Jeff can use the Pythagorean Theorem to check if the corner of the room forms a right triangle, indicating a right angle between the walls.
Jeff can use the Pythagorean Theorem to determine if the walls form a right angle by following these steps:
1. Identify the two sides adjacent to the angle in question: the side that is 3 inches from the corner (Side A) and the side that is 4 inches from the corner (Side B).
2. Measure the distance between the two marks along the floor (Side C). This distance will act as the hypotenuse of the right triangle.
3. Apply the Pythagorean Theorem: A² + B² = C². In this case, A = 3 inches and B = 4 inches. Calculate A² + B², which equals 3² + 4² = 9 + 16 = 25.
4. Compare the calculated value (25) to the square of the measured distance (C²). If A² + B² equals C², then the walls form a right angle, and the corner is a right triangle.
5. If the values match, it confirms that the angle between the two walls is a right angle (90 degrees), meaning the corner forms a right triangle. If the values do not match, then the walls do not meet at a right angle.
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Hello everyone! I've been struggling with this problem for about an hour now and I wanted to ask for some assistance. Its asking me to find the perimeter and the area of this octogon. For the perimeter, I got 80 meters. Thank you guys for the help! :)
The perimeter of the regular polygon is approximately 61.2 m
The area of the regular polygon is approximately 282.8 m²
Calculating the Perimeter and Area of a regular polygonFrom the question, we are to determine the perimeter and area of the given polygon.
The given polygon is an octagon.
Consider the right triangle drawn in the octagon. The length of a side of the regular octagon is twice the length of the base of the right triangle.
Let the base of the right triangle be b.
In the triangle, the measure of the angle close to the center of the octagon is 22.5° (That is, (360° / 2) ÷ 2).
From SOH CAH TOA,
We can write that
sin (22.5°) = b/10
b = 10 × sin (22.5)
Length of a side of the octagon = 2 × 10 × sin (22.5)
Thus,
Perimeter of the octagon = 8 × 2 × 10 × sin (22.5)
Perimeter of the octagon = 61.2293
Perimeter of the octagon ≈ 61.2 m
Area of the octagon,
Area of a regular octagon = (Perimeter × Apothem) / 2
|Apothem|² = 10² - (10 × sin (22.5))²
|Apothem|² = 100 - 14.64466
|Apothem|² = 85.35534
|Apothem| = √85.35534
|Apothem| = 9.2388
Thus,
Area of the octagon = (61.2293 × 9.2388) / 2
Area of the octagon = (565.68525684) / 2
Area of the octagon = 282.8426
Area of the octagon ≈ 282.8 m²
Hence,
The area is 282.8 m²
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Several months ago while shopping, I was interviewed to see whether or not I'd be interested in signing up for a subscription to a yoga app, I fall into the
category of people who have a membership at a local gym, and guessed that, like me, many people in that category would not be interested in the app. My
friend Rachel falls in the category of people who do not have a membership at a local gym, and I was thinking that she might like a subscription to the app.
After being interviewed, I looked at the interviewer's results. Of the 99 people in my market category who had been interviewed, 19 said they would buy a
subscription, and of the 107 people in Rachel's market category, 24 said they would buy a subscription.
Assuming that these data came from independent, random samples, can we conclude, at the 0.01 level of significance, that the proportion p, of all mall
shoppers in my market category who would buy a subscription is less than the proportion P₂ of all mall shoppers in Rachel's market category who would a
subscription?
Perform a one-talled test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of
formulas.)
(a) State the null.hypothesis H, and the alternative hypothesis ₁.
H. :D
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
0
(d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.)
0
(e) Can we conclude that the proportion of mall shoppers in my market category who would buy a
subscription is less than the proportion in Rachel's market category who would?
OYes ONO
(a) The Null Hypothesis (H₀): The proportion of mall shoppers in my market category who would buy a subscription is greater than or equal to the proportion in Rachel's market category (P₂). Conversely, Alternatvie Hypothesis H₁ insinuates that this proportion is less.
How to explain the hypothesis(b) In order to evaluate the legitimacy of these speculations; we have decided to employ the z-test statistic.
(c) In order to determine the test statistic: we will use the formula:
z = (p₁ - p₂) / √(p(1-p)(1/n₁ + 1/n₂))
where p = (x₁ + x₂) / (n₁ + n₂), where x₁ and x₂ denote the number of successes (or people who said they would purchase a subscription) in each sample, whereas n₁ and n₂ represent the sample sizes, respectively.
