Answer:
x = 50
Step-by-step explanation:
The sum of the measures of the interior angles of a polygon of n sides is
(n - 2)180
This polygon is a quadrilateral with 4 sides. n = 4
(n - 2)180 = (4 - 2)180 = 2(180) = 360
The sum of the measures of the interior angles of the quadrilateral is 360 degrees.
We have angles of 110 deg, 2x deg, x + 10 deg, and 90 deg. We add their measures and set teh sum equal to 360. Then we solve for x.
x + 10 + 2x + 110 + 90 = 360
3x + 210 = 360
3x = 150
x = 50
Write in standard form (4x10)+(3x1)+(7x1/10+(6x1/100)
9514 1404 393
Answer:
43.76
Step-by-step explanation:
Add up the terms:
4×10 +3×1 +7×1/10 +6×1/100
= 40 +3 +0.7 +0.06
= 43.76
_____
If you're in a part of the world where "standard form" and "scientific notation" are the same thing, then this would be ...
4.376×10¹
Simplify using the order of operations. 2+6*8=
Answer:
The answer is 50.
Step-by-step explanation:
Use MDAS
Multiplication, Division, Addition and Subtraction
2 + 6 * 8 =
Multiply first then add
2 + 6*8 = ?
= 2 + 48
= 50
Miss Wan and Miss Lim left their school at 2.50 p .m and drove along the same
route to Orchard Road. Miss Wan drove at an average speed of 60 Km/h and
reache Orchard Road 30 min later. Meanwhile, Miss Lim was still 5 km away from Orchard
Road.
a) What was the Miss Lim's average speed for the whole journey?
b) What time would Miss Lim reach Orchard Road?
Answer and explanation:
a) To find the average speed of Miss Lim for the whole journey, we need to use the formula:
Average speed = Total distance ÷ Total time
Let's first calculate the total distance traveled by both Miss Wan and Miss Lim. We know that Miss Wan drove at an average speed of 60 km/h and reached Orchard Road 30 minutes later. So, the total distance traveled by her would be:
Distance = Speed × Time
Distance = 60 km/h × (30/60) h
Distance = 30 km
Now, we also know that Miss Lim was still 5 km away from Orchard Road when Miss Wan reached there. Therefore, the total distance traveled by both of them would be:
Total distance = Distance covered by Miss Wan + Distance left for Miss Lim
Total distance = 30 km + 5 km
Total distance = 35 km
Next, let's calculate the total time taken by both of them. We know that Miss Wan took 30 minutes less than Miss Lim to reach Orchard Road. So, if we assume that Miss Lim took t hours to reach Orchard Road, then Miss Wan took (t - 0.5) hours. Therefore, the total time taken by both of them would be:
Total time = Time taken by Miss Wan + Time taken by Miss Lim
Total time = (t - 0.5) h + t h
Total time = 2t - 0.5 h
Now, we can use the formula to find the average speed of Miss Lim:
Average speed = Total distance ÷ Total time
Average speed = 35 km ÷ (2t - 0.5) h
Therefore, the average speed of Miss Lim for the whole journey is 35/(2t-0.5) km/h.
b) To find out what time Miss Lim would reach Orchard Road, we can use the formula:
Time taken = Distance ÷ Speed
We know that Miss Lim was 5 km away from Orchard Road when Miss Wan reached there. Therefore, the distance left for Miss Lim to cover would be:
Distance = 5 km
We also know that Miss Lim's average speed for the whole journey is 35/(2t-0.5) km/h. Therefore, the time taken by her to cover the remaining distance of 5 km would be:
Time taken = Distance ÷ Speed
Time taken = 5 km ÷ 35/(2t-0.5) km/h
Time taken = (2t - 0.5) ÷ 7 h
Now, we need to add this time to the time when Miss Wan reached Orchard Road, which was 30 minutes past 2.50 p.m. So, the time when Miss Lim would reach Orchard Road would be:
Time = Time when Miss Wan reached Orchard Road + Time taken by Miss Lim
Time = 2.50 p.m. + 30 min + (2t - 0.5) ÷ 7 h
Simplifying this equation, we get:
Time = (14t + 11) ÷ 14 p.m.
Therefore, Miss Lim would reach Orchard Road at (14t + 11) ÷ 14 p.m.
Answer:
a) 50 km/h
b) 3:26 p.m.
Step-by-step explanation:
You want to know Miss Lim's average speed and arrival time at Orchard Road if Miss Wan gets there in 30 minutes at 60 km/h, starting at 2:50 pm.
