Answer:
14 feet
Step-by-step explanation:
There are 3 feet in 1 yard, so 36 feet in 12 yards. The remaining ribbon will be the original amount less the amount used.
36 - 22 = 14 . . . . feet remaining
After decorating the blankets, Olga will have 14 feet of ribbon remaining. The conversion from yards to feet and subtraction calculates this remaining amount accurately.
Calculating Remaining Ribbon
To determine how much ribbon Olga has left after decorating the blankets, we need to perform a couple of conversions and a subtraction.
First, let's convert the total ribbon from yards to feet:
→ 1 yard = 3 feet
→ 12 yards = 12 * 3
= 36 feet
Next, Olga uses 22 feet of ribbon to decorate the blankets:
→ Total ribbon in feet: 36 feet
→ Ribbon used: 22 feet
Now, subtract the amount used from the total:
→ Remaining ribbon = 36 feet - 22 feet
= 14 feet
Olga will have 14 feet of ribbon remaining.
Which percent is equivalent to 3/4 ?
A) 25%
B) 50%
C) 60%
D) 75%
Answer:
d is the correct answer
Answer:75
Step-by-step explanation:
99 POINTS BRAINLIEST!!! No fake answers!
Find the mean for the binomial distribution. Round to the nearest tenth.
n=1632; p=0.57
A) 939.9
B) 937.5
C) 922.7
D) 930.2
ALSO QUESTION IN PICTURE PLEASE
Answer:
The mean of a binomial distribution is given by mean = n x p where n = the number of items and p equals the probability of success. Here we have:
mean = 1632 x 0.57 = 930.2
Step-by-step explanation:
The mean for a binomial substitution = n x p
Mean = 1632 x 0.57 = 930.24
The answer would be D.
Picture:
Multiply P(x) by X, then add those together:
0 x 0.42 = 0
1 x 0.12 = 0.12
2 x 0.34 = 0.68
3 x 0.05 = 0.15
4 x 0.07 = 0.28
Mean = 0 + 0.12 + 0.68 + 0.15 + 0.28 = 1.23
A clock was showing the time accurately on Wednesday at 4pm. On the following Saturday, at 2pm, the clock was running late by 35 seconds. On average, how many seconds did the clock skip every 30 minutes?
Answer: The clock skip 0.25 seconds every 30 minutes.
Step-by-step explanation:
Since we have given that
Clock was correct on Wednesday at 4 pm.
At 2 pm , on saturday, the clock was running late by 35 seconds.
From 4 pm wednesday to 4 pm thursday = 24 hours
From 4 pm thursday to 4 pm friday = 24 hours
From 4 pm friday to 2 pm saturday = 22 hours
So, total hours = 24+24+22 = 70 hours
We need to find the number of seconds that the clock skip every 30 minutes.
So, it becomes
[tex]\dfrac{70}{0.5}=\dfrac{35}{T}\\\\70T=35\times 0.5\\\\T=\dfrac{35\times 0.5}{70}\\\\T=0.25[/tex]
Hence, the clock skip 0.25 seconds every 30 minutes.
The clock was 35 seconds late over a period of 70 hours, which equals 140 intervals of 30 minutes. Therefore, the clock skipped an average of 0.25 seconds every 30 minutes.
To determine the average number of seconds the clock skipped every 30 minutes, we first need to calculate the total time difference and then divide by the number of 30-minute intervals.
The clock was showing the correct time on Wednesday at 4 pm.
It was 35 seconds late by Saturday at 2 pm.
Time elapsed from Wednesday 4 pm to Saturday 2 pm is 2 days and 22 hours, which equals (2×24 + 22) hours = 70 hours.
Converting 70 hours into minutes: 70×60 = 4200 minutes.
Number of 30-minute intervals in this period: 4200 / 30 = 140 intervals.
Average seconds skipped per 30-minute interval: 35 seconds / 140 intervals = 0.25 seconds.
Thus, the clock skipped an average of 0.25 seconds every 30 minutes.
Q3:
A company sells bikes for $120 each. They pay a monthly rent of $1,800 for their store and each bike costs them $60 in materials. Write the revenue and cost functions and find the break-even point by graphing.
Let the number of bikes = x and total money = y.
