Answer: 17.5 miles
Step-by-step explanation:
P=price, L=length
Firm A:
P=2L+10
Firm B:
P=2.40L+3
2.40L+3=2L+10
L=17.5
The fare would be the same for 17.5 miles for both firms.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have, 20=5x+k. . . (1)
30=10x+k. . . .(2)
solving these two equations we get x=2 and k = 10
Now let the length of the journey that both firm charge the same is equal to L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get
2L+10=2.40L+3
0.40L=7
L=17.5
Hence, The fare would be the same for 17.5 miles for both firms.
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One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
Each serving of a pancake recipe calls for 1/4 cup of flour. How many servings can be made with 2 cups of flour?
Answer:
The correct answer is 8 servings of pancakes.
Step-by-step explanation:
If each serving of pancakes calls for 1/4 cup of flour, to find how many servings can be made with 2 cups of flour, we should divide 2 cups by 1/4 cup.
To do this, we can first convert 1/4 to a decimal by dividing the numerator by the denominator.
1/4 = 0.25
Next, we can go ahead with the division.
2 / 0.25 = 8
Therefore, 8 servings of pancakes can be made with 2 cups of flour.
Hope this helps!
On a plane trip, baggage over 40 pounds is charged at the rate per pound of 1% of the one-way fare. The charge for a bag weighing 52 pounds on a trip where the one-way fare is $98 is:
Answer:
$11.76 is the charge for bag.
Step-by-step explanation:
Given:
One way fare = $98
Weight of bag = 52 pounds
Rate per pound Charges on baggage over 40 pounds = 1% of the one-way fare
To find:
Charge for bag = ?
Solution:
Pounds more than 40 pounds = Weight of baggage - 40 pounds
[tex]\Rightarrow 52-40 = 12\ pounds[/tex]
Charges on extra baggage = 1% of one-way fare multiplied by pounds more than 40.
Here one way fare is $98.
So, charges on extra baggage will be:
[tex]1\%\ of\ 98 \times (52-40) \\\Rightarrow 1\%\ of\ 98\times (12)\\\Rightarrow \dfrac{1}{100}\ of\ (98 \times 12)\\\Rightarrow \dfrac{1}{100}\times (98 \times 12)\\\Rightarrow \bold{\$11.76}[/tex]
So, the charge for the baggage is $11.76.
Tony knew there was a solution to his math problem in one of four textbooks. He got some information from his classmates about it: Andy: "The solution is in either book 1 or 2"; Billy: "The solution is in either book 3 or 4"; Charlie: "The solution is in book 4"; Danny: "There is no solution in book 3". Emily helped Tony by saying that only one of his classmates was right, and the other three were mistaken. Which book has the solution in it?
Answer:
Charlie is the right person.
Step-by-step explanation:
The right person is Charlie because he was sure of what he was saying. Others were not sure making them mention two textbooks while Danny didn't answer the question Tony asked because he was talking about the one that doesn't have the solution.
What's the correct answer to this..? Need help
Answer:
A.
Step-by-step explanation:
All of those graphs represent functions. You are able to tell because they all pass the vertical line test. The vertical line test is conducted by drawing a line that goes vertically and intercepts any point of the line in question. If the function crosses the vertical line twice, it is not a function. If it only intercepts once, it is a function. In this case, every graph is a function because they would intercept a vertical line once.
Help a friend out I don’t understand it
Answer:
THEY ARE COMPLIMENTARY BUT NOT NECESSARILY CONGRUENT.
Step-by-step explanation:
This is so because their lines don't meet.
standard form of 6,32,94,000
Answer:
6.3294✖️10^7
Step-by-step explanation:
To find the statdard form, you place the decimal after the largest unit, int his case 6.
Then you write down all the numbers except for "0".
This becomes:
6.3294
Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.
6.3294✖️10^7
Hope this helped!
Have a nice day:)
Complex numbers
[ = square root symbol
-[-64
How would I find this?
[tex]-\sqrt{-64}=-\sqrt{8^2\cdot (-1)}-8\sqrt{-1}=-8i[/tex]
A line passes through point (4,-3) and has a slope of 5/4. Write an equation in Ax + By = C
Answer:
The answer is
5x - 4y = 32Step-by-step explanation:
To write an equation of a line using a point and slope use the formula
y - y1 = m(x - x1)where
m is the slope
(x1 , y1) is the point
So we have
Equation of the line using point (4 , -3) and slope 5/4 is
[tex]y + 3 = \frac{5}{4} (x - 4)[/tex]
Multiply through by 4
4y + 12 = 5(x - 4)
4y + 12 = 5x - 20
5x - 4y = 20 + 12
The final answer is
5x - 4y = 32Hope this helps you
the work in an office takes 180 hours to complete every work
each person in the office works for 35 hours a week
what is the smallest number of people needed to complete the work?
Answer:
Minimum People required = 5
Step-by-step explanation:
Total hours required to complete the work every week = 150 hrs.
Number of hours worked per week by one person = 32 hr
∴ Number of people required to complete the work per week = Total number of hrs to complete the work ÷ No of hrs work per person
∴ Number of people = 150 ÷ 32
∴ Number of people = 4.6875
This is the minimum number of people. But no of people cannot be a fraction.
