what is 1 1/5 subtracted by 3 1/10
whoever gets it right I will choose as the brainliest
Answer:
6/5÷31/10=12/31
Step-by-step explanation:
6/5÷31/10=?Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
6/5×10/31=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
6×10 5×31=60/155
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 60 and 155 using
GCF(60,155) = 5
60÷51 55÷5=12/31
Therefore:
65÷3110=12/31
You can retry this question below
A6 inch personal pizza has 610 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices.
Estimate the number of calories in one slice of a 12 inch pizza.
Answer:
305 calories, 120 from fat
Step-by-step explanation:
The ratio of the area of the larger pizza to that of the smaller pizza is the square of the ratio of the diameters. So, the larger pizza has an area that is ...
(12/6)² = 4
times that of the smaller pizza. When that area is divided into 8 parts, each part has an area that is 4/8 = 1/2 the area of the smaller pizza.
We expect a slice of the larger pizza to have 1/2 the calories of a smaller pizza, so 305 calories, 120 from fat.
__
610/2 = 305; 240/2 = 120.
Which statement is not one of the axioms of Euclidean geometry
Answer:
D. If two planes intersect, their intersection is a point.
Step-by-step explanation:
Let's verify the answer choices:
A. Given any two distinct points, there is exactly one line that contains them.
Yes, correctB. Every plane contains at least three points that do not lie on the same line.
Yes, correctC. If two points lie in a plane, the line containing these points also lies in the plane.
Yes, correctD. If two planes intersect, their intersection is a point.
No, incorrect. The intersection of the plains is a line.Answer: geometry Euclidean
Step-by-step explanation:
A car’s value varies inversely with its age. Jackie bought a 10-year-old car for $2,400. Write the equation that relates the car’s value, v, to its age, a. What will be the value of Jackie’s car when it is 15 years old ?
Answer:
$1,600
Step-by-step explanation:
Inverse relation:
v = k/a
where v = value of car, and a = age in years.
To find k, we use a known value
2400 = k/10
k = 24000
The inverse relation is
v = 24,000/a
At 15 years, a = 15.
v = 24,000/15 = 1,600
The value of Jackie’s car when it is 15 years old will be $1,600.
What is the equation?
A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given data;
Let y be the car’s value and x is the age then, if there is an inverse relation between them;
y = k/x
Substitute the given values;
k=xy
k=2400 × 10
k = 24000
Substitute the value of k;
y = 24000/x
Condition 2;
at x = 15 and y = ?
y = 24,000/15
y= 1,600
Hence, the value of Jackie’s car when it is 15 years old will be 1600.
To learn more, about equations, refer;
https://brainly.com/question/10413253
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3) The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the
United States. During a speed test, the train traveled 8.0 x 10^2 miles in 2.5 hours. Compute the
speed of the train. (Try solving this problem using scientific notation.)
Answer:
[tex]3.2*10^2=320[/tex] mph
Step-by-step explanation:
hello,
it travels [tex]8.0*10^2[/tex] miles in 2.5 hours
So in 1 hours it travels
[tex]\dfrac{8.0*10^2}{2.5}=3.2*10^2[/tex]
miles
hope this helps
PLEASE HELP AND SHOW WORK
Answer:
7.5
Step-by-step explanation:
If we look at the 4 by 4 square around the triangle we can just do the area of the square minus the area of the 3 little triangles which is:
4 * 4 - 4 * 1 / 2 - 3 * 3 / 2 - 4 * 1 / 2
= 16 - 2 - 4.5 - 2
= 16 - 8.5
= 7.5
38â% of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball. Complete partsâ (a) throughâ (d) below.(a) Find the mean of the binomial distribution.
μequals= ( ) (Round to the nearest tenth asâ needed.) â
(b) Find the variance of the binomial distribution.
sigmasquared= ( ) â(Round to the nearest tenth asâ needed.)
â(c) Find the standard deviation of the binomial distribution.
sigma = ( ) (Round to the nearest tenth asâ needed.) â
(d) Interpret the results in the context of theâ real-life situation.
Onâ average ( ) out of 6 women would consider themselves baseball fans. The standard deviation is ( ) âwomen, so in most samples of 6â women, the number of women who consider themselves baseball fans would differ from the mean by no more than ( ).â(Type integers or decimals rounded to the nearest tenth asâneeded.)
