The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4. Is the
triangle acute or obtuse?
Justify your answer.
A.) Acute; the measure of the interior angle must be 144º.
B.)Acute; the measure of the interior angle must be 36°.
C.)Obtuse; the measure of the interior angle must be 144º
D.)The triangle could be acute or obtuse, depending on the measures of the other two angles.
Simplify the expression 4 to the power of 3 + 2(3 − 2).
Find a formula for RN for the function f(x) = (5x)² on [-1, 5] in terms of N.
Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.
Compute the area under the graph as a limit.
lim RN=1050
Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).
What is function?Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.
Here,
In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.
The given function is f(x)=(5x)^2 on [1, 5].
Ax = (5-1)/N
Ax = 4/N
X = 1+iAx
X = 1+i4/N
f(x) = 25X^2
f(x) = 25(1+i4/N)^2
f(x) = 25(1+i8/N+16/N^2 i^{2})
R(N) = 1ƒ(X) Ax
Now putting the value of f(x) and Ax
R(N)==1 [25 (1+ &i + 16i2)]
R(N) = 1001 (1 +Ni + 16i2)
N100 (1+i+12)N
100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)
R(N)=100 (N + √2/ N(N+1) x 100
R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2
[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3
[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67
[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)
Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).
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Employee B got a one time bonus of $90. He makes $13 an hour. If he was paid $415, how
many hours did he work?
Answer:
y=mx+b format... 8th grade math class memories...ahhh
Step-by-step explanation:
Employee B-
one time bonus of 90 gets plugged into the b spot
13 an hour goes into the m space
415 total paid goes into the y spot
415=13(x)+90
subtract 90 from 415 and 90
325=13(x)
divide 325 by 13 and 13
25=(x)
Now plug x into the y=mx+b format with all your other numbers to check
y=13(25)+90
y=415!!
Hope this wasn't too confusing, good luck!
Select the correct answer.
Which function has an inverse function?
Answer:
d
Step-by-step explanation:
so the first part is multiplication and the second part is division bc it's a fraction hope this helps <3
Pls help me, if you get it right I will give you Brainlist!
Answer:
Step-by-step explanation:
3.14x (3)^2
28.3ft
Answer:
The area of the circle is 28.3 [tex]ft^2[/tex].
Step-by-step explanation:
The formula to find the area of a circle is [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]3.14 * 3^2 = 3.14 * 9 = 28.26[/tex] ≈ 28.3 [tex]ft^2[/tex].
Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = mx + c
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\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}{7}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{ 1 }{ 2 }x+1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x+8 \end{array}}[/tex]
James bought a movie ticket
and popcorn for $12.20. The movie ticket cost $8.45.
Use the equation c + $8.45 = $12.20 to find which size
popcorn James bought. How much change did James get
if he paid with a $20 bill?
If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).
What is change?Change is a natural part of life. It is the process of making or becoming different, and can happen in an instant or over a long period of time. Change may refer to a transformation in a person’s life, such as a career switch, a change in lifestyle, or growth in maturity. It can also refer to a shift in the environment, such as a change in the weather, a demographic shift, or a dramatic event.
The equation c + $8.45 = $12.20 can be rewritten as c = $12.20 - $8.45. Solving this equation yields c = $3.75. This means James bought a popcorn for $3.75.
If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).
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pls help i’ve been stuck on this question ‼️
30. Find the distance travelled by an object in 35.0 seconds, it it has a constant
speed of 24.0m/s.
A: 1.46 meters
C. 840 seconds
B. 840 m/s
D. 840 meters
Answer:
D is correct option 840 meters
Step-by-step explanation:
S=vt
S= (24)(35)
S= 840 meters
The probability of raining on Saturday is 0.09. If today is Saturday, then find the
probability of raining today.
A. 0.63
B.0.49
C.0.37
D.1
Answer:
I Think it is A
Step-by-step explanation:
It is a because 9×7=63
The probability of raining today is equal to the probability of raining on Saturday, which is 0.09.
To find the probability of raining today, given that today is Saturday and the probability of raining on Saturday is 0.09, we can use conditional probability.
The conditional probability of an event A occurring, given that event B has already occurred, is denoted as P(A|B) and is calculated as follows:
P(A|B) = P(A ∩ B) / P(B)
In this case, event A represents the event of raining today, and event B represents the event of it being Saturday.
We are given that P(B) = 0.09 (the probability of raining on Saturday). Since today is Saturday, we know that event B has occurred.
Now, let's assume that event A and event B are independent. This means that the probability of raining today (event A) is not affected by whether it is Saturday (event B) or not.
Under the assumption of independence, we can say that P(A ∩ B) = P(A) * P(B).
Given that P(B) = 0.09, we can substitute these values into the conditional probability formula:
P(A|B) = (P(A) * P(B)) / P(B)
= P(A)
Therefore, the probability of raining today is equal to the probability of raining on Saturday, which is 0.09.
