Answer:
The cheap one is 8 while the costly one is 17.5
Step-by-step explanation:
Let the cheaper candle be x
And the costly candle b y
X+y = 25.5.... equation one
2.20x +7.3y = 25.5(5.7)
2.2x + 7.3y = 145.35....equation two
Solving simultaneously
X+y = 25.5
2.2x + 7.3y = 145.35
2.2X+2.2y = 56.1
2.2x + 7.3y = 145.35
5.1y= 89.25
Y= 17.5
X+y = 25.5
X+ 17.5 = 25.5
X= 25.5-17.5
X= 8
The cheap one is 8 while the costly one is 17.5
please help me, i will give you brainliest
Answer:
3rd
Step-by-step explanation:
i got it right on khan academy
It is a well-known fact that Dr. Barnes rides a skateboard, sometimes even on campus. Suppose that Dr. Barnes selects a skateboard by first picking one of two skateboard shops at random and selecting a skateboard from that shop at random. The first shop contains two "rad" skateboards and three "gnarly" skateboards, and the second shop contains four "rad" skateboards and one "gnarly" skateboard. What is the probability that Dr. Barnes picked a skateboard from the first shop if he has selected a "gnarly" skateboard?
Answer:
75%.
Step-by-step explanation:
In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.
The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.
Hope this helps!
A que hora después de las 3 las agujas de un reloj determinan un ángulo que mide 54 por primera vez
Answer:
3:06
Step-by-step explanation:
primero debemos calcular a cuántos minutos equivale un ángulo de 54°. Para hacer esto utilizamos una regla de 3 simple donde 60 minutos equivale a 360° grados, entonces:
60 minutos ----- 360°
x minutos -------- 54°
Resolviendo para x, tenemos:
[tex]x=\frac{54*60}{360}=9[/tex]
Entonces si las manecillas están a 9 minutos de diferencia, el ángulo será 54°. Si la hora es después de las 3, significa que la manecilla de la hora estará en el minuto 15 y la otra debe estar 9 minutos antes, es decir en el minuto 6.
Por lo tanto, la hora después de las 3 en la cual se forma un ángulo de 54° por primera vez es a las 3:06
The profit y (in dollars) for a company for selling x games is represented by y=32x. Graph the equation. ANSWER BEFORE 11 FOr BOnUs PoINTS!!!
Answer:
I guess that we have the linear equation:
y = 32*x
Where y is the profit, and x is the number of games sold.
Then the first step may be doing a table.
Give x different values, then find the value of y.
if x = 0
y = 32*0 = 0
if x = 1, y = 32*1 = 32
if x = 2, y = 2*32 = 64
Then the points:
(0,0) (1,32) and (2, 64) belong to this line, now we need to conect them with a straigth line and its ready.
The graph will be:
PLEASE HELP ASAP!!!!Write the ratio as a fraction in lowest terms. 9 pounds to 36 pounds.(50 points!!)
Answer:
1/4
Step-by-step explanation:
9 lbs
---------
36 lbs
We can write this because the units are the same
Divide the top and bottom by 9
9/9
----------
36 /9
1/4
Answer:
1/4
Step-by-step explanation:
9 pounds
36 pounds
Ratios are written as x:y, fractions are written as x/y.
9:36 as a fraction will be 9/36
Simplify the fraction.
1/4
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.82 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.
Answer:
Yes the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 51[/tex]
The sample mean is [tex]\= x = 2.03[/tex]
The sample standard deviation is [tex]\sigma = 0.82[/tex]
The population mean is [tex]\mu = 1.75[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is
[tex]H_o : \mu = 0.82[/tex]
The alternative hypothesis is
[tex]H_a : \mu >1.75[/tex]
The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]
[tex]t = 2.44[/tex]
From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we reject the null hypothesis
Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. A) Determine the cooling constant k.B) What is the differential equation satisfied by the temperature F(t) of the bar?C) What is the formula for F(t)?D) Determine the temperature of the bar at the moment it is submerged.