According to our data, we received the following: x₁ = 19, n₁ = 99, x₂ = 24, and n₂ = 107. Taking into consideration the aforementioned variables, we obtained p₁= 0.191, p₂= 0.224, and P = 0.208 for the equation above. Therefore,
z= (0.191 - 0.224)/√(0.208(1-0.208)(1/99+1/107)) ≈ -1.238
(rounded to three decimal places).
(d) For the single tailed test at 0.01 level of significance, the critical value generated by the z-test was -2.33.
(e) As a result of the calculated test statistic(-1.238) being greater than the produced critical value (-2.33); we cannot refute the null hypothesis. In other words, with an alpha of 0.01, we cannot conclude that the ratio of mall buyers in my market sector wanting to buy a subscription is less than that of the ones from Rachel's.
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Use the Remainder Theorem to find the remainder when P(x) = 5x^4+5x^3 - 2x^2 - 5x + 3 is
divided by x -5
Show your work
Therefore, the remainder when P(x) is divided by x - 5 is 3128.
What is Remainder Theorem?The algebraic Remainder Theorem asserts that when a polynomial P(x) is divided by x-a, the division's remainder equals P(a). In other words, we can replace a for x in the polynomial and evaluate it if we have a polynomial P(x) and we want to know the remainder after it is divided by x-a. The remainder of the division will be the value.
Here,
So to find the remainder when P(x) is divided by x - 5, we need to evaluate P(5).
P(x) = 5x⁴ + 5x³ - 2x² - 5x + 3
P(5) = 5(5)⁴ + 5(5)³ - 2(5)² - 5(5) + 3
P(5) = 3128
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Help out with this pls o
The value {( p ∧ q¹ ) → r¹ } is said to be a form of expression that is seen as a logical formula and it is then written in propositional logic made up of logical operators.
What are the logical operators?The logical operators are seen as "and" (∧), "not" and (→).
Note that the terms:
p: is one that denote the proposition or variable standing for a statement.q¹: Is seen as a proposition or variable standing for a statement that is said to be negated (e.g. "not q").∧: It is the Logical "and" operator, standing for conjunction.r¹: is seen as a proposition or variable standing for a statement that is said to be negated (e.g. "not r").Therefore, the full formula {( p ∧ q¹ ) → r¹ } can then be said to be or read as "if (p and not q) is true, then not r is said to be true".
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See text below
{( p ∧ q¹ ) → r¹ }
Write an equation in slope intercept form for the line parallel to y=-3x-4 and containing the point (-2,5)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-3}x-4\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -3 and it passes through (-2 , 5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y -5 = - 3 ( x +2) \\\\\\ y-5=-3x-6\implies {\Large \begin{array}{llll} y=-3x-1 \end{array}}[/tex]
How many ways are there to arrange the letters in the word GRIFFIN?
Step-by-step explanation:
There are 720 ways to arrange the letters in the word GRIFFIN.
To see why, we can use the formula for permutations of a set with n elements, which is n! (n factorial).
The word GRIFFIN has 7 letters, so we have:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
However, since the letters in GRIFFIN are not all unique (there are 2 Fs and 2 Is), we need to divide by the number of ways the repeated letters can be arranged. This is the product of their factorials:
2! x 2! = 4
So the final answer is:
7! / (2! x 2!) = 5040 / 4 = 720
Examples of different arrangements of the letters in GRIFFIN are:
- FIGRINF
- IRGIFNF
- NGRIFFI
- IFRIGNF
- GFRINIF
- NRIGIFF
- FFIRIGN
And so on, for a total of 720 possible arrangements.
Does this answer your question.
289,894 divided by 5
what is the measure of <T?
A. 60°
B. 100°
C. 110°
D. 125°
Answer:
The sum of angles in a quadrilateral is 360°.
75° +125° +∠T +60° = 360°
∠T = 360° -260° = 100°
Step-by-step explanation:
C = 360 - 260 = 100 The answer is definitely 100 for T as well since the figures are similar. Answer 100 = T <<<<<<<
jcherry99 avatar
R = 75 and A therefore is 75. Now you have 3 angles whose value you know: D, A, and B. These three are 60 75 and 125. (125 is the second best answer). D + A + B = 60 + 75 + 125 = 260
jcherry99 avatar
If the figures are similar, then D = 60 and U = 60
jcherry99 avatar
D is on your left and U is on your left.
