Jasmine wants to start saving to purchase an apartment. Her goal is to save $225,000. If she deposits $180,000 into an account that pays 3. 12% interest compounded monthly, approximately how long will it take for her money to grow to the desired amount?
The first step to solving the problem is to understand the formula for calculating interest on a compounded monthly basis.The formula for calculating compound interest on a monthly basis is as follows:
FV = P(1 + i/n)^(n * t) whereFV = future valueP = principal amounti = interest raten = number of times interest is compounded per yeart = number of years In this case:FV = 225,000 (the desired amount)P = 180,000i = 3.12% = 0.0312n = 12 (since the interest is compounded monthly)t = unknown Substituting these values into the formula, we get:225,000 = 180,000(1 + 0.0312/12)^(12t) Dividing both sides by 180,000, we get:1.25 = (1 + 0.0312/12)^(12t) Taking the natural log of both sides, we get:ln(1.25) = 12t ln(1 + 0.0312/12)Solving for t, we get:t = ln(1.25) / [12 ln(1 + 0.0312/12)]t = 7.64 years (rounded to the nearest year)Therefore, it will take approximately 8 years (rounded to the nearest year) for Jasmine's money to grow to the desired amount.
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The correct answer is 6 years. Compound interest is the interest rate applied to the principal and interest earned. it will take Jasmine approximately 6 years to save $225,000.
Essentially, it implies that interest is earned on both the principal and interest accumulated over time.
We may use the formula [tex]A=P(1+r/n)^{(nt)[/tex]
to calculate the time it will take for Jasmine's money to grow to $225,000,
where
A is the desired amount,
P is the principal amount deposited,
r is the annual interest rate,
n is the number of times interest is compounded per year, and
t is the number of years.
Here's how we'll go about it.
[tex]A=P(1+r/n)^{(nt)[/tex]
Here,
A = $225,000
P = $180,000
r = 3.12%
n = 12
t = ?
Let's plug in the numbers and solve for t.
[tex]225000=180000(1+0.0312/12)^{(12t)}[/tex]
[tex]225000/180000=(1+0.0312/12)^{(12t)[/tex]
[tex]1.25=(1.0026)^{(12t)[/tex]
Log (1.25) = Log [tex](1.0026)^{(12t)[/tex]
Log (1.25) = 12t(Log (1.0026))
t = [Log (1.25)] / [12 Log (1.0026)]
t ≈ 6 years (rounded to the nearest year)
Therefore, it will take Jasmine approximately 6 years to save $225,000.
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4.10.1 checkup, answer questions about the unit circle
Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:
a. t > w.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.
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Ed wants to buy a new video game system which costs $250. he has
saved $135. ed charges $9 for each lawn he mows. which equation could
be used to find the number of lawns, x, ed must mow to have more than
the amount he needs to buy the video game system?
The required equation is 135 + 9x > 250.
The number of lawns Ed must mow is assumed to be x.
The amount Ed charges for each lawn he mows is $9.
Thus, the total amount Ed earns by mowing x lawns = $9x.
The savings which Ed has is $135.
Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).
The cost of the video game is given to be $250.
We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.
This can be shown as the equation:
Total amount Ed has > Cost of the video game,
or, 135 + 9x > 250.
Thus, the required equation is 135 + 9x > 250.
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How much does a $5.40 lunch cost if it is discounted by 10%
Answer:
$4.86
Step-by-step explanation:
Original price: $5.40
Discount: 10%
Discount amount:
10% of $5.40 = 0.1 × $5.40 = $0.54
Discounted price:
$5.40 - $0.54 = $4.86
Answer:
$4.86
Step-by-step explanation:
There are two approaches to this problem.
1:
You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.
2:
You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.
A worker at a shoe factory is required to box at least
8
pairs of shoes per minute, but is not allowed to box more than
12
pairs of shoes per minute. According to this information, what is a possible amount of time, in minutes, that it could take the worker to box
168
pairs of shoes?
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.
For 168 pairs of shoe:
Maximum time = 168 pair / 8 pairs per minute = 21 minutes
Minimum time = 168 pair / 12 pairs per minute = 14 minutes
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
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‼️‼️PLEASE HELP I WILL MARK BRAINLIEST ‼️‼️Dilate the figure by the scale factor. Then enter
the new coordinates.
