Sathish will pay $64.8
When Satish is alone, kilometres:
Beginning at 150 kilometres and ending at 150 kilometres will be travelled 300 kilometres in total
When Satish is with friends, the total kilometres travelled is 2100 km:
And when Satish went alone he travelled 300 km
When Satish is with friends, total kilometres travelled: 2100-300 = 1800 km
Gas consumed in litres when Satish is alone: 100 kilometres use 6 litres of gas.
300 kilometres at 6 x 3 equals 18 litres.
So, when Satish is with friends, litres of gas are consumed: 100 kilometres use 6 litres of gas.
So, 6 × 18 for 1800 kilometres is equal to 108 litres.
Gas prices when Satish is on his own:
$1.2 per litre
18 x $1.2 = $21.6
Gas prices when Satish is travelling with friends
$1.2 per litre
108 x 1.2 = $129.6
Cost for each friend = $129.6/3 = $43.2
Satish will pay: Cost when travelling with friends + Cost when travelling alone
=$43.2+ $21.6
=$64.8
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The distance that Evan has left to hike is 13/30 mile.
How to calculate the distance left?From the information, Eva is hiking a real that has a length of 5/6 miles.
He has also hiked 2/5 miles. Therefore, in this situation, the distance that he has left will gotten by subtracting the fractions.
This will be:.
Distance left = Total distance - Distance hiked
Distance left = 5/6 - 2/5
= 25/30 - 12/30
= 13/30
The distance is 13/30 miles.
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Can someone answer this?
The values indicated trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
How to find the trigonometric functions?Trigonometric functions are the periodic functions that denote the relationship between angle and sides of a right-angled triangle e.g sine, cosine, tangent, etc.
Given: tan(β) = 7
Thus, β = arc tan 7 = 81.87
(a) cot(β) = 1/tan(β) = 1/7 = 0.14
(b) cos(β) = cos 81.87 = 0.14
(c) tan(90-β) = tan(90-81.87) = tan 8.13 = 0.14
(d) csc(β) = 1/sinβ = 1/sin(81.87) = 1.01
Therefore, the value of the trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
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I need some help with this question about graphed functions
The equation of the function graphed for 0 ≤ x ≤ 360 is
y = -1 + cos 2xWhat is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation that took place in the graph is of two types namely
translationvertical stretchThe translation involves moving the graph downward by 1 unit. This movement shifts the graph from running across the x axis to making x axis the crest
The vertical stretch is by a factor of 2. A complete cycle would have been rom 0 to 180. however two cycles are now covered within this period.
The graph is of showing cos x (blue) and y = -1 + cos 2x (red) is attached
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Nicole has $40 in a savings account. The account earns 5% simple interest. She wants to determine the amount in her account after 1 year if she makes no deposits or withdrawals.
Answer:
16
Step-by-step explanation:
40/5 then x the answer by 2 and you get 16 with now deposits or withdraws
please help me out. i’ll give brainliest
Answer:
y = -2x + 1
Step-by-step explanation:
y = mx + b you must find the m (slope) and the b (y intercept) to write the equation for the graph.
The slope is negative. If you start on the very left side of the graph and follow it, you will see that it goes in a down hill direction. That means that the slope is negative. If I start on the very left and the line goes up from there, the slope is positive. If the line is a straight horizontal line, then the slope is zero, it does not go up or down.
The slope is -2. Select one of the dots and travel to the next dot, but you can only move horizonaly and vertically. You cannot move diagonally. You will notice that the two closes dots are two units up (or down) and only 1 unit left (or right) depending on which dot you start at. Since you move 2 units up and 1 unit left that is a slope of 2. 2/1 = 2.
The b (y-intercept) is just where you see the line cross the y axis. It crosses it at 1.
Answer:
y = -2x + 1
Step-by-step explanation:
Slope intercept form: y= mx + bHere m is the slope and b is y-intercept.
Pick any two points on the line.
(-1,3) & (2,-3).
Find the Slope.
[tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-3-3}{2-[-1]}\\\\=\dfrac{-6}{2+1}\\\\=\dfrac{-6}{3}\\\\=-2[/tex]
m = -2.