(x-4 8/11) + 1 9/11= 7 3/11 solve for x pls i need big help
Answer:
The answer is 8 6/11
At what x-values do the graphs of the functions y = cos 2x and y equals 1 minus sine squared x intersect over the interval 0 less than or equals x less than or equals pi? Select all that apply.
The graphs of the functions y = cos 2x and y = 1 - sin² x intersect at x = 0 and x = π over the interval 0 ≤ x ≤ π.
Finding the intersecting points:
To find the intersection points of two functions set the two functions equal to each other, simplify the equation using trigonometric identities, and then solved for the values of x that satisfied the equation. And check the values if the given function is satisfied or not.
Here we have
The functions y = cos 2x and y = 1 - sin²x
And the interval 0 ≤ x ≤ π
To find the x-values where the graphs of the functions y = cos 2x and y = 1 - sin² x intersect over the interval 0 ≤ x ≤ π,
We need to set the two functions equal to each other and solve for x.
So, we have:
cos 2x = 1 - sin² x
Using the identity cos 2x = cos²x - sin² x, we can rewrite this as:
cos²x - sin² x = 1 - sin² x
On Simplifying, we get the:
cos² x = 1
Taking the square root of both sides, we have:
cos x = ±1
Since we're only considering the interval 0 ≤ x ≤ π,
the possible values of x are:
x = 0, π/2, π
Now, we need to check which of these values of x satisfy the original equation:
For x = 0, cos 2x = cos 0 = 1 and 1 - sin² x = 1 - sin² 0 = 1,
So they intersect at x = 0.
For x = π/2, cos 2x = cos π = -1 and 1 - sin² x = 1 - sin² (π/2) = 0,
So they don't intersect at x = π/2.
For x = π, cos 2x = cos 2π = 1 and 1 - sin² x = 1 - sin² π = 1,
So they intersect at x = π.
Therefore,
The graphs of the functions y = cos 2x and y = 1 - sin² x intersect at x = 0 and x = π over the interval 0 ≤ x ≤ π.
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Please help ASAP math question
Answer:
[tex]14000( {1.07}^{7} ) = 22480.94[/tex]
$22,480.94 > $20,400, so accepting the $14,000 prize now would be more profitable in 7 years.
2. Pretend your homeowners policy has a premium of $150, a deductible of $5,000, and
limit of $300,000. Your home suffers $170,000 in damages.
How much will your insurance pay?
Answer:
your insurance will pay $165,000 for the damages to your home. You will have to pay the remaining $5,000 as your deductible.
Step-by-step explanation:
The amount that the person get after he home suffers $170,000 in damages is $-130000.
What is deductible amount?Deductible amount is the amount which is paid by one in the starting of any policy.
The homeowner’s policy has a premium of $150. Thus, the amount paid in a year is,
[tex]150\times12=1800[/tex]
The home suffers $170,000 in damages and the deductible is of $5000. Thus, the amount remain is,
[tex]\text{A}=170000-5000[/tex]
[tex]\text{A}=165000[/tex]
The limit of the policy is $300000. Thus, the amount will be remained as,
[tex]\text{A}=165000-300000[/tex]
[tex]\text{A}=-135000[/tex]
If we include the deductible amount, then,
[tex]\text{A}=-135000+5000[/tex]
[tex]\text{A}=-130000[/tex]
This amount does not include the premium paid by the homeowner. Hence the amount that the person get after he home suffers $170,000 in damages is $-130000.
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There are 50 houses in my neighborhood.
5 of the houses are one-story
1
of the houses are two-story
The rest of the houses are three-story
A.3 houses
B.5
C.10
D.15
E.18
The answer is 44 houses, none of the given options match the number of three-story houses.
How to find the number of three-story housesTo find the number of three-story houses in the neighborhood, we need to subtract the number of one-story and two-story houses from the total number of houses:
50 - 5 - 1 = 44
So there are 44 three-story houses.
Therefore, the answer is 44 houses. None of the given options match the number of three-story houses.
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Joey wants to make enough fruit salad for 30 servings.