C(-2,1)
A(1,4)
B(2,2)
K = 6
A' ([?], [])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:After dialation
A'=6,24
B'=12,12
C'=-12,6
Don't forget to mark me Brainliest
If you substitute 12 2x for y in the second equation, how is the resulting equation written in standard form?
The resulting equation written in standard form is 16x² - 22x + 6 = 0.
What is equation in standard form?Quadratic Equation in Standard Form: ax² + bx + c = 0
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
The "solutions" to the Quadratic Equation are where it is equal to zero.
They are also called "roots", or sometimes "zeros"
We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)
Or we can Complete the SquareOr we can use the special Quadratic Formula:Quadratic Formula: x = [ -b (+-) √(b² - 4ac) ] / 2a, Just plug in the values of a, b and c, and do the calculations.Calculation for the given equation-
Now, y=-16x²+24x+6
Substitute, y = 12+2x in y = -16x²+24x+6.
=> 12+2x = -16x²+24x+6
=> 16x²-24x-6+12+2x = 0
=> 16x²-22x+6 = 0
Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.
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The complete question is-
The two equations are given below;
Y = 12 + 2x linear equation
Y = -16x² + 24x + 6 quadratic equation
If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?
Please help me! Giving brainliest!
Identify the surface area
A. S=2332 m²
B. S=2283 m²
C. S=2234 m²
D. S=1919 m²
Using it's formula, the surface area of the figure is:
A. S=2332 m²
What is the surface area of a rectangular prism?The surface area of a rectangular prism of dimensions l, w and h is given by:
S = 2(lw + lh + wh)
In this problem, the dimensions are:
35m, 9m, 16m
Hence the surface area of the rectangular prism is:
S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².
What is the surface area of a cube?The surface area of a cube of side length l is given by:
S = 6l².
In this problem, we have that l = 7 m, hence the surface area is:
S = 6 x 7² = 294 m².
What is the total surface area?
The total surface area is the sum of the surface areas, hence:
T = 2038 m² + 294 m² = 2332 m².
Which means that option A is correct.
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Find the probability of randomly selecting 3 red pencils from a box containing 5 red, 3 blue, and 4 green pencils.
The probability of selecting 3 pencils from a box of 5 red , 3 blue, 4 green pencils is 60/1320.
Given that box contains 5 red pencils, 3 blue pencils abd 4 green pencils.
We have to calculate the probability that 3 red pencils are selected from box. Probability is the likeliness of happening an event among all the events possible.It lies between 0 and 1. The formula of calculating probability is as under:
Probability = number of items/ total items.
Number of pencils in box=12
Number of red pencils=5
Number of blue pencils=3
Number of green pencils=4
Probability of randomly selecting 3 red pencils will be 5*4*3/12*11*10 if pencil is not replaced after drawn of pencil.
=60/1320
=1/22
Hence the probability that 3 red pencils are selected is 1/22.
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The ratio of boys and girls in a class with 40 students = 3:2. If 4 new boys are added, what will be the new ratio?
Answer: 7:4
Step-by-step explanation:
40 boys and girls 3:2 = 24 boys + 16 girls
4 boys are added 28 boys + 16 girls /4 = 7:4
Answer:
7:11
Step-by-step explanation:
We know the total number of students and the ratio of boys to girls. The total for the ratio of boys and girls would be 5 (3+2). Now we can set up proportions knowing these numbers.
b = 3
g =2
t =5
Let's find out how many actual boys there are by setting up a proportion
3/5 = b/40
I will look at the denominators to find x. 5 times what gives me 40? (8). So, I will multiple the top number (numerators). Since I need to multiple the bottom number by 8 to get the number 40, I will now multiple the top number by 8 and get 24.
Now, I know how many actual boys and girls were in the original class. There were 24 boys, 16 girls (40 - 24) and 40 total students.
Now I will take this new information and apply it to the new situation. Now I have 28 boys (24 + 4) and a new total 44.
The ratio of boys to girls would not be 28: 16 or 7:4
Determine the area of the figure.