Set up two equations:
The first equation is the cost function, which would be rent plus 60 times the number of bikes:
y = 1800 + 60x
The second equation would be revenue, where total money would be equal to 120 times the number of bikes sold:
y = 120x
Now you can graph both equations by setting the equations to equal each other. The point on the graph, where the loib=ne crosses the X axis is the break even point
Graph
120x = 1800 +60x
See attached picture for the graph and you can see the break even point is 30 bikes.
You can check by replacing X with 30 to see if the equations equal each other:
1800 + 60(30) = 1800 +1800 = 3600
120(30) = 3600
Late shows Some TV shows begin after their scheduled times when earlier programs run late. According to a network’s records, about 3% of its shows start late. To find the probability that three consecutive shows on this network start on time, can we multiply (0.97)(0.97)(0.97)? Why or why not?
Answer:
No because the probability of consecutive shows starting late are not independent events
Step-by-step explanation:
Is good begin with the definition of independent events
When we say Independent Events we are refering to events which occur with no dependency of other evnts. Basically when the occurrence of one event is not affected by another one.
When two events are independent P(A and B) = P(A)xP(B)
But for this case we can't multiply 0.97x0.97x0.97 in order to find the probability that 3 consecutive shows start on time, because the probability for shows starting late are not independent events, because if the second show is late, the probability that the next show would be late is higher. And for this reason we can use the independency concept here and the multiplication of probabilities in order to find the probability required.
Yes, you can multiply (0.97)(0.97)(0.97) because the events are independent.
Yes, you can multiply (0.97)(0.97)(0.97) to find the probability that three consecutive shows on this network start on time. This is because the events are independent; the outcome of one show starting on time does not affect the outcome of the others.
Therefore, the probability that three consecutive shows start on time is the product of the probabilities of each show starting on time: P(all three shows start on time) = 0.97 * 0.97 * 0.97 = 0.912673.
What is the binomial expansion of (2x – 3)^5?
A) (2x)^ 5 – 15(2x)^ 4 + 90(2x)^ 3 – 270(2x)^ 2 + 405(2x) – 243
B) (2x)^ 5 + 15(2x)^ 4 – 90(2x)^ 3 + 270(2x)^ 2 – 405(2x) + 243
C) (2x)^ 5 + 15(2x)^ 4 + 90(2x)^ 3 + 270(2x)^ 2 + 405(2x) + 243
D) 2(x)^ 5 – 30(x)^ 4 + 180(x)^ 3 – 540(2x)^ 2 + 810(x) – 243
Answer:
C
Step-by-step explanation:
(2x + 3)^5 = C(5,0)2x^5*3^0 +
C(5,1)2x^4*3^1 + C(5,2)2x^3*3^2 + C(5,3)2x^2*3^3 + C(5,4)2x^1*3^4 + C(5,5)2x^0*3^5
Recall that
C(n,r) = n! / (n-r)! r!
C(5,0) = 1
C(5,1) = 5
C(5,2) = 10
C(5,3) = 10
C(5,4) = 5
C(5,5) = 1
= 1(2x^5)1 + 5(2x^4)3 + 10(2x^3)3^2 + 10(2x^2)3^3 + 5(2x^1)3^4 + 1(2x^0)3^5
= 2x^5 + 15(2x^4) + 90(2x^3) + 270(2x^2) + 405(2x) +243
= 32x^5 + 15(16x^4) + 90(8x^3) + 270(4x^2) + 810x + 243
= 32x^5 + 240x^4 + 720x^3 + 1080x^2 + 810x + 243
Answer:
the answer is C
Step-by-step explanation:
If a weight hanging on a string of length 5 feet swings through 6° on either side of the vertical, how long is the arc through which the weight moves from one high point to the next high point?\
Answer:
1.047 ft
Step-by-step explanation:
The length of an arc is given by ...
s = rθ
where s is the arc length, r is the radius, and θ is the central angle in radians. Your arc subtends an angle of 12° = (12·π/180) = π/15 radians. The length of the arc is then ...
s = (5 ft)(π/15) = π/3 ft ≈ 1.047 ft
The weight swings through a total angle of 12°, corresponding to an arc length of approximately 1.047 feet on the circumference of the circle with radius 5 feet.
Explanation:To answer this question, we need to understand that the weight swings through an arc, and this arc is a part of the circumference of a circle. Given the length of string (5 feet) is the radius, and the weight swings through 6° on either side of the vertical, we can calculate the total arc length.
