Answer:Let x km/hr be the speed of train
Let y be the time taken by the train
Distance = speed x time
= x y
To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.
it clearly says that speed is increased by 6 and time is reduced by 4
So , (x + 6) (y - 4) = x y
x y - 4 x + 6 y - 24 = x y
x y - x y - 4 x + 6 y = 24
- 4 x + 6 y = 24
divided by (-2) => 2 x - 3 y = -12 ----- (1)
To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.
it clearly says that speed is reduced by 6 and time is increased by 6
So , (x - 6) (y + 6) = x y
x y + 6 x - 6 y - 36 = x y
x y - x y + 6 x - 6 y = 36
6 x - 6 y = 36
divided by (6) => x - y = 6 ----- (2)
2 x - 3 y = -12
(2) x 2 => 2 x - 2 y = 12
(-) (+) (-)
---------------
- y = -24
y = 24
Now we have to apply the value of y in the first equation to get value of x
Substitute y = 24 in the first equation we get
2 x - 3 (24) = -12
2 x - 72 = -12
2 x = -12 + 72
2 x = 60
x = 60/2
x = 30
Speed of the train = 30 km/hr
Time taken by the train = 24 hours
Distance covered by the train = x y = 30 x 24 = 720 km
Verification:
2 x – 3 y = -12
2(30) - 3(24) = -12
60 - 72 = -12
-12 = -12
Which box-and-whisker plot best represents the information from the data?
10 12 15 19 22 22 23 26 30 32
(x^2-4x)^2+7x^2-28x+12=0
Answer:
[tex]x^4-9x^2-28x=-12[/tex]
Step-by-step explanation:
[tex](x^2-4x)^2+7x^2-28x+12=0[/tex]
[tex](x^4-16x^2)+7x^2-28x=-12[/tex]
[tex]x^4-9x^2-28x=-12[/tex]
Bernita and Derek each plot a number on a number line. the numbers are unique but have the same absolute value. the sum of the absolute values of the numbers is 50. what are the two numbers
Answer:
-25, 25
Step-by-step explanation:
Since the numbers have the same absolute value and the sum of their absolute values is 50, they both must have an absolute value of 50/2 = 25.
Unique numbers with the same absolute value will have opposite signs.
The numbers are -25 and 25.
If the initial amount of iodine-131 is 537 grams , how much is left after 10 days?
Answer:
225.78 grams
Step-by-step explanation:
To solve this question, we would be using the formula
P(t) = Po × 2^t/n
Where P(t) = Remaining amount after r hours
Po = Initial amount
t = Time
In the question,
Where P(t) = Remaining amount after r hours = unknown
Po = Initial amount = 537
t = Time = 10 days
P(t) = 537 × 2^(10/)
P(t) = 225.78 grams
Therefore, the amount of iodine-131 left after 10 days = 225.78 grams
The table shows the annual profits (in thousands of dollars) of a county fair from 2013 to 2016. What must the 2017 profit be (in hundreds of dollars) to break even over the five-year period?
Answer:
8 hundred dollars
Step-by-step explanation:
The break even value means zero profit or loss over the five years period. So if 2017 profit is x, then we get:
2.5 + 1.4 - 3.3 - 1.4 + x = 0x - 0.8 = 0x = 0.8 thousands of dollars x= 800 dollarsThe mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
(a) What is the likelihood the sample mean is at least $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(c) Within what limits will 90 percent of the sample means occur? (Round your answers to 2 decimal places.)
Answer:
a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
b. [tex]P(22.5<X<25) = 0.9043[/tex] ( to four decimal places )
c. The limits will be between the interval of ( 22.33,24.67 )
Step-by-step explanation:
Given that :
mean = 23.50
standard deviation = 5.00
sample size = 50
The objective is to calculate the following:
(a) What is the likelihood the sample mean is at least $25.00?
Let X be the random variable, the probability that the sample mean is at least 25.00 is:
[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex] to two decimal places
From the normal tables :
[tex]P(X \geq 25) = 1 - 0.9830[/tex]
[tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]
[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]
[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]
[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]
[tex]P(22.5<X<25) = 0.9043[/tex] to four decimal places
(c) Within what limits will 90 percent of the sample means occur?
