Answers
Related Questions
Please Help!! Find the measure of angle 2. Image Attached
Answers
opposite angles have to equal 180
so 180-111 = 69
angle 2 is 69 degrees
In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080% confidence interval for the population mean muμ. what is the margin of error of muμ? interpret the results.
Answers
The margin of error can be calculated using the t statistic. The formula for margin of error is given as:
Margin of error = t * s / sqrt (n) ---> 1
Where,
t = the t score based on the given confidence level and degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
If the average price of four pairs of shoes is $50, and three of those pairs of shoes are priced at $35, $40 and $55, what is the price of the fourth pair of shoes?
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average price= price1+price2+...priceN/N
In our case , we have four pairs of shoes.So, N=4.
We also know the average price. average price=$50
We also know the price of the first pair of shoes (price1), of the second (price2) and the third (price3). We need to find out Price4:
$50=$35+$40+$55+Price4/4
50*4=$35+$40+$55+Price4
$200=$130+Price4
Price4=200-130
Price4=$70
For her phone service, Kala pays a monthly fee of $13 , and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
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0.05m >= 50.15
m >= 1003 minutes
Therefore at least 1003 minutes were consumed to be billed $63.15 or more.
Hope this helps.
What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?
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[tex]\bf S_8=3\left( \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{1-\frac{1^8}{2^8}}{1-\frac{1}{2}} \right) \\\\\\ S_8=3\left( \cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{255}{256}\cdot \cfrac{2}{1} \right) \\\\\\ S_8=3\left( \cfrac{255}{128} \right)\implies S_8=\cfrac{765}{128}[/tex]
The sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625
Sum of geometric seriesSeries are the sum of sequences. The sum of geometric series is expressed as:
Sn = a(1-r^n)/1-r
Given the following
n = 8
a = 3
r = 1/2
Substitute
S8 = 3(1-(1/2)^8)/0.5
S8 = 3(1-1/256)/0.5
S8 = 3(255/256)/0.5
S8 = 5.9765625
Hence the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625
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Need help on 4.9.2 project: performance task: the subway stop
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The subject of this question is Mathematics.
Explanation:The subject of this question is Mathematics.
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Your computer monitor has a width of 13.93 inches and a height of 10.45 inches. what is the area of the monitor display in square meters
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__________________________________________________
Explanation:
__________________________________________________
First, calculate the area in square inches:
(13.93 in) * (10.45 in) = 145.5685 in² .
Now, convert this value into "square meters" (or: " m² ") .
__________________________________________________
Note: 0.00064516 square meters = 1 square inch .
So: 145.5685 in² * (0.00064516 square meters / 1 in²) =
___________________________________________________
= [ (145.5685) * (0.00064516) ] m² ;
= 0.09391497346 m² ; round to: " 0.09391 m² " .
___________________________________________________
The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.
Explanation:To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.
Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.
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Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 – 25?
(x – 5)(x – 5)
(x + 5)(x + 5)
(x – 20)(x + 5)
(x – 5)(x + 5)
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positive sign in one bracket and negative in the other
Answer:
its D
Step-by-step explanation:
In triangle KLM LM = 7 and angle k equals 45 Find KL.
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In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.
Explanation:In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.
Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.
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A principal of $2600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 8 years?
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HELP! What is the volume of the regular pyramid below????
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hope this helped!
How many hours are in 2 weeks?
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Final answer: 336 hours
Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
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Side of each cutout = x
Length of the base = 12 - x - x = 12 - 2x
width of the base = 8 - x - x = 8 - 2x
area of the base = (12 - 2x) (8 - 2x) = 12*8 - 12*2x - 8*2x + 4x^2 = 96 - 40x + 4x^2
height = x
Volume = (96 - 40x + 4x^2) x = 96x - 40x^2 + 4x^3
Equation of the volume of the box = 96x - 40x^2 + 4x^3
Zeros of the function: use the factored form:
x (12 - 2x) (8 -2x) = 0
=> x = 0, x = 6 and x = 4
Sketch of the graph:
The graph comes growing from (- infinity, -infinity), crosses the origin (0,0), grows until a local maximum before 2, starts to decrease, intercepts the x axis at x = 4, continues decreasing until a local minium before 6, starts to increase again, crosses the x axis at x = 6, and continues increasing toward infinity. If you are using derivatives, you can find the local minimum and maximum.
Answer:
Step-by-step explanation:
Any equation that is equivalent to V = x(12 - 2x)(8 - 2x) is accepted. Any graph that is similar to the graph of the function is accepted.
Sample Student Response:
The box is a cube, so the volume is the length × width × height. The height is the side length of the cardboard, which is x.