How should Joey adjust the recipe to find the total amounts of sugar, juice, and fruit needed for 30 servings? Explain your answer. What is the total amount of sugar, the total amount of juice, and the total amount of fruit needed for 30 servings? Show your work.
The total number of cups for sugar, juice and fruits are:
5cups of sugar
10 cups of juice
20 of fruits
How to solve Algebra Word problems?To adjust the recipe for 30 servings, Joey needs to use proportional reasoning. If the original recipe serves 6, and Joey wants to make 30 servings, he needs to multiply the amount of each ingredient by 5.
Let's say the original recipe requires 1 cup of sugar, 2 cups of juice, and 4 cups of fruit. To find the total amount of each ingredient needed for 30 servings, we need to multiply each ingredient by 5:
1 cup of sugar x 5 = 5 cups of sugar
2 cups of juice x 5 = 10 cups of juice
4 cups of fruit x 5 = 20 cups of fruit
Therefore, Joey needs 5 cups of sugar, 10 cups of juice, and 20 cups of fruit to make fruit salad for 30 servings.
Let's verify the calculations, we can use the ratio of the ingredients to the total number of servings:
1 cup of sugar : 2 cups of juice : 4 cups of fruit
For 6 servings, the ratio is:
1 cup of sugar x 1 : 2 cups of juice x 1 : 4 cups of fruit x 1 = 1:2:4
For 30 servings, the ratio becomes:
1 cup of sugar x 5 : 2 cups of juice x 5 : 4 cups of fruit x 5 = 5:10:20
Thus, we can see that the ratio is still the same, indicating that the adjusted recipe is correct.
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Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, p, σ) for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 48° F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.
Question 6 options:
H0 : μ ≠ 48°
H1 : μ = 48°
H0 : μ ≤ 48°
H1 : μ > 48°
H0 : μ ≥ 48°
H1 : μ < 48°
H0 : μ = 48°
H1 : μ ≠ 48°
The correct null hypothesis for this question is H0 : μ = 48° and H1 : μ ≠ 48°
What is null hypothesis ?
In statistical hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between a specified population parameter (such as μ) and a hypothesized value (such as 48° F in this case).
The alternative hypothesis (H1), on the other hand, is a statement that there is a significant difference between the population parameter and the hypothesized value. For this particular scenario, the null hypothesis is H0 : μ = 48° F, which means that the refrigerators are maintaining the true mean temperature of 48° F as they are supposed to. The alternative hypothesis is H1 : μ ≠ 48° F, which means that the refrigerators are not maintaining the true mean temperature of 48° F, as claimed by the owner of the brewery.
To test these hypotheses, a sample of refrigerator systems can be taken and their mean temperature can be calculated. If the sample mean is significantly different from 48° F, then the null hypothesis can be rejected in favor of the alternative hypothesis, indicating that the refrigerators are not maintaining the desired temperature.
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DO THE MATH: Groceries Galore is offering baby formula at the sale price of
$12.00 per can, a discount from the regular price of $20.00 per can.
How much is the percentage discount on this sale?
60%
6%
40%
4%
A projectile is launched from ground level with an initial velocity of
v0
feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by
s=−16t2+v0t.
Find the time(s) that the projectile will (a) reach a height of
80
ft and (b) return to the ground when
v0
is
32
feet per second.
Question content area bottom
Part 1
(a) Find the time(s) that the projectile will reach a height of
80
ft when
v0=32
feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The time(s) that the projectile to reach a height of 80 ft is 3.5 s and time to return to the ground is 1.5 seconds.
What is the time when the projectile reaches the height?
The equation of motion of the projectile is given as;
s = -16t² + v₀t
where;
t is the time of motionv₀ is the initial velocity = 32 ft/ss is the height reachedwhen the height reached = 80 ft, the time of motion is calculated as;
-80 = -16t² + 32t
16t² - 32t - 80 = 0
t = 3.5 seconds or t = -1.5 seconds
Based on the negative sing, we can conclude that the time to return to the ground is 1.5 seconds.
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The table represents a linear relationship between the number of hours a computer repair takes and the total cost of the repair. What is the
slope of the line?