Firstly, you should know that the total angle a circle encompasses is 360°. So, the weight swings through a total angle of 6° x 2 = 12°.
Secondly, recall the formula for the circumference of a circle is 2πr, or in our case 2π x 5 feet. Now, to find the length of the arc corresponding to 12°, we will use the proportion of the swing angle to the total angle, i.e., (12/360) x (2π x 5 feet).
In this way, the length of the arc travelled is almost 1.047 feet.
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John can jog twice as fast as he can walk. He was able to jog the first mile to his grandmas house but then he got tired and walked the remaining 4 miles. If the total trip took 0.75 hours, then what was his average jogging speed
Answer:
12 mph
Step-by-step explanation:
The relationship between jogging speed and walking speed means the time it takes to walk 4 miles is the same as the time it takes to jog 8 miles. Then the total travel time (0.75 h) is the time it would take to jog 1+8 = 9 miles. The jogging speed is ...
(9 mi)(.75 h) = 12 mi/h . . . average jogging speed
__
Check
1 mile will take (1 mi)/(12 mi/h) = 1/12 h to jog.
4 miles will take (4 mi)/(6 mi/h) = 4/6 = 8/12 h to walk.
The total travel time is (1/12 +8/12) h = 9/12 h = 3/4 h. (answer checks OK)
_____
Comment on the problem
Olympic race-walking speed is on the order of 7.7 mi/h, so John's walking speed of 6 mi/h should be considered quite a bit faster than normal. The fastest marathon ever run is on the order of a bit more than 12 mi/h, so John's jogging speed is also quite a bit faster than normal. No wonder he got tired.
help me solve this problem!!
Answer:
initial size: 75doubling time: 7.51 minutesafter 115 minutes: about 3,056,900reaches 11,000: 54.03 minutesStep-by-step explanation:
For given points (t1, y1), (t2, y2), I like to write the exponential function as ...
y(t) = y1·(y2/y1)^((t-t1)/(t2-t1))
This can be converted to other forms (such as a·b^t or a·e^(kt)) fairly easily, but those tend not to reproduce the given numbers exactly as this form does.
Using (15, 300) and (35, 1900) as our data values, the exponential function can be written as ...
y(t) = 300·(19/3)^((t-15)/20)
__
a) The initial size of the culture is the value of y(0).
y(0) = 300·(19/3)^(-15/20) ≈ 75.144
y(0) ≈ 75 . . . initial population
__
b) The doubling period will be the value of t that satisfies ...
(19/3)^(t/20) = 2
Taking logarithms, we have ...
(t/20)·log(19/3) = log(2)
t = 20·log(2)/log(19/3) ≈ 7.5104 . . . . minutes
The doubling time is about 7.51 minutes.
__
c) Evaluating the formula for t=115, we have ...
y(115) = 300·(19/3)^(100/20) ≈ 3056912.346
The count after 115 minutes will be about 3,056,900.
__
d) Solving y(t) = 11,000, we have ...
11000 = 300·(19/3)^((t-15)/20)
11000/300 = (19/3)^((t-15)/20)
log(110/3) = (t-15)/20·log(19/3)
t = 20·log(110/3)/log(19/3) + 15 ≈ 54.027
It will take about 54.03 minutes for the count to reach 11,000.
_____
I find a graphing calculator to be a nice tool for solving problems like this.
Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they work together they can do the entire prospectus in five hours. How long will it take each of them working alone to repair the prospectus? Round answers to the nearest 10th of an hour
Time taken by jerry alone is 10.1 hours
Time taken by callie alone is 8.1 hours
Solution:
Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can
Let the time taken by Terry be "a" hours
So, the time taken by Callie will be (a-2) hours
Hence, the efficiency of Callie and Terry per hour is [tex]\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }[/tex]
If they work together they can do the entire prospectus in five hours
[tex]\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}[/tex]
On cross-multiplication we get,
[tex]\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}[/tex]
[tex]\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}[/tex]
On cross multiplication ,we get
[tex]\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}[/tex]
using quadratic formula:-
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
[tex]x=\frac{12 \pm \sqrt{144-40}}{2}[/tex]
[tex]\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}[/tex]
If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value
Let us take a = 10.1
So time taken by jerry alone = a = 10.1 hours
Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours
Tyler reads of a book on Monday, of it on Tuesday, of it on Wednesday, and of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
There are total of 32 pages in the complete book.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that Tyler reads 2/15 of a book on Monday, 1/3 of it on Tuesday, 2/9 of it on Wednesday, and 3/4 of the remainder on Thursday. He still has 14 pages.