Answer:
a) 2.3
b) 1.4
c) 1.2
d) On average, 2.3 out of 6 women would consider themselves baseball fans. The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.
Step-by-step explanation:
For each woman, there are only two possible outcoes. Either they are a fan of professional baseball, or they are not. The prbability of a woman being a fan of professional baseball is independent of other woman. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
38% of women consider themselves fans of professional baseball.
This means that [tex]p = 0.38[/tex]
Six women are sampled:
This means that [tex]n = 6[/tex]
(a) Find the mean of the binomial distribution.
[tex]E(X) = np = 6*0.38 = 2.3[/tex]
(b) Find the variance of the binomial distribution
[tex]V(X) = np(1-p) = 6*0.38*0.62 = 1.4[/tex]
(c) Find the standard deviation of the binomial distribution.
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6*0.38*0.62} = 1.2[/tex]
(d) Interpret the results in the context of theâ real-life situation.
On average, 2.3 out of 6 women would consider themselves baseball fans. The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.
Consider the initial value problem my′'+ c y′+ k y=F(t),y(0)=0,y,(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t),where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k= 80 Newtons per meter, and F(t)=20sin(6t)Newtons.a. Solve the initial value problem.b. Determine the long-term behavior of the system.c. Is limt→[infinity]y(t)=0?If no, enter a function that approximates y(t)for very large positive values of t.
Answer:
A) [tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]
B) [tex]\frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]
Step-by-step explanation:
- The following initial value problem is given as follows:
[tex]my'' + cy' + ky = F(t) \\\\y(0) = 0\\y'(0) = 0[/tex]
- The above equation is the Newtonian mathematical model of a spring-mass-dashpot system. The displacement ( y ) and velocity ( y' ) are zeroed at the initial value t = 0.
- The equivalent mass ( m ) , damping constant ( c ) and the equivalent spring stiffness ( k ) are given as follows:
[tex]m = 2 kg\\\\c = 8 \frac{kg}{s} \\\\k = 80 \frac{N}{m} \\\\[/tex]
- The system is subjected to a sinusoidal force F ( t ) given. We will plug in the constants ( m , c, and k ) and applied force F ( t ) into the given second order ODE.
[tex]2y'' + 8y' + 80y = 20sin(6t)[/tex]
- The solution to a second order ODE is comprised of a complementary function ( yc ) and particular function ( yp ).
- To determine the complementary function ( yc ) we will solve the homogeneous part of the given second order ODE. We will assume the independent solution to the homogeneous ODE takes the form:
[tex]y = e^-^a^t[/tex]
Where,
a: The root of the following characteristic equation
- Substitute ( y ) into the given ODE as follows:
[tex]( 2a^2 + 8a + 80 )*e^-^a^t = 0\\\\2a^2 + 8a + 80 = 0[/tex]
- Solve the above characteristic quadratic equation:
[tex]a = 2 +/- 6i[/tex]
- The complementary solution for the complex solution to the characteristic equation is of the form:
[tex]y_c = e^-^\alpha^t * [ Acos (\beta*t) + Bcos (\beta*t) ][/tex]
Where,
a = α ± β
Therefore,
[tex]y_c = e^-^2^t * [ Acos (6t) + Bcos (6t) ][/tex]
- To determine the particular solution we will scrutinized on the non-homogeneous part of the given ODE. The forcing function F ( t ) the applied force governs the form of the particular solution. For sinusoidal wave-form the particular solution takes form as following:
[tex]y_p = Csin (6t ) + Dcos(6t )[/tex]
Where,
C & D are constants to be evaluated.
- Determine the first and second derivatives of the particular solution (yp) as follows:
[tex]y'_p = 6Ccos(6t) - 6Dsin(6t)\\\\y''_p = -36Ccos(6t) - 36Dcos(6t)\\[/tex]
- Plug in the particular solution ( yp ) and its derivatives ( first and second ) into the given ODE.
