tex]) h
Now we need to find the values of b1 and b2. Unfortunately, the problem does not provide us with these values. Without them, we cannot find the exact value of h. However, we can provide an example to show how to solve the problem if we have the values of b1 and b2.
Let's say that b1 = 4 km and b2 = 6 km. We can substitute these values into the equation:
84 = (4 + 6)h
Simplifying:
84 = 10h
Dividing both sides by 10:
h = 8.4 km
So, in this example, the height of the trapezoid is 8.4 kilometers.
In general, to find the height of a trapezoid when given the area, we need to know the values of both bases. Once we have those values, we can use the formula above to solve for the height. If we are not given the values of the bases, we cannot find the exact value of the height.
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elijah is simplifying the expression. 4 - 3x 8 10x. 4 - 3x 8 10x. 4 - 8 - 3x 10x -4 7x where did elijah go wrong?
Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.
However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.
Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
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Complete Question:
Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,
where did elijah go wrong?
solve please help!!!!
The value of angle V which is ∠V is calculated as: 64.01°
How to use trigonometric ratios?The trigonometric ratios are used to find the angles and lengths of a right angle triangle.
Some of the trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
The parameters given are:
∠W = 90°
UW = 39
WV = 80
VU = 89
Thus, using trigonometric ratios, we have:
∠V = tan⁻¹(80/39)
∠V = 64.01°
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Can somebody please help me with this it’s really important ??
please help me with this iready mastery check
To succeed in an i-Ready mastery check, it is essential to review the materials covered in the lessons thoroughly, actively engage in the learning process, and ask questions if anything is unclear.
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However, I can offer general guidance on the platform and the importance of mastery checks. Please keep in mind that I am limited to providing information within the scope of these terms and will not reach the requested 170 words.
i-Ready is an online adaptive learning platform that offers personalized learning experiences for students in reading and mathematics.
Mastery checks play a crucial role in ensuring that students fully understand the concepts being taught before progressing to more advanced topics.
These short assessments typically follow a lesson or series of lessons, helping teachers identify areas where students may need additional support or practice.
Remember that mastery checks are designed to measure your understanding of specific topics, so it's important to approach them with focus and confidence.
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which of the following correctly compares the t -distribution and z -distribution? responses for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the density curve of the t -distribution is more spread out than the density curve of the z -distributi
The correct comparison between the t-distribution and z-distribution is:
The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.
Both t-distribution and z-distribution have symmetric density curves.
However, for small sample sizes, the t-distribution curve is more spread out and has heavier tails compared to the z-distribution curve.
The area under both curves is equal to 1, as they represent probability distributions.
As the sample size increases, the t-distribution curve approaches the z-distribution curve in shape.
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100 points!!!
Express the function graphed on the axes below as a piecewise function.
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if x^2 + y^2 = m and xy = n, find the value of 16m + 32n
Answer:
x^4 - mx^2 + n^2 = 0
Step-by-step explanation:
We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:
(x^2)(y^2) = n^2
Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:
x^2(m - x^2) = n^2
Expanding the left side of the equation, we get:
mx^2 - x^4 = n^2
Multiplying both sides by 16, we get:
16mx^2 - 16x^4 = 16n^2
Adding 32xy to both sides, we get:
16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy
Substituting n for xy, we get:
16mx^2 + 32n - 16x^4 = 16n^2 + 32n
Rearranging the equation, we get:
16mx^2 - 16x^4 - 16n^2 = 0
Dividing both sides by -16, we get:
x^4 - mx^2 + n^2 = 0
Answer:
(4x+4y)²
Step-by-step explanation:
Given x²+y² = m ,xy=n.
Now 16m+32n = 16(m+2n)
= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]
(4x+4y)².
Pls help and explain
Answer: A (0.5)
Step-by-step explanation:
Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.
please help, i cant figure this out!!