Answer:
A) cooling constant = 0.0101365
B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]
c) F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]
D)137.46 ⁰
Step-by-step explanation:
water temperature = 60⁰F
temperature of Bar after 20 seconds = 120⁰F
temperature of Bar after 60 seconds = 100⁰F
A) Determine the cooling constant K
The newton's law of cooling is given as
= [tex]\frac{df}{dt} = k(60 - F)[/tex]
= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)
= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt
= In (60 -F) = -kt - c
60 - F = [tex]e^{-kt-c}[/tex]
60 - F = [tex]C_{1} e^{-kt}[/tex] ( note : [tex]e^{-c}[/tex] is a constant )
after 20 seconds
[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60
therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1
after 60 seconds
[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40
therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2
solve equation 1 and equation 2 simultaneously
= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]
= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]
= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k
cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365
B) what is the differential equation satisfied
substituting the value of k into the newtons law of cooling)
60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]
F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
The differential equation that the temperature F(t) of the bar
[tex]\frac{df}{dt} = k ( 60 - F )[/tex]
C) The formula for F(t)
t = 20 , F = 120
F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]
[tex]C_{1} e^{0.0101365(20)}[/tex] = 60
[tex]C_{1} = 60 * 1.291[/tex] = 77.46
C1 = - 77.46⁰ as the temperature is decreasing
The formula for f(t)
= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]
D) Temperature of the bar at the moment it is submerged
F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]
F(0) = 60 + 77.46(1)
= 137.46⁰
Lily is 14 years older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined age?
Answer:
30 years
Step-by-step explanation:
let the age of Ezekiel be x years
Given
Lily is 14 years older than her little brother Ezekiel
Age of Lily = x + 14 years
Next condition
after 8 years\
age of Ezekiel = x+8
age of Lily = x + 8 +14 = x + 22 years
Given
. In 8 years, Lily will be twice as old as Ezekiel will be then.
Thus,
x + 22 = 2(x+8)
=> x + 22 = 2x + 16
=> 22-16 = 2x -x
=> x = 6
Thus, age of Ezekiel = 8 years
age of lily = 8+14 = 22 years
sum of their age = 22 + 8 = 30 years answer.
What single transformation maps Triangle ABC onto A’B’C’
Answer:
Your answer is B
Step-by-step explanation:
rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a quiz competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 2, the second goes to 7, the third goes to 4, and the last goes to 10. A) A total of 10 students won all the prizes. B) Four students won 12, 13, 14, 15, 16, or 17 prizes. C) A total of 10 prizes were won by all the students. D) Four prizes were won by 12, 13, 14, 15, 16, or 17 students.
Answer: B.
Four students won 12, 13, 14, 15, 16, or 17 prizes
Answer:
Four students won 12, 13, 14, 15, 16, or 17 prizes!
Step-by-step explanation:
what is the slop of y= -5+4x
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
Which point is a solution to the system of inequalities graphed here? y -5 x + 4 A. (1,6) B. (-6,0) C. (0,5) D. (5,0)
Answer:
D
Step-by-step explanation:
this is the only one inside the overlapping inequalitlies
Express the following ratio in the simplest form vii) 4.5km: 450m
Answer:
4.5 ×1000 =4500m
Step-by-step explanation:
450/1000=0.45km
Answer: 10 : 1
Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.
Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.
What is the slope of the line described by the equation y-1=3x
Answer:
Hey there!
The line can be expressed into y intercept form, y=3x+1.
Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.
Let me know if this helps :)
Find a formula for an for the arithmetic sequence.
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
Last week Holly took a math test. She got 98 out of 123 question correct. What percentage did Holly get correct? Round to the nearest hundredth.
Answer:
79.67%
Step-by-step explanation:
To find the percentage correct, take the number correct over the total
98/123
.796747967
Change to a percent by multiplying by 100 %
79.6747967%
Round to the nearest hundredth
79.67%
Answer:
79.67%
Step-by-step explanation:
percent = part/whole * 100%
percent = 98/123 * 100%
percent = 79.67%
Given the diagram below, what is cos(45*)?
A.
B.
C.
D.
Answer:
The answer is option B
Step-by-step explanation:
To find cos 45° we must first find the adjacent and the hypotenuse
Let the adjacent be x
Let the hypotenuse be h
To find the adjacent we use tan
tan ∅ = opposite / adjacent
From the question
the opposite is 9
So we have
tan 45 = 9 / x
x tan 45 = 9
but tan 45 = 1
x = 9
Since we have the adjacent we use Pythagoras theorem to find the hypotenuse
That's
h² = 9² + 9²
h² = 81 + 81
h² = 162
h = √162
h = 9√2
Now use the formula for cosine
cos∅ = adjacent / hypotenuse
The adjacent is 9
The hypotenuse is 9√2
So we have
cos 45 = 9/9√2
We have the final answer as
cos 45 = 1 / √2Hope this helps you
Write the point slope equation of the line with the given slope that passes through the given point
M= -3, (3,5)
Answer:
y - 5 = -3(x - 3).
