Answer:
85°
Step-by-step explanation:
So in geometry, the formula to find the sum of all interior angles is denoted as follows:
n = number of sides in the polygon
( n - 2 ) × 180° = sum of the interior angles
Using that formula, a triangle has 3 sides, so
n = 3 , therefore:
= ( 3 - 2 ) × 180°
= 1 × 180°
= 180°
Since the total sum of the interior angles of a triangle all have to add up to 180°, you can create the following equation and solve:
34° + 61° + x = 180°
Solve for x.
Find the 6terms of the series 247
The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.
To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.
Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.
The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.
Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.
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The distances, in light years, of four stars from a space probe are shown. Put the stars in order from the closest one (least distance) to the farthest one (greatest distance). 0.886 0.883 1.25 0.89
A.
0.883, 0.886, 0.89, 1.25
B.
0.883, 0.886, 1.25, 0.89
C.
1.25, 0.89, 0.886, 0.883
D.
0.886, 0.883, 0.89, 1.25
The stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.
That means we need to start with the smallest value and move toward the largest value.
Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.
Putting the given distances in ascending order, we get:
0.883, 0.886, 0.89, 1.25
Therefore, the stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
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tell whether you will add, subtract or multiply the exponents. Then simpilfy by finding the value of the expression (3^2)^3
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression (3²)³ is 729.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the given expression can be simplified as shown below. Therefore, the value of the expression is,
(3²)³
= \(3^{2 \times 3}\)
= 3⁶
= 3× 3 × 3 ×3 × 3 × 3
= 729
Hence, the value of the expression is 729.
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help me I'm lost on this unit.
Answer:
degree 3
Step-by-step explanation:
Note that
(- 3)³ + 4 = - 27 + 4 = - 23
(- 2)³ + 4 = - 8 + 4 = - 4
0³ + 4 = 0 + 4 = 4
1³ + 4 = 1 + 4 = 5
2³ + 4 = 8 + 4 = 12
3³ + 4 = 27 + 4 = 31
Then
f(x) = x³ + 4 ← a polynomial of degree 3
Find the value of x in the isosceles triangle shown below.
V13
/13
2
Answer:
x = 6Step-by-step explanation:
use Pythagorean theorem:
a² + b² = c²
where a = 2
b = x/2
c = √13
plugin values into the formula:
2² + (x/2)² = (√13)²
4² + x² = 13
4
16 + x² = 13 (4)
x² = 52 - 16
x = √36
x = 6
Answer:
x=6
Step-by-step explanation:
khan is never wrong yall
Write the percent as a fraction or mixed number in simplest form.
150%
Answer:
3/2 or 1 1/2
Step-by-step explanation:
what is the volume of a sphere with a radius of "60.5" Ft, Rounded to the nearest tenth of a cubic foot?
Answer:
\(volume = 927,587.2ft^3\)
Step-by-step explanation:
The equation to find the volume of a sphere is as follows:
\(volume = \frac{4}{3}\pi r^3\)
We have a radius of 60.5ft, let's plug this into the equation and solve:
\(volume = \frac{4}{3} \pi (60.5)^3 \\volume = 927,587.17\\volume = 927,587.2\)
Therefore, the volume of a sphere with a radius of 60.5ft is 927,587.2ft^3.
Hope this helps!!
- Kay :)
Volume of the sphere is 927587.2 cubic feet (nearest tenth).
What is Volume of the sphere?"A sphere is a set of points in space that are a given distance r from the center. The volume of a 3 -dimensional solid is the amount of space it occupies."
Formula to find the volume of a sphere
Volume of the sphere = \(\frac{4}{3} \pi r^{3}\)
V = \(\frac{4}{3} \pi (60.5)^{3}\)
V = 927,587.167
Using calculator, we get
V ≅ 927587.2 cubic feet
Hence, Volume of the sphere is 927587.2 cubic feet (nearest tenth).
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dos hombres recorren 10km partiendo desde un mismo cruce y siguiendo dos caminos rectos en el mismo sentido que forman 30° entre ellos. ¿A que distancia en linea recta se encontraran uno del otro al terminar la caminata?
Therefore, the two men will be 5 km apart from each other in a straight line at the end of the walk.
Two men walk 10 km starting from the same intersection and following two straight paths in the same direction, forming a 30° angle between them. How far apart will they be from each other in a straight line at the end of the walk?
To solve this problem, we can use trigonometry. Let's consider the triangle formed by the starting point, the point where they meet, and the endpoint of the walk. In this triangle, we have a known side length of 10 km and an angle of 30°.