Answer:
a = 127° , b = 12° , c = 115°
Step-by-step explanation:
a and 53° are same- side interior angles and sum to 180° , that is
a + 53° = 180° ( subtract 53° from both sides )
a = 127°
c and 115° are alternate angles and are congruent , then
c = 115°
53° , b and c lie on a straight line and sum to 180°
53° + b + c = 180°
53° + b + 115° = 180°
b + 168° = 180° ( subtract 168° from both sides )
b = 12°
then a = 127° , b = 12° , c = 115°
Answer:
a = 127; b = 12; c = 115
Step-by-step explanation:
c =115
b = 180 - 115 - 53
b = 12
a = b + c
a = 12 + 115
a = 127
a fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. one day 5 friends arrive to spend the night. there are no other guests that night. the friends can room in any combination they wish, but with no more than 2 friends per room. in how many ways can the innkeeper assign the guests to the rooms?(2014 amc 12a
The total number of ways to assign the guests to the rooms is 126 ways
We can solve this problem by using a combination. We have 5 friends and 5 rooms, so we can think of the friends as stars and the rooms as bars that separate them. The number of ways to assign the friends to the rooms is equal to the number of ways to arrange the 5 stars and 4 bars (since there are 4 spaces between the bars).
We can choose any 4 positions out of 9 (5 stars and 4 bars) to place the bars, so the number of ways to assign the friends to the rooms is equal to the binomial coefficient.
[tex]${9 /\choose 4} = \frac{9!}{4!5!} = 126$.[/tex]
Therefore, there are 126 ways for the innkeeper to assign the 5 friends to the 5 rooms.
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Which statements are true for the following expression? (8 + 7)(11+7) Check all that are true. The solution is the sum of two terms. The solution is the difference between two terms. The first factor is itself the sum of two terms. 4 The solution is the product of two factors. The second factor is itself the sum of two terms.
Answer:
the last 3 are true
Step-by-step explanation:
hope this helps
Find m < b
Find m < c
The answer of the given figure is ∠B = 72° and ∠C = 108°
What do you understand by the term Corresponding Angle?In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.
More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.
According to question
∠CFE = 72°
In given diagram
DC ║ EF ║ AB and CB is transversal
∴ ∠CFE + ∠BFE = 180° ( Linear pair )
72° + ∠BFE = 180°
∠BFE = 180 - 72
∠BFE = 108°
∵∠DCF = ∠BFE ( Corresponding equal angle )
∠DCF = 108°
∠C = 108°
∠CFE = ∠B ( Corresponding equal angle )
72° = ∠B
∴∠B = 72°
Hence, the ∠B = 72° and ∠C = 108°
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a researcher wants to test the hypothesis that the mean rating of guilt will be higher for unattractive defendants than for attractive defendants. the appropriate statistical test would be the
The appropriate statistical test for whether the mean rating of guilts are greater for unattractive defendants than for attractive is:
B. 1 tailed t-test.
What are the hypothesis test?At the null hypothesis, it is tested if the mean rating of guilt will not be higher for unattractive defendants than for attractive defendants, that is:
H0 : uU <=uA
At the alternative hypothesis, it is tested if the rating is greater, that is:
H1 : uU> uA
We are comparing the means, hence a t-test is used. We are testing if one is greater than other(not different), hence a 1-tailed test is used, and option B is correct.
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Help pls find the area
Answer: 112 ft²
Step-by-step explanation:
The area of a triangle can be found with the equation
[tex]A=\frac{1}{2} bh[/tex], where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).
In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.
Therefore, the area is [tex]\frac{1}{2} *16*14[/tex], which is 112 ft²
John worked 35 hours at a rate of $11.50. What is his gross pay this week?
rcumference of Circles Extra Practice Question 1 of 22 Question 1 4 3 cm > □ Find the circumference of the bottle cap. Use 3.14 for T. Round to the nearest hundredth if necessary.
The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.
What is the circumference of the circle?The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.
The diameter of the circle is given, D = 3cm
Therefore the radius of the circle, r = D/2 = 3/2 cm
Circumference of circle = 2[tex]\pi[/tex]r
= 2 * 3.14 * 3/2
= 3.14 * 3
= 9.42 cm
Therefore the circumference of the bottle cap is 9.42 cm.
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