The length is the original length minus two side lengths of the cutout, so the length is 12 - 2x.
Similarly, the width is the original width minus two side lengths of the cutout, so the width is 8 - 2x.
A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...
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Each ball has mass = m.
The initial velocity of the blue ball = u.
The initial velocity of the red ball = 0.
Initial total momentum is
P1 = m*u + m*0 = mu
Final momentum is
P2 = mv + 3mv = 4mv
Because momentum is conserved,
mu = 4mv
u = 4v
Answer:
The velocity of the blue ball before the collision is 4v.
Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.
A. use a protractor to measure ∠BAC
B. Draw a line through point B that intersects arc 2.
C. Measure the distance between AB and AC along arc 1 with a ruler.
D. Measure the distance between AB and AC along arc 1 with a compass.
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Answer:
Option A is correct
Step-by-step explanation:
In the given figure to draw the parallel line to AC passing through B we have to tell the next step.
As lines AC and AB given and we know if lines are parallel then alternate angles are equal.
Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.
∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.
Hence, Option A is correct.
The roots of the equation are 3 + 8i and 3 – 8i.
What is the value of c?
x2 – 6x + c = 0
c = [1]
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taking x=3+8i and substituting it in our equation we get:
(3+8i)^2-6(3+8i)+c=0
-55+48i-18-48i+c=0
collecting the like terms we get:
-55-18+48i-48i+c=0
-73+c=0
c=73
the answer is c=73
Jones is the chairman of a committee. in how many ways can a committee of 5 be chosen from 10 people given that jones must be one of them?
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So your equation is
1(Jones) • 9( possibilities left) •8( possibilities left)• 7( possibilities left)• 6( possibilities left)
Or
1 • 9 • 8 • 7 • 6
=
3,024 possible ways in which a committee of 5 can be chosen from 20 people given that Jones must be one of them.
Final answer:
A committee of 5 can be chosen in 126 different ways from 10 people if Jones must be one of them, by using the combination formula C(9, 4) to choose the remaining four committee members from the other nine people.
Explanation:
To determine in how many ways a committee of 5 can be chosen from 10 people given that Jones must be one of them, we need to apply the concept of combinations in probability and combinatorics. Since Jones must be on the committee, we are actually choosing the remaining 4 members from the remaining 9 people.
The number of ways to choose 4 people out of 9 is calculated using the combination formula, which is:
C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
Applying this to our scenario:
C(9, 4) = 9! / (4! * (9 - 4)!) = 126
Therefore, there are 126 different ways to form the committee if Jones is already chosen as one member.
At 2:00 Tony rented a mountain bike from the slick rock cyclery. He returned the bike at 5:00 after cycling 18 mi.Tony paid 24 for the rental. Find the rental rate in dollars per mile. Take the number of dollars and divide by the number rate mile
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24/18 = 1.33 per mile
that time that he rented it and returned it is just extra info that is not needed
Give the number of significant figures in this number 34.20
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1. All nonzero numbers are significant.
2. All zeros between nonzero numbers are significant.
3. All zeros after the decimal point are significant.
Following the rules, I think all of the numbers in 34.20 are significant. Thus, there are a total of 4 significant figures.
Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.
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Answer:
To show: [tex]\sqrt{21}[/tex] is between 4 and 5
We know:
21 is lies between two consecutive integer i.e, 16 and 25
We can write this as:
[tex]16 < 21 < 25[/tex]
or
[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]
Simplify:
[tex]4 < \sqrt{21} < 5[/tex]
⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.
Therefore, [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.
Answer:
We know that
[tex]16<21<25[/tex]
Because, 16 is less than 21 and 25 is more than 21.
Now, if we apply a square root to each part, we would have
[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]
Then, we solve each square root, except the square root of 21, because it doesn't have an exact result
[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]
So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.
For what values of x is the rational expression below undefined?
Check all that apply.
x-4/3x^2-75
A. -3
B. -4
C. 3
D. -5
E. 4
F. 5
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In order for the rational expression to be undefined, the denominator must be equal to 0.
Thus, set 3(x+5)9(x-5)=0
x=5 and -5
Justin is evaluating the expression 12.5 + 3.8x, when x is 7.9
Answers
Answer:
Justin should have Multiplied 3.8 and 7.9 first
Step-by-step explanation:
Because all these people that have the wrong answer got me mad
Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 12.5 + 3.8x.
When x=7.9 in the given expression, we get
12.5+3.8(7.9)
= 12.5+30.02
= 42.52
Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Justin is evaluating the expression 12.5 + 3.8x, when x is 7.9.