Using trigonometric functions, we can find the length of the side opposite the 30° angle. The sine function is appropriate for this calculation:
sin(30°) = opposite / hypotenuse
sin(30°) = opposite / 10 km
opposite = sin(30°) * 10 km
opposite = 0.5 * 10 km
opposite = 5 km
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Find the solution for the equation. 3 (n - 4) = -12
Answer:
0
Step-by-step explanation:
3n-12=-12
-3n=-0
n=0
Answer:
n=0.0
Step-by-step explanation:
3(n-4) = -12
3n-12 = -12
3n = 0
n = 0
In a survey of 259 professional athletes, it was found that 110 of them owned a convertible, 91 of
them owned a giant screen TV, and 120 owned a sporting goods store. 15 owned a convertible and a
store, 43 owned a TV and a store, and 44 owned a covertible and a TV. 9 owned all three items.
1. How many athletes did not own any of the three items?
2. How many owned a covertible and a TV, but not a store?
3. How many athletes owned a convertible or a TV?
4. How many athletes owned exactly one type of item in the survey?
5. How many athletes owned at least one type of item in the survey?
6. How many owned a TV or a store, but not a convertible?
1. Number of athletes did not own any of the three items = 259 - 228
= 31.
2. Number of athletes own a convertible and a TV but not a store = 44 - 9
= 35.
3. Number of athletes own a convertible or a TV = 110 + 91 - 44
= 157.
4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
5. Number of athletes owned at least one type of item = 259 - 31
= 228
6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71
= 118.
The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.
Total number of athletes surveyed = 259
Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228
Number of athletes who did not own any of the three items = 259 - 228 = 31.
The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.
Number of athletes who own a convertible and a TV = 44
Number of athletes who own all three items = 9
Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35
The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.
Number of athletes who own a convertible or a TV = 110 + 91 - 44
= 157.
The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.
Number of athletes own a convertible only = 110 - 15 - 9 = 86
Number of athletes own a TV only = 91 - 44 - 9 = 38
Number of athletes own a store only = 120 - 15 - 43 - 9 = 53
Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
The number of athletes who owned at least one type of item can use the result from part (1).
Number of athletes who owned at least one type of item = 259 - 31
= 228
The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.
Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159
Number of athletes own a TV or a store not a convertible = 13 + 34 +71
= 118.
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Choose a definition for the function
The correct option for the given graph is option b) as is satisfies the criteria of the given graph
What is a function and linear equation?
A linear equation is an expression in one variable with an equal sign. A function is an equation which satisfies for a line or a curve
We are given a graph and we are asked to find the correct function
We can see that when x< 0
And when x = -1 the value of y =0
And the function that satisfies these value is y = 2x + 2 when x<0
And this condition is present only in second option
Hence the correct option is option b)
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Sales of a new line of athletic footwear are crucial to the success of a newly formed company, Fleet Shoes. Fleet wishes to estimate the average weekly sales of the new footwear within $200 with 95% reliability. The initial sales indicate the standard deviation of the weekly sales figures to be approximately $1,500. How many weeks of data must be sampled for Fleet to get the information is desires?
Answer:
The number of weeks required = 216 weeks
Step-by-step explanation:
Given that:
Margin of Error E = 200
Confidence interval = 95% = 0.95
Level of SIgnificance = 1 - C.I
= 1 - 0.95
= 0.05
Standard deviation = 1500
The Critical value for Z :
\(Z_{\alpha/2} =Z_{0.05/2} \\ \\ = Z_{0.025} = 1.96\)
The number of weeks( i.e the sample size (n) ) required is :
\(n = (\dfrac{Z_{\alpha/2} \times \sigma}{E})^2\)
\(n = (\dfrac{1.96 \times 1500}{200})^2\)
\(n = (14.7)^2\)
n = 216.09
n ≅ 216 weeks
Order from least to greatest .9, 8/9, .86
Answer:
least to greatest
.86, 8/9, .9
Answer:
.86,8/9,9 ttttttttttttttttttftfffff
15 points
Draw a square
side 5cm
Diagonal 5cm
how will i draw it
with both 5cm
Answer:
that's easy
Step-by-step explanation:
first we should check the 5 cm in scale .
Then we can easily draw 5 cm in side and diagonal.
hope it's clear to you.
Assume that by contributing your education you increase your yearly earning potential from 21,484 to 39,746 if the additional education cost $36,000 in about many years, will a it pay for itself
Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.
To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.
The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.
To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).
Payback Period = Cost of Education / Annual Increase in Earning Potential
Payback Period = $36,000 / $18,262
The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.
If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.
In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.
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The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f
Complete question:
The amount of garbage, G produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f
Answer:
The information of town Tola can be represented in function as 6 = f(45)
Step-by-step explanation:
Given;
population of Tola, p = 45,000
amount of garbage produced in tons per week, G = 6 tons = 6,000 kg
The function is given by;
G = f(p)
where;
G is the amount of garbage produced in tons per week
p is the population of Tola
Substitute in the given values into the function
6000 = f(45,000)
6 = f(45)
Therefore, the information of town Tola can be represented in function as 6 = f(45)
The slope of the line below is 1.5. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(4,3)
Answer:
\( y - 3 = 1.5(x - 4) \)
Step-by-step explanation:
Given:
Slope = m = 1.5
Coordinates of labelled point = (a, b) = (4, 3)
Point-slope equation takes the form of \( y - b = m(x - a) \).