DistanceThe distance Miss Wan traveled is ...
distance = speed × time
distance = (60 km/h) × (1/2 h) = 30 km
a) SpeedIn the same 30 minutes that Miss Wan traveled 30 km, Miss Lim traveled 5 km less, so 30 -5 = 25 km. Miss Lim's speed was ...
speed = distance/time
speed = (25 km)/(1/2 h) = 50 km/h
Assuming Miss Lim maintained that speed for the remaining 5 km, her average speed for the journey was 50 km/h.
b) TimeMiss Lim's travel time is ...
time = distance/speed
time = (30 km)/(50 km/h) = 3/5 h = 36 min
The clock time 36 minutes after 2:50 pm is 3:26 pm.
Miss Lim reached Orchard Road at 3:26 p.m..
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answer:
8 and 5
Step-by-step explanation:
Answer:
8 and 5
Step-by-step explanation:
Find the exterior of a rectangle in a polygon
The measure of each exterior angles of rectangle is 90°
Finding the exterior of a rectangle in a polygonFrom the question, we have the following parameters that can be used in our computation:
A rectangle
A rectangle is a polygon with 4 sides
So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon
The exterior angles in a polygon are found by using:
Exterior of a rectangle in a polygon = 360°/Number of sides of the polygon
In this case,
The number of sides of the rectangle = 4
So, we have
Exterior of a rectangle = 360°/4
Evaluate
Exterior of a rectangle = 90°
Hence, the value of the measure of each exterior angles of rectangle is 90°
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Complete question
Find the measure of each exterior angles of rectangle?
Step by step
in the diagram, AE is tangent to the circle at point a and secant DE intersects the circle at point C and D. the iines intersect outside of the circle at point E
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.
The figure shows a right triangle with legs marked 30 and 16.
Answer:
A:
Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65
a large clinical trial was designed to determine whether a certain vitamin improves the general health of adults. the investigators first identified 85 variables that measure various aspects of the general health of adults. because each adult in the clinical trial was to serve as his or her own control, the 85 variables were measured for each adult, both before taking the vitamin and after taking the vitamin for three months. the investigators then performed 85 matched-pair t-tests, one for each variable. they found statistically significant results at the 0.05 level in 2 of the variables, both in the direction of improved general health. which of the following should the investigators conclude?
The investigators should conclude (C) There is insufficient evidence that the vitamin improves the health of adults because, at the 0.05 significance level, one could easily get statistically significant results in 2 out of 85 tests just due to chance variability.
In statistical hypothesis testing, a significance level of 0.05 indicates that there is a 5% chance of obtaining a statistically significant result due to chance variability if the null hypothesis is true.
In this study, the investigators performed 85 separate tests, increasing the chance of obtaining at least one false positive result due to chance variability.
This is known as the multiple comparisons problems, and to control for this issue, the investigators should have used a correction for multiple comparisons, such as the Bonferroni correction, which would have adjusted the significance level to 0.05/85 = 0.0006.
Therefore, finding two statistically significant results out of 85 tests does not provide sufficient evidence to conclude that vitamin improves the health of adults. Further studies with larger sample sizes, corrected for multiple comparisons, and controlling for confounders, are needed to draw a valid conclusion.
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-6-2y^2-3+3y-2y^2+4y+6y^2
Answer:
-9 + 2y^2 + 7y
Step-by-step explanation:
- 6 - 2y^2 - 3 + 3y - 2y^2 + 4y + 6y^2
just combine
-9 + 2y^2 + 7y
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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Solve the equation.
4x – 2 = -3x2 + 3x
x = [ ? ],
Answer:
\(x = - 4\)
Step-by-step explanation:
\(4x - 2 = - 3 \times 2 + 3x\)
Calculate the product:
\(4x - 2 = - 6 + 3x\)
Rearrange the terms:
\(4x - 3x = - 6 + 2\)
Combine like terms:
\(x = - 6 + 2\)
Calculate:
\(x = - 4\)
Answer:
x = 1/2
Step-by-step explanation:
Combine exponents
4x-x-2=-3^2+3xx
4x-x-2=-3x^2+3x^2
Combine like terms
4x-2=-3x^2+3x^2
4x-2=0
Add 2 to both sides
4x-2=0
4x-2+2=0+2
Simplify:
Add the numbers
4x-2+2=0+2
4x=0+2
Add the numbers again
4x=0+2
4x=2
Divide both sides by the same factor
4x=2
4x/4 = 2/4
Simplify:
Cancel terms that are in both the numerator and denominator
4x/4 = 2/4
X= 2/4
Divid the numbers
X= 2/4
X= 1/2
Solution/ Answer
x= 1/2
Hope this helps
4. Saul wants to cash a check for $715 at his bank. He has
$436 in his bank account. How much more money will
he need in his bank account to cash the check?