[tex]-72Csin(6t) - 72Dcos(6t) + 48Ccos(6t) - 48Dsin(6t) + 80Csin(6t) + 80Dcos(6t) = 20sin(6t) \\\\sin(6t)* ( 8C -48D ) + cos(6t)*(8D + 48C ) = 20sin(6t)\\\\D + 6C = 0\\\\C - 6D = 2.5\\\\C = \frac{5}{74} , D = -\frac{15}{37}[/tex]
- The particular solution can be written as follows:
[tex]y_p = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]
- Now we use the principle of super-position and combine the complementary and particular solution and form a function of general solution as follows:
[tex]y_g = y_c + y_p \\\\y_g = e^-^2^t* [ Acos(6t) + Bsin (6t) ] + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]
- To determine the complete solution of the given ODE we have to calculate the constants ( A and B ) using the given initial conditions as follows:
[tex]y_g ( 0 ) = 1*[A(1) + 0 ] + 0 - \frac{15}{37}(1) = 0\\\\A = \frac{15}{37}\\\\y'_g = -2e^-^2^t*[Acos(6t) + Bsin(6t) ] +e^-^2^t*[-6Asin(6t) + 6Bcos(6t) ] + \\\\\frac{15}{37}cos(6t) +\frac{90}{37}sin(6t) \\\\y'_g(0) = -2*[A(1) + 0] + 1*[0 + 6B] + \frac{15}{37}(1) +0 = 0\\\\B = \frac{15}{6*37} = \frac{5}{74}[/tex]
- The complete solution to the initial value problem is:
[tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]
- To determine the long term behavior of the system we will apply the following limit on our complete solution derived above:
[tex]Lim (t->inf ) [ y_g ] = \frac{15}{37}cos(6t)* [ 0 - 1 ] + \frac{5}{74}sin(6t)* [ 0 + 1 ]\\\\Lim (t->inf ) [ y_g ] = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]
- We see that the complementary part of the solution decays as t gets large and the particular solution that models the applied force F ( t ) is still present in the system response when t gets large.
a box is filled with chocolates and its mass is 480g. The same box is now filled with mints and its mass is 350g. The chocolates weigh twice as much as the mints. what is the mass of the box
Answer:
The box weighs 220 grams.
Step-by-step explanation:
Since the box full of chocolates weighs 480 grams, and the same box full of mints weighs 350, the weight difference between them is 130 grams. According to the statement, the quantity of chocolate weighs twice that of mint, while the weight of the box does not vary.
Therefore, since chocolate weighs twice as much as mints, and the weight is reduced by 130 grams, that is the difference in weight between the two, with which chocolate weighs 260 grams and mints 130 grams.
Therefore, the box weighs 220 grams: 220 + 130 = 350, and 220 + 260 = 480.
A football coach compared the yards per game of two of his running backs over the course of 10 games. Based on the data represented in the box plots, which football player had greater success during the 10 games? Nasir was more successful because he had the greatest number of yards in one game. Aaron was more successful because he had the greater total spread. Nasir was more successful because he had the greater measure of center. Aaron was more successful because he had an outlier.
Answer:
C Nasir was more successful because he had the greater measure of center
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Marlon built a ramp to put in front of the curb near his driveway so he could get to the sidewalk more easily from the street on his bike. A rectangular prism with a length of 6 inches, width of 18 inches, and height of 6 inches. A triangular prism. The triangular sides have a base of 8 inches and height of 6 inches. The prism has a height of 18 inches. If the ramp includes the flat piece as well as the angled piece and is made entirely out of concrete, what is the total amount of concrete in the ramp? 768 inches cubed 936 inches cubed 984 inches cubed 1,080 inches cubed
Answer: 1,080 in. cubed
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
What is the area W. Please help geometry
Answer:
C. 9π
Step-by-step explanation:
r=x-1
A=πr^2
--------
(x-1)^2+(2x-4)^2= (x-1+2)^2x^2-2x+1+4x^2- 16x+16= x^2+2x+14x^2 -20x +16=0x^2-5x+4=0(x-1)(x-4)=0x=1 - not possible as radius can't be zerox=4 is the solution--------
A= πr^2= π*(4-1)^2= 9π, option C.
A right triangle has two shorter sides that differ in length by 7cm. The length of the
hypotenuse is 8 cm longer than the shortest side. Find the lengths of the three sides.
Show all of your steps.
Pls help!!! 75 points
Answer:
a = 5
b = 12
c = 13
Step-by-step explanation:
a^2+b^2=c^2
b-a=7(b=a+7)
c=a+8
Then, substitute
a^2+((a+7)*(a+7))=c^2
a^2+a^2+7a+7a+49=c^2
2a^2+14a+49=c^2
Because c = a+8
2a^2+14a+49=(a+8)(a+8)
2a^2+14a+49=a^2+16a+64
a^2-2a=15
a^2-2a-15=0
(a-5)(a+3)=0
a = 5,-3
a = 5(a side cannot be negative)
Plug in a=5 to the other equations to get
a = 5, b = 12, c = 13
Hope it helps <3
Answer:
The lengths of the sides are 5, 12, 13.