12.5+3.8(7.9)
16.3(7.9)
128.77
What was Justin's error?
1) Justin should have multiplied 12.5 and 7.9 first.
2) Justin should have added 12.5 and 7.9 first.
3) Justin should have multiplied 3.8 and 7.9 first.
4) Justin should have added 3.8 and 7.9 first.
Evaluate | 4t+n | if t=-2 and n=5
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= | 4(-2) + 5 |
= | -8 + 5 |
= | -3 |
= 3
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 200 pounds requires 250 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?
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Solve the inequality. Graph the solution set. 26+6b (>=) 2(3b+4 A. All real numbers b. b> or less than 1/2 c. no solutions
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Write the standard equation for the circle center (10,-6), r=6
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Therefore, since the center is (10,-6), h=10 and k=-6. The radius is 6 which means r=6.
Substitute these values into the standard form equation.
(x-(10))²+(y-(-6))²=(6)²
(x-10)²+(y+6)²=36
Therefore, the standard equation for the circle centered at (10,-6) where r=6 is (x-10)²+(y+6)²=36.
PLEASE HELP ME FIGURE THIS OUT if i have 6 questions on a test, how many would i get wrong to get a score of 48%
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now, how much is 52% of 6?
whatever% of anything is just (whatever/100) * anything.
thus 52% of 6 is just (52/100) * 6, that many.
X+y=13and x-y=2 what is the value of x^2-y^2
Answers
x-y=2
Add the equations (elimination method)
x+y+x-y=13+2
2x=15
x=7.5
Plug in this y value
7.5-y=2
-y=-5.5
y=5.5
Plug in both the x and y values into the equation asked for
(7.5)^2-(5.5)^2
56.25-30.25
Final answer: 26
[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ x+y=13\qquad x-y=2 \\\\\\ x^2-y^2\implies (x+y)(x-y)\implies (13)(2)[/tex]
Mr. Chavez spent $199.99 for a new smart phone, 3
Answers
Mr. Chavez spent $299.97 altogether. The estimated total matches approximately with the calculated total, confirming the accuracy of our answer.
To find the total amount Mr. Chavez spent, we need to add the costs of the smartphone, carrying case, and accessories.
Total amount = |-199.99| + |-39.99| + |-59.99|
Now, let's evaluate each absolute value:
|-199.99| = 199.99
|-39.99| = 39.99
|-59.99| = 59.99
Now, let's add them together:
Total amount = 199.99 + 39.99 + 59.99
Total amount = 299.97
So, Mr. Chavez spent $299.97 altogether.
Now, let's check the answer using estimation:
Round each amount to the nearest ten:
- $199.99 is approximately $200.00
- $39.99 is approximately $40.00
- $59.99 is approximately $60.00
Now, let's add them together:
Total estimation = $200.00 + $40.00 + $60.00
Total estimation = $300.00
The estimated total matches closely with the calculated total, confirming the accuracy of our answer.
The complete question is:
Mr. Chavez spent $199.99 for a new smart phone,$39 .99 on a carrying case, and $59.99 on accessories. The expression |-199.99|+|-39.99|+|-59.99| represents the total amount that Mr. Chavez spent. How much did Mr. Chavez spend altogether? Check your answer using estimation.
Joe and Mary each pay the same price for a T-shirt. Before they buy it, Mary has $\$ 2$ more than Joe. To buy the T-shirt, Joe spends $ \$1 $ less than $\frac{2}{5}$ of his money, and Mary spends $\frac{1}{3}$ of her money. What was the total amount of money Joe and Mary originally had altogether?
Answers
i) "Before they buy it, Mary has 2$ more than Joe":
means M=J+2
ii)
"To buy the T-shirt, Joe spends 1 $ less than \frac{2}{5} of his money"
so [tex]T= \frac{2}{5}J-1 [/tex]
iii)
"Mary spends \frac{1}{3} of her money"
means [tex]T= \frac{1}{3}M [/tex]
equalize equations ii) and iii):
[tex]\frac{2}{5}J-1= \frac{1}{3}M[/tex] (they are both equal to T)
substitute M=J+2 from equation i:
[tex]\frac{2}{5}J-1= \frac{1}{3}(J+2)[/tex]
[tex]\frac{2J-5}{5}= \frac{J+2}{3}[/tex]
[tex]3(2J-5)=5(J+2)[/tex]
6J-15=5J+10
J=25
so M=25+2=27 (dollars)
Together Mary and Joe had 27+25=52 (dollars)
Answer: 52 $
Answer:
52
Step-by-step explanation:
Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.