Therefore, to write the equation, substitute a = 4, b = 3 and m = 1.5 into \( y - b = m(x - a) \).
Thus:
\( y - 3 = 1.5(x - 4) \)
A clothing salesperson earns a 10% commission on a $65
sale. How much is the commission?
Each of 184 guests at a Sunday brunch will be served ½ pound of peeled, diced cantaloupe. The average cantaloupe weighs 2 pounds. If cantaloupes come 12 to a case, how many cases of canta- loupe should you purchase? (For this question, round your answer up to a whole number.)
we must round up to a whole number, we need to purchase 4 cases of cantaloupe.
How to solve?
First, we need to calculate how many pounds of cantaloupe are needed in total:
184 guests ×0.5 pounds per guest = 92 pounds of cantaloupe
Next, we need to determine how many cantaloupes are needed. Since the average cantaloupe weighs 2 pounds, we can divide the total pounds of cantaloupe needed by the weight of one cantaloupe:
92 pounds of cantaloupe / 2 pounds per cantaloupe = 46 cantaloupes
Finally, we need to figure out how many cases of cantaloupe to purchase, given that they come 12 to a case:
46 cantaloupes / 12 cantaloupes per case = 3.83 cases
Since we must round up to a whole number, we need to purchase 4 cases of cantaloupe.
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she works a 35
-hour week earning $17.10
an hour.
How much does she earn in one year? (Use 52
weeks in one year.)
$
Answer:
$31122.00
Step-by-step explanation:
We know
She works 35 hours a week, earning $17.10 an hour.
17.10 x 35 = $598.50 a week
How much does she earn in one year?
We Take
598.50 x 52 = $31122.00
So, she earns $31122.00 one year.
please help me with this math question
Answer:
Step-by-step explanation:
C
Find one value of x that is a solution to the equation:
(4x + 1)^2 + 9(4x + 1) = -18
x =
Answer:
There are two solutions
1: -7/4
2: -1
Step-by-step explanation:
Hope this helps
Brain-List?
Need help with this please
Answer:
HELP WITH WHAT?
Step-by-step explanation:
I'm not understanding which statement is correct, to me they all look wrong
Answer:
it is the third option because -3.2 is greater than -5.4
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
help me please ill give brainlest
Answer:
D is the answer I think......
A pound of chocolate cost 7 dollars. Ryan buys p pounds. Write an equation to represent the total cost c that Ryan pays.
Answer:
c = 7p
Step-by-step explanation:
According to the Centers for Disease control and prevention, 20.8 of high school students currently use electronic cigarettes. A high school counselor is concerned that the use of e-cigs at her school is higher.
(a) Determine the null and alternative hypotheses.
(b) If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the school counselor.
(c) Suppose, in fact, that the proportion of students at the counselor's high school who use electronic cigarettes is 0.034. Was a Type I or Type II error committed?
Answer:
H0 : p = 0.028
H1: p > 0.028
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
Type 11 error
Step-by-step explanation:
H0 : p = 0.028
H1: p > 0.028
If null should not be rejected then;
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
3.)
If the actual proportion is 0.034, which means 3.4%, this means it is actually higher. For failing to reject a false Null, then a type 11 error has been committed
A manufacturer claims that its rechargeable batteries are good for an average of more than 1.000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at a significance level of 0.01?
a. State the hypotheses.
b. State the test statistie information
c. State either the p-value or the critical information d. State your conclusion and explain your reasoning
It's 1000 charges and not 1.000 charges
Answer:
A)Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = 1.4286
C) p-value = 0.15628
D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges
Step-by-step explanation:
We are given;
x = 1002 charges
s = 14
μ = 1000 charges
n = 100
degree of freedom = n - 1 = 100 - 1 = 99
A) The hypotheses are;
Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = (x - μ)/(s/√n)
(1002 - 1000)/(14/√100) = 1.4286
C) From the t-score calculator results attached, the p-value is approximately 0.15628
D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.
Sin θ = 12/37. Find tan θ. Right Triangle Trigonometry.
Answer:
\(\huge\boxed{B.\ \dfrac{12}{35}}\)
Step-by-step explanation:
Look at the picture.
We know:
\(\sin\theta=\dfrac{a}{c}\\\\\tan\theta=\dfrac{a}{b}\)
We have
\(\sin\theta=\dfrac{12}{37}\Rightarrow a=12,\ c=37\)
Use the Pythagorean theorem.
\(a^2+b^2=c^2\\\\12^2+b^2=37^2\\\\144+b^2=1369\qquad|\text{subtract 144 from both sides}\\\\b^2=1225\to b=\sqrt{1225}\\\\b=35\)
Calculate tangent:
\(\tan\theta=\dfrac{12}{35}\)