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WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
The number of atoms that are there in 400 grams of hydrogen will be 2.408 × 10^26.
How to illustrate the scientific notation?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.
In this case, there are 6.02 × 10^23 atoms in 1 gram of hydrogen.
The number of atoms that are there in 400 grams of hydrogen will be:
= 6.02 × 10^23 × 400
= 2408 × 10^23
= 2.408 × 10^3 × 10^23
= 2.408 × 10^26
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The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density in terms of pounds per cubic foot is 101.2 pounds/ft³
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039
= 101.2
Hence, The density in terms of pounds per cubic foot is 101.2 pounds/ft³
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In a school orchestra, the ratio of girls
to boys is 3:2. There are 36 girls in the
orchestra. How many boys are in the
orchestra?
Answer:
54 boys
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
the ratio 3/2 means 1.5 so we divide 36 over 1.5 we get 24…
to make sure we 36/24= 3/2=2.5
Select all the relations which represent a function.
- (1,3), (2,5), (2,7), (4,9) (1,3), (1,5), (1,7), (4,9) 0 (1,2), (2,5), (2,1), (4,5)
(1,3), (2,5), (3,7), (4,9) (1,3), (2,3), (3,3), (4,3)
Therefore , (1, 3), (2, 5), (3, 7) (4, 9) and (1, 3), (2, 3), (3, 3) (4, 3) are the relations that represent a function.
Function is what?According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.
Here,
The relationship is (1, 3), (2, 5), and (2, 7) (4, 9)
Given that 2 is repeated, the connection is not a function.
The relationship is (1, 3), (2, 5), and (3, 7) (4, 9)
Since there are no repeating numbers, the relation is a function.
The relationship stated is (1, 3), (1, 5), and (1, 7). (4, 9)
The relationship is not a 1 repeated function.
The relationships are (1, 3), (2, 3), and (3, 3). (4, 3)
Since there are no repeating numbers, the relation is a function.
The relationship stated is (1, 2), (2, 5), and (2, 1) (4, 5)
As 2 repeated, the relationship is not a function.
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In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=15°, and JH = 54 feet. Find the length of HI to the nearest tenth of a foot
Answer:
46
Step-by-step explanation:
The spring sale at a local store advertises one price for all items in a particular department. You buy 5 small pots and q packages of seeds for 3 dollars each. An expression for the total cost of your purchases is 3(5+q). Use the Distributive Property to write an expression equivalent to 3(5+q).
Answer:
3*(5 + q) = 15 + 3*q
Step-by-step explanation:
The distributive property is:
A*(B + C) = A*B + A*C
We know that you buy 5 small pots and q packages of seeds for $3 each.
And we know that the equation that models the cost is:
3*(5 + q)
Now we can simply apply the distributive property to rewrite this expression as:
3*(5 + q) = 3*5 + 3*q = 15 + 3*q
So the equivalent expression is: 15 + 3*q
A couch and coffee table cost a total of $1172. The cost of the couch is three times the cost of the coffee table. Find the cost of each item.
Answer:
x + 3x = 1172, where x is the cost of the coffee table and 3x equals the cost of the couch.
4x = 1172
x = 293
thus, 3x = 293
293 x 3= 879
The couch is $879 and the coffee table is $293
Which BEST DESCRIBES 3y + 2x + 18?
A)
3y + 2x + 18 is an equation because values can be substituted for x and y.
B)
3y + 2x + 18 is not an expression because both x and y are variables,
C)
3y + 2x + 18 is an expression because it cannot be solved
D)
3y + 2x + 18 is an equation because there are 3 terms
Answer:
C)is an expression because it cannot be solved
HELP ASAP I WILL MARK BRAINLIST!!!!
Find the volume of the following
square pyramid.
10 cm
12 cm
V = [?] cm3
Answer:
The volume is 384 cm^2.
Step-by-step explanation:
The equation for a pyramid is the base area times the height divided by 3, so [tex]a^2h/3[/tex]. In this case, we know the side length but we do not know the height. We can use the Pythagorean Theorem to get:
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 64
b = 8
Therefore, our height is 8. Plug this into the equation to get:
12^2 (8) / 3
144 (8) / 3
1152 / 3
384
Randy worked 4 2/9 hours on Sunday. If he
worked a total of 10 1/3 hours on Saturday
and Sunday, how many hours did he work
on Saturday?
Answer:
6 1/9 hours
Step-by-step explanation:
10 3/9 - 4 2/9 = 6 1/9
(25 points)
What is the value of k?
Please explain your answer
Answer:
que?
Step-by-step explanation:
Alisa needs 4.65 feet of fencing to
complete the fence she is building.
She has a piece of fencing that is 4 ft
long. Does she have enough fencing?
Explain.
No Alisa do not have enough fence.