Equation of the line:
y = -2x + b
Substitute any one point in the above equation and find the y-intercept. (-1,3)
3 = -2*(-1) + b
3 = 2 + b
3 - 2 = b
b = 1
Equation of the line:
y = -2x + 1
It is given that AC ≅ AD and ∠CAB ≌ ∠DAB
Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
Answer:
SAS
Step-by-step explanation:
∠CBA ≌ ∠DBA are equal by SAS
Kylie just accepted a job at a new company where she will make an annual salary of $67000. Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000. How much would Kylie make as a salary after 3 years working for the company? What would be her salary after t years?
The amount that Kylie make as a salary after 3 years working for the company is $76000.
Her salary after t years will be 67000 + 3000t.
How to calculate the value?In this situation, Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000 every years.
Her salary after three years will be:
= $67000 + ($3000 × 3)
= $67000 + $9000
= $76000
Her salary after t years will be:
= 67000 + (3000 × t)
= 67000 + 3000t
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Using completing the square method to solve x^2-10x+25=0
The solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
According to the question,
We have the following expression:
[tex]x^{2} -10x+25 = 0[/tex]
Now, we will use completing the square method to solve this expression.
We will first try to convert the first and last term into perfect squares and rewrite the expression by splitting the middle term in multiplication of 2 and the squares .
[tex]x^{2}[/tex]-2*x*5+[tex]5^{2}[/tex] = 0
Now, we know that this expression fits in the identity:
[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]
In this case, we have a = x and b = 5
[tex](x-5)^{2}[/tex]
Hence, the solution of the expression, [tex]x^{2} -10x+25 = 0[/tex], using completing the square method is [tex](x-5)^{2}[/tex].
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What’s is 3/20as a decimal I need HELP!
Scores for a common standardized college aptitude test
are normally distributed with a mean of 507 and a
standard deviation of 104. Randomly selected students
are given a Test Preparation Course before taking this
test. Assume, for sake of argument, that the
preparation course has no effect.
If 1 student is randomly selected, find the probability
that their score is at least 555.3.
P(X> 555.3) =
The probability that their score is at least P(X> 555.3) = 0.8275
What is a normal distribution?
A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.
Here, we have
Let x denotes the score of a man.
standard deviation (σ) = 104
mean (μ) = 507
If 1 of the men is randomly selected, find the probability that his score is at least 553.5 will be :-
P(X > 553.5) = 1 - P(X ≤ x)
= 1 - P{((x - μ)/σ) ≤ (553.5 - 507/104)}
= 1 - P(z ≤ 0.447)
= 1 - 0.1725
= 0.8275
Hence, the probability that their score is at least P(X> 555.3) = 0.8275
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Why is every rhombus a parallelogram but not every parallelogram is a rhombus? Why is every square a rectangle but not every rectangle is a square? Why is every square a rhombus but not every rhombus
square?
A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
We need to identify the properties of the given figure in order to answer why one figure can not be the other one:
A rhombus has all sides equal as well as parallel but all angles might not be right angles.
A square has all four sides equal and has 4 right angles.
A rectangle has equal opposite sides and 4 right angles.
A parallelogram has opposite parallel sides.
Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
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Solve the equation given a domain of {-3}.
3x - 2y = 5
The solution to the equations is y = -7
How to solve the equations using the domain of the replacement sets?From the question, we have the equation to be given as
3x - 2y = 5
The above equation is a linear equation
The domain or the replacement set is given as
{-3}
Rewrite properly as
Domain = {-3}
or
x = -3
So, we replace the variables using the elements in the replacement set
When x = -3, we have
3 x -3 - 2y = 5
Evaluate the products
This gives
-9 - 2y = 5
Add 9 to both sides
-2y = 14
Divide both sides by -2
y = -7
So, we have
x = -3 and y = -7
Hence, the solution to the equation is y = -7
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The radius of a circle is 599 cm. What is the diameter of this circle?
Answer:
1,198 cm
Step-by-step explanation:
To find the diameter, use the formula d = 2r.
d = 2(599)
d = 1,198
Kwai bought `15` potage tamp for `\$8. 25`. All tamp cot the ame amount. How many tamp can Kwai purchae with $12
Lamp that can be bought with $12 is 21
What is an example of a unitary method?
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
How is the unitary method divided?
