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Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations is the standard deviation of the y-values corresponding to all the x-values the greatest?
a) y = x/3
b) y = x/2+40
c) y = x
d) y = 2x + 50
e) y = 3x − 20
Answer:
Option E
Step-by-step explanation:
y = x /3
let x = 1, 2, 3
y = 0.333, 0.667, 1
y = x/2 + 40
let x = 1, 2, 3
y = 40.5, 41, 41.5
y = x
let x = 1, 2, 3
y = 1, 2, 3
y = 2x + 50
let x = 1, 2, 3
y = 52, 54, 56
y = 3x - 20
let x = 1, 2, 3
y = -17, -14, -11
The standard deviation is the spread of data, the data that is most spread is option E.
Which represents the value of c?
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
Which of the following box plot best represents the set of data below
Answer:
C. Box plot B
Step-by-step explanation:
Find the value of x, rounded to the nearest tenth.
Answer:
x = 8.9 units
Step-by-step explanation:
We will use the theorem of intersecting tangent and secant segments.
"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."
8(8 + 2) = x²
x² = 80
x = √80
x = 8.944
x ≈ 8.9 units
Therefore, length of the tangent = 8.9 units
Help with inequality
Answer:
1. x>20 2. x≤1 3.x<4 4.x>9 5.x≥-13
Every year the United States Department of Transportation publishes reports on the number of alcohol related and non-alcohol related highway vehicle fatalities. Below is a summary of the number of alcohol related highway vehicle fatalities from 2001 to 2010.
Line graph about Alcohol related fatalities
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
Complete question:
The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.
Answer:
17,209
Step-by-step explanation:
The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.
Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.
The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :
From the graph:
Year - - - - - - - - - - Number of fatalities
2001 - - - - - - - - - - 17401
2002 - - - - - - - - - 17525
2003 - - - - - - - - - 17013
2004 - - - - - - - - - 16694
2005 - - - - - - - - - 16885
2006 - - - - - - - - - 17738
To get the average :
Sum of fatalities / number of years
(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6
= 103256 / 6
= 17209.333
Average number of alcohol related fatalities is 17,209 (to the nearest whole number)
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
find the maximum value of c=6x+2y
Answer:
∞
Step-by-step explanation:
c can have any value you like.
There is no maximum. We say it can approach infinity.
__
Additional comment
There may be some maximum imposed by constraints not shown here. Since we don't know what those constraints are, we cannot tell you what the maximum is.
A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given
approximately by the function H(1) 0.0004.x2 + 2.582 + 700, where H is measured in
feet above the river and is the horizontal distance from his launch ramp.
How high above the river was the launch ramp?
What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?
Correct question:
A motorcycle stunt rider jumped across the Snake River. The path of his motorcycle was given
approximately by the function H(t) = - 0.0004.x2 + 2.582 + 700, where H is measured in
feet above the river and is the horizontal distance from his launch ramp.
How high above the river was the launch ramp?
What was the rider's maximum height above the river, and how far was the ramp when he reached maximum height?
Answer:
A) 700 feet ; 4866.7025 feet above the river
3227.5 Feets from the ramp
Step-by-step explanation:
Given the Height function:
H(t) = 0.0004x^2 + 2.582x + 700
H = height in feet above the river
x = horizontal distance from launch ramp.
How high above the river was the launch ramp?
H(t) = - 0.0004x^2 + 2.582x + 700
To find height of launch ramp above the river, we set the horizontal distance to 0, because at this point, the motorcycle stunt rider is on the launch ramp and thus the value of H when x = 0 should give the height of the launch ramp above the river.