Let the total number of pages in the book will be [x]. Then, we can write -
{2x/15} + {x/3} + {2x/9} + {3x/4} = x + 14
x{2/15 + 1/3 + 2/9 + 3/4} - 14 = x
259x/180 - 14 = x
1.44x - 14 = x
0.44x = 14
x = (14/0.44)
x = 32 (approx.)
Therefore, there are total of 32 pages in the complete book.
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Fresh pond has a population of 854 and is increasing by 3 people per year. Strawberry has a population of 427 and is increasing by 10% per year. Write an equation that models the growth for each town.
Answer:
Fresh Pond: p(t) = 854 +3tStrawberry: p(t) = 427·1.10^tStep-by-step explanation:
(a) The general term of an arithmetic sequence is ...
an = a1 + d(n -1)
If we let the sequence of population numbers be modeled by this, and we use t for the number of years, we want n=1 for t=0, so n = t+1 and we have ...
p(t) = 854 +3(t+1-1)
p(t) = 854 +3t
__
(b) The general term of a geometric sequence is ...
an = a1·r^(n-1)
were r is the common ratio. Here, the multiplier from one year to the next is 1+10% = 1.10. Again, n=t+1, so the population equation is ...
p(t) = 427·1.10^(t+1-1)
p(t) = 427·1.10^t
The ___________ of a lens or mirror is a rotational symmetry axis of the surfaces.
Answer:
Optical axis
Step-by-step explanation:
Optical axis is the rotational symmetry axis of the surfaces.
A line with a certain degree of rotational symmetry is called as the optical axis in an optical system.
It is the straight line that passes through the geometric center of the lens and joins two curvature centers of its surfaces.
It is also called as the principal axis.
Simplify the function f(x) = 1/3 (81) 3x/4 Then determine the key aspects of the function.
Answer:
[tex]f(x)=3^{3x-1}[/tex].
The domain of the function is the set of all real number and the range is [tex](0,\infty)[/tex]
Step-by-step explanation:
Given:
The function is given as:
[tex]f(x)=\frac{1}{3}(81)^{\frac{3x}{4}}[/tex]
Using the rule of the exponents, [tex]a^{mn}=(a^m)^n[/tex],
[tex]f(x)=\frac{1}{3}((81)^{\frac{1}{4}})^{(3x)}\\f(x)=\frac{1}{3}(\sqrt[4]{81} )^{3x}\\f(x)=\frac{1}{3}(3)^{3x}\\f(x)=\frac{3^{3x}}{3^1}[/tex]
Using the rule of the exponents,[tex]\frac{a^m}{a^n}=a^{m-n}[/tex],
[tex]f(x)=3^{3x-1}[/tex]
Therefore, the simplified form of the given function is:
[tex]f(x)=3^{3x-1}[/tex]
Key aspects:
The given function is an exponential function with a constant base 3.
Domain is the set of all possible values of [tex]x[/tex] for which the function is defined.
The domain of an exponential function is a set of all real values.
The range of an exponential function is always greater than zero.
Therefore, the domain of this function is also all real values and the range is from 0 to infinity.
Domain: [tex]x \epsilon (-\infty,\infty)[/tex]
Range: [tex]y\epsilon (0,\infty)[/tex]
Answer: 1/3 27 all real numbers y>0
Step-by-step explanation:
One leg of a right triangle is 4 mm shorter than the longer leg in the hypotenuse is 4 mm longer than the longer leg find the links of the sides of the triangle
Answer:
Step-by-step explanation:
The right triangle has three sides which can be called legs. The legs are; shorter leg. Longer leg and hypotenuse
Let the longer leg be x
One leg of a right triangle is 4 mm shorter than the longer leg. This means
The shorter leg = x - 4
the hypotenuse is 4 mm longer than the longer leg. This means
The hypotenuse = x + 4
So the legs of the triangle are
Shorter leg or side = x-4
Longer leg or side = x
Hypotenuse = x + 4
The lengths of the sides of the triangle are 12 mm, 16 mm, and 20 mm.