Thus, rounding the number to next integer.
∴ Smallest number of people needed to complete the work = 5
243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
Simplify the radical
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{54c}=\sqrt[3]{3*3*3*2c} =3\sqrt[3]{2c}[/tex]
Solve for u.
– 22 = -8u + 6(u-7)
Simplify your answer as much as possible.
Step-by-step explanation:
- 22 = -8u + 6(u-7)
-22 = -8u + 6u - 42
8u - 6u = 22 - 42
2u = -20
u = -20/2
u = -10
Answer:
[tex] \boxed{ \boxed{ \mathrm{ \bold{ \blue{ - 10}}}}}[/tex]Step-by-step explanation:
[tex] \mathrm{ - 22 = - 8u + 6(u - 7)}[/tex]
Distribute 6 through the parentheses
⇒[tex] \mathsf{ - 22 = -8u + 6u - 42}[/tex]
Collect like terms
⇒[tex] \mathrm{ - 22 = - 2u - 42}[/tex]
Swap the sides of the equation
⇒[tex] \mathrm{ -2u - 42 = - 22}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \mathrm{ - 2u = - 22 + 42}[/tex]
Calculate
⇒[tex] \mathrm{ - 2u = 20}[/tex]
Divide both sides of the equation by -2
⇒[tex] \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }[/tex]
Calculate
⇒[tex] \mathrm{u = - 10}[/tex]
Hope I helped!
Best regards!
How do you graph y=2/3x-4
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
The fraction subtracted from 5/3 to get 1 is_____
Answer:
2/3
Step-by-step explanation:
I am not sure
Answer:
2/3Step-by-step explanation:
[tex]Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\[/tex]
which one is irrational?
Basically everything but choice C
==========================================
Explanation:
sqrt is shorthand for square root
sqrt(4) = 2 = 2/1 showing that sqrt(4) is rational. We can write it as a fraction of two whole numbers, where 0 is not in the denominator.
-------
In contrast, we cannot write sqrt(2), sqrt(3), or sqrt(5) as a fraction of two whole numbers. Using your calculator, note how
sqrt(2) = 1.4142135623731
sqrt(3) = 1.73205080756888
sqrt(5) = 2.23606797749979
all of those decimal expansions go on forever without any pattern, which is a sign that those numbers are irrational. If they were rational, then a pattern would repeat at some point or the decimals would terminate at some point.
Answer:
a, b, d are irrational
Step-by-step explanation:
root 2 = 0.414.....
root 3 = 0.732.....
root 5 = 2.236.....
Hope this helps.....
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The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
Answer:
2,041 square centimeters
Step-by-step explanation:
surface area = (2 × π × r × h) + ((π × r) × (r+ (√(c² + r²))))+(π × r²)
where,
cylinder base radius (r) = 10 cm
height of cylinder (h) = 16 cm
total height = 28 cm
cone height (c) = total height - height of cylinder = 28 - 16 = 12cm
π = 3.14
surface area = (2 × 3.14 × 10 × 16) + ((3.14 × 10) × (10+ (√(12² + 10²))))+(3.14 × 10²)
surface area = 1004.8 + (31.4 * 25.6) + 314
surface area = 2122.64 cm²
therefore the approximate surface area given is 2,041 square centimeters
You move at 45/mph and a bullet is shot at you, the bullet is moving at 44/mph
Would you be able to dodge the bullet, you factor in the fight or flight or freeze response
Answer:
See explanation below.
Step-by-step explanation:
A bullet shot at you will definitely hit you because of the direction it is travelling.
Your fight and flight response won't be activated either because of the speed of the event (bullet) or if you don't know how harmful a gun is (you'll remain calm/ignorant in this case)?
Try to post academic problems.
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commom difference of an AP -4 , -4 , -4 ,............is...
Answer:
0
Step-by-step explanation:
Common Difference = Difference between any two consecutive terms
= - 4 - (-4)
= - 4 + 4
= 0
if b is the midpoint of ac and if c is the midpoint of bd, then what percent of cd is ac
Answer:
ac is 200% of cd
Step-by-step explanation:
To answer this question, we shall be making a visual representation.
Let’s take it one at a time.
Given;
b is the midpoint of ac
a b c
What this means is that a-b represents 50%, while bc represents another 50%
okay, we move on:
c is the midpoint of bd
b c d
What this means is that bc is 50%, while cd is another 50%.
So let’s combine the representations;
a 50% b 50% c 50% d
Now what does the question says again?
What percent of cd is ac?
From a to c, we can see two 50% which means 100%
while cd is just the regular 50%
So we can see that ac is actually twice cd
What we are saying here is , if cd is x, then ac is 2x
So we can restructure our question to mean, what percent of x is 2x?
That is simply 2x/x * 100 and that is 200%
Answer: ac is 200% of cd
Step-by-step explanation:
what is the lcm of 7÷25 and 3÷25
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
Which geometric figure has 120 rotational symmetry?