Hours, x
3
5
7
Total Cost, y
320
470
620
Need help with that. thanks
For the estimated regression equation,
1. SST = 1946 SSR = 1602.747 SSE = 343.256
2. coefficient of determination r² = 0.824
3. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. Option D
How do you solve for SST, SSR, and SSE looking at the estimated regression equation?Looking at the estimated regression equation, Start by getting the Predicted Scores, which are;
21.257525 + 0.327425 x 180 = 80.194025
21.257525 + 0.327425 x 150 = 70.371275
21.257525 + 0.327425 x 95 = 52.3629
21.257525 + 0.327425 x 70 = 44.177275
21.257525 + 0.327425 x 70 = 44.177275
21.257525 + 0.327425 x 35 = 32.7174
Step 2, find mean
Mean = (74 + 73 + 59 + 56 + 38 + 24) / 6 = 54
SST = Σ(yi - y_mean)²
SST = (74 - 54)² + (73 - 54)² + (59 - 54)² + (56 - 54)² + (38 - 54)² + (24 - 54)² =1946
SSR = Σ(yi_predicted - y_mean)²
SSR = (80.194025 - 54)² + (70.371275 - 54)² + (52.3629 - 54)² + (44.177275 - 54)² + (44.177275 - 54)² + (32.7174 - 54)² = 1602.74660285
SSE = Σ(yi - yi_predicted)²
(74 - 80.194025)² + (73 - 70.371275)² + (59 - 52.3629)² + (56 - 44.177275)² + (38 - 44.177275)² + (24 - 32.7174)² = 343.255852847
r² = SSR / SST = 1602.747/1946 = 0.82361099691
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If the volume of the cylinder is 90 cm3, what is the volume of the cone?
Answer:
Give that the volume of the cylinder is 90cm³, the volume of the cone is (1/3)*90cm³ =30cm³
In the figures below, none of the angles are right angles. In which figure is <1 congruent to <2
The figure in which ∠1 is congruent to <2 is figure 2.
What is the vertical angles theorem?In Mathematics and Geometry, the vertical angles theorem is sometimes referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
By applying the vertical angles theorem to geometric figure 2, we have the following congruent angles:
m∠1 = m∠2 (same side interior and exterior angles are congruent).
In this context, we can reasonably infer and logically deduce that angle 1 is congruent to angle 2 in geometric figure 2 only.
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A new drug is released to market and it has been determined that the drug is responsible for causing hypertension among those individuals who take the drug. If 30,276 individuals were prescribed the drug in its first year on the market and 17,620 individuals developed hypertension, what is the point prevalence of hypertension among those individuals prescribed the drug, after the drug's first year on the market?
The point prevalence of hypertension among those individuals prescribed the drug is 0.58200
How to solvePoint prevalence of hypertension among those individuals prescribed the drug
=17620/30276
=0.58200
Option C is correct(0.58200)
The percentage of a population that is afflicted by a specific illness or condition at a particular period is known as point prevalence.
To find out how a disease or condition affects a community, this method is used by epidemiological studies.
For instance, the point prevalence of diabetes in a group would be 5% if studies showed that at a given moment, 5 out of 100 people in that population had the ailment.
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Choose the missing step in the given solution to the inequality −2x − 14 > −4 + 3x.
−2x − 14 > −4 + 3x
−5x − 14 > −4
_______________
x < −2
−5x < 10
−5x > −28
x < 2
−5x > 10
The missing step is −5x > −28. This is obtained by adding 14 to both sides of the inequality. Then, to get x < −2, we divide both sides by −5 and reverse the direction of the inequality sign.
NO LINKS!!! URGENT HELP PLEASE!!!
Consider the following
θ = 1.4, d= 160 cm
a. Find the length of the arc that subtends the given central angle θ on a circle of diameter d. _________ cm
b. Find the area of the sector determined by θ. _________ cm^2
Answer:
a) 112 cm
b) 4480 cm²
Step-by-step explanation:
Given:
θ = 1.4 radiansd = 160 cmThe diameter of a circle is twice its radius. Therefore, the radius of the circle is:
[tex]\implies r=\dfrac{d}{2}=\dfrac{160}{2}=80\; \sf cm[/tex]
Part (a)To find the length of the arc that subtends the given central angle θ on a circle of diameter d, use the arc length formula.
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the values into the formula:
[tex]\begin{aligned}\implies \sf Arc\; length&=r \theta\\&=80 \cdot 1.4\\&=112\; \sf cm\end{aligned}[/tex]
Therefore, the length of the arc that subtends the given central angle θ on a circle of diameter d is 112 cm.