Step-by-step explanation:
In a right triangle, the two shorter sides are the legs. The longest side is the hypotenuse.
Let the shorter leg = x.
The longer leg is 7 cm longer, so its length is x + 7.
The length of the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8.
The lengths are:
x, x + 7, x + 8
Since the triangle is a right triangle, we can use the Pythagorean theorem.
a^2 + b^2 = c^2
x^2 + (x + 7)^2 = (x + 8)^2
Square the trinomials.
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
Combine like terms and place them all on the left side equaling zero.
x^2 - 2x - 15 = 0
Factor the left side.
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Since the length of a side of a triangle cannot be negative, we discard the solution x = -3.
x = 5
x + 7 = 5 + 7 = 12
x + 8 = 5 + 8 = 13
Answer: The lengths of the sides are 5, 12, 13.
The product of three consecutive integers is 210. What is their sum?
Answer: 69, 70, 71
x + x + 1 + x + 2 = 210
3x + 3 = 210
3x = 210 - 3
x = 207 / 3
x = 69
x + 1 = 70
x + 2 = 71
The average distance from earth to the sun is 92, 589, 230 miles. The distance from earth to the moon is 92,350,373 miles less than the distance from earth to the sun. Find the distance from earth to the moon and sun to moon.
Distance from earth to moon =238,857 miles ; Distance from sun to moon. = 92,350,373 miles
Distance from earth to moon=184,939,603 miles; Distance from sun to moon. = 277,528,833 miles
Distance from earth to moon=238,857 miles ; Distance from sun to moon. =92,828,087 miles
Answer:
Step-by-step explanation:
Distance from earth to moon =238,857 :
x-92350373 = 92589230
x= 238857
Distance from sun to moon. = 92,350,373 miles
Distance from earth to moon=184,939,603 miles
Distance from sun to moon. = 277,528,833 miles
Distance from earth to moon=238,857 miles
Distance from sun to moon. =92,828,087 miles
Answer:
1 AU is the grade point answer
According to the american red cross, 10.3% of all connecticut residents have type b blood. a random sample of 26 connecticut residents is taken. X= the number of CT residents that have Type B blood, of the 17 sampled. What is the expected value of the random variable X?
Answer:
The expected value of the random variable X is 2.678.
Step-by-step explanation:
We are given that according to the American red cross, 10.3% of all Connecticut residents have type B blood.
Also, a random sample of 26 Connecticut residents is taken.
Let X = the number of CT residents that have Type B blood
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 26 residents
r = number of success
p = probability of success which in our question is % of all
Connecticut residents who have type B blood, i.e; 10.3%.
So, X ~ Binom(n = 26, p = 0.103)
Now, the expected value of the random variable X is given by;
E(X) = [tex]n \times p[/tex]
= [tex]26 \times 0.103[/tex] = 2.678
The expected value of the random variable X is 2.678.
Important information:According to the american red cross, 10.3% of all connecticut residents have type b blood. a random sample of 26 connecticut residents is taken. X= the number of CT residents that have Type B blood, of the 17 sampled.
Calculation of expected value:= 26 (10.3%)
= 2.678
Here we multiplied the random sample with the given percentage so that the expected value could come.
Learn more about the variable here: https://brainly.com/question/21444495
finding the missing angles 35° and 145°
Answer:
145°Step-by-step explanation:
There are two ways to find the value of X
[tex]x + 35 = 180[/tex] ( sum of co-interior angles)
Move constant to R.H.S and change its sign
[tex]x = 180 - 35[/tex]
Calculate the difference
[tex]x = 145[/tex]°
You can use another way too.
[tex]x = 145[/tex]° ( being vertically opposite angles)
Vertically opposite angles are always equal.
Hope this helps...
Best regards!!
Answer:
x = 145°
Step-by-step explanation:
Vertically opposite, also interior angles always add up to 180° so if you want to double check this, do 145° + 35° you should get 180°
I hope this helped you :)
The Nielsen Company reported that U.S. residents aged 18 to 24 years spend an average of 32.5 hours per month using the Internet on a computer.13 You wonder if this it true for students at your large university because so many students use their smartphones to access the Internet. You collect an SRS of n=75 students and obtain ¯x=28.5 hours with s=23.1 hours.