At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10
The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65
Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Standard Error = [tex]\dfrac{5}{\sqrt{50}}[/tex]
Standard Error = 0.7071
Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]
Lower limit = ( 23.5 - (1.65×0.707) )
Lower limit = ( 23.5 - 1.16655 )
Lower limit = 22.33345
Lower limit = 22.33 (to two decimal places).
Upper Limit = ( 23.5 + (1.65*0.707) )
Upper Limit = ( 23.5 + 1.16655 )
Upper Limit = 24.66655
Upper Limit = 24.67
The limits will be between the interval of ( 22.33,24.67 )
What’s is the greatest common factor of 100x^2 - 250xy + 75x
Answer:
The greatest common factor of the expression is 25x
Step-by-step explanation:
Here, we are interested in giving the greatest common factor of the expression.
We can do this by factorization till we have no common factors left.
the expression is;
100x^2 -250xy + 75x
we start with the common factor x;
x(100x -250y + 75)
The next thing to do here is to find the greatest common factor of 100,250 and 75.
The greatest common factor here is 25.
Thus, we have;
25x(4x -10y + 3)
There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable
So the greatest common factor we have is 25x
Solve. 2x−y+3z=6 2x+y=3 2y−4z=−4 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(3/2, 0, 1)
Step-by-step explanation:
From 2x+y=3 we have => y=3-2x
From 2y-4z=-4 we have -4z=-2y-4 => z=1/2y+1 => z=1/2 (3-2x) +1 => z=5/2-x
Plug in y & z to find x
2x−y+3z=6 => 2x+(3-2x)+3(5/2-x)=6 => 2x+3-2x+15/2-3x=6 => 21/2-3x =6 => x=3/2
plug in x to find y
2x+y=3 => 2(1.5) + y =3 => y=0
plug in y to find z
2y -4z =-4 => 2(0)-4z=-4 => -4z=-4 => z=1
What are the solutions of x2 + 20 = 12x.
Answer:
x₁ = 2
x₂ = 10
Step-by-step explanation:
x² + 20 = 12x
x² - 12x + 20 = 0
(x-2)(x-10) = 0
then:
x₁ = 2
x₂ = 10
Check:
x₁
2² + 20 = 12*2
3 + 20 = 24
x₂
10² + 20 = 12*10
100 + 20 = 120
I am so confused Please Help it is DUE NOW!!
Select the polynomial that is a perfect square trinomial.
9x^2 + 9x + 1
36b^2 − 24b + 8
16x^2 + 24x + 9
4a^2 − 10a + 25
Answer:
16x^2 + 24x + 9
Step-by-step explanation:
perfect square trinomial is of the form
a^2 + 2 * a * b + b^2
9x^2 + 9x + 1 = (3x)^2 + 3*3x*1 + 1^2 not a perfect square trinomial
36b^2 − 24b + 8 = ( 6b)^2 -2 * 6b *2 + ( 2 sqrt(2)) ^2 not a perfect square trinomial
16x^2 + 24x + 9 = ( 4x) ^2 + 2 * ( 4x) * 3 + 3^2 = perfect square trinomial
4a^2 − 10a + 25 = ( 2a) ^2 - 1 * 2a *5 + 5^2 not a perfect square trinomial
Answer:
The third answer listed:
[tex]16x^2+24x+9[/tex]
Step-by-step explanation:
The trinomial:
[tex]16x^2+24x+9[/tex]
can be factored out as follows:
[tex]16x^2+24x+9\\(4x)^2+24x+3^2\\(4x)^2+12x+12x+3^2\\4x(4x+3)+3(4x+3)\\(4x+3)\,(4x+3)\\(4x+3)^2[/tex]
which as can be seen,is the perfect square of a binomial, so this trinomial is what is called a perfect square trinomial.
Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit
Answer:
its not 1, its the second one (B)
Step-by-step explanation:
Answer:
I know I'm 1 year late but B is the correct answer choice. I just did it on edge 2021.