Answer: 3x - 6 (in^2)
Step-by-step explanation:
base * height / 2
=
3 ( 2x - 4) / 2 (in^2)
= 3x - 6 (in^2)
Answer: 3x-6 in^2
Step-by-step explanation:
There is no way to figure out what x is without additional information, so you have to leave the answer in this form
which unit of measure would be appropriate for the volume of a sphere with aradius of 2 meters?
Answer:
The unit of measuring volume of the sphere is cubic meters.
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U. Next, draw PT, QU, and RS. Which statements are true
The statements that are true based on the midpoint given in the question include:
m∠P + m∠Q + m∠R = 180°PT, QU, and RS intersect at the same point.What is midpoint?In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Also, it should be noted that the midpoint bisects the segment.
In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.
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Complete question:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
4. Based on the triangle sum theorem, solve for x.
Answer:
x = 10
Step-by-step explanation:
180 = 90 + 40 + (4x + 10)
180 = 130 + (4x + 10)
4x + 10 = 180 - 130
4x + 10 = 50
4x = 50 - 10
4x = 40
x = 40/4
x = 10
Answer:
x = 10
Step-by-step explanation:
An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.
In the given triangle, we know three measurement:
4x+1040°90°You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.
Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.
[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]
Evaluate and solve for the x-variable:
[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]
Therefore, the value of x is 10
It is estimated that the average person in the US uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conducted a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a standard deviation of 25.99 gallons. Calculate the appropriate test statistic to test the hypotheses.
The value of test statistic is Z = -2.42.
According to the statement
we have given that the person in the US uses 123 gallons of water per day.
And conducted a survey of 40 randomly selected Americans and get a mean value is 113.03 gallons and a standard deviation of 25.99 gallons.
And we have to test the hypotheses with test statistic.
So,
Here we use the the z- test for one population =
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Here the sample mean = 113.03
And claimed hypothesis mean = 123
Standard deviation = 25.99
Sample size = 40
Now put the values in the above written formula is
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Z = 113.03 - 123 / (25.99/(40)^1/2)
Z = -9.97 / (25.99 / 6.32)
Z = -9.97 / 4.11
Z = -2.42
So, The value of test statistic is Z = -2.42.
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A card is randomly chosen from the cards in the image. Find the probability of choosing the cards with either Q or R on them.
P(Q or R) = ________
The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.
Given that a card is randomly chosen from 8 cards shown in figure.
We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.
Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Number of cards=8
Number of repeated cards=0
Number of cards showing Q and R =1 each.
Probability of getting Q or R is P(X=Q)+P(X=R)
= 1/8+1/8
=2/8
=1/4
=0.25
Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.
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PLS HELP WITH THIS AND SHOW WORK SHOW WORK
Answer:
option 3
Step-by-step explanation:
6x + 3x² - 4x ← collect like terms
= 6x - 4x + 3x²
= x(6 - 4) + 3x²
= x(2) + 3x²
= 2x + 3x²
Answer:
Option 3: [tex]2x+3x^{2}[/tex]
Step-by-step explanation:
Combine like terms: [tex]6x-4x=2x[/tex]
Put the equation together: [tex]2x+3x^{2}[/tex]
The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].
Who am I ?
- My thousands digit is 4
- My hundreds digit is 4 less than the digit in the thousands place
- The sum of my tens digit and ones digit is 7
- My tens digit is 3 more than my ones digit
- The digits in the thousands period have a sum of 10
- My first digit is half the digit that immediately follows it.
I am the number_______________
I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )
Use the drop-down menus to complete each equation so the statement about its solution is true. CLEAR CHECK No Solutions 3x 9 4x x
The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
How to complete the equation?The equation is given as:
3x+9+4x+x=
Represent the blank with y
So, we have:
3x + 9 + 4x + x = y
Evaluate the like terms
8x + 9 = y
For the equation to have no solution the value of y and 8x + 9 must not be equal.
Take for instance
y = 8x + 1
So, we have:
8x + 9 = 8x + 1
Subtract 8x from both sides
9 = 1
The above equation is false because 1 and 9 are not equal
Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
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Complete question
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
3x+9+4x+x=
How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
Using the law of sines, it is found that 1 triangle can be formed with the given conditions.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Hence, for this problem, we have that the relation is:
[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]
[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]
[tex]\sin{G} = 0.8089[/tex]
[tex]G = \arcsin{0.8089}[/tex]
G = 54º
A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.
