Step-by-step explanation:
the slower truck travels x miles in 5 hours.
the faster truck travels x + 5×2 = x + 10 miles in 5 hours.
so,
x + x + 10 = 315 miles
2x = 305 miles
x = 152.5 miles (in 5 hours)
therefore, the slower truck's speed was 30.5 mph.
the faster truck's speed was 30.5 + 2 = 32.5 mph.
The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3
51.2 44.2 45.4 49.2 43.6
(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.
(b) The manufacturer claimed that this new model of cell phone has the mean battery standby duration of longer than 46.5 hours. Test at 1% significance level if this claim is true.
x = number of hours
want to find probability (P) x >= 13
x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.
P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
To convert that to percentage, multiply 100, to get 84.13%
Answer for this question?
Answer:
B
Step-by-step explanation:
Lie should factor out 3 from the expression
Find the square root of 1764 by factorisation method
Answer:
42
Step-by-step explanation:
prime factorisation of 1764 = 2^2 × 3^2 × 7^2
hence,
√1764 = √(2^2 × 3^2 × 7^2) =2 x 3 x 7 = 42
Answer:
42
Step-by-step explanation:
1764 = 2 * 882
= 2 * 2 * 441
= 2 * 2 * 3 * 147
= 2 * 2 * 3 * 3 * 49
= 2 * 2 * 3 * 3 * 7 * 7
[tex]\sqrt{1764} = \sqrt{2*2*3*3*7*7} = 2*3*7 = 42[/tex]
Which is the graph of f(x) = (2)* ?
Answer:
the graph of f(x)=×2 called a parabola
Find the equation of a line perpendicular to y = (75)x - 1 and has a y-
intercept of 1.
Answer:
6y = -5x + 6
y = -5/6 x + 1
Step-by-step explanation:
y = -5/6 x + b
1 = b
A traveling salesman figures it costs 28
cents for every mile he drives his car. How much does it cost him (in dollars) a week to drive his car if he travels 315 miles a week?
HELP ASAP PLEASE!!! 100 point!!!!!!!!!!
FOR THE GRAPHS JUST GIVE ME TWO POINTS FOR EACH ONE!!!!!!!!!!!!!!
Answer:
y=4x+7
Step-by-step explanation:
use the slope intercept formula to find the equation.
y =4
passess through (-1,3)
what is the correct expansion of this expression (w-p)(3p+w)
Answer:
3pw + w^2 - 3p^2 - pw = 2pw + w^2 - 3p^2
Step-by-step explanation:
Multiply every term of the first binomial by every term of the second binomial.
(w - p)(3p + w) = 3pw + w^2 - 3p^2 - pw = 2pw + w^2 - 3p^2
Resuelve los siguientesTriángulos semejantes, Obteniendo el valor de la incógnita faltante en cada caso
Answer:
hjk
Step-by-step explanation:
What are the simplest forms for red, blue, and green line
Answer:
Red line: y=-1/2x+1 Blue line: y=-1/3x-2 Green line: y=x
Step-by-step explanation:
f(x) red line m=-1/2 b=1
g(x) blue line m=-1/3 b=-2
h(x) green line m=1 b=0
The triangle below is equilateral. Find the length of side x in simplest radical form
with a rational denominator.
12
Answer:
4sqrt(3)
Step-by-step explanation:
If the triangle is equilateral, the hypotenuse is 2x
We can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
x^2 + 12^2 = (2x)^2
x^2 + 144 = 4x^2
144 = 4x^2 -x^2
144 = 3x^2
48 = x^2
Taking the square root of each side
sqrt(48) = sqrt(x^2)
sqrt(16*3) = x
4 sqrt(3) =x
In Circle H with m<GKJ=38, Find the m<GHJ
Answer:
the angle GHJ would be 76 because the central angle is always double the measurement of the inscribed angle
Another of Bhaskara's problems results in a quadratic equation Parthava was enraged and seized a certain number of arrows to slay Karna. He expended one-half of them in defending himself. Four times the square root of the number of arrows were discharged against the horses. With six more, he transfixed Shalya, the charioteer. With three more, he rent the parasol, the standard, and the bow; and with the last one he pierced the head of Karna. How many arrows did Parthava have?
Answer:
Parthava had 100 arrows.