I'm just big brain.I need help with this question badly
Step-by-step explanation:
[tex] {9}^{ - 53} . {9}^{37} [/tex]
To solve this question we use the rules of indices
Since the bases are the same and are multiplying we add the exponents using the formula
[tex] {a}^{b} \times {a}^{c} = {a}^{b + c} [/tex]So for the above question we have
[tex] {9}^{ - 53} \times {9}^{37} = {9}^{ - 53 + 37} [/tex]We have the final answer as
[tex] {9}^{ - 16} [/tex]Which is the same as
[tex] \frac{1}{ {9}^{16} } [/tex]Hope this helps you
2( -4n+ 2)
6n = 4(-2 - 2n)
Answer:
(n^(2)+6n-4)(2n-4)
Add the matrices to find the answer.
Answer:
[tex]\large \boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
What is the greatest common factor? Need help fast!
Answer:
Step-by-step explanation:
9x^3,15x^5= 3x^3
The GCF is constructed by multiplying all the factors that are common to all the given expressions, exponentiated to the smallest power.
In our example, the following factors are common to all the given expressions: 3, x^3
Therefore, the GCF is equal to 3x^3.
A square has a perimeter of 24cm. Work out its area.
Answer:
A = 36 cm^2
Step-by-step explanation:
The perimeter of a square is given by
P =4s
24 = 4s
Divide by 4
24/4 = 4s/4
6 =s
The area of a square is
A =s^2
A = 6^2
A = 36 cm^2
Solve the equation for x. the square root of the quantity x plus 4 end quantity minus 7 equals 1 x = 4 x = 12 x = 60 x = 68
Answer:
x = 60
Step-by-step explanation:
Given
[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )
[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )
([tex]\sqrt{x+4}[/tex] )² = 8² , that is
x + 4 = 64 ( subtract 4 from both sides )
x = 60
2. A boy and his father played 26 games of checkers. For every game the boy lost, he gave his father 5 cents. For every game the boy won, his father gave him 8 cents. When all the games were played, neither had won nor lost anything. The number of games the boy won i
Answer: the boy won 10 games
Step-by-step explanation:
Let's call B as the number of games won by the boy, and F as the number of games won by the father.
We know that, there is a total of 26 games:
B + F = 26.
We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:
B*8 + F*(-5) = 0.
Then we have a system of equations:
B + F = 26
8*B - 5*F = 0.
The first step is isolating one of the variables. Let's start isolating F in the first equation:
B + F = 26
F = 26 - B.
Now we can replace this in the second equation:
8*B - 5*F = 0
8*B - 5*(26 - B) = 0
8*B + 5*B - 5*26 = 0
13*B = 5*26
B = 5*26/13 = 5*2 = 10
So the boy won 10 games (then the father won the other 16 games)
What are the solutions to the quadratic equation 4x2 = 64? A. x = −16 and x = 16 B.x = −8 and x = 8 C.x = −4 and x = 4 D.x = −2 and x = 2
Answer:
x = ±4
Step-by-step explanation:
4x^2 = 64
Divide each by 4
4x^2 /4= 64/4
x^2 = 16
Take the square root of each side
sqrt(x^2) = ±sqrt(16)
x = ±4
Answer:
[tex]\boxed{\boxed{x=\pm 4}}[/tex]
Step-by-step explanation:
[tex]4x^2 = 64[/tex]
Divide both sides by 4.
[tex](4x^2)/4 = 64/4[/tex]
Simplify.
[tex]x^2 =16[/tex]
Take the square root on both sides.
[tex]\sqrt{x^2 } =\pm \sqrt{16}[/tex]
Simplify.
[tex]x=\pm 4[/tex]
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 3150 . i. Sketch Musah's movement [Mark 4] ii. How far west is Musah's final point from the centre?
Answer:
Musah's final point from the centre = 60.355 steps
Step-by-step explanation:
From the given information:
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°
The sketch for this information can be seen in the attached file below.
How far west is Musah's final point from the centre?
In order to determine how far west is Musah's,
Let d be the distance of how far;
Then d = QR + RS cos θ
In the North West direction,
cos θ = cos 45°
d = 25 + 50( cos 45°)
d = 25 + 50( [tex]\dfrac{1}{\sqrt{2}}[/tex] )
d = 25 + 50( 0.7071)
d =25 + 35.355
d = 60.355 steps
Musah's final point from the centre = 60.355 steps
help!! im stuck on this and i can't remeber how to sove this.... 6/3c = 2/3
Hello!