Explanation:Let's use variables to represent the lengths of the sides:
Shorter leg: x mmLonger leg: x + 4 mmHypotenuse: x + 8 mmAccording to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse:
a² + b² = c²
Plugging in the values, we have:
x² + (x + 4)² = (x + 8)²
Expanding and simplifying, we get:
x² + x² + 8x + 16 = x² + 16x + 64
Combining like terms, we get:
x² - 8x - 48 = 0
Factoring the quadratic equation, we find:
(x - 12)(x + 4) = 0
Therefore, x = 12 or x = -4. We discard the negative value, so the lengths of the sides of the triangle are:
Shorter leg: 12 mmLonger leg: 16 mmHypotenuse: 20 mmRover eats 3/4 of a can of cat food each day and Bono eats 1/2 of a can food each day.Cat food costs $5.00 for three cans.It is only sold in 3 can packs.How much does it cost for a 60 day supply of cat food?
Answer:
It would Cost $125 for a 60 day supply of cat food.
Step-by-step explanation:
Given:
Rover eats cat food each day = [tex]\frac{3}{4}[/tex] = 0.75 can
Bono eats cat food each day = [tex]\frac{1}{2}[/tex] = 0.5 can
Each day consumption for both cats = 0.75+0.5 = 1.25 can
Each day both cats consume = 1.25 cans
For 60 days both cats consume = Number of cans in 60 days.
By Using Unitary method we get;
Number of cans in 60 days = [tex]1.25\times60=75 \ cans[/tex]
Now Cans are sold in a pack of 3.
Hence we will divide number of cans in 60 days with 3 we get;
Number of can packs required for 60 days = [tex]\frac{75}{3}=25 \ can \ packs[/tex]
Now Cost for each Can packs(3 can) = $5.00
Hence Cost for 25 Can packs (75 cans) = Price for 25 can packs(75 can)
By Using Unitary method we get;
Price for 25 can packs (75 cans) = [tex]5\times 25 = \$125[/tex]
Hence Price for 25 can packs (75 cans) which are used for 60 supply of cat food is $125.
For a group of graduating college seniors, a researcher records each student’s rank in his/her high school graduating class and the student’s rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables?
Answer:
Spearman's correlation
Step-by-step explanation:
A researcher records each student’s rank in his/her high school graduating class and the student’s rank in the college graduating class.
The correlation that should be used to measure the relationship between these two variables is - Spearman's correlation
This correlation gives a statistical measure of similar relationship between paired data.
This is used to evaluate relationships involving ordinal variables.
Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5,000 more than twice the amount she put into the CD. How much did she invest in each account? Call the amount that Daniela invested in the CD d and the amount she invested in bonds b.
Answer:
The amount invested in bonds = 35,000
The amount invested in CD = 15,000.
Step-by-step explanation:
The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds [tex]b[/tex], and the amount invested in CD [tex]d[/tex], then we have:
[tex]b+d=50,000[/tex] this says the total amount Daniela invested is $50,000.
And since the amount invested in bonds [tex]b[/tex] is $5,000 more than twice the amount Daniela put into the CD, we have:
[tex]b=5,000+2d[/tex].
Thus, we have two equations and two unknowns [tex]b[/tex] and [tex]d[/tex]:
(1). [tex]b+d=50,000[/tex]
(2). [tex]b=5,000+2d[/tex],
and we solve this system by substituting [tex]b[/tex] from the second equation into the first:
[tex]b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}[/tex]
or, the amount invested in CD is $15,000.
With the value of [tex]d[/tex] in hand, we now solve for [tex]b[/tex] from equation(2):
[tex]b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}[/tex]
or, the amount invested in bonds is $35,000.
URGENT!!!
Find the equation x^2 + y^2 + Dx + Ey + F = 0
of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.
(0, 0), (8, 8), (16, 0)
Answer:
D= -16
E= 0
F= 0
Step-by-step explanation:
The given equation is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex]
It is also given that the circle passes through (0,0) (16,0) and (8,8).
Inserting (0,0) in the equation, it gives
[tex]0 + 0 + 0 + 0 + F = 0[/tex]
This gives F = 0 .