Required:
a. Report the 95% confidence interval for μ, the average number of hours per month that students at your university use the Internet on a computer.
b. Use this interval to test whether the average time for students at your university is different from the average reported by Nielsen. Use the 5% significance level. Summarize your results.
Answer:
a) [tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
b) For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
Step-by-step explanation:
Information given
[tex]\bar X=28.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=23.1 represent the sample standard deviation
n=75 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=75-1=74[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] and the critical value would be [tex]t_{\alpha/2}=1.993[/tex]
Now we have everything in order to replace into formula (1):
[tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]
[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]
Part b
For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong
Find the measure of each angle: Supplementary angles with measures (2x+3)° and (3x+2)°.
Answer: 73 degrees and 107 degrees.
Step-by-step explanation:
The total of supplementary angles are 180 degrees. So you add 2x+3 and 3x+2. Then you get 5x+5=180.
Subtract 5 from both sides. Now the equation is 5x=175.
Divide 5 on each side. x=35
Replace x with 35 in the equations. The angles are 73 and 107.
They both add up to 180 degrees so it is correct.
6 drinks make a six-pack. Marty has 23 drinks. name the mixed number of 6- packs Marty has.
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]3\frac{5}{6}[/tex]
▹ Step-by-Step Explanation
6 drinks = 6 Pack (one pack)
23 ÷ 6 = [tex]\frac{23}{6} = 3\frac{5}{6}[/tex]
Mixed number - [tex]3\frac{5}{6}[/tex]
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer: It's 3 5/6
but isn't this 4th-grade work?
Step-by-step explanation:
The Ship It Anywhere Company bought a truck for $245,000. According to the company’s accounting department, the truck will depreciate $32,500 per year. 1. Find a linear function V(t) of the form V(t) = mt + b that models the value of the truck. V is the value of the truck and t is the number of years after the truck was bought. a. What is the slope of the function? Interpret what the slope means. b. What is the V intercept? Interpret what the V intercept means. c. Give the formula for the function. 2. Usethefunctiontofindthetintercept.Interpretwhatthetinterceptmeans. 3. Graphthefunction. 4. What is the domain and range of V(t)? 5. Find V(8) and explain what it means. Does your answer make sense? 6. When will the truck have a value of $128,000? 7. When will the truck have a value between $62,000 and $140,000?
Answer:
1. [tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2. t-intercept: [tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3. Graph in the image attached.
4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5. [tex]V(8) = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6. After 3.6 years.
7. Between 3.23 years and 5.63 years.
Step-by-step explanation:
1.
The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:
[tex]V(t) = -32500t + 245000[/tex]
a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.
b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).
c. The formula is: [tex]V(t) = -32500t + 245000[/tex]
2.
To find the t-intercept we just need to use V(t) = 0 and then find the value of t:
[tex]0 = -32500t + 245000[/tex]
[tex]32500t = 245000[/tex]
[tex]t = 7.5385[/tex]
The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.
3.
The graph of the function is in the image attached.
4.
The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].
5.
[tex]V(8) = -32500*8 + 245000 = -15000[/tex]
It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.
6.
[tex]128000 = -32500t + 245000[/tex]
[tex]32500t = 117000[/tex]
[tex]t = 3.6[/tex]
After 3.6 years.
7.
[tex]62000 = -32500t + 245000[/tex]
[tex]32500t = 183000[/tex]
[tex]t = 5.6308[/tex]
[tex]140000 = -32500t + 245000[/tex]
[tex]32500t = 105000[/tex]
[tex]t = 3.2308[/tex]
Between 3.23 years and 5.63 years.
If a quadratic function has two solutions, what would you expect to see on the graph of its parabola? The parabola crosses the x-axis twice. The parabola touches the x-axis once. The parabola does not touch or cross the x-axis. The parabola has an infinite number of solutions.
The graph of a curve crosses the x-axis n times, where n is the amount of solutions (roots) it has.
So if it's a quadratic function (with 2 solutions) we can say that it the graph will cross the x-axis twice
The parabola crosses the x-axis twice. Therefore, option A is the correct answer.
Given that, a quadratic function has two solutions.
We need to find what would you expect to see on the graph of its parabola.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree. It is an algebraic function.
The solutions to a quadratic equation are the values of x where the graph crosses the x-axis at two points.
The parabola crosses the x-axis twice. Therefore, option A is the correct answer.