Step-by-step explanation:
The point-slope form is y - y1 = m(x - x1).
In this case, y1 = 5, x1 = 3, and m = -3.
y - 5 = -3(x - 3).
Hope this helps!
Answer:
[tex]\boxed{y-5= -3(x-3)}[/tex]
Step-by-step explanation:
Point-slope is in the general form:
[tex]y-y_1 = m(x-x_1)[/tex]
The values are given.
[tex]m=-3\\x_1=3\\y_1=5[/tex]
Plug in the values,
[tex]y-5= -3(x-3)[/tex]
Solve the equation 2x^2-3x-6=0 give your answer correct to two decimal places
Answer:
x = - 1.14 or x = 2.64Step-by-step explanation:
2x² - 3x - 6 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = 2 , b = - 3 , c = 6
Substituting the values into the above formula
We have
[tex]x = \frac{ - - 3± \sqrt{ { - 3}^{2} - 4(2)( - 6)} }{2(2)} [/tex]
[tex]x = \frac{3± \sqrt{9 +48 } }{4} [/tex]
[tex]x = \frac{3± \sqrt{57} }{4} [/tex]
[tex]x = \frac{3 - \sqrt{57} }{4} \: \: \: \: or \: \: \: \: \: x = \frac{3 + \sqrt{57} }{4} [/tex]
We have the final answer as
x = - 1.14 or x = 2.64Hope this helps you
A rectangular waterbed is 8 ft long, 5 fr, wide and 1 ft tall.
How many gallons of water are needed to fill the waterbed?
Assume 1 gallon is 0.13 ft.³ round to the nearest whole gallon
Answer: 308 gallons of water.
Step-by-step explanation:
First find the volume of the water been.
The volume of a rectangular prism uses the formula
V= L * W *H
V = 8 * 5 * 1
V = 40 ft^3
Now we will convert 40ft into gallons using what they gave us that 1 gallon is 0.13 ft^3
[tex]\frac{1}{x} = \frac{0.13}{40}[/tex] which means if 1 gallon is 0.13 cubic feet how much will 40 cubic feet be when converted to gallons.
Solve by cross product.
0.13x = 40 divide both sides by 0.13
x= 308
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
may someone assist me ?
Answer:
x = 6
Step-by-step explanation:
I will use some symbols, please refer to the image I attach to understand my answer.
Since BC = 2 using Thales theorem we get that
3/x = 2/4 then 3/x = 1/2 and 6 = x
Justin's hot water tank quits working and the landlord purchases a new one. He is concerned about its size and whether or not it can hold about 700 gallons. To do
so, it must have a volume of around 94 cubic feet.
What is the volume of a cylindrical water tank with a diameter of 4 and a height of 7 feet?
Answer:
87.92 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is πr² · h
1. Set up the equation
π2² · 7
2. Solve
(3.14)(4)(7) = 87.92
The volume of a cylindrical water tank with a diameter of 4 feet and a height of 7 feet is 87.92 cubic feet.
Given that, a cylindrical water tank with a diameter of 4 feet and a height of 7 feet.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
We know that, the volume of a cylinder πr²h
Here, radius =4/2 = 2 feet
The volume of a cylinder = 3.14×2²×7
= 3.14×4×7
= 87.92 cubic feet
Therefore, the volume of a cylindrical water tank with a diameter of 4 feet and a height of 7 feet is 87.92 cubic feet.
To learn more about the volume visit:
https://brainly.com/question/13338592.
#SPJ2
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x) 2. If we multiply a polynomial by a constant, is the result a polynomial? 3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.
Please answer in the form of an angle or degree
Step-by-step explanation:
angle A = angle B( Corresponding angles)
so,
5x - 5 = 3x + 13
=> 5x - 3x = 13 + 5
=> 2x = 18
=> x = 9
angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40
Answer:
x=9, ∠B=40
Step-by-step explanation:
In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,
2x=18, x=9
∠B=3(9)+13=27+13=40
Write these numbers in standard form 906000000
Answer:
9.06×10 to the power of 8(8 is superscript above 10)
Answer:
9.06 x 10^8
Step-by-step explanation:
906000000 = 9.06 x 10^8
8 decimal places in
The geometric probability function is f (x) = (1-P) x-1 P. what is the approximate probability of rolling a standard die and getting the first 6 on the 3rd try?
Answer:
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = (1-P)^{x-1} P[/tex]
We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Find (f•g)(x) for the given functions: f(x) = 5/x and g(x) = 3 + x/5.