Now inserting (16,0) , it gives
[tex]16^{2} + 0^{2} + D(16) + E(0) + 0 = 0[/tex]
[tex]D(16) = -256[/tex]
[tex]D = \frac{-256}{16}[/tex]
D = -16
Now inserting (8,8) , it gives
[tex]8^{2} + 8^{2} + (-16)(8) + (E)(8) + 0 = 0[/tex]
[tex]-16 + E = -16[/tex]
E = 0
Thus the equation of circle is
[tex]x^{2} + y^{2} + (-16)x = 0[/tex]
We can draw the following graph and thus verify that points (0,0) (8,8) and (16,0) lie on graph.
The equation of the circle passing through points (0, 0), (8, 8), and (16, 0) is x^2 + y^2 - 16x - 16y = 0. Solving the system of equations derived from substituting the given points into the circle equation confirms these coefficients for D and E.
Explanation:To find the equation of the circle that passes through the points (0, 0), (8, 8), and (16, 0), we can use the standard form of a circle's equation:
x
2
+
y
2
+ D
x
+ E
y
+ F = 0
Because the circle passes through the origin (0,0), we know that F = 0. With the remaining points (8, 8) and (16, 0), we can substitute these coordinates into the equation to form a system of equations.
Using point (8,8), the equation becomes:
64 + 64 + 8D + 8E + F = 0
Using point (16,0), the equation becomes:
256 + 16D + F = 0
Since F = 0, the system of equations is:
8D + 8E + 128 = 016D + 256 = 0Solving these equations, we get:
D = -16E = -16The equation of the circle is therefore:
x2 + y2 - 16x - 16y = 0To verify the result, plotting the points and the graph of the circle on a graphing utility should show that the points lie on the circumference of the circle.
Emma and Leah are both jewelry makers. Gemma made 106 beaded necklaces. Leah made 39 more necklaces than Gemma. Each necklace they make has exactly 104 beads on it. How many beads did both jewelers use altogether while making their necklaces?
Both jewelers used 26104 beads altogether while making necklaces.
Step-by-step explanation:
No. of necklaces made by Gemma = 106
Necklaces made by Leah = 106+39 = 145 necklaces
Total necklaces made = Gemma's + Leah's
Total necklaces made = [tex]106+145 = 251\ necklaces[/tex]
Beads used in 1 necklace = 104 beads
Beads used in 251 necklaces = 104*251 = 26104
Both jewelers used 26104 beads altogether while making necklaces.
Keywords: multiplication, addition
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In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12 2 We can conclude that:
A. The variables are dependent
B. The variables are independent
C. The probability of getting these results by random chance alone is 5
D. Being in a certain socioeconomic class causes arrests
You want to buy a $230,000 home. You plan to pay 20% as a down payment, and take out a 30 year fixed loan for the rest. Round all answers to the nearest cent as needed.
Amount of down payment = $46000
Mortgage needs = $184000
Solution:
From the given,
Cost of the house = [tex]\$230000[/tex]
Percentage of down payment = [tex]20\%[/tex]
Number of years of fixed loan = 30
[tex]\text { Total down payment }=\text { cost of the house } \times \text { Percentage of down payment }[/tex]
[tex]\Rightarrow \frac{230000 \$\times 20}{100} \rightarrow 46000 \$[/tex]
[tex]\text {Mortgage needs}=\text { Total cost - Total down payment }[/tex]
[tex]\Rightarrow 230000 \$-46000 \$=184000 \$[/tex]
It can be concluded that the total down payment for the house and mortgage needs would be [tex]\$46000 \text{ and } \$184000[/tex]
Earth orbits the sun at an average speed of 29.79 kilometers per second. Find how long it take, to the nearest hundredth of a second, for earth to travel 500 kilometers
Answer:
16.78 seconds
Step-by-step explanation:
speed = Distance Traveled / time
thus speed =29.79 Km/sec
time =distance Traveled/speed (from above formula)
time taken=500 km ÷ 29.79 Km/sec
∴time taken=16.78 seconds
Suppose that textbook weights are normally distributed. You measure 28 textbooks' weights, and find they have a mean weight of 76 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Round answers to 2 decimal places.
Answer:
Step-by-step explanation:
We want to find 95% confidence interval for the mean of the weight of of textbooks.