To learn more about a quadratic function visit:
https://brainly.com/question/27918223.
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Please answer this correctly
Answer:
1/6
Step-by-step explanation:
P(8) = number of 8's / total = 1/3
Then keeping the card so we have 7 and 9
P(7) = number of 7's / total = 1/2
P(8, keep, 7) = 1/3 * 1/2 = 1/6
Phoenix hiked the Rocky Path Trail last week. It took four days to complete the trip. The first two days she hiked a total of 26 miles. The second and third days she averaged 12 miles per day. The last two days she hiked a total of 28 miles. The total hike for the first and third days was 22 miles. How many miles long was the trail?
Answer:
50 miles
Step-by-step explanation:
let he hiked a,b,c and d miles on each of the four days respectively.
then, according to the question.
a+b=26...i
b+c= 24...ii
c+d=28...iii
a+c=22...iv
now, adding i,ii,iii,iv we get
2(a+b+c+d) = 100
a+b+c+d= 50 miles.
Hence, he traveled in all 50 miles.
There is good evidence that moderate alcohol use improves health. Some people think that red wine is better for your health than other alcoholic drinks. You have recruited 300 adults aged 45-65 who are willing to follow your orders about alcohol consumption over the next five years. You want to compare the effects on heart disease of moderate drinking of just red wine, just beer, or just spirits.what experimental design will you use?
Answer:
Independent measures, or repeated measures,
Step-by-step explanation:
I would use those experimental designs because it is used to compare different participants over a length of time.
Peter has 30 pens and Tony has 14 pens .How many pens must Tony give Peter so that Peter shall have 3 times as many as Tony?
Answer:
Let p be the number of pencils.
3(14-p)=30+p
42-3p=30+p
4p=12, p=3.
So Peter ends up with 33 and Tony with 11. 3*11=33, so that confirms that Tony gave Peter 3 pencils.
The University of Arkansas recently reported that 43% of college students aged 18-24 would spend their spring break relaxing at home. A sample of 165 college students is selected.
a. Calculate the appropriate standard error calculation for the data.
b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
Answer:
a. 0.0385
b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.43, n = 165[/tex]
a. Calculate the appropriate standard error calculation for the data.
[tex]s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385[/tex]
b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
This is 1 subtracted by the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.43}{0.0385}[/tex]
[tex]Z = 1.82[/tex]
[tex]Z = 1.82[/tex] has a pvalue of 0.9656
1 - 0.9656 = 0.0344
3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Pleaseeeeeee helppppppp
Answer:
[tex]\boxed{Option \ D}[/tex]
Step-by-step explanation:
The combination of a rational number (3) and an irrational no. ([tex]4i[/tex]) is called a complex number.
So,
[tex]3+4i[/tex] is a complex no.
Answer:
D. Complex number.
Step-by-step explanation:
This number is not irrational, since 3 is rational.
The number is not entirely rational, since 4i is irrational.
The number is not real because i is not real.
So, the number is a Complex number, since it includes both real and nonreal numbers.
Hope this helps!
What are the steps to determine which
solutions will be extraneous in a rational
equation?
Answer:
There are four different steps involved in determining extraneous solutions in any of the rational equation.
Step-by-step explanation:
Steps involved are:
1. The very step involved is to find the "common denominator".
2. The second step includes multiplying every single thing with the "common denominator".
3. The third step includes "simplifying".
4. The last and the fourth step involves checking the answer obtained in order to assure that there's no "extraneous solution".
Example of an extraneous solution in a rational equation:
4÷x+3 + 7÷x²+3x = 4-x÷x
What is the solution to the system of equations below? HELP!!!! y = negative one-fourth x + 2 and 3 y = negative three-fourths x minus 6 no solution infinitely many solutions (–16, 6) (–16, –2)
Answer:
No solution
Step-by-step explanation:
Step 1: Write out equations
y = -1/4x + 2
3y = -3/4x - 6
Step 2: Substitution
3(-1/4x + 2) = -3/4x - 6
Step 3: Distribute
-3/4x + 6 = -3/4x - 6
From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.
Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.
Answer:
No solution
Step-by-step explanation:
y = -1/4x + 2
3y = -3/4x - 6
Plug y as -1/4x + 2 in the second equation.
3(-1/4x + 2) = -3/4x - 6
-3/4x + 6 = -3/4x - 6
-3/4x + 3/4x = -6 -6
0 = -12
No solution.