At x = 0
Height (H) =
- 0.0004(0)^2 + 2.582(0)+ 700
0 + 0 + 700 = 700 Feets
B) Maximum height abive the river and how far the rider is from the ramp when maximum height is reached :
Taking the derivative of H with respect to x
dH'/dx = 2*-(0.0004)x^(2-1) + 2.582x^(1-1) + 0
dH'/dx = 2*-(0.0004)x^(1) + 2.582x^(0) + 0
dH'/dx = - 0.0008x + 2.582
Set dH'/dx = 0 and find x:
0 = - 0.0008x + 2.582
-2.582 = - 0.0008x
x = 2.582 / 0.0008
x = 3227.5 feets
To get vertical position at x = 0
Height (H) =
- 0.0004(3227.5)^2 + 2.582(3227.5)+ 700
- 4166.7025 + 8333.405 + 700
= 4866.7025 feet
4866.7025 feet above the river
3227.5 Feets from the ramp
Using quadratic function concepts, it is found that:
The launch ramp was 700 feet above the river.The maximum height is of 4866.7 feet.The ramp was 3227.5 feet along when he reached maximum height.The height after x seconds is given by the following equation:
[tex]H(x) = -0.0004x^2 + 2.582x + 700[/tex]
Which is a quadratic equation with coefficients [tex]a = -0.0004, b = 2.582, c = 700[/tex]
The height of the ramp is the initial height, which is:
[tex]H(0) = -0.0004(0)^2 + 2.582(0) + 700 = 700[/tex]
Thus, the launch ramp was 700 feet above the river.
The maximum height is the h-value of the vertex, given by:
[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Then, substituting the coefficients:
[tex]h_{MAX} = -\frac{(2.582)^2 - 4(-0.0004)(700)}{4(-0.0004)} = 4866.7[/tex]
The maximum height is of 4866.7 feet.
The horizontal distance is the x-value of the vertex, given by:
[tex]x_V = -\frac{b}{2a} = -\frac{2.582}{2(-0.0004)} = 3227.5[/tex]
The ramp was 3227.5 feet along when he reached maximum height.
A similar problem is given at https://brainly.com/question/24705734
What is 0.09% written as a decimal?
A. 0.9
B. 0.009
C. 0.0009
D. 0.09
Answer:
C. 0.0009
Step-by-step explanation:
0.09/100
= 0.0009
Answer:A
Step-by-step explanation:0.09=0.9
Find the volume of each solid. Round to the nearest tenth. IMG_7097.HEIC
Answer:
You didn't put an attachment to show what solid you wanted rounded
Step-by-step explanation:
(x*129)-3=126 what is x
Answer:
x should equal 1
Step-by-step explanation:
(1*129)-3=126
129-3=126
126=126
Answer:
x=1
Step-by-step explanation:
We can start by adding 3 to both sides to get rid of the -3
That leaves us with 129x=129
It ends up working out really evenly because by dividing both sides by 129, we are left with x=1
3(x+4)-1=-7 plz help
Answer:
x = -6
Step-by-step explanation:
3(x+4)-1=-7
Add 1 to each side
3(x+4)-1+1=-7+1
3(x+4)=-6
Divide by 3
3/3(x+4)=-6/3
x+4 = -2
Subtract 4 from each side
x+4-4 = -2-4
x = -6
Answer:
- 6Step-by-step explanation:
[tex]3(x + 4) - 1 = - 7[/tex]
Distribute 3 through the parentheses
[tex]3x + 12 - 1 = - 7[/tex]
Calculate the difference
[tex]3x + 11 = - 7[/tex]
Move constant to R.H.S and change it's sign
[tex]3x = - 7 - 11[/tex]
Calculate
[tex]3x = - 18[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{ - 18}{3} [/tex]
Calculate
[tex]x = - 6[/tex]
hope this helps
Best regards!!
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
29% of workers got their job through networking. A researcher feels this percentage has changed. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
Answer: [tex]H_0:p=0.29[/tex]
[tex]H_a: p \neq0.29[/tex]
Step-by-step explanation:
A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.
Let p be the population proportion of workers got their job through networking.
Given: 29% of workers got their job through networking.
i.e. [tex]H_0:p=0.29[/tex]
A researcher feels this percentage has changed.
i.e. [tex]H_a: p \neq0.29[/tex]
Hence, the required null and alternative hypotheses in symbolic form for this claim:
[tex]H_0:p=0.29[/tex]
[tex]H_a: p \neq0.29[/tex]
NEED HELP AS SOON AS POSSIBLE which interval describes where the graph of the function is negative
Answer:
2 < x < ∞
Step-by-step explanation:
We want where the value of y is less than zero
The value of the graph is less than zero is from x=2 and continues until x = infinity
2 < x < ∞
Answer:
[tex]\boxed{2 < x < \infty}[/tex]
Step-by-step explanation:
The value of y should be less than 0 for the graph of the function to be negative.
In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.