Answer:
he needs $279
Step-by-step explanation:
715-436= 279
The function is defined below. Find all values of that are NOT in the domain of g. g(x)=x^2+13+40 / x^2-9
Answer:
g(x)=x-2/x^2-9
If there is more than one value, separate them with commas.
Step-by-step explanation:
what do you need to know ask me
Answer:
i got a whole lotta math questiosn to ask, answer them for me I give u bigger points
Step-by-step explanation: please n thanks man
Answer:
Can you please answer my question?
Step-by-step explanation:
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consider the following system of equations:2x+3y=45,x+y=10 what is the x value of the solution for this system?
Step-by-step explanation:
The answer for x in the solution is -5
Given: KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
Prove:
An incomplete flowchart proof is shown.
By ASA congruency triangle KBH is congruent to triangle NWH.
Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
From the given figure,
Consider ΔKBH and ΔNWH,
∠KHB=∠NHW (Vertically opposite angles)
∠HKB=∠HWN (Interior alternate angles parallelogram)
KH=HW (Diagonals bisect each other)
By ASA congruency ΔKBH ≅ ΔNWH
Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.
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7x7+3-2 (4-5+-6)(77x8)
?????????????????????/
Step-by-step explanation:
7 x7+3-2(-7) (618)
=7 x7+3-2(-4326)
=-4341
you have 51 coins in your pocket, all dimes and quarters. You have $10.20. How many dimes and quarters do you have?
To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.
To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.
We know that there are 51 coins in total, so we can write the equation: d + q = 51.
We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
Rearrange the first equation to solve for d: d = 51 - q.
Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.
Simplify and solve for q: 510 - 10q + 25q = 1020.
Combine like terms: 15q = 510.
Divide both sides by 15: q = 34.
Now substitute this value back into the first equation to solve for d: d + 34 = 51.
Subtract 34 from both sides: d = 17.
Therefore, you have 17 dimes and 34 quarters.
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Challenge) Solve for a. Answer as a mixed number. A=______
The value of the a in the mixed form is \(-1 \frac{5}{43}\).
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To solve for a, we can begin by isolating the variable on one side of the equation.
First, we can subtract 3 from both sides to get:
-7/12 - 3 = 4/a
Next, we can simplify the left side by finding a common denominator of 12:
-7/12 - 3 * 12/12 = 4/a
-7/12 - 36/12 = 4/a
-43/12 = 4/a
To solve for a, we can multiply both sides by a/4:
(-43/12) * (a/4) = 1
Multiplying the left side gives:
-43a/48 = 1
Dividing both sides by -43/48 gives:
a = -48/43
To express this as a mixed number, we can divide the numerator by the denominator:
-48 ÷ 43 = -1 with a remainder of 5
Therefore, the value of the a in the mixed form is \(-1 \frac{5}{43}\).
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Complete question:
Challenge) Solve for a. Answer as a mixed number. A=?
-7/12 = 4/a+3.
Simplify the expression: 4(2x - 4)
Answer: 8x-16
Step-by-step explanation:
Answer: 8x-16
Step-by-step explanation:
Which of the following statements are true regarding the reflection of A(1 1/2,-2)? Select all that apply..
The correct statements are:
A) When this point is reflected across the x-axis, the x-coordinate stays the same and the y-coordinates are opposites.C) When this point is reflected across the y-axis, the x-coordinates are opposites and the y-coordinate stays the same.D) When this point is reflected across the x-axis, the x-coordinates are opposites and the y-coordinate stays the same.How to explain the statementsWhen a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.
When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.
It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.
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Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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Solve five and six-eighths plus four and four-fifths minus two and six-tenths equals blank line
The solution for the given expression is 7 + 5/12
How to solve this expression?First we need to write the expression, using fractions, we will get:
(5 + 6/8) + (4 + 4/15) - (2 + 6/10)
We can group like terms, and we will get:
(5 + 6/8) + (4 + 4/15) - (2 + 6/10) = (5 + 4 -2) + (6/8 + 4/15 - 6/10)
Now just simplify that to get.
(5 + 4 -2) + (6/8 + 4/15 - 6/10) = 7 + 3/4 + 4/15 - 3/5
= 7 + 3/4 + 4/15 - 9/15
= 7 + 3/4 - 5/15
= 7 + 9/12 - 4/12
= 7 + 5/12
That is the answer.
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True or false
-y = -112 + 4; (0, -4)
Answer:
False
Step-by-step explanation:
Tyler invests $9700 in two different accounts. The first account paid 10%, the second account paid 9% in interest. At the end of the first year he had earned $931 in interest. How much was in each account?
Answer:
First account: $6380.
Second account: $4251.