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Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?
110y = –29x + 333
29x + 110y = 333
29y = –110x + 333
110x + 29y = 333
Answer:
correct answer is 110x + 29y = 333
Step-by-step explanation:
solve this pls>>>>>>>there’s a pic
Answer:
x = 5, 1
Step-by-step explanation:
To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.
In the following diagram, BC is parallel to DE.
What is x?
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
Answer:
x is 21
Step-by-step explanation:
add 54 and 105, then subtract it by 180 and you get 21.
Find a linear and an exponential equation that matches f(2)=12 and f(4)=48.
please help :))
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
For the exponential function, when f(2) = 12:
12 = ab² (1)
Also, at f(4) = 48:
48 = ab⁴ (2)
Hence:
a = 3, b = 2
f(x) = 3(2)ˣ
For the linear function using the points (2, 12) and (4, 48):
y - 12 = [(48 - 12) / (4 - 2)](x - 2)
y = 18x - 24
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
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Tara has 4 and 4 over 5 feet of rope.
part a: how many 2 over 5 foot pieces can tara cut from the 4 and 4 over 5 feet of rope? show your work. (5 points)
part b: using the information in part a, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
the answer box is a writing thing so might have to explain it differently
Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.
Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.
How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] rope. ?
from part A
we solve the fraction
[tex]4\frac{4}{5} =24/5[/tex] rope
And Tara needs to pieces of [tex]2/5[/tex] foot
So we need to divide
[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]
For part B
When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.
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What is the polar form of -2√3-6i ?
Any complex number [tex]z[/tex] can be written in polar/exponential form as
[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]
In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.
The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have
[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]
so (D) (the last option) is the correct choice.
Island A is 160 miles from island B. A ship captain travels 170 miles
from island A and then finds that he is off course and 200 miles from
island B. What bearing should he turn to, SO he is heading straight
towards island B?
The ship captain should be turned 129.49 so it's heading straight for Island B.
Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.
So we gave it
a = 200 feet
b = 170 feet
c = 160 feet
We need to find angle C which goes directly to island B.
We apply the "cosine law":
[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]
Now we multiply both sides by cos⁻¹, we get
cos⁻¹(cos C)= cos⁻¹(0.636)
C = 50.51
The interior angle is 50.51°
We need to find the outer angle to find the bearing the captain needs to turn
Applying the additional angle ruler:
The outside angle = 180 - 50.51 = 129.49°
Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.
from Island A and then discovers that it is off-road and 200 miles away
Island B is 129.49.
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By the definition of complementary angles, since
∠
1
is complementary to
∠
2
,
m
∠
1
+
m
∠
2
=
90
∘
. By the vertical angles theorem,
∠
4
≃
_
∠
1
, and
m
∠
4
=
m
∠
1
by the definition of congruence. Combined with the given equation,
m
∠
4
=
40
∘
, the substitution property of equality means that
40
∘
=
m
∠
1
. Using the ,
40
∘
+
m
∠
2
=
. Finally, using the ,
m
∠
2
=
50
∘
.
Blank 1: Substitution property of equality
Blank 2: 50
Blank 3: Subtraction property of equality
The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.
What are the missing statements in the proof?Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.
Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.
Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.
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One student can paint a wall in 12 minutes. Another student can paint the same wall in 24minutes. Working together, how long will it take for them to paint the wall?
Answer:
8 minutes.
Step-by-step explanation:
We work in fractions of the wall they can paint in 1 minute, so
1/12 + 1/24 = 1/x where x is the time it takes when working together.
Multiplying through by 24x:
2x + 1x = 24
3x = 24
x = 8 minutes.
Scott counted 23 beats in 10 seconds. What is his approximate heart rate?
123 bpm
130 bpm
138 bpm
230 bpm
Anyone is here
Answer:
138
Step-by-step explanation:
There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.
23 * 6 = 138
One of the reasons to use the bootstrap method is because the formula for the confidence interval is too hard to derive. Group of answer choices True False
The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.
What purposes serve the bootstrap method?A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.
The advantages of the bootstrap methodThe benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.
Therefore it can be concluded that the said query statement is true.
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