This can be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees. In order to determine the value of one unit, we essentially divide the total value of a set of items by the number of units. The unitary approach is this.
Given that
Kwai bought 15 lamp for $8.25
$8.25 = 15 lamp
$1 = 15/8.25
$12 = (15/8.25)*12 = 21 approx.
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If f is continuous everywhere, f'(3) = 0 and f" (3) = 4, then there must be a local minimum at z = 3.
Answer:
True
Step-by-step explanation:
f'(3) = 0 says the tangent line at x = 3 is horizontal.
f"(3) = 0 means the graph of f is concave up at x = 3.
Together, these tell you the graph has a local minimum at x = 3. The graph is U-shaped at the point where x = 3.
The sum of two consecutive integers is less than -9. What is the smallest value that will make this true? Write and solve an inequality. Show your work using 3 or 4 steps.Use s as your variable. Round your initial answer to the nearest hundredth.
The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.
How to calculate the value?It is vital to note that an inequality simply shows that the expressions aren't equal.
In this case, the sum of two consecutive integers is less than -9.
Let the integers be x and x + 1.
Therefore, x + x + 1 < -9
2x + 1 < -9
Collect like terms
2x < -9 - 1
2x < -10
Divide
x < - 10 / 2
x < - 5
The value is x < - 5.
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5(4 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answer: i think its -18
Step-by-step explanation:
5*(4-9*2)-2*(3*2+4)+7
= 5*(4-18)-2*(3*2+4)+7
= 5*(-14)-2*(3*2+4)+7
= 5*-14-2*(3*2+4)+7
= 5*-14-2*(6+4)+7
= 5*-14-2*(10)+7
= 5*-14-2*10+7
= -70-2*10+7
= -70-20+7
= -90+7
= -83
For which value of 0 is sin 0=-1?
y
sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.
Given,
sin 0 = -1
We have to find the value of 0.
Lets see the trigonometric table for sin.
sin 0 = sin 0 = 0sin 30°= sin π/6 = 1/2sin 45° = sin π/4 = 1/√2sin 60° = sin π/3 = √3/2sin 90° = sin π/2 = 1sin 180° = sin π = 0sin 270° = sin 3π/2 = -1sin 360° = sin 2π = 0From the above table we get the value of sin 0
The value -1 is for sin 270° which is equal to sin 3π/2
That is,
sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.
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consider performing a partial f test to test for the inclusion of pctrush in the model. either in words or formula, what are the null and alternative hypotheses for this test?
The null and alternative hypothesis of the pctrush are explained below.
Given that;
By performing a partial F-test;
In hypothesis testing, the F test is a statistical test that is used to determine whether or not the variances of two populations or two samples are equal. The data in a f test follows a f distribution. In this test, two variances are divided and compared using the f statistic. Depending on the problem's characteristics, a f test can be either one- or two-tailed.
The one-way ANOVA (analysis of variance) test is run using the f value discovered after running the f test. More information on a f test, the f statistic, its critical value, formula, and how to perform a f test for hypothesis testing will be provided in this article.
The f test statistic is used in a test called the f test to determine if the variances of two samples (or populations) are equal. An f test needs a f distribution in the population and independent events for the samples in order to be valid. The null hypothesis can be rejected after conducting the hypothesis test if the f test results are statistically significant; otherwise, it cannot be rejected.
Null hypothesis:
The idea that there is no influence on the population is known as the null hypothesis.
We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). If not, we are unable to rule out the null hypothesis.
Although it may sound odd, statisticians only accept the phrase "fail to reject." Avoid using words like "prove" or "accept" when referring to the null hypothesis.
Alternative hypothesis:
The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected.
Your research hypothesis and your alternate hypothesis are frequently identical. It is, in other words, the assertion that you anticipate, or hope will be accurate.
The complement of the null hypothesis is the alternative hypothesis. The exhaustive nature of null and alternative hypotheses ensures that they account for all potential outcomes. Additionally, they are mutually exclusive, so only one of them can be true at once.
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The variable p represents number of presents. If it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used. If there are 7 presents, how much ribbon is needed? Ribbon is sold in 15 feet packages. How many do you need to buy?
The number of ribbons needed is 73
The number of ribbons to buy is 109. 5
What is a function?A function can be described as an expression or rule that explains the relationship between two main variables in an equation.