What is perimeter?The perimeter of an object is given by adding the side lengths of the object.
Given that Alisa needs 4.65 feet of fencing to complete the fence she is building. She has a piece of fencing that is 4 ft long.
We need to determine whether she have enough fencing or not,
Since we know that the fencing can be considered as perimeter of the building,
So, if she only has 4 ft long fence, she cannot cover a 4.65 ft long fence.
Hence Alisa do not have enough fence.
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PLEASE HELP ME PLEASE I NEED IT RN
Answer:
A. -9/2
Step-by-step explanation:
Rate of change of y in respect to x = change in y/change in x
Using two pairs of values, say (-6, 33) and (-2, 15),
Rate of change = (15 - 33)/(-2 - (-6))
Rate of Change = -18/4
Simplify
Rate of change = -9/2
Help fast please !!!!!
Answer:
Step-by-step explanation: reduce mean divide so 400 divided by 4 =28
Jordins dog eats 3/4 bag of dog food in 1 month how many bags of dog food does Jordan dog eat in 6 months
This probability distribution shows the typical grade distribution for a Geometry course with 35 students. Frequency 5 10 15 3 2 Find the probability that a student earns a grade of B
Answer:
0.29
Step-by-step explanation:
Total number of students = 35
Number of students who got B = 10
Probability that a student earns grade B :
Probability = required outcome / Total possible outcomes
P(grade B) = 10 / 35 = 0.2875
= 0.29
A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 14 feet and a depth of 3 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest tenth.
Answer:
Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to
y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2
which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.
Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,
6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a
and
a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32
Thus we have
32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16
So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.
Can someone please help me like fast??
Answer:
a= 5
b= 9
c= -7
d= 12
Step-by-step explanation:
A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least three pounds. Eight subjects use the product for one month, and the resulting weight loss data are reported as follows.
Subject Initial Weight (lbs) Final Weight(lbs)
1 165 161
2 201 195
3 195 192
4 198 193
5 155 150
6 143 141
7 150 146
8 187 183
a) Do the data support the claim of the producer of the dietary product with the probability of Type 1 error of .05?
b) Do the data support the claim of the producer of the dietary product with the probability of Type 1 error of .01?
c) In an effort to improve sales, the producer is considering changing its claim from "at least three pounds" to "at least five pounds". Repeat parts a and b to test this new claim.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Please find the table in the attached file.
mean and standard deviation difference: [tex]\bar{d}=\frac{\Sigma d}{n} =\frac{-4-6-.......-4-4}{8}=-4.125 \\\\S_d=\sqrt{\frac{\Sigma (d-\bar{d})^2 }{n-1}}=\sqrt{\frac{(-4 + 4.125)^2 +.......+(-4 +4.125)^2 }{8-1}}= 1.246[/tex]
For point a:
hypotheses are:
[tex]H_0 : \mu_d \geq -3\\\\H_a : \mu_d < -3\\\\[/tex]
degree of freedom:
[tex]df=n-1=8-1=7[/tex]
From t table, at[tex]\alpha = 0.05[/tex], reject null hypothesis if [tex]t <-1.895[/tex].
test statistic:
[tex]t=\frac{\bar{d}-\mu_d }{\frac{s_d}{\sqrt{d}}}=\frac{ -4.125- (-3)}{\frac{1.246}{ \sqrt{8}}} =-2.55[/tex]
because the [tex]t=-2.553 <-1.895[/tex], removing the null assumption. Data promotes a food product manufacturer's assertion with a likelihood of Type 1 error of 0.05.
For point b:
From t table, at [tex]\alpha =0.01[/tex], removing the null hypothesis if [tex]t<-2.998[/tex].
because [tex]t=-2.553 >-2.908[/tex], fail to removing the null hypothesis.
The data do not help the foodstuff producer's point with the likelihood of a .01-type mistake.
For point c:
Hypotheses are:
[tex]H_0: \mu_d \geq -5\\\\H_a: \mu_d < -5[/tex]
Degree of freedom:
[tex]df=n-1=8-1=7[/tex]
From t table, at [tex]\alpha =0.05[/tex], removing the null hypothesis if [tex]t <-1.895[/tex].
test statistic: [tex]t=\frac{\bar{d}-\mu_d}{\frac{s_d}{\sqrt{n}}} =\frac{-4.125-(-5)}{\frac{1.246}{\sqrt{8}}}=1.986[/tex]
Since [tex]t-1.986 >-1.895[/tex], The null hypothesis fails to reject. The results do not support the packaged food producer's claim with a Type 1 error probability of 0,05.
From t table, at[tex]\alpha= 0.01[/tex], reject null hypothesis if[tex]t<-2.998[/tex].
Since [tex]t=1.986>-2.998[/tex] , fail to reject null hypothesis.
Data do not support the claim of the producer of the dietary product with the probability of Type 1 error of .01.