Step-by-step explanation:
Let's define N as the number of arrows that Parthava originally has.
He uses one-half of them in defending himself, so he used N/2 arrows
Now he uses four times the square root of the number of arrows, so now he uses:
4*√N
Then he uses 6
Then he uses 3
Then he uses the last one.
If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:
N/2 + 4*√N + 6 + 3 + 1 = N
Now we have an equation that we can try to solve.
First, let's move all the terms to the same side:
N/2 + 4*√N + 6 + 3 + 1 - N = 0
now we can simpify it:
(N/2 - N) + 4*√N + (6 + 3 + 1) = 0
-(1/2)*N + 4*√N + 10 = 0
Now we can define a new variable x = √N
Then we have: x^2 = N
now we can replace these new variables in our equation to get:
-(1/2)*x^2 + 4*x + 10 = 0
Now we just have a quadratic equation.
Remember that for a quadratic equation of the form:
0 = a*x^2 + b*x + c
The solutions were given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]
Then in our case, the solutions will be:
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]
So there are two solutions:
x = 4 + 6 = 10
x = 4 - 6 = -2
And remember that x = √N
Then x should be positive, then we take x = 10 as our solution here.
then we can use the equation:
x = 10 = √N
then
10^2 = √N^2 = N
10^2 = 100 = N
Parthava had 100 arrows.
what is -2t-5t ? is it -7t or is it something else?
Answer:
-7t
Step-by-step explanation:
you are correct
slove for inequality of -6> t-(-13)
Step-by-step explanation:
-6>t-(-13)
= -6>t+13
= -6-13>t
= -19>t
= t<-19
Answer:
t < - 19
Step-by-step explanation:
Given
- 6 > t - (- 13) , that is
- 6 > t + 13 ( subtract 13 from both sides )
- 19 > t , then
t < - 19
how many line of symmetry is this figure
Answer:
There are sixteen lines.
Using the proportion you found in Question 3, write an equation for the length of arc EF in terms of the radii of AB and AC and the length of arc CD.
Answer:
Step-by-step explanation:
PLS HELP
Choose the inequality that represents the following graph,
+
-4
-5
-3
- 2
-1
0
1
2
3
4
5
Choose 1 answers
ISO
IO
D
>O
Answer:
The option which represents the inequality is option D ; stated as x ≥ 0
Step-by-step explanation:
The marked or dotted position is 0 ; which represents the position of x, when graphing inequality statements, if the point IS SHADED, then it means GREATER THAN EQUAL TO.
Option A is incorrect, the inequality sign is not the same as the direction of the arrow.
Option B, says LESS THAN EQUAL TO, instead of GREATER THAN EQUAL TO
Option C SAYS GREATER THAN instead of GREATER THAN EQUAL TO.
Therefore, Option D is the correct expression which means x is GREATER THAN EQUAL TO.
Learn more : https://brainly.com/question/24065770
If the class contains 11 boys and 14 girls, what is the probability of calling on a girl?
Answer: P (girl) = 14 / 25
Concept:
Here, we need to know the idea of probability.
Probability is a measure of the likelihood of an event to occur.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Number of boys = 11
Number of girls = 14
Total number of people = 11 + 14 = 25
P (girl) = Favorable / Total (refer to the attachment)
P (girl) = 14 / 25
Hope this helps!! :)
Please let me know if you have any questions
the Marked price of an article is rupees 1600 if it is sold for rupees 1472 what is the discount rate
Step-by-step explanation:
1600-1472=128
128/1600×100
18) Mala gave Kamala half the number of sweets she had. She then had 7 sweets left. How many sweets did Mala have at the start?
Answer:
Mala had 14 sweets at the start.
Step-by-step explanation:
7 x 2 = 14
To check, 14/2 = 7. (Dividing by 2 is the same as multiplying by 1/2)
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1 : 4
Sample 2 : 1
Sample 3 : 9
What margin of error is reasonable for these samples?
Answer:
Sample 1 MOE = 37.24%
Sample 2 MOE = 29.4%
Sample 3 MOE = None
Step-by-step explanation:
We are told that 250 sheep grazes over a 40-acre pasture.