These variables are called;
Independent variableDependent variableWe have the expression;
N = 10p + 3
Where 'p' represents the number of presents
N is the number of ribbons
Now, let's substitute the value of p as 7
N = 10(7) + 3
N = 70 + 3
N = 73 ribbons
If 10 feet = 73 packages
15 feet = x
cross multiply
x = 73(15)/10
x = 109. 5 ribbons
Hence, the value is 73
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20 POINTS PLEASE HELP!!!
Solve the following system of equations. Show your work.
y=x−5
y=5x−17
Solution:
The solution to the system of equations y = x − 5 and y = 5x − 17 is x = 3 and y = -2
How to determine the solution to the system of equations?The system of equations is given as
y = x − 5
y = 5x − 17
Substitute y = x − 5 in the equation y = 5x − 17
So, we have
x - 5 = 5x − 17
Evaluate the like terms
4x = 12
Divide both sides by 4
x = 3
Substitute x = 3 in y = x − 5
y = 3 − 5
So, we have
y = -2
Hence, the solution is x = 3 and y = -2
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A box contains 3 red marbles and 4 black marbles. You simultaneously draw 3 marbles. What is the probability
that at least one marble is black?
A.4/35
B.34/35
C.19/21
D.None of the above
Answer:
Probably b or c. Not great with probabilities.
Expand and simplify:
3(2p - 5) + 2(p + 3)
Answer:
8p - 9
Step-by-step explanation:
→ Expand brackets
6p - 15 + 2p + 6
→ Collect like terms
8p - 9
I need examples of surds
A wheel has a radius of 45 millimeters. Below is the table from the previous screen. About how many rotations does the wheel make when it travels 100,000 millimeters?
The number of revolutions taken by a wheel will be 353.68 millimeters.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given data as:
The radius of the wheel r = 45 millimeters
Circumference of wheel = Circumference of a circle
Circumference of wheel = 2πr =2π(45) = 282.74 millimeters
The distance traveled by wheel = 100,000 millimeters
Now, the number of revolutions taken by a wheel will be
⇒ distance traveled by wheel / Circumference of wheel
⇒ 100,000 / 282.74
⇒ 353.68
Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.
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the little twelve basketball conference has two divisions, with six teams in each division. each team plays each of the other teams in its division twice and every team in the other division once. how many conference games are scheduled?
There are 96 basketball conference games are scheduled.
What is termed as the division?Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 classified into three groups of equal size results in 4 in each group. Developing equal groups or defining how many people are within each group after a fair distribution is the basic function of division.For the given question;
Every squad competes in ten games within its own division and six games against opponents from the opposing division. The 12 teams thus play a total of 16 conference games.There are N games on the schedule because there are two teams in each game.
N = 12×16/2
N = 96
Thus, there are 96 basketball conference games are scheduled.
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What are some vocabulary words for slopes and equations in math?
Answer:
Vocabulary: slope and variable m rise over run slope formula y-intercept/variable b parallel lines and parallel equation perpendicular lines and perpendicular equatio Introduce or review key terms related to slope and angle: slope, grade, pitch, cardinal direction, slope angle, angle of depression/declination, and angle of elevation/inclination.
14 workers can dig 9 m long trench in one day. How many workers would dig 27 m long trench of the same type in 1 day?
Answer:
42 workers
Step-by-step explanation:
27 divided by 9 = 3 (how much we need to multiply workers by)
14x3=42
researchers want to decrease the margin of error by adjusting the confidence level. which confidence interval will have the smallest margin of error (moe)?
One-sided confidence interval which have the smallest margin of error.
Given that;
Researchers want to decrease the margin of error by adjusting the confidence level.
You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.
one-sided confidence interval:
The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.
Hence, we use one-sided confidence interval which have the smallest margin of error.
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Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–72, –71, –70, –69, ..
Answer:
-73 +n
the first term is -73+1
the secound is -73+2
and so on
Answer:
[tex]a_{n}[/tex]= n - 73
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 71 - (- 72) = - 70 - (- 71) = - 69 - (- 70) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 72 and d = 1 , then
[tex]a_{n}[/tex] = - 72 + 1(n - 1) = - 72 + n - 1 = n - 73