Number of samples. n = 28 textbooks weight
Mean, u =76 ounces
Standard deviation, s = 12.3 ounces
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
76 +/- 1.96 × 12.3/√28
= 76 +/- 1.96 × 2.3113
= 76 +/- 4.53
The lower end of the confidence interval is 76 - 4.53 =71.47
The upper end of the confidence interval is 76 + 4.53 = 80.53
Therefore, with 95% confidence interval, the mean textbook weight is between 71.47 ounces and 80.53 ounces
Evaluate (x + y)^0 for x = -3 and y = 5.
Answer:
The answer is 1.
Answer:
1
Step-by-step explanation:
any variable of power 0 equal to 1
A model is made of a car. The car is 3 meters long and the model is 3 centimeters long. What is the ratio of the length of the car to the length of the model? A. 3 : 3 B. 1 : 100 C. 1 : 3 D. 100 : 1
Answer:
D
Step-by-step explanation:
a meter is 100 centimeters so the ratio of the real car to the model is 300 centimeters to 3 centimeters, or 100:1 so D
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 141°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by
T = 0.005x² + 0.45x + 125.
Will the temperature of the part ever reach or exceed 141F? Use the discriminant of a quadratic equation to decide.
A. yes
B. no
Answer:
Yes, it will reach or exceed 141 degree F
Step-by-step explanation:
Given equation that shows the temperature T in degrees Fahrenheit x minutes after the machine is put into operation is,
[tex]T = 0.005x^2 + 0.45x + 125[/tex]
Suppose T = 141°F,
[tex]\implies 141 = 0.005x^2 + 0.45x + 125[/tex]
[tex]\implies 0.005x^2 + 0.45x + 125 - 141 =0[/tex]
[tex]\implies 0.005x^2 + 0.45x - 16=0[/tex]
Since, a quadratic equation [tex]ax^2 + bx + c =0[/tex] has,
Real roots,
If Discriminant, [tex]D = b^2 - 4ac \geq 0[/tex]
Imaginary roots,
If D < 0,
Since, [tex]0.45^2 - 4\times 0.005\times -16 = 0.2025 + 32 > 0[/tex]
Thus, roots of -0.005x² + 0.45x + 125 are real.
Hence, the temperature can reach or exceed 141 degree F.
The temperature of the part will exceed 141°F during the manufacturing process.
Explanation:To determine if the temperature of the part will ever reach or exceed 141°F, we need to find the value of x when the temperature T equals 141°F. We can do this by setting the equation T = 0.005x² + 0.45x + 125 equal to 141 and solving for x using the quadratic formula.
The quadratic formula is given by x = (-b ± √(b² - 4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 0.005, b = 0.45, and c = 125 - 141 = -16.
Calculating the discriminant, which is the value inside the square root in the quadratic formula, we get b² - 4ac = 0.45² - 4(0.005)(-16) = 0.2025 + 0.32 = 0.5225. Since the discriminant is positive, the quadratic equation has two real and distinct solutions, which means the temperature of the part will exceed 141°F at some point during the manufacturing process.
Learn more about temperature calculation here:https://brainly.com/question/36032928
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Please help me! Picture below
Answer:
A i think
Step-by-step explanation:
A man and a woman agree to meet at a certain location about 12:30 P.M. If the man arrives at a time uniformly distributed between 12:15 and 12:45, and if the woman independently arrives at a time uniformly distributed between 12:00 and 1 P.M., find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?
Final answer:
To find the probability that the first to arrive waits no longer than 5 minutes and the probability that the man arrives first, follow the provided detailed steps.
Explanation:
To find the probability that the first to arrive waits no longer than 5 minutes:
Man arrives first: 1/6
Woman arrives first: 1/4
Man and Woman arrive simultaneously within 5 minutes: 1/12
The probability that the man arrives first: 1/6
11. Solve the problem. A company manufactures televisions in batches of 25 and there is a 1% rate of defects. Find the standard deviation for the number of defects per batch.
0.7
0.9
0.5
72.8
Answer: 0.5
Step-by-step explanation:
For binary distribution with parameters p (probability of getting success in each trial) and n (Total trials) , we have
[tex]\sigma=\sqrt{np(1-p)}[/tex]
We are given that ,
Total batches of televisions : n=25
The probability of defects : p= 0.01
Here success is getting defective batch .
Then, the standard deviation for the number of defects per batch will be :-
[tex]\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5[/tex] [Rounedde to the nearest tenth.]
Therefore, the standard deviation for the number of defects per batch =0.5