Thus, number of sheeps per acre = 250/40 = 6.25 ≈ 6
Thus, n = 6
For the samples given, we can find sample proportions as;
Sample 1: p_o = 4/6 = 0.67
Sample 2: p_o = 1/6 = 0.17
Sample 3: p_o = 9/6 = 1.5
Formula for test statistic here is;
z = √(p_o(1 - p_o)/n)
For sample 1;
z = √(0.67(1 - 0.67)/6)
z ≈ 0.19
For sample 2;
z = √(0.17(1 - 0.17)/6)
z ≈ 0.15
For sample 3;
z = √(1.5(1 - 1.5)/6)
z = √−0.125
We are not given confidence level but we will use 95%.
Value of z_α at 95% Confidence level is 1.96. Thus, we can find the margin of error for the samples;
For sample 1;
Margin of error at z = 0.19 is;
1.96 × 0.19 = 0.3724 = 37.24%
For sample 2;
Margin of error at z = 0.15 is;
1.96 × 0.15 = 0.294 = 29.4%
For sample 3;
Since test statistic has a negative square root, then it has no margin of error.
1 If f(x) = 1/2x + 14, then f ^-1(x)=
Answer:
2x-24
I think that you changes the problem...
you went from a derivative to an inverse ???
y = 1/2x + 14
x = 1/2 y + 14
2x = y + 24
y = 2x-24
Step-by-step explanation:
Answer:
[tex]f^{-1}[/tex] (x) = 2x - 28
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{1}{2}[/tex] x + 14 ( multiply through by 2 to clear the fraction )
2y = x + 28 ( subtract 28 from both sides )
2y - 28 = x
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)
[tex]f^{-1}[/tex] (x) = 2x - 28
Can somebody help me please!!!!!
Answer:
0
Step-by-step explanation:
g[f(x)] = x^2 - 3
= 3x^2
if gf(0) = 3(0)^2
= 0
A bag of marbles contains 3 blue marbles, 2 green marbles and 5 red marbles. A marble is chosen at random. The probability that the marble selected is blue is:
Step-by-step explanation:
the probability will be amount of green marbles over total amount of marbles
if there are 2 green marbles, and 10 total the probability is 2/10, or 20%
A 16-ounce package of frozen peas costs
85¢. Give the unit price in cents per ounce. Round to the nearest tenth of a cent.
The peas cost ___ cents per ounce.
Note: Rounding to the nearest tenth of a cent is the same as rounding to the nearest thousandth of a dollar.
Answer:
5.3 cents
Step-by-step explanation:
85/16
because all 16 ounces cost 85 cents
Answer:
5.3 cents.
Step-by-step explanation:
helppppppppppppppppppp helppppppppppppp
HOPE ITS HELPFUL ^_^
•RHONAIdentify the volume and surface area of the hemisphere in terms of pie.
Answer:
it's off topic but which grade are you in
Please help me to get its HCF
Answer:
x²+x+1
Step-by-step explanation:
1st one,
x³-1
= (x-1)(x²+x+1)
2nd one,
x⁴+x²+1
= x⁴+x³-x³+x²+x²-x²+1+x-x
= x⁴+x³+x²-x³-x²-x+x+x²+1
= x²(x²+x+1)-x(x²+x+1)+(x²+x+1)
= (x²+x+1)(x²-x+1)
3rd one,
x³+1+2x²+2x
= x³+x²+x²+x+x+1
= x³+x²+x+x²+x+1
= x(x²+x+1)+(x²+x+1)
= (x²+x+1)(x+1)
So, here the common part among these three is,
x²+x+1, so it's the H.C.F.
Today, the members of the cabinet Group of answer choices are an informal group of presidential advisers. are limited to the heads of the fifteen executive departments. include fourteen department secretaries and the attorney general, plus other top officials chosen by the president. include only the heads of the Departments of State, Justice, Defense, and Treasury, plus the heads of the EPA, CIA, and FBI. are a subset of any six executive department heads, chosen by the president.
Answer:
include fourteen department secretaries and the attorney general, plus other top officials chosen by the president.
Step-by-step explanation:
The Cabinet of the United States of America is a government body which includes the vice president along with the heads executive branch. The President of the United States in the executive head of the body.
It mainly consists of the secretaries of 14 departments as well as the attorney general and other officials who are chosen by the President of the US.