Answer:
Triangle
Step-by-step explanation:
Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry
Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6
Answer:
y = - [tex]\frac{1}{16}[/tex](x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-1)^2+(y+2)^2^}[/tex] = | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = - [tex]\frac{1}{16}[/tex] (x - 1)² + 2
Geraldo recently saw a newspaper ad for a new version of his laptop. The projected price is $400.00, and the laptop will be out on the market in about one year. Geraldo wants to purchase a new laptop but is wondering if he should wait a year. With 2.5% inflation, what amount would he pay to purchase a laptop today that is the same value as the one he saw in the ad?
Answer:
The answer would be $410.00.
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The price he will have to pay now for laptop will be $390.
What is cost prize ?
The prize at which the good and services have been bought is known as cost prize.
here, the given information is :
The projected price is $400.00, and the laptop will be out on the market in about one year with 2.5% inflation.
Now, if he pay to purchase a laptop today that is the same value as the one he saw in the ad then the cost price he will have to pay will be 2.5% of $400 less that is:
cost price of laptop = $400 - 2.5& x 400
cost price of laptop = 97.5% x $400
cost price of laptop = $390
Therefore, the price he will have to pay now for laptop will be $390.
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On a coordinate plane, triangle A B C is shown. Point A is at (negative 2, negative 4), point B is at (2, negative 1), and point C is at (3, negative 4). Triangle ABC is an isosceles triangle in which side AB = AC. What is the perimeter of triangle ABC? 5 + StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 10 StartRoot 10 EndRoot units 50 units
Answer:
B, 10+ /10 units
Step-by-step explanation:
Please help ! First one to give correct answer gets brainliest!
Answer:
(4x+1)²
Step-by-step explanation:
WILL GIVE BRAINLIEST
intercept is the length from origin to intersection point of respective axis,
it intersects x axis at -7.5 and y is 0 so x intercept is (-7.5,0)
and similarly, y intercept is (0,5.5)
Answer:
(- 7.5, 0 ) and (0, 5.5 )
Step-by-step explanation:
The x- intercept is the value of x on the x- axis where the line crosses.
Here the line crosses the x- axis at - 7.5 , thus the coordinates of x- intercept
(- 7.5, 0 )
The y- intercept is the value of y on the y- axis where the line crosses.
Here the line crosses the y- axis at 5.5 thus the coordinates of the y- intercept
(0, 5.5 )
The family size bottle of sunscreen holds 12121212 fluid ounces (fl oz)(\text{fl oz})(fl oz)(, start text, f, l, space, o, z, end text, )of sunscreen. The regular bottle holds 75%75\%75%75, percent less.How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
The regular bottle holds 9 fl oz less
Step-by-step explanation:
Given
Family Size = 12 fl oz
Required
Determine the size held less by the regular bottle
From the question, we have that the regular bottle holds 75% less;
[tex]Regular\ Size = 75\% * Family\ Size[/tex]
Substitute 12 fl oz for Family Size
[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]
Convert percentage to fraction
[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]
[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = 9\ fl\ oz[/tex]
Hence, the regular bottle holds 9 fl oz less
The table shows the relationship between the cost of renting a car from the Wrecko Car Rental Company and the number of days for the rental. Draw a scatter plot and find an equation for the line of best fit. Use the equation to determine the cost of renting a car for 20 days. Days Cost 1 $44 2 $67 3 $90 4 $113 7 $182 10 $251
Answer:
The cost of renting the car for 20 days is $481
Step-by-step explanation:
The table of values can be formed as follows;
Day, Cost
1, $44
2, $67
3, $90
4, $113
7, $182
10, $251
From the given values and the scatter plot, there is a straight line relationship between the cost and the number of days of rental of a car.
The line of best fit is therefore a straight line and from the constant increase in cost ($23) for each extra day of rental, it is possible to find the slope, m, of the data as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
(x₁, y,) and (x₂, y₂) can be taken as (1, $44) and (3, $90) respectively to give;
[tex]Slope, \, m =\dfrac{90-44}{3-1} = \dfrac{46}{2} = 23 \ as \ stated \ above[/tex]
The equation in slope and intercept form is therefore, y - 44 = 23×(x - 1), which gives;
y - 44 = 23·x - 23
y = 23·x - 23 + 44 = 23·x + 21
The cost of renting the car for 20 days is then;
10×23 + 21 = $481
The cost of renting the car for 20 days = $481.
A small toy car costs $3. A large toy car costs 5 times as much as the small one. Aaron wants to buy one of each. Which equation can he use to find the cost (a) of the two cars?
Answer: He can use 3 x 5 = 15 and 15 + 3.
Step-by-step explanation:
Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.
Here to help!
The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of the two cars be A
Now , the equation will be
Let the cost of the small toy car be = x
The cost of small toy car = $ 3
The cost of the large car = 5 x cost of small toy car
Substituting the values in the equation , we get
The cost of the large car = 5 x 3
The cost of the large car = $ 15
So , the cost of two cars = x + 5x
Substituting the values in the equation , we get
The total cost of the two cars A = 15 + 3
The total cost of the two cars A = $ 18
Therefore , the value of A is $ 18
Hence , the equation is A = x + 5x
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