Part (b)To calculate the area of the sector determined by θ, we can use the area of a sector formula.
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the values into the formula:
[tex]\begin{aligned}\implies \sf Area\;of\;a\;sector&=\dfrac{1}{2}r^2\theta\\\\&=\dfrac{1}{2} \cdot 80^2 \cdot 1.4\\\\&=\dfrac{1}{2} \cdot 6400 \cdot 1.4\\\\&=3200 \cdot 1.4\\\\&=4480\; \sf cm^2\end{aligned}[/tex]
Therefore, the area of the sector determined by θ is 4480 cm².
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 82.5% of their carbon-14. How old were the bones at the time they were discovered?
The bones were approximately 19,070 years old at the time they were discovered.
What is the formula for exponential decay?We can involve the recipe for remarkable rot to take care of this issue, which relates the underlying measure of a substance to the sum staying after a specific time has passed:
[tex]N = N_{0} * e^{-kt}[/tex]
where N is the amount remaining after time t, N₀ is the initial amount, k is the decay constant, and e is the mathematical constant approximately equal to 2.71828.
We are aware that carbon-14 has a half-life of 5750 years, which indicates that half of the initial amount will have decomposed within 5750 years. As a result, the following equation can be used to determine the decay constant:
log(2)/t(1/2) = k
where ln(2) is the natural logarithm of 2, and t(1/2) is the half-life of carbon-14 in years.
Substituting the given values, we have:
log(2)/5750 = k
k = -0.000120968
Now we can use the fact that the bones have lost 82.5% of their carbon-14 to find how much time has elapsed since they were alive. Let N₀ be the initial amount of carbon-14, and let N be the amount remaining, which is 17.5% of N₀:
N = 0.175*N₀
We can use the formula for exponential decay to relate N to N₀:
[tex]N = N_{0} *[/tex] [tex]e^{-kt}[/tex]
Substituting the given values, we have:
[tex]0.175*N_{0} = N_{0}[/tex] * [tex]e^{-0.000120968t}[/tex]
Dividing both sides by N₀, we get:
[tex]0.175 = e^{-0.000120968t}[/tex]
Taking the natural logarithm of both sides, we get:
log(0.175) = -0.000120968t
Solving for t, we have:
t = log(0.175)/(-0.000120968) = 19,070.27 years
Therefore, the bones were approximately 19,070 years old at the time they were discovered.
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Wirte the sum using sigma notation:
1
1
+
1-2
2-3
A =
B =
+
1
3.4
+ +
...
1
117 118
=
n=1
B, where
The sigma notation of the sum for this problem has the parameters given as follows:
A = 117.B = 1/[n(n + 1)]How to write the sigma notation of the sum for this problem?To write the sigma notation for the sum in this problem, we must identify the pattern in the sum.
We have that in each term, a numerator of 1 is divided by the index n multiplied by one plus the index, hence the parameter B is given as follows:
B = 1/[n(n + 1)]
The last terms are 117 and 118, meaning that n = 117, hence the parameter A, representing the upper end of the sum, is given as follows:
A = 117.
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Write an expression to represent:
1 less than the quotient of 4 and x
Answer:
(4/x) - 1 is the way to represent this equation.
State how many real solutions each equation has. x^2 = –100 5x^2 = 1 6x^2 + 17 = 11 7(x^2 + 6) = 42
I need help on this question
The correct option is the third one, it can be written as the equation:
y = A*(1 - 0.073)ˣ
Which one represents an exponential decay?A general exponential decay can be written as:
y = A*(b)ˣ
Where A is the initial value, and b is the base.
It is an exponential decay only if 0 < b < 1.
From the given options, the one that can be modeled with an exponential decay is a car whose price depreciuates at a rate of 7.3% per year, because if the initial price of the car is A, we can write it as:
y = A*(1 - 0.073)ˣ
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Below are various statements about different budgeting techniques. Which are false? Select one or more: A. Budget ratcheting tightens targets when performance fails to meet the target by a predetermined percentage B. Budget lapsing prevents managers from hoarding funds C. Master(static) budgets are prepared for a single level of activity D. Budget lapsing encourages managers to spend money regardless of cost or value E. none of the answers is correct
Answer:
PQRS is a rhombus with S2 =35° calculate the size of all interior angles