Answer:
[tex]\huge\boxed{c = 3}[/tex]
Given:
[tex]\frac{6}{3c} = \frac{2}{3}[/tex]
Cross multiply:
[tex]6 * 3 = 3c * 2[/tex]
Simplify:
[tex]18 = 6c[/tex]
Divide both sides by 6:
[tex]c = 18/6 = 3[/tex]
Answer:
c=3
Step-by-step explanation:
6 2
----- = -----
3c 3
Using cross products
6*3 = 2*3c
18 = 6c
Divide each side by 6
18/6 = 6c/6
3 =c
On the first day in each month, Enid deposited $4 into her bank account and Jim deposited $3 into his. They opened these accounts on May 15, 1990. On December 31, 1990, they each had $72 dollars in their account. How much did each person deposit on May 15?
Answer:
The amount of money in Enid bank account can be written as a linear equation.
Ye = Xe + $4*m
where Ye is the money that Enid has in her account, m is the number of months that have passed since she opened it, and Xe is the initial deposit.
For Jim, the equation is similar:
Yj = Xj + $3*m
where Yj and Xj are similar as above.
Between May 15 and December 31 of the same year, we have 7 months (where i am counting December because the deposit is made in the first day of the month).
Then we have that:
Ye = $72 = Xe + $4*7 = Xe + $28
Xe = $72 - $28 = $44
So in May 15, Enid deposited $44.
For Jim we have:
Yj = $72 = Xj + $3*7 = Xj + $21
Xj = $72 - $21 = $51
So in May 15, Jim deposited $51.
solve for -5x-13(2+x)=5x-10
Answer:
[tex]x=-\frac{16}{23}[/tex]
I hope this helps!
URGENT PLZ HELP THANK YOU!
Answer:
[tex](-5)^{11}[/tex]
Step-by-step explanation:
We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].
b is 5, c is -6, and a is -5 so:
[tex]-5^{5-(-6)}\\-5^{11}[/tex]
Hope this helped!
6r-1+6r=11 explain how to get so
Answer:
r = 1
Step-by-step explanation:
6r - 1 + 6r = 11
Adding 6r and 6r (because they're like terms) gives us:
12r - 1 = 11
Adding 1 to both sides of the equation gives us:
12r - 1 + 1 = 11 + 1
12r = 12
Dividing both sides of the equation by 12 gives us:
12r/12 = 12/12
r = 1
What is the average rate of change from x = 0 to x = 18?
Average rate of change ... of what?
Given some continuous function [tex]f(x)[/tex] and some interval [tex][a,b][/tex], its average rate of change over the interval is
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Without knowing what your function is exactly, I can only give a symbolic answer,
[tex]\dfrac{f(18)-f(0)}{18}[/tex]
Answer: -5/18
Step-by-step explanation: edg
8 kids bought a 3 cakes. How many equal parts will need to divide it so that everyone can have it. Easy one!
Answer:
3/8 is your answer.
Step-by-step explanation:
Given:
8 kids bought a 3 cakes.
Required:
How many equal parts will need to divide it so that everyone can have it.
Solution:
3/8
Hope this helps ;) ❤❤❤
3(q−7)=27 need help plzz 1st peep gets brainlest
━━━━━━━☆☆━━━━━━━
▹ Answer
q = 16
▹ Step-by-Step Explanation
3(q - 7) = 27
3q - 21 = 27
Add 21 to both sides:
21 + 21 = na
27 + 21 = 48
3q = 48
Divide both sides by 3:
3/3 = q
48/3 = 16
q = 16
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
q=16
Step-by-step explanation:
3q-21=27
27+21=48
48/3=16
[tex] \frac{w}{ -6} = 6[/tex]
I cant figure out the answer
Question. 1 The product of a monomial and a binomial is a (a) monomial (b) binomial (c) trinomial (d) None of these
Answer:
The answer to this question is (D)