Step-by-step explanation:
let the first account have $x at the start of the first year
So at the end of 1 year it had x + 0.1x = $1.1x
In the same we we calculate the amount in the second account
= $1.09(9700 - x)
So we have the following equation
1.1x + 1.09(9700 - x) = 9700 + 931
1.1x + 10573 - 1.09x = 10631
0.01x = 10631 - 10573 = 58
x = 58/0.01
=$5800
So at the end of the year there was
5800 * 1.1 = $6380 in first account
and
the second account had
1.09 (9700 - 5800) = $4251.
PLEASE HELP , I NEED A 100%
The quotient is found to be 4/5. The correct option is (B).
What is a fraction?A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0. The number a is called as the numerator and b is the denominator. In order to divide two fractions take the reciprocal of the other fraction and change the sign as multiplication. It can be shown as a/b ÷ c/d = a/b × d/c.
The given expression is -3/5 ÷ (-3/4).
It can be simplified as follows,
Take the reciprocal of the fraction (-3/4) as -4/3.
And, change the sign of division to multiplication to obtain,
-3/5 ÷ (-3/4)
⇒ -3/5 × -4/3 = 4/5
Which the value of the quotient.
Hence, the quotient for the given arithmetic operation is 4/5.
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evaluate 2 - (-4) + 3 + (-6) - (-2)
Answer:
5
Step-by-step explanation:
2 + 4 +3 - 6 +2
5
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A bookshelf at a bookstore is 3 feet 9 inches wide. There are 18 copies of the same book on the shelf, which fit the shelf exactly. What is the width of 1 of the books?
Answer:
2.5 inches
Step-by-step explanation:
Given
Shelf Width = 3ft 9in
Copies = 18
Required
Determine the width of each book
This is calculated by dividing the shelf width by the number of copies.
Width = Shelf Width ÷ Copies
Width = (3 ft 9in) ÷ (18)
[Convert with to inches]
Width = (3 * 12 + 9) ÷ (18)
Width = (36 + 9) ÷ (18)
Width = 45 ÷ 18
Width = 2.5 inches
Hence, the width of each book is 2.5inches
The Michner Corporation is trying to choose between the following two mutually exclusive design projects:
Year Cash Flow (I) Cash Flow (II)
0 −$ 54,000 −$ 19,000
1 25,000 10,200
2 25,000 10,200
3 25,000 10,200
a-1.
If the required return is 11 percent, what is the profitability index for both projects? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.)
a-2.
If the company applies the profitability index decision rule, which project should the firm accept?
multiple choice 1
Project I
Project Il
b-1.
What is the NPV for both projects? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b-2.
If the company applies the NPV decision rule, which project should it take?
multiple choice 2
Project I
Project II
a-1. The profitability index for Project I is 1.180, and for Project II it is 1.414.
a-2. Based on the profitability index decision rule, the firm should accept Project II.
b-1. The NPV for Project I is $9,699.57, and for Project II it is $7,872.48.
b-2. According to the NPV decision rule, the firm should take Project I since it has a higher NPV.
a-1. To calculate the profitability index for both projects, we divide the present value of cash inflows by the initial investment (cash outflow).
For Project I:
PV of cash inflows = $25,000 / (1 + 0.11)^1 + $25,000 / (1 + 0.11)^2 + $25,000 / (1 + 0.11)^3 = $63,699.57
Profitability Index (Project I) = PV of cash inflows / Initial investment = $63,699.57 / $54,000 = 1.180
For Project II:
PV of cash inflows = $10,200 / (1 + 0.11)^1 + $10,200 / (1 + 0.11)^2 + $10,200 / (1 + 0.11)^3 = $26,872.48
Profitability Index (Project II) = PV of cash inflows / Initial investment = $26,872.48 / $19,000 = 1.414
a-2. According to the profitability index decision rule, a project with a profitability index greater than 1 is considered acceptable. Therefore, based on the profitability indexes calculated:
Project I has a profitability index of 1.180
Project II has a profitability index of 1.414
Since Project II has a higher profitability index, the firm should accept Project II.
b-1. To calculate the net present value (NPV) for both projects, we find the present value of cash inflows and deduct the initial investment (cash outflow).
For Project I:
NPV (Project I) = PV of cash inflows - Initial investment = $63,699.57 - $54,000 = $9,699.57
For Project II:
NPV (Project II) = PV of cash inflows - Initial investment = $26,872.48 - $19,000 = $7,872.48
b-2. According to the NPV decision rule, a project with a positive NPV is considered acceptable. Comparing the NPVs calculated:
Project I has an NPV of $9,699.57 (positive)
Project II has an NPV of $7,872.48 (positive)
Based on the NPV decision rule, the firm should take Project I since it has a higher NPV.
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