[tex]2 < x < \infty[/tex]
What is the value of Sine theta in the diagram below?
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
Learn more about Trigonometric functions here:
https://brainly.com/question/24349828
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What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
-4.
-2
оооо
2
5
Answer:
y = -4
Step-by-step explanation:
4x + 5y = -12 ....eq1
-2x + 3y = -16 ...eq2
From eq1, solve for x:
4x + 5y = -12
4x = -12 - 5y
x = -12 - 5y/4
From eq2, substitute value of x:
-2(-12-5y/4) + 3y = -16
3y - 2 (-5y-12/4) = -16
3y - 2(-5y-12)/4 = -16
12y - 2(-5y - 12) = -16
4*3y - 4*2(-5y-12)/4 = 4*(-16)
12y - 2(-5y-12) = -64
12y + 10y + 24 = -64 (divide both sides by common factor 2)
6y + 5y + 12 = -32
11y = -32 - 12
11y = -44
Divide both sides by 11
11y/11 = -44/11
y = -4
Rotation
The triangle DEF with vertices D (-4, 4), E (-1, 2), F (-3, 1). Graph the figure and its image after a 90 ° clockwise rotation about its origin.
Answer:
Step-by-step explanation:
The vertices of the already rotated triangle are:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Answer:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Step-by-step explanation:
When a person throws a ball into the air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the ball's height in feet after t seconds is given by h(t)=-16t^2+32t+2. If possible, determine the time(s) when the ball was at a height of 14 feet.
Answer:
0.5 seconds and 1.5 seconds.
Step-by-step explanation:
h(t) = -16t^2 + 32t + 2
14 = -16t^2 + 32t + 2
16t^2 - 32t - 2 + 14 = 0
16t^2 - 32t + 12 = 0
8t^2 - 16t + 6 = 0
4t^2 - 8t + 3 = 0
(2x - 3)(2x - 1) = 0
2x - 3 = 0
2x = 3
x = 3/2
x = 1.5
2x - 1 = 0
2x = 1
x = 1/2
x = 0.5
So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.
Hope this helps!
Which of the following is the minor arc for the circle shown below?
A. AWR
B. AW
C. RAW
D. RA
Answer:
RA
Step-by-step explanation:
The doubling time of a cityʹs population is 8 years. How long does it take for the population to quadruple.
Answer:
16 Years
Step-by-step explanation:
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
Which of the following is a correct tangent ratio for the figure?
Answer:
C) tan(39°) = 11/15
Step-by-step explanation:
SohCahToa
tangent = opposite / adjacent
The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.
Answer:
tan(39°) = 11∕15
Step-by-step explanation:
A cosine function is graphed below. Use the drop-down menus to describe the graph. The amplitude of the graph is __ . The equation of the midline is __ . The period of the function is __ . The function is shifted __ left. The function is shifted __ units up.
Amplitude:4
Equation of Midline: 2
Period of function:3
Function shifted left:0.5
Function shifted up: 2
From the graphed cosine function we are given, we have;
1) Amplitude = 4
2) Equation of midline; m = 2
3) Period of the function = 3π
4) The function shifted 0.5 units left.
5) The function shifted 2 units up.
1) The amplitude is the distance between the center line and the positive or negative peak of the graph. Now, the positive peak is 6 and the negative one is 2. Thus, Amplitude = 6 - 2 = 42) Equation of the midline is the line that divides the entire sinusoidal curve into 2 equal parts along the x-axis. Since amplitude is 4, then the equation of midline is; m = 4/2 ; m = 2.3) The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3π.4) Looking at the graph, ideally the coordinate (-0.5π, 6) should have been on the y-axis which is at (0π, 6). This means it was shifted by 0.5 units to the left side.5) The positive peak should be equal to the negative peak but in this case, positive is 6 and negative is 2. This means, for them to be equal, they have to each be 4. Thus, the graph was shifted by 2 units upwards .Read more; https://brainly.com/question/16280305
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
which of the binomials below is a factor of this trinomial? 8x^2 + 10x-3
Answer:
The factors are (4x-1) and (2x+3)
Step-by-step explanation:
The factors of 8x^2 + 10x -3 can be found by grouping terms
8x^2 - 2x + 12x - 3
2x (4x -1) + 3(4x-1)
(4x-1)(2x+3)